metadata: authors: 0: author: Ghose,Devaki
1: author: Pinheiro Fraga,Eduardo
2: author: Fernandes,Ana Margarida
count: Sri Lanka,World
docna: 0: docna: Fertilizer Import Bans, Agricultural
            Exports, and Welfare : Evidence from Sri Lanka
docty: Policy Research Working Paper
abstracts: cdata!: In May 2021, Sri Lanka&#x2019;s
            government imposed an abrupt ban on chemical fertilizer
            imports. This paper leverages this natural experiment to
            quantify the costs of a lack of access to fertilizer for
            agricultural production and trade in a developing economy
            heavily dependent on agriculture. Using high-frequency
            firm-level trade data, ground production records, newly
            developed remote sensing crop yield estimates, and event
            study designs, the analysis reveals significant declines in
            fertilizer imports, agricultural output, and exports of
            fertilizer-dependent crops. These findings underscore the
            importance of trade policy for chemical fertilizer, which is
            hard to substitute with organic or domestic alternatives in
            the short run. A quantitative spatial model of trade and
            agriculture shows the ban&#x2019;s average welfare
            effects were equivalent to a 4.35%income reduction, with
            disproportionate losses for farmers, estate workers, and the
            regions that cultivate fertilizer-intensive crops. The model
            also highlights the interaction of massive fertilizer
            subsidies, a domestic agricultural policy common in many
            countries, with trade policy: by nearly eliminating
            fertilizer use, an import ban scales down the subsidy
            program and its associated income transfers from non-farming
            to farming sectors, thus attenuating the welfare losses of
            mobile workers. The findings quantify the costs of lack of
            fertilizer access and the role of trade and industrial
            policy in determining such access.
display_title: Fertilizer Import Bans, Agricultural
            Exports, and Welfare : Evidence from Sri Lanka
listing_relative_url: /research/2023/12/34213411/fertilizer-import-bans-agricultural-exports-welfare-evidence-sri-lanka
topicv3: Crop Production m1326627 174,Trade m1326924 698,Non-Tariff Measures m1326926 778,Fertilizers m1327354 175,Agricultural Trade m1327604 192
publishtoextweb_dt: 2023-12-12T00:00:00Z
dois: 10.1596/1813-9450-10642
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 98
author_keys: 0: author_key: 1947054
1: author_key: 1401560
2: author_key: 658876
model_extractions: Policy Research Working Paper 10642 Trade Policy and Access to Intermediate Inputs Quantifying the Welfare Costs of a Fertilizer Shortage _Devaki Ghose Eduardo Fraga Ana Fernandes_ Development Economics Development Research Group December 2023
Policy Research Working Paper 10642

# **Abstract**

This paper leverages Sri Lanka’s 2021 chemical fertilizer import ban to quantify the costs of restricted fertilizer access for agriculture, trade, and welfare. By leveraging trade and production data, satellite-based yield estimates, and event studies, the authors document sharp declines in fertilizer imports, agricultural output, and exports. A quantitative spatial model of trade and agriculture estimates the ban’s average welfare cost at 7.3%, with farmers, estate workers, and fertilizer-intensive regions bearing disproportionate losses. Model-implied partial-equilibrium elasticities line up with the experimental evidence, but once general-equilibrium price and wage adjustments are accounted for, the elasticities are much smaller—implying that using partial-equilibrium estimates to assess large, economy-wide fertilizer shocks (like those seen during recent conflicts) would substantially overstate their effects. Domestic and trade policy interact: by curtailing fertilizer use, the import ban effectively contracted the country’s fertilizer subsidy program and its implicit transfers from mobile workers to farmers, thereby mitigating the former’s welfare losses.

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at dghose@worldbank.org, epinheirofraga@worldbank.org, and afernandes@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Trade Policy and Access to Intermediate Inputs: Quantifying the Welfare Costs of a Fertilizer Shortage**<sup>*</sup>

## Devaki Ghose<sup>†</sup> Eduardo Fraga<sup>‡</sup> Ana Fernandes<sup>§</sup>

Originally published in the Policy Research Working Paper Series in _December 2023_ . This version is updated in _April 2026_ .

To obtain the originally published version, please email prwp@worldbank.org.

_JEL Codes:_ D58; F13; F14; O13; Q17.

_Keywords:_ Trade, industrial policy, import ban, non-tariff measures, fertilizer, and agriculture.

*Eduardo is extremely grateful to Costas Arkolakis, Sam Kortum, Lorenzo Caliendo, and Ana Cecilia Fieler for their continuous support and guidance. We also thank Doug Gollin, Sebastian Sotelo, Heitor Pellegrina, Michael Peters, Bob Rijkers, Nuno Limao, Lauren Falcao Bergquist, Florence Kondylis, Treb Allen, David McKenzie, John Keyser, Gonzalo Varela, Athula Senaratne, Sheu Salau, Manoj Thibbotuwawa, Camille Reverdy, Daan van Soest, Kari Heerman, and Alejandro Forero for helpful discussions. We thank Mutlu Ozdogan for his work on the remote sensing estimates and Yewon Choi for assistance with Global Trade Alert data. The authors gratefully acknowledge support by the “Whole of Economy” Program, a Climate Support facility administered by the World Bank. We also thank the Umbrella Facility for Trade trust fund (financed by the governments of the Netherlands, Norway, Sweden, Switzerland, and the United Kingdom) and the World Bank’s Research Support Budget for financial support. The findings, interpretations, and conclusions expressed in this paper are solely those of the authors and do not necessarily represent the views of the World Bank, its affiliated organizations, or the Executive Directors or the countries they represent. All errors are our responsibility.

> †Corresponding author, World Bank, DECRG. Email: dghose@worldbank.org

> ‡London Business School. Email: efraga@london.edu

> §World Bank, DECRG. Email: afernandes@worldbank.org
1

# **I Introduction**

Chemical fertilizers are among the most consequential intermediate inputs in the global economy: they have dramatically increased productivity in agriculture, a sector that accounts for 40 percent of employment worldwide.<sup>1</sup> As most countries depend on imports to meet their fertilizer needs (Farrokhi and Pellegrina, 2023), trade restrictions and geopolitical conflicts – such as the 2022 Russian invasion of Ukraine and the 2026 US-Iran war – can cause large-scale disruptions to fertilizer access.<sup>2</sup> The effects of fertilizer availability are studied by a vast literature that focuses on estimating precise elasticities to small, localized shocks using field experiments (Beaman et al., 2013; Duflo et al., 2011). By contrast, the consequences of large-scale disruptions to fertilizer access remain poorly understood (Bergquist et al., 2023; Muralidharan and Niehaus, 2017).<sup>3</sup> Such disruptions can trigger sizeable general equilibrium (GE) adjustments in wages and prices, that are shaped by an economy’s structural features and pre-existing policies such as fertilizer subsidies—adjustments that lie beyond the reach of field experiments. Because observable variation in economy-wide fertilizer access has historically been limited, identifying the effects of such large-scale supply disruptions has remained an elusive empirical challenge.

This paper quantifies the economy-wide costs and distributional effects of restricted fertilizer access by exploiting a unique natural experiment in Sri Lanka: the abrupt ban on imports of chemical fertilizers in May 2021. Sri Lanka is a developing country heavily reliant on agriculture and home to one of the world’s largest fertilizer subsidy programs.<sup>4</sup> Since over 90% of the country’s chemical fertilizer was imported and viable organic alternatives were virtually nonexistent, the import ban created an economy-wide shock— effectively triggering a sudden, nationwide disruption in the supply of a critical production input.<sup>5</sup> This trade policy shock provides a rare opportunity to rigorously quantify the effects of large-scale fertilizer shortages and shed light on the importance of GE adjustments.

Our analysis proceeds in four steps. In the first step, we leverage a rich set of novel data sources 1Chemical fertilizers are shown to significantly boost crop yields, often by up to 50% in temperate settings (Stewart and Roberts, 2012). FAO (2025) reports that two out of every five employed individuals worldwide worked in the agrifood sector in 2022.

2More than 80% of countries rely on imports for 75% or more of their fertilizer needs —a consequence of highly concentrated global production: just five countries account for more than 60% of fertilizer nutrient output worldwide, while ten countries control 95% of the global supply of potassium, a key fertilizer nutrient (U.S. Department of Agriculture, Foreign Agricultural Service, 2022). The Global Trade Alert database described in Evenett and Fritz (2020) documents an increase in fertilizer import bans across countries from 0 in 2019 and 4 in 2020 to 61 in 2022.

> 3Besides scale, another difference between field experiments and large-scale access disruptions is that the former target agents who are initially _not_ using fertilizer, whereas the latter affect agents who _are_ initially using it, and who may thus value it more (by a revealed preference argument). These effects need not be symmetric.

4Sri Lankan subsidies covered 78–83% of the world price (Kishore et al., 2021) and accounted for 53.6% of agricultural spending in 2020 (Weerahewa et al., 2021).

> 5https://www.fao.org/4/ag120e/AG120E12.htm. The stated aim of the ban was a shift to organic farming; the unstated aim was to save foreign exchange.
2 to document three stylized facts on the impacts of the ban. To assess whether the ban was binding, we examine its impact on fertilizer imports, combining high-frequency granular customs data covering the universe of import transactions in Sri Lanka with import ban data hand-digitized from regulatory gazettes. Since the ban was ultimately reversed amid widespread social unrest, we employ the dynamic difference-in-differences (DID) estimator of De Chaisemartin and d’Haultfoeuille (2022) that corrects for bias when treatment is reversed within the study period. Our first stylized fact is a near-total collapse in fertilizer imports – driven primarily by quantity reductions – with volumes falling by more than 99% within four months of the ban and remaining at similarly depressed levels thereafter.<sup>6</sup> We then examine the ban’s impacts on agricultural production using government production data, with a focus on Sri Lanka’s primary food crop—rice—and its major export crop—tea— both of which are highly fertilizer-intensive. Our second stylized fact documents a reduction in rice yields of more than 30% between 2021 and 2022.<sup>7</sup> After adjusting for weather abnormalities, we estimate yield declines of 24.4% for rice and 28.7% for tea in 2022 relative to historical norms.<sup>8</sup> To capture the ban’s impact on downstream agricultural exports, we construct a firm-level exposure metric linking customs data on agricultural firms’ pre-ban crop export portfolios with agronomic data on crop-specific fertilizer requirements. We then employ the dynamic DID estimator of De Chaisemartin and d’Haultfoeuille (2022) to compare the export performance of highly exposed firms to less-exposed firms over time. Our third stylized fact is a relative decline of 35% in the exports of exposed firms within four quarters after the ban, even after accounting for seasonality. These stylized facts are robust to potential confounders arising from the COVID-19 shock and the broader economic crisis that unfolded in Sri Lanka.

While these stylized facts demonstrate the ban’s adverse impacts, they do not quantify its full GE effects. GE effects are less relevant in contexts where fertilizer availability changes only for a small subset of farmers or regions, but become critical when access is disrupted nationwide—as occurred during Sri Lanka’s fertilizer import ban but also during the Russia–Ukraine war and other geopolitical shocks. The second step of our analysis is thus to develop a novel quantitative GE model of trade, space, and agriculture with the goal of estimating average welfare losses and their distribution across regions and occupations, elucidating the relative importance of partial equilibrium (PE) and GE channels in driving observed effects, and conducting policy counterfactuals. Our flexible model features three sectors (agriculture, manufacturing, and fertilizer), three types of economic agents (landowning farmers, mobile workers, and immobile estate workers), multiple Sri Lankan districts, cross-crop heterogeneity in fertilizer intensity as well as geographic hetero-

> 6Furthermore, we find minimal evidence of substitution towards organic fertilizer: the organic share of fertilizer never surpassed 4% (for either fertilizer imports or agricultural use).

> 7This reduction was accompanied by a significant increase in rice imports, which were negligible prior to the ban. 8To account for local weather fluctuations, we combine granular weather data with novel pixel-level yield estimates constructed using a satellite-based remote-sensing methodology described in Ozdo ̆gan et al.<sup> ̈</sup> (2025).
3 geneity in tastes, population, productivity, and crop specialization. It incorporates several structural features and policies that characterize the economy of Sri Lanka and are common across developing economies: land inequality, quantitative restrictions (QRs) on fertilizer imports (as opposed to ad valorem trade costs), a tax-funded fertilizer subsidy program, and non-homothetic preferences that generate a negative relationship between income and the agricultural expenditure share. These features play a key role in shaping the welfare effects of fertilizer access restrictions.<sup>9</sup> The model delivers a closed-form solution for the elasticity of crop yields with respect to fertilizer use as a function of changes in the prices of inputs and outputs, clarifying the distinction between PE adjustments—in which only fertilizer prices change—and GE adjustments—in which wages and output prices also change.

In the third step, we estimate the model’s parameters using a range of empirical strategies and a rich set of novel data sources. Household survey data is used to estimate the income elasticity of food’s expenditure share (Engel elasticity), a policy-relevant parameter widely used to analyze food security concerns in developing countries (Baquedano et al., 2021), but hard to estimate causally. We deploy an instrumental variables (IV) approach relying on unexpected income shocks (lottery winnings and disaster relief). Survey data on crop prices and household expenditures enables us to estimate the elasticity of substitution _across crops_ through another IV approach that leverages the effect of regional crop suitability, exogenously determined by regional geography and measured by the Global Agro-Ecological Zones (FAO-GAEZ) project, on local crop prices. Technology parameters in agricultural production functions are recovered from input cost shares computed from national Input-Output (IO) tables and data on fertilizer requirements and subsidy rates. The (regionspecific) parameters that govern land distributions are estimated using survey data on landholding sizes. Unobserved variables (e.g. productivities and taste shifters) are backed out via model “inversion” by solving the equilibrium system of equations while taking as given the values of observed variables (e.g. populations, wages, land endowments, crop outputs/prices) in 2019, our pre-ban baseline year.

In the fourth and final step, we use the estimated model to quantify the aggregate and distributional impacts of the ban, separate general- from partial-equilibrium mechanisms, examine how trade policies (e.g., import restrictions) interact with domestic policies (e.g., subsidies), and highlight how features of developing economies (e.g., land inequality) shape the welfare costs of trade 9As they link household income and agricultural expenditure share, non-homothetic preferences shape agriculture’s _aggregate_ share of expenditure and employment in equilibrium, and the aggregate size of the agricultural sector (relative to manufacturing) matters for welfare because manufacturing serves as a “buffer” for workers, providing them with an employment alternative during the agricultural downturn induced by the ban. Land inequality also influences the relative size of the agricultural sector: high land inequality leads to high income inequality, which lowers aggregate agricultural consumption because (given non-homothetic preferences) richer households have lower marginal propensity to spend on food. QRs restrict fertilizer imports while driving a wedge between international and domestic fertilizer prices, potentially creating rents that are captured by importers. Subsidies act as a transfer from mobile workers to farmers, so fertilizer import restrictions reduce this transfer, benefiting mobile workers.
4 policy. Modeling the import ban as a strict QR that drives fertilizer imports to zero, we compute a new equilibrium with all GE adjustments, including in labor markets, goods markets, and tax rates. In this new equilibrium, fertilizer use in Sri Lankan agriculture falls by 96.5%, with crop yield declines ranging from 12% for cinnamon to 54% for maize, reflecting each crop’s fertilizer intensity.<sup>10</sup> The ensuing output contraction drives a decrease of 596 million US dollars (USD) in agricultural exports, severely limiting the ban’s (presumed) objective of saving foreign exchange. The resulting average welfare losses are equivalent to a 7.33% income reduction, but incidence is highly heterogeneous. Mobile workers—who can reallocate across sectors—sustain losses averaging 0.67% and not exceeding 12%, even in the worst-affected, most agricultural districts, where the “buffer” provided by manufacturing employment is smallest. In contrast, farmers—whose source of income is intrinsically tied to the agricultural sector—face losses averaging 19.51% and ranging from 9% to 23% depending on geographic location. This substantial spatial variation in farmer losses reflects regional differences in crop specialization and crops’ varying degrees of fertilizer intensity.<sup>11</sup> To disentangle the GE and PE mechanisms driving the ban’s effects, we combine model-derived analytical expressions for yield elasticities with the model’s quantitative predictions for changes in wages, output prices, and fertilizer prices. In GE, the ban indirectly reduces wages—via reduced agricultural labor demand—and raises crop prices—via reduced crop supply, whereas in PE these price adjustments are suppressed, with only fertilizer prices rising. Our main result is that cropyield elasticities with respect to fertilizer are 21–49% lower in GE than in PE, as a result of which the production decline in maize and rice are attenuated by 35% and 39% (respectively) in GE relative to PE. Intuitively, lower wages and higher output prices incentivize agricultural producers to expand labor input, partially offsetting the initial production losses from fertilizer price hikes. Our PE elasticities are very close in values to Carter et al. (2021) and Beaman et al. (2013), further validating the model. These results imply that extrapolations based on PE elasticities from small-scale experimental studies systematically overestimate the adverse effects of large-scale input shocks, underscoring the importance of GE mechanisms that extend well beyond the input market in shaping the aggregate consequences of nationwide supply disruptions.

Finally, we analyze how different features of developing countries that we model matter for welfare. Without non-homothetic preferences, the model underpredicts the size of the agricultural sector at baseline, leading to an underestimation of the ban’s negative effects on mobile workers. The subsidy program functions as an implicit income transfer scheme from mobile workers to farmers, so the model without subsidies overestimates ban-induced worker losses (and underestimates

> 10The existence of a small domestic fertilizer production sector ensures that, even under a full import ban, fertilizer use in agriculture does not fall to zero.

> 11The regional pattern of post-ban income losses predicted by the model replicates 82% of the corresponding pattern implied by nightlights data (7.7 p.p.), supporting the model’s validity.
5 farmer losses) since it misses how the ban (unintentionally) helps workers by scaling down this transfer scheme. The interaction of these two policies carries a paradoxical implication: an import ban—one of the most distortive industrial policy tools (McDonald et al., 2024)—can partially offset the distortions created by domestic fertilizer subsidies—another industrial policy tool. When trade policy is modeled as a shock to multiplicative trade costs rather than as a quantitative restriction, the model fails to account for the import “rents” that are created by the policy, thus overestimating welfare costs.<sup>12</sup>

**Related Literature** Our quantification of the costs of lack of access to fertilizer in general equilibrium adds to an extensive literature that evaluates the effects of fertilizer (or, more broadly, of modern agricultural inputs) on yields, which mainly uses randomized controlled trials (RCTs) (Beaman et al., 2013; Carter et al., 2021; Duflo et al., 2008, 2011). While small-scale field experiments are essential in assessing local effects, they do not inform on GE effects once the intervention is scaled up (Bergquist et al., 2023; Muralidharan and Niehaus, 2017). For example, while providing fertilizer to a few farmers may not affect the rural labor market, a large-scale change in fertilizer availability may shift rural labor demand enough to affect wages.<sup>13</sup> In contrast, our setting of a nationwide, sudden, and unprecedented fertilizer shortage is ideal for estimating the costs of a lack of fertilizer for an entire country. We show that our model-implied crop-specific partial equilibrium (PE) elasticities of yield with respect to fertilizer use replicate the values reported in seminal RCT studies (Beaman et al., 2013; Carter et al., 2021) but are substantially larger than our corresponding model-implied GE elasticities. This is because some of the negative yield effects of fertilizer price increases are offset by endogenous adjustments in crop prices and wages. Our contribution includes deriving analytical expressions for both PE and GE elasticities.

Our paper is complementary to recent work by Bergquist et al. (2023), who develop a spatial model of agriculture and trade to quantify the effects of large-scale agricultural policies such as provision of agricultural inputs. In contrast, we analyze a unique trade policy experiment involving the near-complete removal of fertilizer, rather than the provision of subsidized inputs, whose takeup ultimately depends on the decision of the farmer (Duflo et al., 2011; Suri, 2011). Notably, an underappreciated feature of the global fertilizer market is that most countries rely almost entirely on imports to obtain their fertilizer (Brooks and Donovan, 2024). We provide a framework to model the impact of trade policy on fertilizer access and the associated costs of limited access. Our paper also complements Artuc et al. (2023), who examine the impact of conflict on global agricultural trade, including a simulation where Russia and Ukraine restrict fertilizer exports. While such

> 12While a quantitative restriction-induced price increase creates a price wedge that is captured by domestic importers, a price increases that is driven by an increase in trade costs is entirely lost to nature.

> 13A further limitation of these randomized trials is that they are typically conducted on closely supervised experimental plots, so returns may differ from those on real-world farms (Beaman et al., 2013; Duflo et al., 2011).
6 trade policies affect more countries than in our case, each country suffers less due to the ability to substitute toward unaffected suppliers.

Our theoretical model draws on the growing literature on QSMs focused on agriculture (Aggarwal et al., 2022; Bergquist et al., 2023; Carleton et al., 2024; Costinot et al., 2016; Desmet and Rossi-Hansberg, 2015; Fajgelbaum and Redding, 2022; Farrokhi and Pellegrina, 2023; Nath, 2025; Nigai, 2016; Pellegrina, 2022; Sotelo, 2020; Tombe, 2015), extending these frameworks by incorporating trade policy through QRs that impact fertilizer access. It also introduces real-world features that influence welfare during fertilizer shortages, such as fertilizer subsidies, land inequality, and non-homothetic preferences. We use a specific class of non-homothetic preferences, namely Price-Independent Generalized Linear (PIGL) preferences, borrowed from the structural transformation literature (Boppart, 2014; Eckert and Peters, 2023). Like Eckert and Peters (2023), we assume a particular parametrization for the income distribution and derive closed-form expressions for aggregate demand and indirect utility, which we use to compute the equilibrium in a spatial model with multiple heterogeneous regions. However, our model includes two types of agents (workers and farmers) and assumes a log-normal income distribution, showing that the aggregation properties of PIGL preferences are not limited to Frechet distributions.

The natural experiment of Sri Lanka’s fertilizer import ban relates our work to the literature on the impacts of trade policy and, specifically, of non-tariff measures (NTMs).<sup>14</sup> Most studies have focused on a subset of NTMs – regulatory or anti-dumping measures – often bundling several measures and generally estimating their impacts on the trade flows of the products directly subject to the NTMs (Ederington and Ruta, 2016). Import prohibitions have been much less studied, with only a few case studies on bans of specific agricultural products.<sup>15</sup> Two recent studies that are more related to our work (despite focusing on import licenses rather than import bans) estimate the effects of Argentina’s discretionary import approvals on firm-level imports and import prices (Atkin et al., 2024) and on downstream exporters (Bernini et al., 2024). Another recent study, Artuc et al. (2024), examines the impact of Nigerian import bans on prices and welfare; however, in this case, the bans were not effectively enforced. Our paper’s contribution to this literature is twofold. First, by exploiting a natural experiment, this is the first paper to estimate the causal impacts of banning the imports of a crucial intermediate input on the trade flows of both the input itself and the downstream exports dependent on it. Second, we add to Atkin et al. (2024) and Dhingra et al. (2023), the only two papers (to our knowledge) that incorporate NTMs in a quantitative GE trade model. While much of the NTM literature models NTMs as an increase in multiplicative “iceberg” trade costs, these modeling choices are not always innocuous (Ghose et al., 2024). Whereas QRs create rents

> 14Import bans are a control measure aimed at restraining the quantity of goods that can be imported and are classified under chapter E of the non-tariff measures MAST classification (UNCTAD, 2019).

> 15See e.g., Felt et al. (2011) on Japan’s ban of Taiwanese pork imports; Leroux and Maclaren (2011) on an Australian import ban on bananas, and Peterson and Ord (2008) on a US import ban on avocados from Mexico.
7 for certain domestic agents, price increases from iceberg trade costs are typically modeled as pure losses. We model NTMs as QRs with arbitrary intensity, implemented through import permits granted to middlemen, thus creating a gap between domestic and international prices while still preserving analytical tractability. Our findings are novel to the NTM literature: in the absence of fertilizer subsidies, our model predicts a decline in downstream agricultural exports that is larger than the initial NTM-driven decline in fertilizer imports, thus jeopardizing the NTM’s presumed motivation of saving foreign exchange. Finally, our work also informs the burgeoning debate on the revival of industrial policy: our large welfare loss estimates support the literature’s perception that trade policy measures, such as import bans, are among the most distortive policies that fall under the (admittedly contested) definition of industrial policy (McDonald et al., 2024).

The rest of the paper is organized as follows. Section II discusses the fertilizer import ban in Sri Lanka. Section III presents our set of data sources. Section IV presents reduced-form evidence on the impacts of the ban on imports, production, and exports. Section V lays out a QSM of trade and agriculture. Section VI explains how to estimate the model using Sri Lankan data. Section VII presents our counterfactual exercises and the corresponding estimates of the ban’s effects on production, trade, and welfare across Sri Lankan regions. Section VIII concludes.

# **II Background on the Fertilizer Import Ban in Sri Lanka**

On May 6, 2021, Sri Lanka’s government abruptly banned the imports of chemical fertilizers with the stated goal of transitioning the country’s agricultural sector into organic farming. Although president Gotabaya Rajapaksa had mentioned his aim to provide Sri Lankans with food without harmful chemicals during his 2019 election campaign, the ban was sudden and unexpected.<sup>16</sup> The use of agrochemicals had been linked to chronic health problems and adverse environmental impacts across the country, which was used as a justification for the drastic NTM, but its most pressing rationale was to save the 250 million USD spent annually on fertilizer imports in the context of a large current account deficit that had been exacerbated by the adverse impact of Covid-19 on the tourism industry, one of the country’s main sources of foreign exchange. In fact, to address these external challenges the government had already been imposing bans on imports of non-fertilizer products since April 2020 (Dissanayaka and Thibbotuwana, 2021).<sup>17</sup> However, it is important to note that during the period of the fertilizer import ban (i.e. from May 2021 onward) there were no import bans on other agrochemicals such as pesticides, herbicides, insecticides, and fungicides.<sup>18</sup>

> 16https://www.reuters.com/markets/commodities/fertiliser-ban-decimates-sri-lankan-crops-government-popularityebbs-2022-03-03.

> 17The stated policy goal of such import bans “was ambiguous, as policy statements outlined various objectives ranging from minimising foreign exchange leakages to import substitution” (Wijesinghe et al., 2023). 18Some of these agrochemicals faced import bans in 2017-2018.
8 Proponents of organic farming in Sri Lanka were appalled at the president’s decision to shift into organic farming in a single agricultural season without providing farmers with adequate support and training for the shift. The president of the Lanka Organic Agriculture Movement argued that “The president’s committee of advisers to implement the new agricultural policy had no knowledge of organic farming” and that it takes time to produce results: “It needs two to three seasons to develop microbes that enhance soil quality. It is during this time that the farmers needed governmental support. But that support was missing.”<sup>19</sup> Since domestic production and imports of organic fertilizer were insufficient, organic fertilizers were in short supply and became very expensive. Some farmers ended up using low-quality fertilizers obtained on the black market. More fundamentally, agricultural specialists argue that, in terms of providing necessary nutrients for crop growth, organic fertilizer can only be a supplement and not a substitute for chemical fertilizer (even if organic fertilizer can help reduce the demand for chemical fertilizer over the long-run).

Quantifying the economic consequences of the agrochemicals import ban is the focus of our paper. Preliminary evidence in FAO and WFP (2022) suggests the ban had dramatically adverse effects on agricultural production in the major 2021-2022 growing season, resulting in large increases in food prices and reduced food security. Farmer protests and general social upheaval ensued, eventually inducing the government to lift the import ban later in 2021. However, while the ban was short-lived, it was in place during a very unfortunate time, around the start of the Maha season, which is Sri Lanka’s major rice growing season. Moreover, after the ban ended, international fertilizer prices reached their all-time highs due, in part, to Russia’s invasion of Ukraine in February 2022. Given Sri Lanka’s low foreign reserves and a large depreciation of the Sri Lankan rupee (LKR), the shortage of agrochemicals continued into 2022, with adverse consequences for agricultural production and food security.<sup>20</sup>

# **II.A Organic and Inorganic Fertilizer**

The purpose of fertilizer additions is to provide plants with nutrients (mostly nitrogen, phosphorus, potassium) that are not sufficiently naturally occurring in the soil. However, there are important differences between organic or inorganic (chemical) fertilizers. Organic fertilizers are slow-releasing and may require the correct amount of heat and moisture for nutrient extraction at the time of plant need. Since this need is met with almost the right timing and amounts, leaching is minimized.<sup>21</sup> In contrast, inorganic fertilizers provide nutrient inputs rapidly because they are in plant uptake-ready form, but this can come at the expense of leaching, especially if timed incorrectly.

> 19 https://asia.nikkei.com/Spotlight/Sri-Lanka-crisis/Sri-Lanka-aims-for-food-security-after-ill-fated-fertilizer-ban. 20Over 2022, the rupee devalued by nearly 45% against the USD.

> 21Leaching is the removal of excess water-soluble nutrients from the plant/soil system by runoff or drainage. Leaching is an environmental concern if chemical fertilizers find their way into water bodies.
9 As the ban only applied to agrochemicals, one may ask if the decreased use of inorganic fertilizer was offset by an increased use of organic fertilizer. We show this offset was very limited by examining the use of manure, a typical organic fertilizer. The quantity of manure applied to the soil had been increasing steadily over the twenty years prior to the ban and, importantly, its increase in 2021 merely followed this long-run trend, without any visible “jump” that would occur if farmers resorted to increased organic fertilizer use as a key coping strategy to deal with the ban (Appendix Figure A3a). Moreover, manure’s share of total fertilizer use was not atypically high in 2021 compared to the previous six years and this share was never higher than 2.5% (Appendix Figure A3b). Trade data also confirms that the collapse of chemical fertilizer imports, which decreased to less than 40 million USD in 2021 from a pre-ban baseline of 100-250 million USD, was hardly compensated by organic fertilizer: while the organic share of fertilizer imports did increase after the ban, it was never higher than 4% (Appendix Table A3).

# **III Data**

Our reduced-form and model-driven analyses rely on a rich assortment of mostly novel data. Table I presents our main data sources and variables, grouping them into several categories: trade policy; trade flows; agricultural production, cultivated area, and yields; agricultural prices; fertilizer use and subsidies; potential agricultural yields; labor share in value added; wages, land ownership, occupation, and household characteristics; and night lights. Appendix A provides additional details on all data sources and variables used. Below, we briefly highlight a few important features of our data.

**Trade-related variables** . The list of products targeted by import bans and their time coverage are hand-coded from Sri Lanka’s Extraordinary Gazettes on Imports and Exports. The fertilizer import bans started in May 2021, with most bans lifted by July 2021 or by November 2021 at the latest. We also use novel high-frequency granular data covering the universe of Sri Lanka’s export and import transactions, relying on machine learning and text analysis to clean firm names and assign unique firm identifiers to create a panel of firms involved in exports.

**Agricultural production** . We complement administrative data on crop-district-level yields with remote sensing estimates of rice and tea yields at a highly granular level. Remote sensing provides a spatially granular view of crop cultivation, allowing a detailed assessment of the heterogeneous effects of the fertilizer import ban within Sri Lanka. For rice, we apply an expert-based image classification algorithm to satellite data to identify rice-growing areas using the specific growing conditions for paddy rice in Sri Lanka (Ozdogan et al., 2024).<sup>22</sup> To estimate rice yields, a statistical

> 22The presence of rice-growing areas is determined by factors related to climate, water availability, and topographic position, along with farmer decision-making and technical expertise. The methodology monitors rice-related vegetation
10 model correlates district-level yields from government statistics with a satellite-derived vegetation index (green chlorophyll index) known to be sensitive to rice yields for pixels identified as ricegrowing areas. A random forest-based machine learning model is added to incorporate additional environmental variables known to affect rice yields, resulting in pixel-level rice yield estimates across two decades (2000-2022).<sup>23</sup> For tea, district-level yield data is regressed on a district-level vegetation index derived from satellite data for pixels deemed to be tea plantations.<sup>24</sup>

**Fertilizer subsidies** . Crop-level fertilizer subsidy rates are defined as the “nominal rate of protection at farm gate”, which is computed by comparing the actual (farm-gate) fertilizer price to the price that would be expected given international fertilizer prices and the cost of bringing fertilizer from port to farm. The fertilizer subsidy rate is 81% for rice and 45%-54% for four other crops of interest (potato, maize, tea, and onions).<sup>25</sup>

**Potential agricultural yields** . Our use of FAO-GAEZ data for crop-district-level potential attainable yields follows the literature on agriculture and trade (Bustos et al., 2016; Costinot et al., 2016; Farrokhi and Pellegrina, 2023; Sotelo, 2020).

**Wages and household characteristics** . Three types of information in our survey data are particularly valuable: (i) on estate workers who live and work in Sri Lanka’s tea plantations, for whom changing jobs is nearly impossible in the short run as their housing is tied to the tea estate where they work (Chandrabose, 2015); (ii) on the fraction of income households spend on food; and (iii) on income earned “by chance”, including lottery gains and disaster/relief payments.

**Summary Statistics.** Fertilizer and non-fertilizer products whose imports were banned accounted for 15%-19% of total imports in 2017-2019 (Appendix Table A4). This share declined to 12% in 2020 and 10% in 2021, suggesting the bans were at least partially effective. Summary statistics for some key variables of interest, shown in Appendix A.L, provide evidence of the ban’s effects: the average value of fertilizer imports per firm-year plummeted from 2 million USD to only 491 thousand USD from the pre-ban to the post-ban period, while the average value of agricultural exports per firm-year fell from 1.62 million USD to 1.53 million USD. Remotely sensed crop yields decrease substantially from the pre-ban (2021) to the post-ban (2022) period: average rice yields across divisional secretariats (DSs) fall from more than 4,000 kg/ha to less than 3,000 kg/ha, while average tea yields fall from 1,644 kg/ha to 1,404 kg/ha.

and water management from space and distinguishes it from other land use types using spectral (color) and temporal information included in the satellite signal. Because water and vegetation indexes are more visible for rice than for other crops, crop type mapping and yield are better predicted for rice than for other crops using remote sensing tools (Dong et al., 2016).

> 23These remote sensing estimates aggregated to the DS level are highly consistent with government-reported measures of rice area (from survey-based crop-cutting experiments) and rice yields (from production statistics).

> 24Since tea is a multiyear permanent crop, planted areas do not change annually. Thus, we fix tea-growing areas to the 2021 tea map.

> 25High fertilizer subsidy rates, in the 40-50% range, are also reported in the World Food Programme’s analyses of food security in Sri Lanka (FAO and WFP, 2022, 2023).
11

# **IV Stylized Facts on Fertilizer Imports, Agricultural Production and Exports**

In this section, we present three stylized facts related to the fertilizer import ban’s adverse effects on fertilizer imports, crop yields, and exports of agricultural goods that utilize fertilizer.

## **IV.A Fact 1: Fertilizer Imports Declined After the Ban**

We start by examining whether the import ban was effective in restricting imports. To do this, we estimate dynamic DID regressions using import data at the product-month level, where a product is defined as a unique Harmonized System 8-digit (HS8) code. The treated group consists of fertilizer products whose imports were banned after April 2021 and the control group consists of products that were not banned (both non-banned fertilizers and other types of non-banned products). We compare fertilizer imports in the treatment group with their control group counterparts following the DID methods proposed by De Chaisemartin and d’Haultfoeuille (2022), which allow units to switch in and out of treatment. This is key for our study as the import ban was lifted less than one year after it was first introduced.<sup>26</sup> Our dynamic DID estimator recovers the evolving effects of the ban over time on two outcome variables: a dummy indicating non-zero imports (i.e., extensive margin) and the log of import value (i.e., intensive margin) at the product-month level between January 2019 and September 2022. Estimation details are provided in Appendix B.A.

Figure I plots the DID results, showing a clear decline in imports right after the ban was imposed, with the average probability of nonzero imports across banned products dropping by 31 percentage points in the second month of the ban (Figure Ia). Along the intensive margin, negative effects peaked four months after the ban was introduced, with imports falling by 99.998% (Figure Ib) and remaining low for the next several months.<sup>27</sup> We also obtain DID estimates based on a smaller sample including only fertilizer products, thus comparing how the imports of banned versus non-banned fertilizers evolve over time after the ban is introduced. The results, albeit less precisely estimated, are qualitatively maintained (Appendix Figure A4). Due to complementarities in production, banning the imports of chemical fertilizers may also have negatively affected other fertilizers. On the intensive margin, a large difference in imports across banned and non-banned fertilizers emerged four months after the ban was introduced and persisted for several months thereafter.<sup>28</sup>

> 26See Callaway (2023) for a complete review of DID methods.

> 27The coefficient for month _t_ = 4 in Figure Ib equals -10.8. Given the log specification, the corresponding percentage effect on imports can be recovered through the expression: (exp( _−_ 10 _._ 8) _−_ 1) _×_ 100% _≃−_ 99 _._ 998%.

> 28As an additional check, we also obtain DID estimates using the log of imported product _quantities_ as the outcome variable. The ban’s effects on fertilizer imports remain very similar when imports are measured in kg instead of dollars (Appendix Figure A5). This is unsurprising, as Sri Lanka’s economy is arguably too small to influence the prices of
12 Finally, we establish the robustness of our results to concerns about seasonality and the concurrent Covid-19 pandemic shock. Our results are robust to using deseasonalized versions of our outcome variables (Appendix Figure A6).<sup>29</sup> The Covid-19 pandemic, still ongoing in 2021, would only bias our estimates if it affected imports of banned and non-banned fertilizers to different degrees, which we do not have a strong reason to expect. Still, we implement a falsification test by obtaining DID estimates with the treatment period redefined to start in March 2020 (when Covid-19 arrived) instead of May 2021. The results show that fertilizers who would eventually be banned in 2021 did not suffer a relative import decline in the early months of the pandemic (Appendix Figure A7).

# **IV.B Fact 2: Rice and Tea Production Declined Significantly After the Ban**

We start by examining the production of Sri Lanka’s primary food crop, rice, covering about 40% of total arable land. Figure IIa plots the year-to-year evolution of average rice yields in the main (Maha) growing season.<sup>30</sup> From a high of around 4,500 kilograms per hectare (kg/ha) in 2020, Maha rice yields declined precipitously to below 3,000 kg/ha in 2022. This represents a 31.6% decline in yield relative to the historical average of the previous nine years. The observed rice yield decline is very similar when we use our granular remote sensing estimates. This decline cannot be explained by observed weather variables that typically influence agricultural production (such as temperature, rainfall, sunlight, and vapor pressure): even after controlling for fluctuations in such variables, we still find a 24.4% yield decline relative to the historical average (Appendix C.D).<sup>31</sup> Figure IIb shows that rice imports were negligible before the import ban, as Sri Lanka had achieved self-sufficiency in rice production, but, starting in late 2021, rice imports surged up to January 2022, remaining elevated throughout the rest of the year. Even this surge was not enough to fully make up for lost production, though, with the availability of rice for domestic consumption falling by 22% between 2021 and 2022.<sup>32</sup> Figure III presents rice yields at the DS level for the last Maha season before the ban (September

> internationally traded commodities such as fertilizer.

> 29Both outcome variables (extensive and intensive margins) are deseasonalized by subtracting their HS8 productmonth-specific averages in 2017-2019, before the fertilizer ban.

> 30The Maha season is the main rice cultivation season in Sri Lanka, running from September to March of the following year (the second season, Yala, runs from May to August).

> 31Ozdogan et al. (2024) confirms that the notable decline in remote sensing rice yield estimates over the 2021-2022 period cannot be explained by variation in environmental variables and is directly correlated with the reduction in fertilizer availability ensuing from the import ban.

32We define the amount of rice available for domestic consumption in a given year as the sum of production and net imports. This amount fell from 5.2 billion kg in 2021 to 4 billion kg in 2022. Since we lack trade data for November and December 2022, we instead compute net imports for 2022 based on the period from November 2021 to October 2022. Correspondingly, net imports for 2021 are computed based on the period from November 2020 to October 2021. If there had been no change in net imports, rice availability in 2022 would have been 3.40 billion kg. Therefore, the import surge offset one third of the production losses.
13 2020-March 2021) and the first Maha season after the introduction of the ban (September 2021March 2022). Rice yields fell in almost all regions, with some spatial heterogeneity in the degree of yield reduction. The fall was more pronounced in Sri Lanka’s northern and western regions, including major rice-producing districts such as Ampara, Anuradhapura, Batticaloa, and Polonnaruwa.

We also examine yields of Sri Lanka’s major export crop, tea. Tea yields suffered a large drop of 28.7% in 2022 (after controlling for weather fluctuations) relative to historical averages, as seen in Appendix C.D. This evidence shows that the fertilizer ban harmed Sri Lankan agriculture substantially, consistent with the importance of fertilizer as an import determinant of agricultural productivity across the world (Donovan, 2021; Gollin et al., 2014).

# **IV.C Fact 3: Agricultural Exports Declined After the Fertilizer Import Ban**

Facts 1 and 2 show that fertilizer imports and rice and tea production declined, and rice imports increased, with the fertilizer import ban. We now show the ban also had adverse downstream effects on agricultural exports.

To assess the ban’s effects on the export performance of agricultural firms, we consider the sample of firms who exported in 2017-2019 (i.e. pre-ban) at least one of the 23 crops with fertilizer intensity data. To understand which firms were more exposed to the ban, we define a firm-level exposure measure capturing how much fertilizer is embodied in the crops each firm exports. This exposure measure is the weighted average of the firm’s exported crops’ fertilizer intensities, where the weights are given by the share of each crop in the firm’s agricultural exports portfolio preban.<sup>33</sup> We rank firms by fertilizer exposure and compute the third quartile of that measure. We define exporting firms to be treated if their fertilizer exposure is above the third quartile. As in Fact 1, we use the De Chaisemartin and d’Haultfoeuille (2022) estimator to allow for the fact that the bans were switched on and off. Our dynamic DID estimator recovers the evolving effects of the ban over time on the log of firm export value at quarter level in the period between January 2019 and September 2022.<sup>34</sup> An advantage of our approach is that the firm’s potential exposure to fertilizers is computed using information on its agricultural exports and on each product’s fertilizer requirements. A disadvantage is that the control group may be imperfect, since all agricultural exporters might have been affected to some degree. If anything, this will work against our finding of any effect of the ban on exports. Appendix B.B provides further details on the firm-level fertilizer

> 33Formally, the exposure measure for firm _f_ is given by: _Uf_ =<sup>�23</sup> _v_ =1<sup>_FICv×_</sup> � _Xfv_<sup>2017</sup><sup>_−_2019</sup> _/_<sup>�</sup> _v_<sup>_′ X_</sup> _fv_<sup>2017</sup><sup>_′−_2019</sup> �, where _v_ indexes crops, _FICv_ is fertilizer intensity of crop _v_ (in kg/ha), and _Xfv_<sup>2017</sup><sup>_−_2019</sup> is the firm’s total exports of crop _v_ in the 2017-2019 period.

> 34The use of a quarterly, rather than a monthly time frequency as in our previous import regressions, has two justifications. First, fertilizer inventories might have been available which would take time to be depleted. Second, the agricultural cultivation cycle takes several months from fertilizer application to harvest and export. Our specification allows export effects to materialize some time after the ban was implemented.
14 exposure measure and the estimating equation.

Figure IV presents the DID results, showing that, three quarters after the fertilizer ban was implemented (i.e. in Q1/2022), agricultural exports significantly declined for firms with a high pre-ban fertilizer exposure (relative to low-exposure firms). The magnitude of the estimated effects corresponds to a 35% reduction in firms’ agricultural export value in that quarter (or, correspondingly, 8.6% of their annual export value).<sup>35</sup> The effect’s timing is unsurprising, as Sri Lanka’s major (Maha) growing season ends in Q1. We also show that our findings are robust to seasonality concerns: using a deseasonalized version of the outcome variable, we obtain a similar negative effect of the ban on downstream agricultural exports (Appendix Figure A8).

While these three stylized facts demonstrate the fertilizer ban’s impact on imports, agricultural production, and exports, it is impossible to quantify the GE effects of the resulting lack of access to fertilizer and the associated changes in welfare without a theoretical model.

# **V A Quantitative Spatial Model of Trade and Agriculture**

This section introduces a quantitative GE spatial model of trade and agriculture to analyze the ban’s effects on relative prices, fertilizer use, and welfare across regions and agent types in Sri Lanka. The model highlights the policy relevance of government tools like import restrictions, which limit fertilizer access, and subsidies, which in turn shape the distributional impacts of limited fertilizer access. In Section VII, we use the model to examine the welfare effects of the ban under counterfactual scenarios.

## **V.A General Environment**

In the model, the world is composed of _R_ geographic regions. There are _I_ = _R −_ 1 regions within Sri Lanka, plus one additional region representing the rest of the world (RoW).<sup>36</sup> Each region _i_ has a fixed population of size _Ni_ which cannot move across regions.<sup>37</sup> The population is composed of three types of agents: _Ni_<sup>_e_estate workers (who can only work in tea agriculture),</sup><sup>_N m_</sup> _i_ sectorally mobile workers (who can work in manufacturing or in any agricultural sector except tea), and 35To compute annualized export losses, we use the fact that, in our sample of high-exposure (i.e. “treated”) firms, the first quarter of 2019 accounted for 24.5% of that year’s total exports. Assuming this same percentage would have held in 2022 in the absence of the ban, a 35% export loss in Q1/2022 translates into a 8.6% loss in 2022 as a whole. In any case, the DID nature of this exercise implies that both the 35% and 8.6% figures can be considered lower bounds for the ban’s total effects, which also include GE effects. This distinction also explains the gap between our reduced-form export loss estimate (8.6%) and the corresponding estimate (22.6%) we will show in our model-driven counterfactual exercise (see Table IV in Section VII.B).

> 36When bringing the model to the data, the regions within Sri Lanka are its 25 districts (that aggregate across DSs).

37We argue this immobility assumption is reasonable because our empirical implementation of the model focuses on a relatively short time horizon of less than two years.
15 _Ni_<sup>_F_landowningfarmers,with</sup><sup>_N e_</sup> _i_<sup>+</sup><sup>_N m_</sup> _i_<sup>+</sup><sup>_N F_</sup> _i_ = _Ni_ . Additionally, there is a set of Sri Lankan middlemen who are in charge of domestic fertilizer markets (i.e. they own the domestic fertilizer endowment and also import foreign fertilizer to sell in Sri Lanka).<sup>38</sup> There are two main economic sectors, agriculture ( **A** ) and manufacturing ( **M** ). Agriculture encompasses a finite set of _K_ crops. Each crop (as well as the manufacturing good) is differentiated by regional origin (i.e., the Armington assumption). Furthermore, there is an additional minor sector, fertilizer ( **f** ), which is a single homogeneous good that is exclusively used as an intermediate input in agriculture. All markets are perfectly competitive.

# **V.B Production**

This section presents our assumptions concerning production and trade costs in each of the three sectors of the economy: agriculture, manufacturing, and fertilizer.

## **V.B.1 Agricultural Production**

We model agricultural production similarly to Farrokhi and Pellegrina (2023). Each region _i_ has an agricultural land mass of area _Lik_ that can only be used to grow crop _k_ .<sup>39</sup> This land mass is composed of a continuum of plots indexed by _ω_ , each of size _lik_ ( _ω_ ), which can be used in combination with labor and fertilizer inputs to produce agricultural goods. By combining a land portion of size _lik_ ( _ω_ ) within plot _ω_ with labor input _nik_ ( _ω_ ) and fertilizer input _fik_ ( _ω_ ), it is possible to produce an amount _qik_ ( _ω_ ) of crop _k_ according to the following Cobb-Douglas production function: where _Tik_<sup>_A_is a land productivity parameter and (</sup><sup>_γ_</sup> _k_<sup>_n_,</sup><sup>_γ_</sup> _k_<sup>_f_,</sup><sup>_γ_</sup> _k_<sup>_l_) are Cobb-Douglas coefficients.40These</sup> assumptions allow fertilizer dependence to vary across crops (since parameter _γk_<sup>_f_dependson</sup><sup>_k_),</sup> which was shown earlier to be the case. Furthermore, since productivity parameter _Tik_<sup>_A_varies across</sup> regions, they may differ in terms of absolute and comparative advantage within agriculture.

Individual production decisions can be aggregated to obtain crop production and land rents at the regional level. For a plot _ω_ producing crop _k_ in region _i_ , the optimal unit production cost _cik_ ( _ω_ ) that results from solving its cost minimization problem can be written as:

> 38For modelling convenience, we assume the population of middlemen has measure zero, so they can be omitted from the calculation of average welfare changes in Section VII. See Appendix F for further discussion of this assumption.

> 39This assumption implies that land cannot be reallocated across crops, which is consistent with the short-term horizon of our empirical implementation of the model. Importantly, this assumption finds strong support in the Ozdogan et al. (2024) remote sensing estimates of cultivated rice areas in Sri Lanka, which indicate an extremely high correlation in the pixels classified as growing rice in each year relative to the previous year (for either Maha or Yala seasons). We also provide evidence of no post-ban reduction in cultivated rice area in Appendix C.D.

> 40 _n_ We assume agricultural production functions have constant returns to scale, so _γk_<sup>+</sup><sup>_γ_</sup> _k_<sup>_f_+</sup><sup>_γ_</sup> _k_<sup>_l_= 1 for each crop</sup><sup>_k_.</sup>
16 where _wi_<sup>_k_and</sup><sup>_pf,k_</sup> _i_ are the relevant wage and fertilizer price (respectively) for crop- _k_ agriculture, _rik_ ( _ω_ ) is the rental rate of plot _ω_ , and _κk_ is a composite parameter.<sup>41</sup> Perfect competition then implies that the unit cost _cik_ ( _ω_ ) must equal the local crop price ( _pik_ ) in equilibrium.<sup>42</sup> This equality then allows us to solve for land rent _rik_ ( _ω_ ) as: with composite variable _hik_ “summarizing” the prices that are relevant for the plot. Aggregating over all plots that grow crop _k_ in region _i_ , we can write the total land rent _Rik_ earned by them as: Due to the properties of the Cobb-Douglas production function, we also know that total payments to land must equal a share _γk_<sup>_l_of the agricultural revenue from crop</sup><sup>_k_in region</sup><sup>_i_:</sup> where _Qik_ is the total physical production of crop _k_ in region _i_ . Combining equations (4) and (5), we can solve for production _Qik_ as:<sup>43</sup> We assume that a crop _k_ produced in region _i_ can be either sold locally or exported to other regions. However, to export to region _n_ the seller incurs a multiplicative “iceberg” trade cost _τni,k_<sup>_A≥_1.Therefore, marginal-cost pricing implies that the crop price at the destination must be:</sup> Finally, it is convenient to define an aggregate land rent variable _Ri_ combining the land rent

> 41 _κk ≡_ [( _γkn_<sup>)</sup><sup>_γ_</sup> _k_<sup>_n_</sup> ( _γk_<sup>_l_)</sup><sup>_γ_</sup> _k_<sup>_l_</sup> ( _γk_<sup>_f_)</sup><sup>_γ_</sup> _k_<sup>_f_</sup> ]<sup>_−_1</sup> . Tea agriculture employs estate workers, so its relevant wage _wi_<sup>_tea_</sup> equals _wi_<sup>_e_,</sup> the wage rate of estate workers in region _i_ . For all other crops _k_ other than tea, _wi_<sup>_k_=</sup><sup>_w_</sup> _i_<sup>_m_,where</sup><sup>_w_</sup> _i_<sup>_m_</sup> is the wage rate of mobile workers in region _i_ . The relevant fertilizer price _p_<sup>_f,k_</sup> _i_ can vary across crops because different crops are subsidized by the government at different rates (see Section V.D).

> 42The intuition for this equality is that multiple agricultural entrepreneurs compete for the right to farm plot _ω_ by bidding up the land rent until the ensuing unit cost equals the crop price.

> 43Intuitively, equation (6) shows that equilibrium regional crop production depends positively on land productivity, land endowment, and crop prices, and negatively on labor and fertilizer prices.
17 from all crops in region _i_ :

# **V.B.2 Manufacturing Production**

We assume that manufacturing production uses labor as its sole input. Manufacturing output _qi_<sup>_M_</sup> in region _i_ is a simple linear function of regional manufacturing employment ( _ni_ ), with a multiplicative constant given by productivity parameter _Ti_<sup>_M_.</sup> As in agriculture, the manufacturing good produced in a region _i_ can be either consumed locally or shipped to another region _n_ , with the latter incurring an iceberg trade cost _τni_<sup>_M≥_1.Given these</sup> assumptions, marginal-cost pricing (due to perfect competition) implies that the unit price of the manufacturing good produced in _i_ and offered for sale in _n_ must be: where _wi_<sup>_m_is the wage rate of mobile workers in region</sup><sup>_i_.</sup>

# **V.B.3 Fertilizer Endowments**

As in Farrokhi and Pellegrina (2023), we assume that the quantity of fertilizer _Q_<sup>_f_</sup> _i_<sup>owned by agents</sup> who live in region _i_ is simply given as a natural endowment _Fi_ (rather than being produced). Moreover, fertilizer is a tradable homogeneous good, so _in the absence of import restrictions_ its price must follow the law of one price. This implies that fertilizer price _p_<sup>_f_</sup> _i_<sup>in region</sup><sup>_i_must equal</sup> the international fertilizer price ( _p_<sup>_f_</sup> _RoW_<sup>).44</sup> To model the import ban, we allow the Sri Lankan government to restrict fertilizer imports through the use of QRs. To implement these QRs, the government distributes import licenses to middlemen, allowing them to import up to _f_<sup> ̄</sup> kg of foreign fertilizer.<sup>45</sup> If the QRs are binding, then the domestic fertilizer price across Sri Lankan regions ( _{p_<sup>_f_</sup> _i_<sup>_}_</sup> _i_<sup>_I_</sup> =1<sup>)willbeanumber</sup><sup>_pf_</sup> _LKA_<sup>strictly</sup> greater than the international price _p_<sup>_f_</sup> _RoW_<sup>, with the price difference being pocketed by the middle-</sup> men in the form of license rents _QR_<sup>_rent_</sup> :<sup>46</sup>

> 44Variable _p_<sup>_f_</sup> _i_<sup>is defined as the price of fertilizer</sup><sup>_gross_of subsidies (see Section V.D).</sup>

> 45Whether or not there are QRs in place, we assume that Sri Lanka is a net importer of fertilizer, which is consistent with the observed preponderance of imported chemical fertilizer in its agricultural sector. For example, in 2019 Sri Lanka imported 210 million USD in chemical fertilizer while only exporting 480,749 USD.

> 46Note that variable _QRrent_ is the _total_ , country-wide license rent, which is then distributed equally among middlemen. We assume that Sri Lankan middlemen have the same spatial distribution as Sri Lankan mobile workers. As a consequence, regional license rents are given by: _QRi_<sup>_rent_</sup> = _QR_<sup>_rent_</sup> _× Ni_<sup>_m/_(�</sup><sup>_I_</sup> _k_ =1<sup>_N_</sup> _k_<sup>_m_).</sup>
18

# **V.C Consumers**

The _Nn_ agents living in region _n_ earn income and consume. Mobile workers inelastically supply one unit of labor to local firms and are perfectly mobile across sectors, thus earning the local mobile wage _wn_<sup>_m_independentlyofthesectorinwhichtheywork.47Estateworkersalsosupply</sup> one unit of labor inelastically, but they can only work in tea agriculture, earning the local estate wage _wn_<sup>_e_.Farmers, who own land, rent out this land for agricultural production, earning land rents.</sup> Finally, there is a measure-zero set of middlemen who own Sri Lanka’s fertilizer endowment and the fertilizer import licenses issued by the government (if any), thus deriving their income from fertilizer sales and license rents.

## **V.C.1 Land Ownership**

We allow for inequality in land ownership. Denoting the total extension of land owned by farmer _h_ in region _n_ as _L_<sup>_h_</sup> _n_<sup>, we assume that variable</sup><sup>_Lh_</sup> _n_<sup>follows a log-normal distribution with parameters</sup> _μn_ and _σLn_<sup>2.48Wealsoassumethat,conditionalonhertotallandsize</sup><sup>_Lh_</sup> _n_<sup>,eachfarmerreceivesa</sup> random sample of plots. These assumptions imply the land rent _Rn_<sup>_h_received by a farmer</sup><sup>_h_in region</sup> _n_ is proportional to her land size: where _Ln_ =<sup>�</sup> _k_<sup>_Lnk_is total arable land in region</sup><sup>_n_, and</sup><sup>_Rn_is the aggregate land rent paid to all</sup> land in region _n_ . Given the log-normal distribution of land size, it follows that land rent in region _n_ also has a log-normal distribution, as follows:

## **V.C.2 Consumption Across Sectors**

Preferences for agricultural versus manufacturing goods are non-homothetic.<sup>49</sup> For all agents except middlemen, we represent this non-homotheticity using PIGL preferences (Eckert and Peters, 2023), in which an agent’s indirect utility function is given by:<sup>50</sup>

> 47We relax the perfect mobility assumption in Appendix H by introducing frictions to cross-sector mobility.

> 48This assumption is consistent with the empirical distribution of landholdings observed in Sri Lanka’s household survey data (see Appendix C.C).

> 49This assumption is strongly supported by Sri Lanka’s household survey data, in which the expenditure share of agricultural goods decreases with household income (see Appendix Figure A10).

> 50Similarly to Eckert and Peters (2023), we choose PIGL over other classes of non-homothetic preferences (e.g. Stone-Geary) due to its convenient aggregation properties.
19 where _y_ is income, _P_<sup>_A_</sup> and _P_<sup>_M_</sup> are prices of agricultural and manufacturing goods, respectively, and _η, φ ∈_ (0 _,_ 1) and _ν_ are exogenous parameters.<sup>51</sup> This formulation implies that agriculture’s share of expenditure ( _ξ_<sup>_A_</sup> ) can be written as: Because _η >_ 0, equation (13) implies that agriculture’s expenditure share decreases as the agent’s income _y_ increases, with an asymptote _φ_ . Since the middleman population has measure zero, a middleman’s income _y_ is very high and thus his food share converges to _φ_ . Therefore, to simplify, we assume middlemen have homothetic preferences (i.e. _ν_ = 0) with food share equal to _φ_ .

Because agents (other than middlemen) have non-homothetic preferences, the aggregate agricultural expenditure in a region _n_ (denoted _Xn_<sup>_A_) depends on the distribution of income across agents</sup> within that region and can be written as:<sup>52</sup> where _Pn_<sup>_A_and</sup><sup>_P M_</sup> _n_ are price indices of agricultural and manufacturing goods (respectively) in region _n_ (defined in Sections V.C.3 and V.C.4 below), _t_ is a flat income tax rate (defined in Section V.D below), _rn ≡ Rn/Nn_<sup>_F_istheaveragelandrentearnedbyfarmersinregion</sup><sup>_n_,and</sup><sup>_En_is</sup> aggregate income in region _n_ , which can be written as: The aggregate expenditure of region _n_ on manufacturing goods ( _Xn_<sup>_M_) is then simply determined</sup> by subtracting aggregate agricultural expenditure from aggregate disposable income:

> 51In our context, _P A_ and _P M_ are sectoral price indices that aggregate the prices of multiple goods, as defined below. 52See a proof in Appendix G.A. Empirical evidence for equation (14) is provided in Appendix C.E. This equation is similar to the one in Fan et al. (2023), but our model features multiple agent types and imposes a log-normal income distribution for one of these types (and a degenerate distribution for the others).
20

# **V.C.3 Within-Agriculture Consumption**

Consumers allocate their agricultural expenditure across multiple crops according to Constant Elasticity of Substitution (CES) preferences with elasticity _σA_ . Defining _Pn_<sup>_A_astheagriculturalprice</sup> index in region _n_ and _βnk_<sup>_A_as the expenditure share of crop</sup><sup>_kwithin total agricultural expenditure_,</sup> we can then write: where _bk_ is an exogenous preference shifter, and _Pnk_ is the price index of crop _k_ in region _n_ (defined below). Furthermore, for each crop _k_ , agents consume geographically differentiated varieties from all regions following CES preferences with (Armington) elasticity _σK_ . Defining _βni,k_<sup>_A_as the share</sup> of origin _i_ within the expenditures of region _n_ on crop _k_ , we can then write: where _bi,k_ is an exogenous preference shifter, and _pik_ is the local producer price of the variety of crop _k_ that is produced in origin _i_ .

# **V.C.4 Manufacturing Consumption**

As in agriculture, each agent allocates manufacturing expenses across geographically differentiated manufacturing varieties according to CES preferences with (Armington) elasticity _σM_ . Defining _βni_<sup>_M_as the share of origin</sup><sup>_i within the total manufacturing expenditures_of destination region</sup><sup>_n_, and</sup> _Pn_<sup>_M_as the manufacturing price index in region</sup><sup>_n_, we can then write:</sup> where _p_<sup>_M_</sup> _ni_<sup>is the price in region</sup><sup>_n_of the manufacturing variety from origin</sup><sup>_i_.Substituting pricing</sup> equation (9) into these two expressions, we can rewrite manufacturing expenditure shares and price index as follows:
21

# **V.D Taxes and Subsidies**

Motivated by the widely documented importance of fertilizer subsidies for Sri Lankan agriculture, we assume that the national government subsidizes fertilizer purchases by farmers.<sup>53</sup> For each crop _k_ , a subsidy rate _sk_ is applied on the gross market price of fertilizer ( _p_<sup>_f_</sup> _i_<sup>), so the relevant fertilizer</sup> price _p_<sup>_f,k_</sup> _i_ faced by a farmer who grows crop _k_ in region _i_ is given by: Subsidy costs are paid by the government, who funds itself through a national income tax: all agents (farmers, workers, and middlemen) in all domestic regions pay an income tax with flat rate _t_ , with the rate chosen such that tax revenues exactly cover governmental expenditures. Therefore, given subsidy rates, regions’ aggregate incomes ( _{Ei}i_ ), and agricultural production and producer prices ( _{Qik, pik}i,k_ ), it can be shown that the necessary tax rate _t_ to fund the government is:

# **V.E Equilibrium**

We close the model by stating market clearing conditions in the markets for fertilizer, crops, and labor. First, fertilizer marketing clearing depends on whether QRs are in place. In the absence of QRs, market clearing can be expressed as a single equation for the whole world: where _p_<sup>_f,k_</sup> _i_ is given by equation (20), fertilizer price _p_<sup>_f_</sup> _i_<sup>ineachregion</sup><sup>_i_equalstheinternational</sup> fertilizer price _p_<sup>_f_</sup> _RoW_<sup>, and agricultural production</sup><sup>_Qik_is given by equation (6).Therefore, with no</sup> QRs, there is a single fertilizer price across the whole world. However, with QRs, the international price and the price within Sri Lanka ( _p_<sup>_f_</sup> _LKA_<sup>)maydiverge.Inthatcase,fertilizermarketclearing</sup> consists of two sets of equations, one for Sri Lanka and one for the RoW: 53On Sri Lanka’s fertilizer subsidy policy, see Section A.E and FAO and WFP (2022, 2023).
22 Second, the market clearing conditions of every agricultural crop produced by every region can be written as the following set of equations: where bilateral prices ( _pni,k_ ) are given by equation (7), aggregate agricultural expenditures _Xn_<sup>_A_are</sup> given by equation (14), and crop and origin expenditure shares ( _βnk_<sup>_A_and</sup><sup>_β_</sup> _ni,k_<sup>_A_,respectively)are</sup> given by equations (17) and (18), respectively.

Third, the labor market clearing condition for mobile workers in each region _i_ is given by: with manufacturing expenditure _Xn_<sup>_M_inregion</sup><sup>_n_givenbyequation(16)andoriginexpenditure</sup> shares _βni_<sup>_M_given by equation (19).Demand for mobile labor arises from two sources:agriculture</sup> (excluding tea) and manufacturing. Intuitively, agricultural demand for labor depends on each crop’s total revenue but also on its labor intensity (represented by Cobb-Douglas coefficient _γk_<sup>_n_).</sup> Since manufacturing uses labor as its sole input, its full revenue is paid to labor as wages.

Fourth, the labor market clearing condition for estate workers in each region _i_ is simply: Given the four market clearing conditions described above, we can now formally define the model’s equilibrium as follows:

**Definition 1 (Equilibrium)** _Given the model’s parameters (R, K, η, ν, φ,_ **_σ_** _,_ **_γ_** _) and exogenous variables (_ **_F_** _,_ **_N_** _,_ **_L_** _,_ **_T_** _,_ **_τ_** _,_ **_b_** _, f_<sup> ̄</sup> _,_ **_s_** _) , an_ **_equilibrium_** _is a set of endogenous variables (t,_ **_p_**<sup>**_A_**</sup> _,_ **_p_**<sup>**_f_**</sup> _,_ **_p_**<sup>**_−_**</sup> _,_ **_P_** _,_ **_w_** _,_ **_R_** _,_ **_E_** _,_ **_X_** _,_ **_β_** _,_ **_Q_** _,_ **_QR_**<sup>_rent_</sup> _) satisfying equations 3, 5, 6, 7, 8, 14, 15, 16, 17, 18, 19, 20, 21, 25, 26, 27. Additionally, if QRs are_ **_not_** _in place, equation 22 must hold, with p_<sup>_f_</sup> _i_<sup>=</sup><sup>_pf_</sup> _RoW_<sup>_for_</sup> _all regions i ∈{_ 1 _, ..., R}. Alternatively, if QRs_ **_are_** _in place, equations 23 and 24 must hold, with p_<sup>_f_</sup> _i_<sup>=</sup><sup>_pf_</sup> _LKA_<sup>_for all domestic regions i ∈{_1</sup><sup>_, ..., I}._54</sup> 54Variables in bold are collections of region- and/or crop-level terms, as follows: **_σ_** = ( _σA, σM , σK_ ),
23

## **V.F Welfare**

Equilibrium variables can also be used to express the welfare of various groups of agents. For mobile workers in region _i_ , whose only source of income is wages, welfare _Vi_<sup>_m_</sup> can be written as: Note that the welfare of a mobile worker does not depend on whether she works for agriculture or manufacturing, nor on the specific crop within agriculture in which she is employed. This follows from the regional wage being equalized across sectors and crops due to frictionless worker mobility across sectors. Similarly, the welfare _Vi_<sup>_e_of estate workers in region</sup><sup>_i_is given by:</sup> The welfare of a farmer _h_ depends on the amount of land rent _R_<sup>_h_</sup> she earns, which in turn depends on the amount of land she owns. Averaging across all farmers of a region _i_ , we show in Appendix G.B that average farmer welfare _Vi_<sup>_F_</sup> can be expressed as:

# **VI Estimation**

To use our quantitative model to study the impacts of the fertilizer import ban on the Sri Lankan economy, we start by estimating a pre-ban baseline of the model in 2019. In this section, we describe the steps for such estimation: first parameter estimation, then model “inversion” to back out implied unobserved variables.

## **VI.A Step 1: Estimating Parameters**

### **VI.A.1 Preference Parameters**

This group of parameters consist of PIGL non-homotheticity parameters ( _φ_ , _η_ , _ν_ ) and elasticities of substitution ( _σA_ , _σM_ , _σK_ ). PIGL parameter _φ_ represents the asymptotic expenditure share of agriculture as income grows large (while keeping price indices _Pn_<sup>_A_and</sup><sup>_P M_</sup> _n_<sup>fixed),as implied by</sup>
24 equation (13). Therefore, we simply set _φ_ to 1.05%, the lowest reported food expenditure share in our 2019 household data. Parameter _ν_ is set to 0.12, following Eckert and Peters (2023).

To estimate the Engel elasticity _η_ , we take logs of equation (13), add household subscripts, collect relevant terms into a region fixed effect, and add a household size control variable and an error term, thus obtaining the following equation, which is estimated on 2019 data from Sri Lanka’s Household Income and Expenditure Survey (HIES): where _h_ indexes households, _n_ indexes regions, _ξnh_<sup>_A_is the share of income the household spends on</sup> food, _ynh_ is household income, _hhsizenh_ is household size, _ωn_ is a region fixed effect, and _εnh_ is an error term.<sup>55</sup> To allay concerns about the potential endogeneity of household income (e.g. due to seasonality in prices and employment opportunities), we follow an IV approach. We instrument household income _ynh_ with two arguably exogenous sources of income: income obtained from lottery (and other _ad hoc_ gains) and income obtained from disasters and other relief payments.<sup>56</sup> To our knowledge our paper is the first to estimate the Engel elasticity off exogenous income variation generated by a lottery.<sup>57</sup> The resulting IV estimate for _η_ , shown in Table II, is 0.656.<sup>58</sup> To estimate the elasticity of substitution across crops ( _σA_ ), we take logs of equation (17), add household subscripts, collect relevant terms into crop- and household-specific fixed effects, and add an error term, obtaining the following equation, which is estimated on 2019 HIES data: where _k_ indexes crops, _βnhk_<sup>_A_is the share of crop</sup><sup>_k_in the household’s total food expenditures,</sup><sup>_Pnhk_</sup> is crop price, _ωk_ and _ωh_ are crop and household fixed effects (respectively), and _ε_<sup>_A_</sup> _nhk_<sup>isanerror</sup> term. To address the potential endogeneity of crop prices (e.g. due to unobserved region-specific tastes affecting both prices and expenditure shares), we follow the IV approach in Sotelo (2020), instrumenting price variable ln( _Pnhk_ ) with a dummy variable _Dnk_<sup>_GAEZ_</sup> , which takes value one if the potential yield of crop _k_ in region _n_ is nonzero, according to FAO-GAEZ data (see Appendix A.F). Thus, our identification of the cross-crop elasticity of substitution _σA_ comes from variation in crop prices due to regional shifters of agricultural supply driven by climatic and geological endowments, arguably orthogonal to unobserved factors that affecting consumer behavior. Our

> 55Here a region is one of Sri Lanka’s 25 districts since DS are not recorded in the household data.

> 56Both exogenous sources of income refer to the previous 12 months.

> 57 Boppart (2014) finds Engel elasticities around 0 _._ 20 _−_ 0 _._ 25 for the U.S., Fan et al. (2023) report an IV estimate of 0.395 for India, and Eckert and Peters (2023) calibrate an Engel elasticity of 0 _._ 93 within a spatial model. These estimates are not directly comparable due to differences in context, aggregation, and identification, but our estimates lie within the range estimated in the literature.

> 58See Appendix D.A for details on the 2SLS estimation results of ( _η_ , _σA_ ), including first stage results.
25 estimate, ˆ _σA_ = 1 _._ 714, is lower than 2.39 in Sotelo (2020) but higher than in much of the literature.<sup>59</sup> We calibrate the value of the Armington elasticity of substitution across different origins of the ˆ same crop to _σK_ = 2 _._ 377 so that the average increase in agricultural producer prices generated by the model-driven counterfactual exercise of Section VII.A matches the corresponding increase of 22.65% that can be observed in the data between January 2021 and January 2022 (see Appendix Figure A11).<sup>60</sup> The Armington elasticity of substitution within manufacturing is set to _σM_ = 2 _._ 528, which is consistent with the lower range of estimates from Feenstra et al. (2018).<sup>61</sup>

# **VI.A.2 Trade Costs**

Agricultural and manufacturing firms can trade their goods (both domestically and internationally) by incurring “iceberg” trade costs ( _{τni_<sup>_M}n,i_,</sup><sup>_{τ A_</sup> _ni,k_<sup>_}n,i,k_):they represent how many units of a good</sup> must be shipped from origin _i_ so that one unit will arrive at destination _n_ . To estimate these trade cost matrices, we start by assuming the following parametrizations: where _α >_ 0 is a parameter governing the semi-elasticity of trade costs with respect to distance, _distkmni_ is the (geodesic) straight-line distance in kilometers between the geographic centroids of regions _n_ and _i_ , and _Bk ≥_ 1 is an extra (multiplicative) cost of trading agricultural crop _k_ internationally.<sup>62</sup> To estimate semi-elasticity _α_ , we use the fact that the cost of transporting tea for 100 kilometers within Sri Lanka was _pT,_ 100 = 1 _,_ 496 LKR per metric ton (LKR/MT) in 2019, while the farm-gate price of tea was _ptea_ = 455 _,_ 473 LKR/MT. The corresponding iceberg trade cost can then be written as _τni,tea_<sup>_A_= 1 +</sup><sup>_<u>p</u>_</sup> _p_<sup>_T_</sup> _tea_<sup>_<u>,</u>_100, which, using equation (34), implies a semi-elasticity of</sup><sup>_α_ˆ = 3</sup><sup>_._3</sup><sup>_×_10</sup><sup>_−_5.</sup> For each crop _k_ , we estimate international trade cost _Bk_ as the gap between the crop’s interna-

> 59For example, the estimated elasticity in Behrman and Deolalikar (1989) is 1.2.

> 60Intuitively, a higher value of _σK_ blunts the ban’s effect on crop prices in the model because it implies that each crop’s international variety is a good substitute for its Sri Lankan varieties, thus keeping domestic prices in check through international competition.

> 61See row “Apparel Manufacturing” in Table 3 of Feenstra et al. (2018). We chose this particular value because apparel manufacturing is an important industry within Sri Lankan manufacturing.

> 62When district _l_ in Sri Lanka trades internationally, we assume the relevant distance is the distance between _l_ and the Colombo district, where Sri Lanka’s main port is located. Formally, we set _distl,RoW_ = _distl,Colombo_ and _distRoW,l_ = _distColombo,l_ . Cost _Bk_ can be interpreted as a “border-crossing” cost (e.g. a tariff) that is paid to trade crop _k_ internationally _in addition to_ the transportation cost. We assume the manufacturing sector faces no such additional cost. Unlike international trade costs _Bk_ , the distance semi-elasticity _α_ is the same for all crops (and for manufacturing). This assumption is necessary because data on transportation costs is only available for one crop (tea).
26 tional price and its domestic price at the port of Colombo: where _pRoW,k_ is the 2019 price of crop _k_ in the RoW, and _pColombo,k_ is its 2019 “benchmark price” at the port of Colombo. This estimation approach selects between the ratio of international price to domestic price and its reciprocal the one that is larger than unity.<sup>63</sup> Thus, we implicitly assume that an international price that is larger ( _smaller_ ) than its domestic price reveals a crop’s status as an export ( _import_ ) crop. The magnitude of such price gap reveals the severity of the barriers faced by the crop’s exporters ( _importers_ ). Our estimated _B_<sup>ˆ</sup> _k_ are displayed in Table III.

# **VI.A.3 Production Function Parameters**

Since our paper focuses on agriculture, it is important to find context-appropriate values for the parameters _{γk_<sup>_f, γ_</sup> _k_<sup>_l, γ_</sup> _k_<sup>_n}k_that govern Cobb-Douglas agricultural production function (1).Leveraging</sup> 2022 NFS data on fertilizer intensity, we estimate the fertilizer coefficient _{γk_<sup>_f}k_of each crop</sup><sup>_k_as:</sup> where _Mk_<sup>_f,LKA_</sup> is annual fertilizer expenditure by Sri Lankan farmers for production of crop _k_ (in USD), _p_<sup>_LKA_</sup> _k_ is the price of crop _k_ in Sri Lanka (in USD/kg), and _Q_<sup>_LKA_</sup> _k_ is Sri Lanka’s annual production of crop _k_ (in kg).<sup>64</sup> The resulting estimates are displayed on Table III. The remaining Cobb-Douglas coefficients ( _γk_<sup>_l_,</sup><sup>_γ_</sup> _k_<sup>_n_) must add to (1</sup><sup>_−γ_</sup> _k_<sup>_f_) for each crop</sup><sup>_k_. We apportion this residual</sup> value to land and labor using data from Sri Lanka’s IO matrix on the labor share of value added: where _CEMPs_ is total employee compensation in sector _s_ , _V As_ is total value added (at factor cost prices) in sector _s_ , and _s_ ( _k_ ) is the sector to which crop _k_ belongs. The land coefficient _γk_<sup>_l_is then</sup> computed as: _γk_<sup>_l_= 1</sup><sup>_−γ_</sup> _k_<sup>_f−γ_</sup> _k_<sup>_n_.</sup>

# **VI.A.4 Land Distribution Parameters**

The model’s parameters that govern land distributions ( _{μi_ , _σLi_<sup>2</sup><sup>_}i_) are estimated by leveraging the</sup> properties of the log-normal. We use 2016 HIES data to estimate _σ_ ˆ _Li_ as the (weighted) standard

> 63 _<u>pRoW,k</u>_ As ratios _pColombo,k_<sup>and</sup><sup>_<u>pColombo</u>_</sup> _pRoW,k_<sup>_<u>,k</u>_</sup> are each other’s reciprocals, only one of them can be larger than unity.

> 64Fertilizer use _Mk_<sup>_f,LKA_</sup> is computed at post-subsidy fertilizer prices and includes the three main types of fertilizer used: urea, muriate of potash (MOP), and triple superphosphate (TSP).
27 deviation of the logarithm of landholdings across farmers in district _i_ , and _μ_ ˆ _i_ as: _μ_ ˆ _i_ = ln( _Li/Ni_<sup>_F_)</sup><sup>_−_</sup> ˆ _σLi_<sup>2</sup><sup>_/_2, where</sup><sup>_Li_is total arable land (in ha) and</sup><sup>_N F_</sup> _i_<sup>the number of farmers in district</sup><sup>_i_.65</sup>

## **VI.B Step 2: Inversion to Recover Unobservables**

Equipped with estimates for the model’s parameters, we proceed to recover the remaining unobserved variables needed to fully characterize the 2019 baseline economy. We use the process commonly known as model inversion, which can be informally described as plugging observed variables into the model’s equilibrium system of equations and then solving the system to back out unobserved variables.<sup>66</sup> More formally:

**Definition 2 (Inversion)** _Given the model’s parameters, observed exogenous variables (_ **_N_**<sup>_m_</sup> _,_ **_N_**<sup>_F_</sup> _,_ **_L_** _,_ **_τ_** _,_ **_s_** _), and observed endogenous variables (_ **_w_** _,_ **_Q_** _,_ **_p_**<sup>**_A_**</sup> _,_ **_p_**<sup>**_f_**</sup> _), an_ **_inversion_** _is a set of unobserved exogenous variables (_ **_T_** _,_ **_b_** _,_ **_N_**<sup>_e_</sup> _,_ **_F_** _) and unobserved endogenous variables (t,_ **_p_**<sup>_−_</sup> _,_ **_P_** _,_ **_R_** _,_ **_E_** _,_ **_X_** _,_ **_β_** _) such that the resulting set of endogenous variables is an equilibrium of the economy with the resulting set of exogenous variables and with no QRs._

Intuitively, the inversion process picks values for unobserved variables to rationalize the data. For example, consider equation (6), which expresses equilibrium agricultural production ( _Qik_ ) as a function of productivity ( _Tik_<sup>_A_), prices, and land mass. Suppose that, at a given moment, the observed</sup> _Qik_ is “too high” in the sense that the equation’s left-hand side is larger than its right-hand side. The inversion process will then increase productivity _Tik_<sup>_A_enough to balance the equation.</sup> Appendix E provides details on the inversion procedure. We use data from 2019, which we choose as our baseline year because it precedes the 2021 fertilizer ban and other unusual events, such as the Covid-19 pandemic, and also due to household data availability.<sup>67</sup>

# **VII Counterfactuals**

In this section, we use the estimated model to investigate the GE effects of Sri Lanka’s fertilizer import ban (and of other potential alternative policies). Through counterfactual exercises, we demonstrate how government policies like import restrictions limit fertilizer access and how fertilizer subsidies in turn mediate the distributional impacts of such limitations. The counterfactuals

> 65Landholdings are defined as the total amount of land owned by a household (excluding land with housing built on top) and are measured in ha. The standard deviation is computed using only households with positive landholdings. We use 2016 HIES data because landholding data was not available in the more recent 2019 HIES. See Appendix C.C for more details on the estimation of the land distribution parameters.

> 66Alternatively, inversion consists of recovering unobserved from observed variables using the model’s structure.

> 67We include in the analysis the eight crops ( _K_ = 8) for which there is data on fertilizer intensity and district-level producer prices, namely: cinnamon, cloves, groundnut, maize, onions, potatoes, rice, and tea.
28 also highlight the importance of realistic model features such as non-homothetic preferences in shaping welfare outcomes.

In each counterfactual, we start from our estimated baseline economy and then compute a counterfactual equilibrium in which the government imposes QRs to imports (represented by a maximum allowed amount _f_<sup> ̄</sup> of imported fertilizer) while all other exogenous variables ( **_F_** , **_N_** , **_L_** , **_T_** , **_τ_** , **_b_** , **_s_** ) and parameters ( _η_ , _ν_ , _φ_ , **_σ_** , **_γ_** ) are kept at their original levels. We then compare the values of the endogenous variables in the counterfactual equilibrium to their original values, with the difference being interpreted as the causal effect of the QR in general equilibrium. Since the bulk of the fertilizer used by Sri Lanka is initially imported, the effects of a full ban can also be interpreted as the economy-wide cost of losing access to this critical intermediate input.

# **VII.A Setting Counterfactual Parameters**

Three practical considerations arise when implementing a counterfactual. First, one price must be normalized, as the equilibrium system is homogeneous of degree zero in the set of prices. We set the average wage in the RoW ( _wRoW_ ) to its actual value in the pre-ban period.<sup>68</sup> Second, we must choose a specific value for parameter _f_<sup> ̄</sup> , the amount of fertilizer imports allowed by the government under the QR regime. In our main counterfactual, we focus on a full ban of fertilizer imports, setting _f_<sup> ̄</sup> to zero, which is consistent with both Sri Lanka’s official ban policy and our reduced-form estimated ban effects in Section IV.A.

Third, we need a welfare metric to express the ban’s welfare impacts. While it is possible to compute changes in utility between the baseline and the counterfactual equilibrium using equation (12), it is difficult to interpret the meaning of such metrics.<sup>69</sup> We instead use Equivalent Variation (EV) metrics, defined as the hypothetical change in income that would replicate the welfare effects of the ban under the set of prices of the baseline equilibrium. For each district, we compute welfare effects for multiple types of agents: mobile workers, estate workers, and three types of farmer (median, average, and representative), as well as a cross-type average welfare effect that weights each type by its share of the district’s population.<sup>70</sup> Appendix F provides detailed definitions of EVs and agent types.

> 68We use the world’s income per capita in 2019 of 11,330.5 USD, equivalent to approximately 4.08 million LKR (using the 2022 exchange rate). For convenience of exposition, all results are displayed in USD.

> 69The interpretation of utility as an “aggregated quantity”, which is often used for CES preferences, is not valid for our non-homothetic utility function. Moreover, it is not even guaranteed that our indirect utility is positive in either equilibrium. Therefore, a decrease in utility could, in principle, be larger than 100%, among other issues. 70Workers of a given district are assumed to be identical, so the welfare effect of the ban is the same for all workers. The median (average) farmer of each district is defined as a farmer whose landholding size is equal to the median (average) in that district. The representative farmer of a district is the farmer whose utility is equal to _Vi_<sup>_F_, the district’s</sup> average farmer utility.
29

# **VII.B Baseline Results: The Effect of the Fertilizer Import Ban**

Table IV presents the model-generated impacts of the fertilizer import ban on outcomes measured at the national level. The primary effect of the ban is the full elimination of fertilizer imports, with a resulting increase of 6.41 USD/kg (or 2,068%) in gross fertilizer prices in Sri Lanka between the baseline and the counterfactual equilibrium. This leads to a massive decrease of 4 billion kg (or 96.5%) in fertilizer use in Sri Lankan agriculture. The ensuing decline in the government’s expenses with fertilizer subsidies allows the tax rate to be cut by 2.4 percentage points (or 27%).

Lack of fertilizer causes declines in Sri Lankan crop yields, which ultimately result in a reduction in downstream agricultural exports to the tune of 596 million USD. From a trade balance perspective, these export losses represent a 48% offset of the 1.25 billion USD reduction in fertilizer imports, indicating that the ban’s implicit goal of saving foreign exchange may have been severely limited by the large decline in crop exports. This finding would have been missed by a naive inspection of fertilizer import values that failed to account for such downstream effects. Furthermore, as will be shown in Section VII.D, this offset factor would be even higher, and possibly even higher than 100%, in the absence of Sri Lanka’s large fertilizer subsidies.<sup>71</sup> To better understand the ban’s effects on agriculture, Table V shows crop-by-crop results. Columns (2) and (3) show that, due to the ban, yields fell by 12 to 54%, with considerable heterogeneity across crops. Columns (5) and (6) show that crop exports fell across the board but also with substantial variation across crops. The most fertilizer-intensive crop, maize, saw yields fall 53.7% and exports 36.1%. Less fertilizer-intensive crops like cinnamon saw decreases of only 12.2% in yields and 7.3% in exports. Rice yields decline by 37.9%, which is comparable to the 31.6% drop observed in the 2022 data relative to the historical average (see Section IV.B). Further illustration of the ban’s effects on agriculture is provided by Figure V, which shows a strong negative correlation (-0.986) between crops’ fertilizer intensity coefficients _γk_<sup>_f_and the ban’s effects on</sup> export value. The three most fertilizer-intensive crops (rice, potatoes, and maize) suffer the largest percentage losses in exports.

A crucial benefit of using a quantitative GE model is the ability to provide estimates of the ban’s welfare effects. Column (1) of Table VI displays cross-district average welfare effects for mobile workers, estate workers, farmers, and a (weighted) average of these three agent types.<sup>72</sup> The overall average welfare loss is equivalent to a 7.33% decrease in income.<sup>73</sup> However, there

> 71The intuition for this finding is that subsidies drive farmers to above-optimal fertilizer use. In the absence of subsidies, the cost and marginal revenue product of fertilizer are more closely aligned, so a marginal decrease in fertilizer use leads to reductions of roughly similar magnitude in fertilizer imports and agricultural exports.

> 72Appendix Table A8 displays the full set of welfare changes for all agent types and districts.

> 73Our average welfare loss metric puts zero weight on middlemen (since we assume their population has measure zero), as explained in Appendix F. However, our main results are robust to relaxing this assumption. For example, assuming 1 middleman per Sri Lankan district, the overall average welfare loss due to the ban is 7.32%. Assuming instead 10 middlemen per district, the corresponding loss is 7.18%. Using our preferred estimate of the middleman
30 is much heterogeneity around that average: while welfare effects are generally negative, their sign and magnitude vary considerably by agent type and geography. Farmers and estate workers are harmed disproportionately because they are attached to the agricultural sector, in contrast to mobile workers, who can switch employment to the manufacturing sector even if they initially work in agriculture.<sup>74</sup> This leads to a composition effect in which average welfare decreases more in regions with a relatively high fraction of farmers, shown in Figure VIa. For example, in districts where farmers make up less than 20% of the population, the cross-type average welfare loss is equivalent to an income decline of less than 2%. In contrast, where farmers make up more than half of the population the corresponding damages are equivalent to income losses of at least 10%.

Spatial heterogeneity in welfare impacts is further illustrated by Figure VII. For farmers (Figure VIIa), this heterogeneity is explained by geographic differences in the relative importance of specific agricultural crops. Figures VIb and VIc show that both farmer welfare losses and cross-type average welfare losses were worse in districts whose agricultural sector specializes in relatively fertilizer-intensive crops.<sup>75</sup> For example, in districts with a 6% fertilizer cost share, the harm to the representative farmer was roughly equivalent to a 10% income loss, whereas the corresponding harm in districts with a 11%-12% fertilizer cost share was as high as 23%.

For mobile workers, spatial heterogeneity in welfare losses (Figure VIIb) is explained by a different type of geographic variation, namely in the size of the agricultural sector.<sup>76</sup> Figure VId shows that the welfare of mobile workers decreased by more in districts with a high agricultural share of employment. Thus, although mobile workers suffered less than farmers everywhere, those living in heavily agricultural areas still faced severe losses equivalent to as much as a 12% income reduction, as those areas did not have a vibrant manufacturing sector that could serve as a buffer and absorb the excess labor exiting from the adversely affected agricultural sector.

One potential concern about our counterfactual exercise is that it assumes perfect mobility of workers between manufacturing and agriculture (and across agricultural crops). In Appendix H, we extend the model to account for potential frictions to intersectoral labor reallocation. This extended model predicts similar welfare effects of the ban regardless of the severity of frictions, suggesting that frictionless intersectoral reallocation is not a first-order mechanism driving our main results.

population, namely 25.16 middlemen per district (see footnote 123), the overall average welfare loss is 6.94%.

> 74In some districts, mobile workers even have a gain in welfare (see Appendix Table A8) because their loss from lower agricultural productivity is so small that it is more than offset by their gain from reduced tax rates (see Table IV). 75To measure district-level fertilizer intensity, we compute fertilizer’s cost share across the whole agricultural sector of each district _i_ at baseline as: (<sup>�</sup> _k_<sup>_γ_</sup> _k_<sup>_fpikQik_)</sup><sup>_/_(�</sup> _k_<sup>_pikQik_).</sup> 76The fact that spatial heterogeneity in farmer and worker welfare effects are explained by different factors is also suggested by the substantial differences between Figures VIIa and VIIb in the spatial pattern of welfare changes.
31

# **VII.C Yield Effects: General** **_versus_ Partial Equilibrium**

The literature (reviewed in Section I) that uses small-scale experiments to quantify the value of fertilizer has an important limitation: it does not capture the potential GE effects that would emerge if these interventions were scaled up. To examine the importance of such GE effects, we leverage the structure of our model to separate the influence of partial equilibrium (PE) and general equilibrium (GE) considerations in determining the impact of Sri Lanka’s fertilizer import ban on agricultural yields.

We start from the optimization problem faced by an individual plot _ω_ producing crop _k_ in region _i_ , as described in Section V.B.1. Equations (2) and (3) show that price-taking producers solve their profit maximization and cost minimization problems taking as given the land rent ( _rik_ ( _ω_ )) and the prices of labor (i.e. wage _wi_<sup>_k_),fertilizer(</sup><sup>_pf,k_</sup> _i_<sup>),andcropoutput(</sup><sup>_pik_),whichareconsidered</sup> exogenous from their perspective. Using the optimality conditions of these optimization problems, it is therefore possible to show how optimal crop yields, fertilizer intensity, and labor inputs react to changes in these prices. Denoting the “optimized” version of each variable with a star and defining variable _Yik_ ( _ω_ ) _≡_ ( _lik_<sup>_∗_(</sup><sup>_ω_))</sup><sup>_−_1as the yield in plot</sup><sup>_ω_,it can be shown that the change in yields that</sup> ensues from any set of price changes is given by:<sup>77</sup> Similarly, defining fertilizer intensity in plot _ω_ as _FIik_ ( _ω_ ) _≡ fik_<sup>_∗_(</sup><sup>_ω_)</sup><sup>_/l_</sup> _ik_<sup>_∗_(</sup><sup>_ω_),theresponseof</sup> (optimized) fertilizer intensity to changes in prices is given by: The small-scale experiments in the literature usually induce intensive fertilizer use by lowering the fertilizer prices faced by producers without simultaneously changing other input or output prices.<sup>78</sup> Equations (38) and (39) predict that such an intervention would change (the log of) yields by _−_ ( _γk_<sup>_f/γ_</sup> _k_<sup>_l_)</sup><sup>_d_ln(</sup><sup>_p_</sup> _i_<sup>_f,k_)and(thelogof)fertilizerintensityby</sup><sup>_−_(1 + (</sup><sup>_γ_</sup> _k_<sup>_f/γ_</sup> _k_<sup>_l_))</sup><sup>_d_ln(</sup><sup>_p_</sup> _i_<sup>_f,k_).Dividing</sup> the former expression by the latter, we obtain the implied PE elasticity of crop- _k_ yields with respect to fertilizer intensity:

> 77Land rent _rik_ ( _ω_ ) is absent from equations (38) and (39) because it is a function of the other three prices, as per equation (3). When the other prices change, the land rent reacts endogenously to keep agricultural profits equal to zero. The changes in crop yields and fertilizer intensity shown in equations (38) and (39) are already accounting for this implicit land rent adjustment.

> 78Moreover, these interventions are usually too small to affect these other prices through GE effects.
32 which we denote “PE” elasticity to emphasize that the variation in yields and fertilizer intensity is driven by price changes in the fertilizer market alone, with no simultaneous price changes in the labor or output markets. Equation (40) gives us the PE elasticity of each crop _k_ , which we display in Column (8) of Table V.<sup>79</sup> Reassuringly, the PE elasticities for maize (0.28) and rice (0.21) are very close to the corresponding literature estimates, namely 0.27 for maize (Carter et al., 2021) and 0.21 for rice (Beaman et al., 2013).<sup>80</sup> However, this PE analysis provides an incomplete picture of the ban’s effects on crop yields or fertilizer intensity. Ban-induced changes in the fertilizer market spill over to other markets, as expensive fertilizer reduces both the demand for agricultural labor and the supply of crops. As a result, wages decrease and crop prices increase, affecting yields and fertilizer intensity via equations (38) and (39), which can thus be said to capture the full GE effects of the ban. Combining these two equations, we obtain the implied GE elasticity of crop- _k_ yields to fertilizer intensity in region _i_ as follows:<sup>81</sup> This GE elasticity can then be computed for each district-crop pair using our Cobb-Douglas coefficients (see Table III) and the district-specific price changes ( _d_ ln( _pik_ ), _d_ ln( _p_<sup>_f,k_</sup> _i_<sup>),</sup><sup>_d_ln(</sup><sup>_w_</sup> _i_<sup>_k_))</sup> generated by the counterfactual exercise of Sections VII.A and VII.B.<sup>82</sup> The resulting GE elasticities for each crop (averaged across districts) are displayed in Column (7) of Table V. Comparing Columns (7) and (8) it is clear that GE elasticities are considerably smaller than PE elasticities for all crops. This is mostly due to the influence of crop price increases, which partially counteract the negative effects of the fertilizer price hike on yields and fertilizer use (relatively more strongly for

> 79The elasticity _εP Eik_<sup>(</sup><sup>_ω_)doesnotvaryacrossplotsorregions.</sup> It depends only on Cobb-Douglas coefficients ( _{γk_<sup>_f, γ_</sup> _k_<sup>_l}_) and can thus be computed from the information in Table III.</sup> 80In Figure 2 of Carter et al. (2021), Panel A shows that the treatment increased fertilizer use by 78 log points in the treatment group, while Panel C shows that maize yields increased by 21 log points. Dividing the latter by the former, we obtain an elasticity of approximately 0.27. In Beaman et al. (2013), Column (2) of Table 3 shows that their (full) treatment increased fertilizer quantities by 32.91 kg, which corresponds to an increase of 250% (or 125.2 log points) relative to the control group mean of 13.17 kg, whereas Column (1) of Table 4 shows that the value of output increase by 11,045.78 FCFA, corresponding to an increase of 30.75% (or 26.8 log points) relative to the control group mean of 35,919.50 FCFA. Dividing 26.8 by 125.3, we obtain an elasticity of 0.21.

> 81 The GE elasticity formula is at the region-crop level, not the plot ( _ω_ ) level because equations (38) and (39) hold both at plot and region-crop levels, with the latter version then being used to derive the GE formula.

82 _GE_ Alternatively, the GE elasticity _εik_ can also be computed by dividing the change in (the log of) production by the change in (the log of) fertilizer use, i.e. _ε_<sup>_GE_</sup> _ik_ = ∆ln( _Qik_ ) _/_ ∆ln( _fik_ ). The two approaches yield identical results.
33

## yields).

An alternative approach to assessing the importance of GE effects is to use equation (38) for an “accounting” exercise, decomposing the changes in yields observed in our counterfactual exercise into the partial contributions of (the changes in) each of the three prices. The contribution of fertilizer price increases is displayed in Column (4) of Table V, showing that maize and rice yields would have declined by 69.5% and 55.3% (respectively) if there had been no changes in wages and output prices to counteract the change in fertilizer prices. In other words, GE adjustments in other markets undo 35% and 39% (on average) of the falls in maize and rice yields (respectively) that are brought about by PE price adjustments in the fertilizer market.<sup>83</sup> This suggests that the results of small-scale experimental studies would likely have led to an overestimation of the adverse yield effects of Sri Lanka’s fertilizer import ban.

# **VII.D Influence of Non-Homothetic Preferences and Subsidies**

Our model incorporates non-homothetic preferences and fertilizer subsidies, both of which are notable features of Sri Lanka’s agricultural economy.<sup>84</sup> In this section, we show that neglecting to include these important features in the model would substantially alter its predictions regarding the welfare effects of the fertilizer import ban, thus leading to biased estimates.

To show the importance of non-homothetic preferences, we perform an exercise in two steps. First, starting from the (non-homothetic) baseline equilibrium estimated in Section VI, we change the key PIGL preference parameters to _η_ = 1 and _ν_ = 0 (under which PIGL collapses to homothetic, Cobb-Douglas preferences) and compute a “homothetic baseline equilibrium” by applying Definition 3 with no QRs. Second, we apply Definition 3 again to recompute the homothetic equilibrium but now with QRs ( _f_<sup> ̄</sup> = 0), as in Section VII.<sup>85</sup> Therefore, this exercise amounts to an investigation of the predictions our model would make if it did not feature non-homothetic preferences.

Contrasting Columns (1) and (2) of Table VI shows the predicted effect of the ban on the welfare of mobile workers is less negative in a homothetic economy than in the non-homothetic economy. This finding is explained by the fact that agriculture comprises 24.9% of employment (on average) in the non-homothetic baseline equilibrium but only 15% in the homothetic baseline equilibrium.<sup>86</sup>

> 83The formula in equation (38) implies that the increase in fertilizer prices reduced maize and rice yields by 119 and 81 log points, respectively. For each district, we compute the difference between each of these two numbers and the corresponding actual yield decrease (measured in log points) and divide the result by 119 or 81, obtaining the percentage of the fertilizer price effect that is undone by the wage and output price effects. Averaging these percentages across districts, we obtain 34.8% for maize and 39.5% for rice.

> 84 For direct evidence of non-homothetic preferences, see Appendix C.B.

> 85 While this exercise changes the value of the two PIGL parameters _ν_ and _η_ , the remaining parameters and unobservable variables are kept at their original values estimated in Section VI.

> 86The ILO estimates that Sri Lanka had 25% of its total employment in agriculture in 2019. Thus, the non-
34 The baseline agricultural (resp. manufacturing) sector is smaller (resp. larger) in the homothetic case. Since a large manufacturing sector acts as buffer that attenuates the ban’s negative effects on mobile workers (as explained in Section VII.B), mobile workers suffer less in the homothetic case.

We then run a similar exercise to demonstrate the importance of fertilizer subsidies. Starting from the baseline equilibrium estimated in Section VI, we set subsidy rates ( _{sk}_<sup>_K_</sup> _k_ =1<sup>) to zero, com-</sup> pute the resulting baseline equilibrium, then impose QRs and recompute this equilibrium. Column (3) of Table VI shows the absence of subsidies intensifies the welfare losses of mobile workers while ameliorating those of tea estate workers and the representative farmer. The intuition for this finding lies in the fact that subsidies are financed through a flat tax on the income of all agents. In practice, such scheme corresponds to a net income transfer from mobile workers to farmers and estate workers. By drastically reducing fertilizer use in the country, the ban also reduces the total amount of subsidies and, consequently, the scale of the transfer scheme, thus helping mobile workers and hurting farmers and tea workers. In contrast, in a world without subsidies this transfer scheme does not exist in the first place, so the “subsidy scale-down” channel just described is absent from the ban’s welfare effects. Hence the worse (resp. milder) welfare losses of mobile workers (resp. farmers and estate workers) in the case without subsidies.<sup>87</sup> Interestingly, in this no-subsidy exercise, the ban decreases fertilizer imports by 197 million USD and total agricultural exports by 278 million USD. That is, foreign exchange “savings” through lower imports are _more than completely offset_ by a corresponding reduction in agricultural exports, in contrast to a mere 48% “offset factor” in our main estimates (see Section VII.B).<sup>88</sup> In the absence of fertilizer subsidies, there is a closer correspondence between the import price of fertilizer and its marginal revenue product. As a result, the reduction in fertilizer use induced by the ban decreases agricultural export revenues and fertilizer imports by roughly similar amounts.

# **VII.E Influence of Modeling Trade Policy: Iceberg Trade Costs versus Quantitative Restriction**

In our model, trade policy is represented by QRs. This differs from much of the NTM literature, which models NTMs as an increase in multiplicative “iceberg” trade costs.<sup>89</sup> These modeling choices are often not innocuous: while QRs raise prices and create rents that can be captured by certain domestic agents, the price increases resulting from iceberg trade costs are typically modeled as losses, with no one benefiting from them. Therefore, using iceberg trade costs to model what is

> homothetic model matches the ILO data much more closely than the homothetic model.

> 87This also implies a smaller gap in welfare losses between workers and farmers relative to the case with subsidies (Column 1 of Table VI), leading us to underestimate how unequal the incidence of the ban is across occupations.

> 88The 48% offset factor is computed by comparing the decrease in agricultural exports (596 million USD) to the decrease in fertilizer imports (1.253 billion USD) in our main estimates displayed in Table IV.

> 89One exception is Atkin et al. (2024), who explicitly model a discretionary import licensing system.
35 really a QR tends to lead to overestimation of the welfare losses induced by the policy.

To illustrate this point, we perform two additional counterfactual exercises in which we use different means to reduce the quantity of imported fertilizer by 50%. In the first exercise, this is achieved via QRs, while in the second exercise it is done by increasing the iceberg trade cost of transporting fertilizer from the RoW to Sri Lanka.<sup>90</sup> Results are displayed in Columns (4) and (5) of Table VI. As expected, for all types of agents, welfare losses are less severe under QRs than under iceberg cost increases, with the average welfare effect on mobile workers even switching from negative to positive in the former case.<sup>91</sup>

# **VII.F Model Validation: Evidence from Night Lights**

Our model-driven counterfactual exercise replicates the stylized facts documented in Section IV, with large decreases in fertilizer imports, crop yields, and agricultural exports. To further validate our model, we now show that the decreases in real regional income (and, thus, in regional welfare) that are implied by night light intensity data also align with the predictions of our counterfactual.

A well-established literature (Henderson et al., 2012) has confirmed the validity of night lights as a reliable way to indirectly assess the spatial distribution of real income per capita when direct income metrics with the desired coverage or frequency are unavailable. The elasticity of per capita income to the average night light intensity of a geographical unit is often estimated to be around 0.3. We combine this elasticity with the observed reduction in average night light intensity in each Sri Lankan district between April 2021 (i.e. the last month before the ban was implemented) and January 2022 to estimate districts’ income losses in that period.<sup>92</sup> Estimated income losses are displayed in Figure VIIIa. The decreases in district-level real income predicted by the counterfactual exercise are displayed in Figure VIIIb.<sup>93</sup> A visual comparison of the two figures suggests that the model performs well in terms of replicating the spatial pattern of real income losses during the post-ban period. For example, both maps show that the north and east of Sri Lanka were particularly severely affected relative to the southwest. Moreover, Figure VIIIc shows that these northern and eastern regions are also the ones most economically dependent on fertilizer, thus explaining why they were so affected by the ban.<sup>94</sup>

> 90Note that, regardless of the trade policy instrument, there are no rents to be captured in the extreme cases (such as Sri Lanka’s ban) in which imports are driven down to zero. That is why we perform the comparison exercise between the two instruments using a less restrictive (50%) reduction in the quantity of imported fertilizer.

> 91The mechanism by which welfare losses are attenuated in the QR case is related to the tax rate. In both cases, reduction in fertilizer imports leads to a reduction in fertilizer use in Sri Lanka, which scales down the fertilizer subsidy program, lowering the tax rate that is needed to fund such program. However, the tax rate drops by a greater magnitude in the QR case (0.77 percentage points) than in the iceberg cost case (0.4 percentage points).

> 92For details on our night lights data, see Appendix A.I.

> 93More precisely, Figure VIIIb displays the average EV across agent types (weighted by types’ population shares) in each district, as predicted by our model-generated counterfactual exercise. For details, see Appendix F.

> 94To measure the economic importance of fertilizer for a district, we use the district’s baseline ratio of fertilizer
36 To more formally assess the model’s ability to explain the observed post-ban changes in night lights, we run a dynamic event study analysis at the district-month level, assigning districts to the treatment or control group depending on whether they were above or below the median of fertilizer importance at baseline (see Figure VIIIc). The outcome variable is (the log of) average night light intensity and the treatment period is defined as starting in May 2021 (i.e. the month when the ban was implemented). The results, displayed in Appendix Figure A15, show that night lights decreased by 26.7 log points in treated (i.e. relatively fertilizer-dependent) districts relative to control (i.e. less fertilizer-dependent) districts eight months into the ban, corresponding to an income loss of 7.7%. Using the same assignment of districts into treated and control groups, model-predicted real income losses (Figure VIIIb) are 6.3 percentage points worse in treated districts than in control districts, on average. Therefore, by comparing the model’s predictions to the night lights evidence, we conclude that the model can explain 82% of the differential real income loss of fertilizer-dependent districts observed in the data during the relevant time period.

Finally, we take advantage of our night lights data to further confirm that our main results are not driven by the potentially confounding influence of the Covid-19 pandemic (see Section IV.A). Figure VIIId shows that the spatial pattern of income losses (proxied by night lights) in the period following the pandemic’s arrival in March 2020 was very different from the pattern of losses in the post-ban period (Figure VIIIa), indicating that potentially lingering effects of the pandemic cannot explain the negative economic effects that we attribute to the fertilizer ban.

# **VIII Conclusion**

Trade policy and geopolitical events increasingly affect the ability of many countries to access critical intermediate inputs. This paper quantifies the costs of a nationwide fertilizer shortage and explores its interaction with domestic agricultural policies, such as subsidies. It does so by leveraging an unprecedented natural experiment, an abrupt and unexpected import ban that disrupted the supply of chemical fertilizers in Sri Lanka. Relying on novel high-frequency firm-level trade data, detailed agricultural ground production data, crop yield estimates from state-of-the-art remote sensing techniques, and cutting-edge event study designs, we show that the fertilizer import ban led to dramatic declines in fertilizer imports, agricultural production, and exports of fertilizer-intensive agricultural products.

To better understand the mechanisms and welfare implications of the ban’s effects, we propose and estimate a spatial general equilibrium model of agriculture and trade with quantitative restricexpenditure to aggregate income, as predicted by our model. This metric captures both the relative importance of the agricultural sector in the district’s economy and the agricultural sector’s degree of specialization in fertilizer-intensive crops.
37 tions on imports. The model implies average welfare losses due to the lack of fertilizer equivalent to a 7.33% income decline, with stronger incidence on farmers and estate workers (whose income is tied to agriculture) relative to mobile workers. These welfare effects also vary across Sri Lankan regions, depending on the region’s propensity to grow fertilizer-intensive crops. The ban lowers crop yields substantially, leading to agricultural export losses that offset around half of the foreign exchange savings from reduced fertilizer imports. However, the elasticities of yields to fertilizer use estimated in general equilibrium are much smaller than the corresponding partial equilibrium estimates–with the latter closely matching the findings from the experimental literature. This difference reflects the mitigating effect of endogenous adjustments in crop prices and wages. Thus, the abrupt and nationwide nature of the ban offers a unique setting to estimate the macroeconomic cost of fertilizer shortages in a manner that would not be possible using localized randomized control trials.

The model has wide applicability since it reflects key realistic characteristics of many developing countries, such as high fertilizer subsidies, land inequality, and non-homothetic preferences. These features strongly influence the aggregate and distributional impacts of trade policy. For example, fertilizer subsidies–a very common domestic agricultural policy–interact with trade policy: an import ban nearly eliminates fertilizer use, scaling down the income transfers from non-farming to farming sectors that are engineered through subsidies, and thus attenuating the relative welfare losses of mobile workers. Non-homothetic preferences, by determining the share of income spent on food and thus the size of the agricultural and manufacturing sectors, determine the outside option that workers face when considering whether to move away from the ban-affected sector, thus affecting welfare. While a full ban on fertilizer imports may be a rare and extreme measure, this natural experiment helps identify critical parameters that inform the general equilibrium costs to agriculture of a lack of fertilizer, an estimate that helps inform fertilizer-related policy (such as fertilizer subsidies). Embedding these parameters in a flexible model that is well-suited to study varying degrees of fertilizer availability provides a useful framework for assessing the effects of trade-induced fertilizer shortages across a wide range of countries and scenarios.
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-  ̈Ozdo ̆gan, M., S. Wang, D. Ghose, E. Fraga, A. Fernandes, and G. Varela (2025). Field-scale rice area and yield mapping in sri lanka with optical remote sensing and limited training data. _Remote Sensing 17_ (17: 3065).
42

# **Tables**

## Table I: Data Sources and Variables

|**Topics**|**Variables**|**Time Period**|**Source**|
|---|---|---|---|
|**Trade Policy**|**[1]** List of Harmonized System 8-digit (HS8) codes of products<br>subject to import bans,and bans’ start and end dates|March<br>2020-<br>October 2022|Sri Lanka’s Extraordinary Gazettes on<br>Imports and Exports,digitized byhand|
|**Trade Flows**|**[2]**Import values and weights at HS8 product-month-year level|January<br>2017-<br>October 2022|S&P Global Market Intelligence’s Pan-<br>jiva data platform|
||**[3]**Export values at exporting frm-HS8 product-quarter-year level|January<br>2017-<br>October 2022|S&P Global Market Intelligence’s Pan-<br>jiva dataplatform|
||**[4]** Rice production, cultivated area, and yields at district-season<br>level<br>**[5]**Production, cultivated area, and yields by crop at district-season<br>level (maize, groundnuts, potatoes, onions, cinnamon, cloves, tea)|Maha 2013 to<br>Yala 2022<br>Maha 2020 to<br>Yala 2022|Sri Lanka’s Department of Census and<br>Statistics (DCS)<br>DCS and Sri Lanka Tea Board’s annual<br>reports|
|**Agricultural**<br>**production,**|**[6]**Production by crop at national level|2022|Central Bank of Sri Lanka|
|**cultivated**<br>**area, yields**|**[7]**Remote sensing estimates of rice yields and cultivated areas at<br>pixel level|2000-2022|Landstat and Sentinel-2 satellite, com-<br>puted by authors using Ozdogan et al.<br>(2024) methodology|
||**[8]**Remote sensing estimates of tea yields at pixel level|2014-2022|Planet Satellite Data, computed by au-<br>thors|
||**[9]**Remote sensing estimates of tea map at pixel level|2021|Planet Satellite Data, computed by au-<br>thors|
||**[10]**Producer prices at crop-district level for rice, potatoes, cinna-<br>mon, cloves, onions, groundnuts, maize|2019|DCS|
|**Agricultural**<br>**prices**|<br>**[11]**Producer prices at national level for tea|2019|Food and Agriculture Organization of<br>the United Nations (FAO)|
||**[12]**National Consumer Price Index<br>**[13]** Crop prices at national level for cinnamon, cloves, maize,<br>onions, potatoes,rice,tea|2021-2022<br>2022|DCS<br>Central Bank of Sri Lanka|
||**[14]**Fertilizer requirements by crop|2022|Sri Lanka’s National Fertilizer Secre-<br>tariat (NFS)|
||**[15]**Fertilizer prices|2022|NFS|
|**Fertilizer use**|**[16]**Cultivated area at national level by crop|2022|NFS|
|**and subsidies**|**[17]**Use of organic fertilizer (manure) at national level<br>**[18]**Use of chemical fertilizers at national level<br>**[19]**Fertilizer subsidy rates at crop level|2001-2021<br>2002-2021<br>2013-2022|FAO<br>FAO<br>Department of Agriculture’s Socio Eco-<br>nomics & PlanningCentre|
|**Potential agri-**<br>**cultural yields**|**[20]**Potential attainable yields at crop-district level (all crops rain-<br>fed except rice, which is irrigated; climate conditions of 1981-<br>2010)||FAO-GAEZ|
|**Labor share in**<br>**value added**|**[21]**Employee compensation and value added by agricultural sec-<br>tor|2000|Sri Lanka’s IO table of the Institute of<br>Policy Studies (Amarasinghe and Ban-<br>dara,2005)|
||**[22]** Average wages at district level and total number of mobile<br>workers, estate workers, and farmers at district level|2016, 2019|Sri Lanka’s Household Income and Ex-<br>penditure Survey (HIES), from DCS|
|**Wages,**<br>**land**<br>**ownership,**<br>**occupation,**<br>**household**<br>**characteristics**|**[23]** Household size (number of members), income, expenditure<br>patterns (food prices and quantities, fraction of income spent on<br>food), “income by chance or_ad hoc_gains” (including lottery and<br>disaster/relief payments)|2019|HIES|
||**[24]**Land ownershipand land distribution|2016|HIES|
|**Night Lights**|**[25]**Night light intensity at district-month level|January<br>2016-<br>December 2022|Visible and Infrared Imaging Suite (VI-<br>IRS) Day Night Band (DNB), from Col-<br>orado School of Mines|
43 Table II: Preference Parameters

|Parameter|Value|Standard<br>Error|Source|Description|
|---|---|---|---|---|
|_φ_|0.0105|.|From HIES data|Asymptotic agricultural share|
|_ν_|0.12|.|Eckert and Peters(2023)|PIGL parameter|
|_η_|0.656|0.129|Estimated on HIES data|Engel elasticity|
|_σM_|2.528|.|Feenstra et al (2018)|EoS across origins (manufacturing)|
|_σA_|1.714|0.153|Estimated on HIES data|EoS across crops|
|_σK_|2.377|.|Match crop price increase|EoS across origins(within crop)|

_Notes_ : for each preference parameter in the model, the table displays the value we impose for it, the standard error of its estimate (when applicable), the source from which it is taken or estimated, and a brief description of the parameter.
44 Table III: Other Parameters

||Cobb-Do<br>|uglas Coeffc|ients|International trade costs|
|---|---|---|---|---|
|Crop|Fertilizer(_γ_<sup>_f_</sup><br>_k_ <sup>)</sup>|Labor(_γ_<sup>_n_</sup><br>_k_ <sup>)</sup>|Land(_γ_<sup>_l_</sup><br>_k_<sup>)</sup>|_Bk_|
|Cinnamon|0.032|0.429|0.539|2.36|
|Cloves|0.043|0.424|0.533|2.36|
|Groundnuts|0.066|0.414|0.520|2.36|
|Maize|0.177|0.365|0.458|1.07|
|Onions|0.075|0.410|0.515|2.14|
|Potatoes|0.129|0.394|0.477|2.39|
|Rice|0.110|0.469|0.421|1.43|
|Tea|0.109|0.487|0.404|9.40|

_Notes_ : the table displays our estimates of the model parameters that govern agricultural production technology ( _{γk_<sup>_f, γ_</sup> _k_<sup>_n, γ_</sup> _k_<sup>_l}K_</sup> _k_ =1<sup>) and agricultural</sup> international trade costs ( _{Bk}_<sup>_K_</sup> _k_ =1<sup>).See Sections VI.A.2 and VI.A.3 for descriptions of our estimation methodologies.</sup>
45

# Table IV: Ban Effects (Country-Level)

|**Variable**|**% Effect**|**Effect**|**Description**|
|---|---|---|---|
|_fLKA_<br>|-96.5%|-4,043 MM kg|Fertilizer use (kg)|
|_M _<sup>_f_</sup><br>_q,LKA_<br>|-100%|-4,043 MM kg|Fertilizer imports (kg)|
|_M _<sup>_f_</sup><br>_LKA_<br>|-100%|-1,253 MM USD|Fertilizer imports (USD)|
|_p_<sup>_f_</sup><br>_LKA_<br>|+2,068%|+6.41|Fertilizer price pre-subsidy (USD/kg)|
|_p_<sup>_f,sub_</sup><br>_LKA_<br>|+2,072%|+1.36|(Average) fertilizer price post-subsidy (USD/kg)|
|_EXP _<sup>_A_</sup><br>_LKA_<br>|-22.6%|-596 MM USD|Agricultural exports (USD)|
|_NEXP _<sup>_A_</sup><br>_LKA_|-27.9%|-601 MM USD|Net agricultural exports (USD)|
|_t_|-27.3%|-2.4p.p.|Tax rate(percentagepoints)|

_Notes_ : The table shows absolute and relative (%) changes in several variables between the baseline equilibrium with no QRs and the counterfactual equilibrium with QRs. Fertilizer use ( _fLKA_ ), in MM kg, is the total fertilizer demand by Sri Lanka’s agricultural sector. Imported fertilizer quantity ( _Mq,LKA_<sup>_f_), in MM kg, is the total quantity of fertilizer that Sri Lanka buys from the RoW, while imported fertilizer value (</sup><sup>_M_</sup> _LKA_<sup>_f_), in MM USD,</sup> is the total revenue that foreign sellers obtain from such sales. The fertilizer price in Sri Lanka ( _p_<sup>_f_</sup> _LKA_<sup>), in USD/kg, is the price earned by fertilizer</sup> sellers. The (average) post-subsidy fertilizer price ( _p_<sup>_f,sub_</sup> _LKA_<sup>)atwhichfertilizercanbeboughtbySriLankanfarmersistheratiooffarmers’total</sup> fertilizer expenditures to their total fertilizer use. Gross agricultural exports ( _EXPLKA_<sup>_A_), in MM USD, are the total agricultural sales of Sri Lanka</sup> to the RoW, while net agricultural exports ( _NEXPLKA_<sup>_A_) are gross agricultural exports minus gross agricultural imports.The tax rate (</sup><sup>_t_) is a flat</sup> income tax levied by Sri Lanka’s government on all domestic agents.
46

# Table V: Ban Effects (Crop-Level)

||**Fertilizer**<br>**intensity** (_γ_<sup>_f_</sup><br>_k_<sup>)</sup>||∆**Produ**|**ction**|∆**Gross E**|**xports**|**Elastic**<br>**to fe**|**ity: yield**<br>**rtilizer**|
|---|---|---|---|---|---|---|---|---|
|||**in MM kg**|**in %**|**from**∆_p_<sup>_f_</sup> **(PE)**|**in MM USD**|**in %**|**GE**|**PE**|
|**Crop (**_k_**)**|(1)|(2)|(3)|(4)|(5)|(6)|(7)|(8)|
|Cinnamon|0.032|-2.8|-12.2%|-16.8%|-15.9|-7.3%|0.039|0.057|
|Clove|0.043|-1.1|-16.2%|-21.8%|-3.7|-9.8%|0.055|0.074|
|Groundnuts|0.066|-8.0|-21.9%|-32.1%|-4.7|-13.5%|0.079|0.112|
|Maize|0.177|-168.3|-53.7%|-69.5%|-30.8|-36.1%|0.220|0.279|
|Onions|0.075|-9.2|-26.8%|-35.9%|-4.6|-16.8%|0.091|0.126|
|Potatoes|0.129|-15.0|-42.9%|-56.3%|-7.2|-27.9%|0.165|0.212|
|Rice|0.110|-1,940|-37.9%|-55.3%|-505|-24.2%|0.145|0.207|
|Tea|0.109|-84.0|-30.1%|-56.5%|-24.4|-19.0%|0.109|0.213|

_Notes_ : For each crop, the table shows its fertilizer intensity and the change in Sri Lanka’s crop production and gross exports between the baseline equilibrium with no QRs and the counterfactual equilibrium with QRs. The fertilizer intensity of each crop _k_ is defined as the fertilizer coefficient _γk_<sup>_f_initsCobb-Douglasproductionfunction.Productionofcrop</sup><sup>_k_,inMMkg,iscomputedbyaddingdistrict-levelproductionacrossallSri</sup> Lankan districts (<sup>�</sup><sup>_I_</sup> _i_ =1<sup>_Qik_).Grossexportsofcrop</sup><sup>_k_,inMMUSD,arethetotalcrop-</sup><sup>_k_salesofSriLankatotheRoW,whichiscomputedas:</sup> � _Ii_ =1<sup>_X_</sup> _RoW_<sup>_Aβ_</sup> _RoW,k_<sup>_Aβ_</sup> _RoW,i,k_<sup>_A_.Column (4) shows the change in crop production that is due to fertilizer price adjustments alone,i.e.the “PE”</sup> change that would have happened if wages and crop prices had not also adjusted (see equation 38). Column (7) shows the GE elasticity of crop yields (in kg/ha) with respect to fertilizer use (in kg/ha), which is computed by first dividing the change in (the log of) production by the change in (the log of) fertilizer use for each district-crop pair, and then averaging the result across districts. Column (8) shows the PE elasticity of crop yields with respect to fertilizer use, computed via equation (40). See Section VII.C for more details on Columns (4), (7), and (8).
47

# Table VI: Ban Effects on Welfare, by agent type

|||**Equivale**|**nt Variation**|**(EV)**||
|---|---|---|---|---|---|
||Main<br>CF|Homothetic<br>preferences|No<br>subsidies|Halving<br>(QR)|Halving<br>(Iceberg)|
|**Agent type**|(1)|(2)|(3)|(4)|(5)|
|Mobile Worker|-0.67%|-0.46%|-1.52%|+0.13%|-0.25%|
|Estate Worker|-16.58%|-17.71%|-9.84%|-3.19%|-3.54%|
|Representative Farmer|-19.51%|-21.01%|-11.43%|-3.9%|-4.24%|
|Average across types|-7.33%|-7.84%|-5.04%|-1.30%|-1.66%|

_Notes_ : for each agent type, Columns (1)-(3) show the average % welfare change between the baseline equilibrium with no QRs and the counterfactual equilibrium with QRs. These (unweighted) averages are computed across all Sri Lankan districts. The representative farmer of a district _i_ is defined as a farmer whose utility is equal to the district’s average farmer utility ( _Vi_<sup>_F_).Welfare changes are defined as EVs: starting from the agent’s baseline</sup> (net-of-tax) income, the EV is the % change in (net-of-tax) income that would leave her with the same utility level as she has in the counterfactual equilibrium, keeping prices fixed at baseline levels. For each district, we also define an average welfare change across types, which is computed as the weighted average of type-specific welfare changes, with weights given by each type’s population share in that district. This district-specific average welfare change is then averaged across districts and displayed in the table’s last row. Column (1) refers to our main counterfactual exercise (see Section VII.A), while Columns (2) and (3) refer to alternative counterfactual exercises in which we assume (respectively) homothetic preferences and no fertilizer subsidies (see Section VII.D). Columns (4) and (5) show average % welfare changes in two counterfactual exercises in which the quantity of fertilizer imported into Sri Lanka is reduced by 50% either via QRs (Column 4) or via increases in iceberg trade costs (Column 5).
48

# **Figures**

## Figure I: Dynamic Ban Effects on Imports

<!-- Start of picture text --> −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12<br>Month relative to period when treatment first changes (t=0) Month relative to period when treatment first changes (t=0)<br>(a) Extensive Margin (b) Intensive Margin<br>.5 3<br>.4 2<br>.3 1<br>0<br>.2<br>−1<br>.1 −2<br>0 −3<br>−.1 −4<br>−.2 −5<br>−.3 −6<br>Effect on Pr(imports>0) −.4 Effect on log(imports) −7<br>−8<br>−.5 −9<br>−.6 −10<br>−.7 −11<br><!-- End of picture text --> _Notes_ : The figures show De Chaisemartin and d’Haultfoeuille (2022) estimates of the effects of import bans on the extensive and intensive margins of imports, relative to the last month before the ban takes effect, using an HS8 product-month level panel. The sample covers the January 2019September 2022 period (but only coefficients in January 2021-May 2022 are reported) and excludes non-fertilizer HS8 products whose imports were ever banned. The treatment variable is a set of dummies _ban_<sup>_τ_</sup> _ct_<sup>indicating whether fertilizer product</sup><sup>_c_was first banned</sup><sup>_τ_months before month</sup><sup>_t_, and</sup> the not-yet-treated products serve as the control group, which includes both non-banned fertilizers and other products. The y-axis shows the effects of fertilizer import bans on the probability of nonzero imports (panel Ia) or on the log value of imports (panel Ib), where negative values correspond to a decrease in probabilities/values. The p-values of the joint significance tests for the placebo estimators are 0.70 (panel Ia) and 0.0001 (panel Ib).
49 Figure II: Rice Yields and Imports in Sri Lanka over time <!-- Start of picture text --> 2012 2014 2016 2018 2020 2022 Jan/2020 Jan/2021 Jan/2022<br>year Month<br>(a) Rice Yields (Maha season) (b) Rice Imports<br>4500 40<br>4000 30<br>20<br>3500<br>Imports (in million $)<br>Paddy yield kg per hectare<br>10<br>3000<br>0<br><!-- End of picture text --> _Notes_ : Panel IIa shows the rice yield (in kg/ha) for the Maha season between 2013 and 2022. The Maha season for rice is from September to March of the following year. The red line in 2021 marks the year fertilizer import bans were introduced. The data comes from the DCS. Panel IIb shows monthly rice imports, in millions (MM) of USD. The first red line in May 2021 marks the beginning of the ban, and the second red line in November 2021 marks the end of the ban. The data comes from the S&P Global Market Intelligence’s Panjiva data platform.
<!-- Start of picture text --> rs Mane 202012024 sce vel<br>7<br>E \\. mi 6989-7442<br>pees<br>ee der,<br>nt eee<br>aryQe |<br><!-- End of picture text -->

<!-- Start of picture text --> AU a wee rte,<br>eae<br>Veer J<br>ce<br>Reece ee<br>~ Sane<br><!-- End of picture text -->
51 Figure IV: Dynamic Ban Effects on Firms’ Agricultural Exports (High vs Low Fertilizer Intensity) <!-- Start of picture text --> −4 −3 −2 −1 0 1 2 3 4<br>Quarter relative to period when treatment first changes (t=0)<br>.4<br>.3<br>.2<br>.1<br>0<br>−.1<br>−.2<br>−.3<br>Effect on log(exports) −.4<br>−.5<br>−.6<br>−.7<br><!-- End of picture text --> _Notes_ : The chart shows De Chaisemartin and d’Haultfoeuille (2022) estimates of the effects of fertilizer import bans on firms’ agricultural export value, relative to the last quarter before the ban takes effect, using a firm-year level export panel. The sample covers the Q1/2019-Q3/2022 period (but only coefficients in Q2/2020-Q2/2022 are reported) and includes all firms who exported at least one of 23 crops for which we have fertilizer intensity data in 2017-2019. Each firm’s fertilizer exposure is computed as a weighted average of crops’ fertilizer intensities with weights given by each crop’s share in the firm’s 2017-2019 exports. The treatment group consists of firms whose fertilizer exposure is above the sample’s 75th percentile. Firms below the 75th percentile serve as the control group. The treatment period is defined as the set of all quarters when any fertilizer import bans were in place. The y-axis shows the effects of fertilizer import bans on log value of agricultural exports, where negative values correspond to a decrease in exports. The p-value of the joint significance test for the placebo estimators is 0.22.
52 Figure V: Ban Effects on Exports, by crop <!-- Start of picture text -->
-5<br>  Cinnamon<br>-10   Cloves<br>  Groundnuts<br>-15<br>  Onions<br>  Tea<br>-20<br>  Rice<br>-25<br>  Potato<br>-30<br>-35<br>  Maize<br>-40<br>0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18<br>Crop's fertilizer intensity ( f k )<br>Effect on crop's export value (in %)<br><!-- End of picture text -->

_Notes_ : The figure plots the fertilizer intensity of each crop against the % change in the value of the crop’s exports from Sri Lanka to the RoW between the baseline equilibrium with no QRs and the counterfactual equilibrium with QRs. The fertilizer intensity of crop _k_ is defined as the fertilizer coefficient _γk_<sup>_f_in its Cobb-Douglas production function.The export value of crop</sup><sup>_k_is the total crop-</sup><sup>_k_sales of Sri Lanka to the RoW, which</sup> is computed as:<sup>�</sup><sup>_I_</sup> _i_ =1<sup>_X_</sup> _RoW_<sup>_Aβ_</sup> _RoW,k_<sup>_Aβ_</sup> _RoW,i,k_<sup>_A_.The correlation coefficient between fertilizer intensity and % change in export value is -0.986.</sup>
53

# Figure VI: Ban Effects on Welfare, by district

<!-- Start of picture text --> 0 -8<br>-10<br>-12<br>-5<br>-14<br>-16<br>-18<br>-10<br>-20<br>-22<br>-15 -24<br>0.1 0.2 0.3 0.4 0.5 0.6 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12<br>Farmers' population share Fertilizer cost share (at baseline)<br>(a) Average across agent types (b) Representative Farmer<br>4<br>0<br>2<br>0<br>-5<br>-2<br>-4<br>-6<br>-10<br>-8<br>-10<br>-15 -12<br>0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0 0.2 0.4 0.6 0.8 1<br>Fertilizer cost share (at baseline) Agriculture's employment share (at baseline)<br>(c) Average across agent types (d) Mobile Worker<br>Welfare change (in %) Welfare change (in %)<br>Welfare change (in %) Welfare change (in %)<br><!-- End of picture text --> _Notes_ : The figure displays scatter plots in which eat dot represents one of Sri Lanka’s districts, the vertical axes show the % change in the welfare of (various types of) agents between the baseline equilibrium with no QRs and the counterfactual equilibrium with QRs, and the horizontal axes show various baseline variables that help explain the welfare changes. Panels VIa and VIc show cross-type average welfare changes on the vertical axis, while panels VIb and VId show welfare changes for the representative farmer and the mobile worker (respectively). Type-specific welfare changes are defined as EVs: starting from the agent’s baseline (net-of-tax) income, the EV is the % change in (net-of-tax) income that would leave her with the same utility level as she has in the counterfactual equilibrium, keeping prices fixed at baseline levels. The (district-level) baseline variables in the horizontal axes are the following: in panel VIa, the farmer population share, defined as the number of farmers in the district divided by its total population; in panels VIb and VIc, the fertilizer cost share, defined as farmers’ total fertilizer expenditures divided by total agricultural revenue; in panel VId, the agricultural employment share, defined as the fraction of mobile workers who work in agriculture. The correlation coefficient between the two variables in each panel are -0.878 (panel VIa), -0.951 (panel VIb), -0.722 (panel VIc), and -0.991 (panel VId).
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<!-- Start of picture text --> c =(0.18,0.21]<br>; e m(0.14,0.18]=(0.08,0.14]<br>. =[-0.03,0.08]<br><!-- End of picture text --> <!-- Start of picture text --> 2 = (0.104,0.146]<br>. == (0.082.0.104](0,036,0.082]<br>4 [0.007,0.036]<br><!-- End of picture text --> <!-- Start of picture text --> ‘<br>a(Q. ,0: ff<br>‘ (0.155.339 “<br>; © (0.036.0.155] =<br>_—_—,<br>; (<br><!-- End of picture text --> <!-- Start of picture text --> ff<br>“ = (0.33,0.57]<br>= =hs<br>: [-0.11,0.01]<br>(<br><!-- End of picture text -->
# **Online Appendix**

## **A Data Appendix**

In this section, we list and describe the multiple data sources we use in this paper, as well as the necessary data cleaning and adjustment procedures we perform. Where relevant, we show descriptive statistics based on the data. We cover not only the data sources mentioned in Section III, but also other ancillary data sources.

### **A.A Trade Policy**

We obtained Sri Lanka’s Extraordinary Gazettes on Imports and Exports (Control Regulations) from March 2020 to October 2022, which allow us to identify the HS8 products that were subject to import bans.<sup>95</sup> We digitized the gazettes and manually inspected all entries to create a database with HS8 products and start and end dates of import bans. Appendix Figure A1 shows the timing of the fertilizer import bans, while Appendix Table A1 shows the list of HS8 product codes corresponding to fertilizers subject to the import ban.

Figure A1: Timing of Fertilizer Import Bans <!-- Start of picture text --> Jan/2017 Jan/2018 Jan/2019 Jan/2020 Jan/2021 Jan/2022<br>Month<br>.6<br>.4<br>.2<br>Fraction of fertilizer products banned<br>0<br><!-- End of picture text --> _Notes_ : For each month between January 2017 and September 2022, the chart shows the fraction of HS8 fertilizer products that were subject to an import ban in that month. The denominator of the fraction is 25, which is the number of fertilizer products that were imported by Sri Lanka at any point between 2017 and 2022. A fertilizer product is defined as any HS8 product that is listed in Chapter 31 of the HS system. The data comes from Sri Lanka’s Extraordinary Gazettes.

> 95The Extraordinary Gazettes were accessed at: http://www.imexport.gov.lk/index.php/en/downloads/gazette.html

56
57 Table A1: List of Fertilizer Products Subject to Import Bans

|HS8|Description|
|---|---|
|31024000|Mixtures of ammonium nitrate with calcium carbonate or other inorganic non-fertilizing<br>substances|
|31026000|Double salts and mixtures of calcium nitrate and ammonium nitrate|
|31028000|Mixtures of urea and ammonium nitrate in aqueous or ammoniacal solution|
|31029000|Other, including mixtures not specifed in the foregoing subheadings|
|31031100<br>31031900|Superphosphates containing by weight 35% or more of diphosphorus pentaoxide (P2O5)<br>Other|
|31039000|Other|
|31049000|Other|
|31051000|Goods of this Chapter in tablets or similar forms or in packages of a gross weight not<br>exceeding 10 kg|
|31052000|Mineral or chemical fertilizers containing the three fertilizing elements nitrogen,<br>phosphorus and potassium|
|31053000|Diammonium hydrogenorthophosphate (diammonium phosphate)|
|31054000|Ammonium dihydrogenorthophosphate (monoammonium phosphate) and mixtures<br>thereof with diammonium hydrogenorthophosphate (diammonium phosphate)|
|31055100|Containing nitrates and phosphates|
|31055900|Other|
|31056000|Mineral or chemical fertilizers containing the two fertilizing elements phosphorus<br>and potassium|
|31059000|Other|

_Notes_ : The table displays the list of HS8 fertilizer products that were subject to import bans at some point in 2021. An HS8 product is classified as fertilizer if it is listed in Chapter 31 of the HS system. The data is from Sri Lanka’s Extraordinary Gazettes.

# **A.B Trade Flows**

We use novel high-frequency granular trade data obtained from S&P Global Market Intelligence’s Panjiva data platform covering the universe of Sri Lanka’s export and import transactions from January 2017 to October 2022 based on bills of lading (BoL). The data includes the name and address of the shipper (exporter) and the consignee (importer) of each shipment as well as HS8 product codes. Exporting and importing firms are identified by their names, as BoL data does not require inclusion of tax identification numbers.<sup>96</sup> We use machine learning and text analysis techniques to clean firm names and assign to each name a unique firm identifier, thus constructing a panel of Sri Lankan firms engaged in exports or imports. Appendix A.B.1 below provides details on our fuzzy matching algorithms.

The data is subject to a series of cleaning procedures as in Fernandes et al. (2016). Specifically, we drop observations for which trade value is zero or missing, product codes are missing or not in the HS 2017 revision list, partner country is missing or is Sri Lanka (which may indicate trans-

> 96While Panjiva adds a firm identifier to the BoL data that Flaaen et al. (2023) use for the United States, we found such identifier to be extremely unreliable for Sri Lankan firms. The same firm appearing with a different name spelling has a different identifier, and a given firm making an export transaction has a different identifier than the same firm making an import transaction. On any given day, the same firm transacting more than once could also have different Panjiva identifiers.
58 actions with Special Economic Zones, but this cannot be systematically assessed). Data quality is assessed, as in Fernandes et al. (2016), by a comparison of total exports and total imports obtained from aggregating the transaction-level data at year level with total yearly exports and imports for Sri Lanka from World Integrated Trade Solution (WITS) and from the Central Bank of Sri Lanka. The ratios to WITS in 2017-2021 are in the 97%-100% range for exports and the 83%-94% range for imports. To obtain our final datasets, we drop exports and imports of oil (HS Chapter 27), which are generally not well captured in customs datasets. To focus on true commercial export and import transactions by firms, we also drop transactions of currency paper notes (HS 490700) conducted only by the Central Bank of Sri Lanka, of large machinery entering and exiting Sri Lanka temporarily for construction projects such as dredgers (vessels) (HS 890510, HS 890190), and of arms and ammunition (HS Chapter 93).

We aggregate transaction-level values (in USD) and net weights (in kg) up to the HS8 productmonth-year level for our import analysis by summing across firms and source countries. We aggregate transaction-level values (in USD) up to the firm-HS8 product-year level for our export analysis by summing across destination countries. For our export analysis, we focus on agricultural products, which are listed in HS Chapters 06-24.

# **A.B.1 Cleaning Firm Names**

The names of Sri Lankan firms engaged in export or import transactions are noisy. Names appear with multiple spellings or with spelling errors, and some entries are a number or an address instead of a proper names. In brief, the steps for the cleaning of names are as follows:

1. Eliminate from the list of firm names those entries that are not proper names (numbers, addresses, and the expressions ‘NIL’, ‘N/A’, or ‘To the order’).

2. Remove from firm names a list of stop words, geographic stop words, and symbols that are not letters nor numbers. The list of stop words was selected based on text analysis indicating the most common words appearing in firm names, such as ‘corporation’, ‘international’, ‘limited’, and ‘llc’. We also remove prefixes and suffixes (such as ‘co’, ‘sa’, and ‘pvc’) from firm names.

3. Based on the list of pre-processed firm names obtained in Step 2, we use N-gram similarity (using cosine distance metrics) to identify potential pairs of similar firm names (using a lower similarity threshold of 0.6, where 1 means two names are identical).

4. Potential pairs of similar firm names identified in Step 3 go through an algorithm to more precisely determine if they are really similar based on Levenshtein distance (a measure of similarity between two strings). Distance cutoffs defining what is a “small” distance between a pair of names are determined through machine learning algorithms based on subsamples of firm name pairs whose similarity was determined through manual inspection.
59 5. The pairs of similar firm names identified in Step 4 are then sorted alphabetically to identify neighbor names (i.e., names that appear in consecutive rows after sorting) and correct any potential similarities that may have been missed in Step 4.

6. The algorithms in Step 4 generate “big groups” of firm names that are considered similar because they share several common words. To break up these “big groups”, firm names are sorted alphabetically within each group and, if two consecutive firm names do not have sufficiently similar pre-processed names (as captured by a cutoff in the Levenshtein distance), the group is “broken” at that place, resulting in two separate groups of similar firm names.

7. After similar firm names are identified from the steps above and assigned temporary unique numeric identifiers, firm names are then sorted alphabetically and based on firm address. If two consecutive names have similar addresses and similar names and did not have the same unique numeric identifier, they are joined in a new final unique numeric identifier.

The steps above are applied to clean the names of Sri Lankan firms. A large number of transactions, especially in the import data, are made by firms whose names indicate they are courier companies. Since these transactions are made for a third party, frequently individuals, and since their total trade value is negligible, we dropped all observations whose names are of courier firms.<sup>97</sup> Finally, we also drop from the sample observations for which the firm name corresponds to an individual making personal imports under a permit.<sup>98</sup> Such observations account for a very small total trade value.

# **A.C Agricultural Production, Cultivated Area, and Yields**

We rely on both administrative data and remote sensing estimates.

## **A.C.1 Administrative Data**

For rice, we obtain data on production and cultivated area in each district from the ‘Paddy Statistics’ produced by the DCS for each growing season from 2012-2013 Maha to 2022 Yala.<sup>99</sup> Crucially, this time frame includes the 2019-2020 Maha and 2020 Yala seasons, which we use as the pre-ban baseline to estimate the model in Section VI.B.

For non-rice, non-tea crops (maize, groundnuts, potatoes, onions, cinnamon, and cloves), we obtain data on production and cultivated area at the divisional secretariat (DS) level from the DCS for each growing season from Maha 2019-2020 to Yala 2022, which we aggregate up to the district level. For tea, the DCS data includes information on cultivated area but not on production, so we

> 97Namely: “dhl express parcel delivery”, “d h l”, “fits aviation”, “cargo logistics worldwide aramex courier freight” “non commercial xpress by air freight” “Skynet shipping setrans” “sky international”.

> 98Such firm names have the structure “Person Name+Institution+PERMIT”. For example: “KADAWARAGE C V WING COMMANDER (DENTAL DOCTOR) SRI LANKA AIR FORCE MIN.OF DEFENCE PERMIT”.

> 99Paddy Statistics were accessed at: http://www.statistics.gov.lk/Agriculture/StaticalInformation/Paddy ~~S~~ tatistics.
60 obtain district-level tea production data from the Sri Lanka Tea Board’s annual reports for 20192022.

Production is measured in kilograms (kg) and cultivated area is measured in hectares (ha). For crops with harvests in both Yala and Maha seasons (maize, rice, and groundnuts), we compute total production and total cultivated area in each year and district by summing across the two seasons. For each crop, we obtain yields (in kg/ha) as the ratio between production and cultivated area.

To estimate fertilizer coefficients in our model’s Cobb-Douglas agricultural production functions (see Section VI.A.3), we use national production data for each crop in 2022, in metric tons (MT), from the Central Bank of Sri Lanka’s Economic and Social Statistics 2023 report.<sup>100</sup> We use national production data for cinnamon, cloves, groundnuts, maize, onions, potato, rice, and tea.

# **A.C.2 Remote Sensing Estimates**

We produce novel remote sensing estimates of rice and tea yields and of cultivated rice areas at a highly granular level. For rice, the methodology described in Ozdogan et al. (2024) relies on an expert-based image classification algorithm on satellite observations from Landstat and Sentinel2 enhanced to isolate the rice signal based on the premise that paddy rice has specific growing conditions in Sri Lanka. The presence of rice-growing areas is determined by factors related to climate, water availability, topographic position, and farmer decision-making and technical expertise. The methodology monitors rice-related vegetation and water management from space and distinguishes it from other land use types using spectral (color) and temporal information included in the satellite signal. Since water and vegetation indexes are more visible for rice than for other crops, remote sensing tools can more accurately map crop type and predict yields for the former than for the latter (Dong et al., 2016). To estimate rice yields, we use a statistical model that correlates district-level rice yields from government statistics (described in Appendix A.C.1) with the satellite-derived vegetation index (green chlorophyll index), known to be sensitive to rice yields for the pixels identified as rice areas. A random forest-based machine learning model is then added to incorporate additional environmental variables known to affect rice yields, resulting in pixel-level rice yield estimates across two decades (2000-2022). These remote sensing estimates, aggregated to the DS level, are shown to be highly consistent with government-reported measures of rice area (from survey-based crop-cutting experiments) and rice yield (from production statistics).

For tea, we regress district-level yield data from Sri Lanka Tea Board reports (see Appendix A.C.1) on a district-level vegetation index derived from Planet Satellite Data for pixels deemed to be tea plantations for the period 2014-2022. Since the Tea Board reports only production, not yields, we divide total production by planted area in each district to obtain yields (in kg/ha). In

> 100The report is available at: https://www.cbsl.gov.lk/en/publications/other-publications/statisticalpublications/economic-and-social-statistics-of-sri-lanka/ess-2023.
61 the satellite analysis, tea cultivation areas are held fixed to the 2021 tea map, which is applied to every year. The underlying assumption is that tea planted areas do not change on an annual basis because tea is a multiyear permanent crop. We also generate a derived confidence index reflecting the precision of the satellite-derived tea maps, which we use as statistical weights in our tea yield regressions in Appendix C.D. To obtain the confidence index, we first derive a tea probability map using an ensemble random forest image classification algorithm applied to tea data. In this map, any pixel with less than 50% probability is identified as a non-tea planted pixel. We remove all non-tea planted pixels, leaving only pixels with probabilities between 51% and 100%. We then average these probabilities across the pixels within each DS and round the resulting value to obtain the confidence index (ranging from 50 to 100) for each DS.

# **A.D Agricultural Prices**

To estimate our model, we use data on producer prices for each crop (except tea) and district from the 2016-2019 edition of DCS’ Bulletin of Selected Retail and Producer Prices.<sup>101</sup> We extract average producer prices (in LKR/kg) in 2019 for rice, potatoes, cinnamon, cloves, onions, groundnuts, and maize. For onion and rice, whose prices are available for multiple varieties, we use the prices of red onions and red rice (raw). Whenever the producer price of a crop is missing for a given district, we impute it using the crop’s average price across other Sri Lankan districts. Producer prices are missing for 45% of the district-crop pairs with non-zero agricultural production. Nevertheless, the imputation procedure is unlikely to create biases since producer prices are similar across space: the coefficient of variation of (non-missing) producer prices across districts averages 0.032, ranging from 0.009 to 0.058 across crops. For tea, we use producer price data (in LKR/MT) for 2019 from the Food and Agriculture Organization of the United Nations (FAO) for Sri Lanka as a whole, which we assume to hold in each individual tea-producing district.

The 2018-2021 and 2019-2022 editions of DCS’ Bulletin of Selected Retail and Producer Prices are used to compute crop-level nominal producer price increases between January 2021 and January 2022. By subtracting from each crop’s nominal price increase the aggregate inflation implied by the National Consumer Price Index during the same period, we obtain each crop’s real price increase. This information is used as an input in the calibration of the cross-origin elasticity of substitution of agricultural crops (see Section VI.A.1).

To estimate the fertilizer coefficients of our model’s Cobb-Douglas agricultural production functions (see Section VI.A.3), we use data on national crop prices in 2022 (in LKR/kg) from the Central Bank of Sri Lanka’s Economic and Social Statistics 2023 report (except for groundnuts, whose national price comes from the 2019-2022 edition of the Bulletin of Selected Retail and 101The Bulletins of Prices can be found at: http://www.statistics.gov.lk/InflationAndPrices/StaticalInformation/Bulletins#gsc.tab=0
62 Table A2: Fertilizer Use and Intensity in Sri Lanka, by crop

|||**Fertiliz**|**er Type**||||
|---|---|---|---|---|---|---|
|**Crop**|**Urea**|**TSP**|**MOP**|**Others**|**Total**|**Fertilizer Inten-**<br>**sity (MT/ha)**|
|Chili pepper|3800|3800|3800|0|11400|0.300|
|Cinnamon|15114||7558|0|22672|0.662|
|Cloves|1359||2039|226|3624|0.454|
|Cocoa|178||222|44|444|0.243|
|Coconut|20147|2865|40295|15000|78307|0.173|
|Cowpea|1008|1550|1203|0|3761|0.243|
|Fruits|48359|35353|80067|0|163779|1.279|
|Green gram|1495|2300|1725|0|5520|0.240|
|<br>Horse gram|3|6|2|0|11|0.073|
|<br>Kurakkan|2345|605|908|0|3858|0.351|
|Maize|32300|14000|7000|0|53300|0.381|
|Nutmeg|484||727|80|1291|0.454|
|Onion|2926|1500|1126|0|5552|0.370|
|Paddy|247000|61000|74000|0|382000|0.294|
|Peanuts|1203|1850|1388|0|4441|0.240|
|Pepper|14562||10922|3640|29124|0.710|
|Potatoes|2310|1890|1750|0|5950|0.850|
|Rubber|6767||7151|4391|18309|0.146|
|Sesame|1595|1740|870|0|4205|0.290|
|Soybeans|.|.|.|.|.|0.067|
|Tea|96050||36864|59206|192120|0.959|
|Undu|1755|2700|2025|0|6480|0.240|
|Vegetables|22744|21297|14920|0|58961|0.640|

_Notes_ : for each crop, the table displays total fertilizer use in Sri Lanka (in MT) for four types of fertilizer: urea, triple superphosphate (TSP), muriate of potash (MOP), and other fertilizers. The last column shows fertilizer intensity (in MT/ha), which is computed by dividing the crop’s total fertilizer use (in MT) by its cultivated area (in ha). The data comes from Sri Lanka’s NFS, except for soybeans, whose fertilizer intensity data comes from the International Fertilizer Development Center and the International Fertilizer Association (specifically, from their ‘Asia’ estimates).

Producer Prices). We proxy the national prices of maize, onions, potato, rice, and tea with their (national) unit costs of production.<sup>102</sup> Since unit costs of production are not available for cinnamon and cloves, we use their (national) FOB export prices instead.

# **A.E Fertilizer Use and Subsidies**

To compute chemical fertilizer use in the production of various agricultural crops, we use data provided by Sri Lanka’s NFS. Fertilizer requirements for 2022, displayed in Appendix Table A2, are reported as MT of fertilizer required per ha of cultivated land for each of 23 crops. As explained in Section IV.C, this fertilizer intensity metric is used in our main analysis to build a firm-level fertil102Due to our model’s perfect competition assumption, a crop’s unit cost of production equals its (farm-gate) producer price, which justifies using the former (which is available in the Economic and Social Statistics report) as a proxy for the latter. For tea and rice, unit costs are reported for the whole island, but for maize, onions, and potatoes they are reported for individual districts. We use data from Puttlam for onions and from Badulla for maize and potatoes, as these districts are major producers of their respective crops.
63 izer exposure measure (see equation 42). Sri Lanka’s NFS data also includes estimates of fertilizer prices and of each crop’s total cultivated area, which we combine with fertilizer requirements data to compute country-level fertilizer expenditure for each crop in 2022. Section VI.A.3 discusses how such fertilizer expenditures are used to estimate technological parameters.

NFS data on soybeans’ fertilizer intensity was deemed unreliable by agriculture specialists, so we complement the NFS data with data from the International Fertilizer Development Center and the International Fertilizer Association. Specifically, we use the ‘Asia’ entries in these databases to impute the fertilizer intensity of soybeans that appears in Appendix Table A2. Appendix Figure A2 shows that this alternative fertilizer intensity metric has a close linear relationship with our original metric from the NFS (with the exception of soybeans, which are a clear outlier in the graph), thus also serving as a validation for the latter.

Figure A2: Fertilizer Intensity: Sri Lanka vs Asia <!-- Start of picture text --> 0 200 400 600<br>Fertilizer intensity (kg/ha): Asia<br>3000<br>2000<br>1000<br>Fertilizer intensity (kg/ha): Sri Lanka<br>0<br><!-- End of picture text --> _Notes_ : The figure shows the fertilizer intensity of 22 crops (see Appendix Table A2 for the full list), measured in kg/ha, from two alternative data sources: Sri Lanka’s NFS (on the vertical axis) and the databases of the International Fertilizer Development Center and the International Fertilizer Association (on the horizontal axis). For the latter source, we use the estimates that correspond to Asia. The fertilizer intensity metrics add up the use of urea, TSP, and MOP. The outlier point on the top left corresponds to soybeans. The red line is the regression line when we exclude the outlier point from the sample, with a corresponding correlation coefficient of 0.677.

We use FAO data on the use of manure and chemical fertilizers in Sri Lankan agriculture in the period 2001-2021, namely the total nitrogen content (by weight) of manure applied to the soil and the total use (by weight) of 23 different types of chemical fertilizer. The data also includes the amount of manure that is lost through leaching or volatilization, allowing us to compute the net amount of manure that is applied to the soil.

We obtain data on fertilizer subsidies provided to farmers by Sri Lanka’s government in the 2013-2022 period from the Cost of Cultivation Reports produced by the Department of Agriculture’s Socio Economics & Planning Centre. For each crop, the fertilizer subsidy rate (in %) is
64 based on the “nominal rate of protection at farm gate”, which is defined as the difference between actual and expected farm-gate fertilizer prices, with expected prices computed based on international prices and the cost of transportation from port to farm. Since there is no available subsidy data for cinnamon, cloves, and groundnuts, we impute their fertilizer subsidy rates with the average rate across potato, maize, tea, and onions.

# **A.F Potential Crop Yields**

To estimate the elasticity of substitution across crops of our model’s demand system, we use an IV approach that leverages variation in agricultural productivity across space due to exogenous geographic factors (such as climate and geology). To do so, we use data on district-level potential attainable yields for each of seven crops, which we obtain from the FAO-GAEZ project. The crops are: coconut, groundnut, maize, onion, rice, tea, and white potato. Unfortunately, cinnamon potential yields are not available in GAEZ. We extract potential yield data (in kg/ha) at the grid cell level and aggregate up to the district level. GAEZ offers different yield estimates depending on the irrigation system (rainfed or irrigated) and climate conditions (e.g. historical conditions, various climate change scenarios). To reflect the actual technologies commonly used in Sri Lankan agriculture, we choose the rainfed option for all crops except rice, which is irrigated. We choose the climate conditions of 1981-2010 without climate change. Section VI.A.1 describes how this data is used in estimation.

# **A.G Labor Share in Value Added**

To estimate labor and land coefficients in our model’s Cobb-Douglas agricultural production functions, we use data from Sri Lanka’s IO table for 2000, produced by the Institute of Policy Studies (Amarasinghe and Bandara, 2005). We extract information on employee compensation and value added (at factor cost prices) for a variety of agricultural sectors: “paddy”, “minor export crops”, “highland crops”, “tea growing” (separately for high, medium, and low elevations), and “potatoes”. Section VI.A.3 describes how this data is used in estimation.

# **A.H Wages, Household Characteristics, Occupational Distribution, and Land Distribution**

We use the 2016 and 2019 editions of the HIES for data on wages, employment, land ownership, land distribution, income, and consumption patterns. The HIES is a yearlong survey conducted in consecutive monthly rounds, with a nationally representative sample enumerated in each round to capture seasonal and regional pattern variation. The HIES provides household-level statistical
65 weights. All averages, standard deviations, and counts we compute using HIES data are weighted using these weights.

We extract wage information from the 2019 HIES, which lists household members who “were paid employees during last four weeks/last calendar month”. We compute each district’s average wages as the (weighted) average of compensation in the main occupation across the district’s workers (excluding workers with zero compensation), with compensation defined as the sum of “wages/salaries” and “tips, commissions, overtime pay etc” and measured in LKR. We compute average wages separately for estate and non-estate (mobile) workers. Estate workers are workers who live and work in Sri Lanka’s tea plantations and for which changing jobs is nearly impossible in the short run, as their housing is tied to the tea estate they work in (Chandrabose, 2015). Average wages are multiplied by 12 so that they are expressed in annual terms.

We use information from the 2016 HIES to count the number of mobile workers, estate workers, and farmers in each district (making using of the statistical weights to obtain total counts). We define a “worker” as a person with a main occupation (in agriculture, manufacturing, or services) that paid her above-zero employment compensation in the previous month. We count the total number of such workers in each district and the fraction among these who are estate workers. We then subtract the number of estate workers from the total number of workers to obtain the number of mobile (i.e. non “tea-estate”) workers. To compute the number of farmers, we first count the number of households in each district with positive landholdings. We only count land owned by the household (as opposed to leased, rented, etc.) with no housing built on top of it. We then estimate the number of farmers per district by multiplying the number of farming households by the average number of economically active agents per household. To estimate the average number of economically active agents per household, we divide the number of workers by the number of working households in the district, where a working household is defined as a household with at least one worker. The implicit assumption is that working households and farmer households are similar in terms of household size, structure, and labor force participation. Finally, we scale up the resulting numbers of workers and farmers by Sri Lanka’s population growth between 2016 and 2019 (2.8%) to compute numbers for 2019, our baseline year for model estimation (see Section VI).

For parameter estimation in Section VI.A.1, we also use 2019 HIES data on household size (number of members, regardless of age), income, and expenditure patterns, in particular the fraction of income spent on food. Values and quantities of crops purchased by each household are available, allowing us to compute the prices faced by the household by dividing values by quantities. We also use information on “income by chance or _ad hoc_ gains”, including lottery gains and disaster/relief payments, for our IV estimation in Section VI.A.1.
66

# **A.I Night Lights**

For a model validation exercise in Section VII.F, we use data on night light intensity between January 2016 and December 2022 sourced from the Visible and Infrared Imaging Suite (VIIRS) Day Night Band (DNB) on board of satellites, prepared by the Colorado School of Mines. The key variable of interest is night light intensity at the year-month level for each 0.5 km x 0.5 km grid cell in Sri Lanka. For each month and district, we average the data across all grid cells that compose that district.<sup>103</sup>

# **A.J Weather Variables**

Since a wide array of weather variables have been shown to be important drivers of crop yields for many crops grown in Sri Lanka, it is important to control for weather in our analysis of the effects of the fertilizer import ban on yields (see Appendix C.D). Below, we describe our sources of weather data.

For rainfall data, we use the Climate Hazards Group InfraRed Precipitation with Station (CHIRPS) data, a quasi-global gridded rainfall time series data set based on a combination of high-resolution satellite imagery and in-situ station data covering latitudes between 50<sup>_◦_</sup> S and 50<sup>_◦_</sup> N, all longitudes, and all years from 1981 to the near-present.<sup>104</sup> For each agricultural growing season (Maha and Yala) and year between 1999 and 2022, we obtain three variables from CHIRPS: total rainfall, in millimeters (mm) per season; rainy days (defined as the number of days in the season receiving more than 2mm of rain); and dry spells (defined as the maximum number of consecutive days in the season receiving 1mm or less of rain). The Maha season is defined as starting on September 1 and ending on March 31. The Yala season is defined as starting on May 1 and ending on August 31. We aggregate the data up from the grid-cell level to the level of Sri Lankan districts.

For other weather variables, we use the ERA5-Land dataset, which provides high-resolution data on the evolution of the Earth’s land surface between 1950 and the present.<sup>105</sup> For each growing season and year, we obtain four variables from ERA5-Land: average incoming shortwave solar radiation, in watts per square meter (W/m2); total vapor pressure deficit, in hectopascals; and average minimum and maximum temperatures, in degrees Celsius. Vapor pressure deficit (VPD) is the difference between saturated vapor pressure (temperature dependent) and the actual vapor pressure. Higher VPD values indicate higher air dryness and therefore often negatively correlate with yields. VPD is computed daily and summed over the season. Minimum and maximum temperatures are defined as the mean of daily minimum and maximum temperatures for the entire season. As with rainfall, we aggregate grid-cell level data on these four variables up to the district level.

> 103 VIIRS data can be accessed at: https://eogdata.mines.edu/products/vnl/.

> 104 CHIRPS data can be accessed at: https://www.chc.ucsb.edu/data/chirps.

> 105 ERA5-Land data can be accessed at: https://www.ecmwf.int/en/era5-land.
67

# **A.K Data on the Rest of the World**

Since the rest of the world (RoW) is one of the regions in our quantitative model, we need data on its wages, production, cultivated area, prices, population, and employment so that we are able to bring the model to the data. Wages in the RoW are assumed to be equal to the world’s GDP per capita (in current USD) in 2019 (our baseline year for model estimation), which was 11,330.5 USD according to the World Bank’s World Development Indicators.<sup>106</sup> We set the number of workers in the RoW to the size of the global labor force, which was 3.45 billion in 2019 according to data from the International Labour Organization (ILO). We then estimate the number of farmers in the RoW in two steps. First, we multiply the number of workers in the RoW by the agricultural share of global employment (26%, also from ILO data), thus obtaining the number of agricultural workers in the RoW.<sup>107</sup> Second, we multiply this number by the ratio of farmers to agricultural workers (0.29) which we compute using data from the Brazilian Agricultural Census as a benchmark. To calculate this ratio, we use “number of establishments directed by owner or her business partner” as a proxy for the number of farmers; and “number of occupied people in agricultural establishments” as a proxy for the number of agricultural workers.<sup>108</sup> The resulting estimate for the number of farmers in the RoW is approximately 260 million.

Our data on agricultural production, cultivated area, and producer prices in the RoW comes from the FAO.<sup>109</sup> We obtain data for each country’s production quantities (in MT), harvested area (in ha), and producer price (in USD/MT) of seven crops in 2019, then sum across countries to obtain production and cultivated area in the RoW. The crops we use are listed in the FAO data with the following names: “Cinnamon and cinnamon-tree flowers, raw”, “Cloves (whole stems), raw”, “Groundnuts, excluding shelled”, “Maize (corn)”, “Potatoes”, “Rice”, and “Onions and shallots, green”. Each crop’s producer price in the RoW is set to the median price across all available countries. All variables that are measured in MT are converted to kg.

Finally, it is sometimes necessary in our analysis to convert currency denominations between the USD and the LKR. We use the exchange rate _E_ 2019 = 176 LKR/USD for 2019 and _E_ 2022 = 360 LKR/USD for 2022, both of which were obtained from Google Finance.<sup>110</sup> 106The data portal can be accessed at: https://databank.worldbank.org/indicator/NY.GDP.PCAP.CD/1ff4a498/PopularIndicators

> 107ILO data is available on the World Bank’s data portal at: https://data.worldbank.org/indicator/SL.TLF.TOTL.IN and https://data.worldbank.org/indicator/SL.AGR.EMPL.ZS

> 108These aggregated statistics from Brazil’s 2006 Agricultural Census are available in Tables 2724 and 265 of the online portal SIDRA, which can be accessed at: https://sidra.ibge.gov.br/

> 109This data can be accessed through the FAOSTAT online portal at: https://www.fao.org/faostat/en/data/QCL and https://www.fao.org/faostat/en/data/PP

> 110These two exchange rates are from June 28 2019 and June 24 2022, respectively.
68

# **A.L Descriptive Statistics**

Appendix Table A3 shows the share of fertilizer imports that are organic, while Appendix Figure A3 shows the use of organic fertilizer in agriculture in Sri Lanka. Appendix Table A4 shows the share of imports subject to import bans from 2017 to 2021.

Table A3: Fertilizer Imports, Total versus Organic

|**Period**|Total Fertilizer Imports(in MM USD)|% Organic|
|---|---|---|
|2016|128|0.078%|
|2017|98|0.128%|
|2018|249|0.148%|
|2019|211|0.072%|
|2020|244|0.111%|
|2021 (no-ban months)|23|0.639%|
|2021(ban months)|11|3.763%|

_Notes_ : for each year, the table shows total fertilizer imports by Sri Lanka in millions (MM) of USD and the percentage of these imports consisting of organic fertilizer. The data comes from the S&P Global Market Intelligence’s Panjiva data platform. A fertilizer is any HS8 product listed in Chapter 31 of the HS system. Organic fertilizers are classified as “animal or vegetable” (as opposed to “mineral or chemical”), and are listed under heading 3101 of the HS system. We break 2021 into two subperiods: the “ban months” (May-November) when the fertilizer import ban was in place, and the “no-ban months” (January-April and December) when the ban was not in place.

Figure A3: Use of Manure in Agriculture <!-- Start of picture text --> 2000 2005 2010 2015 2020 2015 2016 2017 2018 2019 2020 2021<br>(a) Use of Manure (b) Manure’s Share (by weight)<br>7 2.5<br>2<br>6.5<br>1.5<br>6<br>1<br>5.5<br>.5<br>Net manure application (N content, MM kg) 5 Manure’s share of total fertilizer weight (in %)<br>0<br><!-- End of picture text --> _Notes_ : for each year between 2001 and 2021, Figure A3a shows the total nitrogen content (measured in MM kg) of the manure that is applied to the soil as an organic fertilizer in Sri Lanka, net of the nitrogen that is lost through leaching or volatilization. Appendix Figure A3b shows the same quantity as in Appendix Figure A3a, but as a share of the total weight of all fertilizer used in Sri Lankan agriculture, which includes both manure and (23 types of) chemical fertilizer products. The data is from the FAO.
69 Table A4: Imports of Products Subject to Import Bans

|Year|Import share|Imports(in MM USD)|
|---|---|---|
|2017|17.18%|2,544|
|2018|18.64%|2,873|
|2019|15.69%|2,088|
|2020|12.41%|1,436|
|2021|10.19%|1,444|

_Notes_ : For each year, the table displays the total import value of the set of HS8 products whose imports were banned at some point starting in 2020. This variable is shown both in absolute terms (in MM USD) and as a % of total imports. The data comes from Sri Lanka’s Extraordinary Gazettes and the S&P Global Market Intelligence’s Panjiva data platform.

Appendix Table A5 displays pre-ban and post-ban summary statistics for some of our key variables of interest. Some of the ban’s effects are apparent even in these basic statistics: comparing the pre-ban to the post-ban period, we see that the average value of fertilizer imports plummeted from 2 million USD to only 491 thousand USD per importer firm per year. Similarly, the average value of agricultural exports fell from 1.62 million USD to 1.53 million USD per agricultural exporter firm per year.

Panel B of Appendix Table A5 focuses on the evolution of crop yields over time, as estimated by our remote sensing methodology. Again, we see large decreases in crop yields between the pre-ban (2021) and post-ban (2022) periods: the average rice yield across DSs falls from more than 4,000 kg/ha to less than 3,000 kg/ha, while average tea yields fall from 1,644 kg/ha to 1,404 kg/ha.

# **B Details on Estimation of Stylized Facts**

## **B.A Stylized Fact 1**

In Section IV.A, we estimate the fertilizer import ban’s effects on fertilizer imports through stateof-the-art dynamic DID regressions following De Chaisemartin and d’Haultfoeuille (2022). The regressions are estimated on a panel of HS8 products at the monthly level, with the treatment group consisting of fertilizers who had their imports banned from May 2021 onward, and the control group consisting of non-banned products. We exclude from the analysis products whose imports were banned at any point prior to May 2021. The estimating equation is: where _c_ indexes HS8 products and _t_ indexes time periods (months), _yct_ is the outcome variable, _ωt_ and _ωc_ are time and product fixed effects, respectively, and _εct_ is an error term. Our main variable of interest is _ban_<sup>_τ_</sup> _ct_<sup>, a dummy variable indicating whether an import ban on product</sup><sup>_c_was first imposed</sup>
70 Table A5: Summary Statistics

|**Panel A: Intern**|**ational Trade**<br>||
|---|---|---|
|**Firm-level variables**|Pre-Ban<br>(1)|Post-Ban<br>(2)|
||2,036,434|491,025.4|
|Fertilizer Imports (USD)|(7,267,773)<br>[_N_=106]|(1,378,846)<br>[_N_=106]|
||1,619,553|1,531,465|
|Agricultural Exports (USD)|(6,206,280)<br>[_N_=1,565]|(6,030,005)<br>[_N_=1,562]|
|**Panel B: Cr**<br>|**op Yields**||
|**Divisional Secretariat-**|Pre-Ban|Post-Ban|
|**level variables**|(1)|(2)|
||4,236.585|2,881.95|
|Rice Yields (kg/ha)|(1,013.066)<br>[_N_=323]|(680.9113)<br>[_N_=323]|
||1,644.278|1,403.798|
|Tea Yields (kg/ha)|(1,165.624)<br>[_N_=134]|(971.3812)<br>[_N_=134]|

_Notes_ : The table shows summary statistics for key variables of interest, separately for pre-ban and post-ban periods. In addition to each variable’s average, the table displays its standard deviation (in parentheses) and sample size _N_ (in square brackets). The unit of observation is the firm in Panel A and the DS in Panel B. The data comes from the S&P Global Market Intelligence’s Panjiva data platform in Panel A and from our remote sensing estimates in Panel B. For each variable and period, the statistics are computed using all available units for which that variable was positive in that period. In Panel A, we define fertilizers as products listed in Chapter 31 of the HS system, and agricultural goods as products listed between Chapters 06 and 24. Imports and exports are measured in US dollars (USD), and crop yields are measured in kg/ha. In the case of tea yields, we use a DS-level confidence index that reflects the precision of the remote sensing estimates as a weight to compute weighted averages and standard deviations. Our definitions of pre-ban and post-ban periods differ across variables: for fertilizer imports, the pre-ban period is May 2020-April 2021 and the post-ban period is May 2021-April 2022; for agricultural exports, the pre-ban period is November 2020-October 2021 and the post-ban period is November 2021-October 2022; in Panel B, the pre-ban period is 2021 and the post-ban period is 2022.
71 _τ_ periods before period _t_ . Note that _ban_<sup>_τ_</sup> _ct_<sup>is always equal to zero for products whose imports were</sup> never banned.

We estimate the evolution of the ban’s effects on two alternative outcome variables ( _yct_ ): an “extensive-margin” dummy indicating non-zero imports and an “intensive-margin” variable consisting of the log of import values. To define our extensive-margin dummy variable, we expand our original HS8 product-month level import data by adding an entry with zero imports for each month (within the January 2017-October 2022 period) when imports of a product are not reported.

The sample period used in the estimation ranges from January 2019 to September 2022. For presentational purposes, the figures with our import results (Figure I and Appendix Figures A5, A6, and A7) only show coefficients for the four months prior and twelve months subsequent to the ban, even though the sample period used in the estimation is longer.

# **B.B Stylized Fact 3**

In Section IV.C, we estimate the fertilizer import ban’s downstream effects on agricultural exports. We follow a firm-level approach, focusing on firms who exported agricultural products in the preban 2017-2019 period. For each firm _f_ , we define the following exposure measure _Uf_ : where _f_ indexes firms and _v_ crops, _FICv_ is fertilizer intensity (in kg/ha) of crop _v_ , and _Xfv_<sup>2017</sup><sup>_−_2019</sup> is total exports of crop _v_ by firm _f_ in 2017-2019. The summation in equation (42) only considers the 23 crops for which we have fertilizer intensity data (see Appendix A.E). This exposure measure is the weighted average of fertilizer intensity across all crops that a firm exports (with weights given by each crop’s share in the firm’s export portfolio).

We then use a firm-quarter panel and the dynamic DID estimator from De Chaisemartin and d’Haultfoeuille (2022) once again to estimate the ban’s impact on firm exports. The treatment group consists of firms above the upper quartile of fertilize exposure variable _Uf_ , with the remaining firms in the sample serving as the control group. The estimating equation is as follows: where _f_ indexes firms, _t_ indexes quarters, _Xft_ is agricultural exports, Ω _t_ and Ω _f_ are quarter and firm fixed effects, respectively, _T_ 0 is the quarter when the fertilizer import ban was introduced (i.e. Q2/2021), and _μft_ is an error term.

The sample period used in the estimation ranges from January 2019 to September 2022. For
72 presentational purposes, the figures with our export results (Figure IV and Appendix Figure A8) only show coefficients for the four quarters prior and twelve quarters subsequent to the ban, even though the sample period used in the estimation is longer.

# **C Additional Empirical Findings**

## **C.A Robustness of Stylized Facts**

Figure A4: Dynamic Ban Effects on Imports: Fertilizer Only <!-- Start of picture text --> −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12<br>Month relative to period when treatment first changes (t=0) Month relative to period when treatment first changes (t=0)<br>(a) Extensive Margin, fertilizer only (b) Intensive Margin, fertilizer only<br>.6<br>.5 5<br>.4<br>.3<br>.2<br>0<br>.1<br>0<br>−.1<br>−.2<br>−5<br>Effect on Pr(imports>0) −.3 Effect on log(imports)<br>−.4<br>−.5<br>−.6<br>−10<br><!-- End of picture text --> _Notes_ : The figures show De Chaisemartin and d’Haultfoeuille (2022) estimates of the effects of import bans on the extensive and intensive margins of imports, relative to the last month before the ban takes effect, using an HS8 product-month level panel. The sample covers the January 2019September 2022 period (but only coefficients in January 2021-May 2022 are reported) and includes only fertilizer HS8 products. The treatment variable is a set of dummies _ban_<sup>_τ_</sup> _ct_<sup>indicating whether product</sup><sup>_c_was first banned</sup><sup>_τ_months before month</sup><sup>_t_, and the not-yet-treated products serve</sup> as the control group. The y-axis shows the effects of fertilizer import bans on the probability of nonzero imports (panel A4a) or on the log value of imports (panel A4b), where negative values correspond to a decrease in probabilities/values. The p-values of the joint significance tests for the placebo estimators are 0.846 (panel A4a) and 0.925 (panel A4b).
73 Figure A5: Dynamic Ban Effects on Import Quantities <!-- Start of picture text --> −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12<br>Month relative to period when treatment first changes (t=0) Month relative to period when treatment first changes (t=0)<br>(a) Quantity Effect (b) Quantity Effect, fertilizer only<br>5 10<br>5<br>0<br>0<br>−5<br>−5<br>Effect on log(quantity) Effect on log(quantity)<br>−10<br>−10<br>−15 −15<br><!-- End of picture text --> _Notes_ : The charts show De Chaisemartin and d’Haultfoeuille (2022) estimates of the effects of import bans on import quantities, relative to the last month before the ban takes effect, using an HS8 product-month level panel. The sample covers the January 2019-September 2022 period (but only coefficients in January 2021-May 2022 are reported) and excludes non-fertilizer HS8 products whose imports were ever banned. In panel A5b, the sample also excludes all non-fertilizer products, even the ones who were never banned. The treatment variable is a set of dummies _ban_<sup>_τ_</sup> _ct_<sup>indicating</sup> whether product _c_ was first banned _τ_ months before month _t_ , and the not-yet-treated products serve as the control group. The y-axis shows the effects of import bans on (the log of) the net weight of imports (measured in kg), where negative values correspond to quantity decreases. The p-values of the joint significance tests for the placebo estimators are 0.005 (panel A5a) and 0.93 (panel A5b).
74

# Figure A6: Dynamic Ban Effects: Deseasonalized Imports

<!-- Start of picture text --> −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12<br>Month relative to period when treatment first changes (t=0) Month relative to period when treatment first changes (t=0)<br>(a) Extensive Margin (b) Intensive Margin<br>−4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12<br>Month relative to period when treatment first changes (t=0) Month relative to period when treatment first changes (t=0)<br>(c) Extensive Margin, fertilizer only (d) Intensive Margin, fertilizer only<br>.4 4<br>.3 2<br>.2<br>.1 0<br>0 −2<br>−.1<br>−.2 −4<br>−.3 −6<br>Effect on Pr(imports>0) −.4 Effect on log(imports)<br>−.5 −8<br>−.6<br>−10<br>−.7<br>.6<br>6<br>.4<br>4<br>.2<br>2<br>0 0<br>−.2 −2<br>−4<br>Effect on Pr(imports>0) −.4 Effect on log(imports) −6<br>−.6<br>−8<br>−.8 −10<br><!-- End of picture text --> _Notes_ : The charts show De Chaisemartin and d’Haultfoeuille (2022) estimates of the effects of import bans on both the extensive and intensive margins of (deseasonalized) imports, relative to the last month before the ban takes effect, using an HS8 product-month level panel. The sample covers the January 2019-September 2022 period (but only coefficients in January 2021-May 2022 are reported) and excludes non-fertilizer HS8 products whose imports were ever banned. In panels A6c and A6d, the sample also excludes all non-fertilizer products, even the ones who were never banned. For each month of the year, we compute the (log of the) product’s historical average import value and the historical average probability of nonzero imports for that month in 2017-2019; then, for every product-month we subtract the relevant historical average from log import value and from the indicator of nonzero imports, thus obtaining deseasonalized versions of these two outcome variables. The treatment variable is a set of dummies _ban_<sup>_τ_</sup> _ct_<sup>indicating whether fertilizer product</sup><sup>_c_was first banned</sup><sup>_τ_months before month</sup><sup>_t_,and the not-yet-treated products serve as the</sup> control group. The y-axis shows the effects of import bans on the (deseasonalized) probability of nonzero imports (panels A6a and A6c) or on the (deseasonalized) log value of imports (panels A6b and A6d), where negative values correspond to decreases in probabilities/values. The p-values of the joint significance tests for the placebo estimators are 0.71 (panel A6a), 0.68 (panel A6b), 0.35 (panel A6c), and 0.85 (panel A6d).
75 Figure A7: Event Study: Imports and the Arrival of Covid-19 <!-- Start of picture text --> −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12<br>Month relative to period when treatment first changes (t=0) Month relative to period when treatment first changes (t=0)<br>(a) Extensive Margin (b) Intensive Margin<br>−4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12<br>Month relative to period when treatment first changes (t=0) Month relative to period when treatment first changes (t=0)<br>(c) Extensive Margin, fertilizer only (d) Intensive Margin, fertilizer only<br>6<br>.4<br>.3<br>.2 4<br>.1<br>0 2<br>−.1<br>Effect on Pr(imports>0) −.2 Effect on log(imports) 0<br>−.3<br>−.4 −2<br>.8<br>8<br>.6 7<br>6<br>.4 5<br>4<br>.2 3<br>2<br>Effect on Pr(imports>0) 0 Effect on log(imports) 1<br>0<br>−.2 −1<br>−2<br><!-- End of picture text --> _Notes_ : The charts show De Chaisemartin and d’Haultfoeuille (2022) estimates of the differential effects of the Covid-19 pandemic on both the extensive and intensive margins of fertilizer imports, relative to the last month before the start of Covid-19, using an HS8 product-month level panel. The sample covers the January 2019-April 2021 period (but only coefficients in November 2019-March 2021 are reported) and excludes non-fertilizer HS8 products whose imports were ever banned. In panels A7c and A7d, the sample also excludes all non-fertilizer products, even the ones who were never banned. The treatment variable is a dummy _covidct_ which equals one if period _t_ is later than February 2020 **and** product _c_ was banned in some period starting in May 2021. Never-banned products serve as the control group. The y-axis shows the differential effects of Covid-19 on the probability of nonzero imports (panels A7a and A7c) or on the log value of imports (panels A7b and A7d), where negative values correspond to decreases in probabilities/values. The p-values of the joint significance tests for the placebo estimators are 0.63 (panel A7a), 0.27 (panel A7b), 0.47 (panel A7c), and 0.36 (panel A7d).
76 Figure A8: Dynamic Ban Effects on Firms: Deseasonalized Agricultural Exports (High vs Low Fertilizer Intensity) <!-- Start of picture text --> −4 −3 −2 −1 0 1 2 3 4<br>Quarter relative to period when treatment first changes (t=0)<br>.3<br>.2<br>.1<br>0<br>−.1<br>−.2<br>−.3<br>−.4<br>−.5<br>Effect on log(exports)<br>−.6<br>−.7<br>−.8<br>−.9<br><!-- End of picture text --> _Notes_ : The chart shows De Chaisemartin and d’Haultfoeuille (2022) estimates of the effects of fertilizer import bans on the (deseasonalized) value of firms’ agricultural exports, relative to the last quarter before the ban takes effect, using a firm-level panel. The sample covers the Q1/2019-Q3/2022 period (but only coefficients in Q2/2020-Q2/2022 are reported) and includes all firms who exported at least one of 23 crops for which we have fertilizer intensity data in 2017-2019. We compute each firm’s fertilizer exposure as a weighted average of crops’ fertilizer intensities with weights given by each crop’s share in the firm’s 2017-2019 exports. The treatment group consists of firms whose fertilizer exposure is above the sample’s 75th percentile. Firms below the 75th percentile serve as the control group. The treatment period is defined as the set of all quarters when any fertilizer import bans were in place. For each quarter of the year, we compute the (log of the) firm’s historical average export value for that quarter in 2017-2019; then, for every firm-quarter, we subtract that historical average from the (log) export value, thus obtaining a deseasonalized version of the outcome variable. The y-axis shows the effects of fertilizer import bans on the log value of agricultural exports, where negative values correspond to a decrease in exports. The p-value of the joint significance test for the placebo estimators is 0.196.

# **C.B Food’s Expenditure Share**

The fraction of the consumer’s income that is spent on agricultural goods is an important variable in our analysis. To illustrate how much this variable can vary, we use data from the 2019 edition of the HIES to display the empirical distribution of food expenditure shares across Sri Lankan households in Appendix Figure A9, which shows a wide dispersion.

Moreover, as detailed in Section V.C.2, we model consumer preferences as non-homothetic. The main motivation for this assumption is the marked negative relationship observed in the data between income and the food expenditure share. This can be seen in Appendix Figure A10, which plots household income against the food share of household expenditures, showing a strong and clear negative correlation between the two variables. The two variables plotted in Appendix Figure A10 are “residualized” versions, i.e. deviations from the (district-level) average.
77 Figure A9: Distribution of Food Expenditure Shares <!-- Start of picture text --> 0 .2 .4 .6 .8 1<br>Food’s share in household expenditures<br>2<br>1.5<br>1<br>Density<br>.5<br>0<br><!-- End of picture text --> _Notes_ : The figure shows kernel density estimates for the share of total household expenditure that is spent on food. A unit of observation is a household. The data comes from the 2019 edition of the HIES. The density is estimated using an Epanechnikov kernel with optimal bandwidth (0.0213) and household-specific statistical weights provided by the HIES.

Figure A10: Association Between Food Share and Income <!-- Start of picture text --> −4 −2 0 2 4<br>Log of household income (residualized)<br>.5<br>0<br>(residualized)<br>Food’s share in household expenditure<br>−.5<br><!-- End of picture text --> _Notes_ : The figure plots a residualized version of the log of household income against a residualized version of the share of total household expenditure that is spent on food. A unit of observation is a household. The data comes from the 2019 edition of the HIES. The residualized version of each variable is obtained by extracting the residual from a regression of that variable on a set of district dummy variables, with the regression estimated by Weighted Least Squares (WLS) using the statistical weights provided by the HIES. A red regression line is overlaid on the graph representing the regression (also estimated by WLS) of residualized food share on residualized log household income.
<!-- Start of picture text --> 2.5 1.6<br>x<br>v<br>3 2 ir 1.4 a<br>= ne]<br>g See 2s<br>2= 15 - “ 8ro<br>-_<br>2 SSS OOo os<br>% YS -e? g<br>5a° 0.5 0.8 =z<br>0 0.6<br>a a a a ci Sal a a a ci a ca N N N N N N<br>vq gqgaqgaqgqgqgqgagagqggragagsgesg |<br>SESeSs2STFSSESREREEES<br>—Rice — Maize ——Potato —— Cloves<br>—— Onion —Groundnuts=—= -Average<br><!-- End of picture text -->
79 Figure A12: Distribution of Landholding Sizes <!-- Start of picture text --> −6 −4 −2 0 2 4 −5 0 5<br>Log of landholding size (in ha) Log of landholding size (in ha), residualized<br>(a) Unadjusted (b) Adjusted for Region<br>.4 .4<br>.3 .3<br>.2 .2<br>Density Density<br>.1 .1<br>0 0<br><!-- End of picture text --> _Notes_ : The figures show kernel density estimates for (the log of) the size of households’ landholdings (measured in ha). A unit of observation is a household. The data comes from the 2016 edition of the HIES. Panel A12a shows unadjusted estimates. Panel A12b shows estimates for a residualized version of the log landholding size variable which is obtained by extracting the residual from a regression of that variable on a set of district dummy variables, with the regression estimated by Weighted Least Squares (WLS) using the statistical weights provided by the HIES. Densities are estimated using Epanechnikov kernels with optimal bandwidth (0.2021 in Panel A12a and 0.1647 in Panel A12b) and statistical weights.

sample. We then estimate the dispersion parameter _σLn_<sup>2for district</sup><sup>_n_as:</sup> where _|_ S _n| ≡_<sup>�</sup> _h_<sup>_′_</sup> _∈n_<sup>1 is the number of surveyed households in district</sup><sup>_n_that own land.</sup>

Given estimates _σ_ ˆ _Ln_<sup>2ofthedispersionparameters,wecanthenestimatethescaleparameters</sup> _μn_ so as to match the average landholding size in each district. Specifically, the properties of the log-normal distribution imply that the average landholding size in district _n_ is exp( _μn_ + _σLn_<sup>2</sup><sup>_/_2), so</sup> we set the empirical analogue of this expression equal to the average landholding size observed in the data and rearrange terms to obtain our estimator of _μn_ : where _Ln_ is total arable land (in ha) and _Nn_<sup>_F_is the number of farmers in district</sup><sup>_n_.</sup>

# **C.D Evolution of Rice and Tea Agriculture over Time**

We combine cutting-edge remote sensing data (described in Appendix A.C.2) with detailed weather data (described in Appendix A.J) to show the evolution of yields of rice and tea (and, for rice, of cultivated area) over time.
80 For rice, we estimate the following regression for each of the two growing seasons (Maha and Yala): where _s_ indexes seasons, _d_ indexes DSs, _y_ indexes years, _A_<sup>_s_</sup> _dy_<sup>isthecultivatedriceareainDS</sup> _d_ during season _s_ of year _y_ , _θy_<sup>_s_(resp.</sup><sup>_ω_</sup> _d_<sup>_s_)isasetofyear(resp.DS)fixedeffects,</sup><sup>**W**</sup> **dy**<sup>**s**isa</sup> vector of weather variables, and _ε_<sup>_s_</sup> _dy_<sup>is an error term.We estimate equation (44) by Ordinary Least</sup> Squares with standard errors clustered at the DS level. The vector of weather variables includes: rainfall, number of rainy days, dry spells, solar radiation, VPD, average minimum and maximum temperatures. We then repeat the process substituting cultivated area for yields as the dependent variable. The results are shown in Appendix Figure A13.

Figure A13: Rice Yields and Cultivated Area, by year <!-- Start of picture text --> Rice yield (in kg/ha) Log of cultivated rice area (in ha)<br>2001<br>2002<br>2003<br>2004<br>2005<br>2006<br>2007<br>2008<br>2009<br>2010<br>2011<br>2012<br>2013<br>2014<br>2015<br>2016<br>2017<br>2018<br>2019<br>2020<br>2021<br>2022<br>−1000 0 1000 2000 −.5 0 .5 1<br>Maha Yala<br><!-- End of picture text --> _Notes_ : The figure plots coefficients and 95% confidence intervals from four panel regressions at the DS-year level in which we regress rice yields (left panel) and the log of cultivated rice area (right panel) on a set of year dummies and DS fixed effects. Regressions are run separately for the Maha season (diamonds) and the Yala season (circles). Yields are measured in kg/ha, and area is measured in ha. Standard errors are clustered at the DS level. All regressions control for the following season- and DS-specific weather variables: rainfall (in mm/season), number of rainy days, dry spells, solar radiation (in W/m2), VPD (in hectopascals), and average minimum and maximum temperatures (in degrees Celsius).

Since we control for weather and DS fixed effects, the year coefficients displayed in Appendix
81 Figure A13 can be interpreted as the portion of the year’s deviation from the historical average that cannot be explained by abnormal weather. Rice yields in the 2022 Maha season (the first growing season after the fertilizer import ban) were 948 kg/ha below the baseline year (2000), with the null hypothesis of zero deviation from baseline being strongly rejected at conventional significance levels. A 948 kg/ha decrease in rice yields corresponds to a 26.9% decrease from the 2000 baseline, or to a 24.4% decrease from the the average yield of the 2000-2021 period. In short, the first rice growing season after the ban was, by far, the least productive in at least 20 years.

In contrast, in the cultivated area regression, the 2022 Maha coefficient is positive. Therefore, we have no evidence of a reduction in cultivated rice area after the ban. This is consistent with our model’s assumption that land cannot be reallocated across crops, which is expected given the short time horizon under study. Moreover, the combination of this finding with the dramatic yield declines in the same season supports our hypothesis that the fertilizer ban had a major negative impact on Sri Lankan rice agriculture.

For tea, we estimate a similar regression as for rice, but pooling Maha and Yala yields together into a single observation per DS-year: where _d_ indexes DSs, _y_ indexes years, _Ydy_ is the tea yield in DS _d_ in year _y_ , _θy_ (resp. _ωd_ ) is a set of year (resp. DS) fixed effects, **Wdy**<sup>**yala**</sup> (resp. **Wdy**<sup>**maha**</sup> ) is a vector of weather variables in DS _d_ during the Yala (resp. Maha) season of year _y_ , and _εdy_ is an error term. Equation (45) is estimated by Weighted Least Squares (WLS) with standard errors clustered at the DS level. Since the precision of the remote sensing tea yield metric varies across regions, the regression is weighted by a DSspecific confidence index that reflects the degree of precision of the metric in each DS. Regression results are displayed in Appendix Figure A14.

As in the rice regression, the year coefficients in Appendix Figure A14 can be interpreted as the yield deviations from the historical baseline (i.e. year 2014) that cannot be explained by abnormal weather. Post-ban tea yields in 2022 were 428 kg/ha (or 26.8%) below the baseline year (2014), a difference that is strongly statistically significant and that corresponds to a 28.7% drop relative to the average yield of the 2014-2021 period. Therefore, controlling for weather fluctuations reveals that the first post-ban agricultural season had remarkably low yields not only for rice but also for tea.

# **C.E Relationship Between Land Inequality and Agricultural Expenditures**

Equation (14) in our model predicts a negative relationship at the regional level between aggregate agricultural expenditure ( _Xn_<sup>_A_) and land inequality (</sup><sup>_σ_</sup> _Ln_<sup>2) when holding aggregate income (</sup><sup>_En_) and</sup>
82 Figure A14: Tea Yields, by year <!-- Start of picture text --> 2015<br>2016<br>2017<br>2018<br>2019<br>2020<br>2021<br>2022<br>−600 −400 −200 0 200<br>Residual tea yield (kg/ha)<br><!-- End of picture text --> _Notes_ : The figure plots coefficients and 95% confidence intervals from a panel regression at the DS level in which we regress tea yields (measured in kg/ha) in each DS-year on a set of year dummies and DS fixed effects. The regression is estimated by Weighted Least Squares (WLS), with weights given by DS-specific confidence weights reflecting the degree of precision of the remote sensing tea yield metric (see Appendix A.C.2 for details), and standard errors clustered at the DS level. All regressions control for the following weather variables: rainfall (in mm/season), number of rainy days, dry spells, solar radiation (in W/m2), VPD (in hectopascals), average minimum and maximum temperatures (in degrees Celsius). These season- and DS-specific weather variables are included separately for the Yala and Maha seasons. See Appendix A.J for definitions of weather variables and further details.
83 other variables constant. That is, for a given level of total income, more unequal regions tend to spend a lower share of that income on agricultural goods. The intuition is that redistributing income away from poor farmers into the the hands of richer farmers moves money into the hands of consumers who spend a relatively lower share of this additional income on agriculture, due to non-homothetic preferences. This intuition is reinforced by the fact that the effect of inequality on agricultural expenditure disappears in the homothetic case ( _η_ = 1).

In this section, we test this prediction using 2019 HIES data. Specifically, we use data on landholdings and expenditures on various goods to construct district-level measures of aggregate food expenditures, aggregate total expenditures, and the variance of (the log of) landholding size as proxies for _Xn_<sup>_A_,</sup><sup>_En_,and</sup><sup>_σ_</sup> _Ln_<sup>2,respectively.Wethenregressthelogoffoodexpenditureson</sup> land inequality and the log of total expenditures. Results are displayed in Appendix Table A6. The coefficient on log total expenditures is 0.893 in Column (1). A 10% increase in total expenditure is associated with an increase of only around 9% in our agricultural expenditure proxy, which is itself indicative of non-homothetic preferences as it implies that agriculture’s expenditure _share_ declines with income. More importantly for us, the coefficient on the land inequality proxy is -0.0035, pointing to a negative association between inequality and agricultural expenditure, as predicted by equation (14). Column (2) repeats the estimation strategy of Column (1) but uses an adjusted version of the dependent variable that maps more closely to the theoretical constructs in equation (14), with very similar results.<sup>111</sup> Table A6: District-Level Food Expenditure and Land Inequality

||**Depende**<br>Logof food|**nt variable:**<br>expenditures|
|---|---|---|
||(1)|(2)|
|Land inequality (ˆ_σ_<sup>2</sup><br>_Ln_<sup>)</sup>|-0.0035<br>(0.0040)|-0.0036<br>(0.0041)|
|Log of total expenditures (ln(_En_))|0.893<sup>_∗∗∗_</sup><br>(0.0259)|0.890<sup>_∗∗∗_</sup><br>(0.0265)|
|Constant|1.700<sup>_∗∗∗_</sup><br>(0.6305)|1.745<sup>_∗∗_</sup><br>(0.6469)|
|Adjustedln(_X_<sup>_A_</sup><br>_n_ <sup>)?</sup>|NO|YES|
|Observations|25|25|

_Notes_ :<sup>_∗∗∗_</sup> denotes significance at the 1% level,<sup>_∗∗_</sup> at the 5% level. The table shows results of district-level regressions relating aggregate food expenditures to land inequality and aggregate total expenditures. Regressions are estimated by Ordinary Least Squares (OLS) using data from the 2019 edition of the HIES. Land inequality in each district is defined as the variance of the log of landholding size across its landholders. Standard Errors are shown in parentheses. Column (2) uses an adjusted version of the dependent variable that maps more closely to the theoretical constructs inˆ equation (14), namely ln( _Xn_<sup>_A−φE_ˆ</sup><sup>_n_),where</sup><sup>_X_</sup> _n_<sup>_A_isaggregatefoodexpendituresand</sup><sup>_En_isaggregatetotalexpendituresindistrict</sup><sup>_n_,and</sup> _φ_ = 0 _._ 0105.

> 111Specifically, in Column (2) the dependent variable is not ln( _XnA_<sup>) but ln(</sup><sup>_X_</sup> _n_<sup>_A−φE_ˆ</sup><sup>_n_), with</sup><sup>_φ_ˆ = 0</sup><sup>_._0105 being our</sup> estimate of _φ_ as displayed on Table II and explained in Section VI.A.1.
84 Figure A15: Dynamic Ban Effects on Districts’ Night Lights (High versus Low Fertilizer Importance) <!-- Start of picture text --> −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12<br>Month relative to period when treatment first changes (t=0)<br>.4<br>.2<br>0<br>−.2<br>Effect on log(night lights)<br>−.4<br>−.6<br><!-- End of picture text --> _Notes_ : The figure shows De Chaisemartin and d’Haultfoeuille (2022) estimates of the effect of the fertilizer import ban on night light intensity, relative to the last month before the ban takes effect, using a district-level panel. The outcome variable is the log of the average night light intensity across the district’s cells in a given month. We compute each district’s baseline fertilizer importance index as the ratio of the value of fertilizer inputs (gross of subsidies) used in its agricultural sector to the district’s aggregate income in our estimated baseline model. The treatment variable is a dummy which takes the value of one from May 2021 onwards for districts above the median of the index. Below-median districts serve as the control group. The y-axis shows the effects of the fertilizer import ban on the log of average night light intensity, where negative values correspond to decreases in night lights.
85

# **D Estimation Details**

## **D.A Preference Parameters**

**Engel Elasticity.** To estimate the Engel elasticity ( _η_ ), we start from model equation (13). Rearranging, taking logs, and adding household ( _h_ ) subscripts, we obtain the following equation:

We then collect relevant terms into a region fixed effect and add a household size control variable and an error term, obtaining equation (31).<sup>112</sup> As explained in Section VI.A.1, equation (31) is estimated using Two-Stage Least Squares (2SLS) with two IVs: income obtained from lottery (and other _ad hoc_ gains) and income obtained from disasters and other relief payments. We use Weighted 2SLS estimation, weighing observations with the sampling weights available in the HIES data, and with standard errors clustered at the Primary Sampling Unit level. Complete estimation results can be seen in Column (1) of Appendix Table A7, including the estimated coefficients, standard errors, and first-stage results.

**Cross-crop Elasticity of Substitution.** To estimate _σA_ , we first take logs of equation (17) and add household ( _h_ ) subscripts, obtaining:

We then collect relevant terms into crop- and household-specific fixed effects.<sup>113</sup> Finally, we add an error term to obtain equation (32), which is then estimated using Weighted 2SLS with standard errors clustered at the household level, with crop price ln( _Pnhk_ ) instrumented by a dummy variable _Dnk_<sup>_GAEZ_</sup> that indicates whether region _n_ has any growing potential for crop _k_ (according to the FAO-GAEZ data). The crops included in the estimation sample are: rice, maize, groundnut, onion, potato, coconut, and tea. See Column (2) of Appendix Table A7 for the complete estimation results. **Cross-origin Elasticity of Substitution.** As explained in the text, _σK_ is set so that the average increase in agricultural producer prices generated by the model-driven counterfactual exercise of Section VII.A matches the corresponding increase that is observed in the data. Formally, for each candidate value _sK_ for parameter _σK_ , we compute the corresponding counterfactual average price increase _p_ ̄<sup>ˆ</sup><sup>_cf_</sup> ( _sK_ ) as follows: 112 Region-specific fixed effects are defined as: _ωn ≡_ ln( _ν_ ) + _ηφ_ ln( _P An_<sup>) + (1</sup><sup>_−η_)</sup><sup>_φ_ln(</sup><sup>_P M_</sup> _n_<sup>).</sup> 113 Crop- and household-specific fixed effects are defined respectively as: _ωk ≡_ ln( _bk_ ) and _ωh ≡_ ( _σA −_ 1) ln( _P Anh_<sup>).</sup>
86 Table A7: Estimates of Preference Parameters (2SLS)

||**Panel A: Se**|**cond Stage**|
|---|---|---|
||Dependen|t variable:|
||Log of food’s<br>expenditure share|Log of crop’s<br>expenditure share|
||(1)|(2)|
|Log of household income [ˆ_η_]|-0.656***<br>(0.129)||
|Log of crop price [1_−_ˆ_σA_]||-0.714***<br>(0.153)|
|Household size|0.135***<br>(0.029)||
||**Panel B: F**|**irst Stage**|
||Dependen|t variable:|
||Log of household<br>income<br>(1)|Log of crop<br>price<br>(2)|
|Lottery/_ad hoc_income|8.81e-07***<br>(1.37e-07)||
|Disaster/other relief payments|8.16e-07***<br>(1.42e-07)||
|Regional potential yield_>_0||-0.062***<br>(0.0044)|
|F-statistic|37.2***|199.4***|
|p-value|0.0000|0.0000|
|Fixed Effects?|PSU|Crop, HH|
|Clustered SEs?|by PSU|by HH|
|Weighted?|Yes|Yes|
|Observations|19,910|91,416|

_Notes_ : *** denotes significance at the 1% level. Columns (1) and (2) display results for the estimation of equations (31) and (32), respectively, by Weighted Two-Stage Least Squares (2SLS), with standard errors in parentheses. PSU stands for “Primary Sampling Unit”, and HH stands for “household”. Weighted regressions use the statistical weights provided by the 2019 edition of the HIES. In Column (1), the dependent variable in the second stage is the log of the _adjusted_ food expenditure share, which is computed as ln( _ξnh_<sup>_A−φ_ˆ) for household</sup><sup>_h_of district</sup><sup>_n_,where</sup><sup>_ξA_is</sup> food expenditure share and _φ_<sup>ˆ</sup> = 0 _._ 0105 is our estimate of parameter _φ_ (see Table II). See Section VI.A.1 for details on data sources, identification strategies, and variables’ definitions.
87 where _pik_ and _Qik_ are baseline producer prices and quantities of crop _k_ in district _i_ , _Nk_ is the number of Sri Lankan districts with nonzero production of crop _k_ , _K_ is the set of crops for which data on price increases is available, and _p_<sup>_cf_</sup> _ik_<sup>(</sup><sup>_sK_)isthecounterfactualproducerpriceofcrop</sup><sup>_k_in</sup> district _i_ assuming _σK_ = _sK_ . The crops for which price increase data is available are: rice, maize, potatoes, cloves, onions and groundnuts.

We test several possible candidate values _sK_ , ultimately choosing the value _s_<sup>_∗_</sup> _K_<sup>=2</sup><sup>_._377that</sup> generates a counterfactual average price increase of _p_ ̄<sup>ˆ</sup><sup>_cf_</sup> ( _s_<sup>_∗_</sup> _K_<sup>) = 1</sup><sup>_._2265, which matches the 22.65%</sup> increase observed in the data between January 2021 and January 2022 (shown in Appendix Figure A11). Specifically, our average crop price increase calculation is done in three steps: (i) computing the nominal price increase of each crop in _K_ between January 2021 and January 2022; (ii) deflating these nominal increases using the period’s cumulative inflation (17.61%) to obtain real price increases; and (iii) computing the average crop price increase as a weighted average of crop-level real price increases, with each crop’s weight given by its revenue share at baseline (as in equation 46). We set _σ_ ˆ _K_ = 2 _._ 377 as our estimate for the elasticity of substitution across origins of the same crop.

# **D.B Trade Costs**

In Section VI.A.2, we estimate the parameters ( _α_ , _{βk}k_ ) that govern trade costs according to equation (34). To estimate semi-elasticity _α_ , we use two key pieces of information: first, the tea transportation cost _pT,_ 100 is 1,496 LKR/MT for a distance of 100 km (according to the Ceylon Petroleum Corporation); second, the price of tea _ptea_ is 455,473 LKR/MT (according to the DCS). The tea transportation cost is calculated based on the average distance from farms to tea brokers’ warehouses in the city of Wattala, assuming that the cargo is transported by a lorry with a capacity of 7,500 kg charging typical prices.<sup>114</sup> To compute domestic “factory-gate” tea prices ( _ptea_ ), the price of green leaf needed to produce one MT of made tea is added to processing costs (labour, fuel, electricity, machinery upkeep, packing materials, and factory sundries). The corresponding iceberg trade cost can be written as _τni,tea_<sup>_A_=1 +</sup><sup>_<u>p</u>_</sup> _p_<sup>_T_</sup> _tea_<sup>_<u>,</u>_100, which we substitute in equation (34) to obtain the</sup> following relationship: where _α_ ˆ is our estimate for the semi-elasticity _α_ . We solve this equation to obtain: _α_ ˆ = 3 _._ 3 _×_ 10<sup>_−_5</sup> . To estimate crop-specific international trade costs ( _{βk}k_ ), we use FAO data on each crop’s producer price in the RoW ( _pRoW,k_ ), in USD/kg, and data on each crop’s “benchmark price” at the

> 114 The data is available at: https://ceypetco.gov.lk/historical-prices/.
88 port of Colombo ( _pColombo,k_ ), in USD/MT (which we then convert to USD/kg).<sup>115</sup> Since data on port prices ( _pColombo,k_ ) is only available for five crops, we use equation (35) to compute _B_<sup>ˆ</sup> _k_ for each of these five crops, then impute the _B_<sup>ˆ</sup> _k_ of the other three crops (cinnamon, cloves, and groundnuts) with the average _B_<sup>ˆ</sup> _k_ among the five crops for which data is available.

## **D.C Production Function Parameters**

As explained in Section VI.A.3, we estimate Cobb-Douglas coefficients _γk_<sup>_f_by matching fertilizer</sup> cost shares (see equation 36). For that, we use data on national crop prices _p_<sup>_LKA_</sup> _k_ , national annual crop production _Q_<sup>_LKA_</sup> _k_ , and crop-level national annual fertilizer expenditure _Mk_<sup>_f,LKA_</sup> .

As shown in equation (37), we then apportion residual input shares to land and labor using data from IO tables on value added and labor compensation. To do that, we map our eight crops to the IO table’s agricultural sectors, which include “minor export crops”, “highland crops”, “tea growing” (separately for high, medium, and low elevations), “paddy”, and “potatoes” as sectors. We classify cinnamon and cloves as “minor export crops”, groundnuts, maize, and onions as “highland crops”, and rice as “paddy”. For tea, we aggregate high, medium, and low elevations into a single sector.

# **E Inversion Details**

In Section VI.B we describe our general approach to backing out unobserved exogenous variables (productivities, preference shifters, fertilizer endowments, and number of estate workers) by combining observed variables with the equilibrium structure of the model. In this section, we explain the details of this “inversion” procedure.

## **E.A Inversion Procedure**

It is possible to rewrite the market clearing equations (22, 25, 26, 27) of the model without QRs to obtain the following system of equations:<sup>116</sup> 115This data is from the Central Bank of Sri Lanka’s Economic and Social Statistics 2023. 116More specifically, to obtain the system of equations, substitute equation (20) and _p_<sup>_f_</sup> _i_<sup>=</sup><sup>_pf_</sup> _RoW_<sup>into fertilizer market</sup> clearing condition (22), substitute equations (7), (17), and (18) into crop market clearing condition (25), and substitute equations (16) and (19) into labor market clearing condition (26).
89 In these four equations, black variables are either directly observed or previously estimated in a prior stage, red variables are the key unobserved variables that the system solves for, and blue variables are “intermediary” variables in the sense that they are functions of black and red variables only.<sup>117</sup> We solve this system of equations numerically to recover all unobserved variables ( **_T_**<sup>_M_</sup> , **_b_** , **_F_** , **_N_**<sup>_e_</sup> , _t_ , **_p_**<sup>_−_</sup> , **_P_** , **_R_** , **_E_** , **_X_** , **_β_** ), and then recover agricultural productivities ( **_T_**<sup>_A_</sup> ) through equation (6), which links observed crop production to underlying productivity, crop prices, and input prices.<sup>118</sup> We should note that the equation system is homogeneous of degree zero in the preference _b_ shifters ( _rice_ = 3 _×_ **_b_** ). 2Therefore, normalizations are necessary.1 _σ_ ˆ _−AσK_ ˆ _−_ 1 . Naturally, these particular normalization choices do not affect the results in anyWe set _bRoW,k_ = 2 for each crop _k_ , as well as meaningful way.

# **E.B Data Requirements for Inversion**

To solve the system of equations in Appendix E.A, we must plug in the “black” observed variables, which include both previously estimated parameters and data from various sources. In that process, it is first necessary to make decisions concerning the basic geographic units of analysis, the set of crops, and the time period for which to run the inversion. We use Sri Lanka’s 25 districts (i.e. _I_ = 25), which are the country’s second-level administrative divisions, because that is the most granular level of aggregation for which we have data on important variables such as wages and producer prices. We use the eight crops (i.e. _K_ = 8) for which we have data on both fertilizer intensity and producer prices, namely: cinnamon, cloves, groundnut, maize, onions, potatoes, rice, and tea. We choose to use 2019 for inversion because it is prior to the 2021 fertilizer import ban (and to other potentially influential events such as the Covid-19 pandemic and Russia’s invasion of Ukraine) while also offering rich household survey data.

Preference parameters ( _σA_ , _σK_ , _σM_ ) are taken from Table II and production parameters ( _{γk_<sup>_f_,</sup>

> 117Blue variables can be recovered from black and red variables by using equations (5), (8), (14), (15), (17), (18), (19), and (21).

> 118Region-specific fertilizer endowments ( _{Fi}Ri_ =1<sup>)arerecoveredbyapportioningtheglobalfertilizerendowment</sup> ( _F_<sup>_G_</sup> ) across regions in two stages. First, total domestic fertilizer endowment (<sup>�</sup><sup>_I_</sup> _i_ =1<sup>_Fi_) is set to 3.5% of total domestic</sup> fertilizer use, with the remainder of the global fertilizer endowment being apportioned to the RoW (i.e., _FRoW_ = _F_<sup>_G_</sup> _−_<sup>�</sup><sup>_I_</sup> _i_ =1<sup>_Fi_).Thischoiceof3.5%forSriLanka’sendowment-to-useratioisbasedonFAOdataonfertilizer</sup> production and use by country and year. Second, the total domestic fertilizer endowment (<sup>�</sup><sup>_I_</sup> _i_ =1<sup>_Fi_)isdistributed</sup> across Sri Lankan districts ( _{Fi}_<sup>_I_</sup> _i_ =1<sup>) in proportion to each district’s number of mobile workers (i.e.,</sup><sup>_Fi_= (�</sup><sup>_I_</sup> _j_ =1<sup>_Fj_)</sup><sup>_×_</sup> _Ni_<sup>_m/_(�</sup><sup>_I_</sup> _j_ =1<sup>_N_</sup> _j_<sup>_m_)).</sup>
90 _γk_<sup>_n_,</sup><sup>_γ_</sup> _k_<sup>_l}k_) from Table III. Additionally, we use data on crop-specific fertilizer subsidy rates (</sup><sup>_{sk}k_)</sup> and crop-district-specific prices ( _{pik}i,k_ ), production ( _{Qik}i,k_ ), and cultivated area ( _{Lik}i,k_ ). And we use district-level annual wages ( _{wi_<sup>_m, w_</sup> _i_<sup>_e}i_), and numbers of mobile workers and farmers</sup> ( _{Ni_<sup>_m_,</sup><sup>_N F_</sup> _i_<sup>_}i_).Bilateral transportation costs (</sup><sup>_{τ A_</sup> _ni,k_<sup>_}n,i,k_,</sup><sup>_{τ M_</sup> _ni_<sup>_}n,i_) are computed using the coeffi-</sup> cients estimated in Section VI.A.2.

For the RoW, we use data on 2019 crop prices ( _{pRoW,k}k_ ), production ( _{QRoW,k}k_ ), and cultivated area ( _{LRoW,k}k_ ), as well as on the 2019 wage ( _wRoW_ ). We assume that the RoW has no estate workers ( _NRoW_<sup>_e_=0) and that its tea sector uses mobile workers instead, and we rely on the</sup> measures of the number of workers ( _NRoW_<sup>_m_) and farmers (</sup><sup>_N F_</sup> _RoW_<sup>) described in Appendix A.K. All</sup> monetary variables expressed in USD are converted into LKR using the 2019 exchange rate. The international price of fertilizer, _p_<sup>_f_</sup> _RoW_<sup>=0.31 USD/kg,from our trade data (see Appendix A.B), is</sup> converted to LKR using the 2019 exchange rate.<sup>119</sup>

# **F Equivalent Variation**

Since we are interested in the welfare effects of the fertilizer import ban, we use our estimated QSM of trade and agriculture to estimate such effects in Section VII. However, to do that we must first address some difficulties that emerge when using PIGL preferences. Careful inspection of equation (12) shows that indirect utility can be negative for some combinations of prices and income.<sup>120</sup> As a result, it is not straightforward to express utility as “real income” (i.e. nominal income divided by a price index), as it is often done for other classes of preferences such as CES. Therefore, we propose an alternative welfare metric to measure changes in welfare between any two equilibria, namely, the EV.

Suppose we are comparing a given initial equilibrium to a given final equilibrium. Starting from the initial equilibrium, the EV for a given agent is defined as the change in income that would leave that agent with the same level of utility as she has in the final equilibrium if prices were held constant at their initial levels. Formally, the EV for that hypothetical agent living in region _n_ is given by: where _v_ 1 is the agent’s utility in the final equilibrium, _y_ 0 is her income in the initial equilibrium, ( _Pn,_<sup>_A_</sup> 0<sup>_, P_</sup> _n,_<sup>_M_</sup> 0<sup>)arethepricesindicesintheinitialequilibrium,and</sup><sup>_V−_1istheinverseoftheindirect</sup> utility function (12) with respect to the income argument ( _y_ ).<sup>121</sup> This formula shows that the EV

> 119See Appendix A for more details on the data that is mentioned in this section.

> 120 For example, if _ν >_ 0 and _P A > P M_ , then utility will be negative for a sufficiently small level of income _y_ .

> 121Simple algebraic manipulation shows that the inverse of the indirect utility function (with respect to the income <u>1 1</u> argument _y_ ) is: _V_<sup>_−_1</sup> ( _v_ ; _P_<sup>_A_</sup> _, P_<sup>_M_</sup> ) = _η η_ ( _v_ + _ν_ ln( _P_<sup>_A_</sup> _/P_<sup>_M_</sup> )) _η_ ( _P_<sup>_A_</sup> )<sup>_φ_</sup> ( _P_<sup>_M_</sup> )<sup>1</sup><sup>_−φ_</sup> . For definitions of the agricultural and
91 depends not only on regional prices, but also on the agent’s initial income level _y_ 0 and her final utility level _v_ 1, both of which differ between workers and farmers of the same district and across farmers with different landholding sizes.

Thus, to assess the welfare changes faced by different agents, we define multiple types of agents in each district _n_ for which we separately compute welfare effects in Section VII. For each type and district, the EV between the initial equilibrium (indexed by a 0 subscript) and the final equilibrium (indexed by a 1 subscript) is obtained from equation (48) by choosing the appropriate final utility ( _v_ 1) and initial income ( _y_ 0):<sup>122</sup>

1. **Worker** : all mobile workers in district _n_ are identical and earn the same (net-of-tax) wage (1 _− t_ ) _wn_<sup>_m_.Their EV is obtained by substituting</sup><sup>_v_1=</sup><sup>_V_</sup> _n,_<sup>_m_</sup> 1<sup>and</sup><sup>_y_0= (1</sup><sup>_−t_)</sup><sup>_w_</sup> _n,_<sup>_m_</sup> 0<sup>in equation</sup> (48): _EVn_<sup>_m_=</sup><sup>_V−_1(</sup><sup>_V_</sup> _n,_<sup>_m_</sup> 1<sup>;</sup><sup>_P A_</sup> _n,_ 0<sup>_, P_</sup> _n,_<sup>_M_</sup> 0<sup>)</sup><sup>_−_(1</sup><sup>_−t_0)</sup><sup>_w_</sup> _n,_<sup>_m_</sup> 0

The same considerations apply to tea estate workers, whose EV can be written as: 2. **Median farmer** : defined as the farmer with a landholding size equal to the median landholding size in district _n_ , which is exp( _μn_ ) due to the log-normality of the land distribution (see Section V.C.1). Her initial disposable income level is thus _y_ 0 = exp( _μn_ )(1 _− t_ 0) _Rn,_ 0 _/Li_ , and her final utility _v_ 1 is obtained by evaluating indirect utility function (12) at final disposable income _y_ 1 = exp( _μn_ )(1 _− t_ 1) _Rn,_ 1 _/Li_ and final prices ( _Pn,_<sup>_A_</sup> 1<sup>,</sup><sup>_P M_</sup> _n,_ 1<sup>).Her EV can thus be</sup> expressed as: 3. **Average farmer** : defined as the farmer with a landholding size equal to the average landholding size in district _n_ , which is exp( _μn_ + _σLn_<sup>2</sup><sup>_/_2)duetothelog-normalityoftheland</sup> distribution (see Section V.C.1). Similarly to the median farmer, it can be shown the average farmer’s EV is:

> manufacturing price indices ( _Pn,_<sup>_A_</sup> 0<sup>,</sup><sup>_P M_</sup> _n,_ 0<sup>), see Sections V.C.3 and V.C.4.</sup>

> 122Some EV expressions also use welfare variables ( _Vnm_<sup>,</sup><sup>_V_</sup> _n_<sup>_e_,</sup><sup>_V_</sup> _n_<sup>_F_,</sup><sup>_V_</sup> _n_<sup>_avg_</sup> ) as inputs. For the definitions of these variables, see Section V.F.
92 4. **Representative farmer:** defined as the farmer whose utility level is equal to _Vn_<sup>_F_,thedis-</sup> trict’s average farmer utility. Her EV can be obtained by substituting _v_ 1 = _Vn_<sup>_F_and</sup><sup>_y_0=</sup> _V_<sup>_−_1</sup> ( _Vn,_<sup>_F_</sup> 0<sup>;</sup><sup>_P A_</sup> _n,_ 0<sup>_, P_</sup> _n,_<sup>_M_</sup> 0<sup>) in equation (48):</sup> When reporting welfare effects in Section VII, we use the relative version (in %) of the EV to make relative welfare losses more comparable across regions and agent types. This relative EV (denoted _EV_ ̃ ) can be computed by dividing the EV by the corresponding initial income level: ̃ _EV_ =<sup>_<u>EV</u>_</sup> _y_ 0<sup>.</sup> Finally, for each district _n_ , we define the average (relative) EV across agent types as follows: ̃ _avg_ The variable _EV n_ is a weighted average of (relative) EV across agent types, with weights given by each type’s share of the population’s district. It is the main metric we use in our counterfactual exercises to measure changes in the average welfare of each district. By weighting typespecific relative EVs by types’ population shares, this metric comes as close to capturing the concept of real income loss faced by a district’s “typical” inhabitant as is possible in the context of a model with non-homothetic preferences and multiple types of (possibly heterogeneous) agents.

Note that equation (49) does not include any terms related to middlemen because, as we mentioned in Section V.A, their population is assumed to have measure zero. This assumption is empirically supported by the very low number of fertilizer suppliers in Sri Lanka.<sup>123</sup> Furthermore, in our model the middleman is both the richest agent type and the one who obtains an outsize financial gain from the ban (by construction, as middlemen own the domestic fertilizer endowment). Therefore, excluding middlemen from our welfare change metric makes it more representative of the overall population (as opposed to the super rich) and avoids the potential distortions that could be caused by including outliers.

> 123In 2022, the NFS listed 17 “fertilizer distributors” in Sri Lanka. It also lists six “local agents of international fertilizer suppliers”. Our Panjiva import data (see Sections III and A.B) shows that 310 firms imported fertilizer (defined as any product listed in Chapter 31 of the HS system) into the country at some point between January 2016 and October 2022. Finally, the NFS lists of fertilizer importers include 629 unique firm names. Using the highest of these numbers (i.e. 629), we obtain an average of 25.16 fertilizer suppliers per district, which is within the range that we examine in the robustness exercise described in footnote 73.
93

# **G Proofs**

## **G.A Aggregate Agricultural Expenditure**

In Section V.C.2, we claim that agricultural expenditure share in region _n_ is given by equation (14): where _Pn_<sup>_A_and</sup><sup>_P M_</sup> _n_ are sectoral price indices, _rn ≡ NRnn_<sup>_F_istheaveragelandrentearnedbythe</sup> region’s farmers, _t_ is the income tax rate, and _En_ is aggregate income.

To derive this equation, we first separately derive aggregate agricultural expenditure by middlemen ( _Xn_<sup>_A,C_</sup> ), by workers ( _Xn_<sup>_A,W_</sup> ), and by farmers ( _Xn_<sup>_A,F_</sup> ), then add them up. Aggregate expenditure by middlemen is simply given by multiplying their total disposable income by _φ_ , the asymptotic agricultural share of expenditure: Aggregate expenditure by workers ( _Xn_<sup>_A,W_</sup> ) is given by multiplying the numbers of mobile and estate workers ( _Nn_<sup>_m_and</sup><sup>_N e_</sup> _n_<sup>),earningsperworker(i.e.wages</sup><sup>_w_</sup> _n_<sup>_m_and</sup><sup>_w_</sup> _n_<sup>_e_),thenet-of-taxrate</sup> (1 _− t_ ), and the fraction of income spent on agricultural goods (given by equation 13 with income _y_ evaluated at the relevant net-of-tax wages): For an individual farmer _h_ who lives in region _n_ and earns land rent _R_<sup>_h_</sup> , expenditure on agriculture is (1 _− t_ ) _R_<sup>_h_</sup> _ξ_<sup>_A_</sup> ((1 _− t_ ) _R_<sup>_h_</sup> _, Pn_<sup>_A, P_</sup> _n_<sup>_M_),theproductofhernet-of-taxincome</sup><sup>_Rh_andher</sup> agricultural expenditure share (see equation 13). Substituting equation (13) and taking the expectation operator across the region’s farmers, the average agricultural expenditure per farmer ( _X_<sup> ̄</sup> _n_<sup>_A,F_</sup> ) can be written as: From equation (11), land rent _R_<sup>_h_</sup> has a log-normal distribution. Therefore, the expectation E[( _R_<sup>_h_</sup> )<sup>1</sup><sup>_−η_</sup> ] can be obtained by using the distribution’s properties. Specifically, a power of a log-
94 normal variable is also log-normal: for any constant _a_ = 0. Evaluating equation (53) with _a_ = 1 _− η_ and using the relationship between the parameters of a log-normal distribution and its average, we conclude that:<sup>124</sup> By using the properties of the exponential and rearranging terms, this expression can be rewritten as follows:<sup>125</sup> It turns out that exp( _μn_ + _σLn_<sup>2</sup><sup>_/_2) is the average landholding size in region</sup><sup>_n_,which can also</sup> be written as _<u>Ln</u>_<sup>Usingthisfact,cancellingterms,andapplyingthedefinitionof</sup><sup>_rn_,wecan</sup> _Nn_<sup>_F_.126</sup> rewrite the previous equation as follows: Substituting (54) into equation (52) and multiplying _X_<sup> ̄</sup> _n_<sup>_A,F_</sup> by the number of farmers ( _Nn_<sup>_F_), we</sup> obtain the total agricultural expenditure by farmers of region _n_ : Total agricultural expenditure _Xn_<sup>_A_in region</sup><sup>_n_is obtained by summing the agro expenditures of</sup> middlemen, farmers, and workers: Using equations (50), (55), and (51) to substitute for _Xn_<sup>_A,C_</sup> , _Xn_<sup>_A,F_</sup> , and _Xn_<sup>_A,W_</sup> , rearranging terms, and noting that _Rn_ = _rnNn_<sup>_F_and</sup><sup>_En_=</sup><sup>_N m_</sup> _n_<sup>_w_</sup> _n_<sup>_m_+</sup><sup>_N e_</sup> _n_<sup>_w_</sup> _n_<sup>_e_+</sup><sup>_Rn_+</sup><sup>_pf_</sup> _n_<sup>_Fn_+</sup><sup>_QR_</sup> _i_<sup>_rent_</sup> (see equation 15), we obtain equation (14).

> 124 2 Namely, we use that fact that the average of any random variable that is distributed log-N( _m, n_ ) is equal to exp( _m_ + _n_<sup>2</sup> _/_ 2).

> 125 _n_ Namely, we use the properties that exp( _m_ + _n_ ) = exp( _m × n_ ) and (exp( _m_ )) = exp( _mn_ ), for any real numbers _m_ and _n_ .

> 126This comes from the fact that landholding size follows a log-normal distribution with parameters _μn_ and _σLn_ 2<sup>, as</sup> described in Section V.C.1.
95

# **G.B Average Farmer Welfare**

In Section V.F, we claim that average farmer welfare in region _i_ is given by equation (30): To prove this equation, consider that the indirect utility of an individual farmer _h_ who lives in region _i_ , earns land rent _R_<sup>_h_</sup> , and pays a tax rate _t_ is given by _V_ ((1 _− t_ ) _R_<sup>_h_</sup> _, Pi_<sup>_A, P_</sup> _i_<sup>_M_).Using</sup> equation (12), taking the expectation operation across farmers, and noting that _Pi_<sup>_A_and</sup><sup>_P M_</sup> _i_ are the same for all the farmers in the region, average farmer indirect utility can be written as: So our remaining task is to find an expression for E[( _R_<sup>_h_</sup> )<sup>_η_</sup> ]. From equation (53) with _a_ = _η_ , we know that random variable ( _R_<sup>_h_</sup> )<sup>_η_</sup> has a log-normal distribution with parameters _η_ ( _μn_ + ln( _Rn_ ) _−_ ln( _Ln_ )) and _η_<sup>2</sup> _σLn_<sup>2.Usingtherelationshipbetweenthelog-normal’sparametersanditsaverage,</sup> we then conclude that: Substituting this expression into equation (56), substituting exp( _η_ ln(1 _− t_ )) for (1 _− t_ )<sup>_η_</sup> , and rearranging, we obtain equation (30).
96 Table A8: Regional Ban Effects

||**Wo**|**rker**||**Farme**|**r**|**Average**|
|---|---|---|---|---|---|---|
|**District**|Mobile|Estate|Median|Average|Representative||
|Ampara|-2.89%|.|-22.38%|-22.38%|-22.38%|-8.47%|
|Anuradhapura|-2.93%|.|-23.08%|-23.08%|-23.08%|-13.69%|
|Baddulla|+0.68%|-16.58%|-22.48%|-22.47%|-22.47%|-11.57%|
|Batticaloa|-0.37%|.|-22.67%|-22.67%|-22.67%|-5.19%|
|Colombo|+2.55%|-16.58%|-20.41%|-20.32%|-20.35%|-0.74%|
|Galle|+2.19%|-16.58%|-9.38%|-9.37%|-9.37%|-1.31%|
|Gampaha|+2.51%|.|-21.96%|-21.94%|-21.94%|-1.34%|
|Hambantota|-0.85%|.|-19.76%|-19.76%|-19.76%|-8.45%|
|Jaffna|+2.18%|.|-19.51%|-19.50%|-19.50%|-4.05%|
|Kaluthara|+2.37%|-16.58%|-16.69%|-16.67%|-16.68%|-1.20%|
|Kandy|+2.30%|-16.58%|-15.72%|-15.70%|-15.71%|-2.98%|
|Kegalle|+2.30%|-16.58%|-16.91%|-16.89%|-16.90%|-3.57%|
|Killinochchi|-6.09%|.|-20.74%|-20.74%|-20.74%|-10.80%|
|Kurunagala|+0.53%|.|-22.78%|-22.78%|-22.78%|-9.90%|
|Mannar|-4.51%|.|-21.02%|-21.02%|-21.02%|-9.40%|
|Matale|+0.93%|-16.58%|-21.22%|-21.21%|-21.21%|-8.03%|
|Matara|+1.94%|-16.58%|-10.29%|-10.28%|-10.28%|-1.89%|
|Monaragala|-2.89%|.|-23.34%|-23.33%|-23.33%|-13.96%|
|Mullaittivu|-11.62%|.|-17.74%|-17.74%|-17.74%|-14.60%|
|Nuwareliya|+1.91%|-16.58%|-20.09%|-20.08%|-20.08%|-10.35%|
|Polannaruwa|-8.51%|.|-20.02%|-20.02%|-20.02%|-14.30%|
|Puttalam|+1.71%|.|-20.87%|-20.86%|-20.86%|-5.11%|
|Rattnapura|+2.07%|-16.58%|-14.46%|-14.45%|-14.45%|-4.12%|
|Trincomalee|-1.88%|.|-22.33%|-22.33%|-22.33%|-8.18%|
|Vavuniya|-0.32%|.|-22.15%|-22.15%|-22.15%|-10.17%|
|**Average**|-0.67%|-16.58%|-19.52%|-19.51%|-19.51%|-7.33%|

_Notes_ : for each district, the table shows the % welfare changes of five types of agents between the baseline equilibrium with no QRs and the counterfactual equilibrium with QRs. The median (resp. average) farmer is defined as a farmer whose landholding size is equal to the median (resp. average) of her district. The representative farmer of district _i_ is defined as a farmer whose utility is equal to the district’s average farmer utility ( _Vi_<sup>_F_). Welfare changes are defined as EVs: starting from the agent’s baseline (net-of-taxes) income, the EV is the % change in (net-of-taxes) income</sup> that would leave her with the same utility level as she has in the counterfactual equilibrium, keeping prices fixed at baseline levels. The table also displays each district’s average welfare change, which is computed as the weighted average of types’ EVs, with weights given by types’ population shares in the district.
97

# **H Frictions to Worker Intersectoral Mobility**

Our main model assumes that mobile workers can costlessly move across different sectors of employment. There may be some concern that our results are being driven by this potentially unrealistic assumption. In particular, estimated welfare effects could be more negative for mobile workers if our model recognized that some of them are stuck in agriculture due to mobility frictions, and are thus unable to move to manufacturing once the ban hits.

In this section, we show that the assumption of frictionless worker intersectoral mobility is not an important driver of our key results. To do that, we extend our main model to account for mobility frictions and then show that the model-predicted average welfare losses vary very little with the severity of these frictions.

## **H.A Model**

To account for frictions to worker intersectoral mobility, we propose a dynamic version of our model.<sup>127</sup> The main change is that, in each period, each mobile worker finds herself employed in a certain sector and must then choose whether she will stay in her current sector or move to the other sector in the next period.

We assume mobile workers are infinitely lived and discount future utility with a discount factor _δ <_ 1. In each period, a worker obtains “flow” utility from consumption and from work enjoyment (represented by a idiosyncratic sector-specific preference shock). She also chooses whether to stay in her current sector or change sectors, in the latter case suffering a “mobility cost” paid in disutility. Using Bellman’s principle of optimality, the expected utility in period _T_ of a worker who lives in region _i_ and works in sector _s ∈{A, M }_ is given by: where _εT ≡_ [ _εAT , εMT_ ] is a vector containing two sector-specific idiosyncratic preference shocks, _V_ is the indirect utility function given by equation (12), _PiT_<sup>_A_(resp.</sup><sup>_P M_</sup> _iT_<sup>)istheagricultural(resp.</sup> manufacturing) price index, _wiT_<sup>_s_isthewageinsector</sup><sup>_s_,</sup><sup>_tT_istheincometaxrate,and</sup><sup>_μ_ ̃</sup><sup>_sr_isthe</sup> mobility cost of moving from sector _s_ to sector _r_ .<sup>128</sup> The preference shocks _εsT_ are independently distributed across workers, sectors, and periods, and follow a Gumbel distribution with location parameter equal to zero and scale parameter equal to<sup><u>1</u></sup> _θ_<sup>_>_0:</sup>

> 127This dynamic formulation is influenced by Caliendo et al. (2019) and Artuc et al. (2010).

> 128We assume that a worker pays no mobility cost when she chooses to stay in her current sector, i.e. _μ_  ̃ _AA_ = _μ_  ̃ _MM_ =

> 0. We further assume that mobility costs are symmetric, i.e. _μ_  ̃ _AM_ = _μ_  ̃ _MA_ = _μ_  ̃.
98 The max operator in equation (57) captures the decision each worker makes in each period of which sector she will work in in the next period.<sup>129</sup> Using the properties of the Gumbel distribution in equation (58), it can be shown that the average utility across workers in a given region-sectorperiod can be written as the following closed-form expression: where _VisT_<sup>_m_is the average utility across workers of sector</sup><sup>_s_and region</sup><sup>_i_in period</sup><sup>_T_, and</sup><sup>_γ≈_0</sup><sup>_._577</sup> is the Euler-Mascheroni constant. Furthermore, the properties of the Gumbel distribution also imply that the probability that a worker who is in sector _s_ and region _i_ in period _T_ will choose to work in sector _r_ in period ( _T_ + 1) is given by: <u>�</u> _k∈{_ [exp( _A,M }V_<sup>[exp(</sup> _ir_<sup>_m_</sup> _<u>,T</u>_ <u>+</u><sup>_V_</sup> 1 _ik,T_<sup>_<u>m−μ</u>_ ̃</sup> +1<sup>_sr_)]</sup><sup>_−θμ_ ̃</sup><sup>_sk_)]</sup><sup>_θ_.Thisclosed-form</sup> expression for the transition probabilities allow us to write a law of motion for employment levels: where _Ni,T_<sup>_s_is employment in sector</sup><sup>_s_of region</sup><sup>_i_in period</sup><sup>_T_,</sup><sup>_V_ ̄</sup> _isT_<sup>_m≡_exp(</sup><sup>_V_</sup> _isT_<sup>_m_),</sup><sup>_μks≡_exp( ̃</sup><sup>_μks_),</sup> and Π _isT ≡_<sup>�</sup> _r∈{A,M }_<sup>_μ_</sup> _sr_<sup>_−θV_ ̄</sup> _irT_<sup>_θ_canbeinterpretedastheoptionvalueofworkinginsector</sup><sup>_s_in</sup> terms of its “access” to other sectors (as measured by _{μ_<sup>_−_</sup> _sr_<sup>_θ}r_).</sup> In the model’s steady state, endogenous variables do not change, so we can eliminate the time subscripts and rewrite the key equilibrium relationships as follows: The new mobility module represented by equations (59), (60), and (61) can be plugged into the main model with minor modifications. First, because intersectoral mobility is imperfect, the equilibrium agricultural wage and manufacturing wage may now differ within the same region. To

> 129Note that, due to idiosyncratic preference shocks, in any given period there exist otherwise identical workers in the same sector and region who will choose to work in different sectors in the following period.
99 reflect this possibility, we must thus adjust the equilibrium relationships governing relevant agricultural prices (equation 3), aggregate expenditure on agriculture (equation 14), aggregate income (equation 15), and manufacturing expenditure shares (equation 19), respectively, as follows: Naturally, the other equilibrium relationship that must be adjusted is labor market clearing. Instead of equation (26), we now need two equations for each region, one for agricultural labor and one for manufacturing labor: With these adjustments, we are now ready to state the equilibrium definition for the case with frictions:

**Definition 3 (Equilibrium with Frictions)** _Given the model’s parameters (R, K, η, ν, φ,_ **_σ_** _,_ **_γ_** _, θ, δ) and exogenous variables (_ **_F_** _,_ **_N_** _,_ **_L_** _,_ **_T_** _,_ **_τ_** _,_ **_b_** _, f_<sup> ̄</sup> _,_ **_s_** _,_ **_μ_** _) , a_ **_steady-state equilibrium with frictions to worker intersectoral mobility_** _is a set of endogenous variables (t,_ **_p_**<sup>**_A_**</sup> _,_ **_p_**<sup>**_f_**</sup> _,_ **_p_**<sup>**_−_**</sup> _,_ **_P_** _,_ **_w_**<sup>**_A_**</sup> _,_ **_w_**<sup>**_M_**</sup> _,_ **_w_**<sup>**_e_**</sup> _,_ **_R_** _,_ **_E_** _,_ **_X_** _,_ **_β_** _,_ **_Q_** _,_ **_QR_**<sup>_rent_</sup> _,_ **_N_**<sup>**_A_**</sup> _,_ **_N_**<sup>**_M_**</sup> _,_ **Π** _,_ **_V_**<sup>** ̄**</sup> _) satisfying equations 5, 6, 7, 8, 16, 17, 18, 20, 21, 25, 27, 59, 60, 61, 62, 63, 64, 65, 66, 67. Additionally, if QRs are_ **_not_** _in place, equation 22 must hold, with p_<sup>_f_</sup> _i_<sup>=</sup><sup>_pf_</sup> _RoW_<sup>_for all regions i ∈{_1</sup><sup>_, ..., R}.Alternatively, if QRs_</sup><sup>**_are_**</sup><sup>_in place, equations 23 and_</sup> _24 must hold, with p_<sup>_f_</sup> _i_<sup>=</sup><sup>_pf_</sup> _LKA_<sup>_for all domestic regions i ∈{_1</sup><sup>_, ..., I}._130</sup>

> ** ̄** 130Variables in bold are collections of region- and/or sector-level terms, as follows: **_μ_** = _{{μrs}r∈{A,M }}s∈{A,M }_ , **_V_** = _{{_  ̄ _Vis}s∈{A,M }}_<sup>_R_</sup> _i_ =1<sup>,</sup><sup>**Π**=</sup><sup>_{{_Π</sup><sup>_is}s∈{A,M}}R_</sup> _i_ =1<sup>,</sup><sup>**_wA_**=</sup><sup>_{w_</sup> _i_<sup>_A}R_</sup> _i_ =1<sup>,</sup><sup>**_wM_**=</sup><sup>_{w_</sup> _i_<sup>_M}R_</sup> _i_ =1<sup>,</sup><sup>**_we_**=</sup><sup>_{w_</sup> _i_<sup>_e}R_</sup> _i_ =1<sup>,</sup><sup>**_N A_**=</sup> _{Ni_<sup>_A}R_</sup> _i_ =1<sup>,</sup><sup>**_N M_**=</sup><sup>_{N_</sup> _i_<sup>_M}R_</sup> _i_ =1<sup>.The othervariables in bold are exactly the same as in the equilibrium of the original</sup>
100 Given the equilibrium variables, we can compute average welfare for various agent types. For the average mobile worker in sector _s ∈{A, M }_ of region _i_ , average welfare is simply given by _Vis_<sup>_m≡_ln( ̄</sup><sup>_V_</sup> _is_<sup>_m_). Average welfare for estate workers (</sup><sup>_V_</sup> _i_<sup>_e_) and farmers (</sup><sup>_V_</sup> _i_<sup>_F_) is still given by equations</sup> (29) and (30), respectively. We can also still use the concept of EV to compare agent welfare across different equilibria and to compute the average EV across agents as a metric of average welfare loss in each district, as explained in Appendix F.

# **H.B Counterfactual Results**

To assess the effect of the ban in a model with frictions to worker intersectoral mobility, we proceed in two steps. First, starting from the frictionless baseline equilibrium estimated in Section VI, we choose a specific value for the parameter _μ_ that governs the severity of frictions (i.e. _μAM_ = _μMA_ = _μ_ ) and compute a “baseline equilibrium with frictions” by applying Definition 3 with no QRs.<sup>131</sup> Second, we use Definition 3 again to recompute the equilibrium with frictions, but now imposing QRs ( _f_<sup> ̄</sup> = 0), as in Section VII.

By repeating this process for several different values of _μ_ , we can evaluate the sensitivity of the ban’s welfare impacts on each agent type to the severity of intersectoral mobility frictions. Appendix Table A9 displays the results of the exercise. Note that we explore a very wide range of ̃ friction intensities, going from the frictionless case ( _μ_ = 1 or _μ_ = 0) to extremely severe frictions ( _μ_ = _e_<sup>21</sup> ). The table shows us that welfare losses vary remarkably little with friction severity. For example, when there are no frictions the average welfare loss is equivalent to a 5.87% income loss, but in the last row of the table, when frictions are most severe, this loss increases only to 7.13%.

Therefore, the takeaway message from the exercise seems to be that while the reallocation of mobile workers across sectors does affect the ban’s welfare consequences, this influence is relatively less important compared to other, more significant factors.

> model with perfect mobility (see Definition 1).

> 131To compute equilibria with frictions, it is also necessary to take a stand on the values of parameters _θ_ and _δ_ . Following Caliendo et al. (2019), we set _δ_ = 0 _._ 99<sup>4</sup> , and _θ_ = 5 _._ <u>134</u><sup>.</sup>
101 Table A9: Ban Effects on Welfare, by agent type (With Frictions to Worker Mobility)

|**Friction**||**Mobile Worker**||**Estate**||**Farm**|**er**|**Average**|
|---|---|---|---|---|---|---|---|---|
|_μ_|Agro|Manufacturing|All|**Worker**|Median|Average|Representative||
|1|-0.95%|-0.81%|-0.85%|-15.49%|-14.55%|-14.55%|-14.55%|-5.87%|
|1.3|-0.96%|-0.82%|-0.86%|-15.52%|-14.62%|-14.62%|-14.62%|-5.90%|
|_e_<sup>1</sup>|-1.00%|-0.84%|-0.88%|-15.63%|-14.83%|-14.82%|-14.82%|-5.98%|
|_e_<sup>2</sup>|-1.04%|-0.86%|-0.90%|-15.76%|-15.11%|-15.10%|-15.10%|-6.10%|
|_e_<sup>4</sup>|-1.08%|-0.85%|-0.90%|-15.98%|-15.70%|-15.69%|-15.70%|-6.31%|
|_e_<sup>6</sup><sup>_._566</sup>|-1.08%|-0.79%|-0.84%|-16.19%|-16.47%|-16.46%|-16.46%|-6.54%|
|_e_<sup>10</sup>|-1.02%|-0.64%|-0.70%|-16.37%|-17.40%|-17.39%|-17.40%|-6.78%|
|_e_<sup>15</sup>|-0.92%|-0.46%|-0.54%|-16.50%|-18.38%|-18.37%|-18.37%|-7.00%|
|_e_<sup>21</sup>|-0.86%|-0.35%|-0.44%|-16.56%|-18.97%|-18.96%|-18.97%|-7.13%|

_Notes_ : for each level of frictions to mobile workers’ intersectoral mobility ( _μ_ ) and for each agent type, the table shows the average % welfare change between the baseline equilibrium with no QRs and the counterfactual equilibrium with QRs, where the (unweighted) average is computed across Sri Lankan districts. Equilibria are computed assuming that the utility cost faced by a mobile worker when moving to a different sector of employment ( _μAM_ = _μMA_ ) is given by the value _μ_ in the “Friction” Column (see Appendix H.A for details on equilibria with frictions). Welfare changes are defined as EVs: starting from the agent’s baseline (net-of-tax) income, the EV is the % change in (net-of-tax) income that would leave her with the same utility level as she has in the counterfactual equilibrium, keeping prices fixed at baseline levels (see Appendix F for details on EVs and agent types). The table also shows (the cross-district average of) the cross-type average welfare change, which is computed as the weighted average of types’ EVs, with weights given by types’ population shares.