metadata: authors: 0: author: Khan,Shafaat Yar
1: author: Khederlarian,Armen
count: World
docna: 0: docna: How Does Trade Respond to Anticipated Tariff
            Changes ? Evidence from NAFTA
docty: Policy Research Working Paper
subtopic: International Trade and Trade Rules,Trade and Services,Rules of Origin,Trade and Multilateral Issues,Trade Policy
teratopic: International Economics and Trade
abstracts: cdata!: Firms anticipate upcoming tariff changes
            by shifting their purchases to periods with lower costs.
            This paper shows that such anticipatory dynamics overstate
            the trade elasticity. Standard identification of the trade
            response to trade cost changes uses tariff variation from
            free trade agreements and assumes that trade flows equal
            their consumption. However, free trade agreements eliminate
            tariffs gradually through announced phaseouts. This allows
            firms to delay their purchases until tariff cuts are
            effective, while consuming their inventories. Indeed, during
            the North American Free Trade Agreement’s staged tariff
            reductions, imports experienced sizable anticipatory slumps
            followed by libseralization bumps. To study the behavior of
            consumed imports, a measure is constructed that uses
            inventory-to-sales ratios to smooth the trade flows. Its
            application to the data yields that the annual trade-flow
            elasticity is 56 percent larger than the trade-consumption
            response and that the ratio of the long- to short-run
            elasticity increases from 2.3 with trade flows to 3.4 with
            consumed imports. The measure is validated through Monte
            Carlo simulations of an (s,S) ordering model that reproduces
            the observed trade pattern.
repnme: repnme: How Does Trade Respond to Anticipated
            Tariff Changes ? Evidence from NAFTA
display_title: How Does Trade Respond to
            Anticipated Tariff Changes Evidence from NAFTA
listing_relative_url: /research/2021/04/33036884/trade-respond-anticipated-tariff-changes-evidence-nafta
topicv3: Trade m1326924 698,Trade in Services m1326928 780,Trade Policy and Integration m1327407 775,Trade Policy m1327640 776,Preferential Trade and Investment
            Agreements m1504283 2581
publishtoextweb_dt: 2021-04-29T00:00:00Z
dois: 10.1596/1813-9450-9646
historic_topic: International Economics and Trade
origu: EAP Chief Economist Unit (EAPCE)
no_of_pages: 54
author_keys: 0: author_key: 1919358
model_extractions: Policy Research Working Paper 9646 How Does Trade Respond to Anticipated Tariff Changes?

Evidence from NAFTA _Shafaat Yar Khan Armen Khederlarian_ East Asia and the Pacific Region Office of the Chief Economist April 2021
Policy Research Working Paper 9646

# **Abstract**

Firms anticipate upcoming tariff changes by shifting their purchases to periods with lower costs. This paper shows that such anticipatory dynamics overstate the trade elasticity. Standard identification of the trade response to trade cost changes uses tariff variation from free trade agreements and assumes that trade flows equal their consumption. However, free trade agreements eliminate tariffs gradually through announced phaseouts. This allows firms to delay their purchases until tariff cuts are effective, while consuming their inventories. Indeed, during the North American Free Trade Agreement’s staged tariff reductions, imports experienced sizable anticipatory slumps followed by libseralization bumps. To study the behavior of consumed imports, a measure is constructed that uses inventory-to-sales ratios to smooth the trade flows. Its application to the data yields that the annual trade-flow elasticity is 56 percent larger than the trade-consumption response and that the ratio of the long- to short-run elasticity increases from 2.3 with trade flows to 3.4 with consumed imports. The measure is validated through Monte Carlo simulations of an (s,S) ordering model that reproduces the observed trade pattern.

This paper is a product of the Office of the Chief Economist, East Asia and the Pacific Region. 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 sykhan@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
# **How Does Trade Respond to Anticipated Tariff Changes? Evidence from NAFTA**<sup>_∗_</sup>

Shafaat Yar Khan<sup>_†_</sup> and Armen Khederlarian<sup>_‡_</sup>

## **JEL Classifications:** F12, F13, F14

**Keywords:** Anticipation, Trade Elasticity, Inventories, NAFTA, Phaseouts

> _∗_ We thank Costas Arkolakis and two anonymous referees for helpful comments and suggestions. We are greatly indebted to George Alessandria for his invaluable discussions, guidance, and support throughout this project. We are also extremely grateful to Mark Bils, Yan Bai and Dan Lu for numerous comments and suggestions. Moreover, we would like to thank Mario Crucini, Alexandre Skiba, B. Ravikumar, George Schaur, Mostafa Beshkar, Ahmad Lashkaripour, Russel Hillberry, John Romalis, Lorenzo Caliendo, Kei Mu Yi, Carter Mix, Oscar Avila and seminar participants at the University of Rochester and conference participants at the ETSG 2018 (Warsaw), the Spring 2019 Midwest Macroeconomics Meetings (UGA), the Spring 2019 Midwest International Trade Meetings (IUB), the 2019 Economics Graduate Student’s Conference (WashU) and Lisbon Meetings in Game Theory & Applications (LSEM).

> _†_ sykhan@worldbank.org, World Bank

> _‡_ armen.khederlarian@gmail.com, University of Rochester
# **1 Introduction**

Most trade policy changes are announced before their implementation, giving firms the opportunity to shift their purchases to periods with lower costs.<sup>1</sup> In particular, Free Trade Agreements (FTAs) are usually put into effect gradually with scheduled phaseouts of the initial tariffs. In the case of the North American Free Trade Agreement (NAFTA), 96% of the tariff reductions were known at least one year in advance. The knowledge of future tariff reductions provides firms with strong incentives to schedule their imports accordingly. Using inventories in the meantime, firms can delay their purchases until the change is effective and then stock up. These anticipatory dynamics create a gap between the trade flows and their consumption. While gravity foundations of the trade elasticity do not distinguish between trade and its consumption, it is commonly estimated using variation in trade flows and tariffs from the FTAs. In this paper, we show that in the presence of anticipatory dynamics this distinction is consequential.

First, we document that in the early years of NAFTA, US imports from Mexico dropped strongly in anticipation and then overshot sharply right after the tariff reduction. Second, we propose a model-based measure of the consumption of imports. Its application to the data demonstrates that these dynamics cause the short run (annual) trade elasticity to be substantially smaller when using consumed imports — trade-consumption elasticity — rather than imports crossing the border — trade-flow elasticity. Third, we show that a <u>(</u> _<u>s s</u>_ <u>) ordering model reproduces the documented trade flow pattern and use Monte Carlo</u> simulations to validate the consumption measure.

NAFTA with its gradual tariff phaseouts provides a clear case of anticipated trade policy changes. Among the goods that were not already tariff-free before NAFTA, 75% were scheduled to be phased-out gradually over up to 15 years. In fact, the original text of the agreement specified the exact schedule of tariff phaseouts at HS-8 product level, including the number of stages, the size and the date of each staged tariff reduction. While there was little time to anticipate the first round of tariff reductions,<sup>2</sup> in the following years, all the phaseout stages were scheduled to take place on January 1. Since

> 1Recently there have been numerous examples of anticipated trade policy changes. Imports of solar panels soared in the three months before the tariff safeguards took effect (Wall Street Journal Jan 03, 2018). Similarly, Iran stockpiled oil tankers during the six months before the actual lifting of export sanctions in January 2016 (The Economist Jan 23,2016).

> 2NAFTA was ratified by the US Congress only 40 days before coming into force on Jan 1, 1994.

1
all traded goods are storable to some extent, the certainty and knowledge of future tariff reductions provided firms with strong incentives to delay their purchases in advance of their implementation and then to stock up in their aftermath.

Indeed, we find strong evidence of _anticipatory slumps_ and _liberalization bumps_ in the response of trade flows to tariff cuts for US imports from Mexico of phased-out goods. We estimate these anticipatory dynamics by using a standard odds ratio or “tetrads” method (Head and Ries (2001), Head et al. (2010)) to construct trade flows, we then consider within-year growth rates of these. First, we find that in anticipation of an upcoming tariff reduction of 1%, imports dropped by a sizeable 6% in November and December relative to the middle of the year. Second, in the first few months after the tariff reduction, imports spiked by 12% with respect to the end of the previous year. The size of these high frequency reversals are large even in comparison to previously documented shortrun (annual) estimates of the trade elasticity. This paper is the first to our knowledge to document how (1) firms anticipate tariff reductions during gradual phaseouts and (2) that the trade elasticity can be quite large even at high frequencies.

Importantly, we find that the anticipatory dynamics are increasing in the degree of product storability. This suggests that trade flows and their consumption might significantly diverge during these episodes. Unfortunately, the consumption or usage of imports is not observed, especially at the level of aggregation used in the estimation of trade elasticities. To make progress, we propose a novel measure of the consumption of imports that builds on monthly trade data and the assumption that a constant fraction of inventory holdings are used for consumption. A product-source country specific inventory-usage ratio is obtained by exploiting the fact that more storable goods are traded less frequently.<sup>3</sup> We validate the measure of consumption by demonstrating that (1) it eliminates the anticipatory slumps documented for NAFTA’s phased-out goods, and (2) it is effective in replicating the actual consumption response in Monte Carlo simulations of a <u>(</u> _<u>s, s</u>_ <u>)</u> ordering model.

With our measure of consumed imports in hand, we examine how the anticipatory dynamics lead to deviations between the trade-flow and the trade-consumption elasticities using annual data. Consistent with the smooth behavior of consumed imports around the tariff changes, the annual or short-run trade-consumption elasticity is smaller

> 3This relationship emanates from the existence of per shipment ordering costs that lead firms to trade off the frequency of orders against the costs of holding inventories.

2
than the trade-flow elasticity, dropping from 4.2 to 2.7. This deviation is driven by the phased-out goods, for which the estimated annual trade-flow elasticity is 7.4, while the trade-consumption elasticity is 2.9. As expected, these differences become less important when considering changes over longer horizons. In effect, the two long-run (7-year) elasticities are almost indistinguishable. A straightforward implication is that the ratio of the long- to short-run elasticities is significantly larger when considering the response of consumed imports, as it increases from 2.3 in the case of trade flows to 3.4. This indicates that the adjustment to trade liberalizations might be even more gradual than previously documented. These findings are important in light of the welfare implications of transitions in dynamic models of trade (Alessandria et al. (2021)). Finally, we show that the average estimates that pool over sample periods with gradual tariff reductions and that are used as an input for the welfare analysis of static models of trade can contain non-negligible deviations between the trade-consumption and trade-flow response.

This paper is related to three main strands of literature. In first place, we contribute to the empirical literature on the anticipatory effects of policy changes. When policy changes are implemented with lags, previous studies have shown that households increase their purchases in anticipation of upcoming local consumption sales tax hikes (Baker et al. (Forthcoming), Agarwal et al. (2017)) or gasoline tax rate increases (Coglianese et al. (2017)). In response to trade policy changes such evidence has been more scant. In the recent wave of US tariff hikes, the evidence of anticipation has been inconclusive. While Cavallo et al. (2019) find that two large US retailers stockpiled before the tariff increases, Fajgelbaum et al. (2020) find less support for this pattern in the overall trade flows. We show that when firms have ample time to anticipate tariff changes the response is similar to the one documented in the case of sales tax changes.

Second, we contribute to the literature on the estimation of the trade elasticity, the most important parameter in international trade (Arkolakis et al. (2012)). As a result of different estimation methods and samples, there is a wide range of estimates in the literature (Anderson and van Wincoop (2004), Hillberry and Hummels (2012)). Estimates based on cross-sectional data range from 4 to 6 (Feenstra (1994), Broda and Weinstein (2006), Simonovska and Waugh (2014), Caliendo and Parro (2015)), while studies using panel data tend to produce larger of estimates of around 7 to 11 (Head and Ries (2001), 3
Romalis (2007)).<sup>4</sup> Although anticipatory dynamics and the deviations between trade flows and their consumption around the tariff reduction are less of a concern in the long run, we show these significantly affect the estimate of the short run or annual trade elasticity. It is well established that trade responds gradually to trade liberalizations (Baier and Bergstrand (2007), Jung (2012), Besedes et al. (2020)). As in Yilmazkuday (2019) and Boehm et al. (2020), our results indicate that the long run trade elasticity is twice as large as the short-run.<sup>5</sup> However, when using trade consumption this ratio increases significantly suggesting an even larger role for the gradual adjustment.

Finally, the paper contributes to the literature of the role of inventories in accounting for observed trade dynamics. Incorporating inventory decisions into standard models of trade has been successful in accounting for the fluctuations of trade flows in response to business cycle shocks (Alessandria et al. (2010b), Alessandria et al. (2011a)), as well as for trade and pricing dynamics in response to large devaluations (Alessandria et al. (2010a), Charnavoki (2017)) or the pricing dynamics following a credit crunch (Kim (2018)). Here, we use a similar model to reproduce the observed trade pattern around NAFTA’s staged tariff reductions and validate our measure of the usage of imports.

The paper is organized as follows. Section 2 describes our methodological approach and documents the anticipation to NAFTA’s staged tariff reductions. Section 3 proposes a measure of the consumption of imports and uses it to estimate the trade-flow and tradeconsumption elasticities over different horizons. Section 4 introduces the <u>(</u> _<u>s, s</u>_ <u>)</u> ordering model and describes the Monte Carlo simulations that validate the measure of trade consumption. Section 5 concludes.

# **2 Anticipation of NAFTA’s Phaseouts**

This section documents that in advance of NAFTA’s staged tariff reductions, importers delayed their purchases and responded strongly after their implementation. First, we lay out our estimation approach. Second, we provide some background to NAFTA’s tariff phaseouts and describe the dataset. Third, we present the results and provide evidence that the anticipatory response was strongest for goods that are relatively more storable.

> 4A notable exception is Boehm et al. (2020) who estimate a long run elasticity of around 2.

> 5Using price data, Gallaway et al. (2003) show similar deviations of the elasticity of substitution.

4
# **2.1 Estimation Approach**

Our estimation of the trade elasticity in the short window around anticipated tariff reductions builds on a product-specific version of the gravity equation that emerges in a wide class of models of international trade.<sup>6</sup> Namely, imports _Miczt_ of good _z_ by country _i_ from country _c_ in year _t_ are described by: where _Aczt_ captures the exporter-product-time specific variables (e.g. supply terms) and _Bizt_ signifies the importer-product-time specific variables (e.g. demand terms), _φiczt_ is the total trade cost and _ε_ the trade elasticity, the object of our interest.<sup>7</sup> To identify _ε_ we implement a ratio-type of estimation approach by considering a reference exporter _c_<sup>_′_</sup> and reference importer _i_<sup>_′_</sup> and taking the double difference of their trade flows, so that:<sup>8</sup> We formulate the total trade cost to take the following form: where _τiczt ≥_ 1 are applied tariff rates, _Dicz_ time invariant bilateral measures of trade barriers such as distance, language or common borders, _Dizt_ ( _Dczt_ ) are importer (exporter) specific non-tariff trade barriers such as customs procedures, regulatory compliance or clearing lead times, and _uiczt_ is a random disturbance term that is assumed to be orthogonal to tariff rates. For notational simplicity, in what follows we denote the double difference of log trade flows as _m_<sup>_DD_</sup> _zt ≡_ ln <u>�</u> _MMiciczt′zt_<sup>_/_</sup> _M_<sup>_M_</sup> _i_<sup>_<u>i</u>_</sup> _′_<sup>_′_</sup> _c_<sup>_<u>czt</u>_</sup> _′zt_ � and do the same for the double difference of tariffs �ln _τzt_<sup>_DD_</sup> _≡_ ln _τ_<sup>_<u>τ</u>_</sup> _ic_<sup>_<u>iczt</u>_</sup> _′zt_<sup>_/_</sup> _τ_<sup>_τ_</sup> _i_<sup>_<u>i</u>_</sup> _′_<sup>_′_</sup> _c_<sup>_<u>czt</u>_</sup> _′zt_ �. Log transformations are noted in lower case. Substituting (3) into (2) and then taking log differences between the periods _t_ + _h_

> 6In Section 3.4 we discuss the implications of our result for the interpretation of the trade elasticity.

> 7Head and Mayer (2014) provide the exact terms included in _A_ and _B_ for a wide class of benchmark models in international trade, including the Dixit and Stiglitz (1977) Krugman, Melitz (2003)-Chaney (2008) and Eaton and Kortum (2002) models and some of their extensions.

> 8The odds ratio or “tetrads” approach to estimate the trade elasticity or trade costs goes back to Head and Ries (2001) and different versions of it have been in Hallak (2006), Romalis (2007), Head et al. (2010) and Caliendo and Parro (2015), among others.

5
and _t_ we obtain the following expression: ̃ where _uzt_ = _ε_ (∆ _huiczt −_ ∆ _huic′zt −_ ∆ _hui′czt_ +∆ _hui′c′zt_ ). Note that taking double differences eliminates all terms included in (3) except for the change in applied tariff rate. The trade elasticity _ε_ now carries the superscript _h_ in reference to the horizon at which it is estimated.

The main departure of our approach with respect to previous formulations is the inclusion of a time dimension that allows for a distinction of the trade elasticity at various horizons.<sup>9</sup> The distinction between short- and long-run trade elasticity is important given the previously documented delayed or gradual effects of trade policy changes (Baier and Bergstrand (2007), Jung (2012), Besedes et al. (2020)). In Section 3 we estimate (4) at various horizons using annual trade flows. For now, we are interested in the response of trade in the few months before and after anticipated tariff reductions. To fix the terminology, we define the short-run trade elasticity to refer to one-year changes as is common in the literature, while we consider the anticipatory dynamics to take place within less than a year. In Section 3 we argue that these anticipatory dynamics lead to deviations between trade flows and their usage that are consequential even when using annual data.

To study the trade pattern around the short window of time of tariff reductions we estimate two slightly modified versions of (4): where _n_ indicates a sub-period of the year _t_ and _<u>n</u>_ is a sub-period after _<u>n</u>_ <u>.</u> The estimation equation (5) captures the response of within-year trade flows to an upcoming tariff change. Note that the dependent variable is the within-year _t −_ 1 growth between sub-periods _<u>n</u>_ and _<u>n</u>_ of _m_<sup>_DD_</sup> _zt_<sup>,whilethetariffchangeisthatoftheupcomingyear</sup><sup>_t_relativeto</sup><sup>_t −_1.</sup> For example ∆10:12 _−_ 4:9 _m_<sup>_DD_</sup> _zt_ takes the log difference between the monthly average of

> 9In recent papers, Yilmazkuday (2019) and Boehm et al. (2020) also distinguish the short- and long-run response of trade to tariff changes.

6
_m_<sup>_DD_</sup> _zt_ from April to September <u>(</u> _<u>n</u>_ <u>)</u> and the monthly average of _m_<sup>_DD_</sup> _zt_ from October to December ( _<u>n</u>_ <u>).</u> The anticipatory slump is quantified by _ε_<sup>_S_</sup> and hence its positive value implies that imports drop in the months before an upcoming tariff reduction relative to a reference period in the year. We include product fixed effects _Dz_ to account for product seasonalities that are not eliminated by the double difference of the trade flows.<sup>10</sup> The estimation equation (6) captures the response of trade flows to the (annual) change in tariffs in the narrow time window between _<u>n</u>_ in year _t −_ 1 and _<u>n</u>_ in year _t_ .<sup>11</sup> For example ∆1:4 _−_ 11:12 _m_<sup>_DD_</sup> _zt_ takes the log difference between the monthly average of _m_<sup>_DD_</sup> _z,t−_ 1 from November to December of the previous year <u>(</u> _<u>n</u>_ <u>)</u> and the monthly average of _m_<sup>_DD_</sup> _zt_ from January to April ( _<u>n</u>_ <u>).</u> Again, to control for seasonal effects we include product fixed effects. A large negative estimate of _ε_<sup>_B_</sup> would indicate firms anticipating the upcoming tariff reduction by delaying their orders until the tariff reduction is implemented.

# **2.2 NAFTA’s Phaseouts**

NAFTA was signed by the three executives of the United States, Canada and Mexico in December 1992 after a lengthy negotiation. It took another year to be approved by legislators in the three countries. The US Congress ratified it on November 20, 1993, and US President Clinton signed it into law on December 8. NAFTA finally came into force on January 1, 1994. The agreement incorporated Mexico to the preferential FTA. Canada and the United States signed in 1988, and brought a major elimination of tariffs for trade with Mexico. By then, Canadian-US tariffs had mostly been removed. As a result of these tariff reductions, Mexico’s share over total US imports almost doubled between 1994 and 1999. Because NAFTA was one of the first major preferential FTA and its tariffs reductions undercut the Most-Favored-Nation (MFN) rates, NAFTA has been widely studied to evaluate the gains from trade and, hence, to estimate the trade elasticity.<sup>12</sup>

> 10 Results are robust to using more aggregate (less restrictive) seasonal fixed effects.

> 11Only for this specification we have used ln(1 + _Micztn_<sup>),sothatwemaintainallobservationsfor</sup> which we estimate the anticipatory decline.

> 12See for example Kruegger (1999), Head and Ries (2001), Fukao et al. (2003), Romalis (2007), Kehoe and Ruhl (2013), Caliendo and Parro (2015).

7
Table 1: Phaseout Categories of HS-8 Goods Imported to US from Mexico

|Classes|Number<br>Goods|1993<br>Scheduled<br>Tarif|Import<br>Share|Number<br>Goods|1999<br>Median<br>Tarif|Import<br>Share|
|---|---|---|---|---|---|---|
|A - 1 stage|438|5.5%|15.4%|367|0%|13.9%|
|B - 5 stages|760|9.0%|9.1%|695|0%|9.8%|
|C - 10 stages|641|6.5%|3.3%|498|2.6%|3.3%|
|C+ - 15 stages|68|19.0%|0.5%|66|10.4%|0.7%|
|D - Zeroed by 1993|4,814|0.01%|62.0%|4,249|0%|36.8%|
|Unclassifed|264|0.9%|9.7%|1,920|0.0%|35.6%|
|TOTAL|6,985|2.2%|100%|7,772|0.3%|100%|

Some of the tariff cuts took place immediately on January 1, 1994 and the rest were scheduled to be phased out gradually over various stages of tariff reductions. Step reductions took place on January 1 for up to 15 years. In fact, 96% of NAFTA’s tariff reductions were known at least one year in advance. Broadly, goods were classified into 5 categories, with class A to be immediately zeroed, classes B, C and C+ to be phased out over 5, 10 and 15 years and class D, goods with zero tariffs before NAFTA, to remain at zero. The annual distribution of US tariffs on imports from Mexico for each of these phaseout categories over the 1990s is illustrated in Figure 1.<sup>13</sup> As can be seen in Table 1, most of the HS-8 goods were already zeroed by 1993, providing little variation to estimate elasticities. Among those that were non-zero by 1993, around three quarters were scheduled to be phased out, while the rest became tariff-free the day NAFTA came into force. Given that there was considerable uncertainty regarding whether NAFTA would become effective, it is unclear that the latter reductions could have been anticipated.<sup>14</sup> But once signed, scheduled reductions of class B, C and C+ goods were certainly anticipated to become effective.<sup>15</sup> Before we document that indeed importers internalized this knowledge and anticipated upcoming tariff reductions during the early years of NAFTA, we describe our methodological approach to identifying anticipation in the next subsection.

> 13Although most tariffs were eliminated in equal annual stages, some schedules differed in the number of years with rate reductions and the size of each reduction. Because of this and different amount of goods per phaseout class, the median scheduled tariff rates declined non-monotonically during the 1990s.

> 14Given how the voting went, there was little political agreement in the US on NAFTA.

> 15We cannot ascertain at which degree agents internalized these scheduled reductions. However, a correlation of 87.42% between scheduled rates and applied duties at HS-8 level for goods that were phased out indicates that the scheduled reductions indeed materialized.

8
<!-- Start of picture text --> {dab |.<br><!-- End of picture text -->
United States ( _i_ ) so that ln _τzt_<sup>_DD_</sup> = ln( _τUS,Mex,z,t/τUS,RoW,z,t_ ). However, the choice of EU12 restricts our sample period to 1990 to 1999, since in 2000 the European Union and Mexico signed an FTA. The large group of reference exporting and importing countries allows to circumvent the lumpiness in monthly HS-6 trade flows. Because our identification of the anticipatory effects relies on the variation in monthly trade flows, the relevant observations are those HS-6 with non-zero trade flows between sub-periods of the 4 directions to obtain growth rates. This reduces the sample size while also selecting the sample towards those goods that are more frequently traded. In Section 2.5 we dig deeper into this sample selection. We find that anticipatory effects are stronger for less frequently traded goods suggesting that the sample selection is more likely to undermine our results.

We obtain monthly US trade flows and applied tariff rates from the US Census Bureau and European trade flows are obtained from Eurostat. Trade flows are aggregate at the most disaggregate HS-6 product level available and measured as the CIF (Customs, Insurance and Freight) value of imports for consumption, which disregards imports for re-export purpose and includes insurance and freight charges. Tariffs are defined as the applied tariff rates, that is, the ratio of duties over the freight-on-board (FOB) value of imports.<sup>19</sup> We obtain the classification of HS-8 goods into their corresponding phaseout category from the original NAFTA text. To classify HS-6 products into their phaseout category we take the trade weight of its HS-8 products and pick the largest category to be the one corresponding to the HS-6 classification. The characteristics of the resulting sample by HS-6 phaseout category are very similar to the original at HS-8 level and reported in Table 2.

Table 2: Sample Characteristics at HS6 Level

|Categories|HS6 Goods|HS6-Year|M<br>%|exico’s Import Share<br>1990-1993|Median Duty<br>1993|
|---|---|---|---|---|---|
|Phased-out|451|5,283|16.5%|12.3%|7.7 %|
|Class A|129|1,541|4.8%|14.0%|6.5%|
|Non NAFTA|2,274|15,182|78.7%|73.6%|0.2 %|
|TOTAL|2,854|32,006|100%|0.8%||

> 19We drop observations at HS10, month, country of origin, district of entry level - the most disaggregate level available in census data - when applied duties are larger than 100%. These are outliers that were not subject MFN nor NAFTA rate provisions. Results are not sensitive to this choice.

10
# **2.4 Baseline Results**

We now discuss the results of estimating (5) and (6) reported in Table 3. Panel A presents the elasticity estimates distinguishing the goods that were phased out and those that were not. To obtain this, we interact _τzt_<sup>_DD_</sup> with an indicator variable that is one if the HS-6 good belongs to phaseout categories B, C or C+. The first three columns report the estimates of _ε_<sup>_S_</sup> from (5) with different sub-periods _<u>n</u>_ and _<u>n</u>_ <u>.</u> The first column shows that in anticipation of an upcoming tariff reduction of 1 percentage point (pp), imports fell by a substantial 6% in the last two months relative to the middle of the year. The last three columns report the estimates of _ε_<sup>_B_</sup> from (6). In the trimester after the tariff reduction, a 1 percentage tariff reduction is associated with a 12% increase in imports relative to the two months before the tariff reduction. Both, the slump and bump in trade flows around the time of the tariff reduction, are quantitatively stronger as we consider the sub-period closer to the tariff reduction, moving from column 3 to 1 and 6 to 4. In Table D.2 of the Appendix we report that these results are unchanged when we consider different choices of product/industry fixed effects that control for seasonality.

The second row of Panel A indicates that goods which were not scheduled to be phased out did not experience any significant fluctuations in their trade flows around the short window of tariff changes. Panel B of Table 3 reports the results of estimating (5) and (6) for all goods irrespective of their phase out category. There is no significant slump in advance of upcoming tariff reductions, but a significant bump in its aftermath.

Overall, these results show that for goods on which tariffs were phased-out, US imports from Mexico first _slumped_ and then _bumped_ in the short window around the tariff reductions. In Section 4 we show that this pattern is consistent with a <u>(</u> _<u>s, s</u>_ <u>)</u> ordering model in which tariff reductions are anticipated and firms use up their inventories to attend their demand for inputs while delaying their orders. In the next subsection we provide suggestive evidence of this mechanism by exploring the interaction between the anticipatory dynamics and the degree of storability of a good.

11
Table 3: Anticipatory Slumps & Bumps

||Dep.|Var.:||∆_n_<br>:<br>_n_<sup>_mDD_</sup><br>_z,t−_|1||∆_n_<br>:<br>_n_<sup>_mDD_</sup><br>_z,t_||
|---|---|---|---|---|---|---|---|---|
||||Slump|Slump|Slump|Bump|Bump|Bump|
|||_n_|11:12|11:12|10:12|1:4|1:3|1:4|
|||_n_|4:8|4:10|4:9|11:12|11:12|10:12|
||||(1)|(2)|(3)|(4)|(5)|(6)|
|_Panel A_: Phaseout Categories|||||||||
|**1**_{Phased}_∆_τ _<sup>_DD_</sup><br>_z,t_|||6.1<sup>_∗∗∗_</sup>|4.6<sup>_∗∗∗_</sup>|4.1<sup>_∗∗∗_</sup>|-12.2<sup>_∗∗_</sup>|-9.2<sup>_∗∗_</sup>|-7.6<sup>_∗∗_</sup>|
||||(2.1)|(1.3)|(1.5)|(4.5)|(4.0)|(3.1)|
|**1**_{Other}_∆_τ _<sup>_DD_</sup><br>_z,t_|||-1.6|-1.0|-0.2|-5.3<sup>_∗_</sup>|-4.5|-5.8|
||||(2.8)|(2.3)|(2.4)|(2.8)|(2.7)|(2.6)|
|_Panel B_: All Goods|||||||||
|∆_τ _<sup>_DD_</sup><br>_z,t_|||0.7|0.7|1.1|-7.4<sup>_∗∗∗_</sup>|-5.9<sup>_∗∗_</sup>|-6.3<sup>_∗∗∗_</sup>|
||||(1.5)|(1.4)|(1.7)|(2.5)|(2.4)|(2.2)|
|HS6 FE|||✓|✓|✓|✓|✓|✓|
|_N_|||6023|6285|7076|7014|7014|8323|
|Adj R2|||0.075|0.103|0.087|0.26|0.237|0.257|

_Note:_ Estimates are obtained using (5) (columns 1 to 3) and (6) (columns 4 to 6). Estimates in Panel A separate between the effect of ∆ _τzt_<sup>_DD_</sup> for good’s whose tariffs were phased-out (class B,C,C+) and the rest. Standard errors, in parentheses, are clustered at HS-2 product * ** *** level, _p <_ 0 _._ 10, _p <_ 0 _._ 05, _p <_ 0 _._ 01.

# **2.5 Anticipation and Storability**

Measuring storability for a wide range of products is not a straightforward task and no off-the-shelf measure is readily available. To make progress we follow Alessandria et al. (2010a) and proxy it by considering the lumpiness of a goods’ trade flows.<sup>20</sup> In the model we present in section 4, more storable goods with lower depreciation rates are characterized higher inventory-sales ratios and more infrequent orders. We build on this insight and relate the goods inventory intensity with its observed trade lumpiness.<sup>21</sup> We measure trade lumpiness using the Herfindahl–Hirschman index of monthly concentration of the annual imports, calculated as follows:

> 20Alessandria et al. (2010a) also use a direct measure of a product’s physical depreciation and obsolescence rate but only for a limited number of goods and at more aggregate levels than HS-6.

> 21Lumpiness in trade flows can be explained by lumpiness of demand or the usage of inventories. We take the second view. The importance of inventories in international trade has been widely documented as we emphasized in the introduction.

12
where _v_ ( _g, m_ ) is the value of US imports of good _g_ in month _m_ .<sup>22</sup> _HHg_ is defined over the interval [1 _/_ 12 _,_ 1]. For _HHg_ = 1 _/_ 12, _g_ is traded equally every month of the year, and, for _HHg_ = 1, _g_ is traded in only one month of the year. For this measure, we define goods at the most disaggregate level (HS-10 product, district of entry and source country) and consider _HHg_ in the second year _g_ enters our sample.<sup>23</sup> Then we take the median _HHg_ at HS 6-digit level to obtain _HHz_ .

To study the link between a products’ degree of storability and the anticipatory dynamics we estimate (5) with the interaction of _τzt_<sup>_DD_</sup> and the measure of the products HH index, _HHz_ , and an indicator for whether the product was phased-out as above. We also include the squared term of the HH index given that is important in capturing the interaction. Figure 2 shows the anticipatory slump in response to a 1% drop in tariffs at different percentiles of the HH Index for phased-out goods.<sup>24</sup> The total response of imports is calˆ ˆ ˆ culated as ∆11:12 _−_ 3:10 _m_<sup>_DD_</sup> _z,t_ = _σ_ 0<sup>_S×_∆</sup><sup>_τ DD_</sup> _zt_ + _σ_ 1<sup>_S×_∆</sup><sup>_τ DD_</sup> _zt × HHz_ + _σ_ 2<sup>_S×_∆</sup><sup>_τ DD_</sup> _zt × HHz_<sup>2.</sup> Between the 20th and 70th percentile of the HH index the decline in imports before the tariff change is increasing. The anticipatory elasticity peaks at a value of around 10 at the 70th percentile. Moreover, precision increases over the x-axis, until the 70th percentile. Afterwards, the response is imprecise.<sup>25</sup> We also estimate (5) and (6) with a _τzt_<sup>_DD_</sup> interacted with an indicator variable that takes the value of one if the good was phased-out and above the median _HHz_ , i.e. it is relatively more storable. Consistent with the results of the continuous measure of storability, the results reported in Table D.3 of the Appendix suggest that baseline results in Table 3 are driven by the goods which are more storable.

> 22 Alternatively we could have used number of shipments. This doesn’t change the results.

> 23To achieve variation in the HH index it is necessary to consider it at very disaggregate levels. We take the second year to eliminate the bias coming from the month it was first imported. We exclude US imports from Canada and Mexico to forego possible endogeneity in the frequency of trade and the preferential tariff rates from NAFTA. The distribution of the HH index is reported in Figure D.1 in the Appendix. Results are robust to including averages over more than the second year and including Canada and Mexico.

> 24Table D.4 of the Appendix reports the corresponding point estimates. 25 _DD_ The results are similar when we consider ∆11:12 _−_ 5:10 _mz,t_ or ∆10:12 _−_ 4:9 _m_<sup>_DD_</sup> _z,t_ and are reported in Figure D.2 of the Online Appendix.

13
<!-- Start of picture text --> ‘N<br>‘N<br>N<br>‘N<br>‘N<br>8 \<br>‘N<br>.<br>“<br>bo .‘.<br>aTMo --— TT NST<br>& ~~<br>2 —<br>ae ws yA ae<br>=¢ ~~. ~~ “<br>4 ve “se<br>+ rae<br>wo<br>20% 30% 40% 50% 60% 70% 80%<br>Percentile HH Index<br><!-- End of picture text -->
# **3 Trade-Consumption Elasticity**

In the previous section we showed that in advance of NAFTA’s staged tariff reductions, US imports from Mexico experienced sizeable _anticipatory slumps_ and _liberalization bumps_ thereafter. These dynamics are consistent with a model in which importing firms anticipate tariff reductions by delaying their input orders and attend to their demand using inventories. This suggests that trade flows and their actual usage might deviate substantially when tariff changes are anticipated.<sup>26</sup> In this section, we provide evidence that this was indeed the case and that the deviation between trade flows and their usage around the time of the tariff reductions is especially consequential in the estimation of short-run (annual) trade elasticities. First, we propose a parsimonious measure of the consumption of imports. Second, we estimate elasticities with annual trade flows and our trade consumption flows. Third, we consider several alternative formulations of the measure of import consumption to show robustness of our baseline results. Finally, we discuss the implications of the results.

## **3.1 Measure of the Consumption of Imports**

A difference between import flows and their consumption can arise due to fluctuations in inventory holdings. However, neither the imports consumed nor their inventories are generally observed, especially at the disaggregated product and country of origin level at which trade data is used in the trade elasticity estimation. To make progress, we propose a measure of consumption of imports that is based on (1) the law of motion for inventories; and (2) a constant product and origin country specific inventory-usage ratio.

The starting point of our measure is the standard law of motion of inventories according to which the end-of-period inventory holdings are given by: where _i_ denotes the destination and _c_ the source country, _n_ denotes the month and _z_ is a HS-6. The tilde on top of inventory holdings, _s_ ̃, and consumption of imports, _q_ ̃, indicates that they are imputed. Monthly imports, _m_ , are the observable monthly trade flows.

> 26Alessandria et al. (2010a), Alessandria et al. (2010b), Alessandria et al. (2011a) and Charnavoki (2017) provide evidence on how in the face of large devaluations or business cycle shocks trade flows and their consumption can diverge significantly at high frequencies.

15
We begin by assuming an initial inventory level and then roll (8) forward to obtain the series.<sup>27</sup> The crucial step lies in the estimation of consumption process, _q_ ̃. Rather than assuming that goods crossing the border are immediately used, we assume that firms use a constant fraction of available goods at hand, The right hand side of (9), establishes that a constant fraction 1 _/kcz_ of current inventory holdings, _s_ ̃ + _m_ , is used for consumption. Note that the constant fraction _kcz_ is product and country of origin specific. This is because the inventory-usage depends on product characteristics such as the depreciation rate as well as the source country specific aspects such as the fixed cost of ordering or the shipping lag. We obtain _kcz_ by exploiting its relationship with the lumpiness of trade. Intuitively, a high inventory-sales ratio is associated with less frequent shipments. We calculate the inventory-usage as the inverse of HH index of the monthly concentration of annual imports as in Section 2.5 with the exception that here _k_ is country specific as well.<sup>28</sup> Figure 3 illustrates the behavior of our baseline measure in the case of vehicles used for transport of goods exported from Mexico to the United States. The time series of consumption of imports is much smoother than actual imports. First, imported goods are used even though they are not imported.<sup>29</sup> This can be observed in the abrupt halt in importing in the middle of 1994. During this gap in imports, our measure suggests a gradual running down of inventories. Second, the consumption mutes high frequency drops and rises. For example, in the months before January of 1997 only imports fell and then spiked, while the consumption of imports remained relatively stable. However, despite these high frequency differences, over the long run the consumption process tracks the import process.

> 27We set the inventory holdings in the first month of the first year to be the monthly average of imports in the first year multiplied by the inverse HH index (or inventory-usage ration). To make sure our results do not depend on this assumption, we exclude 1990 from the sample used in this section. Results are robust to including 1990 or assigning zero initial inventory holdings.

> 28In Section 3.3 we show that results are robust to alternative calculations of _k_ .

> 29This is a convenient feature of the measure of consumption of imports in light of the problems associated with missing values due to trade lumpiness, especially at high frequencies (Silva and Tenreyro (2006)).

16
<!-- Start of picture text --> EE Actal Imports<br>— Baseline Consumption Imports<br><!-- End of picture text --> 1990m1 1391m1 1992m1 1993m1 1994m1 1995m1 1998m1 1997m1 1998Mm1 1999M1 2000MI
̃ ̃ _<u>qUS,MEX,z,t</u>_ equivalent of the double difference trade flows as _qzt_<sup>_DD_</sup> _≡_ ln � _q_ ̃ _US,RoW,z,t_<sup>_/_</sup><sup>_<u>q</u>_ ̃</sup> _q_ ̃<sup>_EU_</sup> _EU,RoW,z,t_<sup>_<u>,MEX,z,t</u>_</sup> �, where _q_ ̃ _i,c,z,t_ is the summation of monthly flows from (9) to the annual frequency. The trade-flow and trade-consumption elasticities are then estimated following equation (4) derived in Section 2.1, providing an estimate at each horizon _h_ .

Columns 1 and 2 of Table 4 report the results of estimating (4) with _h_ = 1, i.e. the annual elasticities. Panel A shows the results of the average elasticities of all goods. There is a sizable difference of around 56% in the two elasticities. The estimate drops from 4.2 when using import flows to 2.7 when using consumed imports. Panel B suggests that this difference is driven almost entirely by the phased-out goods. For phased-out goods, the annual elasticity drops from 7.4 to 2.9. This is consistent with the strong anticipatory responses of phased-out goods found in Section 2.4. In contrast, non-phased-out goods yield similar estimates when using imports flows or consumption of imports. It is also noticeable that the estimated annual elasticity for the phased-out goods becomes almost equal to the one for the non-phased-out goods when considering the consumed imports.

Columns 3 to 8 estimate the two elasticities at longer horizons, with _h_ = 3 _,_ 5 _,_ 7. Throughout the different specifications of _h_ , the difference between the trade-flow and trade-consumption elasticity is now much smaller. In the case of the average over all goods (Panel A), the difference diminishes to only 8% after 7 years. The diminished difference between the two elasticities is also the case of the phased-out goods, although the trade-consumption elasticity remains 20% smaller. This permanent difference can be explained by the fact that as tariffs are fully phased-out the _liberalization bumps_ dissipate, but the preceding _anticipatory slumps_ remain in the denominator of the growth rates. Consistent with this explanation, the difference between the two elasticities disappears entirely in the case of non-phased-out goods.

18
Table 4: Trade-Flow vs. Trade-Consumption Elasticities over Time

|||1-Y|ear|3-Y|ear|5-Y|ear|7-Y|ear|
|---|---|---|---|---|---|---|---|---|---|
|Dep.|Var.:|∆1_m_<sup>_DD_</sup><br>_z,t_<br>(1)|∆1 ̃_q_<sup>_DD_</sup><br>_z,t_<br>(2)|∆3_m_<sup>_DD_</sup><br>_z,t_<br>(3)|∆3 ̃_q_<sup>_DD_</sup><br>_z,t_<br>(4)|∆5_m_<sup>_DD_</sup><br>_z,t_<br>(5)|∆5 ̃_q_<sup>_DD_</sup><br>_z,t_<br>(6)|∆7_m_<sup>_DD_</sup><br>_z,t_<br>(7)|∆7 ̃_q_<sup>_DD_</sup><br>_z,t_<br>(8)|
|_Panel A:_ All Goods||||||||||
|∆_hτ _<sup>_DD_</sup><br>_z,t_||-4.2<sup>_∗∗∗_</sup>|-2.7<sup>_∗∗∗_</sup>|-7.5<sup>_∗∗∗_</sup>|-6.7<sup>_∗∗∗_</sup>|-9.3<sup>_∗∗∗_</sup>|-8.0<sup>_∗∗∗_</sup>|-9.8<sup>_∗∗∗_</sup>|-9.1<sup>_∗∗∗_</sup>|
|||(1.2)|(0.8)|(1.2)|(1.1)|(1.3)|(1.3)|(1.5)|(1.5)|
|Diference|||56%||12%||15%||8%|
|_Panel B:_ Phaseout Cate|gories|||||||||
|1 _{ Phased } ×_∆_hτ _<sup>_DD_</sup><br>_z,t_||-7.4<sup>_∗∗∗_</sup><br>(2.1)|-2.9<sup>_∗∗_</sup><br>(1.3)|-10.4<sup>_∗∗∗_</sup><br>(1.8)|-9.2<sup>_∗∗∗_</sup><br>(1.6)|-12.2<sup>_∗∗∗_</sup><br>(1.8)|-10.0<sup>_∗∗∗_</sup><br>(1.7)|-12.6<sup>_∗∗∗_</sup><br>(2.2)|-10.5<sup>_∗∗∗_</sup><br>(2.1)|
|Diference|||154%||13%||22%||20%|
|1 _{ Others } ×_∆_hτ _<sup>_DD_</sup><br>_z,t_||-3.2<sup>_∗∗_</sup>|-2.6<sup>_∗∗∗_</sup>|-6.3<sup>_∗∗∗_</sup>|-5.7<sup>_∗∗∗_</sup>|-7.7<sup>_∗∗∗_</sup>|-7.0<sup>_∗∗∗_</sup>|-8.2<sup>_∗∗∗_</sup>|-8.2<sup>_∗∗∗_</sup>|
|||(1.3)|(0.9)|(1.4)|(1.3)|(1.7)|(1.7)|(1.9)|(2.0)|
|Diference|||19%||11%||10%||0%|
|_N_<br>||11,693|11,693|8,402|8,402|5,550|5,550|3,155|3,155|
|Adjusted _R_<sup>2</sup>||0.002|0.001|0.009|0.010|0.018|0.017|0.026|0.025|

_Note:_ All estimates are obtained using (4). Odd columns use trade flows as dependent variable ( _m_ ); and even columns use imputed consumed imports as dependent variable ( ̃ _q_ ). The subscript _h_ in the dependent variable, ∆ _hτzt_<sup>_DD_</sup> , is 1 in columns 1 and 2 (1-year change), 3 in column 3 and 4 (3-year change) and so on. Estimates in Panel B separate between the effect of ∆ _hτzt_<sup>_DD_</sup> for good’s whose tariffs were phased-out (class B,C,C+) and the rest. The difference is calculated as the difference between the estimate using _m_ and _q_ ̃ over the ̃ * estimate with _q_ . Standard errors, in parentheses, are clustered at HS-6 level, _p <_ 0 _._ 10, ** *** _p <_ 0 _._ 05, _p <_ 0 _._ 01.

A corollary of these findings is that the ratio of the long-run to short-run elasticity is much larger in the case of the trade-consumption.<sup>30</sup> In the specification with all goods, this ratio is 3.4 (9.1/2.7) for the trade-consumption elasticity, while it is 2.3 (9.8/4.2) for the trade-flow elasticity.<sup>31</sup> Again, the difference is driven by the phased-out goods (3.6 versus 1.7). These results suggest that the well documented gradual adjustment of trade after liberalization is even more pronounced once the anticipatory effects are removed.

> 30In a previous versions we made this point by estimating short- and long-run elasticities using the restricted and unrestricted error-correction model as in Gallaway et al. (2003). The results are very similar to the ones presented here and are reported in Section A of the Appendix.

> 31The long-run to short-run ratio of 2.3 in the case of the trade-flow elasticity is in line with previous estimates of time-varying trade elasticities. Using a structural VAR Yilmazkuday (2019) estimates it to be slightly below 2, while Boehm et al. (2020) estimates it to be slightly above 2 using panel data and an instrumental variable approach.

19
Finally, we estimate the average trade-flow and trade-consumption elasticities as: This specification is the same as in Romalis (2007) with the exception that we use _yzt_<sup>_DD_</sup> = ̃ _m_<sup>_DD_</sup> _zt_ to obtain the trade-flow elasticity and _yzt_<sup>_DD_</sup> = _qzt_<sup>_DD_</sup> to estimate the trade-consumption elasticity. Product and year fixed effects are included to account for relative shipment costs to the US and the EU12. Note that this cross-sectional or pooled approach is the most common in the literature and is usually interpreted as the long run elasticity.<sup>32</sup> Table 5 reports the results.<sup>33</sup> Panel A shows that for the average of all goods, the trade elasticity drops from 8.9 to 7.7 when consumed imports are used instead of imports.<sup>34</sup> This implies a considerable difference of 16%. Not surprisingly, Panel B shows that this is also driven by the phased-out goods, for which the difference is 21%. Note that the difference in the average elasticities is larger than the ones documented for the long run or 7-year elasticities. We view this as being driven by the fact that the average elasticities are the outcome of averaging over the elasticities at all horizons _h_ in (4) and hence assign more weight to the anticipatory slumps than the long run elasticities.

# **3.3 Robustness**

The results described above are robust to several alternative choices in the measurement of consumed imports. All results are reported in Table 6.

_One Period Time to Market Lag._ - Under the baseline measure, once imports are received at the destination, they are immediately available for consumption. If instead there are lags in domestic deliveries or lead times to market the imported goods, current imports would be unavailable for consumption or usage. The process that assumes a one

> 32See Eaton and Kortum (2002), Simonovska and Waugh (2014) or Caliendo and Parro (2015).

> 33We delete the first year of our sample since our measure does not generate sales in the first month of the sample and makes our assumption on the initial inventory holdings more relevant. This does not the results.

> 34Our estimate using import flows is below that obtained by Romalis (2007), who obtains 10.9. This is most likely from the fact that we exclude 1989 and 1990 from our sample period. In fact as we exclude earlier years from our sample the estimate falls, suggesting that the early years with less trade contribute towards larger elasticity estimates.

20
Table 5: Average Trade-Flow vs. Trade-Consumption Elasticities

|Dep.|Var. :|(1)<br>_m_<sup>_DD_</sup><br>_z,t_|(2)<br> ̃_q_<sup>_DD_</sup><br>_z,t_|Diference|
|---|---|---|---|---|
|_Panel A:_ All Goods|||||
|_τ _<sup>_DD_</sup><br>_z,t_||-8.9<sup>_∗∗∗_</sup><br>(1.1)|-7.7<sup>_∗∗∗_</sup><br>(1.1)|16%|
|_Panel B:_ Phaseout Cat|egories||||
|1 _{ Phased } × τ _<sup>_DD_</sup><br>_z,t_||-13.2<sup>_∗∗∗_</sup><br>(1.6)|-10.9<sup>_∗∗∗_</sup><br>(1.6)|21%|
|1 _{ Others } × τ _<sup>_DD_</sup><br>_z,t_||-6.6<sup>_∗∗∗_</sup><br>(1.4)|-6.0<sup>_∗∗∗_</sup><br>(1.3)|10%|
|Year FE||✓|✓||
|HS6 FE||✓|✓||
|Observations||15,153|15,153||

_Note:_ All estimates are obtained form equation 10 and by varying the dependent variable. Column 1 uses imports and column 2 uses our baseline measure of consumption of imports. Estimates in Panel B separate between the effect of _τzt_<sup>_DD_</sup> for good’s whose tariffs were phased-out (class B,C,C+) and the rest. Standard errors, in parentheses, are clustered at * ** *** HS-6 level, _p <_ 0 _._ 10, _p <_ 0 _._ 05, _p <_ 0 _._ 01.

period lag in the reception and consumption of imports has the following representation: The results of estimating (4) for _h_ = 1 and _h_ = 7 under this version of _q_ ̃ are contained in columns 3 and 4 of Table 6. The estimates are very similar to the baseline results.

_Different Inventory-Sales Ratios._ - In the baseline measure we use a different inventorysales ratio, _kcz_ , for different exporter countries _c_ , but not for the different destination countries _i_ . To check whether our results are sensitive to this lack of data we impose a common _kz_ across all four directions of trade in our baseline measure. Again, as can be seen in columns 5 and 6, the estimates are very similar to the baseline results. Results are also robust to calculating _kcz_ using the average over HS10-district of entry HH indexes or different levels of aggregation of the HH index.

_Demand Shock._ - In our baseline we assume that the usage of inputs is a constant fraction of inventory holdings. Here, we extend the baseline measure of _q_ ̃ by including a demand shock, _νiczt_ . Under this extension the consumption of imports takes the following 21
form: The first term on the right hand side of (12) is our baseline measure. The second term ˆ on the right hand side is the shock component of _q_ . The demand shock assumes that next period’s import volume reveals information about the contemporaneous demand shock. We model it as the deviation between actual monthly imports and its expected value the period before. In other words, we infer a favorable contemporaneous demand shock if we observe orders higher than the good’s average imports. This requires the existence of a delivery lag between purchase orders and reception of imports of one month, so that the consumption of imports cannot exceed contemporaneous inventory holdings as reflected in (13). We divide _mt_ +1 by _k_ to account for the fact that purchase orders are intended to satisfy consumption for an average _k_ periods and calculate E _tmt_ +1 by taking the average 0 of imports of the previous year, i.e. 1 _/_ 12 � _mt_ + _i_ . Results are similar if we use the _i_ = _−_ 11 previous 6 months or the year before and after _t_ .

The result of estimating (4) using this alternative measure of the consumed imports is reported in column 7 and 8 of Table 6. The long-run estimate (7-year change) for all goods (Panel A) indicates a slightly larger drop of 15% relative to the one using trade flows (column 2) than our baseline (8%). Again it is driven by phased-out goods (Panel B). The short run (annual) elasticity estimates drop much more under this formulation of consumed imports than under the benchmark. Although phased-out goods display a much larger effect, other goods’ trade-consumption elasticity is now also smaller than their trade-flow elasticity, albeit not statistically different.

22
Table 6: Robustness: Alternative Measures of Consumed Imports

||Trade|Flows|Time to|Market|Inventor|y-Usage|Deman|d Shock|
|---|---|---|---|---|---|---|---|---|
|Dep. Var.:|1-Year<br>∆1_m_<sup>_DD_</sup><br>_z,t_<br>(1)|7-Year<br>∆7_m_<sup>_DD_</sup><br>_z,t_<br>(2)|1-Year<br>∆1 ̃_q_<sup>_DD_</sup><br>_z,t_<br>(3)|7-Year<br>∆7 ̃_q_<sup>_DD_</sup><br>_z,t_<br>(4)|1-Year<br>∆1 ̃_q_<sup>_DD_</sup><br>_z,t_<br>(5)|7-Year<br>∆7 ̃_q_<sup>_DD_</sup><br>_z,t_<br>(6)|1-Year<br>∆1 ̃_q_<sup>_DD_</sup><br>_z,t_<br>(7)|7-Year<br>∆7 ̃_q_<sup>_DD_</sup><br>_z,t_<br>(8)|
|_Panel A:_ All Goods|||||||||
|∆_hτ _<sup>_DD_</sup><br>_z,t_|-4.2<sup>_∗∗∗_</sup>|-9.8<sup>_∗∗∗_</sup>|-2.6<sup>_∗∗∗_</sup>|-8.6<sup>_∗∗∗_</sup>|-2.9<sup>_∗∗∗_</sup>|-9.3<sup>_∗∗∗_</sup>|-1.6<sup>_∗∗∗_</sup>|-8.5<sup>_∗∗∗_</sup>|
||(1.2)|(1.5)|(0.8)|(1.5)|(0.8)|(1.5)|(0.6)|(1.5)|
|Diference|||66%|14%|46%|6%|170%|15%|
|_Panel B:_ Phaseout Categories|||||||||
|1 _{ Phased } ×_∆_hτ _<sup>_DD_</sup><br>_z,t_|-7.4<sup>_∗∗∗_</sup>|-12.6<sup>_∗∗∗_</sup>|-2.3|-10.0<sup>_∗∗∗_</sup>|-3.4<sup>_∗∗_</sup>|-10.9<sup>_∗∗∗_</sup>|-1.8|-9.5<sup>_∗∗∗_</sup>|
||(2.1)|(2.2)|(1.5)|(2.1)|(1.4)|(2.1)|(1.1)|(2.1)|
|Diference|||216%|26%|118%|16%|310%|32%|
|1 _{ Others } ×_∆_hτ _<sup>_DD_</sup><br>_z,t_|-3.2<sup>_∗∗_</sup><br>(1.3)|-8.2<sup>_∗∗∗_</sup><br>(1.9)|-2.6<sup>_∗∗∗_</sup><br>(1.0)|-7.8<sup>_∗∗∗_</sup><br>(2.0)|-2.8<sup>_∗∗∗_</sup><br>(1.0)|-8.3<sup>_∗∗∗_</sup><br>(2.0)|-1.5<sup>_∗∗_</sup><br>(0.7)|-7.9<sup>_∗∗∗_</sup><br>(2.1)|
|Diference|||20%|6%|15%|-1%|111%|4%|
|_N_<br>|11,693|3,155|11,650|3,139|11,693|3,155|11,693|3,155|
|Adjusted _R_<sup>2</sup>|0.002|0.025|0.001|0.019|0.002|0.025|0.001|0.021|

_Note:_ All estimates are obtained using (4). The first two columns use trade flows as dependent variable ( _m_ ); the rest use alternative measures of the imputed consumed imports as dependent variable ( ̃ _q_ ). The calculation of the alternative measures of consumed imports is described in Section 3.3. The subscript _h_ in the dependent variable, ∆ _hτzt_<sup>_DD_</sup> , is 1 in odd columns (1-year change) and 7 in even columns (7-year change). Estimates in Panel B separate between the effect of ∆ _hτzt_<sup>_DD_</sup> for good’s whose tariffs were phased-out (class B,C,C+) and the rest. The difference is calculated as the difference between the estimate ̃ ̃ using _m_ and _q_ over the estimate with _q_ . Standard errors, in parentheses, are clustered at * ** *** HS-6 level, _p <_ 0 _._ 10, _p <_ 0 _._ 05, _p <_ 0 _._ 01.

# **3.4 Discussion**

The interpretations of the trade elasticity can be broadly classified into two classes, depending on the underlying microfoundation of the gravity equation (Arkolakis et al. (2012)): (1) demand-side models in which the trade elasticity relates to the elasticity of substitution (Armington (1969), Anderson (1979), Dixit and Stiglitz (1977)); and (2) supply-side models in which it is the inverse measure of productivity dispersion (Eaton and Kortum (2002), Melitz (2003), Chaney (2008)). Both interpretations abstract from the distinction between imports and their consumption, implicitly assuming that imported goods are immediately consumed and/or that potential deviations do not matter in the long run. Given that the results of this Section show only small differences in the 23
long run trade-flow and trade-consumption elasticities, their welfare implications might be less important in static models of trade.<sup>35</sup> However, our results become more important when viewed through the lens of dynamic trade models in which trade adjusts gradually to tariff changes. In models with sunk costs of exporting (Alessandria and Choi (2014)) the short-run trade response to trade cost changes is dominated by the intensive margin or the elasticity of substitution (demandside); and the long-run is dominated by the elasticity of the extensive margin or firm entry (supply-side). Importantly, in this class of models, welfare gains that account for the transition can be very different from the steady state welfare change (Alessandria et al. (2021)). Our results indicate that at an even shorter horizon, the trade-flow response is dictated by inventory considerations leading to an overestimation of the short run intensive margin response. In that sense, our findings and their implication for the ratio of the long-run to short-run trade elasticity are important for the quantification of welfare gains in such models.

# **4 Monte Carlo Simulations of** _<u>s s</u>_ **Model** **<u>(</u>** _<u>,</u>_ **<u>)</u> Ordering**

This section lays out a standard <u>(</u> _<u>s</u>_ <u>,</u> _<u>s</u>_ <u>)</u> inventory model that captures the dynamics documented in Section 2. In this model, the trade elasticity is only related to the intensive margin adjustment, i.e. the elasticity of substitution.<sup>36</sup> The goal is to show how the estimated intensive margin adjustment is affected by firms’ high frequency inventory decisions. The mechanism we present has no implications for the long-run adjustment to trade cost changes and, therefore, we abstract from modelling the deviations between the short- and long-run response documented in Section 3.<sup>37</sup> We proceed as follows. First, we describe the model. Second, we show how it can reproduce the trade flow pattern around NAFTA’s tariff reductions. Third, we demonstrate through Monte Carlo simulations that our measure of consumed imports effectively estimates the true trade-consumption

> 35A subtle implication of our findings is that elasticity estimates using data pooled over several years may understate the actual long run elasticity.

> 36This is only approximately correct because, as tariffs decline and firms’ revenues expand, retailers re-optimize their ordering schedule and order more frequently. This leads to a decline in the inventory holding costs and a pass-through of tariffs to consumer prices larger than one. However, this mechanism is quantitatively less important.

> 37In addition to models with sunk costs of exporting, other mechanisms that generate gradual adjustment to trade liberalizations include market penetration costs (Arkolakis (2010), Drozd and Nosal (2012)), the persistence of shocks (Ruhl (2008)) or distributional capital (Crucini and Davis (2016)).

24
elasticity in the model.

# **4.1 Model Description**

We consider the partial equilibrium problem of a monopolistically competitive retailer that decides when to order a homogeneous storable good and how to price its variety as in Alessandria et al. (2010a). In advance of an upcoming tariff reduction, the retailer delays its purchases to when the good is cheaper, while in the meantime it continues to satisfy its demand by running down its inventories.<sup>38</sup> Retailers hold inventories for two reasons. First, in addition to the per unit cost _ωt_ = _ω_ (1 + _τt_ ), ordering implies a fixed shipment cost _f_ , causing firms to economize on it by ordering infrequently and in large shipments.<sup>39</sup> Second, retailers face demand uncertainty and a one period delivery lag, leading to precautionary inventory holdings. However, holding inventories is costly, since goods depreciate at the rate _δ_ and the future is discounted at _β_ . Under this setup, retailers’ purchases are lumpy as they run down their stocks to _<u>s</u>_ and then replenish it up to _<u>s</u>_ <u>.</u> Retailer _j_ faces the following demand _cjt_ for its variety: where _pjt_ denotes the retailer’s sales price and _νjt ∼_<sup>_iid_</sup> _N_ (0 _, σν_<sup>2) its demand shock, assumed</sup> to be i.i.d. over time.<sup>40</sup> The response of consumption to changes in prices is dictated by the elasticity of substitution, _σ_ . Note that demand _cjt_ is not necessarily equal to actual sales. This is because (1) purchases, _mjt_ , are irreversible, _mjt ≥_ 0; and (2) the one period delivery lag implies that sales can never exceed current inventory holdings, so that:

> 38The choice to model the anticipatory dynamics as those of a firm’s inventory decisions as opposed to that of a consumer’s durable purchases is justified by the fact that international trade is dominated by trade in intermediate goods. Moreover, using the Broad Economic Categories classification, Table D.6 of the Appendix demonstrates that the results of Section 3 are driven by non-consumer goods.

> 39By setting the purchase price to be a constant we assume that exporters are perfectly competitive, so that the pass-through (to retailers) of the tariff reduction is complete. This is consistent with the fact that we do not observe any significant movements in unit values in advance of NAFTA’s tariff reductions when estimating (5) using unit values as the dependent variable. See Table D.9 of the Appendix.

> 40The iid demand shock allows for some variation in the anticipation to a tariff reduction. With perfectly correlated demand shocks all firms would respond equally to the incentives of anticipating the demand shock.

25
Assuming the goods only depreciate in the warehouse, the law of motion for the inventories is: A firm’s problem is the following. At the beginning of each period it observes its inventory holdings, _sjt_ , and its level of demand, and then decides (1) the price of its good and (2) whether to import or not, and, if so, how much. Formally, denote the firm’s value of adjusting inventories by _V_<sup>_a_</sup> ( _s, ν_ ) and of not adjusting by _V_<sup>_n_</sup> ( _s, ν_ ).<sup>41</sup> Every period, retailers optimize by choosing _V_ ( _s, ν_ ) = max _{V_<sup>_a_</sup> ( _s, ν_ ) _, V_<sup>_n_</sup> ( _s, ν_ ) _}_ , where are subject to (16) and (15). Solving for the optimal policies generates an <u>(</u> _<u>s</u>_ <u>,</u> _<u>s</u>_ <u>)</u> policy of ordering in which purchases are a function of current inventory holdings and the demand shock, i.e. _m_ = _m_ ( _s, ν_ ). Similarly, the pricing schedule is characterized by a constant markup over the marginal value of an additional unit of inventory, _p_ = _θ−θ_ 1<sup>_Vs_(</sup><sup>_s, ν_).In</sup> contrast with the different models that microfound the gravity equation, demand for the good, _qjt_ , can be satisfied using inventories. Moreover, because firms optimize the timing of their purchases, _mjt_ , will respond to the incentives of anticipated tariff reductions.

Before we simulate the model under a wide range of parameter values, we show that to reproduce the trade flow pattern observed during NAFTA’s staged tariff reductions, two ingredients are required. First, the tariff reduction has to be anticipated. Second, the inventory-usage ratio has to be non-negligble.<sup>42</sup> The first three panels of Figure 4 show the aggregate response of imports and their consumption of an industry. Only in the benchmark case (Panel A), in which the equilibrium amount of inventories is worth 2.2 months of sales and the tariff reduction is known in advance, there is a significant _anticipatory slump_ and _liberalization bump_ .<sup>43</sup> The lower right panel illustrates that the

> 41For simplicity, we drop the firm subscript _j_ from here on.

> 42In Section C of the Appendix we show that for an individual retailer that does not face demand uncertainty there is a closed form expression of the anticipatory drop in imports. Indeed, the drop is increasing in the equilibrium inventory-sales ratio and the upcoming tariff cut.

> 43The parameter values and moments corresponding to the three simulations of Figure 4 are in Table D.7 of the Appendix. The parameter values of the benchmark case and unanticipated shock are reported in the first row. The low I/S calibration is reported in the second column.

26
<!-- Start of picture text --> Panel A: Benchmark Panel B: Low I/S<br>to),! ro): |<br>|<br>||<br>=~ | ~ |<br>x | x |<br>hed eho<br>22<br>|<br>""<br>i——— Imports<br>> | * —— Consumption<br>Panel C: Unanticipated Panel D: Stock<br>ro) ! ro)<br>, | , —— Benchmark I/S<br>N N —— Lowl/S<br>a | a ———— Unanticipated<br>x | Go:<br>hed fhe<br>xe) | xe)<br>"<br>—— Imports " '<br>? ———= Consumption * |<br><!-- End of picture text -->
an anticipated permanent decrease in the tariff rate _τ_ of 1 pp in period 25.<sup>44</sup> In addition to a benchmark calibration and a low inventory-sales ratio calibration, we simulate the model under another 50 different calibrations described in Table D.7 of the Appendix. We focus on varying the parameters that determine the equilibrium inventory-usage ratio, since these are the ones determining the dynamics around the tariff reductions. Namely, we vary _f, δ, β, σν_ one-by-one while holding constant the other three parameters at their benchmark value. We also assess the sensitivity to the depreciation rate when _f_ = 0 and inventory holdings are only due to the precautionary motive. The elasticity of substitution is set to 4 in all simulations.

The implementation of the model equivalent of the measure of the consumption in (9) is straightforward. In each of the 52 simulations we set _k_ to be the average inventory sales ratio of the first year. The main difference with respect to (9) is that in the model, contemporaneous orders only become available for consumption in the next period. Hence, in the model simulations, _mt_ drops out of (9). To study how anticipatory dynamics lead to deviations between the trade-flow and the trade-consumption elasticities when using annual data we estimate the following equation for each one of the 52 simulations: where the dependent variable _yjt_ = _{mjt, qjt,_ ̃ _qjt}_ is aggregated at firm level to the annual frequency. Using _mjt_ as the dependent variable estimates the trade-flow elasticity, using _qjt_ the true trade-consumption elasticity and _q_ ̃ _jt_ the trade-consumption elasticity under the measure of consumption in (9).

The deviation between the trade-flow and the trade-consumption increases in the degree of anticipation to the tariff reduction. Similar to the estimation equation (5) of Section 2 we estimate the _anticipatory slump_ as: where _ε_<sup>_S_</sup> captures the elasticity of the end of the year import decline in response to the

> 44The model is solved using a shooting algorithm where importers solve their problems backwards starting from a new steady state. We first simulate 2,000 firms over 5,000 periods using their initial policy functions so that we can initiate the distribution of firms at the stationary inventory holdings distribution.

28
upcoming tariff reduction.

Figure 5 illustrates the main results of the simulations. On the y-axis it plots the elasticity estimates of _σ_ when using the year before and after the change in tariffs relative to the one when using consumed imports ( _qjt_ ) in the years 1 and 4, i.e. those without the _slump_ and _bump_ . Note that when using years 1 and 4 the elasticity of imports and consumed imports are identical.<sup>45</sup> The estimate of _ε_<sup>_S_</sup> of each simulation is shown on the x- axis.<sup>46</sup> There are three main findings.<sup>47</sup> First, the trade-consumption elasticity in the two years around the tariff reduction is almost identical to the trade-consumption elasticity using years 1 and 4 (blue line) for any degree of anticipation. This indicates that the slumps and bumps of trade flows are absent in the response of consumed imports as these adjust immediately and uniformly to the tariff reduction. Second, the deviation between the trade-flow elasticities (red dots) and the trade-consumption elasticities (blue dots) is substantial even when the anticipatory slump is within reasonable values of 5 and 10, as during NAFTA’s staged tariff reductions. Third, the trade-consumption elasticity when using our measure of consumed imports (blue crosses) is very close to the actual tradeconsumption elasticity for the entire range of anticipatory elasticities (and calibrations of the model). Hence, the performance of our measure of consumption within this framework supports the empirical results of Section 3.2. Altogether, these findings indicate that even when using annual trade flows, in the presence of anticipatory dynamics, trade and their consumption can deviate substantially, with important implications for the estimation of the short-run intensive margin adjustment to trade cost changes.

> 45Note that this approach to side stepping the bias requires knowledge about the existence of anticipation. In contrast, using _qjt_ does not require information about the existence of anticipation.

> 46If instead the x-axis was the equilibrium inventory-sales ratio, Figure 5 would look very similar.

> 47Table D.8 illustrates the three findings with the point estimates of three specific calibrations.

29
<!-- Start of picture text --> =<br>S ‘<br>= TI 4/* Trade-Flow<br>x * Actual Trade-Consumption<br>= + Imputed Trade-Consumption<br>2<br>Eo °<br>w<br>Cc<br>° *<br>Oo * 6<br>keSs— “ . e .o f°A : so * e<br>cc)<br>* t s oe<br>2 — ae s * oe ft *<br>a<br>0 5 10. 15 20 25<br>Anticipatory Slump<br><!-- End of picture text -->
There are several insights from this paper that open up interesting future research avenues. The consumption of imports process we propose is easily implementable since it requires only high-frequency trade data and estimates of the inventory-sales ratios. However, its necessity arises only due to the lack of data on inventories (consumption of imports) at the same level of aggregation at which elasticities are estimated. Although Alessandria et al. (2011a) have shown similar dynamics with inventory data for the automotive industry, our paper illustrates that incorporating inventory data is important to fully understand the response of trade to liberalizations and that progress can be made once more disaggregate inventory data becomes available.

Moreover, in the episode studied in this paper, the implementation of the tariff reductions was certain to take place. Nonetheless, the anticipatory effects we document here are potentially sizable even when the policy change is uncertain. In fact, during the annual renewal of China’s MFN status in the 1990s, US imports from China rose systematically before the US Congress approved the renewal in anticipation of higher future tariffs (Alessandria et al. (2019)). In that sense, besides the uncertainty surrounding the current rise of protectionism, our paper provides a mechanism to understand the stockpiling in advance of events such as Brexit and a way to study the consumption response of imported goods in this context.

31