The International Gains from Declining Transport Costs

Transcription

1 The International Gains from Declining Transport Costs Ahmad Lashkaripour Indiana University October 2017 Abstract This paper examines the welfare gains from transport cost reduction across six major economies. As a key step, I use detailed firm-level trade data to estimate the transport cost elasticity, β, (i.e., the elasticity at which the unit transport cost varies with unit price) for a wide range of industries. I estimate that (i) the transport cost elasticity varies greatly across industries, and (ii) exhibits a value of β = 0.8 for the average industry, which contrasts with the widely-assumed but somewhat arbitrary unit elasticity specification. Under the estimated elasticities, the gains from a 10% increase in transportation efficiency are 2.34% for the average economy. In comparison, assuming a uniform and unit transport cost elasticity for all industries understates the gains from transport cost reduction by around 25%. 1 Introduction The mass reduction in international transport costs is one the most striking economic developments of last few decades. Driven by factors such as containerization, this mass reduction has not only boosted the share of trade in world GDP, but it has transformed the anatomy of global trade. Perhaps expectedly, this mass development has attracted the attention 1

2 of economists and policy-makers alike, with a multitude of quantitative models being developed to quantify the welfare consequences of declining transport costs. From the perspective of a state-of-the-art quantitative trade model, the gains from a reduction in transport costs are governed by two reducedfrom elasticities: (i) the trade elasticity, which reflects the rate at which trade values decline with transport costs, and (ii) the transport cost elasticity, β, which is the rate at which unit transport costs rise with the unit price of traded goods. Of the two elasticities, the literature has devoted considerable attention to estimating and incorporating the role of the trade elasticity. But the transport cost elasticity is often arbitrarily normalized to one (i.e., β = 1), leading to the well-known multiplicative or iceberg transport cost specification. The widespread normalization of the transport cost elasticity is motivated by two considerations. First, under β = 1, the welfare gains from transport cost reduction can be calculated based solely on macro-level import shares see Arkolakis et al. (2012); Costinot and Rodríguez-Clare (2013), as well as Donaldson (2018) for an empirical application. To be more specific, the iceberg specification implied by β = 1, entails that an across-the-board reduction in transport costs does not distort relative prices across firms. Hence, one can quantify the resulting welfare effects based solely on macro-level import shares, without explicit knowledge about micro-level price heterogeneity. Correspondingly, relaxing β = 1, the gains from transport cost reduction depend not only on macro-level import shares but also on the entire schedule of firm-level prices. The second consideration is that we know surprisingly little about the empirical magnitude of the transport cost elasticity. Many studies have challenged the iceberg specification arising from β = 1; 1 but less attention has been paid to the actual estimation of β itself. A notable exception is Hummels and Skiba (2004), who estimate the economy-wide transport cost elasticity to test the celebrated Alchain-Allen hypothesis. The aggregate and scant nature of the data employed by Hummels and 1 See for example Irarrazabal et al. (2014), Sørensen (2014), and Martin (2012). 2

3 Skiba (2004), however, exposed them to two basic challenges. First, to measure unit prices and transport costs, they had to infer import quantities from data on physical weight. As a result, they estimate β conditional on the identifying assumption that unit weight is uniform within product categories. Second, they had to deal with simultaneity between unit prices and transport costs, which is increasingly difficult when dealing with highly-aggregated data. Perhaps due to these limitations, the estimates of Hummels and Skiba (2004) were never fully implemented into subsequent analyses of global transport cost reduction. Considering the above background, to credibly quantify the gains from transport cost reduction, I employs rich transaction-level trade data to estimate the transport cost elasticity for a wide range of industries. As an intermediate step, I show that the identifying assumption in Hummels and Skiba (2004) regarding the uniformity of import unit weights is empirically violated. That is, import unit weights vary widely even within narrowly-defined categories, and theses variations are systematic: (i) import unit weights increase systematically with unit prices (i.e., valuable merchandise are heavier), (ii) heavy merchandise are sourced relatively more from rich countries and relatively less from distant suppliers, and (iii) imported merchandise are becoming lighter over time. Importantly, not accounting for these systematic variations can lead to an omitted variable bias that attenuates β. To deal with the simultaneity problem underlying the estimation of β, I employ two strategies that capitalize on the detailed nature of the data. First, I identify β while conditioning on firm-product-year fixed effects. Second, I utilize transaction-level information on the identity of exporting firms and importing entities. This information allows me to instrument for shipment-level prices, with the average price paid by an importing entity on alternative routes for goods purchased from alternative suppliers. This instrument is a remarkably strong predictor of import price levels, and is conceivably orthogonal to route-specific movements in transportation costs. Overall, my estimation results suggest that the transport cost elasticity varies considerably across industries. The estimated transport cost elas- 3

4 ticity is lowest in the Food and Beverage industries, where it averages round β = 0.3, and highest in Transportation Equipment and Machinery, where it averages around β = 1. For the average industry I estimate that β = 0.8, which rejects the iceberg specification but not as extremely as traditional estimates. Aside from utilizing more detailed data, my higherthan-traditional estimate for β is primarily a consequence of accounting for the systematic variation in import unit weights. 2 In the second stage of my analysis, I plug the micro-estimated transport cost elasticities into a structural model to quantify the gains from transport cost reduction for six major economies: Brazil, China, the European Union, India, Japan, and the United States. My analysis here involves calibrating a multi-country trade model to match industry-level production and trade data across 7 regions and 33 industries. Using the calibrated model, I calculate that (on average) a 10% increase in transportation efficiency leads to 2.34% increase in real per capita income with respect to the manufacturing and agricultural sectors. In comparison, assuming a uniform and unit transport cost elasticity (β = 1), which is standard in the literature, reduces the calculated gains by 25%. There is a simple intuition behind this finding. When β < 1, transport costs distort the distribution of relative consumer prices. The dominant approach in the literature neglects this distortion. However, in practice, by mitigating this distortion, transport cost reductions can lead to greaterthan-perviously-estimated welfare gains. The above results contribute to a vibrant empirical literature on the gains from inter- or intra-national transport cost reduction (e.g., Donaldson (2018); Donaldson and Hornbeck (2016); Atkin and Donaldson (2015)). As note earlier, the dominant approach in the literature is to calculate welfare gains conditional on the unit transport cost elasticity specification, 2 There is a simple intuition for why overlooking the variation in import unit weights attenuates the estimated transport cost elasticity. High-price items are costlier to transport due to (i) being heavier and (ii) the greater insurance, packaging and handling requirements associated with high-value merchandise. By treating unit weight as uniform, traditional estimates overlook the former channel, and understate the elasticity of transport cost with respect to unit price. Accounting for both channels, however, transport costs increase near proportionally with unit price, thereby resembling iceberg melt costs. 4

5 i.e., β = 1. The results presented in this paper suggest that this approach may systematically understate the corresponding welfare gains. The present paper is also closely related to a literature that studies the determinants of international transport costs (Hummels and Skiba (2004); Clark et al. (2004); Hummels et al. (2009); Blonigen and Wilson (2008); Abe and Wilson (2009)). My contribution to this literature is two-fold. First, this paper is the first to explicitly account for the role of physical weight in international transportation. Second, whereas previous studies have focused on country-level trade data, I shed new light on the anatomy of international transportation using detailed transaction-level data. Given the focus of the paper and in-line with Hummels and Skiba (2004), I employ the direct approach of estimating the transport cost elasticity using data on freight plus insurance rates. Nonetheless, my estimation results are consistent with those in Irarrazabal et al. (2014), who use an indirect approach to infer the underlying structure of international trade barriers, which are broadly-defined and includes tariffs, transport cost, and non-tangible red tape barriers among other things. At a broader level, this paper sheds new light on an ongoing debate about the consequences of micro-level heterogeneity for the welfare gains from trade. On one hand, Arkolakis et al. (2012) argue that the incorporation of micro-level heterogeneity may be of no consequence for the macro-level gains from trade. On the other hand, several studies including Melitz and Redding (2015) and Simonovska and Waugh (2014) have challenged this assertion. From a theoretical point, this paper demonstrates that micro-level price heterogeneity is consequential for macro-level welfare gains, except in the knife-edge case were β = 1. Empirically, I show that while this knife-edge assumption holds in certain industries, it is violated in many others. Finally, this paper provides a glimpse into an unexplored avenue that warrants further research. While often neglected in the literature, I find that physical weight plays a dominant role in international transportation, and that its role has been evolving rapidly over time. A better understanding of global trade conceivably requires a better understanding of these developments. 5

6 2 Theoretical Framework I first present a basic theory that highlights the welfare gains from transport cost reduction. To this end, I use a generic trade model that nests an important class of workhorse quantitative trade models as a special case. This level of generality will allow me to put the dominant approach in the literature in perspective and to outline its underlying limitations. Economic Environment and Preferences. The global economy consists are N countries indexed by j and i, plus K industries index by k. The utility of the representative consumer in country i can be stated as W i = U i (Q i,1,..., Q i,k ), where Q i,k is a utility aggregator across all firm varieties from various countries of origin in industry k. More specifically, Q i,k = Q i,k (q ωi,k ), where q ωi,k denotes the quantity purchased from firm ω in industry k. Production and Transportation. On the production side, country i is populated with L i units of a Hicksian composite factor of production, which is employed in either final good production or transportation. w i denotes the factor price in country i. Each country is also populated with a mass of perfectly competitive firms, indexed by ω. The total cost facing firm ω from industry k in country i is c ω,k = c ω,k (q; w i ), which is increasing in total output q. Firm ω collects a factory-gate (f.o.b.) price, p ω,k, for its output that is equal to marginal cost. The consumer (c.i.f. ) price for firm ω s output in market i, π ωi,k, is the sum of the f.o.b. price plus a transportation cost, τ ωi,k. In particular, π ji,k = p ω,k + τ ωi,k. The transportation cost, τ ωi,k is composed of (i) an aggregate cost-shifter that accounts for factors such as aggregate transportation efficiency, geodistance, and administrative barriers, plus (ii) a firm-specific term that accounts for the fact that freight companies charge rates based on the 6

7 value of transported items. Formally stated, 3 τ ωi,k = t ji,k f k (p ω,k, w i ), where f k (.,.) is increasing in both arguments. Note that the dependence of τ ωi,k on p ωi,k accounts for, among other things, scale effects in transportation. Specifically, the variation in f.o.b. price affects total sales and therefore shipment scale, which can ultimately alter the unit cost of transportation. Following Hummels and Skiba (2004), I hereafter define β k ln τ ωi,k ln p as ω,k the international transport cost elasticity in industry k. In the following, I will argue that this elasticity is key to understanding the welfare consequences of international trade. But to put β k in perspective, notice that workhorse trade models often assume that β k = 1, which delivers the well-known iceberg transport cost specification: π ωi,k = ( 1 + t ji,k ) pωi,k. 4 Equilibrium. Equilibrium is a vector of factory-gate prices, {p ω,k }, consumption quantities, {q ωi,k }, and national wage rates, {w i }, such that (i) the utility of the representative consumer in country i, U i (q ωi,k ), is maximized subject to k j ω Ωj,k π ωi,k q ωi,k = Y i, where Y i denotes country i s total expenditure; (ii) f.o.b. price, p ωi,k, equals the marginal cost; and (iii) total expenditure equals total factor income, i.e., Y i = w i L i. I will hereafter use V i (Y i, π ωi,k ) to denote the indirect utility of country i s representative consumer in this trading equilibrium. The Gains from Transport Cost Reduction. Different variations of the above model have been used to analyze the welfare consequences of a reduction in international transport costs such a reduction can either have technical origins such as containerization or administrative origins. 3 The above transport cost specification has deep roots in the literature and is analogous to the transport cost function introduced by Hummels and Skiba (2004) see Section When β k = 1, the transportation cost function becomes τ ωi,k = t ji,k g k (w i )p ωi,k, where g(.) is some increasing function. Taking labor in i as the numeraire (i.e, w i = 1) and supposing that g k (1) = 1, then the c.i.f. price in country i is the f.o.b. price ) times and iceberg (ad-valorem) transport cost: π ωi,k = p ωi,k + t ji,k p ωi,k = (1 + t ji,k p ωi,k. 7

8 Noting that W i = V i ( Yi, π ji,k ), and choosing labor in country i as the numeraire, the change in country i s welfare in response to a reduction in international transport costs, d ln t ji,k, will be given by: d ln W i = ln V i ln Y i k j ω Ω j,k λ ωi,k [ sωi,k ( d ln tji,k + β k d ln w j ) + (1 sωi,k ) d ln w j ], where the above formula is derived using Roy s identity that V i/ π ωi,k V i / Y i = q ωi,k, with λ ωi,k π ωi,k q ωi,k /Y i denoting the share of income spent on firm ω varieties and s ωi,k τ ωi,k /π ωi,k denoting the variety-specific share of transport costs in c.i.f. price. Evaluating the above expression requires credible estimates for the industrylevel transport cost elasticity, β k. However, since such estimates are lacking, researchers often set β k = 1, which is somewhat arbitrary but leads to the tractable iceberg (ad-valorem) transport cost specification. Specifically, setting β k = 1, the welfare effects of a change in transportation costs can be expressed as d ln W i = ln V i ln Y i k (1) [ ( ) ] λ ji,k d ln 1 + tji,k + d ln wj, (2) j where λ ji,k = ω Ωj,k λ ωi,k denotes the share of country i s expenditure on country j varieties in industry k. A well-known special case of the above formula is the case where the within-industry utility aggregator is also CES. In that case, d ln λ ji,k d ln λ ii,k = ɛ k ( d ln wj + d ln ( 1 + t ji,k )), where (i) λ ji,k λ ji,k /e i,k is the conditional expenditure share on country j varieties within industry k, with e i,k denoting the total share of expenditure on industry k, and (ii) ɛ k denotes the industry-level trade elasticity. Plugging the CES condition into Equation 2 yields the well-known gainsfrom-trade formula popularized by Arkolakis et al. (2012): d ln W i = ln V i e i,k ln Y i d ln λ ɛ ii,k, (3) k k Digging deeper, the iceberg assumption (β k = 1) allows the computation of aggregate welfare effects without explicit knowledge about micro- 8

9 level price heterogeneity. Relaxing the iceberg assumption, however, a reduction in aggregate trade costs will alter the distribution of relative c.i.f. prices across firms. Hence, the resulting welfare effects will depend not only on the macro-level trade shares, but also on the initial distribution of firm-level prices. 5 It should be clear by now that the transport cost elasticity, β k, has firstorder implications for the welfare gains from trade. But due to a lack of credible estimates, the literature has often resorted to the practical but somewhat arbitrary convention of setting β k = 1. In the following section, I use micro-level data to formally estimate β k across an extensive set of industries. Subsequently, in Section 4, I plug the estimated elasticities into a quantitative multi-country trade model calibrated to macro-level trade/production data. In addition to delivering more credible estimates for the gains from transport cost reduction, the exercise allows me to examine the limitations of the widely-used iceberg specification. 3 Estimating the Transport Cost Elasticity To formally estimate the industry-level transport cost elasticity, β k = ln τ ln p, I should address two issues. First, my estimation should account for the systematic variation in import units weights, an issue which has received less attention in the prior literature. Second, the identification of β k is complicated by the simultaneity between p and τ an issue that has been historically recognized in light of the seminal Alchian and Allen (1964) hypothesis but requires rich data to circumvent. 6 In what follows, I first describe the data set used in my estimation. Then, I highlight the systematic variation in import unit weights (i.e., weight per item). which have been generally neglected in the prior literature but are a key driver of international transport costs. Finally, I propose an 5 Some derivative of this observation has already been outlined in Irarrazabal et al. (2014) and Martin (2012), among others. 6 The simultaneity problem can be stated as follows. The price/value of transported goods determines the transportation rate. At the same time, the cost of transportation determines the price-mix of traded goods see Hummels and Skiba (2004) for more details. 9

10 estimation methodology that accounts for both the systematic variation in import unit weights and handles the simultaneity between the unit price and transport cost. 3.1 Data I use proprietary transaction-level data on Colombian imports in the period. The data has been collected and made available by the National Tax Agency. For each import transaction the data identifies the exporting firm s id, the Colombian importing firm s tax id, the corresponding 10-digit Harmonized System (HS10) product category, plus the f.o.b. value, freight cost, insurance charge (all in US dollars), quantity and net weight of the imported goods. 7 The detailed structure the Colombia data set enables me to conduct my estimation with an extensive set of fixed effects. Nonetheless, I show that all estimation outcomes hold equally in the publicly available but more aggregate US import data. A detailed description of the US sample is provided in Appendix A. I also use export data from Colombia and the US to complement the import data. The export data for each country has a similar format to that of the import sample, but does not report freight, insurance, and tariff charges. The Colombia data reports the imported quantities in 1 of 10 different units of measurement. Count is the most frequent unit of measurement (see Table 1). In total, there are 17,281,272 data entries with 12,258,450 entries reporting quantity in counts in line with the literature (most notably, Hummels and Skiba (2004)) I restrict my main analysis to these observations The Systematic Variation in Import Unit Weights As an intermediate step in the estimation analysis, I uncover a set of new regularities about the systematic variation in import unit weights. Recall that, to overcome data limitations, existing analyses of international 7 Colombian imports from 2007 to 2013 include 7,296 distinct HS10 product categories. 8 When analyzing US import data, Hummels and Skiba (2004) restrict attention to observations that report quantity in counts and consist of a single invoice. 10

11 Table 1: The composition of imports by unit of measurement. The unit in which quantity is reported in Sample Count of items Kilograms and its derivatives Other Units Colombia Imports 51.60% 38.57% 9.83% US Imports 45.2% 18.9% 35.9% Note: In the Colombia sample the vast majority of shipments that report quantity in counts, report the number of items ( UNIDADES O ARTICULOS ) with a few shipments reporting pairs ( PAR ) and thousands ( MILLAR ). In the US data, various units correspond to item count (e.g. N, NO, DOZ, DPC, DPR, PCS, PRS, PK, HUN, THS ). Similarly, the US data contains various derivatives of kilograms: K, KG, TON, T, kg, GRS, GM, GKG, G, CYK, GTN. transport costs often assume that unit weight is uniform within product categories. This assumption enables researchers to infer import quantity from data on physical weight, when calculating the unit price, p, and the unit transport cost, τ. 9 The evidence presented here show that contrary to what is widely-assumed, import unit weights vary considerably and systematically within narrowlydefined categories. My analysis exploits information on weight, W s,ωht, and quantity, Q s,ωht, which are reported separately for each individual shipment s sourced from firm ω, in a given HS10 product h, in year t. Similar variables are reported in the US sample, but the US data is aggregated up to a given country of origin port of entry product year. The analysis on the US sample therefore requires a different notation and utilizes different variations in the data; the description of which is relegated 9 To elaborate, if unit weight is uniform within say an HS10 or HS6 product category, physical weight can perfectly proxy for quantity up to a constant multiplier. To give an example, suppose one assumes that all TV units (classified within the same HS10 code) weigh 10 kgs. Consider two import shipments consisting of TVs: shipment A weighing W A kilograms and shipment B weighing W B = 2 W A kilograms. Knowing this information alone, one can deduce that the quantity of TVs in shipment B is 2-times the quantity in shipment A: Q B = 2 Q A. This assertion, however, hinges strongly on the initial assumption that all TVs weigh the same. If instead each TV unit in shipment B is 2-times heavier, the two shipments will involve the same quantity despite different physical weights. Considering that the credibility of our price measure depends on the credibility of our quantity data, deviations from the uniform unit weight assumption can thus lead to substantial bias in price measurement. 11

12 to Appendix A. 10 But one should bear in mind that while I occasionally report evidence from both data sets, I present the empirical strategy based solely on the transaction-level Colombia data described earlier. Given the information on total weight and quantity, one can calculate the unit weight associated with shipment s, ωht as: wgt s,ωht = W s,ωht Q s,ωht. An elementary analysis of import unit weights uncovers four basic facts that underlie both samples. Importantly, while I confine my benchmark analysis to import transactions reporting quantity in counts, the documented facts apply more broadly. The only exception are import transactions that report quantity in some derivative of kilograms. For such observations (which constitute less than 19% of US imports, for example) unit weight is by definition one and import quantity is exactly equal to import weight: Q s,ωht W s,ωht. For the remaining majority of import transactions, however, the variation in import unit weights are both substantial and systematic. FACT 1. Unit weights vary widely even within narrowly defined categories. Table 2 reports the variation in import unit weights for various levels of aggregation. Within the median country product year cell, the heaviest (95 percentile) item imported by Colombia is 18-times heavier than the lightest (5 percentile) item. The variation in import unit weights remain significant even across shipments from the same firm, of the same product, in the same year. A similar pattern is also visible in the US data, where within the median year port of entry product cell, the heaviest (95 percentile) imported item weighs 16-times more than the lightest (5th percentile) item The US sample reports the quantity (Q s,ωht ) and weight (W s,ωht ) of aggregate imports from country s to US district ω, in a given HS10 product h, in year t. Therefore, while s indexes individual shipments in the benchmark analysis (conducted on the Colombia sample) it denotes exporting country in the US data. Similarly, ω indexes an exporting firm in the benchmark analysis, whereas it indexes the port-of-entry in the US data. 11 Two clarifications about this and others statistic reported in Table 2 with relation 12

13 Table 2: The variation in unit weight within narrowly-defined categories Median 1st quartile 3rd quartile Colombia (within country-product-year) 95-5 pctile ratio coefficient of variation 98% 50% 161% Colombia (within firm-product-year) 95-5 pctile ratio coefficient of variation 52% 22% 93% US (within product-year-district) 95-5 pctile ratio coefficient of variation 102% 61% 141% Note: The US sample includes 4,575,197 observations and the Colombia sample includes 12,258,450 observations See Appendix A for a description of the US sample. These observations obviously challenge the standard practice of using physical weight as a proxy for quantity. For instance, consider a situation where we observe data on the physical weight, W, of shipments A and B but not the actual quantities, Q. As a matter of accounting, the relative quantity of the two shipments will depend on their relative weight based on the following equation: Q A Q B = W A W B wgt B wgt A. Considering the above equation, Fact 1 indicates that the high variance of the term wgt B /wgt A can undermine the widely-assumed link between physical weight and quantity. However, one may rightfully suspect that the tremendous variation in import unit weights is mere noise and driven by measurement errors. In what follows, however, I present three facts, to the US Sample: (i) this statistic describes the median category, not the median observation, and (ii) it is calculated for the sample of 4,575,197 observations, which report quantity in numbers ( N and NO ) and provide full information on total weight, value, freight charge, and quantity (see Section 3.1) 13

14 each indicating that the variation in unit weights are systematic. FACT 2. Unit weight (bulkiness) increases systematically with f.o.b. unit price. One way to interpret Fact 2 is that high-quality merchandise are heavier; presumably due to their more extensive use of material inputs. To establish this fact, I calculate the f.o.b. unit price per shipment as: p s,ωht = V s,ωht Q s,ωht, where V s,ωht and Q s,ωht, respectively, denote the f.o.b. value and quantity pertaining to shipment s from firm ω in product category h in year t. Fact 2 is then documented using the following estimating equation 12 ln wgt s,ωht = α ln p s,ωht + δ ωht + ε s,ωht, (4) where δ ωht denotes firm-product-year fixed effects. The extensive set of fixed effects control for firm-product-year characteristics that are invariant across shipments. Elasticity α is thus identified by exploiting across shipment variation within provider-hs10 product-year cells. The above equation presents the benchmark estimation. Alternatively, I also estimate α ln wgt/ ln p conditioning on country of origin-product-year effects, in which case I exploit the across-firm variation in unit prices and weights. The first two columns in Table 3 report estimation results corresponding to the Colombia sample. The results point to a strong, significant, and tight relationship between unit weight and price that is robust across various specifications. Roughly speaking, a 10% increase in f.o.b. unit price is associated with an 8% increase in unit weight. Remarkably, unit price alone can explain up to 70% of the variation in unit weight across shipments within narrowly-defined categories. 13 Moreover, the weight- 12 It should be noted that the estimated weight-price relationship should not be treated as behavioral/structural. We can only interpret the sign of α as the sign of a conditional correlation that does not necessarily reflect causality. 13 Fact 2 exposes yet another fundamental problem with constructing unit price measures based on physical weight data which is inevitable with datasets such as COMTRADE-BACI that only report physical weight. Based on this approach, unit price is measured as the value-to-weight ratio; that is simply unit price divided by unit weight: p = p wgt. Considering the above equation, the strong covariance between unit price, 14

15 Table 3: The relationship between unit weight and f.o.b. unit price. Dependent variable: (log) unit weight Colombia sample US sample Regressor firm-product-year FE country-product-year FE product-year FE product-year-district FE (log) f.o.b. unit price 0.90*** 0.73*** 0.76*** 0.75*** (0.008) (0.008) (0.005) (0.006) Observations 12,254,253 12,254,253 4,574,112 4,574,112 FE groups 2,907, ,288 57, ,845 Within-R Note: The standard errors are clustered by HS10 product and reported in parentheses (*** denotes significance at the 1% level). See Appendix A for a description of the US sample. price relationship is not a peculiar feature of the Colombia data as it holds equally in the US sample, where a 10% increase in f.o.b. unit price is associated with an 7.5% increase in unit weight within year port of entry product cells. 14 Importantly, the strong relationship between weight and price is not driven by outlier categories. To illustrate this, I run Regression 4 separately for 2836 HS10 product categories in the Colombia sample. Table 4 summarizes the product-specific estimation results, and Figure 1 displays a histogram of the estimated HS10-specific weight-price elasticities. The results indicate that the weight-price relationship is significant and positive for more than 90% of the product categories. The relationship is relatively stronger for HS72 (pearls, precious stones, metals, and imitation jewp, and unit weight, wgt, can lead to a weak relationship between the value-to-weight measure, p and the actual unit price, p. This caveat, however, has gone largely unnoticed, with p being used frequently as a proxy for p in the current literature the origins of the value-to-weight proxy dates to as far back as Moneta (1959). 14 As noted earlier, the US sample is more aggregated with limited within-provider variation. The different structure of the data requires a slightly different notation. Specifically, as described in Appendix A, each observation in the US sample correspond to total annual imports from a given country, through a specific port-of-entry, in an HS10 product category. I can thus estimate Equation 4 by exploiting the cross-national variation within either (i) product year or (ii) port of entry product year cells. The estimation results under both specifications are qualitatively similar to the benchmark estimation conducted on the Colombian sample (see Table 3). Also, separately estimating α for the 4259 HS10 categories in the US sample, I find that he weight price relationship is positive and statistically significant for 3951 of the 4295 product categories (Table 4). 15

16 Table 4: The weight-price relationship by HS10 product. Colombia sample US sample Statistic Median 1st quartile 3rd quartile Median 1st quartile 3rd quartile α ln unit weight ln p F-test p-value Variation cross-shipment (within firm-product-year) cross-national (within product-year-district) No. of HS10 codes in the sample Positive relationship (α > 0) Stat. Sig. at the 95% level Note: This table estimates Equation 4 separately for various HS10 products that report quantity in units of count. The standard errors are clustered by HS10 product. elry), and relatively weaker for HS61 and HS62 (apparel and clothing accessories). For the curious reader, Appendix B delves deeper into the weight-price relationship by proving specific examples, including those corresponding to suspect product categories like watches and bicycles. 15 FACT 3. Heavier merchandise are imported relatively more from rich countries and relatively less from distant suppliers. Fact 3 states that the cross-national and spatial variation in import unit weights are also systematic. To demonstrate this, I run the following regression: ln wgt jht = θ 1 ln DIST j + θ 2 ln GDPcap jt + θ 2 ln GDP jt + δ ht + ε jht, where wgt jht denotes the average unit weight of all shipments originating from country j in product h, year t that is, the weighted average of all 15 The weight-price relationship is no confined to goods reporting quantity in units of count. Estimating the relation across all goods in the US import data (except only those that report quantity in units of kilograms) yields: ln wgt s,ωht = 0.60 (0.007) ln p s,ωht + δ ωht + ε s,ωht, within-r 2 = 0.50 where s denotes the exporting country; ω denotes the US district of entry; h denotes the HS10 product category; and t is the corresponding year. The above regression is conducted on 15,158,404 observations and includes product-year-district fixed effects. The standard error reported in parenthesis is clustered by HS10 product. 16

17 17 Figure 1: The weight-price relationship across HS10 product categories. 400 Colombia Sample (within firm variation) 300 Frequency α (elasticity of unit weight w.r.t. unit price) U.S. Sample (cross national variation).; 300 Frequency α (elasticity of unit weight w.r.t. unit price) ln weight ln price Note: This figure describes the estimated α = across various HS10 categories in the U.S and Colombia Samples. The estimation is preformed across 4259 and 2836 HS10 categories in the US and Colombia sample, respectively. For illustration, I drop outlier categories with an estimated α that falls above or below the 1st and 99th percentile. Also, note that both samples include only HS10 categories that report quantity in units of count.

18 Table 5: Cross-national and spatial variation in import unit weights. Dependent variable: (log) unit weight Colombia sample US sample (log) Distance -0.06*** -0.21*** (0.008) (0.013) (log) GDPcap 0.14*** 0.09*** (0.006) (0.004) (log) GDP -0.04*** -0.08*** (0.004) (0.04) Observations 286, ,231 HS10 years 22,693 57,427 R Note: Both regressions include HS10-year fixed effects, and cluster errors (reported in parentheses) by HS10 product (*** denotes significance at the 1% level). wgt s,ωht s for which the exporting firm ω resides in country j. DIST j denotes geographical distance (in kilometers) from country j, while GDPcap jt and GDP jt respectively denote the per capita and total GDP of exporting country j. The fixed effect δ ht absorbs the product-year invariant determinants of import unit weights. The results, displayed in Table 5, suggest that the unit weights of traded merchandise vary systematically with the characteristics of the supplier. In particular, heavier or bulkier merchandise are sourced relatively more from rich countries and relatively less from distant suppliers. These patterns that underlie both the US and Colombian samples indicate that physical weight or bulkiness is a variable taken into consideration by economic agents. FACT 4. Import merchandise have become less bulky over time. The last of the four facts highlights the systematic variation in unit weights along the time-series dimension. These variations are particularly visible in the US sample that spans over a longer period from 1989 to The declining unit weight of US imports is displayed in Figure 2, where 18

19 Figure 2: The unit weight of US imports over time 1.9 unit weight (average) year Note: The average unit weight of US imports in 1989 is normalized to one. the average unit weight or bulkiness of imported merchandise drops by around 50% over the span of 27 years. The same trend is also visible within HS10 product categories, where (on average) the unit weight of imported merchandise drops by around 3 kgs per year. While this declining trend is statistically significant (at the 99% level) in the US sample; it is less pronounced in the Colombia sample where the data spans only 7 years. 3.3 Estimating β Bearing in mind the systematic variation in import unit weights, I I turn to formally estimating the transport cost elasticity, β. As a first step, I conduct a pooled estimation on the entire sample, assuming that β k is uniform across industries. The estimating equation in that case can be stated as ln τ s,ωht = β ln p s,ωht + κ ln S s,ωht + δ ωht + ε s,ωht (5) 19

20 where τ s,ωht and p s,ωht respectively denote the unit transport cost and the unit price associated with observation s, ωht (shipment s firm ω product h year t). The above formulation estimates β controlling for (i) providerproduct-year fixed effects, δ ωht, and (ii) shipment scale, S s,ωht, since international transportation may be subject to scale economies. 16 The remaining idiosyncratic error term, ε s,ωht, reflects measurement error plus non-systematic cost-shifters specific to shipment s, ωht. In my benchmark estimation I fit Equation 5 to the universe of Colombian import transactions, identifying β using the within firm-product-year variation in τ and p. For comparison, I also estimate β using the country-level US import data, which has been used extensively in the prior literature. Given its highly aggregated nature, the US data permits the estimation of β based on only the cross-national variation in τ and p within HS10 product categories the details of which are relegated to Appendix A. Parametrically, Equation 5 closely resembles the aggregate cost function estimated by Hummels and Skiba (2004) labeled as Equation 10 in their paper. However, aside from being based on transaction-level (as opposed to country-level) data and controlling for firm fixed effects, my estimation strategy differs from Hummels and Skiba (2004) in two key aspects: (i) I formally control for the systematic variation in import unit weights, and (ii) I utilize detailed information on importer-exporter characteristics to handle the simultaneity problem underlying the estimation of β. Below, I elaborate on these two distinctive features. Accounting for the Variation in Unit Weights. The traditional transport cost estimation employed by Hummels and Skiba (2004) and Hummels et al. (2009), among others, identifies β conditional on unit weight being uniform within product categories. Recall that this identifying 16 I control for scale effects using the number of packages in shipment s, ωht. Intuitively, shipping out ten boxes at once is more cost-efficient than sending out ten single-box shipments throughout the year. When analyzing the US sample, I subscribe to the estimation strategy proposed by Hummels and Skiba (2004), which is reflective of the limited information available in the data set. In particular, I control for scale with the total weight of all shipments aggregated into a given data entry, and employ bilateral distance (DIST s ) and the GDP per capita of the origin country as additional controls see Appendix A for a thorough description. 20

21 assumption is imposed in face of data limitations, as it allows researchers to infer the import quantity, Q s,ωht, from data on shipment weight, W s,ωht. Put differently, the uniform unit weight assumption allows researcher to estimates β as the elasticity of transport cost per kg, τ to the value per kg, p = p wgt of the traded goods. wgt τ with respect The traditional approach can be formally described by re-writing the estimating Equation 5 in terms of τ wgt τ and p = p wgt : ln τ s,ωht = β ln p s,ωht + κ ln S s,ωht + δ ωht + (β 1) ln wgt }{{ s,ωht } omitted variable +ε s,ωht When unit weight is uniform within firm-product-year cells (i.e., wgt s,ωht = wgt ωht ), the omitted term is absorbed by the fixed effect, δ ωht, and the traditional approach delivers an unbiased estimate of β. Factually, however, not only is wgt non-uniform, but it is negatively correlated with value per kg, p. As a consequence, the traditional approach suffers from a classical case of omitted variable bias that attenuates β. Another way of casting the above nuisance is that overlooking the variation in import unit weights neglects a key determinant of transportation cots. Specifically, given that τ = τ wgt, one can decompose the transport cost elasticity into two distinct components as follows: where the term β β ln τ ln p ln τ ln p ln τ ln p ln wgt = + ln p ln p ln p, is the elasticity identified by the traditional approach (e.g., Hummels and Skiba (2004); Hummels et al. (2009)), while ln p ln wgt ln p = 1 α and ln p = α, by construction. Plugging these values into the above equation delivers the following decomposition: β = β (1 α) + α. (6) The above expression highlights the two distinct components of the transport cost elasticity: 1. Value-driven component, β(1 α), which reflects the rate at which insurance, packaging and handling requirements increase with ship- 21

22 ment value. 2. Weight-driven component, α, which accounts for the fact that highpriced items are heavier and, therefore, costlier to transport. Considering the above decomposition, conditional on unit weight being uniform (i.e., α = 0), the transport cost elasticity equals β, which is the elasticity estimated under the traditional approach. However, in practice, given that α 0.75, the traditional approach delivers a systematically attenuated elasticity estimate, β = β α 1 α < β. Dealing with the Simultaneity between p and τ. Another identification challenge underlying the estimation of β is that unit price (and also shipment scale) may be correlated with the idiosyncratic transport cost shifter, ε s,ωht. In fact, transport costs are know to influence the import price-mix through various channels: (i) the celebrated Washington apples effect posits that an increase in transport costs increases the relative demand for high-priced import varieties (Hummels and Skiba (2004)); (ii) productivity-sorting models, like Melitz (2003), predict that higher transport costs increase the productivity-mix and thus lower the price-mix of imports; and (iii) quality-sorting models predict a similar effect but in the opposite direction (Baldwin and Harrigan (2011)). To deal with reverse causality, I construct two instruments that are correlated with the f.o.b. unit price but plausibly orthogonal to ε s,ωht. One straightforward choice of instrument here is the import tax, which has been widely applied in the prior literature as an exogenous price-shifter see for example Caliendo and Parro (2015) who use import tariffs to identify the trade elasticity. Theoretically, it is well understood that import taxes are strongly correlated with import price levels, as they improve the importing country s terms-of-trade by inducing foreign firms to lower their price-markups (Graaff (1949); Johnson (1953)). The issue with taxes, however, is that they do not vary substantially within firm-product-year cells. Nonetheless, import taxes still offer a non-negligible source of variation. The standard deviation of the import tax rate (value-added tax + tariff) applied by Colombia on different shipments from the same firm in the same HS10 product code is around 1.7%. These variations are 22

23 prompted by the fact that (i) a different value-added tax rate may apply to different shipments pertaining to the same firm-product-year category, and (ii) import tariff rates vary over time due to trade agreements or WTO disputes and settlements (see Eaton et al. (2010)). The detailed nature of the Colombian import data, however, allows me to construct a second instrument that is notably stronger. In a given year, Colombian firms import intermediate inputs (or final goods) from various foreign providers. In my data, each observation identifies both the exporting firm, ω, and the Colombian importing firm, m. For an importing firm, m, the quality of imported inputs from various providers are correlated. That is, if firm m imports high quality (high price) inputs from provider ω, it most likely has a history of importing high quality inputs from other providers in prior years. Considering this, foreach shipment s, ωht that is imported by Colombian firm m, the unit price, p s,ωht, can be instrumented with the average unit price of firm m s imports from alternative suppliers in the prior year, P m,ht 1. The identifying assumption being that concurrent idiosyncratic movements in τ s,ωht are not correlated with the price of firm m s imports from other suppliers in prior years: cov(ε s,ωht, ln P m,ht 1 ) = 0. To determine the joint strength of my instruments, I run the following first-stage regression on 7,316,491 observations for which I can construct both instruments: ln p s,ωht = 0.38 (0.0010) ln P m,ht (0.0008) ln t s,ωht + δ ωht + ε s,ωht. In the above regression δ ωht denotes firm-product-year fixed effects; robust standard errors are reported in parenthesis; and the R 2 is Importantly, the first-stage regression delivers the expected coefficient signs, and displays an F-statistic on the excluded instruments with a p-value well below 1% The equation expressed above, describes the first stage of the benchmark 2SLS estimation. Later, to conduct sensitivity analysis, I construct additional instruments that exploit auxiliary variations in the data. 23

24 3.4 Estimation Results The benchmark estimation results are displayed in Table 6. For comparison, the table also reports ordinary least square (OLS) estimates of the transport cost elasticity, which maybe upward biased due to the simultaneity between τ and p. Encouragingly, the two-stage least square (2SLS) estimator delivers lower estimates of β than the OLS estimator, which indicates that the IV approach is correcting the bias inflicted by the simultaneity problem. As expected, the corrective power of the IV approach is considerably less in the case of the less-detailed and highly aggregated US data. In summary, my preferred estimate for the transport cost elasticity is β = 0.84, which though higher than traditional estimates, rejects the exact iceberg (β = 1) specification. The estimation results also confirm the prevalence of scale effects in transportation, whereby a 10% increase in shipment scale reduces the unit shipping cost by 1.3% across various various specifications. 18 To put my estimates in perspective, I also estimate β using the traditional approach of regressing τ = τ/wgt on p = p/wgt. As noted earlier, this widely-used approach delivers attenuated estimates of β due to an omitted variable bias. The results arising from the traditional approach are reported in Table 7 and, as projected, point to a systematically lower elasticity, β 0.4. To dig deeper, the difference between the traditional estimation and the benchmark estimation is that the latter accounts for the role of product weight in transportation. Following Equation 6, the transport cost elasticity, β d ln τ d ln p, is composed of a weight-driven component, α, and a value-driven component, β (1 α). Noting that β The estimation conducted on the US sample (which exploits across country variations) confirms two well-established results: (i) Distance matters. A 10% increase in geographical distance to the US increases the transport cost by more than 2.4%, and (ii) High-income countries face systematically lower transport costs. Specifically, high-income countries are significantly more efficient in transportation, and face lower costs despite paying higher wages. 24

25 Table 6: Benchmark Estimation Dependent Variable: (log) Unit Transport Cost Variables (in logs) Unit Price Shipment Scale Distance GDP per capita within-r 2 Observations Colombia sample (firm-product-year FE) OLS ,316,491 (0.000) (0.000) 2SLS ,316,491 (0.002) (0.000) US sample (product-year-district FE) OLS ,341,703 (0.000) (0.000) (0.002) (0.001) 2SLS ,341,703 (0.001) (0.001) (0.002) (0.001) Note: The estimating equation is Equation 5. All 2SLS estimates pass the over-identifying restrictions test and have low first-stage F-statistic p-values. All regressions cluster errors (reported in parentheses) by HS10 product. All reported coefficient are significant at the 1% level. and α 0.75, we can decompose the transport cost elasticity as 19 β d ln τ d ln p 0.4(1 0.75) }{{} value-driven + }{{} 0.75 = 0.85 weight-driven The above decomposition indicates that more than 80% of the relationship between the unit transport cost and unit price is driven by the withincategory variation in unit weights. Industry-Level Estimates. In the second step of my analysis, I estimate an industry-level transport cost elasticity for 33 industries using the GTAP industry classification. The industry-level estimation involves estimating Equation 5 independently for each of the 33 industries in the Colombia sample, with results reported in Table 8. Overall, the estimated transport cost elasticities display a considerable amount of cross-industry variation. Most industries feature an elasticity greater than one-half (i.e., β > 0.5), 19 Alternatively, we can use the estimated β and β to cross-check the estimated weightprice elasticity, α, from the previous section. Doing so, the estimated β 0.84 and β 0.4 imply an α 0.75, which is consistent with direct estimates in Section