Import processing and trade costs

Carballo, Jerónimo; Graziano, Alejandro; Schaur, Georg; Volpe Martincus, Christian Working Paper Import processing and trade costs IDB Working Paper Series, No. IDB-WP-01454 Provided in Cooperation with: Inter-American Development Bank (IDB), Washington, DC Suggested Citation: Carballo, Jerónimo; Graziano, Alejandro; Schaur, Georg; Volpe Martincus, Christian (2023) : Import processing and trade costs, IDB Working Paper Series, No. IDB-WP-01454, Inter-American Development Bank (IDB), Washington, DC, https://doi.org/10.18235/0004752 This Version is available at: https://hdl.handle.net/10419/289955 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/3.0/igo/legalcode IDB WORKING PAPER SERIES Nº IDB-WP-01454 Import Processing and Trade Costs Jerónimo Carballo Alejandro Graziano Georg Schaur Christian Volpe Martincus Inter-American Development Bank Integration and Trade Sector February 2023 Import Processing and Trade Costs Jerónimo Carballo Alejandro Graziano Georg Schaur Christian Volpe Martincus February 2023 Cataloging-in-Publication data provided by the Inter-American Development Bank Felipe Herrera Library Import processing and trade costs / Jeronimo Carballo, Alejandro Graziano, Georg Schaur, Christian Volpe Martincus. p. cm. — (IDB Working Paper Series ; 1454) Includes bibliographic references. 1. Ports of entry-Peru. 2. Customs administration-Peru. 3. Commercial policy-Peru. 4. Tariff-Peru. 5. Peru-Commerce. I. Carballo, Jerónimo. II. Graziano, Alejandro. III. Schaur, Georg. IV. Volpe Martincus, Christian. V. Inter-American Development Bank. Integration and Trade Sector. VI. Series. IDB-WP-1454 JEL Codes: F10, F13, F14. Keywords: Trade Costs, Border Processing, Trade Policy. http://www.iadb.org Copyright © 2023 Inter-American Development Bank. This work is licensed under a Creative Commons IGO 3.0 Attribution- NonCommercial-NoDerivatives (CC-IGO BY-NC-ND 3.0 IGO) license (http://creativecommons.org/licenses/by-nc-nd/3.0/igo/ legalcode) and may be reproduced with attribution to the IDB and for any non-commercial purpose, as provided below. No derivative work is allowed. Any dispute related to the use of the works of the IDB that cannot be settled amicably shall be submitted to arbitration pursuant to the UNCITRAL rules. 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The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the Inter-American Development Bank, its Board of Directors, or the countries they represent. Import Processing and Trade Costs† Jeronimo Carballo Alejandro Graziano University of Colorado University of Nottingham Georg Schaur Christian Volpe Martincus University of Tennessee and CESifo Inter-American Development Bank and CESifo Abstract We estimate import processing costs based on the time it takes to import. Our theory extends existing time-cost measures to account for uncertainty in import processing. We use detailed, highly disaggregated data on import processing dates and import values to provide evidence for our theory and estimate processing costs consistent with the theory. The evidence shows that our extensions to time-cost estimates are economically relevant to determine processing costs. We estimate that the tariff equivalent import processing costs is as high as 18 percent. WTO estimates suggest that the full implementation of the 2013 Trade Facilitation Agreement would reduce the time to trade by 1.5 days. In that case, processing costs would decrease to 13 percent. Keywords: Trade Costs, Border Processing, Trade Policy J.E.L. Classification: F10, F13, F14 †We thank Vanessa Alviarez, Joaquin Blaum, Bruce Blonigen, Matilde Bombardini, Julia Cajal Grossi, Davin Chor, Jonathan Eaton, Keith Head, Wolfgang Keller, Kala Krishna, Keith Maskus, Denis Novy, Roberta Piermartini, Alexandre Skiba, Jim Tybout, and Woan Foong Wong and seminar participants at TIGN/Ridge Conference, Geneva Trade and Development Workshop, ETH Zurich, Singapore Management University, National University of Singapore, IBS and at EIIT at Oregon, Midwest Meetings at IUPUI, RMET, CAF and CORE conferences. The views and interpretations in this paper are strictly those of the authors and should not be attributed to the Inter-American Development Bank, its executive directors, its member countries, or SUNAT. Other usual disclaimers also apply. Contact: [email protected], [email protected], gsc[email protected], and c[email protected] 1. Introduction The 2013 WTO Trade Facilitation Agreement is a major worldwide policy initiative that consists of provisions to simplify the processing of international shipments to reduce trade costs, but only limited research exists to inform such an initiative. This lack of evidence is partially due to the difficulty of measuring non-tariff barriers (Goldberg and Pavcnik, 2016). A valuable measure to evaluate the restrictiveness of non-tariff regulations employed by academic research, firms, policymakers, and international organizations is the time it takes to import.1For such a measure to reach its full potential to inform policy, time must be translated into cost. To quantify processing costs requires a cost function to estimate. We use theory to derive a cost function consistent with firms’ optimal management of the import process. Our starting point is that processing times, the time it takes to physically handle, move, and clear shipments through the port of entry is uncertain due to port congestion and conditionally random inspections. Then, firms must choose the lead time, the time between initiating and desired completion of a single or multiple steps in the supply chain before they know the shipments’ processing performance. Short lead times save money, but run a greater risk of missed delivery obligations. Delayed shipments are costly due to late fees, reputation effects, and disruption of production processes (Boehm et al., 2019). By weighing the risk of late delivery against the cost of a slow supply chain, firms choose optimal lead times to minimize the total expected processing costs. Based on this theory, we derive firms’ expected import processing cost. To estimate this expected import processing cost, we take advantage of a unique dataset consisting of highly detailed, transaction-level import data for Peru’s main seaport, Callao. In particular, we observe import values across importing firms, origin countries, and products. The data also report the completion dates for various steps 1e.g. Doing Business Trading Across Borders http://www.doingbusiness.org/data/ exploretopics/trading-across-borders/what-measured 2 in the import process, including vessel arrivals, unloading, storage at wharehouse, customs processing, and if customs processing involved an inspection of documents and/or the shipment. Based on our transaction level data, we provide evidence that long unloading times lead to subsequent shorter storage times. This is consistent with our theory where firms allocate longer lead times to avoid running late in the case of a random processing delay. Next, we estimate firms’ expected import processing cost. The theory shows that we need to estimate two parameters: an import processing cost elasticity with respect to the median processing time, and a multiplier that captures costs associated with the risk of missing desired delivery dates. Both parameters need to be combined with the median processing time to evaluate the total import processing cost. Consistent with our theory, we estimate the first parameter, the processing cost elasticity, from the import demand elasticity with respect to processing times. To do so, our theory relates import values to firms’ beliefs about their median processing time. The main challenge to estimate the processing cost elasticity is that we do not observe what the firms know about the median processing time. Instead, we relate import values to observed median processing times. This potentially results in measurement error that leads to substantial bias in fixed-effect specifications (Grilliches and Hausman, 1986; McKinish, 2008). To address this bias, we generate instrumental variables based on port congestion and customs inspections. The identifying assumption is that they affect firms’ anticipated median processing time and observed processing time, but do not enter the import equation otherwise. Firms may anticipate median processing times based on learning including lagged observation, and information they obtain from shipping and logistics companies. We examine these specific mechanisms with robustness checks. The second parameter, the cost multiplier, is not recoverable from fixed-effect regressions that relate import values to processing times. We use our detailed import processing information to determine this parameter and provide several robustness checks. 3 Instrumental variable estimates show that a 1percent increase in the median processing time lowers import values by .24 percent.2Given an import demand elasticity of 4 (Soderbery, 2015), our theory translates the import processing time elasticity of .24 into a processing cost elasticity of .06. Hence, a 1percent increase in the median time raises import processing costs by .06 percent. For the cost multiplier, we obtain an estimate of 1.104 and we provide evidence that it significantly affects import processing costs based on bootstrapped standard errors. Evaluated at a median processing time of three days, our estimates combine to result in an import processing cost that equals a 18 percent import tariff.3Hopes for the 2013 Trade Facilitation Agreement are high.4Based on our estimates this is justified. WTO estimates suggest that the full implementation of the Trade Facilitation Agreement may result in a reduction of the time to import of 1.5 days.5Our estimates imply that this would reduce import processing costs from about 18 to 13 percent.6For comparison, average import tariffs worldwide equal about 5percent in 2017.7 Existing literature shows that long delivery times reduce trade and increase costs (Persson, 2008; Djankov et al., 2010; Freund and Rocha, 2011; Hummels and Schaur, 2013; Volpe Martincus et al., 2015; Heid et al., 2017; Oberhofer et al., 2018; Fernandes et al. 2021). This literature assumes empirically convenient functional forms and relates import and export values to various measures of the time it takes to trade.8We combine 2This elasticity is somewhat lower compared estimates in the existing literature based on export processing. For example, Djankov et al. (2010) estimate that a 1percent increase in the time it takes to deliver a shipment from the factory gate to the port lowers trade by 0.4percent. Instrumenting raises the magnitude of our elasticity estimates by a factor of five compared to OLS. This increase is comparable to existing IV applications (Costinot et al., 2012; Paravisini et al., 2015). 3Consistent with our theory it is simply computed according to the log linear cost function λ× (MedianProcessingT ime)χ−1 = 1.104 ×3.061 −1 = 0.18 where λis the cost multiplier and χis the processing-time cost elasticity. 4Roberto Azevedo, former Director General of the WTO, noted that “The impact will be bigger than the elimination of all existing tariffs around the world.” https://www.wto.org/english/news_e/ news17_e/fac_31jan17_e.htm 5https://www.wto.org/english/news_e/news17_e/fac_31jan17_e.htm 6Formally, λ×(MedianProcessingT ime)χ−1 = 1.104 ×1.5.061 −1 = 0.132. 7https://data.worldbank.org/indicator/TM.TAX.MRCH.WM.AR.ZS? 8We follow this literature and develop time costs as a ad-valorem tariff equivalent. For a discussion 4 theory and data to extend and improve our understanding of these elasticity and timecost estimates. Our theory shows that available elasticities likely do not apply to evaluate import processing costs because they depend on the shape of the processing distribution. Our empirical results provide evidence that our extensions of existing cost estimates to account for uncertainty are economically meaningful and relevant to evaluate policy. Our uniquely detailed import processing data has several advantages to accomplish this. These data allow us to compute a measure of processing time consistent with the theory, estimate the time cost multiplier that cannot be identified from import regressions, and, generally, provide evidence for the theory. In addition, we leverage these data for multiple robustness checks. Who gains from trade facilitation is policy relevant. Often the hope is that small firms and new relationships will benefit and grow.9However, without cost estimates, it is a priori not clear how high processing costs are for these firms and relationships, and it is difficult to measure policies’ ability to reduce these costs. We provide evidence that experienced importers incur a processing tariff of about 12 percent. New importers pay a processing cost tariff equivalent more than double compared to experienced firms. This is evidence that border-related processing costs are especially relevant to the formation of new trade relationships (Bernard et al., 2017a, 2017b; Fitzgerald et al., 2017; Rodrigue and Tan, 2019). The next section provides background information on import processing and import processing times. Section 3 develops a theory for expected costs of import processing. Section 4 introduces our detailed import data. Section 5 explains how we identify the effect of processing times on imports and reports estimates. Section 6 develops estimates for border processing costs based on the estimation results in Section 5. Section 7 presents the results of several robustness checks. Section 8 examines the heterogeneity of border of identification of per-unit costs versus ad-valorem costs, see Irarrazabal et al. (2015). 9https://www.wto.org/english/news_e/news17_e/fac_31jan17_e.htm 5 ule longer lead times t∗ lif (i) late fees are more elastic in missing the delivery date (i.e. if ωincreases), (ii) late fees are a greater proportion of the import value (i.e. if rincreases), (iii) if lead time costs are less elastic (i.e. if ϑdecreases). For proof see Section A.1. Proposition 1 has implications for the cross-country evaluation of trade facilitation measures based on processing times. Two countries’ processing time distributions may be identical, but lead times and expected costs associated with import processing differ. Therefore, simple comparisons of processing time distributions, in our case tmin and φ, do not necessarily result in cost rankings of import processing. Thus, for data on the time it takes to import to be fully informative for policy, we must translate it into cost. Proposition 1 also shows that comparing border processing performance based on total border times can be misleading. For two ports of entry with the same processing-time distribution, firms allow longer lead times if lead time costs are less elastic perhaps due to differences in available storage space. Therefore, longer lead times may not be a sign that processing costs are high, but that storage space is cheap.25 In this case, longer lead times may be a sign of lower import costs and we would expect that longer lead times are associated with an increase in trade. This result emphasizes the importance of measuring effects of trade facilitation and import processing costs based on the fundamentals of the processing distribution. We make two steps to translate import-processing times to costs. First, substitute t∗ linto (3) to obtain minimized expected costs as a function of the minimum processing time. Second, based on the Pareto distribution, substitute tmin =T/φ √2, to obtain total 25Applying the envelope theorem to equation (3) in optimum, ET C(t∗ l), it is straightforward to see that ∂ET C(t∗ l) ∂ϑ >0as long as the processing times take at least one day, tp>1, and we are at an interior solution. 12 minimized expected costs as a function of the median processing time T: ET C =λ T χv, (5) where χ=φϑ/(φ+ϑ)and λ(r φ−ω, φ, ϑ)=(r φ−ω)ϑ ϑ+φ(ϑφ ϑ+φφ−φ−ϑ ϑ+φ+ϑ−ϑ ϑ+φφ2ϑ ϑ+φ)2−ϑ φ+ϑ(6) The multiplier, λ, median processing time, T, and elasticity, χ, combine to define the border-processing cost factor, λ T χ, as an ad-valorem tariff equivalent on the total import value, v. Trade facilitation policy emphasizes costs associated with slow shipment processing due to regulations of international commerce. Equation (5) then highlights potential benefits of trade facilitation policy. The elasticity χand the multiplier λtranslate policy driven reductions in median processing times, T, into lower border processing costs. To understand what determines the benefits of trade facilitation policy, we may further examine the fundamentals of χand λ. According to equation (5), the processing-time cost elasticity, χ=φϑ/(φ+ϑ), increases in ϑand φ. Therefore, processing costs are more elastic with respect to a percentage change in median processing times, if lead time costs are more elastic (a greater ϑ) and the processing time distribution is subject to less probability of long delays (a greater φ) due to a steeper processing-time distribution. In addition to providing fundamentals for existing elasticity estimates, this has an important consequence for the evaluation of import-processing costs. The processing distribution, including φ, is determined by local regulations, port procedures, equipment failures, and risk management methods. Therefore, to evaluate import-processing costs, we cannot rely on existing elasticity estimates based on data from different countries, modes of transport, and legs of the international 13 supply chain (Djankov et al., 2010; Hummels and Schaur 2013; Volpe Martincus et al., 2015; Fernandes et al., 2019). Instead, we must estimate our own processing cost elasticities. To do so, we follow the existing literature and relate processing times to trade flows. In addition to the shape parameter, φ, and the lead time cost elasticity, ϑ, the multiplier λalso depends on costs of supply chain disruptions and late fees collected in rand ω. For a given shape of the processing distribution and lead time cost elasticity a greater cost of supply chain disruptions, an increase in ror ω, raises the multiplier λand the expected border processing costs.26 Consequently, the multiplier λcaptures costs associated with missing desired delivery windows that are not included in the processing cost elasticity χ. Estimating border processing costs requires an empirical strategy for λ. Taking advantage of the structure of our model and detailed data, we provide a estimation strategy for r/(φ−ω)to obtain estimates for λ. In particular, conditional on the processing-time distribution and elasticity parameters (φ,ϑ), equation (4) shows that firms choose a greater optimal lead time t∗ lthe greater r/(φ−ω). Therefore, information on the processingtime distribution, elasticities, and a proxy for the optimal lead time determine a value for r/(φ−ω)from our data. To determine the remaining parameters in λ, (φ,ϑ), we examine the elasticity χ. 3.2. Import-Processing Cost and Imports To link import-processing times to import values, let us focus on a given importerexporter relationship.27 Firm iimports mihxy units of product hfrom country xin year 26If λ > 1, then import processing is costly even if the median processing time is one, T= 1. The intuition is that even in that case where firms at the median do not experience delays, they take into account the probability of experiencing a delay and the associated costs of missing the delivery window determined by the parameters r,ωand the probability distribution, as well as the costs of hedging against such delays by scheduling longer lead times determined by ϑ. 27Bernard et al. (2017a) model the endogenous sorting of importers and exporters. This is beyond our object in this paper and we take an importer-exporter relationship as given. Nevertheless, we derive a log-linear import value relationship similar to their theory. 14 y. The firm combines the imported product with a domestic input, lihxy.28 Output, qihxy, is produced and distributed according to the Cobb-Douglas production function qihxy =αihx ×αiy ×mβ ihxy ×l1−β ihxy. We maintain 0< β < 1. The productivity parameters αihx and αiy allow for heterogeneity in productivity across importers, origin, products, and time.29 Final products are differentiated and demand on the domestic market follows CES, qihxy =Ay(pf ihxy)−σ. Final goods producers are monopolistically competitive on output markets and optimally source the local and international input taking prices as given. Domestic factor markets are competitive such that the price of the domestic input, why, varies across products and time, but not across firms. Let phxy be the f.o.b. price of the imported input and τhxy >1be the ad-valorem import cost factor including freight and tariffs.30 Taking into account import processing costs, an importer’s profit maximizing31 import demand then is mihxy =κiy ×κihx ×κhy ×(λ T χ ihxy)−γ×p−γ hxy, where the constants κihx,κiy,κhy absorb productivity and demand parameters and γ=β(σ−1) + 1. The exporter produces a differentiated variety with constant marginal cost zhxy, takes the importers demand as given and charges the profit maximizing constant markup over marginal cost price phxy =γ γ−1zhxy. Combining import demand with the exporter’s pricing rule the import value equals vihxy =mihxyphxy =κiyκihxδhxy ×(λ T χ ihxy)−γ.(7) 28Note that the local factor lihxy has a x subscript. This is to distinguish that a firm may import the same product from multiple source countries and allocates some labor to finish and distribute each of these products on the market. 29Alternative sourcing modeling assumptions, such as CES production, result in similar log-linear import demand functions. For example, see Halpern et al. (2015), Gopinath and Neiman (2015) and Antràs et al. (2017). In that case we can think of firms importing varieties to combine to a single output according to a CES production function, but we would obtain a similarly log-linear import equation. 30In the empirical section we discuss how our identification strategy extends to the case where export prices vary across importers pihxy, and we provide robustness checks considering exporting firms. 31Firms maximize expected profits: A 1 σ y(αihxmβ ihxyl1−β ihxy)1−1 σ −λ Tχ ihxyτihxypihxymihxy −whylihxy. 15 The constant δhxy now accounts for demand in the importing country as well as the exporter’s marginal cost. The processing costs parameters λand χtranslate an increase in the median processing time into an increase in processing cost. The parameter γ translates this cost increase into a reduction in trade flows. In the following sections, we take advantage of equation (7) to estimate import elasticities, γχ, and to back out estimates for χ. The time cost multiplier, λ, is not separable from other constants in this log-linear demand equation. We use our elasticity estimates to develop an alternative estimation strategy to determine λ. Before we explain how we obtain elasticity estimates and determine import processing costs, the next section explains the import data we use throughout the rest of the paper. 4. Data To implement equation (7) empirically requires data on imports and border processing. In this section, we discuss data sources and summary statistics. We observe highly detailed import data obtained from Peru’s National Tax Agency, SUNAT, from 2007 to 2013. Our dataset reports import values, quantities in kilograms, freight, and tariff charges for each recorded transaction. In addition, for each record we see the ID of each importing firm, the origin country of the flow, the exporting firm, the product code (10-digit HS), the customs office clearing the shipment, and the vessel that carried the shipment. These data cover all transactions entering Peru. We merge these import data with our detailed information on processing times we observe for the port of Callao described in Section 2 at the transaction level and generate an estimation sample to identify the import demand equation.32 Before doing so, Table 3 compares the universe of import transactions for Peru with the sample of imports that arrive at the seaport of Callao. Imports clearing Callao 32We do not lose data due to this merge since we have transaction IDs that connect processing data with customs data. 16 account for approximately three quarters of the total import value, two thirds of the total number of importers, and 90% or more of all imported products and countries of origin. We therefore capture most of Peru’s imports. An advantage of focusing on Callao is that the majority of business activity is concentrated around Lima which mitigates concerns that heterogeneity in inland transportation impacts our results. Furthermore, the Callao-average importer is similar to the national-average importer. More specifically, the Callao-average importer has 65 employees, is eight years old, and buys 12.4 products from 2.8 countries for approximately 650,000 US dollars (See Table A1 in the appendix for details).33 There are 22 customs offices in Peru, but the average firm uses only 1.03 customs offices and does not appear to use multiple ports of entry in response to port congestion, long queues at customs, or other delays. Consequently, imports arriving at Callao represent the majority of the firm’s imports. Therefore, merging the processing information at Callao with the firm’s import information is akin to merging the firm’s total imports with its processing data. We aggregate firms’ import data processed at the seaport of Callao to the importerproduct-origin-year level. Similarly, using the shipment level processing data for the port of Callao described in Section 2, and applying our definition of processing times, we generate median processing times, ˆ Tihxy, across all shipments within each importerproduct-origin-year unit of observation. In addition to median processing time, we will also use a measure of the total border time. Section 2 defines the total border time for each shipment as the difference in days between the date when the vessel arrives and the shipment clears from customs. For the following empirical sections, we employ the median 33The national-average importer has 52 employees, is seven years old, and buys 14 products from 3.1 countries for roughly one million US dollars (See Table A1 in the appendix for details). Hence the Callaoaverage importer looks like the national-average importer, but imports less in terms of value spread over a smaller number of shipments. The difference are due to heavy goods being imported through other ports located closer to the production facilities and imports entering through airports which typically consists of smaller and more frequent transactions (see Table A1 in the appendix). 17 of the total border time across all shipments within each importer-product-origin-year unit of observation as our measure of total border time. Aggregation to the importer-product-origin-year level facilitates standard empirical approaches. For example, it is straight forward to account for time varying fixed effects and use lagged variables to achieve identification. This is much more challenging in transaction level data where shipments across different importers, exports, and products arrive on different days resulting in much noisier variation. While convenient, this aggregation results in a seeming disconnect between our theory and data. Our theory is based on an importer-exporter relationship, but for most of our empirical applications, we aggregate to the importer-product-origin-year level. Aggregating across exporting firms is relatively inconsequential. Within an importer-product-origin-year combination, Peruvian firms tend to source only from a few exporters. Nevertheless, we will examine this with a robustness check. Aggregating to annual observations sums over multiple shipments within the year. Our theory is mute on the frequency of shipments, but we also examine potential consequences of this aggregation with robustness checks. Combined, we have an estimation sample that includes f.o.b. import values (vfob ihxy), freight charges, tariffs, insurance charges, the median processing time, ˆ Tihxy, and a measure of the median total border time within each importer-product-origin-year unit of observation. See Table A4 for descriptive statistics on these variables computed using our main estimation sample. 5. Identification of Import Elasticities w.r.t. Border Processing Time With detailed import data at hand, in this section we explain how we identify the effect of import-processing times on imports. We develop the empirical model, discuss the identification strategy, and report baseline results. We discuss robustness checks in a later section. 18 5.1. Empirical Specification and Identification We take equation (7) to our data to estimate γχ. This presents a challenge. In our theory, firms know the median processing time, Tihxy. Unfortunately, we do not see what firms know, but observe realized median processing times, ˆ Tihxy, for importer iacross products h, origin of exports x, and within each year y. To bridge this gap, we apply a proxy variable approach. Let actual processing performance equal a firm’s beliefs regarding shipment processing time plus a random shock such that, ln ˆ Tihxy = lnTihxy +eihxy where E(eihxy) = 0. Then, taking logs of the import value equation, equation (7), and substituting the proxy ˆ Tihxy for the unobserved information Tihxy we obtain the empirical model: ln(vihxy) = δhxy +κiy +κihx +γχln ˆ Tihxy +uihxy,(8) where the disturbance uihxy contains measurement error eihxy. The main parameter of interest is γχ < 0. The empirical model shows that log-linear specifications, the common approach in this literature, implicitly fix the shape of the processing-time distribution, φ, within the elasticity χ. We follow the literature and treat γχ as a parameter to estimate.34 Importer-year fixed effects account for firm-level changes in productivity. Importer-product-origin fixed effects, κihx, absorb heterogeneity in importer-exporter relationships. Product-origin-year fixed effects, δhxy, account for exporter productivity and changes in supply as well as trade policy conditions.35 Our identification strategy depends on the assumption that firms have knowledge about the median processing time Tihxy and that this median processing time is related 34The alternative is to treat the shape parameter as data. This would require a non-linear identification strategy that accommodates a large number of fixed effects, avoids the incidental parameter problem, and handles instrumental variables to break endogeneity. We are not aware of a convenient estimator to handle these challenges. 35These fixed effects also account for the seasonality of products. Furthermore, we assume that firms take the shipment schedule as given. If firms have means to reduce the cost of delays by adjusting their shipment schedule, then we expect that this reduces the elasticity of imports with respect to delays. 19 to the observed processing time ˆ Tihxy. There are several sources of information that firms may use to gain knowledge about the median processing time. They may obtain information from carriers and logistic companies, they may use past experience, and there may be learning from individual shipments within annual observations, i.e., firms that import frequently are able to observe year-to-year changes in processing times within the calendar year, and are thus able to update their priors about current processing times and adjust their import decisions accordingly. We will take advantage and examine all of these mechanisms. If firms do not have information about the median processing time which they can use to evaluate import processing costs, or, if their priors about the median processing costs are false and are not related to observed processing times, then we expect ˆγχ = 0. The main challenge to obtain a consistent estimate for γχ is that measurement error, eihxy, is contained in the disturbance and is correlated with the main regressor of interest, ln ˆ Tihxy, according to our proxy variable approach.36 In fixed-effects regressions, classical measurement error is known to lead to substantial attenuation bias because variation of the independent variable around the fixed effects usually emphasizes variation in idiosyncratic measurement error (Griliches and Hausman, 1986; Mckinish, 2008). We develop two instruments based on port congestion and inspection probabilities to solve this problem. We will first introduce the instruments and then discuss their necessary identification assumptions. Simultaneous arrival of several vessels translates into longer border handling and processing times due to congestion. In our data, we observe the arrival date of each vessel and use it to compute the number of vessels that arrived the day before each shipment. Then, for each importer-product-origin-year combination, we take the median of this measure 36The alternative is to make the much more convenient assumption that Tihxy =ˆ Tihxy +eihxy and eihxy is not systematically related to ˆ Tihxy. In that case, OLS is consistent and we would expect that IV and OLS estimates are similar, unless there are additional sources of bias. 20 across all shipments as a measure of congestion and our first instrument. Consequently, even if we aggregate to annual frequencies, this measure exploits within year variation of arrival dates of shipments. For example, for two shipments of the same product from the same origin the congestion measure may differ if they are imported on different dates within the year. As a consequence, for a given time period, the congestion instrument varies across importers, products and origins. 37 Our second instrument is based on the fact that handling time in customs depends on the assignment to different inspection channels. A customs’ risk management model allocates shipments to different processing channels. Some shipments pass customs without further inspection. Other shipments experience additional processing burden due to document and physical inspections. Within each importer-product-origin-year observation, we compute the fraction of shipments that were assigned to more intensive inspection channels. We focus on this unit of observations, because the customs risk management model takes into account, firm, product, and origin information. As a result, the instrument captures the exogenous probability of assignment to more time-consuming inspection channels across time and importer-product-origin triplets within the same period. We examine sensitivity of our results with respect to alternative definitions of the instruments, including lagging the instruments, in the robustness section. The instruments must predict realized median processing times, ln ˆ Tihxy. This is easily verifiable from first stage statistics. The instruments must also not be related to the outcome in specification (8) after conditioning on the other explanatory variables. To achieve this, we absorb omitted variables that may be correlated with inspection probabilities and port congestion with fixed effects. If customs selects inspection probabilities based on relationship specific information, or, based on the origin country and product, 37A concern might be that importers would bring large shipments right before the Christmas shopping season, which is exactly the time of high congestion in the port. This is challenging to examine at high frequency, because of lumpy shipments in international trade. However, we estimated our baseline model at quarterly frequency and report the results as a robustness check in the appendix. In general, they confirm our findings. 21 and potential tariff liberalizations. World Bank data show that the average world wide applied tariffs have decreased to about 6 percent in 2010.40 Consequently, evaluated at the median, import processing costs are much greater than applied import tariffs. Eliminating all import tariffs, a reduction in tariffs of 100 percent, reduces import tariffs by 6 percentage points. If trade facilitation policy reduces processing times by 1.5 days41, then at the overall median processing time of 3 days, this reduces import processing costs by about 4.9 percentage points.43 What would it take to achieve a 6 percentage point reduction in processing costs with trade facilitation policy? Table 1 shows that, at the 50th percentile, processing times in the orange channel equal 5 days, while processing in the green channel takes 2. Eliminating all document inspections, by switching from the orange channel to the green channel, therefore reduces processing times from 5 to 2 days at the median. This results in a 6.6 percentage point reduction in import processing cost.44 Thus, according to our estimates, eliminating all document inspection, perhaps with the use of information technology, lowers import processing costs by the same amount as completely eliminating a 6 percent applied import tariff. Following the same steps as above, we also estimate the model parameters at γ= 6. We report results in Table 4 column 4. In this case, a 10 percent increase in the processing time raises costs by χ=.4percent and the total border processing cost tariff equivalent drops to 11.3 percent. Based on existing demand elasticity estimates, we consider this value at the low end of the potential import processing tariff equivalent. 40See http://data.worldbank.org/indicator/TM.TAX.MRCH.SM.AR.ZS 4142 43This is a straight application of the tariff equivalent: 1.104 ×30.061 −1.104 ×1.50.061 = 0.049. 44We compute 1.104 ×50.061 −1.104 ×20.061 = 0.066. 28 7. Robustness Checks This section reports robustness checks for the import specification, the cost multiplier, and the processing cost. We start with the import specification and then explore the sensitivity of the cost multiplier. 7.1. Robustness Checks for Import Estimates The following subsections examine the robustness of the instrumental variable estimates for the import regressions in the left hand panel of Table 4. We consider alternative definitions of the instrumental variables, import regulations and corruption, specification error, and aggregation bias. 7.1.1. Alternative Definitions of the Instruments and Learning We start by examining the robustness of our main instrumental variable estimates, reported in Table 4, with respect to alternative definitions of the instruments. Results are reported in Table 5. Rows of results report various robustness checks. For all robustness checks, we re-estimate our import specification, equation (8), using 2SLS. In each case, we report the IV estimate for the effect of processing time on import values, γχ. Before explaining details, it is straight forward to summarize the results. Across all robustness checks in Table 5, the estimated effect of the processing time on import values is very similar to our estimate in Table 4, −0.243.45 The top panel of Table 5 examines robustness of our customs inspection instrument, channel. Our main specification uses the fraction of inspected shipments within importerproduct-origin-year observations as a measure of the probability of getting inspected. Volpe Martincus et al. (2015) propose an alternative instrument. Their instrumental variable is an indicator that equals one if more than 50 percent of the shipments in a given year within an existing trade relationship were inspected. The first row of Table 45Our first-stage F-Statistics corroborate that our instruments are strong. 29 5 reports the results when we apply this median channel assignment as an instrument. The effect of processing times on imports remains similar as in the baseline IV estimate in Table 4. The fraction of inspected shipments may be a noisy measure of the inspection probability in small samples. To examine this, we re-estimate our baseline focusing on annual observations for the instruments and all other variables that contain at least 10 and 20 transactions at the importer-product-origin-year level. Limiting the sample to annual firm-product-origin triplets that consist of at least 10 or 20 transactions also allows us to better assess whether the learning mechanism is at work, because such a sample includes observations with a sufficient number of shipments for firms to learn and update their prior about the median processing time to evaluate import processing costs as discussed in the identification section. Table 5 rows 2 and 3 show that over the samples that condition on at least 10 or 20 observations the effect of the border processing time on the import value remains negative and significant and similar to the baseline estimate, albeit slightly larger in magnitude. The middle panel of Table 5 examines the robustness of our port congestion instrument. Firms’ ability to update beliefs about the processing time may depend on the time window we consider before arrival of the shipment to compute the measure of congestion. For our main estimates, we focused on vessel arrivals the day before each shipment arrives at the port. We now extend that time window from 1 to 5 days. The estimates of border processing costs on import values are very similar to our baseline specification. In the bottom panel of Table 5 we report estimates when we lag both instruments by one period. Even though our instruments are due to a random customs process and aggregate port congestion, one may be concerned that contemporaneous instruments are correlated with the contemporaneous disturbance. Coefficient estimates are similar to our main specification. A one log point increase in import processing time reduces import values by about 0.214 log points. For completeness, the last rows report results 30 where we condition on observations that include at least 10 or 20 transactions in all variables. The elasticity remains negative and significant. The magnitudes of the elasticities decrease slightly compared to the baseline estimates. A potential reason is that these esimates emphasize lagged information as predictors of processing time and de-emphasize the within-year learning mechanism. 7.1.2. Alternative Specifications of Fixed Effects In Table A5 we examine robustness of the baseline IV estimate reported in Table 4 with respect to alternative specifications of fixed effects. We estimate the import regression, equation (8), with 2SLS applying our standard inspection and port congestion instrument as explained in the identification section, but vary the set of fixed effects. More rigorous fixed effects lend credibility that our instruments meet the exclusion restriction, but they also absorb useful identifying variation. The first row of results in Table A5 reports the IV estimates for the effect of processing time in import values. Across the columns, the effect varies between −0.19 and −0.268. This is remarkably similar to the effect we report in Table 4, −0.243. First stage results show that both the congestion instrument and the inspection instrument significantly predict the processing time. F-statistics confirm the strength of the instruments. We conclude that the choice of fixed effects does not significantly affect our results. Finally, even if we account for Origin-Product-Year, or, Firm-Origin-Year, or, Firm- Product-Year fixed effects, there is still sufficient variation in the instruments to predict the first stage. Consequently, we conclude that there is relevant importer-product-origin variation within years to identify the coefficients. 7.1.3. Import Processing Regulations, Tariffs, and Non-Tariff Measures In Table 6 we examine how regulations in import processing, tariffs, and non-tariff measures affect our conclusions. Across the columns, we report 2SLS estimates for the effect of the log processing time on log import values according to equation (8). The 31 instruments are port congestion and inspection frequencies as explained in the identification section. Across the columns, we estimate the effect from various sub-samples that exclude shipments subject to special regulations and policies. To clear the border Peruvian firms may use an express channel for their shipments. This channel allows firms to file customs documents while still in transit. Column 1 provides estimates when we drop shipments that cleared through this channel. The coefficient estimate on the processing time equals −0.247, is statistically significant, and comparable to the baseline estimate in Table 4, −0.243. In column 2 we report estimates focusing on low tariff products. We consider trade flows with less than a 5% tariff. Dutt and Traca (2010) and Sequeira (2016) consider the possibility of tariff evasion. The concern is that especially when tariffs are high firms interact with officials to lower their tariff burden. In that case, they may also attempt to reduce the processing burden. The estimates remain comparable to our baseline.46 We conclude that tariff evasion does not significantly affect our conclusions. Column 3 augments the baseline specification with ad-valorem freight, tariff, and insurance charges.47 The theory maintains that tariffs, transportation, and insurance markets are independent of processing time. If transportation providers’ quality depends on processing speed and higher quality providers charge higher rates, then excluding this information may result in omitted variable bias. Our results show that this is not the case. Estimates remain similar to the baseline estimates. We conclude that freight charges do not lead to omitted variable bias and that our fixed effects sufficiently account for this information. Column 4 reports results where we exclude all products that require special import permits (Bown and Crowley, 2016; Carballo et al. 2016b). These products require additional processing that may affect the estimates. Again, we conclude that this does 46We also estimated the model for high tariff products and the estimates are comparable. 47We first compute τihxy as the sum of f.o.b import value, freight charges, insurance charges, tariff charges and divide this sum by the f.o.b. value. We then augment our baseline specification with τihxy. 32 not affect our baseline estimates and that our fixed effects sufficiently account for this potential product heterogeneity. 7.1.4. Aggregation Next we examine a seeming disconnect between the theory and the empirics. In the theory, we model the processing costs for an individual shipment. In the data, as is standard in many empirical trade papers involving firm level data, we aggregate to annual levels. There are several reason why some level of aggregation is useful. It keeps the results comparable to the literature. Also, at the transaction level trade data includes tiny one-time shipments due to experimentation or emergency shipments unrelated to our theory. On the other hand, aggregating to annual levels potentially eliminates useful identifying variation within annual observations. Table 7 reports two robustness checks with respect to this aggregation problem. First, we estimate the effect of import processing times on import values according to specification (8) with quarterly data and monthly data. To do so, we construct the import processing time and associated congestion and inspection instruments at the quarterly and monthly levels. Quarter-year and month-year fixed as well as country-product-quarter and country-product-month fixed effects account for product characteristics as well as seasonality and shopping seasons. Columns 1 and 2 of Table 7 report the 2SLS estimates for quarterly and monthly data respectively including quarter-year and month-year fixed effects. A one percent increase in processing time reduces imports by about 0.154 percent at quarterly observations and 0.130 percent at monthly observations. Columns 3 and 4 report similar results for specifications when we account for country-product-quarter and country-product-month fixed effects. Overeall, the estimates are slightly smaller than the baseline estimate in Table 4. Perhaps this is to be expected, as the coefficient captures the effect of the processing time only for a quarter as opposed to the entire year. Furthermore, quarterly and monthly observation limit identifying variation due to learning mechanisms 33 as explained in Section 5.1. Second, we examine the effect of import processing time on the import value per shipment. To do so, we divide the annual import value by the total number of shipments within each firm-product-origin-year observation and take logs. We then estimate the effect of log processing times on the log import value per shipment applying 2SLS and our congestion and inspection instruments. Table 7 column 5 reports the results. The effect of the processing time on the import value per shipment is −0.238 and almost identical to the effect of processing times on total import values reported in Table 4. We conclude that considering the number of shipments does not affect the results.48 Finally, we estimate specification (8) at the (importing)firm-product-carrier-exporter(firm)- year unit of observation. We re-construct our instruments and estimate 2SLS. We extend the fixed effects to account for exporting firm heterogeneity. In addition, we account for heterogeneity across carriers.49 Ben-Daya and Abdul (1994) consider that firms may shorten lead times, but at an added cost. A way to accomplish this may be to choose faster carriers. We note that our identification approach relies on processing times, not lead times. Nevertheless, accounting for carrier fixed effects accounts for this mechanism. Appendix Table A6 reports the results. Across all specifications an increase in import processing times reduces imports. Coefficient estimates are comparable to the baseline IV estimate in Table 4. 7.1.5. Alternative Measures of Border Time In the previous sections we estimate import-processing cost elasticities based on the actual processing time as defined in Section 2. In this subsection, we examine if the definition of the time it takes to import matters for elasticity estimates. 48For theory that determines shipping frequency see Hornok and Koren (2015a, 2015b) and Kropf and Sauré, (2014). 49Unfortunately we do not observe customs brokers in our data. If carriers sort systematically across customs workers, then we expect that carriers fixed effects account for this heterogeneity. 34 Measurements of the time it takes to import vary across publicly available data sources. For example, in 2017, the Enterprise Survey reports the number of days to clear shipments from customs in Peru as 14 days, on average.50 Compared to our statistics in Section 2, this measure is closer to our definition of the total time to clear imports, including storage steps in the import process, rather than actual processing time. For comparison, the 2010 Doing Business Business Trading Across Border’s data reports that the time to import into Peru is 24 days. However, a recent methodology change results in much lower measures, 72 hours for border compliance and 72 hours for documentary compliance to cross the border.51 Thus, while the previous methodology seems more consistent with our definition of the total time shipments take to import, the current methodology is closer to our measure of processing time. Does the distinction between processing time and total border time matter for elasticity estimates? We use our data to answer this question. We estimate our import specification, equation (8), but instead of our measure of processing time, we focus on a measure of median total border time. As defined in Section 6, let ˆ t∗ihxy be the median total border time (including all storage steps in the import process) of all shipments within each importer-product-origin-year observation. Then, we estimate ln(vihxy) = δhxy +κiy +κihx +βln ˆ t∗ihxy +uihxy.(11) Table 8 reports OLS and 2SLS estimates. The instruments are inspection rates and port congestion, as explained in the identification section. The estimated import elasticities with respect to the total border time are −0.057 and −0.556. For comparison, Table 4 reports import elasticity estimates with respect to the median processing time as −0.049 and −0.243 for OLS and IV estimates. Therefore, our preferred import elasticities 50https://www.enterprisesurveys.org/en/data/exploreeconomies/2017/peru#trade 51http://www.doingbusiness.org/data/exploretopics/trading-across-borders/whatmeasured 35 based on processing time lead to a more conservative estimate of the import processing cost elasticity. 7.2. Robustness Checks for Cost Multipliers In addition to elasticity parameters, the key component we back out from the data to obtain λis r/(φ−ω). In section 6 we used a measure of total border time, b t∗ihxy, as proxy for lead time. We examine the sensitivity of λwith respect to several alternative choices of lead time proxies. Equation (9) shows that our approach overestimates r/(φ−ω)and therefore λ, if our lead time proxy is greater than the optimally chosen lead time. All else equal, the greater the proxy for t∗, the greater r/(φ−ω). Our lead time proxy overstates the unobserved lead time chosen by firms if, for example, a firm chooses a lead time of five days, but the actual processing takes six. In this case, we observe a total border time of six days and overstate the optimal lead time by one day. Then, the identification issue is that the longest total border times are actually measures of long processing time instead of lead time. To examine this, we use our transaction level data. First, we compute the median processing time at firm-product-origin-year observations. Second, we drop the highest 5th and 10th percentiles of total border time. We then compute the median total border time, b t∗ihxy, over this more limited sample as proxy for our lead time measure. Following the same approach as in section ??, but using the corrected lead time proxy, we obtain a new ˆ λ. Table 9 column (1) repeats the baseline estimates for comparison. Columns (2) and (3) show the results with the corrected measures with different cutoffs. We find that by correcting the lead time proxy r/(φ−ω),λincrease compared to the baseline specification. This means that when total border times are high in our sample, they are high due to long storage times instead of unusually high processing times. Next, we recognize that we do not observe the ocean transit time. It is possible that 36 the storage time we observe at the border is not just buffering for random shocks in border processing, but also captures the lead time for ocean transit. To examine the sensitivity of λwith respect to this data problem, we make two adjustments. First, we focus on countries that are close by to eliminate lengthy ocean transit times.52 In this case, we re-estimate all of the structural parameters over the restricted sample and compute ˆ λ. Table 9 column (4) shows the results. The multiplier λincreases due to a greater cost of late delivery, r/(φ−ω). Therefore, imports sourced from countries close by are subject to especially high costs of running late. This evidence complements Evans and Harrigan (2003) who provide evidence that firms move closer to the destination market if they face short selling seasons and high demand uncertainty. Second, we focus on the top 6 source countries in the sample.53 We collect average ocean transit times from searates.com and add them to the processing time and total border time for that sample. Then we re-estiamte the elasticities and the cost parameters. Table 9 column (5) shows the results. With increased time measures due to ocean transit, λdecreases by about 4 percentage points. Therefore, accounting for ocean transit time results in slightly lower import processing costs. Finally, it is possible that shipments are stored after clearing customs, which we do not observe in our data. If there is storage after the port then our lead time proxy, b t∗ihxy, underestimates optimal lead time, t∗, and we underestimate λ. In this case, our cost multipliers are conservative estimates for import processing costs. 8. Border Processing Costs, New Trade Relationships, and Product Categories In this section we examine if import processing-costs differ across trade relationships and different product categories. 52More specifically, we consider Ecuador, Chile, Colombia, Panama, Costa Rica, Nicaragua, Guatemala, Mexico, Brazil, Argentina and Uruguay as the closest countries. 53More specifically, we consider import flows from China, United States, Germany, Italy, Spain, and Brazil. 37 10. Tables Table 1: Border Times (in Days): Total and Stages in 2013, by Customs Verification Channel Stage Channel Average Percentile 5th 10th 25th 50th 75th 90th 95th Total Border Time All 14.7 4 5 7 10 18 29 42 Green 11.6 4 4 6 8 13 21 31 Orange 15.7 5 6 8 13 20 28 38 Red 23 7 8 13 19 28 42 56 Processing Time All 4.3 1 2 2 3 6 12 16 Green 1.8 1 1 2 2 3 5 6 Orange 6 2 2 3 5 9 13 17 Red 10.3 3 4 6 9 15 20 24 Storage Time All 10.4 2 3 4 7 12 20 31 Green 9.8 2 3 4 6 11 19 28 Orange 9.8 2 3 5 7 12 20 28 Red 12.7 2 3 5 8 15 27 40 Source: Authors’ calculations based on data from SUNAT. The table reports the average and percentiles of the distribution of the total time to import, the total processing time, and storage time by customs verification channel (i.e., green, orange, and red) for 2013. The sample corresponds to all maritime imports entering into Peru through the port of Callao. 44 Table 2: Effect of Unloading Time on Storage Time (1) (2) (3) (4) Unloading Time -0.152*** -0.169*** -0.111*** -0.132*** (0.011) (0.013) (0.011) (0.012) Firm Fixed Effect Yes No Yes No Product-Origin Fixed Effect Yes No Yes No Firm-Product-Origin Fixed Effect No Yes No Yes Day Fixed Effects No No Yes Yes Source: Authors’ calculations based on data from SUNAT. The table presents the effect of unloading times on storage times conditional on fixed effects. The dependent variable is the natural log of storage time and the main explanatory variable is the natural log of the unloading time at the port. Standard errors clustered at importing firm-level are reported in parentheses below the estimated coefficients. * significant at the 10% level; ** significant at the 5% level; *** significant at the 1% level. 45 Table 3: Aggregate Import Indicators All Imports Year Import Value Number of Number of Number of Importers Origins Products 2007 19,100 19,290 199 6,989 2008 27,900 22,542 205 6,230 2009 20,600 23,597 201 6,174 2010 28,200 25,592 203 6,233 2011 36,100 26,804 210 6,177 2012 40,200 28,799 211 6,302 2013 41,100 30,131 209 6,303 Percentage Share Callao 2007 72.3 64.0 86.4 92.4 2008 72.4 65.4 87.3 92.6 2009 73.8 65.7 93.0 93.0 2010 75.5 64.8 84.7 92.9 2011 76.7 65.8 84.8 93.2 2012 75.9 65.5 90.5 93.3 2013 74.7 65.6 88.5 93.2 Source: Authors’ calculations based on data from SUNAT. The table reports aggregate import indicators for each year of our sample period. In the first panel, all imports are considered. Import values are expressed in millions of US dollars. In the second panel, only maritime imports entering through Callao are considered. This panel shows the percentage share of total Peruvian imports accounted for by these maritime imports along the dimensions that correspond to the selected indicators. 46 Table 4: Effect of Processing Time on Imports and Processing Costs Estimation Quantification (1) (2) (3) (4) OLS IV γ= 4 γ= 6 Processing Time (γχ)-0.049*** -0.243*** χ0.061*** 0.040*** (0.005) (0.015) (0.004) (0.004) First Stage φ2.072*** 2.072*** Congestion 0.028*** (0.037) (0.037) (0.000) ϑ0.063*** 0.041*** Channel 0.743*** (0.007) (0.007) (0.009) F-Test 4,317.239 r/(φ−ω)0.299*** 0.189*** [0.000] (0.039) (0.039) Hansen Test 0.025 (λ−1) 0.104*** 0.066*** [0.874] (0.008) (0.008) Fixed Effect Firm-Year Yes Yes (λ·Tχ−1) 0.180*** 0.113*** Origin-Product-Year Yes Yes (0.012) (0.011) Observations 589,842 589,842 Source: Authors’ calculations based on data from SUNAT. The table reports OLS and IV estimates of equation (8) along with the first stage estimates and the effective F-test statistics and the Hansen test statistics for the latter. The dependent variable is the change in the natural log of import values at the firm-product-origin-year level. In the IV estimation, the instruments are port congestion as proxied by the median number vessels that arrived at the port the day before the vessel carrying the shipment in a given year, and the average allocation to inspection (either documentary or physical) in a given year. Firm-year and origin country-product-year fixed effects are included (not reported). Standard errors clustered by importing firm are reported in parentheses below the estimated coefficients. Unit of observation: importing firm by origin by product by year. In the case of the right panel (Quantification), bootstrapped standard errors with 500 replications are reported. * significant at the 10% level; ** significant at the 5% level; *** significant at the 1% level 47 Table 5: Robustness Checks: Instrumental Variables IV Estimate Processing Time Robustness Channel Instrument Median Channel -0.239*** (0.014) 10 or more transactions -0.285*** (0.029) 20 or more transactions –0.295*** (0.039) Robustness Congestion Instrument Window: 2 Days -0.238*** (0.015) Window: 3 Days -0.239*** (0.015) Window: 4 Days -0.238*** (0.015) Window: 5 Days -0.239*** (0.015) Robustness Lagged Instruments Lag 1 -0.214*** (0.013) Lag 1 and 10 or more transactions -0.153** (0.076) Lag 1 and 20 or more transactions -0.176** (0.087) Source: Authors’ calculations based on data from SUNAT. The table reports IV estimates of equation (8). The dependent variable is the change in the natural log of the import value at firm-product-origin- year level. The independent variable is the change in the log of the import processing time. Firm-year and origin country-product-year fixed effects are included (not reported). Unit of observation: importing firm by origin by product by year. Standard errors clustered by firm are reported in parentheses below the estimated coefficients. * significant at the 10% level; ** significant at the 5% level; *** significant at the 1% level 48 Table 6: Robustness Checks: Port and Customs Regulation (1) (2) (3) (4) No Express Low Tariffs Transport No Permits Quality Processing Time -0.247*** -0.235*** -0.240*** -0.241*** (0.016) (0.020) (0.015) (0.016) Trade Costs -1.535*** (0.068) First Stage Congestion 0.028*** 0.029*** 0.028*** 0.029*** (0.001) (0.001) (0.001) (0.001) Channel 0.744*** 0.719*** 0.742*** 0.733*** (0.009) (0.008) (0.008) (0.009) F-Test 4,249.0 3,705.1 4,317.0 3,727.2 [0.000] [0.000] [0.000] [0.000] Fixed Effect Firm-Year Yes Yes Yes Yes Origin-Product-Year Yes Yes Yes Yes Observations 566,082 343,002 589,842 493,384 Source: Authors’ calculations based on data from SUNAT. The table reports IV estimates of equation (8) along with the first stage estimates and the effective F-test statistics. The dependent variable is the change in the natural log of the import value at the firm-product-origin-year level. The main explanatory variable is the change in the natural log of the median processing time. The instruments are inspection frequency and port congestion. In column (1) imports processed through the expressed channel are excluded. In column (2) imports with tariffs above 5% are excluded. In column (3), the baseline regression is augmented incorporating the change in the natural log of the freight, tariff and insurance costs at firm-product-origin-year. In column (4) imports from products with additional documents required are excluded. Standard errors clustered by firm are reported in parentheses below the estimated coefficients. * significant at the 10% level; ** significant at the 5% level; *** significant at the 1% level 49 Table 7: Robustness Checks: Aggregation (1) (2) (3) (4) (5) Quarterly Monthly Quarterly Monthly Value Per Shipment Processing Time -0.154*** -0.130*** -0.160*** -0.137*** -0.238*** (0.013) (0.012) (0.013) (0.013) (0.014) First Stage Congestion 0.024*** 0.087*** 0.024*** 0.086*** 0.028*** (0.001) (0.003) (0.001) (0.003) (0.001) Channel 0.715*** 0.693*** 0.715*** 0.694*** 0.743*** (0.008) (0.009) (0.009) (0.009) (0.009) F-Test 4737 4368 4847 4201 4317.239 [0.000] [0.000] [0.000] [0.000] [0.000] Fixed Effects: Firm-Year Yes Yes Yes Yes Yes Country-Product-Year Yes Yes Yes Yes Yes Country-Product-Frequency No No Yes Yes Yes Frequency-Year Yes Yes Yes Yes No Observations 2,020,086 2,676,416 1,967,939 2,523,212 589,842 Source: Authors’ calculations based on data from SUNAT. The table reports IV estimates of alternative specifications of equation (8) along with the first stage estimates and the F-test statistics. For quarterly estimates the dependent variable is the change in the natural log of the import value at the importing firm-product-origin-quarter-year level. For monthly estimates the dependent variable is the change in the natural log of the import value at the importing firm-product-origin-month-year level. For value per shipment estimates the dependent variable is the log changes in the log annual value per shipments. Standard errors clustered by firm are reported in parentheses below the estimated coefficients. * significant at the 10% level; ** significant at the 5% level; *** significant at the 1% level 50 Table 8: Robustness Checks: Effect of total border time on Imports (1) (2) OLS IV Total Time -0.057*** -0.556*** (0.005) (0.026) First Stage Congestion 0.009*** (0.000) Channel 0.281*** (0.003) F-Test 834 [0.000] Fixed Effects: Firm-Year Yes Yes Origin-Product-Year Yes Yes Observations 589,842 589,842 Source: Authors’ calculations based on data from SUNAT. The table reports OLS and IV estimates of log import values on the log of the total border time along with the first stage estimates and the F-test statistics for the latter. Standard errors clustered by firm are reported in parentheses below the estimated coefficients. * significant at the 10% level; ** significant at the 5% level; *** significant at the 1% level 51 Table 9: Robustness Checks: Different Lead Time Measures and Sourcing Patterns (1) (2) (3) (4) (5) Baseline Lead Time Sourcing 5% 10% Close Ocean Time χ0.061*** 0.073*** 0.066*** (0.004) (0.003) (0.004) φ2.072*** 1.888*** 1.958*** (0.037) (0.039) (0.036) ϑ0.063*** 0.077*** 0.069*** (0.007) (0.004) (0.005) r/(φ−ω)0.299*** 0.600*** 0.607*** 0.615*** 0.078*** (0.039) (0.075) (0.076) (0.0789) (0.049) (λ−1) 0.104*** 0.127*** 0.128*** 0.155*** 0.0631*** (0.008) (0.009) (0.009) (0.008) (0.007) (λ·Tχ−1) 0.180*** 0.205*** 0.206*** 0.235*** 0.136*** (0.012) (0.015) (0.014) (0.010) (0.012) Source: Authors’ calculations based on data from SUNAT. Column (1) reports our baseline estimates. Columns (2) and (3) re-estimate r/(φ−ω)and subsequent parameters dropping all the observations where the difference between total time and processing time is below the 5 and 10 percentiles. Columns (4) re-estimates all the parameters including only trade flows from the following countries: Ecuador, Chile, Colombia, Panama, Costa Rica, Nicaragua, Guatemala, Mexico, Brazil, Argentina and Uruguay. Column (5) re-estimates all the parameters with average ocean transit times added to total and processing times only for trade flows from the following countries: China, United States, Germany, Italy, Spain and Brazil. Bootstrapped standard errors clustered by firm based on 500 repetitions are reported in parentheses below the estimated coefficients. * significant at the 10% level; ** significant at the 5% level; *** significant at the 1% level 52 Table 10: Processing Costs by Importer Experience New Importer Experienced Importer (1) (2) Estimation Processing Time -0.269*** -0.164*** (0.018) (0.018) Fixed Effect: Firm-Year Yes Origin-Product-Year Yes Observations 589,842 Quantification χ0.067*** 0.041*** (0.027) (0.008) φ2.020*** 2.058*** (0.039) (0.180) ϑ0.069*** 0.042*** (0.017) (0.008) r/(φ−ω)0.346*** 0.120*** (0.050) (0.050) (λ−1) 0.117*** 0.057*** (0.033) (0.013) (λ·Tχ−1) 0.283*** 0.118*** (0.011) (0.010) Source: Authors’ calculations based on data from SUNAT. The table reports IV estimates of variants of equation (8) that allows for different effects across types of firms: new importers (firms that never imported before) and incumbent importers (firms that have imported before). Firm-year and product-origin country-year fixed effects included (not reported). Standard errors clustered by firm are reported in parentheses below the estimated coefficients. In the case of the lower panel (Quantification), bootstrapped standard errors with 500 replications are reported. * significant at the 10% level; ** significant at the 5% level; *** significant at the 1% level 53 Table A6: Robustness Checks: Exporting Firms and Carriers IV (1) (2) (3) (4) (5) (6) (7) Time -0.184*** -0.180*** -0.167*** -0.187*** -0.156*** -0.174*** -0.153*** (0.009) (0.008) (0.008) (0.010) (0.013) (0.010) (0.012) First Stage Congestion 0.030*** 0.030*** 0.030*** 0.030*** 0.031*** 0.030*** 0.031*** (0.0003) (0.0002) (0.0002) (0.0003) (0.0004) (0.0003) (0.0004) Channel 0.682*** 0.680*** 0.681*** 0.685*** 0.682*** 0.677*** 0.690*** (0.002) (0.002) (0.002) (0.002) (0.003) (0.002) (0.003) Test Statistics F-Test 26726 31519 31207 23499 15917 19917 13088 [0.000] [0.000] [0.000] [0.000] [0.000] [0.000] [0.000] Fixed Effects: Firm-Year Yes Yes No No No Yes No Origin-Product-Year Yes No Yes Yes Yes Yes Yes Carrier-Year Yes Yes Yes Yes Yes Yes Yes Exporter-Year Yes Yes Yes Yes Yes Yes Yes Firm-Origin-Year No No No Yes No No No Firm-Product-Year No No No No Yes No No Firm-Origin-Product No No No No No Yes No Firm-Origin-Product-Year No No No No No No Yes Exporting Firm-Year No No No No No No Yes Observations 685,971 685,971 685,971 685,971 685,971 685,971 685,971 Source: Authors’ calculations based on data from SUNAT. The table reports IV estimates of alternative specifications of equation (8) along with the first stage estimates and the effective F-test statistics. The dependent variable is the change in the natural log of the import value at the firm-product-carrier-exporter-year level. The main explanatory variable is the change in the natural log of the median processing time. The instruments are port congestion as proxied by the median number of other vessels that arrive at the port the day before the vessel carrying the firm-product-carrier-exporter imports in question does in a given year and the average allocation to inspection. Columns correspond to different sets of fixed effects as indicated in the table. Standard errors clustered by importing firm are reported in parentheses below the estimated coefficients. * significant at the 10% level; ** significant at the 5% level; *** significant at the 1% level 60 A. Appendix - Theory A.1. Proof Proposition 1 By observation, as long as φ>ω, then ∂t∗ ∂ω >0. By the envelope theorem, ∂ET C(t∗ l) ∂ω = t∗φtφ minφrv (ω−φ)2>0. Also by the envelope theorem it is easy to observe that ET C(t∗ l) ∂r >0, because for any t∗ lthe term φrv tpdtpincreases in r. By observation of equation (4), ∂t∗ l ∂ω >0 and ∂t∗ l ∂r >0. In order to prove that ∂t∗ ∂ϑ <0, we show that the semi-elasticity is negative. Taking logs on (4) and the partial derivative with respect to ϑwe obtain: ∂ln t ∂ ϑ =−ln tφ min [ϑ+φ]2−1 [ϑ+φ]2ln (rφ2 (φ−ω))−[ϑ+φ]1 ϑ−ln ϑ [ϑ+φ]2 ∂ln t ∂ ϑ =−1 [ϑ+φ]2[ln (tφ minrφ2 (φ−ω)ϑ)]−1 ϑ[ϑ+φ] Then ∂ln t∗ ∂ϑ <0as long as (tφ minrφ2 (φ−ω)ϑ)>1. Imposing an interior solution then we can show that rφ2 (φ−ω)ϑ>1. Hence for tmin ≥1then ∂ln t ∂ ϑ <0. The condition derived from the interior solution goes as follows: t φ ϑ+φ min (rφ2 (φ−ω)ϑ)1 ϑ+φ > tmin t φ ϑ+φ−1 min (rφ2 (φ−ω)ϑ)1 ϑ+φ >1 t −ϑ ϑ+φ min (rφ2 (φ−ω)ϑ)>1 t −ϑ ϑ+φ min (rφ2 (φ−ω)ϑ)>1 (rφ2 (φ−ω)ϑ)> t ϑ ϑ+φ min >1 61 Appendix - Figures Figure A.1: Import Product Shares, Callao versus U.S. (Source Data: UN Comtrade Database, Copyright ©United Nations 2012, and, SUNAT) 62