metadata: authors: 0: author: Darko,Francis Addeah
1: author: Ricker-Gilbert,Jacob Edward
2: author: Kilic,Talip
count: Africa
docna: 0: docna: Profitability of Fertilizer Use in
            Sub-Saharan Africa : Evidence from Malawi
docty: Policy Research Working Paper
abstracts: cdata!: This paper estimates the profitability
            of inorganic fertilizer use in maize production in Malawi.
            It employs a two-wave, nationally representative panel of
            data on smallholder households and plots to estimate
            household fixed effects, plot fixed effects, and multilevel
            regressions. The results suggest that inorganic fertilizer
            use is generally unprofitable at prevailing market prices
            when, assuming that farmers incur positive transaction costs
            in the use of fertilizer. The low fertilizer profitability
            is driven by low nitrogen use efficiency, the kilograms of
            maize produced per kilogram of nitrogen, which is estimated
            to range from 9.2 to 12.1. For fertilizer use to be
            profitable, the nitrogen use efficiency would have to
            increase by at least 137 percent (from 11.89) if maize
            output is valued at the farmgate price and by 50 percent
            (from 11.89) if maize is valued at the lean season market
            price. For farmers who receive the fertilizer subsidy, it
            improves the profitability of fertilizer use by increasing
            the maize-nitrogen price ratio at all rates of subsidy (0 to
            100 percent). However, unless farmers can store their
            produce and sell during the lean season when the output
            price is relatively higher, they would be better off by at
            least MKW 66.16 (US$0.18) per kilogram of subsidized
            nitrogen with the cash equivalent of the subsidy than with
            subsidized fertilizer. The analysis also finds that,
            compared to the current rate of nitrogen application, the
            government recommended rate of application is between 116
            and 119 percent more profitable on smallholder fields.
display_title: Profitability of Fertilizer Use in
            Sub-Saharan Africa : Evidence from Malawi
listing_relative_url: /research/2024/07/34368381/profitability-fertilizer-use-sub-saharan-africa-evidence-malawi
topicv3: Agriculture and Related Subsidies m1325974 1978,Agriculture and Food Security m1326205 435,Fertilizers m1327354 175
publishtoextweb_dt: 2024-07-24T00:00:00Z
dois: 10.1596/1813-9450-10859
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 45
author_keys: 0: author_key: 1384799
1: author_key: 1298223
2: author_key: 886702
model_extractions: Policy Research Working Paper 10859 Profitability of Fertilizer Use in Sub-Sahara Africa Evidence from Malawi _Francis Addeah Darko Jacob Ricker-Gilbert Talip Kilic_ Agriculture and Food Global Practice September 2024
Policy Research Working Paper 10859

# **Abstract**

This paper estimates the profitability of inorganic fertilizer use in maize production in Malawi. It employs a two-wave, nationally representative panel of data on smallholder households and plots to estimate household fixed effects, plot fixed effects, and multilevel regressions. The results suggest that inorganic fertilizer use is generally unprofitable at prevailing market prices when, assuming that farmers incur positive transaction costs in the use of fertilizer. The low fertilizer profitability is driven by low nitrogen use efficiency, the kilograms of maize produced per kilogram of nitrogen, which is estimated to range from 9.2 to 12.1. For fertilizer use to be profitable, the nitrogen use efficiency would have to increase by at least 137 percent (from 11.89) if maize output is valued at the farmgate price and by 50 percent (from 11.89) if maize is valued at the lean season market price. For farmers who receive the fertilizer subsidy, it improves the profitability of fertilizer use by increasing the maize-nitrogen price ratio at all rates of subsidy (0 to 100 percent). However, unless farmers can store their produce and sell during the lean season when the output price is relatively higher, they would be better off by at least MKW 66.16 (US$0.18) per kilogram of subsidized nitrogen with the cash equivalent of the subsidy than with subsidized fertilizer. The analysis also finds that, compared to the current rate of nitrogen application, the government recommended rate of application is between 116 and 119 percent more profitable on smallholder fields.

This paper is a product of the Agriculture and Food Global Practice. 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 fdarko@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
# **Profitability of Fertilizer Use in Sub-Sahara Africa: Evidence from Malawi**

Francis Addeah Darko Jacob Ricker-Gilbert Talip Kilic Originally published in the Policy Research Working Paper Series on _July 2024._ This version is updated on _September 2024._ To obtain the originally published version, please email prwp@worldbank.org.

JEL Classification: Q18 Key Words: Fertilizer profitability, fertilizer response rate, fertilizer subsidy, Malawi
# **Introduction**

Improving agricultural productivity is widely regarded as a channel for reducing poverty and food insecurity in Sub-Saharan Africa (SSA). This view is based on the heavy reliance that poor and food insecure households place on agriculture. Unfortunately, agricultural productivity has been very low in SSA: since the 1960s, average per capita annual growth in agricultural productivity has been less than 1% for the continent as a whole, and – at times – negative for some sub-regions (FAO statistics, 2013). The lagging agricultural growth in SSA has often been explained by low utilization of inorganic fertilizer (for example, see Morris et al., 2007). Morris et al (2007) observed that when countries and crops in similar agro-ecological zones are compared, the rate of fertilizer application is much lower in SSA than in other developing regions of the world. Meanwhile fertilizer use is viewed as particularly important in SSA because the continent’s soils are inherently poor in nutrients, and over the last several decades, land-use practices have further worsened soil fertility through leaching, nutrient mining by crops and inadequate erosion control (Henao and Baanante, 2006).

The low use of inorganic fertilizer in crop production in SSA can be attributed to both demand-side and supply-side factors. The first and perhaps most obvious demand-side factor that could potentially explain the low use of fertilizer in Africa relates to profitability. Farmers’ demand for commercial fertilizer is weak because fertilizer use is probably unprofitable or only barely profitable to most farmers. Incentives to use fertilizer are often undermined by the low fertilizer response rate, high variability of crop yields, and high fertilizer prices relative to crop output prices. Demand for fertilizer is further weakened by lack of information about the availability and cost of fertilizer, the inability of farmers to raise resources needed to purchase fertilizer at planting when they are paid for their output months later at harvest (credit constraint), and lack of knowledge on the part of many farmers about how to use fertilizer efficiently (Morris et al., 2007; Kelly et al., 2
2003). On the supply side, the factors that potentially undermine the use of commercial fertilizer by farmers include unfavorable business climate, excessive regulations, an abundance of taxes and fees, and high levels of rent seeking (Morris et al., 2007).

With these considerations in mind, the objective of the present study is to use nationally representative household level data from Malawi to analyze the profitability of fertilizer use in maize production. Specifically, the study seeks to answer the following questions: 1) what is the level of nitrogen use efficiency (NUE)<sup>1</sup> and how does it vary across Malawi? 2) to what extent is the use of fertilizer in maize production profitable in Malawi? Given the NUE estimates from our study, we seek to then answer two key policy questions. First, would the majority of smallholders in Malawi be better-off with subsidized fertilizer or with an equivalent cash transfer? Second, could the majority of smallholders increase their profits by applying fertilizer at the rates recommended by the government?

The study focuses on Malawi for two reasons. First, productivity growth in Malawi’s agriculture is typical of countries in SSA. For the past two decades, the productivity of most agricultural crops in the country has increased only modestly. Even now, the already modest increase in productivity is further undermined by an annual population growth of 2.7% (MoAFS, 2010). In addition, the Ministry of Agriculture and Food Security (2010) estimates that Malawi’s yield gap – the difference between potential yield and the actual yield of the average farmer (1,536 kg/ha for maize in 2013) – ranges between 38% and 53% for cereals, and between 40% and 75% for legumes (Lobell et al., 2009). This implies substantial room for productivity improvements. Yield improvements likely will be essential for reducing poverty and improving food security in Malawi because given Malawi’s already high average population density of 178 people per square

> 1 NUE is defined as output (kg maize) over input (kg of nitrogen applied). We focus on nitrogen use efficiency because nitrogen is a limiting nutrient in many soils in SSA and its estimated net loss from soils is higher than any other nutrient (World Bank, 1998).

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kilometer, there is limited room for area expansion among smallholders (Dorward 2006; RickerGilbert et al. 2014). Second, Malawi is also an important case study to estimate inorganic fertilizer profitability because it has been implementing a large-scale Farm Input Subsidy Program (FISP) since the 2005/2006 agricultural season. In terms of scope and coverage, FISP is perhaps the most well-known farm input subsidy program in Africa. Through FISP, the Government of Malawi currently provides approximately 50 percent of the country’s agricultural households with coupons that allow for inorganic fertilizer and improved maize seed purchases at up to a 95% discount for fertilizer and 100% discount for seed. Focusing on Malawi provides an opportunity to analyze how fertilizer profitability can inform the geographical targeting of large-scale farm input subsidy programs, and how the subsidy program affects the profitability of fertilizer use.

The present study adds to the existing literature by extending the work of Xu et al. (2009) and Sheahan et al. (2012). Xu et al. (2009) and Sheahan et al. (2012) use nationally representative panel data from Zambia and Kenya, respectively, to analyze the profitability of fertilizer use in maize production. We build upon and extend their work in three main ways. First, by virtue of the availability of a variable that identifies plots over time in the two-wave nationally representative panel data used in the analyses, this study is able to control for plot-level unobserved heterogeneity using plot-level fixed-effects (FE) estimation.<sup>2</sup> Controlling for such plot-level unobserved heterogeneity helps improve upon the validity of the NUE estimates in the study. To our knowledge, this is the first study on SSA to use plot-level FE with nationally representative, nonexperimental data when estimating fertilizer profitability.

Second, this study accounts for different spatial and temporal maize prices in Malawi, including i) farm-gate harvest-season maize price, ii) lean season retail-market maize price and iii)

> 2 A plot is defined as a continuous piece of land that is not split by a river or a path wide enough to fit an oxcart or vehicle, and can contain multiple sub-plots.

4
import parity price. While most farmers sell their produce at the farm gate, others sell at nearby market centers and depending on the month in which sales are made, face either the harvest season (May to October) price or the lean season price (November to April). Apart from representing a price that farmers can potentially face in the maize market, the lean season maize price also represents the opportunity cost to farmers of purchasing maize if they are not able to produce enough maize to avoid household-level, seasonal maize deficits. The import parity price of maize is also considered in order to account for the government’s opportunity cost to home production of having to import maize. Accounting for all of these maize output prices will help to provide a broader picture of the expected profitability of fertilizer use.

The present paper also extends the scope of previous work on fertilizer profitability by using the NUE and profitability estimates that are likely more internally and externally valid than in previous studies from Malawi. For, example, the NUE estimates used in the official evaluation of Malawi’s FISP is assumed to be 16.8 on average (Dorward et al. 2008). These estimates are based on work from the late 1990s from the Malawi maize productivity task force (MPTF) and use data on master farmer fields to estimate NUE (Benson 1999). Arndt et al. (2015) use the estimates from the MPTF to employ a CGE model of benefits from FISP and find that with an NUE of 16.8, FISP generates an economywide benefit/cost ratio of 1.62 when spillover benefits are considered in addition to direct benefits from increased maize production. They find that the benefit-cost ratio falls below 1.0 (break-even level) at an NUE of 13. Harou et al. (2017) also use the MTPF data from the late 1990s to estimate fertilizer profitability in Malawi. The authors find that bundles of fertilizer distributed under FISP (100 kilograms) are almost always profitable on average in Malawi, and profitability of fertilizer is robust to tripling of fertilizer prices, and to a 50% decrease in maize price and to drought. The objective of our paper is to build on the previous literature using the most recent data in Malawi from a nationally representative sample of panel households, along 5
with plot-level FE to estimate fertilizer profitability. Doing so can provide guidance for the geographical allocation of fertilizer subsidies and shed light on the question of whether farmers would be better-off with subsidized fertilizer or the cash equivalent of subsidized fertilizer, and whether or not government recommended rates of fertilizer application are profitable.

Our results find a mean NUE of 11.89 kg using plot-level FE. This indicates that when we assume positive transactions costs for smallholders in the use of inorganic fertilizer, the input is not profitable in Malawi on average at commercial prices when maize is valued at either the farm gate price or lean season market price. In this scenario, the plot-level analyses show that fertilizer use is profitable on only less than 1% of plots when maize is valued at the farm gate price; and profitable on only 17.61% of plots when maize is valued at the lean season market price. At prevailing market conditions, in order for the use of fertilizer to be profitable, the current nitrogen efficiency estimated to be will have to increase by at least 137.17% (28.20 kg) when maize is valued at the farm gate price and by at least 50.46% (17.89kg) when maize is valued at the lean season market price. We also find that unless smallholders are able to store their maize and sell it during the lean season when prices rise, the average smallholder will be at least MKW 66.16 (US$ 0.18) per kg of subsidized nitrogen better-off with the cash equivalent of the subsidy than participating in the subsidy program if maize is valued at the farm gate price. Finally, the study finds that the government recommended rate of fertilizer application is between 116% and 119% more profitable than the rate at which the average smallholder currently applies fertilizer.

6
# **Conceptual Framework**

We derive the yield function and the profitability of fertilizer from the farm profit component of the agricultural household model of Sing, Squire and Strauss (1986). Smallholder farmers are considered to be firms whose production set is made up of food and cash crops. Maize is the most widely cultivated crop in Malawi – it is cultivated by about 90% of farmers on 70% of their farm plots – and the most important crop in terms of fertilizer application (NSO, 2013). The study therefore focuses on farmers’ decision to produce maize using inorganic fertilizer and other inputs, with the objective of maximizing farm profit, . The profit function is given by: ππ where YY and are quantity and price of maize respectively; II is a vector of inorganic fertilizer ππ= PP YY(II) −PP II (1) YY and other inputs used in the production of maize; and YY PP is a vector of the prices of the inputs. The II II term _Y(I)_ represents the agronomic production function where a vector of inputs is turned into PP maize output _Y_ . Guan et al. (2006) classify the inputs into _growth inputs_ and _facilitating inputs_ based on the agronomic ideology that different inputs affect yield differently. The _growth inputs_ include such inputs as soil nutrients, seed and water that are directly involved in the biological process of plant growth and development, while the _facilitating inputs_ involve such inputs as labor and pesticides that are not directly involved in the growth and development process of plants but influence the response rate of plants to the _growth inputs_ (Guan et al, 2006). Previous literature extends the _facilitating inputs_ to include household characteristics such as wealth, education, household size and dependency ratio (Xu et al, 2009; Sheahan et al. 2012).

The present study categorizes the _growth_ and _facilitating_ inputs into plot-level and household-level variables. The plot-level variables include soil nutrients, seed application rates and labor, as well as variables such as soil quality, slope of the plot, whether or not the plot is swampy, soil type and the extent of soil erosion that capture the conditions of the plot. The factors 7
capturing the conditions of the plot are important because they influence the extent to which crops take up nutrients from the soil. The household-level variables include wealth, education, household size and dependency ratio and age of household head. Household wealth is measured in terms of ownership of agricultural tools and durable goods. It has also been well established that crop yield is lower on female-managed plots than on male-managed plots and has inverse relationship with plot size; as such, we also control for plot size and the gender of the plot manager in out model (Carletto et al., 2011; UN and World Bank, 2018; Kilic et al; Darko and Purnamasari, 2019). The study also controls for temperature and precipitation, the two most important weather variables affecting crop production in Malawi.

Although the complementarity between soil nutrients in terms of their effect on crop yield are well documented, we only focus on nitrogen. We do so for several reasons. First, the fertilizers used in maize production in Malawi are predominantly _chitowe_ (NPK 23:21:0 +4S) and the urea fertilizers, both of which are nitrogenous fertilizers. This is probably the case because nitrogen is a limiting nutrient in many soils in Malawi (and SSA as a whole) and its estimated net loss from soils is higher than any other nutrient (World Bank, 1998). Second, while all applied nitrogen is used by plants in the same growing season, only about 20% of applied phosphorus (the second most important nutrient in the fertilizers used in maize production in Malawi), is used by plants in the first growing season of application (Griffith, n.d.; Sheahan, 2013). Third, the nitrogen variable in our model strongly correlates with the other nutrient variables, especially the phosphorus variable. Hence including other nutrient variables in the model will result in multicollinearity, a condition that would result in large variances and covariances of the estimates thereby rendering the estimates inconsistent. Fourth, including other nutrients and their interaction terms with the nitrogen variable in the model will complicate the computation of the spatial variation of the nitrogen response which is of particular interest in this study. The reasons notwithstanding, we do 8
acknowledge that ignoring the complementarity between nitrogen and the other nutrients may affect the affect the estimates. The findings should therefore be interpreted with this caveat in mind.

Taking the first order condition of profit maximization with respect to nitrogen, N, and rearranging terms results in equation (2) below: PY * = PN (2) NN MMPP where is the marginal product of nitrogen (NUE) in maize production; and and NN YY represent the prices of maize and nitrogen respectively. Accordingly, the left-hand side of MMPP PP NN equation (2) is the marginal value product of inorganic fertilizer application, which measures the PP rate at which revenue from maize production increases with the amount of nitrogen used. A household’s decision to use inorganic fertilizer in the production of maize is influenced by the extent to which the input is expected to be profitable – the higher the profitability of fertilizer use, the higher the incentive for farmers to use the input. From equation (2), the extent of fertilizer profitability to a household is given by ( ), thus profitability of fertilizer use YY NN NN depends on the household’s NUE, and the prices of maize and fertilizer. PP ∗MMPP − PP

# **Empirical Model and Estimation Strategy**

In order to estimate NUE and assess the profitability of inorganic fertilizer use by smallholders in Malawi, we estimate a production function for maize as follows: smallholders in Malawi, we estimate a production function for maize as follows: i 1 i i i h i i ii ii ii xx ii ii ww ii YY = ββ NN + XX ββ + HH ββ + WW ββ + εε (3aa) i i ii ii ii εε = cc + ee (3bb) 9
where _i_ and _t_ represent sub-plot and time respectively; _j_ is the indicator for fixed effects (district, enumeration area, household or plot); i is a composite error term made up of time-invariant ( ) ii ii and time-varying ( i ) unobserved factors. εε 1 is our estimate of the NUE on the specific sub-cc ii plot; and is the vectors of parameters for the other plot-level variables (ee ββ i ); h is a vector of xx ii parameters of the household variables (ββ i ); is a vector of parameters of the weather variables. XX ββ ii ww The list of the plot-level, household-level and weather variables are as provided under the section HH ββ on “conceptual framework” and in table 1.

Yield is measured as maize-equivalent output per hectare of land. Maize-equivalent output is used instead of maize output because, as in other developing countries, maize is usually intercropped in Malawi. Total output from any particular plot is converted to maize equivalent output ( _ME_ ) using an output index given by equation (4) (Liu and Myers, 2009; Sheahan et al., 2013): Multilevel specifications are also considered in addition to the fixed-effects specifications because they allow for the estimation of households-specific and plot-specific NUE. The estimation of NUE at these disaggregated levels is of particular interest in this study because it allows us to analyze the variation in NUE, and subsequently the profitability of fertilizer use, at the lowest disaggregated level possible. The use of multilevel models has two additional advantages. First, the data for the analysis has a hierarchical structure: sub-plots are nested within plots which are in turn nested within households (farm households in Malawi and other parts of 10
developing countries usually cultivate crops on multiple sub-plots). The existence of such a hierarchy in the data has implications for statistical validity and therefore should not be ignored (Goldstein, 1995; Elhorst, 2014; Carrado and Fingleton, 2011). The multilevel model accounts for the hierarchical structure between sub-plots, plots and households by modelling variations at all levels. Moreover, yield from sub-plots belonging to the same plots and same household are likely to be correlated because they share the same management and related conditions. The multilevel specification corrects for these intra-garden and intra-household correlations.<sup>3</sup> Second, the multilevel model distinguishes (explicitly) between sub-plot-level and household-level covariates in the model by allowing for the coefficients of the sub-plot-level variables to vary within plots and households. This is particularly important in this study because of the interest in observing the geographical variation of NUE, and the multilevel specification allows us to obtain an individual NUE for each plot. Two multilevel models are estimated: 1) a two-level, multilevel model where sub-plot and household are the first and second levels respectively (henceforth “plot” multilevel model), and 2) a two-level, multilevel model where sub-plot and plot are the first and second levels respectively (henceforth “household” multilevel model). The specification of the “household” multilevel model is provided in appendix A. We leave out the specification of the “plot” multilevel model in appendix A because it is very similar to the specification of the “household” multilevel model – replacing the _household_ index with the _plot_ index in the specification of the “household” multilevel model results in the “plot” multilevel model.

> 3 The use of single-level models (which assume that yields are independent across plots) in the presence of intra-household correlations in yield will lead to spuriously small standard errors, which will in turn result in too small confidence intervals and too small p-values.

11
_Potential Endogeneity of Inorganic Fertilizer Use in the Crop Yield Function_ The nitrogen variable in the yield function is potentially endogenous because both the decision to apply nitrogen, and the rate of nitrogen application on a particular plot are likely to be correlated with unobserved farmer characteristics such as managerial skills or ability, and unobserved plot specific characteristics such as variation in soil quality characteristics, that are likely to affect crop yield. For instance, farmers may be more likely to apply additional kilograms of nitrogen to plots of good soil quality in order to maximize the returns to the input. Conversely, they may apply additional kilograms of nitrogen to plots of poor soil quality in order to improve soil fertility and obtain a higher marginal product of nitrogen. Failure to account for such correlation between the nitrogen variable and the unobserved household and plot-level characteristics would render the estimates of NUE inconsistent.

The study addresses the potential bias resulting from unobserved time-invariant household and plot-level variables using plot-level FE. To the best of our knowledge, this study is the first to use non-experimental data to measure returns to fertilizer use while controlling for unobserved time-invariant factors with plot-level FE. The plot-level FE estimates reduce the potential bias by using the variation in nitrogen application within a particular plot over time to more accurately identify an arguably causal effect of the rate of nitrogen application on yields, than does a pooled analysis or a model estimated by household FE. Plot-level FE does not however deal with unobserved time-varying factors at the plot level, so even after controlling for unobserved heterogeneity with fixed effects, the estimate of the effect of the rate of nitrogen application on yield will still be inconsistent if i is correlated with i , unobserved time-varying factors. The ii ii study accounts for the potential correlation between the nitrogen variable and the unobserved time-NN εε varying factors by taking advantage of the availability of variables on soil characteristics to control for plot-level factors such as slope, extent of erosion, type of soil, whether or not the plot is 12
swampy, and the overall soil quality of the plot. Soil quality was measured by farmers’ subjective judgement of the quality of their plots (1= very good; 2 = good; and 3 = poor). After controlling for such important but seldom available plot-level variables, the remaining unobserved time varying factors should pose no significant bias to the validity of the NUE estimates. However, the study is unable to control for the potential bias that could result from the possibility of access to a FISP voucher affecting the application (decision to apply and quantity applied) of fertilizer. Hence endogeneity may still persist even after we used plot-level fixed effects to control for unobserved time-invariant factors, and after controlling for numerous plot level variables.

In the face of such potential endogeneity, an instrumental variable (IV) approach is a novel way to ascertain the validity of the NUE estimates but we are unable to use an IV model because of lack of good instrumental variables in the data available for this study. The validity of the NUE estimates would be highly compromised – worse than the current – if weak instruments are used. Hence instead of using an IV approach, we use the Oster (2015) approach to assess the robustness of our results to potential endogeneity resulting from other unobserved time-varying factors that we could not control for. Assuming that observables and unobservables have the same explanatory power in explaining the dependent variable, Oster (2015) demonstrates that the “ _controlled estimate_ ” (the coefficient on the variable of interest from the model with the full set of observable controls) and the “ _bias-adjusted estimate_ ” (the coefficient on the variable of interest after controlling for both observables and unobservables) provide a useful range that can be used to examine the robustness of the “ _controlled estimate_ ” to omitted variable bias. The “ _controlled estimate_ ” is robust to omitted variable bias if the range does not contain zero and is within the confidence interval of the “ _controlled estimate_ ”. The Oster (2015) approach considers not only 13
coefficient movements but also movements in R-squared values when including additional independent variables. The _“bias-adjusted estimate”_ is calculated as: ) ∗<sup>RRm</sup> (5)<sup>xx−RRcc</sup> where ββ<sup>∗</sup> = ββ<sup>cc</sup> −(ββand<sup>uucc</sup> − ββ are the “<sup>cc</sup> _controlled estimate_ ” and the of the regression from which the RR<sup>cc</sup> − RR<sup>uucc</sup> “ _controlled estimate_ ββ<sup>cc</sup> RR<sup>cc</sup> ” was obtained respectively; and and RR<sup>2</sup> are respectively the coefficient estimate and of the uncontrolled regression, the regression in which the variable of interest is ββ<sup>uucc</sup> RR<sup>uucc</sup> the only independent variable. RR<sup>2</sup> m is the of a hypothetical regression in which both xx observables and unobservables are controlled for, which is clearly unknown. Oster (2015) suggests RR RR<sup>2</sup> that m , 1}. The from our models are such that > 1, suggesting that we xx choose RR m= min{2.2RR= 1 based on Oster (2015). Meanwhile Gonzalez and Miguel (2015) argues that<sup>cc</sup> RR<sup>cc</sup> 2.2RR<sup>cc</sup> xx m of 1 or close to 1 is likely to be too high. Based on relatively high-quality US data, Gonzalez RR xx and Miguel (2015) suggested that RR m should not be greater than 0.9. An m of 0.89 was xx xx therefore chosen for our analyses. RR RR

# _Fertilizer Profitability_

We measure fertilizer profitability by calculating the Marginal Value Cost Ratio (MVCR) which represents the extent to which farm income will increase if the rate of nitrogen application increases. MVCR is expressed as follows: N M (6) NN ∗ PPYY MMRR= PPNN where N is the nitrogen use efficiency; and and are the prices of maize and nitrogen YY NN respectively. Maize prices change over time and space, so three prices of maize are considered in MM PP PP the profitability analyses – i) the farm gate price at harvest, ii) the lean season market price, and iii) the import parity price. All three of these prices are considered in order to account for potential 14
differences in maize prices that farmers are likely to face. The price of nitrogen, , is computed NN using the prices and nitrogen composition of _chitowe_ (NPK 23:21:0 +4S) and the urea fertilizer, PP the two main fertilizers used in maize production. Following Xu et al. (2009), let _f_ be the amount of each of _chitowe_ and urea required for a kilogram of nitrogen. Given the 1:1 application ratio of _chitowe_ and urea and their nitrogen components (23% for chitowe and 46% for urea), we have the following expression: ; and solving for _f_ results in . This means that a kilogram of nitrogen costs approximately 1.449 kilograms of each of 23%ff+ 46%ff= 1 ff= 1.449k _chitowe_ and urea; hence [ = 1.449 ∗(p . NN PP ppccee ooff cchppiiooiiee+ p ppccee ooff uuppeeaa)] Whether or not fertilizer is likely to be profitable depends on outcomes that are uncertain when fertilizer decisions are made, as well as costs associated with the use of fertilizer that are unknown to the analyst. If these uncertainties and unobserved costs are assumed to be zero, fertilizer use is deemed profitable if MVCR is at least one, an indication that an increase in the rate of fertilizer application will increase income from maize production. In the face of these uncertainties and unobserved costs however, an MVCR of at least 2.0 (meaning a risk premium of one) has been recommended in the literature to be required in order for fertilizer to be profitable (Xu et al., 2009; Sauer and Tchale, 2009; Bationo et al., 1992; FAO, 1985). We discuss the implications of our results when profitability is assumed to be obtained with an MVCR of 1.0 and 2.0.

# **Data and Sample Selection**

The data used in the analyses is a two-wave, nationally representative, panel dataset collected by the national Statistical Office of Malawi (NSO) with support from the World Bank Living Standards Measurement Study – Integrated Surveys on Agriculture (LSMS-ISA) program.

15
The survey for the first wave of the dataset (Malawi’s Integrated Household Survey – IHS3) was conducted from March 2010 through March 2011, and covered 12,271 households in 768 enumeration areas (i.e. 16 households from each EA). A sub-sample of the households considered in IHS3 were re-surveyed in 2013 to create the second wave of the dataset (Integrated Household Panel Survey -IHPS). IHPS tracked and re-interviewed 4000 households (3,247 original households, and 753 split-off households) from 204 of the 768 enumeration areas. An overwhelming majority, 76.80%, of the 3104 baseline households did not split over time; 18.49% split into two households; and the remainder (4.70%) split into 3-6 households. Considering the 20 baseline household that died in their entirety between 2010 and 2013 and the fact that 4,000 households could be traced back to 3,104 baseline households, the dataset has an overall attrition rate of only 3.78% at the household level.

The households that were not resampled in IHPS were dropped from the dataset used in the analyses. Households from the urban enumeration areas were also dropped because farming in Malawi is predominantly rural. Among the rural households, the study focused on farm sub-plots on which maize is the main crop. In the end, the sample size for the analyses consisted of 4,688 households (2,175 from IHS3 and 2,513 from IHPS) and 6,619 maize plots (3,070 from IHS3 and 3,549 from IHPS). Attrition bias in the data could not be explicitly tested because there are no direct regression-based tests for attrition when FE estimators are used in a panel of only two waves (Wooldridge, 2010; Mason and Smale, 2013). That notwithstanding, we are confident that attrition bias is not likely to be a concern because, as indicated earlier, the attrition rate is only 3.78% at the household level.

# **Results**

_Descriptive Statistics_ 16
The descriptive statistics of the variables in the yield function are presented in table 2. The average maize yield in the 2009/2010 agricultural year was 1,240.61kg/ha and increased significantly to 1,536.27kg/ha (24% increase) in the 2012/2013 agricultural year. The average yield estimates are higher than those reported for Nigeria over the same period of time (1,154 kg/ha in 2010 and 1,282 kg/ha in 2012), but lower than the average reported for Kenya (2,707 kg/ha over 1997, 2000, 2004, 2007 and 2010) and Zambia (1,779 kg/ha in 2009) (Liverpool-Tasie et al. 2015; Sheahan et al. 2012; Xu et al. 2009).

One would expect the increase in yield between survey waves to have resulted from an increase in the use of improved inputs such as inorganic fertilizer and hybrid seed, but the use of these inputs in the sample actually decreased significantly between the two agricultural seasons: the rate of nitrogen application decreased by about 13% (from 49.18 to 43.37 kg/ha), and the percentage of plots planted to hybrid maize varieties decreased by 4 percentage point (from 43.0% to 38.6%). Over the same period, labor utilization rate, seed application rate, the number of plots on which organic fertilizer was applied, and the number of plots on which the right type of basal fertilizer was applied increased significantly; and the average plot size and the number of plots managed by females decreased significantly. The combined yield-increasing effect of the significant changes in these variables likely outweighed the yield-decreasing effect of the reduction in the use of inorganic fertilizer and hybrid seed. The increase in yield could also have been partly due to farmers becoming relatively more efficient in the use of farm inputs in crop production.

Soil erosion appears to be a concern in maize production in Malawi. Nearly 40% of the maize plot operators report that their plots show signs of erosion. This could be related to the fact that about the same proportion of plots are not flat. Depending on the extent, soil erosion can potentially have a yield-decreasing effect by washing away the top soil and eventually depleting 17
the soil of major nutrients. The high proportion of erosion-affected plots notwithstanding, only about 15% of the plots are reported by farmers to be of poor soil quality (about 45% of the plots are reported to be of good soil quality and the rest are reported to be of fair quality).

# _Production Function Results_

Results of the maize production function are presented in table 3. The results are presented for seven estimator choices: i) pooled OLS, ii) district FE, iii) enumeration area (EA) FE, iv) household FE, v) plot FE, vi) a two-level, multilevel model where sub-plot and household (HH) are the first and second levels respectively, and vii) a two-level, multilevel model where sub-plot and plot are the first and second levels respectively. These different specifications provide a way to evaluate the robustness of the estimates, and test the direction of the potential bias in the NUE coefficient estimates as we control for unobserved heterogeneity at increasingly lower levels of aggregation.

The coefficient estimate on nitrogen, the main variable of interest in table 3, is consistent across estimators and the variation in estimates across estimators changes in a direction that we would expect. Depending on the estimator used, table 3 shows that average NUE in our sample ranges from 9.24kg to 12.09kg. The NUE estimated using the pooled OLS estimator (12.09kg) is the highest. This is to be expected because the pooled OLS estimator does not account for unobserved characteristics at any level (district, enumeration area, household or plot-level) such as agro ecological potential, community infrastructure, or household head ability that we would all expect to be positively correlated with fertilizer application and yields. NUE rates get progressively lower as district level FE, community level FE and Household level FE estimators are used. The estimates also show that the NUE using plot FE (11.21kg) is higher than that of the household FE estimator (9.24 kg). This is an interesting finding and could be explained by the 18
likelihood that some unobservable, plot-level factors such as soil quality attenuate the nitrogen coefficient in the household FE estimates if farmers put nitrogen on plots of lower soil quality in an effort to get a higher marginal response and/or to improve longer term soil fertility on the plot. These plot-level unobservable factors are controlled for in the plot-level FE estimates, but not in the household-level FE, EA FE, District FE or pooled OLS estimates.

Yield on plots on which the rate of nitrogen application was above the government recommended rate is about 332.63 kg/ha lower than it is on plots on which the recommended rate was followed according to the garden FE estimates. It is usually recommended that basal fertilizer application in maize production be done within a week after planting in order to ensure higher yields. The results indicate that compliance with this recommendation increases yield by about 169.24kg/ha, all thing being equal. The results further indicate that the use of organic fertilizer increases maize productivity by about 126.46 kg/ha.

There is a significant, inverse relationship between plot size and maize yield. All things being equal, a hectare increase in plot size will decrease yield by 847.80 kg/ha. Larger farms are usually not farmed as intensively as smaller farms and therefore are underutilized, resulting in lower productivity. This inverse relationship between plot-size and productivity is common in the literature (Carletto et al. 2013).

Labor utilization has a positive and significant effect on agricultural productivity. All things being equal, an increase of one day in total labor (sum of family, hired and exchange labor) increases maize yield by 0.95 kg/ha. The positive effect is expected but the actual magnitude is low, indicating a low return to labor productivity. The positive effect of labor is perhaps not surprising because labor (family or hired) is needed for land preparation, weeding, mulching, fertilizer application and pest control without which yield would be very low.

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Soil quality has a positive and significant yield-increasing effect. The estimates show that, on average, yield on plots of good and fair quality is about 259.84kg/ha and 179.14kg/ha respectively higher than yield on plots of poor soil quality. As mentioned, the “soil quality” variable is a measured by farmers’ subjective judgement (1 = good; 2 = fair; 3 = poor). The estimate should therefore be viewed with his caveat in mind.

The gender and years of education of the plot manager are also significantly correlated with maize yield. Yield on female-managed plots is 113.27kg/ha lower than it is on male-managed plots. In a similar study in which agricultural productivity was measured by value of output per hectare, Kilic et al. (2015) observed that productivity on female-managed plots is 25% lower than on male-managed plots. The authors find that 82% of the gender differential in agricultural productivity is attributable to differences in endowments. It has been shown that closing this gender gap in agricultural productivity can potentially reduce the poverty rate by 2.2% and accordingly lift 23,800 people out of poverty each year in Malawi (World Bank, 2015). The production function of this study also show that a year increase in the education of plot managers will all things being equal increase yield by 10.54 kg/ha.

Maize yield is also positively affected by ownership of agricultural tools and durable assets. A unit increase in the index of agricultural tools and durable assets will all things being equal increase yield by 68.96kg/ha and 93.73kg/ha respectively. The positive relationship between asset ownership and maize yield is expected because farmers with more equipment are more likely to purchase and use fertilizer and other modern inputs in production.

Rainfall has a positive and significant effect on maize yield. A millimeter increase in total annual rainfall increase maize yield by 1kg/ha, all things being equal. This finding suggests that increasing farmers’ access to irrigation facilities in low rainfall years could help boost agricultural productivity.

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# _Distribution of Nitrogen Use Efficiency (NUE)_

Generating the NUE at the most disaggregated level possible is of particular interest for the analysis of spatial fertilizer profitability in this study. The “plot” multilevel model allows for the estimation of NUE at the plot-level. Moreover, as table 3 indicates, the estimated mean NUE of the “plot” multilevel model is very similar in magnitude to that of the mean plot-level FE model, which is our most consistent estimate. Using the “plot” multilevel model, the NUE is estimated to range from 2.82kg to 25.98kg with a mean and standard deviation of 11.82kg and 2.42 respectively (figure 1). NUE ranges between 10kg and 15kg for majority of the plots (75%); between 5kg and 10kg for 16% of the plots; between 15kg and 20kg for about 8% of the plots; and at least 20kg for only about 1% of the plots.

Overall, the average NUE estimated in this study is quite low, and lower than those calculated by the MPTF task force using data from master farmers in the late 1990s in Benson (1999) and used by the official FISP evaluation (Dorward et al. 2008), and other recent studies by Arndt et. Al (2015) and Harou et al. (2017). However, these estimates are consistent with other studies using recent data on smallholders in Malawi. NUE estimates in these studies range from 7.1 kg to 11.0 kg by Snapp et al (2013), between 6.6kg and 11.5kg by Ricker-Gilbert and Jayne (2011, 2012); and 11.3kg by Holden and Lunduka (2011). The low NUE in Malawi is likely to be one of the main reasons why the use of commercial fertilizer for crop production is very low in the country. The fertilizer use literature suggests that the low NUE observed in this and other studies in Malawi is not an isolated case in SSA. The NUE has been estimated to be between 8kg and 13kg in Nigeria, and between 11kg and 20kg in Kenya (Liverpool-Tasie et al. 2015; Matsumoto and Yamano, 2011; Marenya and Barrett 2009; Sheahan et al, 2012).

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We also estimate the mean NUE for each district and use these estimates to categorize the districts into five groups. Such categorization can be useful in guiding the geographical allocation of the farm input subsidy program that the government is currently implementing, along with providing more location specific recommendations about the profit maximizing level of fertilizer use. We find that NUE ranges from 12.19kg to 13.14kg for the first group of districts, 11.62kg to 12.18kg for the second group, 11.05kg to 11.61kg for the third group, 9.98kg to 11.04kg for the fourth group, and 9.58kg to 9.97kg for the fifth group (figure 2a).<sup>4</sup> Overall, the mean NUE for the districts in the central region are relatively higher than those in the northern and southern regions in that order. The study also finds a strong, positive correlation (0.87) between the spatial distribution of NUE and the spatial distribution of maize yield, implying that districts with the highest mean NUE have the highest mean yield (figures 2a and 2b). This categorization can serve as the basis for the geographical targeting for the farm input subsidy program that the government is currently applying. However, we also see that the price of N is lowest in southern Malawi, and higher in the central and northern regions. This is because N almost always enters Malawi through the southern corridor through Mozambique so transport costs are lowest in southern Malawi and get progressively higher as fertilizer moves northward. This has implications for fertilizer profitability and fertilizer use.

# _Profitability of Fertilizer Use_

At the commercial price of inorganic fertilizer, the average marginal value cost ratio, MVCR, (the measure of fertilizer profitability) is estimated to be 0.81 when maize is valued at 4 The first group of districts consists of Dowa, Ntchisi, Salima and Chiradzulu; the second group consists of Mchinji, Kasungu, Nkhota kota, Karonga, Chitipa, Dedza, Ntcheu, Mangochi, Blantyre and Zomba; the third group consists of Nkhata Bay, Lilongwe and Balaka; the fourth group consists of Rumphi, Mzimba, Machinga, Neno, Mwanza, Phalombe, Mulanje and Thyolo; and the fifth group consists of Chikwawa and Nsanje.

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farm gate price, 1.32 when maize is valued at lean season market and 2.18 when maize is valued at import parity price (figure 3). Figure 3 shows that if we assume positive transaction costs (where break-even MVCR=2.0), the use of commercial fertilizer in the production of maize is not profitable on average when maize is valued at farm gate price and lean season market price; but profitable when maize is valued at the import parity price. However, when transaction costs are assumed to be zero (where break-even MVCR=1.0), the use of commercial fertilizer in maize production is profitable on average when maize is valued at lean season market price and import parity price, but still unprofitable when maize is valued at the farm gate price.

The plot-level analyses show that, under the assumption of positive transaction costs, fertilizer use is profitable on only less than 1% of plots when maize is valued at farm gate price; profitable on 17.61% when maize is valued with lean season market price; and profitable on 67% of gardens when maize is valued at import parity price. Under the zero transaction costs assumption however, the number of gardens on which fertilizer use is profitable increases to 30.78% at farm gate price of maize; 77.96% at lean season market price of maize; and 96.58% at import parity price of maize.

Generally, the estimates show that the profitability of fertilizer use in maize production is encouraging when transaction costs are assumed to be zero and when maize is valued with the lean season market price or import parity price. However, the assumption of zero transaction cost is not likely to hold in Malawi because of the uncertainty and additional costs associated with use of fertilizer in crop production. Also because many smallholders have immediate needs for cash to meet pressing needs at harvest, they have limited ability to defer the selling of maize to the lean season when prices are relatively higher. It seems likely that farm households may consider the lean season price of maize as their opportunity cost of having to purchase maize at market during the lean season. This could make the purchase and application of inorganic fertilizer more 23
profitable in expectation when they make that decision during the planting season, before yields and maize prices are known.

At the district-level, under the assumption of positive transaction costs, fertilizer use is on average not profitable in all the districts when maize is valued at farm gate, but profitable in Mulanje and Blantyre when maize is valued at lean season market price; and profitable in Dowa, Mangogochi, Chikwawa, Blantyre, Chiradzulu, and Mulanje when maize is valued at import parity price (figure 4). Apart from Dowa, which is located in the Central region of the country, all the other districts in which fertilizer use is profitable, are located in the Southern region. Districts in the southern region have relatively lower NUE but higher maize prices and lower nitrogen prices than the districts in the Northern and Central regions. Hence, the higher profitability of fertilizer use in the districts in the Southern region can be attributed to the fact that farmers in these district face higher maize prices and lower nitrogen prices. This makes sense because southern Malawi has low NUE, low yields and high population density; a condition that results in the area being maize deficit with high maize prices, often leading to maize coming in to Southern Malawi from the central region and Mozambique.

These results suggest that the profitability of inorganic fertilizer use can be improved by increasing NUE and/or increasing the maize-nitrogen price ratio. On average, assuming positive transaction cost, in order for the average farmer to break-even from using fertilizer (MVCR=2.0), the NUE will have to increase to 28.20kg (137.17%) when maize is valued at farm gate price, and to 17.89kg (50.46%) when maize is valued at lean season market price (figure 5). At the plot-level, in order for fertilizer use to be profitable, NUE will have to increase by more than 100% on 69.5% of the plots when maize is valued at farm gate price, and 22% of the plots when maize is valued at the lean season market price. Also, NUE will have to increase by 40%-100% on about 25.78% of 24
the plots in order for fertilizer to be profitable when maize is valued with either farm gate price or harvest season price.

# _Profitability of Subsidized Fertilizer vs. Cash Transfer Equivalent for Smallholders_

Using the average NUE of 11.89, average nitrogen price of MK 348.15 per kg, and the average farm gate and lean season maize price of MK 23.72 and MK 38.69 per kg respectively, we compared the cash amount of fertilizer subsidy with how much the average farmer will gain from using subsidized fertilizer in maize production. The results indicate that at all rates of fertilizer subsidy (0 – 100%), unless farmers are able to store their produce and sell in the lean season, the average farmer would be MK 66.16 (US$ 0.18) per kg of subsidized nitrogen betteroff with the cash equivalent of the subsidy than participating in the subsidy program if maize is valued at the farm gate (figure 6).<sup>5</sup> If farmers are able to store maize and sell in the lean season however, they will be MK 111.70 (US$ 0.30) per kg of subsidized nitrogen better off with the subsidized inputs than with the cash amount of the subsidy. The estimates should be interpreted as lower bounds because we could not account for the opportunity cost and the other operational costs associated with maize production in the estimation, both of which will make the cash equivalent of the subsidy more favorable than the subsidized inputs to the beneficiary smallholders. Hence, although a fertilizer subsidy increases the profitability of fertilizer use, farmers would, on average, be better off with

> 5 As an example, for a 90% fertilizer subsidy rate, the cash equivalent of the subsidy would be MK 313.34 (i.e. 90% of MK 348.15, the price of nitrogen). If a farmer participated in the fertilizer subsidy program and uses the subsidized fertilizer to produce maize, he or she would gain a net income of MK 247.18 [i.e. (11.89*23.72) – 34.82]. Where 11.89 is the NUE, 23.72 is the farm gate price of maize, and 34.82 is the price (10%) that the farmer would pay for a kilogram of subsidized nitrogen. Given the cash equivalent of MK 313.34 and the net gain of using subsidized fertilizer to produce maize of MK 247.18, the amount by which the farmer would be better-off with the cash equivalent instead of subsidized nitrogen is given MK 66.16 (i.e. MK 313.34 - MK 247.18). This is true for all rates (0 to 100%) of fertilizer subsidy. An excel sheet showing the calculation at all rates of the subsidy (0 to 100%) is available upon request.

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the cash equivalent of the subsidy than with subsidized inputs at current market and agronomic conditions, unless they are able to defer the selling of their output to the lean season.

# _Profitability of Government Recommended Rates of Nitrogen Application_

As a final exercise, the study investigates the profitability of fertilizer use at rates recommended by the Ministry of Agriculture and Food Security of Malawi (MoAFS). The government recommended rate of nitrogen application in maize production is 35kg/ha, 69kg/ha or 92kg/ha depending on the geographical location. The corresponding NUE of the nitrogen recommended rate was computed at the plot-level using the estimates from the production function estimated via the “plot” multilevel model. With this NUE and the prices of nitrogen and the various prices of maize, the MVCR of the government recommended rates is computed to be 1.77 at farm gate maize price, 2.89 at the lean season maize price, and 4.71 at import parity maize price (figure 7).

Thus, compared to the actual rate of nitrogen application, the government rate of application is about 116% to 119% more profitable depending on the price at which maize is valued (figure 7). These results also show that, compared to the actual rate of application, the number of gardens on which fertilizer is profitable is between 26 and 50 percentage points higher. Figure 8 reveals that the actual rate of N application on a majority (about 82%) of plots is lower than the government recommended rates. This suggests that fertilizer profitability can be improved by encouraging farmers to adopt the government recommended rates.

# **Conclusions and Policy Recommendations**

This study uses two-wave nationally representative household panel data from Malawi to estimate the profitability of fertilizer use. Specifically, the study assessed the extent to which 26
inorganic fertilizer use is profitable and how that varies across space, the profitability of subsidized fertilizer vs. an equivalent cash transfer to beneficiaries, and the profitability of government recommend fertilizer application rates vs the actual application rates of smallholders in our sample. The study adds to the fertilizer profitability literature by controlling for plot-level unobserved heterogeneity, in addition to considering various maize prices that farmers face across time and space, and by relating the estimates to the geographical targeting of large-scale fertilizer subsidy programs.

The main results of our study suggest that when we assume farmers face positive transaction costs when using fertilizer, the input is on average not profitable at commercial price of fertilizer when maize is valued at either the farm gate price or lean season market price. The study also finds that, in order to make fertilizer more profitable at prevailing market conditions, the current average nitrogen use efficiency of 11.89kg would have to increase by at least 137.17% and by 50.46% if maize output is valued at farm gate price and lean season market price, respectively. Though these NUE estimates are lower than those used in other recent studies, such as Dorward et al. (2008), Arndt et al. (2015) and Harou et al. (2017) our use of recently collected nationally representative panel data on smallholders using plot-level FE could provide internally and externally valid estimates that are useful for policy analysis.

Our results are consistent with Arndt et al. in that our NUE of 11.89 suggests that FISP does not break-even. This is why we find that at all rates of subsidy, unless farmers are able to store their produce and sell in the lean season, the average farmer is MK 66.16 (US$ 0.18) per kg of subsidized nitrogen better off with the cash equivalent of the subsidy than participating in the subsidy program if maize is valued at the farm gate. Finally, the study finds that, compared to the current rate of nitrogen application, the government recommended rate is 116% to 119% more profitable depending on the price at which maize is valued.

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Based on these findings, the study makes the following recommendations. First, in order to improve the profitability of fertilizer use in maize production in Malawi, NUE needs to improve. Applying basal fertilizer within a week after planting and applying organic manure has yieldincreasing effects. NUE can therefore be raised by encouraging farmers to comply with these recommendations.

Second, the Ministry of Agriculture and Food Security should encourage farmers to increase their current rates of nitrogen application to the government recommended rates in order to improve the profitability of fertilizer use. This will require concerted investment in extension efforts that should be done alongside or in place of subsidized fertilizer and maize seed distribution.

Third, fertilizer profitability can be improved by encouraging agricultural households to store most of their maize to consume or sell during the lean season when prices are relatively high. This can be done by promoting the adoption of improved grain storage technologies. In addition, farmers are usually compelled to sell their produce soon after harvesting for financial reasons, so another way of encouraging them to store and sell during the lean season would be by providing them with credit that could be paid back later on in the lean season rather than at harvest.

Fourth, efforts should be made to reduce the real costs of input supply, through investment in roads, and infrastructure (Jayne et al, 2003). This will lower commercial fertilizer prices and make it more profitable to use the input. Finally, the study recommends that, in the context of fertilizer profitability, it is also important for the government to consider transferring the cash equivalent to farmers in areas where NUE on maize production is extremely low. Households in these areas likely would obtain a higher benefit from the cash than they do from subsidized fertilizer.

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# Table 1: Definition of variables

|**Variable**|**Definition**|
|---|---|
|N application rate|Nitrogen application rate (Kg/ha)|
|Below recommended N application rate|= 1 if nitrogen application is more than 10% below the recommended application rate|
|Above recommended N application rate|= 1 if nitrogen application is more than 10% above the recommended application rate|
|Applied basal fertilizer on time|= 1 if basal fertilizer was applied within a week after planting|
|Applied organic fertilizer|= 1 if organic fertilizer was applied|
|Seed rate|Seed application rate (Kg/ha)|
|Used hybrid seed|= 1 if hybrid seed was used|
|Pure stand|= 1 if plot was pure stand|
|Plot size|GPS-measured plot size (ha)|
|Labor|Days of labor (family, hired and exchange) used for non-harvesting activities|
|Soil is of good quality|= 1 if plot is of good soil quality; 0 otherwise|
|Soil is of fair quality|= 1 if plot is of poor soil quality; 0 otherwise|
|Plot is not flat|= 1 if plot is not flat; 0 otherwise|
|Plot is swampy|= 1 is plot is swampy; 0 otherwise|
|Soil is sandy-clay|= 1 if soil is sandy-clay; 0 otherwise|
|Plot show signs of erosion|= 1 if plot showed signs of erosion; 0 otherwise|
|Female plot manager|= 1 if plot manager is female; 0 otherwise|
|Age of plot manager|Age of plot manager (years)|
|Years of education of plot manager|Years of education of plot manager|
|African Adult Male Equivalent|African Adult Male Equivalent household size|
|Dependency ratio|Dependency (child and adult) ratio|
|Distance to boma|Distance to district capital (Km)|
|Index of ownership of agricultural tools|1<sup>st</sup>principal component analysis of agricultural tools owned by the household|
|Index of ownership of durable good|1<sup>st</sup>principal component analysis of durable assets owned by the household|
|Annual mean rainfall|Avg 12-month total rainfall(mm) for July-June|
|Annual mean temperature|Annual mean temperature (<sup>o</sup>C*10)|

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Table 2: Descriptive Statistics

||Pooled||2010||2013||
|---|---|---|---|---|---|---|
||Mean|SD|Mean|SD|Mean|SD|
|Maize yield (Kg/ha)|1,401.66|1,071.56|1,240.61|920.973|1,536.273***|1,166.27|
|Nitrogen application rate (Kg/ha)|46.014|44.657|49.181|44.595|43.367***|44.599|
|Above recommended nitrogen application rate (1/0)|0.143|0.356|0.161|0.372|0.129***|0.341|
|Applied basal fertilizer on time (1/0)|0.284|0.456|0.355|0.482|0.224***|0.424|
|Applied inorganic fertilizer twice (1/0)|0.746|0.437|0.778|0.422|0.720***|0.448|
|Fertilizer used is basal fertilizer|0.507|0.5|0.484|0.5|0.527***|0.499|
|Applied organic fertilizer (1/0)|0.162|0.364|0.131|0.335|0.187***|0.385|
|Seed rate (Kg/ha)|25.019|21.447|22.814|25.273|26.863***|17.437|
|Used hybrid seed (1/0)|0.406|0.492|0.43|0.496|0.386***|0.489|
|Pure stand (1/0)|0.467|0.5|0.511|0.499|0.431***|0.499|
|Plot size (ha)|0.409|0.265|0.422|0.255|0.398***|0.272|
|Labor (days)|135.58|98.763|119.599|80.505|148.937***|109.886|
|Soil is of good quality (1/0)|0.444|0.496|0.457|0.498|0.433|0.495|
|Soil is of fair quality (1/0)|0.42|0.495|0.409|0.492|0.429|0.497|
|Plot is not flat (1/0)|0.449|0.497|0.451|0.498|0.446|0.496|
|Plot is swampy (1/0)|0.159|0.362|0.158|0.358|0.16|0.365|
|Soil is sandy clay (1/0)|0.548|0.495|0.554|0.495|0.542|0.496|
|Plot show signs of erosion (1/0)|0.378|0.486|0.38|0.489|0.376|0.482|
|Female plot manager (1/0)|0.309|0.457|0.297|0.453|0.318|0.46|
|Age of plot manager (years)|42.608|15.184|41.783|14.927|43.298***|15.353|
|Years of education of plot manager|4.822|3.84|4.735|3.83|4.895|3.847|
|African Adult Male Equivalent|3.961|1.648|3.843|1.597|4.059***|1.683|
|Dependency ratio (%)|122.008|90.398|124.345|92.688|120.054***|88.426|
|Distance to main district market (Km)|38.023|27.151|49.483|27.265|28.443***|23.413|
|Index of ownership of agricultural tools|0.289|1.354|0.508|1.695|0.105***|0.934|
|Index of ownership of durable goods|-0.793|1.552|-0.568|1.573|-0.981***|1.509|
|Annual mean rainfall (mm)|827.249|80.186|830.507|86.039|824.526***|74.715|
|Annual Mean Temperature (°C * 10)|215.331|17.816|215.482|18.045|215.205|17.625|

*** implies significant difference in mean between 2013 and 2010 at the 1% level

33
# Table <u>3: Maize Production function</u>

|||||||Multile<br>(Level 1|vel models<br> =sub-Plot)|
|---|---|---|---|---|---|---|---|
|VARIABLES|OLS|DistrictFE|CommunityFE|HouseholdFE|PlotFE|<br>Level 2 = HH|<br>Level 2 = Plot|
|N application rate (Kg/ha)|12.092***<br>(1698)|11.284***<br>(1678)|10.637***<br>(1741)|9.237***<br>(2248)|11.213***<br>(3174)|11.552***<br>(1484)|11.887***<br>(1521)|
|Nitrogen application rate (Kg/ha) squared|.<br>-0.017|.<br>-0.016|.<br>-0.015|.<br>-0.014|.<br>-0.027|.<br>-0.017*|.<br>-0.018*|
||(0.011)|(0.010)|(0.011)|(0.013)|(0.016)|(0.009)|(0.009)|
|Below recommended N application rate|<br>59.641<br>(83.920)|<br>21.955<br>(83.242)|<br>-4.043<br>(83.399)|<br>-14.258<br>(87.246)|<br>57.552<br>(100.810)|<br>69.972<br>(76.992)|<br>82.740<br>(78.777)|
|Ab dd N liti t|<br>281236***|<br>240122***|<br>214159**|<br>199043**|<br>236136***|<br>211968**|<br>233993***|
|ove recommene appcaon rae|-.<br>(93.450)|-.<br>(86.948)|-.<br>(87.359)|-.<br>(92.964)|-.<br>(62.194)|-.<br>(84.074)|-.<br>(88.874)|
|Applied basal fertilizer on time|<br>153.624***<br>|<br>114.864***<br>|<br>114.642***<br>|<br>184.009***<br>|<br>171.070**<br>|<br>172.323***<br>|<br>169.239***<br>|
||(39.746)|(41.541)|(40.853)|(66.360)|(78.907)|(40.290)|(36.331)|
|Fertilizer used is basal fertilizer|194.653***|206.447***|224.489***|196.515***|259.993***|180.716***|182.223***|
||<br>(38.478)|<br>(37.399)|<br>(36.026)|<br>(49.299)|<br>(73.855)|<br>(34.260)|<br>(33.186)|
|Applied organic fertilizer|132.084**|132.407***|135.516***|121.343**|87.521**|136.256***|126.458***|
|<br>|(51.262)<br>|(47.636)<br>|(43.187)<br>|(52.494)<br>|(36.686)<br>|(42.020)<br>|(40.595)<br>|
|Seed rate (Kg/ha)|3.769***|3.164***|3.314***|3.651***|2.513*|3.625***|3.453***|
|<br>|(0.920)<br>|(0.892)<br>|(0.870)<br>|(0.951)<br>|(1.293)<br>|(0.809)<br>|(0.789)<br>|
|Used hybrid seed|31.985<br>(33.965)|26.574<br>(33.007)|38.291<br>(29.982)|51.413<br>(38.839)|136.536*<br>(69.693)|30.901<br>(30.243)|40.850<br>(30.724)|
|Pure stand|<br>-86.076**|<br>-175.919***|<br>-174.341***|<br>-191.329***|<br>-210.800***|<br>-109.635***|<br>-101.360***|
||(40.030)|(34.995)|(36.081)|(42.867)|(48.028)|(31.010)|(30.209)|
|Sub-Plot size (ha)|<br>-676.112***<br>|<br>-894.862***<br>|<br>-883.008***<br>|<br>-1,401.012***<br>|<br>-1,800.821***<br>|<br> <br>-916.596***<br>|<br>-847.798***<br>|
||(222.339)|(214.805)|(235.539)|(350.108)|(395.619)|(189.547)|(183.287)|
|Sub-Plot size (ha) squared|<br>193891|<br>273539*|<br>275557*|<br>581543**|<br>752706**|<br>344274***|<br>286124**|
||.<br>(146.553)|.<br>(152.918)|.<br>(163.325)|.<br>(259.038)|.<br>(314.832)|.<br>(130.718)|.<br>(127.525)|
|Labor (days)|0.925***|0.934***|0.913***|0.952***|0.962***|0.942***|0.950***|
|<br>Soil is of good quality|<br>(0.209)<br>283.499***|<br>(0.207)<br>239.698***|<br>(0.206)<br>219.820***|<br>(0.268)<br>168.253***|<br>(0.282)<br>178.885**|<br>(0.197)<br>253.805***|<br>(0.183)<br>259.843***|
||(50273)|(48692)|(50062)|(54691)|(75471)|(41783)|(41783)|
|Soil is of fair quality|.<br>173.437***|.<br>156.578***|.<br>147.593***|.<br>181.907***|.<br>230.479***|.<br>179.355***|.<br>179.136***|
||(50434)|(44756)|(43679)|(49679)|(62539)|(40327)|(40557)|
|Sub-Plot is not flat|.<br>-47.802|.<br>-41.290|.<br>-44.742|.<br>-76.431*|.<br>-78.986|.<br>-59.257*|.<br>-53.645*|
||(35.259)|(35.148)|(34.091)|(39.650)|(66.640)|(31.338)|(31.160)|
|Sub-Plot is swampy|<br>-5.287<br>(38.283)|<br>-8.920<br>(35.238)|<br>-33.823<br>(37.309)|<br>-83.808<br>(52.386)|<br>-115.656<br>(89.498)|<br>-32.024<br>(40.500)|<br>-26.390<br>(39.466)|
|Soil is sandy clay|<br>25.051<br>|<br>33.361<br>|<br>33.122<br>|<br>-13.825<br>|<br>-8.740<br>|<br>24.675<br>|<br>29.723<br>|
||(35.023)|(31.709)|(33.549)|(38.385)|(57.240)|(30.402)|(29.994)|
|Sub-Plot show sins of erosion|<br>38679|<br>-15097|<br>-11732|<br>5421|<br>46803|<br>31250|<br>41151|
|g|.<br>(46.275)|.<br>(42.716)|.<br>(43.577)|.<br>(53.265)|.<br>(45.854)|.<br>(36.397)|.<br>(34.315)|
|Female plot manager|-102.625***|-90.399**|-107.605***|-150.468**|-198.198**|-111.814***|-113.273***|
||<br>(36.295)|<br>(35.365)|<br>(36.724)|<br>(63.280)|<br>(82.736)|<br>(34.716)|<br>(32.751)|
|Age of plot manager|-1.483|-1.201|-0.993|2.853|0.612|-0.704|-1.126|
|<br>|(1.377)<br>|(1.285)<br>|(1.275)<br>|(1.939)<br>|(2.211)<br>|(1.185)<br>|(1.106)<br>|
|Years of education of plot manager|13.855***|10.930**|8.181*|8.614|-7.623|10.638**|10.353**|
||(5201)|(4830)|(4752)|(10485)|(12591)|(5020)|(4674)|
|African Adult Male Equivalent|.<br>-5.412|.<br>-2.932|.<br>-0.071|.<br>10.825|.<br>29.695|.<br>-5.356|.<br>-5.070|
||(13.647)|(13.647)|(14.650)|(27.334)|(38.042)|(12.150)|(10.909)|
|Dependency ratio|<br>0.289<br>|<br>0.215<br>|<br>0.245<br>|<br>0.226<br>|<br>0.046<br>|<br>0.298<br>|<br>0.249<br>|
|Distance to main district market|(0.195)<br>0481|(0.183)<br>-0354|(0.188)<br>-0455|(0.286)<br>-0809|(0.272)<br>-0219|(0.197)<br>0068|(0.186)<br>0373|
||.<br>(0.803)|.<br>(0.896)|.<br>(0.885)|.<br>(0.983)|.<br>(1.314)|.<br>(0.616)|.<br>(0.568)|
|Index of ownership of agricultural tools|77.715***<br>|67.763***<br>|52.832***<br>|-6.816<br>|-7.012<br>|56.861***<br>|68.958***<br>|
|Index of ownership of durable goods|(19.448)<br>88.175***|(17.097)<br>92.435***|(13.962)<br>98.621***|(19.674)<br>83.865***|(28.193)<br>108.644***|(14.832)<br>92.980***|(13.108)<br>93.727***|
|<br>Annual mean rainfall(mm)|<br>(15.353)<br>0.815**|<br>(15.075)<br>0.903|<br>(15.597)<br>1.472|<br>(27.362)<br>3.411*|<br>(30.276)<br>3.403|<br>(13.880)<br>1.049***|<br>(12.545)<br>1.006***|
|<br>|(0.374)<br>|(0.599)<br>|(1.116)<br>|(1.871)<br>|(3.007)<br>|(0.250)<br>|(0.236)<br>|
|Annual mean temperature (°C * 10)|-8.853***<br>(1897)|-4.313*<br>(2587)|-5.212<br>(3797)|-10.718<br>(6943)|-17.927<br>(12535)|-7.751***<br>(1274)|-7.841***<br>(1204)|
|Year (2013)|.<br>347.955***<br>(40.732)|.<br>313.956***<br>(43.804)|.<br>307.908***<br>(42.329)|.<br>272.768***<br>(48.234)|.<br>263.957***<br>(45.960)|.<br>317.304***<br>(33.288)|.<br>317.289***<br>(30.993)|
|Agro-ecological zone fixed effects<br>Constant|<br>Yes<br>1,662.699***|<br>Yes<br>980.193|<br>Yes<br>810.346|<br>Yes<br>524.097|<br>Yes<br>2,302.636|<br>Yes<br>1,424.072***|<br>Yes<br>1,428.150***|
||<br>(598.780)|(867.096)|(1,294.931)|(2,492.269)|<br>(4,859.146)|<br>(409.097)|<br>(380.119)|
|Observations<br>R-suared|4,913<br>0283|4,913<br>0318|4,913<br>0246|4,913<br>0226|4,913<br>0247|4,913<br>--|4,913<br>--|
|q<br>Number of groups|.<br>--|.<br>26|.<br>194|.<br>2,135|.<br>3,365|<br>2,135|<br>3,365|

Robust standard errors in parentheses. HH = Household.

34
***, **, and * imply significant at 1%, 5% and 10% levels respectively

Figure 1: Distribution of maize response rate to fertilizer based on multilevel model (Level 1 = sub-plot; Level 2 = plot) <!-- Start of picture text --> 0 5 10 15 20 25 30<br>Nitrogen Use Efficiency (Kg Maize/Kg Nitrogen)<br>40<br>30<br>20<br>Percent of sub-plots<br>10<br>0<br><!-- End of picture text --> Mean: 11.82; Minimum: 2.82; Maximum: 25.98; Standard deviation: 2.42 35
<!-- Start of picture text --> a<br>2<br><!-- End of picture text --> <!-- Start of picture text --> =<br>g<br><!-- End of picture text --> <!-- Start of picture text --> Lay<br>&<br><!-- End of picture text -->
Figure 3: Average profitability of Nitrogen use at different prices of maize <!-- Start of picture text --> 2.18<br>1.32<br>0.81<br>Farm gate Lean season Import parity<br>2<br>1.5<br>1<br>.5<br>Marginal value cost ratio (MCVR)<br>0<br><!-- End of picture text --> 37
<!-- Start of picture text -->
-<br>=<br><!-- End of picture text -->

<!-- Start of picture text --> &<br><!-- End of picture text -->
Figure 5: Current and optimal levels of nitrogen use efficiency at different prices of maize in Malawi Kwacha/Kg.

<!-- Start of picture text --> 28.20<br>17.89<br>14.10<br>11.89 11.89<br>8.94<br>Farm gate Lean season<br>Current Break-even (MVCR=1) Break-even (MVCR=2)<br>30<br>20<br>10<br>Nitrogen use efficiency (Kg maize / Kg N)<br>0<br><!-- End of picture text --> 39
Figure 6: Profitability of subsidized fertilizer versus cash transfer equivalent for smallholders (maize output is valued at farm-gate price).

<!-- Start of picture text --> 330<br>280<br>230<br>180<br>130<br>80<br>30<br>-20<br>-70<br>0 10 20 30 40 50 60 70 80 90 100<br>Subsidy rate<br>Price of subsidized N<br>Net gain from producing 1kg of maize with 1kg of subsidized N<br>Amount by which farmers would be better-off with cash transfer<br>Amount in Malawian Kwachas<br><!-- End of picture text --> 40
Figure 7: Average profitability of government recommended rate of fertilizer application at different prices of maize <!-- Start of picture text --> 4.71<br>2.89<br>2.18<br>1.77<br>1.32<br>0.81<br>Farm gate Lean season Import parity<br>Actual Gov't recommneded rate<br>5<br>4<br>3<br>2<br>1<br>Marginal value cost ratio (MVCR)<br>0<br><!-- End of picture text --> 41
Figure 8: Distribution of recommended N application rate minus actual N application rate <!-- Start of picture text -->
-100 -50 0 50 100 150<br>Actual N rate - Government recommended N rate<br>.01<br>.008<br>.006<br>Density<br>.004<br>.002<br>0<br><!-- End of picture text -->

42
# **Appendix A: Specification of the “household” multilevel model**

For yield on plot _p_ , belonging to household _h_ , the model at the various level of the hierarchy is specified as: <u>Plot-level model</u> 0h 1h where YYpph = ββ is yield; + ββ NNpph + XX is nitrogen application rate; pphββxx + εεpph (AA1) is a vector of other plot-level variables affecting maize yield; and represents the plot-level error term. 0h is the random intercept, varying across pph pph pph YY NN XX households, but has the same value for individual plots belonging to household _h._ 0h therefore pph measures the mean yield for plots in household εε _h_ . 1h is the random slope for the nitrogen variable ββ which varies across households. is a vector of fixed coefficients for the other plot-level variables, ββ where the subscript _x_ represents the corresponding plot-level variable in vector ββ . Unlike NUE 1h) , xx ββ these coefficients are fixed because their variation across households is not of any particular interest in pph XX (ββ this study. Moreover, fixing these coefficients will reduce the complexity of the full model specified below.

<u>Household-level model</u> The study hypothesizes that variability in the random intercept ( 0h) is explained by household level variables. Thus, in the household-level model, equations (3.7a) and (2.7b), the random intercept is ββ expressed as a function of household-level variables. 0h 00 h 0h (A2a) ββ 1h = ββ 10 + HH1hαα (A2b) 0mm0 + NN where ββ = ββh is a vector of household-level variables + NN . 00 and 10 are the household-level group effect for the intercept and the NUE (i.e. the mean yield and NUE ) respectively; and household-specific variation around these values are represented by HH 0h and 1hββ . ββ represents the contribution of household variables to the variation in the random intercept, where the subscript _m_ represents the corresponding 0mm0 household-level variable in vector h . NN NN αα <u>Full model</u> HH Substitution of equations (3.7a) and (3.7b) into equation (3.6) results in the full multilevel model which is given by: 00 10 h 0h pphccii pph pph kk 0mm0 1hccii pph pph The terms in bracket, YY = ββ + ββ0h NN + XX ββ + HH�, represent the total error term in the full model — αα + �NN + NN NN + εε � (AA3) from the plot level, and 0h a 1h from the household level. 1hccii pph pph pph �NN + NN NN + εε εε pph NN aa NN NN 43