metadata: authors: 0: author: Behar,Alberto
1: author: Manners, Phil
2: author: Nelson, Benjamin
count: World
docna: 0: docna: Exports and international logistics
docty: Policy Research Working Paper
subtopic: International Trade and Trade Rules,Trade and Services,Macroeconomic Management,Trade Facilitation,Transport Services
teratopic: Law and Development,Macroeconomics and Economic Growth,Industry,International Economics and Trade
abstracts: cdata!: Do better international logistics reduce
            trade costs, raising a developing country's exports?
            Yes, but the magnitude of the effect depends on the
            country's size. The authors apply a gravity model that
            accounts for firm heterogeneity and multilateral resistance
            to a comprehensive new international logistics index. A
            one-standard deviation improvement in logistics is
            equivalent to a 14 percent reduction in distance. An
            average-sized developing country would raise exports by
            about 36 percent. Most countries are much smaller than
            average however, so the typical effect is 8 percent. This
            difference is chiefly due to multilateral resistance: it is
            bilateral trade costs relative to multilateral trade costs
            that matter for bilateral exports, and multilateral
            resistance is more important for small countries.
repnme: repnme: Exports and international logistics
display_title: Exports and international logistics
listing_relative_url: /research/2011/06/14410257/exports-international-logistics
topicv3: Transport m1326661 135,Trade m1326924 698,Trade in Services m1326928 780,Trade Facilitation and Logistics m1327174 772,Trade Balance m1327679 1136
publishtoextweb_dt: 2011-06-01T00:00:00Z
historic_topic: Law and Development,Macroeconomics and Economic Growth,Industry,International Economics and Trade
no_of_pages: 38
author_keys: 0: author_key: 944072
model_extractions: WPS5691 Policy Research Working Paper 5691 Exports and International Logistics _Alberto Behar Phil Manners Benjamin Nelson_ The World Bank Development Research Group Trade and Integration Team June 2011
Policy Research Working Paper 5691

# **Abstract**

Do better international logistics reduce trade costs, raising a developing country’s exports? Yes, but the magnitude of the effect depends on the country’s size. The authors apply a gravity model that accounts for firm heterogeneity and multilateral resistance to a comprehensive new international logistics index. A onestandard deviation improvement in logistics is equivalent to a 14 percent reduction in distance. An average-sized developing country would raise exports by about 36 percent. Most countries are much smaller than average however, so the typical effect is 8 percent. This difference is chiefly due to multilateral resistance: it is bilateral trade costs relative to multilateral trade costs that matter for bilateral exports, and multilateral resistance is more important for small countries.

This paper is a product of the Trade and Integration Team, Development Research Group. 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://econ.worldbank.org. The author may be contacted at abehar@imf.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
# EXPORTS AND INTERNATIONAL LOGISTICS

Alberto Behar Phil Manners Benjamin Nelson<sup>�</sup> May 2011 Abstract Do better international logistics reduce trade costs, raising a developing country’s exports? Yes, but the magnitude of the e¤ect depends on the country’s size. We apply a gravity model that accounts for ...rm heterogeneity and multilateral resistance to a comprehensive new international logistics index. A one-standard deviation improvement in logistics is equivalent to a 14% reduction in distance. An average-sized developing country would raise exports by about 36%. Most countries are much smaller than average however, so the typical e¤ect is 8%. This di¤erence is chie‡y due to multilateral resistance: it is bilateral trade costs relative to multilateral trade costs that matter for bilateral exports, and mutlilateral resistance is more important for small countries.

JEL Classifications: F10, F13, F14, F17, O24 Keywords: Logistics, Trade facilitation, Gravity, Firm Heterogeneity, Multilateral Resistance

## 1 Introduction

Integration into the world economy is widely viewed as one of the key factors underlying the success of the fastest growing economies (Growth Commission, 2008), yet many developing countries remain isolated. This manifests itself in the form of relatively low international trade. Trade costs can be an important factor that shape trade patterns. Although tari¤s on industrial products have generally declined, nontari¤ barriers to trade remain. One example of non-tari¤ barriers is the cost of transporting products to foreign markets, both in pecuniary terms (freight costs) and in terms of the delays experienced in moving

> �Nelson: participated in this research while at Nu¢ eld College, Oxford. Current a¢ liation Bank of England (benjamin.nelson@bankofengland.co.uk). Please note : the views expressed in this paper are those of the authors and not necessarily those of the Bank of England, the Monetary Policy Committee, or the Financial Policy Committee. Manners: The Centre for International Economics (pmanners@thecie.com.au). Behar: (abehar@imf.org), who participated in this research while at the Trade and International Integration Unit of the Development Economics Research Group, World Bank, for which ...nancial support from the governments of Finland, Norway, Sweden and the United Kingdom through the Multidonor Trust Fund for Trade and Development is gratefully acknowleged; the Centre for the Study of African Economies and St Anne’s College, for which funding from the Biegun Warburg Junior Research Fellowship and the United Kingdom Economic and Social Research Council is gratefuly acknowledged. An earlier version was written as a background paper for the 2009 World Development Report on Reshaping Economic Geography. The authors would like to thank Peter Neary, Caroline Freund, Tony Venables, Alberto Portugal-Perez, Luis Serven and Adrian Wood; organisers and participants at the IVIE Workshop on "Gravity, specialization and the geography of world trade: recent developments" and the CSAE "Economic Development in Africa" Conference; and seminar participants at the University of Oxford and University of Gothenburg.

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goods (Behar & Venables, 2011). For this reason, multilateral and donor organizations have sought to view “aid-for-trade” packages as a promising new developmental tool (Huchet-Bourdon, Lipchitz & Rousson, 2009).

Does such assistance work? Economists have studied the potential impact of transport and other costs on trade using gravity since at least Tinbergen (1962).<sup>1</sup> This paper makes a substantive contribution to our understanding of the importance of logistics for developing countries because we use a new World Bank index, which o¤ers a number of advantages. It draws on a wide range of criteria, has broad country coverage from a single source, and is based on detailed evaluations provided by logistics professionals (Arvis, Muster, Panzer, Ojala & Naula, 2007).

This paper also makes a methodological contribution to the estimation and interpretation of gravity models and hence our understanding of the importance of transport costs for trade. We develop a new gravity model, which shows that standard approaches would produce an almost three-fold exaggeration of the typical impact of such factors for developing countries.

We uncover this dramatic exaggeration because our novel gravity modelling approach simultaneously accounts for two issues, namely multilateral resistance ...rm heterogeneity. Regarding the ...rst issue, Anderson & van Wincoop (2003) show that it is not just bilateral trade costs, but those costs relative to multilateral trade costs, captured by price indices, that are relevant for predicting bilateral trade ‡ows. In particular, imports by country i from country j, Mij, are an increasing function f (�) of, inter alia, bilateral trade costs tij relative to the product of the two countries’price indices Pi � Pj, such that Anderson & van Wincoop call the price indices multilateral resistance because they work to aggregate trade costs across the two countries’multiple trading partners. Omitting controls for multilateral resistance (MR) can lead to biased coe¢ cient estimates. More importantly, it can lead to grossly misleading comparative static estimates of the impact of changes in trade barriers on trade ‡ows. This is because changes in trade costs a¤ect both the denominator and the numerator of the argument on the right hand side of (1); empirical studies typically ignore the latter. Economically, for the exporter j, it is the trade cost associated with exporting to i relative to those trade costs incurred when trading with all other traders that matters for its exports to i. If a reduction in trade costs reduces tij but also reduces costs associated with trading with other countries, exports by j to i will increase by relatively less compared to the case where multilateral resistance, acting through Pi � Pj, is ignored.

Trade elasticities are approximately proportional to country size because bigger countries are less a¤ected by MR. Intuitively, since larger countries typically trade a smaller fraction of their total output

> 1 See Clarke, Dollar & Micco; Limão & Venables, (2001); Wilson, Mann & Otsuki (2005); Djankov, Freund & Pham (2010) .

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internationally, a change in international trade costs a¤ects a proportionately smaller subset of their total production. Accordingly, their price indices, and hence multilateral resistance, change by less. MR therefore provides a smaller dampening e¤ect on bilateral trade elasticities, such that the overall elasticity net of MR is larger. Conversely, smaller countries will have smaller elasticities net of MR. Given the skewness in the world’s distribution of country size, most countries are small. Therefore, standard estimates overstate the impact of changes in logistics on bilateral trade ‡ows for most countries. Conversely, for a handful of large developing countries, the impact is underestimated.

The second issue was addressed by Helpman, Melitz & Rubinstein (2008), who develop a method to account for the consequences of heterogeneous ...rm productivity in gravity models. Firm heterogeneity gives rise to two margins of adjustment to changes in trade barriers: the intensive margin, which captures exports per ...rm, and the extensive margin, which captures the number of exporting ...rms. If ...xed trade costs are su¢ ciently high, no ...rms in a given country may export to a particular destination, which explains the zeros observed in aggregate trade data. These issues a¤ect estimation and ignoring the e¤ects of trade costs on ...rm entry results in misleading country-level comparative statics even if the countries do trade.

Behar & Nelson (2009) develop a model which accommodates both MR and ...rm heterogeneity. They demonstrate the importance of these e¤ects for comparative statics when trade costs are captured by bilateral distance. In this paper, we adapt that approach to the case of logistics. Unlike distance, logistics might not be exogenous, so we take potential endogeneity seriously. Further, unlike bilateral distance, the logistics index is a country-speci...c variable which precludes the use of ...xed e¤ects to control for MR in estimation. Instead, we proxy MR terms using an adaptation of Baier & Bergstrand’s (2009) method. Our approach allows us to implement this method together with Helpman, Melitz & Rubinstein’s procedure to account for ...rm heterogeneity. While the application in this paper is to logistics, the implications fall on a wide class of country-speci...c international trade costs.

Section 2 provides an overview of the existing literature on logistics and international trade before expanding on the importance of MR and the selection issues associated with ...rm heterogeneity. Section 3 describes the data. The World Bank constructed its logistics performance index (LPI) using a principal component analysis of six indicators. We describe those indicators and describe how we extract only those that are relevant to international trade (as opposed to within-country trade) to produce what we call the International Logistics Index (ILI).

Section 4 formalizes our gravity modelling framework, which accounts for both ...rm heterogeneity and MR, and derives the Baier & Bergstrand (2009) approximation for country-speci...c trade costs in this context. In deriving the full comparative statics that take account of MR, this section illuminates how the trade impact varies with country size. Section 5 discusses estimation issues. Because trade ‡ows may a¤ect investments in logistics, logistics may be an endogenous regressor. To deal with this, 3
we motivate and propose an instrumentation strategy based on the business start-up procedures in the importing country. We brie‡y recount the issues of MR and ...rm heterogeneity as omitted variable bias. While the homogeneous goods model can be estimated by OLS as in Baier & Bergstrand (2009, 2010) or two-stage-least-squares, we also incorporate Helpman, Melitz & Rubinstein’s (“HMR’s”) two-step procedure to estimate the heterogeneous ...rm model.

In section 6, the benchmark linear speci...cation suggests a one standard deviation improvement in logistics quality, which would put Rwanda on a par with Tanzania, raises exports 27%. We use our homogeneous ...rms model to model the impact of MR on estimation and to suggest that potential endogeneity is not materially biasing the logistics coe¢ cient. Consistent with HMR and Behar & Nelson (2009), accounting for ...rm heterogeneity using the two-stage procedure produces bigger country-level comparative statics for an average-size country than does the homogeneous goods model estimated by OLS.

The estimates imply a one standard deviation rise in the index is equivalent to a reduction in distance of about 14% while our simulations in section 7 indicate it would raise exports by about 36% for an average-size country. Since the impact of MR varies by country size, we compute the elasticity for each of our exporters. For example, because Rwanda is small, its trade response would be 1% of the response implied by the benchmark speci...cation. Because Brazil is big, its response would be three times the benchmark. Averaging over all exporters, the typical e¤ect is only 8%, which is about one ...fth of the average-size country e¤ect, because most countries are small. The linear benchmark would exaggerate this almost three-fold. Section 8 concludes that small countries have much smaller trade responses than the average, but cautions against interpreting these results as a weak case for logistics upgrades in those countries.

# 2 Literature

This section reviews two important methodological advances and brie‡y discuss empirical work on transport costs in this context.

## 2.1 Methodological concepts

Our approach accounts for two important insights provided by the recent gravity literature on trade ‡ow estimation. In particular, our estimation and comparative static exercises account for both MR and ...rm heterogeneity.

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# 2.1.1 Multilateral resistance

Anderson & van Wincoop (2003) show that it is essential to account for the general equilibrium e¤ects of changes in trade costs on imports by country i from country j, Mij, if the trade elasticity @ ln Mij=@ ln tij is to be calculated correctly. General equilibrium e¤ects work through the price indices Pi �Pj that enter the bilateral gravity equation, as illustrated in equation (1) above. Since these indices aggregate the trade costs incurred in consuming a given bundle of traded goods, Anderson & van Wincoop (2003) refer to them as indices of multilateral resistance (MR). The e¤ects of MR are as follows. The bilateral trade ‡ow between two countries depends not only on the bilateral trade barrier between them tij, but the severity of this barrier relative to those confronted when the two countries trade with others (including domestic trade), Pit�ijPj<sup>.Itfollowsthattheoverallimpactofachangeinatradebarriermustaccountforthese</sup> potentially signi...cant ‘third party’e¤ects. The impact on Brazil’s exports to Peru of signing a trade agreement depends also on whether other countries are party to that agreement. Were the agreement bilateral only, a reduction in the Brazil-Peru trade barrier would stimulate Brazilian exports to Peru, potentially reducing exports to third parties (e.g. Uruguay) and to itself. Were the agreement to include Uruguay, the relevant cost for Brazilian exports to Peru is the new cost of exporting to Peru relative to that of exporting to Uruguay; in relative terms, these costs have not changed. In this case, the only change in relative trade costs is that between domestic and international trade, with the costs associated with the latter falling relative to the former.

These e¤ects are shown to be quantitatively important by Anderson & van Wincoop in explaining the so-called US-Canada ‘border puzzle’of McCallum (1995). Behar & Nelson (2009) show that the e¤ects of MR are large for changes in trade costs that are multilateral in nature. Changes in a given country’s logistics quality share some of this multilateral characteristic: if Kenya were to achieve an improvement in its logistics, its relative trade barrier across all export destinations would be a¤ected, and our comparative statics on exports to a particular destination must re‡ect this. Put di¤erently, since the gravity equation for bilateral trade ‡ows is derived from a general equilibrium system, any statement about the likely impact of this change on bilateral trade ‡ows must take general equilibrium e¤ects, through MR, into account. Without doing so, comparative statics exercises will generally overestimate the true magnitude of the response of bilateral trade ‡ows to a change in trade costs.

Furthermore, larger countries typically trade a larger fraction of their output domestically for a given international trade cost. For large countries, a smaller proportion of their total (i.e. domestic plus international) trade is a¤ected by changes in international trade costs with all destinations, which are captured by changes in MR. As a result, MR e¤ects are less important and hence trade elasticities are greater for larger countries. This is ‘Implication 1’in Anderson & van Wincoop (2003).<sup>2</sup>

> 2 AvW’s Implication 1 states that “trade barriers reduce size-adjusted trade between large countries more than between small countries”. So small countries experience smaller trade elasticities with respect to uniform changes in trade barriers. The reason, as AvW state, is that “a uniform increase in trade barriers raises multilateral resistance more for a small

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There are a number of empirical approaches to controlling for MR in estimation. First, since MR terms are country-speci...c, they can be controlled for by including country ...xed e¤ects. This is not appropriate for our purposes as we want to identify the e¤ect of country-speci...c logistics quality. Second, some attempts have been made to control for MR by using price data to construct the appropriate price indices. Data limitations are among the problems with this method. As noted in Feenstra (2004), published price indices are typically stated relative to an arbitrary base period, making comparison of levels impossible. Furthermore, they tend to include too many non-tradeable goods and thus fail to capture the additional costs embedded in internationally traded goods (Anderson & van Wincoop, 2004). Third, Anderson & van Wincoop (2003) propose solving for a system of price indices together with the gravity equation, but this involves a potentially problematic customized non-linear program. The research community has shown that, while gravity models are popular in empirical trade, estimating the entire non-linear system is not.<sup>3</sup> Fourth, Baier & Bergstrand (2009) introduce a method by which the MR terms are approximated using a ...rst-order Taylor expansion, yielding a log-linear expression for MR which contains exogenous variables only. These approximated MR terms can then be included in a single linear equation. This approach has the advantage of yielding tractable comparative statics; in particular, the role of country size in determining the appropriate comparative static e¤ect is made explicit, while Baier & Bergstrand show that the approximation error associated with this method is small for the majority of country pairs.

# 2.1.2 Firm heterogeneity

Models of monopolistic competition with ...rms of heterogeneous productivity predict selection into export markets in the presence of ...xed costs of trade. The reason is that the least productive ...rms do not generate pro...ts su¢ cient to cover the ...xed costs incurred, preventing entry into overseas markets. As illustrated by HMR, this has at least two further implications. First, the impact of a change in a trade barrier a¤ects both the amount a given ...rm exports, the intensive margin, and the number of ...rms that export, the extensive margin. The latter is a ...rm selection e¤ect. ‘Traditional’gravity equations con‡ate these two e¤ects, whereas HMR’s method allows for their decomposition. Second, for ...xed costs su¢ ciently high, no ...rms in a given country may ...nd it pro...table to export to a particular destination. This is o¤ered as an explanation of the ‘zeros’observed in bilateral trade data: many country-pairs do not appear to trade at all. This is a country selection e¤ect, and it induces bias in traditional gravity estimates. HMR propose a two stage estimation procedure to construct controls for both of these e¤ects. In the procedure described below, we use the elements of their approach that allow us to control for the e¤ects of ...rm heterogeneity and simultaneously account for MR using the Baier & Bergstrand (2009,

> country than a large country” (p. 177).

> 3 Furthermore, this method is especially demanding when considering about 100 countries and allowing for asymmetries in trade frictions. Bergstrand, Egger & Larch (2007) have shown that the system solution can yield complex numbers.

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2010) approximation in both estimation and comparative statics.

# 2.2 Studies on transport costs

Behar & Venables (2010) summarise the literature on the determinants of transport costs and their consequent impact on trade. These determinants include geography, hard infrastructure and procedural/institutional characteristics of a country. For example, Limão & Venables (2001) map information on road, rail and phone infrastructure to shipping cost information garnered from freight forwarders. They calculate that variation in infrastructure accounts for 40 per cent of variation in transport costs. In a gravity framework, they ...nd that a country improving its infrastructure from the median to the 75th percentile would increase its trade 68 per cent.

Clarke, Dollar & Micco (2004) study the importance of ports. A deterioration in port facilities and general infrastructure from the 25th to 75th percentile is associated with a 12% rise in ocean freight costs. They ...nd that these costs, which are based on containerization, the regulatory environment, seaport infrastructure and other variables also materially impact trade. Nordås & Piermartini (2004) adopt a similar approach to Limão & Venables but use more infrastructure measures. They have separate speci...cations for a number of indicators –airports, roads, telephone lines, port e¢ ciency and the median port clearance time –which are estimated separately. They ...nd all components are signi...cant determinants of trade, with port e¢ ciency being the most in‡uential.

Moving beyond infrastructure, Djankov, Freund & Pham (2010) calculate that a transit delay of one day reduced trade by 1%, which is equivalent to an additional bilateral distance of about 70km. Hummels (2001) ...nds that improvements in customs clearance su¢ cient to reduce waiting times by a day would be equivalent to a 0.8 per cent reduction in ad valorem tari¤s.

These papers make important contributions to our understanding of the relationship between transport costs and trade ‡ows. A number control for MR in estimation indirectly through the use of ...xed e¤ects. However, they do not explicitly control for MR or ...rm heterogeneity<sup>4</sup> in estimation and comparative statics. As suggested by the methodological discussion in this section, this means the e¤ects of reforms on trade can be severely miscalculated. We are particularly concerned with grand simulations of worldwide trade e¤ects based on gravity models. For example, Wilson et al (2005) ...nd that improvements in all four di¤erent trade facilitation measures would have material impacts on world trade but the simulations are aggregates of simulations for 75 individual countries and take no account of the issues on which we focus in this study.

> 4 Drawing on an earlier version of our paper, Portugal-Perez & Wilson (2010) follow our estimation approach but do not fully explore the comparative static implications.

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# 3 Data

The 2007 Logistics Performance Index (LPI) is sourced from the World Bank<sup>5</sup> and is constructed on a scale from 1-5. The LPI is calculated by the World Bank using a Principal Components Analysis of six di¤erent sub-indicators. The indicators are listed below together with their weights in the LPI:<sup>6</sup>

1. E¢ ciency of the clearance process by customs and other border agencies (0.18);

2. Ease and a¤ordability of international shipments (0.20); 3. The facility to track and trace shipments (0.16); 4. The timeliness with which shipments reach their destination (0.15).

5. Transport and information technology infrastructure (0.15); 6. Local logistics industry competence (0.16).

Further details of the construction of each indicator are available in Arvis et al (2007). In summary, the index is based on more than 5,000 country evaluations by logistics professionals. The perceptionsbased measure is corroborated with a variety of qualitative and quantitative indicators. For example, Arvis et al (2007) calculate that, on average, a one-point rise in the LPI corresponds to exports taking three more days to travel from the warehouse to port. Unlike other studies, for example Wilson et al (2005), the components of the index are drawn from the same source.

E¢ ciency of the clearance process by customs and other border agencies, the ease and a¤ordability of arranging international shipments, the ability to track and trace those shipments as well as the speed with which they reach their destinations are directly relevant to international trade. Transport and IT infrastructure are relevant to all trade, whether international or domestic, as is the competence of the local logistics industry. Originally, the World Bank also collected data on a seventh component: domestic logistics costs. This component was found to be uncorrelated with the others and was consequently dropped by the World Bank.

Costs given by tij (i 6= j) re‡ect international trade cost factors relative to trading within borders. As a result, it is conceptually correct to measure those aspects of logistics which a¤ect international trade costs and are relevant for cross-border trade. In fact, strictly speaking, measures that a¤ect both internal and international costs equally have no impact on exports in fully-speci...ed gravity models. We should focus on the relevant components listed, but separate treatment of each component would lead to serious

> 5 http://go.worldbank.org/88X6PU5GV0

> 6 The weights that are used are not reported by the World Bank but can be backed out. For each country i, we have Li = wCi where Li is i’s LPI score, Ci is a [6x1] vector of i’s component scores, and w is a [1x6] vector of the weights. We can then use six di¤erent country LPI scores to form a [6x1] matrix L in which row i corresponds to country i’s LPI score, Li, together with each country’s component scores to form a [6x6] matrix C, in which column i corresponds to country i’s vector of scores Ci. Then we solve L = wC for w = C<sup>�1</sup> L to obtain the weights. We do this for a number of di¤erent sets of countries to ensure that the weights we calculate are una¤ected by rounding errors.

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multicollinearity problems because the components are highly correlated. Therefore, we construct our own International Logistics Index (ILI) based on components 1-4 using the relative weights listed. A regression of the LPI on the ILI has an R<sup>2</sup> of more than 0.99, so the international logistics index explains a large proportion of the overall index. Therefore, while the ILI is conceptually more appropriate, using it makes little practical di¤erence.<sup>7</sup> Table 1 presents summary statistics for the full LPI and for our new International Logistics Index (ILI). High income countries have measures of quality that are of the order of three standard deviations higher. Approximately 70% of developing countries have an ILI of between 2 and 3, but there is still considerable variation. Appendix Table 1 lists the values for all countries. The worst performing country in our sample is Rwanda with an ILI value of 1.90 (although there is evidence of subsequent improvement from various anecdotal and data sources). Singapore has the best international logistics with an ILI of 4.28. South Africa (3.66) and Malaysia (3.63) have the highest ILI values out of the developing countries.

Our interest is exports from developing countries. Based on the availability of logistics data and possible instruments and controls, our sample consists of 88 low- and middle-income exporters. We have 116 importers regardless of income classi...cation.<sup>8</sup> We use merchandise exports data for 2005, using the IMF Direction of Trade Statistics. We observe 7,246 positive cross-border trade ‡ows, 2,548 zeros and 826 instances of missing values. We therefore need to account for potential sample selection issues in our model and econometric methodology.

We use 2005 GDP measured in constant (2000) US Dollars from the World Development Indicators. As will become clear, each country’s GDP share is an important component of our analysis. We calculate each country’s share of world GDP by dividing its GDP by world GDP, where world GDP is the sum of the 116 countries in our sample.

The measure of bilateral distance that we use captures the internal distance in a country, accounts for the distance from a number of major cities and is constructed by CEPII.<sup>9</sup> Border data are also sourced from CEPII. Our control variables, including dummies for whether or not two countries share a common language,<sup>10</sup> a common colonizer or were once the same country, as well as a dummy for a landlocked country, are sourced from CEPII. Additional variables for identi...cation as ...xed export costs or instruments are taken from the World Bank Doing Business database. These data include the number of procedures needed to start a business, the number of days it takes to start a business and the cost of registering to start a new business in a country. We also considered data on the number of documents required to export or to import goods. Finally, we took the newly recoded data on religious similarity used by Helpman, Melitz & Rubinstein (2008) from Elhanan Helpman’s website.

> 7 The 2009 version of this paper used the full LPI. That paper also restricted the sample to developing countries that are not islands or are not classi...ed as having neighbouring countries su¢ ciently close to their major cities.

> 8 Further discussion of why we drop rich exporters is postponed until Section A.3.

> 9 The distance measure used is distw and is described at http://www.cepii.fr/anglaisgraph/bdd/distances.htm

> 10 We construct a dummy that is equal to one if two countries share either a common o¢ cial or common ethnic language.

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# 4 Theory

We model the relationship between exports and logistics using a gravity equation. This equation has a long and successful history in explaining bilateral trade patterns, with much of the explanatory power coming from the two countries’GDPs and the distance between them. Theory has subsequently provided grounding for the empirical success of the gravity model (Anderson 1979, Bergstrand 1985). The importance of multilateral resistance was highlighted in Anderson & van Wincoop (2003) (“AvW”) and that of ...rm heterogeneity by Helpman, Melitz and Rubinstein (2008). We present the full heterogeneous ...rms model ...rst, before showing how it can be understood as a generalisation of its homogeneous ...rms counterpart. Empirically, we will distinguish between the two, highlighting the role played by multilateral resistance in each.

## 4.1 The Model

There are J countries, j = 1; :::; J. Within each country are monopolistically competitive ...rms which produce a continuum of di¤erentiated products. Consumers have a ‘taste for variety’, embodied in CES preferences given by where x(�) is consumption of variety �, contained in the set of varieties available in j, B. Let � � 1=(1��) be the elasticity of substitution. In this endowment<sup>11</sup> economy with exogenous income in j of Yj, ...rms face demand of <u>1</u> where pj(�) is the price of variety � in j and Pj is j’s ideal price index, given by Pj = �R�2B<sup>pj(�)1��d�</sup> � 1�� .

Each country produces a number of varieties of measure one, with one variety per ...rm. The unit cost of production is a, which is ...rm-speci...c as in Melitz (2003). Firms draw a independently from the identical distribution function G(a) with support [aL; aH ], such that aL is the lower bound on possible unit input requirement draws, while aH is the upper bound. We can identify a ...rm’s variety with its cost draw a: though there may be a measure of varieties with the same cost, each variety with a given cost draw behaves symmetrically, such that they can be indexed by a alone.

There are two types of cost of exporting. The ...rst is an ‘iceberg’variable trade cost tij > 1, which we will specify further later. The second is a ...xed cost of exporting fij > 0, fii = 0. Taken together, a ...rm in j exporting to i producing qij units of output has a cost function given by

> 11 As in Anderson van Wincoop (2003) and most of the gravity literature, we do not allow for endogenous or excess capacity in any economy. This precludes the use of previously idle resources for exports. It also precludes vent-for-surplus exports, where goods are exported as a result of insu¢ cient domestic demand.

10
Given demand and costs, each ...rm chooses price so as to maximise its pro...ts. This gives the price and pro...t function for a ...rm exporting from j to i as Sales by ...rms in country j are only pro...table in country i if �ij(a) > 0. Hence we de...ne a productivity cut-o¤ aij by �ij(aij) = 0, which is the cost level (or inverse productivity level) below which it is pro...table to export. Firms with a > aij do not generate pro...ts high enough to cover the ...xed costs of exporting fij. Using an exporting ...rm’s pro...t function above then gives us the cut-o¤ as This gives us the extensive margin of trade. When aij is higher, the extensive margin is greater, implying a larger subset of ...rms exports. It rises as the income of the importing country rises, and as both ...xed and variable costs of trade fall. Whenever aij < aH , there will be ...rm selection into exporting. In particular, ...rms with the highest variable costs will choose not to export.

The total value of imports by country i from country j is given by Mij = R aaLij<sup>pjqidG(a).Substituting</sup> in for prices and quantities, we obtain aij We then de...ne Vij � RaL<sup>a1��dG(a) as a term capturing the ...rm selection e¤ect.Note that as aijrises,</sup> indicating that the cost level above which ...rms ...nd it unpro...table to export rises, Vij rises. In other words, as this export cut-o¤ rises, a larger set of ...rms export. Using this, we have bilateral exports from j to i given by Vij in equation (9), which is the same as in Helpman, Melitz and Rubinstein (2008), forms the basis for acaij counting for ...rm heterogeneity. In (9), country i’s price index is given by Pi<sup>1��</sup> =<sup>P</sup> R pij(a)<sup>1��</sup> dG(a).<sup>12</sup> j aL Using pij(a) = atij=� the price index can be written where we have made use of the de...nition of Vij above. Since Pi<sup>1��</sup> aggregates trade costs, Anderson and

> 12 We have abstracted from di¤erences in the sets of active traders across countries. See Behar and Nelson (2009) for discussion.

11
van Wincoop interpret the price indices in the gravity equation as multilateral resistance terms, which we discuss further below. In the presence of ...rm heterogeneity, they are a¤ected by Vij, the extensive margin.

# 4.2 General Equilibrium

Next we assume trade balance in order to close the model. We will show that this allows us to write an AvW style gravity equation for bilateral exports. In addition, Behar and Nelson (2009) show that trade balance allows us to derive a gravity equation for the extensive margin. Both of these equations make explicit the role of price indices, or multilateral resistance, in general equilibrium.

Assume trade balance for each country, such that Yj =<sup>P</sup> Mij. Using this in (9) allows one to write i where Pi is country i’s multilateral resistance term, and Y �<sup>P</sup> h<sup>Yhistotalincome.Inarrivingatthis</sup> equation, using trade balance allows one to write these price indices as In these price index equations, the sk terms represent country k’s GDP as a share of the total income of all the countries. That is, si � Yi=Y is country i’s GDP as a share of total income.

The inclusion of two price terms makes system (11)-(13) resemble that of AvW, with the crucial di¤erence that it allows for ...rm heterogeneity. Reductions in trade costs a¤ect both the numerator and the denominator of the gravity equation. Because a reduction in tij a¤ects the multilateral resistance terms, the resulting increase in bilateral trade will be smaller than in the absence of changes in multilateral resistance, all else being equal.

# 4.3 The extensive margin

A further implication of imposing trade balance is that equation (7) for the extensive margin also takes a gravity-like form. In particular Behar and Nelson (2009) show that which is a gravity equation for the cost cut-o¤ de...ning the extent of the extensive margin. Just as for bilateral exports, it responds positively to the product of the trading countries’ GDPs, negatively to 12
bilateral trade costs, and positively to multilateral resistance, captured by the PiPj term. Note also that the ...xed trade cost fij enters equation (14), such that higher ...xed costs reduce the cost level below which exporting is pro...table. In this way, ...xed costs a¤ect the number of exporting ...rms, but not how much each exports. In other words, ...xed costs a¤ect the volume of bilateral exports, but only indirectly through their impact on aij, which determines Vij. This is important for the identi...cation strategy in the empirical section.

Further, (14) makes explicit the role of multilateral resistance on the extensive margin. Just as for bilateral trade ‡ows, a multilateral increase in trade costs increases both the numerator and the denominator of (14); the e¤ect of trade costs on the price indices in the denominator therefore acts to mitigate the direct e¤ect in the numerator. Just as AvW show for bilateral trade ‡ows, comparative statics on the extensive margin will be misleading where the latter e¤ect is accounted for, but the former is not.

Imposing an assumption about the distribution of productivities grants us further analytical tractability. Following much of the recent trade literature, we impose a Pareto distribution on ...rm speci...c variable costs<sup>13</sup> , such that where aL and aH de...ne the support of the distribution, consistent with above, and k is the shape parameter. In particular, this implies G(a) = aa<sup>k</sup> H<sup>k</sup> �<sup>�</sup> a<sup>ak</sup> <u>L</u><sup>k</sup> L<sup>,andg(a)=k</sup> a<sup>k</sup> Ha<sup>�kak</sup> L a1<sup>.Usingthis,wewritethe</sup> extensive margin Vij as such that whenever aij < aL, or no ...rms in j generate pro...ts su¢ cient to cover the ...xed costs of exporting, Vij = 0. From (11), this generates zero bilateral exports from j to i when aij < aL. When will this scenario arise? Following HMR, one way to operationalise (15) is to consider the pro...ts of the ...rm in j with the lowest variable costs aL. If this ...rm does not ...nd it pro...table to export to i, then no ...rm in j will. Accordingly, for ...rm aL, the ratio of variable pro...ts to ...xed export costs can be written as It then follows that Zij is HMR’s latent variable. It is unobserved, but can be estimated using a combination of the distributional assumption on ...rm-speci...c costs a; and observable variables such as GDP and trade costs. A

> 13 See, inter alia, Chaney (2008) and Helpman, Melitz and Yeaple (2004), who use Pareto distributed ...rm productivity in theoretical and empirical work.

13
further consequence of the trade balance assumption is that HMR’s Zij can be written as where That is, the latent variable can be decomposed into two components: multilateral resistance, and a component Z<sup>e</sup> ij independent of prices. Next, using (14), (18) and (19) allows us to relate the extensive margin cut o¤ and the latent variable according to which gives (15) according to where � � <u>k����+11</u> and where k � a<sup>k</sup> H<sup>�</sup> <u>k</u><sup>ak</sup> L<sup>.ThisagainmakesexplicitthepointthatMRa¤ectsthe</sup> extensive margin too; increases in trade costs will decrease Z<sup>e</sup> ij, but will increase PiPj, mitigating the net e¤ect on the latent variable Zij and hence on the extensive margin Vij.

Taking logs of (11) yields the equation we work with for estimation and comparative statics. Specifying trade costs (� � 1) ln tij = �dij �<sup><u>�</u></sup> 2<sup>(Li + Lj),wheredijislogbilateraldistanceandLkisameasure</sup> of country k’s export logistics (such that trade frictions fall with better logistics) gives<sup>14</sup> where is a constant and where the role of the<sup><u>1</u></sup> 2<sup>coe¢cientonlogisticswillbecomeclear.wijisgiven</sup> by which is the term containing the extensive margin. This term contains zij = ln Zij, which since Zij = Zeij (PiPj)<sup>��1</sup> , is in which � is a constant. As in (22), better international logistics increase the extensive margin of bilateral trade ‡ows.

> 14 Dummies can be included on trade frictions to capture di¤erences across subsets of countries if necessary. See A.3.

14
Accounting for MR requires a way of dealing with price index terms. We will use an extension of the approach taken by Baier and Bergstrand (2009), set out in Behar and Nelson (2009), which is a workhorse in macroeconomics: Taylor’s method. In particular, Behar and Nelson show that when the extensive margin terms Vij entering the price indices are approximately Vij ' Z<sup>e</sup> ij<sup>�(PiPj)�(��1),theMR</sup> term ln (PiPj)<sup>��1</sup> is well approximated by This provides a tractable and intuitive way of controlling for multilateral resistance, and can be used for computing comparative statics. Equation (24) extends Baier and Bergstrand’s (2009) approximated MR term to the case of ...rm heterogeneity. The expression includes not only an intensive margin e¤ect e (� � 1) ln tij in each component of the MR term, but also an extensive margin component through �zij. This approximated MR term shares with BB’s method the advantage of yielding analytical tractability and a clear intuition for the comparative statics e¤ects we subsequently compute. It also preserves a role for asymmetries in trade costs.

(24) shows that MR can be conveniently decomposed into three terms. The ...rst of these captures world trade resistance, which averages the importing MR of all importers from j. When this world resistance term is higher, world trade in general is subject to higher trade frictions, reducing bilateral trade all else being equal. The second two terms in (24) are i’s importing MR and j’s exporting MR respectively. When either of these two terms is high, trading with other countries in the world trade system is subject to high trade costs, encouraging i and j to trade with each other instead. This clearly captures the idea that it is relative trade costs that matter in determining bilateral trade ‡ows. For example, when<sup>P</sup> h<sup>sh [(��1) ln tih ��zeih]islarge,allexporterstoiincurhightradecostsintrading</sup> with i. Country i therefore incurs relatively small trade costs in importing from j, raising exports from j to i.

Substituting our expression for trade frictions (� � 1) ln tij = �dij �<sup><u>�</u></sup> 2<sup>(Li + Lj)into(24)allowsus</sup> to write multilateral resistance terms for distance and logistics and ...xed costs more compactly as<sup>15</sup>

> 15 Note conveniently that the 1=(1 + �) coe¢ cient on (24) cancels out for MRijdist and MRij<sup>logistics</sup> .

15
K 6

-

/ i, y

-7y( - ) ~~A~~ KMR

{ ~" } — 7 ( _ ) ~~A~~ ( yo

- / / y

-(- ~~)~~ - ( ~~4~~
where the constant<sup>0</sup> now contains an additional term re‡ecting the magnitude of aL. This is useful in that we can assess empirically the impact of allowing for ...rm heterogeneity in our application, and compare the empirical implications of this modelling feature to the quantitative impact of accounting for multilateral resistance.

# 4.5 Comparative statics

## 4.5.1 Homogeneous ...rms model

Next we consider comparative statics. In the simplest case, ...rm heterogeneity is abstracted from. Then when the exporter’s logistics quality improves, the partial equilibrium e¤ect, which ignores MR, is given simply by<sup>@m</sup> @L<sup>i</sup> j<sup><u>j</u>=</sup><sup><u>�</u></sup> 2<sup>.19ButwhenaccountingforMRthefullgeneralequilibriume¤ectisgivenby</sup> The ...rst term in the f�g brackets in (31a) gives the partial equilibrium e¤ect in the absence of MR. The third term is the e¤ect operating through the importer’s multilateral resistance, which falls by the exporter’s GDP share, dampening the partial equilibrium e¤ect. The fourth term is the exporter’s multilateral resistance, which falls across all export destinations relative to domestic trade. The proportion of j’s export demand this covers is 1 � sj. The second term is the e¤ect operating through “world resistance”, which captures how costly international trade is relative to domestic trade for all countries. sj (1 � sj) enters twice because, on the one hand, it makes j export more directly. On the other hand, it also makes it import more, which through trade balance makes it export more.<sup>20</sup> The net general equilibrium e¤ect after one allows for terms to cancel is �sj (1 � sj). It illustrates the diversion away from domestic trade and towards international trade as international trade costs fall.

Simplifying (31a) clearly shows that the net comparative static e¤ect is not<sup><u>�</u></sup> 2<sup>,butsomethingmuch</sup> smaller. The comparative static e¤ect (31c) is increasing in country size. This is consistent with Anderson & van Wincoop (2003), who found that smaller countries experience smaller comparative static e¤ects because they are more a¤ected by MR. As discussed in section 2.1.1, the reason for this is that smaller countries consume a smaller proportion of their produce domestically and export a larger proportion of their products abroad. More of their trade is international trade, so more is subject to international

> 19 If both the importer and exporter were to improve logistics, the e¤ect at the intensive margin, not accounting for MR, would be �:

> 20 If we do not specify importer logistics as part of the bilateral trade cost function, then we end up with the same comparative static e¤ect, except we attribute it entirely to the ...rst world resistance e¤ect. It is impossible to identify how much of the e¤ect is due to "exports" and how much is due to "imports", but the Anderson & van Wincoop cost symmetry assumption implies it is half each.

17
trade costs, so MR has more of an e¤ect.

Speci...cation (30) allows one to interpret the coe¢ cient on (Li + Lj) as the e¤ect of an improvement in international logistics quality on trade for an average-size country, for which sj = n1<sup>.</sup> Thus, the comparative static e¤ect for an average-size country is

# 4.5.2 Heterogeneous ...rms model

In the presence of ...rm heterogeneity, comparative statics must take into account three e¤ects. As well as the intensive margin and MR, there is the e¤ect of ...rm heterogeneity. In particular, a change in logistics quality must account for As in the homogeneous case, combining e¤ects (1) and (2) gives �sj (1 � sj) (cf. equation (31)). Adding the third e¤ect at the extensive margin yields The gravity parameter<sup><u>�</u></sup> 2<sup>isthee¤ectattheintensivemargin,notaccountingforMR.The...rstsquare</sup> bracket is the adjustment for MR. The second square bracket, which exceeds unity, is the ampli...cation brought about by allowing for the e¤ect at the extensive margin. Note that ignoring this term gives the intensive margin provided we have controlled for wij in estimation in our heterogeneous ...rm model. If we have not controlled for ...rm selection and we estimate a homogeneous ...rms model, then the ...rm and country-level response is the same: in this case there is no ...rm entry or exit into overseas markets and all ...rms experience the same trade elasticity.

In the heterogeneous model, the �<sup>^</sup> coe¢ cient on (Li + Lj) still forms the approximate intensive margin change for an average-size country, while �<sup>^</sup> e<sup><u>�e�xij^�xij^</u></sup> �1<sup>givestheapproximateextensivemarginchangeforan</sup> average-size country. The overall bilateral country-level e¤ect for an average-size country is therefore 18
# 5 Estimation

To place our model in a stochastic framework, we allow for measurement error in the reporting/recording of trade ‡ows and unobserved trade costs. A necessary condition for consistent estimates is that the error term is Independently and Identically Distributed (IID). This section will discuss potential reasons why the IID assumption might not hold. It also discusses the dropping of high-income exporters from our sample.

## 5.1 Endogeneity bias

The IID assumption rules out reverse causation. There is ambiguity regarding the relationship between logistics and trade. Our theoretical framework describes a unidirectional impact of improved logistics on exports. However, it may be that higher trade volumes stimulate the construction of new infrastructure and the introduction of more e¢ cient clearance technologies: the marginal value of investments in trade facilitating measures may be higher if exports are high, while some aspects of the logistics technology are subject to scale economies and thus only worthwhile at very high volume. This could cause an upward bias in the estimated coe¢ cient. On the other hand, high trade volumes may increase the strain on the system, leading to queues at the border and longer customs processing times (Djankov et al, 2010), and causing downward bias in the estimates. The instrumental variables (IV) speci...cations we include provide a check for robustness. For e¤ective IV estimation, we need instruments that have explanatory power (they are su¢ ciently correlated with logistics) but are exogenous (uncorrelated with exports except through logistics). While explanatory power can be checked by examining the ...rst-stage IV regression for logistics, the validity of the instrument is ultimately not testable. We tried a number of plausible candidates.

## 5.2 Omitted multilateral resistance terms

While we have emphasised the importance of multilateral resistance for comparative statics, it can have an e¤ect on estimation. If we have the bilateral trade cost variables but omit their multilateral resistance analogues, these terms would be in the error term. By construction, this would make the error term correlated with the regressors, would invalidate IID and lead to biased estimates of the coe¢ cients. We construct multilateral resistance terms for all bilateral variables and include importer-equivalents for all country-speci...c variables. Following Baier & Bergstrand (2009,2010), we perform estimation with the equality restrictions implied by (30) imposed. For example, we include the sum of exporter and importer logistics as a single variable and include dij � MRij<sup>dist</sup> as a single variable. Furthermore, we construct the MR terms by taking simple averages, which assumes s = 1=n for all countries (see Appendix A.2). Melitz (2008) also uses simple averages and applies it to the context of both bilateral and country19
speci...c variables.<sup>21</sup> We emphasize that taking the simple mean is for the purposes of estimation and not comparative statics (see Baier & Bergstrand, 2010).

# 5.3 Firm-heterogeneity

The heterogeneous ...rms model also indicates potential violation of the IID assumption. Leaving out the control for the proportion of ...rms exporting would lead to omitted variables bias. Furthermore, the model suggests how country-selection into trade is a function of the variables of interest and a potential source of sample selection bias. To address these issues and implement the heterogeneous ...rms model, a two-step procedure is needed.

In the ...rst stage, we estimate a probit model for the probability that country j exports to i, denoted �ij. Letting Tij be unity when exports from j to i are observed and zero otherwise, we write Predicted values of �ij are used to generate normalized predicted values for zij, z^ij (cf. equation (23)). The predicted probability �^ij can be used to estimate the inverse Mills ratio �^ij, which controls for the country selection e¤ect. Furthermore, HMR show how z^ij and �^ij can be used to account for ...rm selection. De...ne the propensity to export xbij � z^ij + ^�ij, which is a positive function of �ij. This is an estimate of the latent variable zij as a function of both observable and (an estimate of) unobservable trade frictions. As above, attaching a Pareto distribution to ...rm productivities allows us to map xbij to a b consistent estimate of the number of ...rms pro...table enough to export. We include this wij = ln(e<sup>�xbij</sup> �1), together with �^ij, in the second stage of our regression, modifying (29) to yield We estimate this second stage using non-linear least squares and use bootstrapped standard errors to allow for the fact that we have generated regressors in the second stage.<sup>22</sup> The ...rst stage and homogeneous goods models use standard errors clustered by country-pair. For reliable identi...cation, we need to have one variable in the probit equation that is not in the second stage. Our theoretical framework suggests variables that a¤ect a ...rm’s ...xed costs (fij) of exporting but not its variable costs.

Our ...rst-stage probit only di¤erentiates between zeros and ones and ignores the missing observations. Baranga (2009) suggests this may induce further selection bias. Addressing these concerns, we also ran speci...cations in which we estimated a preliminary probit for missing variables. Including an analogous

> 21 We thank an anonymous referee for the reference. Melitz’s derivation of MR terms in the country-speci...c case is similar to ours (cf Melitz’s equation 7 and footnote 10) but not exactly the same. This is in part due to di¤erences in treatment of the country-speci...c variable when i = j.

> 22 We perform 50 replications. Furthermore, we reject draws that spawn theoretically illegitimate values for xbij and �^ij :

20
inverse Mills ratio in the "...rst-stage" probit for positive trade yielded a coe¢ cient of virtually zero with a p-value of close to unity. This suggests ignoring missing values is not an issue for our data. Results are available on request.

# 6 Results

This section discusses the estimation results. In a homogeneous-...rm setting, we start with benchmark speci...cations. We discuss the impact of MR on the estimates and then we assess potential endogeneity. Thereafter, in a heterogeneous-...rm setting, we show the results of our two step procedure. The results in this section estimate trade ‡ows using developing countries. It is quite plausible that the logistics issues faced by richer exporters di¤er from those faced by poorer exporters such that the gravity parameter � may di¤er. Nonetheless, we explore the implications of estimation based on the fuller sample in Appendix A.3. As discussed there, we were not satis...ed with the extent to which an interaction between logistics and a developing country dummy captured di¤erences by income group. More importantly, our results were not as reliable or robust when estimated on the full sample, especially when trying to employ IV methods or the HMR procedure. It is important to stress that, although we estimate trade ‡ows using developing countries only, we calculate multilateral resistance terms by summing over all 116 countries and perform comparative statics accordingly.<sup>23</sup> Homogeneous ...rms In Table 2, column 1 presents a standard augmented gravity model. The signs of the coe¢ cients are as one would expect. In particular, the international logistics coe¢ cient (on Li + Lj) is signi...cant with a value of 0:606. To get a sense of magnitude, we calculate the e¤ect on exports of a one standard deviation rise in the ILI. This modest 0.4 unit rise would for example put Rwanda’s logistics on a par with nearby Tanzania’s, make Bulgaria’s like Romania’s or place Brazil just above Argentina. Such a rise would raise exports e<sup>0:6�0:4</sup> � 1 = 27%. Alternatively, we can use the coe¢ cients on logistics and distance to calculate this is equivalent to a reduction in distance of <u>��^</u> �0:4 = 17%: In column 2, we add a full set of controls for MR for each bilateral variable - dij is replaced with �dij � MRij<sup>dist</sup> � for example - and the logistics coe¢ cient is 0:597: More generally the coe¢ cients are quite similar. While the in‡uence of MR on estimation is negligible in this case, we will see later that its comparative static impact will be very important.

Column 3 presents the second stage of a two-stage-least-squares estimation by instrumental variables, where the ...rst stage has the number of procedures needed to start a business in the importer instru-

> 23 For comparative statics, a prior version of this paper multiplied by only the 88 countries for which we estimate trade ‡ows. We are grateful to an anonymous referee for pointing out it is more appropriate to proxy for the whole world with the full sample of countries in our dataset. Anderson & van Wincoop (2003) have a two-country model as well as a multi-country model. In the former, they use only US and Canada information. In the latter, they estimate bilateral trade ‡ows using only Canadian Provinces and US states but include data from another twenty industrial countries in their system of price equations. Our approach here is analogous to their multi-country model.

21
menting for logistics (Li + Lj). A priori, we expect this to be correlated with our logistics variable, because both variables (speci...cally, the importer component of logistics) share common institutional bureaucratic features. Furthermore, while the exporter’s business start-up procedures may or may not be correlated with exports, there is no good reason to believe the importer’s business start-up procedures should be directly related to the exporter’s exports. In the ...rst stage, the instrument was signi...cant with a p-value of less than 0.0015 (using a t-test or F-test). There is only one instrument so no overidentifying restriction to test.<sup>24</sup> The coe¢ cient on logistics in column 3 is 0:437, which is a bit lower than in column 3, but the speci...cation was deemed insigni...cantly di¤erent by a Hausman test.

We also have a speci...cation where we have the sum of procedures in both exporter and importer as one instrument and their product as another. Both variables have explanatory power in the ...rst-stage and the overidenti...cation test was insigni...cant (with a p-value of 0.17). Thus, conditional on one of these instruments being valid, we can legitimately exclude both. This condition cannot be tested, but our regression of the residuals on the exogenous variables yielded individually and jointly insigni...cant terms. This generates a coe¢ cient of 0:697 on logistics, which was also deemed insigni...cantly di¤erent by a Hausman test.<sup>25</sup> The evidence is against the OLS coe¢ cient being incorrectly estimated due to endogeneity. Column 4 produces an insigni...cantly lower estimate, while column 5 represents estimates which were insigni...cantly higher. We prefer to use the column 2 estimates, which lie inbetween, for the homogeneous ...rm comparative static exercise we will perform later. However, we also need to take into account another source of bias, namely ...rm heterogeneity and country selection.

Heterogeneous ...rms In Table 3, we produce the results which account for ...rm- and/or countryselection. In column 1, the probit model yields all the expected signs. We note logistics a¤ects the probability that a country exports, which in our framework means logistics a¤ect ...xed costs. In particular, we note that the Samecountry variable is also signi...cant.

In column 2, we present the second stage of the Heckman two-step procedure, where we have excluded the Samecountry variable.<sup>26</sup> The logistics coe¢ cient is somewhat higher than in Table 2. Analogous to HMR, this is because failure to account for country selection induces a negative correlation between logistics quality and the error term, because a low logistics quality means that unobserved trade frictions must be low on average for countries to be observed as trading pairs. This in turn induces a downward 24 We ran an alternative speci...cation in which we include both importer and exporter procedures as separate instruments. This produces a coe¢ cient of 0.49. Informatively, an auxilliary regression of the residuals found that the exporter logistics variable is signi...cant while the importer’s was not.

> 25 We experimented with alternative variables and functional form, including the importer’s documentation for imports, the importer’s documentation for exports, the importer’s costs of starting a business, the importer’s duration in days of starting a business and combinations thereof. These tended to produce signi...cant coe¢ cients in residuals regressions and/or signi...cant overidenti...cation tests as well as instances of insu¢ cient explanatory power in the ...rst stage.

> 26 We also ran a just-identi...ed model with all ...rst-stage variables included in the second stage. The results were very similar. We also attained similar results using the number of regulations in the ...rst stage probit and excluding those from the second stage.

22
bias in the homogeneous logistics coe¢ cient. However, the Inverse Mills Ratio is insigni...cant, which suggests that country-selection is not an important issue in our application.

In column 3, we implement the full HMR procedure to account for both country- and ...rm-selection. When accounting for both ...rm and country selection, it becomes especially important to exclude a variable from the second stage. Economically, this is a variable which a¤ects the ...xed costs of exporting, but not the variable costs (Helpman, Melitz & Rubinstein, 2008). We omit the Samecountry variable but preserve the MR component to be consistent with the theoretical speci...cation (equation 36).<sup>27</sup> This speci...cation assigns low coe¢ cients to logistics and distance but a high estimated �. This would indicate that the in‡uence of logistics is only through the extensive margin. However, as in column 2, the Inverse Mills Ratio is still insigni...cant, so the next two speci...cations countrol for ...rm-selection but not country-selection.

In column 4, we follow Manova (2008) by excluding no explanatory variables from the second stage but dropping the Inverse Mills Ratio. This produces a logistics coe¢ cient of 0:489 and a � of 0:307. Excluding the Samecountry variable from column 5, the logistics coe¢ cient is 0:445 and � is 0:416.<sup>28</sup> Column 5 is our preferred speci...cation but we stress that, provided we exclude the Inverse Mills Ratio, our results are not materially a¤ected by the choice of exclusion variable, for example religious similarity or the number of procedures or days needed to start a business as used by HMR. Column 5 implies a one standard deviation improvement in the ILI is equivalent to a 14% reduction in distance.<sup>29</sup> Consistent with HMR, allowing for ...rm heterogeneity produces lower coe¢ cients. Comparing our two benchmarks for example, the homogeneous coe¢ cient (column 2 of Table 2) is 0:597 while the ...rm-level coe¢ cient (column 5 of Table 3) is 0:445: However, this does not mean that the country-level e¤ect is smaller.

Table 4 in fact demonstrates much higher bilateral country-level e¤ects, which are calculated for each country-pair by allowing for the extensive margin (cf. equation (34)). For reference, the ...rst column presents values from the homogeneous ...rms model. This is followed by the ...rm-level coe¢ cient from our preferred heterogeneous ...rms model. The subsequent values reveal substantial variation in the extensive margin and hence the country-level e¤ect; for example the standard deviation is 0:147. We see that even the minimum value of 0:648 is greater than that implied by the homogeneous model. Therefore, the homogeneous ...rm model has in this application underestimated the country-level e¤ect of logistics

> 27 Excluding the MR component made no di¤erence. Furthermore, as done by HMR, we attempted speci...cations which exclude religious similarity or the procedures or days needed to start a business. The speci...cations yielded a large signi...cantly negative Inverse Mills Ratio, a GDP coe¢ cient well below unity and a positive distance coe¢ cient. These all suggest excluding these variables from the second stage is not appropriate for our dataset. We also attempted export documentation and/or import documentation in the importer and/or exporter, or combinations theoreof. While these are a priori highly plausible candidates for ...xed but not variable trade costs, the results suggested they are not reliable identifying variables.

> 28 We do not discuss the signi...cance of this variable because it must be non-zero for a well-de...ned gravity model, so it cannot be zero under the null hypothesis. Furthermore, the term ln(e<sup>�x^ij</sup> � 1) is only the ij�speci...c compnent of !. The rest of it is subsumed in the constant.

> 29 Because all trade costs are equally a¤ected by ...rm heterogeneity and multilateral resistance, we still calculate this by taking the quotient of the logistics and distance coe¢ cients.

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for all countries. The source of variation across country-pairs and hence across income-groups is driven by variations in the extensive margin. Di¤erentiation of (34) with respect to x^ij would show that the extensive margin e¤ect is higher for countries with a lower value of x^ij; which implies the extensive margin e¤ect is higher for those who tend to have a lower proportion of ...rms exporting. This in turn implies, for example, that more distant countries with lower logistics quality would have a bigger increase in bilateral exports, ceteris paribus.

The average country-level e¤ect of 0:882 on bilateral trade is almost 50% higher than that implied by the homogeneous ...rms model. It also suggests that the country-level e¤ect is on average half due to the intensive margin and half due to the extensive margin. In other words, approximately half the country-level e¤ect is due to new ...rms entering the export market.

# 7 Simulations: total country-level exports

To understand the e¤ects of logistics on a country’s total exports in the heterogeneous goods model, we must aggregate over the bilateral elasticities calculated in Table 4. It is also about time we recognized the importance of MR more explicitly by factoring in the actual size of the country. The distribution of world GDP is highly skewed. China accounts for about 5% of world output. This is about the same as the next three biggest developing countries combined (Brazil, India and Mexico). This 10% share exceeds that of the other 84 developing countries in our sample! Mean GDP is about seven times as big as the median and, in our full sample, the world mean for non-African countries is almost forty times as big as that for African countries.

Because of multilateral resistance, this extreme skewness means the e¤ect on a particular country or subset of countries can be very di¤erent to the average. We illustrate the importance of this issue in a homogeneous setting before performing the aggregation necessary if ...rms are heterogeneous. We do not allow for country-level entry in the simulations. HMR attribute very little of the rise in international trade to the formation of new bilateral relationships. Furthermore, the Inverse Mills Ratio was insigni...cant in our application.

Homogeneous ...rms To calculate the e¤ect for a particular country j, equations (31) and (30) imply that we multiply the logistics coe¢ cient by n to get � and then multiply that by sj (1 � sj) : Using the estimate<sup><u>�</u>0:597andn=116gives��69:China’sshareofworldGDPis5:34%soitsvalueof</sup> n<sup>=</sup> sj (1 � sj) � = 3:5 . Table 5 has the (semi-)elasticities for all 88 developing countries. China’s value is at the top left. As we move down, we see the steep fall in size as measured by the share of world GDP. As a result, the homogeneous elasticities fall dramatically. Many semi-elasticities are less than 1%; the bottom right produces elasticities of less than 0:1%. Clearly, the elasticity depends on whether you are the Comores or China. Calculating this for all 88 exporters, we average over these to get the 24
mean elasticity of 0:16: This value, which we call the "typical" elasticity, is about a quarter of that for a country of average-size n<sup><u>1</u>:Argentina’sshareofGDPisonlyslightlyhigherthantheaverage(1=116)</sup> and its comparative static e¤ect is accordingly only slightly higher than that given by the homogeneous coe¢ cient. China’s elasticity is more than twenty times bigger than the typical elasticity. Similarly, Brazil, India and Mexico all have elasticities more than double those implied if we ignore MR. On the other hand, 82 out of 88 countries are below average, so ignoring MR typically overestimates the elasticity and sometimes does so by a large amount. While this calls for estimation of elasticities at a country-level, we are not necessarily saying that �<sup>^</sup> is inappropriate: by implicitly giving a greater weighting to bigger countries, it may be a good summary measure.

Heterogeneous ...rms For each exporter, the elasticity varies by importer when ...rm heterogeneity is included. Therefore, for each exporter, we sum the bilateral response over all its importers, weighting by the level of exports:<sup>30</sup> The average-size total country response is 0:766, which is higher than the homogeneous ...rms benchmark that did not account for MR in estimation (0:606). The value of 0:766 implies a one standard deviation improvement in the ILI would raise exports by e<sup>0:297</sup> = 36%. To incorporate MR fully in comparative statics, we follow analogous procedures to before and compute �j is a key object of interest and forms the basis for our main substantive result. We expect bigger exporters to have smaller elasticities in general because they have a lower extensive margin e¤ect, but this e¤ect is empirically dominated by the MR e¤ect. Overall, the biggest countries have the biggest elasticities, which would be true for all country-speci...c determinants of trade costs, not just logistics.

Alongside the homogeneous model elasticities, Table 5 presents the heterogeneous model elasticity for each country with respect to an improvement in its own logistics. The average value of �j across 88 exporters is 0:185, which implies a one standard deviation rise in a country’s ILI would raise exports by 7:67% or about 8%: Recall that such an improvement would place Brazil on a par with Argentina next door. Brazil’s size means its calculated response of 84% is more than triple the benchmark of 27%. More dramatically, Rwanda’s small size means its trade response of 0:028% would be barely one per cent of the benchmark.

By way of summary, we make two ...nal comparisons using estimates we have already presented. Our

> 30 We did this with actual trade ‡ows but predicted trade ‡ows produced similar results.

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...nal estimate of the response to a one standard deviation improvement in logistics quality for a country of average size is 36%. This is somewhat higher than the 27% response implied by our benchmark model in column 1 of Table 2. However, this masks the huge variation in response by country and, due to the skewed distribution of country size, is not typical. Averaging over each country-level response, our measure of the typical response is only 7:67%, which is about one quarter of the e¤ect implied by the benchmark. This di¤erence is an order of magnitude greater than the estimation issues with which empirical economists are typically concerned.

# 8 Concluding discussion

We have seen consistent evidence that an exporter’s logistics increase exports. Our preferred heterogeneous speci...cation indicates that the elasticity of total exports with respect to a change in logistics for a country of average size is 0:74. However, most countries are much smaller than the average, so most countries have much smaller e¤ects. After calculating elasticities for all countries, the typical (mean) elasticity is only 0:185. This implies a one standard deviation improvement in logistics would raise exports by 8%.

By contrast, the benchmark linear model would have produced estimates of 27% –a ...ve-fold exaggeration. The exaggeration for Rwanda would have been 100-fold, for example. The chief reason for these exaggerations is that standard methods ignore the general equilibrium e¤ects operating through multilateral resistance, which are stronger for smaller countries and hence dampen their trade responses by more. In contrast, a handful of large countries have elasticities that are much higher than that given by the benchmark. To be clear, our critique focusses on the comparative static impacts on trade. Statements about one transport cost expressed in other trade cost equivalents are generally still valid because MR a¤ects all trade costs equally.

One of our key results is that economically small countries have small export elasticities. When evaluating the case for logistics upgrades, this result should be considered alongside the costs of improving logistics, which are also likely to increase with country size. Upgrading international logistics for the whole of Brazil requires far more resources than upgrading in Rwanda.<sup>31</sup> This is an important factor in the context of broader evaluations of net welfare gains and evaluations of aid-for-trade on a country-bycountry basis.

While we have emphasised the importance of multilateral resistance for individual country responses, a summary view is arguably better captured by the elasticity for the average-size country, where bigger countries are implicitly given a bigger weighting. Here, it is important to stress that allowing for ...rm

> 31 Furthermore, the functional form we have chosen does not readily allow for decreasing returns, nor does it allow for variations in the gravity parameter �<sup>^</sup> .This is standard in the literature. However, this parameter may vary across countries because the products they export may di¤er (Djankov et al, 2010) or because the elasticity of substitution is not constant. Even so, it would take very large variations in �<sup>^</sup> to extinguish the relationship between size and the general equilibrium response. More generally, a proper evaluation of welfare gains and losses would be needed.

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heterogeneity generates a higher trade response. A one standard deviation improvement gives a trade response of 36% for an average-size country, which is higher than given by the benchmark. For any country, such an improvement is equivalent to a 14% reduction in distance. Nonetheless, the crosscountry variation in trade responses is overwhelmingly driven by di¤erences in multilateral resistance.

Our study has been of a unilateral improvement by a country, but a global analysis requires an investigation of multilateral improvements. Wilson et al (2005) simulate the e¤ect of bringing all countries with below-average measures of trade facilitation half way up to the global average. Such a simulation is beyond the scope of this paper, but one that takes proper account of ...rm heterogeneity and especially MR would be an informative enterprise.

# A Appendix

## A.1 Deriving equation 11

Trade balance requires Yj =<sup>P</sup> i<sup>Mij,sosummingbothsidesof(9)yields</sup> which we use in (9) to give

## A.2 Simplifying MRij<sup>logistics</sup>

When si = 1=n;we have where L = n<sup><u>1</u></sup> Pl<sup>Ll.</sup> 27
# A.3 Dropping high-income exporters

We are interested in the less developed countries. Nonetheless, we explore the implications here of performing estimates on the full sample and including a dummy for developing countries. Theoretically, if we want to capture a di¤erent e¤ect of a trade friction on a developing versus rich country, our equation becomes where D<sup>k</sup> = 1 if country k is ‘developing’, and �<sup>0</sup> is the additional logistics coe¢ cient. Analogous to MRij<sup>logistics</sup> , when si = 1=n , the MR e¤ect of the dummies is captured by where DL = n<sup><u>1</u></sup> Pl<sup>DlLl:Then,asabove,</sup> A priori, we have technical econometric concerns regarding high-income exporters. First, as part of the HMR procedure, very high values of �^ij can be predicted for many country pairs such that they are practically indistinguishable from unity and from one another. HMR truncate the values of �^ij that are greater than 0:9999999 at that value. As a result, there is a mass of estimates of �ij and zij at a particular value. Baranga (2009) notes that a seemingly innocuous truncation can have a very big impact on estimates of �. He speculates this may have been done to ensure<sup>^</sup> � comfortably exceeds zero, which is required for a well-de...ned gravity model. Preliminary analysis revealed that all our predicted values above 0:9999999 were generated by high-income exporters and that high-income countries generally generated high predicted probabilities. Rather than being stuck with indistinguishable values or truncating arbitrarily, we remove a well de...ned group of countries, namely high-income exporters. Second, including logistics and its interaction with the income level means we have two potentially endogenous variables for which instruments must be found. This places a greater demand on the instrumentation procedure.

Turning to the results, Column 1 of Table A2 presents the OLS results for a homogeneous ...rms model with MR controls. It now includes a dummy equal to one if the exporter is classi...ed as a high income 28
country and an interaction between logistics and income level which applies only to developing countries as in equation (39). This produces a higher logistics coe¢ cient than the analogous estimate in Table 2 together with insigni...cant estimates for the income dummy and interaction. The insigni...cance may be due to high multicolinearity - the variance in‡ation factors for the income dummy and the interaction are 118 and 72 respectively - but could imply that income level makes no di¤erence. However, the coe¢ cient is di¤erent to that for developing countries estimated alone. This may be in part to di¤erent coe¢ cient estimates for the other trade costs variables. In other words, fully isolating separate developing country e¤ects may require a number of interactions with income for a large number of trade cost variables and not just logistics. IV estimates are unreliable. Using the sum of start-up procedures in both exporter and importer as one instrument and their product as another - as done before - yields very poor identi...cation of the coe¢ cients of interest. They are all individually insigni...cant, but the.coe¢ cients imply logistics quality reduces exports in rich countries and has a huge positive impact on developing country exports.

Moving onto the heterogeneous ...rms model, we present two estimates where the bilateral component of the Samecountry variable is excluded. Column 4 controls for country and ...rm selection. The estimates implied for developing countries are individually insigni...cant but jointly signi...cant at the 5% level. Compared to the speci...cation controlling for country and ...rm selection for developing countries, this assigns a relatively greater role to the intensive margin and a smaller role to the extensive margin. As was the case for developing countries only, speci...cations controlling for country and ...rm selection were not robust to the choice of excluded variable. Unlike the developing country estimates, there is a large and negatively signi...cant IMR term. Therefore, it is not entirely surprising that attempting to control only for ...rm-selection yields nonsensical results. Most importantly, it produces a negative delta term, which is theoretically inconsistent and precludes the calculation of country-level comparative statics.

While we ave provided estimates based on the exclusion of the Samecountry variable for consistency and brevity, we stress that these results are representative of a range of alternative speci...cations, including those which exclude the bilateral component of the trade cost, alternative excluded variables and specifying a reduced-form interaction of D<sup>j</sup> (Li + Lj) instead of our theoretically derived estimates and speci...cations which exclude the high_income dummy to reduce colinearity. We also tried a number of alternative instrument combinations and functional forms for the IV estimates. These consistently yielded poorly identi...ed results as well as negative delta coe¢ cients or IMR terms.

We additionally estimated speci...cations on the full sample without the income dummy or interactions. The results were more plausible for the IV estimates but equally untrustworthy for the heterpgeneous ...rms models. Furthermore, the OLS coe¢ cient on logistics (0:876) was higher than that for the analogous developing country estimate.

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