The Composition of Exports and Gravity∗ Scott French† February, 2011 Version 1.1

Abstract Gravity estimations using aggregate bilateral trade data implicitly assume that there are no systematic patterns of comparative advantage across products and countries. However, such patterns are clearly present in the product-level trade data. For instance, low-income counties’ product-level exports are highly correlated and concentrated in a small set of products. As a result, estimating trade costs in a gravity framework using aggregate data can lead to biased estimates and incorrect predictions. In this paper, I show that bilateral trade cost parameters are not identified by aggregate bilateral trade data if systematic patterns of comparative advantage exist. I then use detailed product-level bilateral trade to estimate bilateral trade costs, using an iterative procedure to account for unobserved product-level output. This results in trade cost estimates of about half the magnitude of those typically estimated from aggregate data and accounts for much of the correlation between countries’ income level and trade share of output while reducing the erroneous negative correlation between income level and tradable goods price level predicted by aggregate gravity models. The model also predicts that a given trade barrier is more harmful to low-income countries whose exports are concentrated in a few products. ∗ I am thankful to Dean Corbae for his guidance and support. I am also thankful for advice and comments from Kim Ruhl, Jason Abrevaya, and Kripa Freitas as well as seminar participants at the University of New South Wales. † School of Economics, University of New South Wales. [email protected]

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1

Introduction

Empirical gravity models typically estimate the parameters of a trade cost function using data on aggregate bilateral trade flows and country-level measures of total output or value added. Given that the structure used in the estimation is consistent with trade theory, this practice implicitly assumes that the world is a one-sector economy and that no systematic patterns of comparative advantage exist across countries in the production of the products that make up this sector. However, a look at the product-level trade data reveals that, for instance, a country’s per capita income level is strongly associated with the set of products it exports relatively intensively. This implies that trade cost estimates from gravity estimations using only aggregate data are potentially biased, and further, that the counterfactual predictions and policy implications of general equilibrium models based on such estimates may be misleading. In this paper, I develop a gravity model that has the flexibility to take into account product-level patterns of comparative advantage and show that only under very special circumstances, which are inconsistent with the available data, are bilateral trade costs properly identified by aggregate variables alone. I estimate this model using highly disaggregated product-level trade data and find that estimations that ignore product-level production differences across countries significantly overestimate bilateral trade costs. I also find that product-level gravity specification can go quite far in accounting for two stylized facts that have received recent attention in the literature: 1) that the fraction of country’s output that is trade is positively correlated with per capita income and 2) that the correlation between per capita income and the domestic price of tradable goods is small and negative. The gravity model was historically an atheoretic relationship exploited in empirical studies purely because of its apparent success at fitting the data. Due to Anderson (1979) and subsequent work, however, it is now well-known that a wide variety of trade models give rise to a “gravity” relationship between importer and exporter economic size and the volume of trade flows between the two. The theory also has made clear that most empirical exercises were misspecified – neglecting to properly account for effect of resistance to trade with the rest of the world on the size of trade flows between a pair of countries – and could lead to large errors in the estimates of barriers to trade. While this has been largely corrected in recent studies, a similar failure to take into account the composition of countries’ output and trade flows could lead to a similar bias in estimates. If products within a narrowly

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defined category are more substitutable than products across different categories, then two countries whose production is concentrated in the same product categories will not trade as much, and the volume of their trade flows will be more sensitive to trade barriers. In addition, the composition of all other countries’ output will affect trade between a given pair of countries. For instance, if the types of products in which an exporter’s output is concentrated are also produced in large quantities by third country that is in much closer proximity to a given importer, then the pair of countries will trade relatively little. So, it is potentially quite important to take into account the inward and outward resistance effects brought to light by Anderson and van Wincoop (2003) at the product level in order to prevent confounding the effects of the interactions among the distributions of countries’ output and those of bilateral trade barriers. In the next section, I develop a simple multi-country, multi-product trade model in which exogenous levels of production for each country can differ across a potentially large number of products. A CES demand structure and proportional ad-valorem trade costs ensure that the model delivers a product-level gravity equation that is identical to the one in Anderson and van Wincoop (2003). However, different elasticities of substitution within and across product categories imply that the composition of countries’ output, not just the overall level, plays a role in determining aggregate bilateral trade flows. I show that it is only possible to derive an aggregate gravity equation that can be used to estimate trade costs in the extreme cases in which either trade is frictionless or the fraction of output made up by each product is identical across all countries. In every other case, each exporter’s outward resistance term varies by importer, as the interaction between the exporter’s product-level outward resistance terms and the importer’s product-level inward resistance terms matter in determining aggregate bilateral trade flows. Since trade costs are typically specified as functions of bilateral relationships, omitting this term leads to biased coefficient estimates. And, since it is a function of product-level variables, an estimation based on aggregate data alone cannot control for it’s omission. In section 3, I use highly disaggregated product-level bilateral trade data from the United Nations’ Comtrade database to show that, in fact, the world is far from the case that would imply a traditional aggregate gravity equation. I also show that the composition of low-income countries’ exports is systematically farther from the world distribution than higher income countries. Furthermore, low-income countries’ exports are concentrated in

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a common set of products that make up a small fraction of world trade flows. Given the results from section 2, this observation implies that a traditional gravity estimation could overestimate the barriers to trade faced by poor countries. In section 4, I present the estimation strategy. For the most part it is a product-level version of the nonlinear least squares estimator of Anderson and van Wincoop (2004), in which, the inward and outward resistance terms are solved for within the estimation routine and then included in a traditional log-linear gravity equation that predicts trade flows as a function of trade costs and levels of output and consumption. However, product-level output or consumption data are not available at a level of disaggregation comparable to the trade flow data, so these values must be imputed. To do this, I employ an iterative procedure that, for a given set of bilateral trade costs, uses aggregate production data and the values of product-level imports and exports to find a set of product-level production values that is consistent with the product-level inward and outward resistance terms, predicted demand, and total world trade flows for each product. Section 5 presents the coefficient estimates of both the product-level estimation and an estimation using only aggregate data (i.e. implicitly assuming that the product-level production shares in each country are constant). The key finding is that estimated trade costs are over 40% lower in the product-level estimation. The intuition for this is that the concentration of low-income countries’ production into a small set of products implies that there is a high degree of resistance among them and that they will also trade little with high-income countries if they are not their nearest neighbor. However, the only way for the aggregate model to predict the low amount of trade of poor countries is to estimate high border costs and magnify the effect of distance. Two major implications of this are that a) the product-level model predicts the positive correlation between per capita income and the share of countries’ output that is traded – a topic that has received considerable attention recently – and b) it attenuates the negative relationship between per capita income and the prices of tradable goods that the aggregate model counterfactually predicts. This paper is related to several strands of the trade literature. First, it adds to previous attempts to use theory to inform the empirical implementation of gravity models, for example Anderson and van Wincoop (2003), Helpman et al. (2008), and Eaton and Kortum (2002). Those papers each provided a theoretical underpinning for an aggregate gravity estimation and could then proceed to use the results in a structural model for welfare analysis

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and counterfactual prediction. This paper takes the theory a step further and motivates a product-level gravity estimation, showing that the predictions of these models, based on coefficients from an aggregate gravity estimation, may be inaccurate. For example, since low-income countries’ exports are concentrated in a small number of products, their exports face a high trade cost elasticity, so a reduction in trade barriers will benefit these countries relatively more than is predicted by these models. Second, it is related to a large number of recent papers that estimate various versions of industry-level gravity equations. These include Costinot and Komunjer (2008) and Chor (2010). The main difference between this work and theirs is that the focus of this paper is modeling and estimating the effects of observed patterns of product-level comparative advantage (at a very low level of aggregation) on aggregate trade flows and the predictions of trade models that rely on trade cost estimates from gravity models, rather than estimating the degree to which various factors explain specialization in certain industries. Finally, it is relevant to recent papers that explore the implications of the observation that poor countries trade a smaller share of their output than rich countries. For instance, Waugh (2009) shows that large asymmetric trade costs faced by low-income countries accounts for this and is consistent with data on the prices of tradeable goods across countries, and shows that removing these barriers could have a very large impact on countries’ relative income levels. The results of this paper suggest that this inferred barrier to exporting is largely the result of the composition of poor countries’ exports, rather than a tangible barrier to exporting which may be easily ameliorated through policy changes. Also, Fieler (2010) shows that an Eaton-Kortum model with non-homothetic preferences and productivity distributions can account for the lack of trade among poor countries. The results of this paper imply a related, but distinct explanation. In this paper, like hers, the lack of trade is related to the specialization of poor countries in a particular set of products. However, in the context of an Eaton-Kortum model, as I show in the appendix, this specialization is equivalent to the existence of deterministic differences in the average productivity level across products within a country, as opposed to different productivity dispersion parameters across products. A key implication of this difference is that the model of this paper does not imply the patterns of price dispersion of Fieler (2010) that, according to Waugh (2009), appear to be at odds with the data.

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2

Model

Anderson and van Wincoop (2003) show that only a few model conditions are necessary for trade flows to follow a gravity relationship. Three sufficient conditions are 1) that consumption and production levels are determined separately from bilateral trade flows, 2) demand for products from all countries is given by identical CES functions in every country, and 3) trade costs are of the “iceberg” form. These conditions are consistent with a wide array of trade models that are common in the literature. The following is a simple model that adheres to these conditions and has the flexibility to incorporate systematic patterns of product-level comparative advantage. It is also, conveniently, consistent with slightly generalized versions of many well-known general equilibrium models that predict aggregate gravity relationships, such as Eaton and Kortum (2002) and Chaney (2008).1

2.1

Environment

Consider a world made up of N countries, n = 1, 2, ..., N , that each produce and consume varieties of J products, j = 1, 2, ..., J. A country, i, produces (or is endowed with) a nominal value of good j given by Yij , and a country, n, demands a nominal value of the varieties of good j produced by country i given by the following 2-stage demand function: j Xni

pjni

=

!−θ

Pnj

Xnj ,

(1)

where θ − 1 > 0 is the elasticity of substitution across varieties of a product, pjni is the local price (or price index) that consumers in country n pay for a unit of product j that comes from country i, and Pnj is the consumer price index for all varieties of product j in country n, given by !− 1 Pnj =

X j (pni )−θ

θ

.

(2)

i

Xnj is the expenditure by country n on product j, given by !−σ Pnj j Xn = Yn , Pn 1

(3)

The appendix shows how an Eaton-Kortum model with deterministic product-level productivity differences implies this setup.

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where σ − 1 ∈ (0, θ − 1) is the elasticity of substitution across product categories, and Pn is the aggregate consumer price index in country n:  − 1 σ X j −σ   . Pn = (Pn )

(4)

j

Finally, bilateral trade costs take the “iceberg” form, meaning that dni > 1 units of a product must be shipped from country i in order for one unit to arrive in country n, with dii assumed equal to 1. As a result, pjni = dni pji , where pji is the price of a unit of product j produced and consumed in country i.2

2.2

Gravity

Using the market clearing condition that total production by country i in product category P j j is equal to total sales (Yij = n Xni ), it is straightforward to solve for the set of productj level prices, pji . Substituting the equilibrium prices into (36), it can be shown that Xni is

given by j Xni

Xnj Yij = Yj

where (Πji )−θ

dni

(5)

Pnj Πji

X  dni −θ Xnj = Yj Pnj n

and (Pnj )−θ

!−θ

=

X

dni

i

Πji

!−θ

Yij Yj

(6)

(7)

and Y j is total world expenditure on products in category j.3

2.3

Aggregate Trade Flows

Thus the model predicts a gravity relationship at the product level. However, aggregating over all product categories shows that this economy does not imply the standard gravity relationship at the aggregate level. Instead total spending by country n on all products from country i can be expressed as Xni

Yn Yi = Y



2

dni ˜ ni Pn Π

−θ (8)

This is assuming that the price net of trade costs is the same in all countries, which is consistent both the perfect competition and monopolistic competition market structures most often assumed in structural gravity models. 3 j Pn is also the same value as that defined in (2).

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where Pn is as given in (4), and 

1 ˜ Πni

−θ =

X Y j /Y j i

j

Yi /Y

1

!−θ

Πji

Pnj Pn

!θ−σ (9)

˜ ni , the The key departure from a conventional, aggregate gravity equation is that Π outward resistance term, varies by importing country. Since variation in levels of production across product categories leads to variation and product-level price indexes, expenditure in each country is shifted toward product categories with lower prices. And, the fact that varieties within a product category are more substitutable than those across categories implies that it is easier for an exporter to sell its products to a given importer if the other exporters nearby intensively produce products other than those which the exporter does. As a result, aggregate trade flows are not simply a function of overall levels of production, consumption, and trade costs. Rather, it also depends on the composition of an exporter’s production in relation to the entire set of prices – and, by extension, the production profiles of every country – across all product categories for each importer. ˜ ni is an index of the product level outward resistance terms for an More formally, Π exporter, weighted by the level of concentration of its production in each product,

Yij /Y j Yi /Y ,

and the product level prices in the importing country. Since θ > σ, a given exporter will have a lower level of outward resistance to an importer if it has lower product level outward resistance and concentrated production in the product categories in which the importer has the highest prices. To understand how the composition of a country’s output and bilateral trade costs affect its aggregate outward resistance term and, in turn, its aggregate trade flows, it is helpful to examine two special cases in which aggregate trade flows can be expressed as a function solely of aggregate variables. First, consider the case of frictionless trade. In this case, the point of origin has no impact on the price of a good because it can reach any destination costlessly. As a result, relative expenditure on each variety is identical in every country, and the revenue an exporter receives from every country for a particular product is proportional to each country’s total expenditures. So, only the overall economic size of each country matters in determining aggregate bilateral trade flows. Theorem 2.1. Suppose dni = 1, ∀n, i. Then, Xni is a function only of aggregate variables. Next, consider the case in which each country’s output is distributed identically across all product categories. In this case countries differ only in the level of aggregate output and 8

the bilateral trade costs they face. As lemma (2.2), below, shows, countries’ product level inward and outward resistance terms are separable into a component related to the relative world production of the product and aggregate country specific resistance terms that are independent of the country’s trading parter. In addition, as with the frictionless trade case, a constant fraction of expenditure is devoted to each product category in every country. Lemma 2.2. Suppose 1. Pnj = (αj )

Yij Yi

=

Yj Y

≡ αj , ∀j. Then, the following relationships also hold:

−1 σ Pn , ∀n, j 1

2. Πji = (αj ) σ Πi , ∀i, j 3.

Xnj Xn

= αj

The intuition for this result is straightforward. Since each country produces an each product in equal proportion, relative prices are the same in every country. While, the presence of bilateral trade costs raises the price of a given imported good relative to one produced domestically, it does not alter relative prices across product categories because the exporter with which a given importer has high bilateral trade costs produces varieties of each product in the same proportion as every other country (including itself). This result leads to the finding of theorem (2.3): Theorem 2.3. Suppose

Yij Yi

=

Yj Y

≡ αj , ∀j. Then, Xni is a function only of aggregate

variables. However, when trade barriers and patterns of product-level comparative advantage exist, aggregate trade flows are not independent of product level variables and estimations based only on aggregate variables will lead to biased estimates. But, which case is most relevant in the data? In the following section, I discuss some evidence that the latter case is more consistent with the product level trade data.

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Data

To evaluate the degree to which the composition of countries’ output adheres to the assumption of theorem (2.3) – that each country’s relative production in a particular product category is equal to world relative production – I turn to product-level bilateral trade flow

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data from the United Nations’ Comtrade database. Data are available for 4,612 6-digit Harmonized System manufacturing product codes4 for over 200 countries. It turns out not only that the composition of most countries’ output appears to be quite different from the world distribution but also that this composition varies systematically with income per worker. While the assumption of theorem (2.3) is concerned with the composition of countries’ output, rather than exports, I proceed using data on exports for two reasons. First, under the hypothesis that all countries’ relative output in each product category is constant, their relative exports in each category are constant as well, so evaluating whether the composition of exports fits such a pattern is a valid test of whether the composition of output does. Second, even in countries that report disaggregated production data (which is a much smaller sample than those that report disaggregated trade data), the level of disaggregation is not nearly as great as in the trade data, so the trade data provide a much more detailed picture of what products are being produced most intensively by countries. To begin, I calculate the fraction of a country’s exports that fall in each product category: P j Exji n6=i Xni =P Exi n6=i Xni

(10)

I, then, measure the degree to which each country’s export profile differs from that for the world as a whole:

P Exji Exj = Pi Ex i Exi

(11)

I do this by calculating the following export composition deviation index:5 j

ECDi =

i X ( Ex Exi −

Exj 2 Ex )

Exj Ex

j

(12)

This index is equal to zero if the assumption of theorem (2.3) holds exactly and is increasing in the average degree of deviation of a country’s export composition from that of the world as a whole. This calculation leads to two major observations: 1. The average country’s level of deviation from the world product-level distribution of trade is large. 4

The analysis here is restricted to manufactured products in order to ameliorate the effects of natural resource endowments. A Harmonized System product code is taken to be composed of manufactured products if it corresponds to ISIC industries 16-37, according to the United Nations’ concordance. 5 This index is identical to the test statistic of a Pearson’s chi-squared test for the fit of a distribution. However, since I’ve made no assumptions as to the nature of the distribution of world trade flows over product categories, it is not possible to formally test whether the country-level distributions are identically distributed.

10

0

2

Log ED Index 4

6

8

Figure 1: Export Deviation Index by Income Level

4

6

8 10 Log GDP per Worker (US Dollars)

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2. The level of deviation is strongly negatively correlated with income per worker. The average value of ECDi is 300, and the median is 61.8. By comparison, if the value of

Exji Exi

for a given country differed from

Exj Ex

by exactly 100% for each product category,6

then ECDi would be equal to 1.17. This indicates that the distribution of output and exports over the set of product categories for the typical country is very different from that of the world as a whole. While this is not a surprising result given that the benefits to specialization and trade have been widely studied since the dawn of economic thought, it does indicate that gravity estimations that utilize only aggregate data (or even industry level data) can be severely misspecified. Figure 1 further illustrates that the degree to which a country’s export composition differs from that of the world is systematically related to the country’s level of development. The figure plots the log of ECDi against the log of PPP GDP per worker. It is clear that low-income countries’ exports deviate much more widely from the world distribution that do the exports of high-income countries. One might be concerned that the exports of countries with higher total output levels (which is correlated with GDP per worker) would be distributed more like that of the world distribution of exports simply because they make 6

j

That is, for half of the categories

Exi Exi

j

is equal to zero, and for the other half,

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Exi Exi

=2∗

Exj Ex

Table 1: Correlation of Export Deviation Index to GDP Components Variable Coeff. GDP / Worker −0.213 Man. Output −0.539 Number of obs: 146 *

s.e. .0626 .0368

Statistically Significant at 1% level

(Coefficient on constant omitted)

up a larger portion of world trade. Table 1 reports the coefficients from a regressoin of the the log of ECDi on the log of total manufacturing output and the log of GDP per worker, showing that, while this relationship is present, even after controlling for the economic size of a country, there is still a strong negative relationship between income level and the deviation of export composition from the world distribution. Looking deeper into which product categories tend to exported more intensively by highand low-income countries reveals two more observations that are relevant to this study: 3. The exports of poorer countries are concentrated in a few, common products. 4. Rich countries’ exports are spread rather evenly across all products, including those intensively exported by poor countries. In order to see these observations, it is first necessary to identify which products tend to be exported more intensively by countries with different income levels. To this end, I use the following measure of the fraction of each country’s exports that fall into each product category relative to the fraction of world exports in that category: RCAji =

Exji /Exi Exj /Ex

(13)

Interestingly, not only is this the exporting counterpart to the relative output measure (

Yij /Yi Y j /Y

˜ ni and is the basis for theorem (2.3), but it ) that is present in the expression for Π

is also exactly equal to the “revealed comparative advantage” index developed in Balassa (1965). I use the ratio of the average value of this measure across the set of high-income countries and the average across the set of low-income countries to rank the set of product categories from those exported relatively intensively by low-income countries to those exported relatively intensively by high-income countries.7 With this ranking in hand, I 7

Low-income countries are defined as those with PPP GDP per worker less than $10,000, and highincome countries are those for which it is greater than $45,000. The remaining countries are classified as middle-income.

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organize the set of products into 20 quantiles that each make up 5% of total world trade8 and show in figure 2 how the exports of rich and poor countries are distributed across these product quantiles. Within each quantile (ordered along the horizontal axis), the line represents the percentage of the median country’s exports that fall into that group. The upper and lower bars represent this figure for the 25th and 75th percentiles, and the “whiskers” represent the maximum and minimum values.9 If the distribution of a country’s exports were exactly equal to that of the world as a whole – as most gravity estimations require – its percentage of trade in each group would be exactly 5%. The degree to which more than 5% of a country’s exports fall in one group of products is the degree to which it’s exports are relatively more concentrated in those products than the average country. As was illustrated using the ECD index above, for the set of rich countries, this is nearly the case. However, the left graph shows that the exports of most poor countries are highly concentrated in the products in the first few groups. This evidence, then, implies that the exports of poor countries are not only concentrated in a small number of products, but the exports of most poor countries are concentrated in the same types of products. The exports of rich countries, on the other hand, are spread very evenly across the entire range of products – relative to the world consumption levels of the products – including those in which poor countries’ exports are concentrated. For the median country in the high-income group, 2.2% of it’s exports fall in the first quantile, and 5.1% fall in the last quantile, while for the median low-income country, 23% of it’s exports fall in first quantile, and 0.1% fall in the last quantile. The reasons for this pattern of comparative advantage that varies systematically with countries’ income levels are beyond the scope of this paper.10 However, the implications for gravity estimation are significant. While a gravity estimation utilizing only aggregate data may not be severely misspecified for high-income countries, this evidence suggests that for samples including low-income countries, coefficient estimates may be significantly biased, and the corresponding predictions of structural gravity models may be misleading. In what follows, I will assess the magnitude of these errors empirically. 8 This grouping strategy is followed for two reasons. First, for expositional purposes, it aggregates out much of the product level noise, so that the overall pattern emerges. Second, using a trade volume based definition of a set of products avoids issues of comparing product categories that may contain very different levels of product variety. Broda and Weinstein (2006) and Armenter and Koren (2008) also discuss the perils of not properly accounting for this dispersion. 9 A very small number of outliers are omitted. 10 French (2009) offers one explanation.

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Figure 2: Percentage of Exports by Product Group

Percent of Country Exports .2 .4 .6 .8 0

0

Percent of Country Exports .2 .4 .6 .8

1

Developed Countries

1

Least Developed Countries

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

excludes outside values

4

excludes outside values

Estimation

Since a bilateral trade cost function is not identified using aggregate trade and output data due to interactions among the distributions of countries’ output across product categories, I will estimate a the coefficients of a parameterized function of trade costs using the highly disaggregated product-level trade flow data described above. The estimation strategy is, in essence, a product level version of the nonlinear least squares strategy employed by Anderson and van Wincoop (2003). The key difference is that, while aggregate output data, which is necessary for this strategy, is readily available for many countries, it does not exist at a level of disaggregation comparable to the trade data for any countries.11 As a result, it must be imputed using a combination of the available aggregate data and theory. In this section, I detail this procedure and then compare the results with an estimation in which the assumption of theorem (2.3) is assumed to hold, so that only the use of aggregate trade flow data is necessary. To proceed with this strategy, I parameterize bilateral trade costs in the following, relatively standard, way: ( 0 ln(dni ) = P

k k k (αd Ini )

b + α Il + α Ic + αb Ini c ni l ni

if n = i otherwise

(14)

k (k = 1, ..., 6) is an indicator that the distance between countries n and i lies in where Ini b that n and i share a border, I l that they share a common the kth distance interval,12 Ini ni 11 Output data at the industry level does exist and has the potential to improve the quality of the coefficient estimates below. However, concording this data with the trade data can be perilous. For example, using data from the United Nations’ INDSTAT database and the UN’s ISIC-HS concordance, I found that in 1/3 of country-industry pairs, exports exceeded output. 12 The six distance intervals are (in kilometers) [0, 625), [625, 1,250), [1,250, 2500), [2,500, 5,000), [5,000,

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c that they share a colonial relationship. language, and Ini

In its log linear form, (37) then becomes ! j X X j j j k b l c ni = ln(X ) + ln(Y ) − θ (αdk Ini ) − θαb Ini − θαl Ini − θαc Ini ln(zni ) = ln n i Yj

(15)

k

+ θ ln(Pnj ) + θ ln(Πji ) + εjni where the appended error term can be thought of as reflecting measurement error. The values of Pnj and Πji cannot be obtained directly from data and must be solved for as implicit functions of trade costs and product level production and expenditure levels. Since the data on production or expenditure are not available at a level of disaggregation comparable to the trade data, they must also be solved for as implicit functions of trade costs and the available production and trade flow data. Given a set of trade cost parameters, α, I follow the following procedure: j ˆ nn 1. Set initial values for X for all n and j.

P P j j j j ˆ nn ˆ nj = X ˆ nn + i6=n Xni . + n6=i Xni and X 2. Compute Yˆij = X ˆ j up to a normalization for each product category. 3. Solve for Pˆnj and Π i ˆ j by factor P¯ j that equates predicted and actual total world trade 4. Scale Pˆnj and Π i flows for product j. 5. Update

j ˆ nn X Xnn

to be the model’s predicted value.

ˆ j, X ˆ nj , and Yˆ j are constant within the system. 6. Iterate steps 2 - 5 until all Pˆnj , Π i i 7. Compute dˆni = αIni 8. Compute

hjni

=

ˆ nj Yˆ j X i Yˆ j



dˆni ˆj Pˆnj Π i

−θ

Substituting the implicit solutions of Pnj , Πji , Xnj , and Yij into (15), the stochastic loglinear gravity equation becomes ln(z) = h(I, x; α) + ε

(16)

where I is the set of bilateral gravity relationship indicators and x contains the total imports and exports of each country in each product category and the value of Xnn for all n. I estimate (16) with nonlinear least squares. 10,000), [10,000, max].

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Table 2: Nonlinear Least Squares Estimates Aggregate Variable Coeff. s.e. Dist. 10,000 −8.63 0.12 Border 0.10 0.05 Language 0.96 0.03 Colony 5.49 0.02

Product Level Coeff. s.e. −2.74 0.04 −3.52 0.03 −4.09 0.03 −4.70 0.04 −5.46 0.03 −5.74 0.04 0.98 0.04 0.86 0.04 0.74 0.03

Number of obs: 14,691 (Aggregate Estimation); 4,174,460 (Product Level Estimation) All coefficients significant at 1% level.

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Results

Table 2 reports the trade cost parameter estimates from the product level gravity estimation and the restricted estimation that utilizes only aggregate data – that is the gravity estimation of Anderson and van Wincoop (2003). The most notable difference between the two sets of coefficients is that those from the product level estimation imply much lower overall trade barriers, and the barriers are increasing at a somewhat slower rate with increasing distance. Taking the value of θ estimated in Waugh (2009) of 5.5, the product level estimates imply an average ad-valorem equivalent trade barrier (for countries lying between 1,250 and 2,500 kilometers apart) of 110% compared to 195% from the aggregate gravity estimation. This indicates that there is, in fact, a substantial level of bias introduced into trade cost estimates due to omitting the effect of the interaction of distributions of product level efficiency among countries. The second key result is that taking into account the correlation of product level efficiency among countries reduces the counterfactual prediction of gravity models that poor countries trade a much larger fraction of their output than rich countries. Figure 3 illustrates this point. It plots the predicted percentage of each country’s consumption of manufactured goods that is produced by the country against the log of each country’s GDP per worker. For comparison the best-fit lines from the same measures in the data and the predicted values from the aggregate gravity estimation are included. While the estimates from the product level gravity equation still predict a positive relationship between the two

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Figure 3: Predicted Home Share of Expenditure Predicted Values

Percentage of Expenditure on Domestic Goods

1 0.9 Agg. Gravity Best Fit

0.8 0.7 0.6

Data Best Fit

0.5 0.4 0.3 0.2 0.1 0

5

6

7

8 9 Log GDP per Worker

10

11

12

(regression slope = 0.0593) variables, the magnitude of the relationship is greatly reduced. The slope of the regression line is 30% lower than that of the aggregate gravity estimation. In addition, table 3 shows that, controlling for the level of output of countries, the product level gravity model explains 68% of the observed correlation between GDP per worker and the home share of manufacturing consumption. The estimates from the product level gravity equation also improve the ability of the model to predict another important relationship in the data. Waugh (2009) shows that there is little relationship between the average price of tradeable goods and a country’s

Table 3: Correlation of Home Expenditure Share to GDP Components Data Variable Coeff. s.e. ∗ GDP / Worker −0.1879 0.0506 Man. Output 0.1823∗ 0.0298 Number of obs: 146 *

Agg. Grav. Coeff. s.e. −0.0477 0.0866 0.5054∗ 0.0509

Statistically Significant at 1% level

(Coefficient on constant omitted)

17

P.L. Grav. Coeff. s.e. ∗ −0.1288 0.0387 0.3822∗ 0.0228

income level in the data, but gravity models predict a strong negative correlation. Figure 4 shows that the product level gravity model predicts a much weaker relationship between a country’s level of income and its aggregate price level and is in line with the magnitude predicted by the model of asymmetric exporter specific trade costs of Waugh (2009). The intuition for this result is similar to that for the other results discussed. Since aggregate gravity models lack the mechanism by the concentration of low-income countries’ exports leads to less trade as a fraction of output by these countries, so this is accounted for by high estimated trade costs. And, the higher are overall barriers to trade, the higher are prices in countries whose output per worker is low. However, once the missing mechanism is accounted for, and estimated trade barriers are lower, the predicted price level for these countries is much lower because a) the prices of products that they (and much of the world) produce intensive are very low, especially because is little demand for them abroad, and b) lower estimated trade barriers imply that it is less costly to import the products that they do not produce intensively.

Figure 4: Predicted Price Level 2 Agg. Gravity Best Fit

Price Level (Relative to US)

1.75

1.5

1.3

1.15

1

0.87

5

6

7

8 9 Log GDP per Worker

18

10

11

12

6

Conclusion

Controlling for a country’s level of output, poor countries trade a much smaller share of their manufacturing production than do wealthy countries. At the same time, poor countries’ manufacturing exports are concentrated in a small, common range of products. This paper shows that accounting for the latter observation goes quite far in explaining the inability of structural gravity models to explain the former. Intuitively, poor countries consume disproportionately more of their manufactured goods because there is a high level of resistance to trade in the products for which these countries are especially efficient. That is, they have a comparative advantage at producing the same products as many other poor countries. Even moderate barriers to trade, then, lead consumers in these countries to purchase domestic varieties because the differences across countries in the efficiency of labor for producing these products is small. As the model of product level trade can account for the low share of poor countries’ output that is traded, it does not require high trade barriers to predict the small trade flows among these countries. Therefore, it estimates trade barriers that are much lower than those estimated using a model that implies an aggregate gravity equation. In fact, it estimates trade barriers that are much more in line with estimates based on trade flows among only developed countries. One major implication is that the resistance to the exports of low income countries, which is modeled as an exporter specific trade cost in Waugh (2009), may not be a result of trade policy, indicating that the potential welfare gains to poor countries of lowering trade costs could be much smaller than previously thought.

19

A

Proofs

Proof of Theorem (2.3). Conjecture that Πji = Πj , ∀i. Substituting this into equation (39) gives that (Pnj )−θ

 =

1 Πj

−θ X i

Yij Yj

(17)

j θ

= (Π ) . Substituting this this into equation (38) we have that (Πji )−θ = (Πj )−θ

X Xnj n

Yj

,

(18)

and the conjecture is verified. Now, summing equation (3) over n and imposing the market P j clearing condition that Yij = n Xni , this implies that Pj =

Yj P, Y

(19)

where P is the aggregate price level common to all countries. Using equation (37) it is now easy to show that j Xni =

Yn j Y , Y i

(20)

Xni =

Yn Yi . Y

(21)

which implies that

Proof of Lemma (2.2). First, note that it follows immediately that

P

j

αj = 1 and

Next, conjecture that Πji takes the form β j Πi . From equation (39) we know that !−θ X dni Yij j −θ (Pn ) = Yj Πji i X  dni −θ Yi j θ = (β ) Πi Y

Yij Yj

=

Yi Y .

(22)

i

≡ (β ) P˜n−θ j θ

which implies that Pnj = (β j )−1 P˜n .

(23)

Now, substituting into equation (4), (Pn )−σ =

X

(β j )−1 P˜n

−σ

j

= (P˜n )−σ

X j

20

(β j )σ

(24)

which, along with equation (3) implies that (β j )σ Xnj = P j σ Yn . j (β )

(25)

Summing over n and using the market clearing condition that Yij =

j n Xni ,

P

this implies

that (β j )σ Y j = P j σ Y. j (β )

(26) 1

And, since Y j = αj Y by assumption, it must be the case that β j = (αj ) σ , and, therefore P j σ j (β ) = 1 and P˜n = Pn .

(27)

Finally, substituting the values for Pnj and Xnj into equation (38), we have that (Πji )−θ

= (α

j

−θ )σ

= (αj )

X  dni −θ Yn Pn Y n (28)

−θ σ Π−θ i

= (β j Πi )−θ which verifies the conjecture above. Proof of Theorem (2.3). Applying the results of Lemma (2.2) to equation (9) implies that 

1 ˜ Πni

−θ =

1

X j

 =  =

1 Πi 1 Πi

!−θ

Πji −θ X

Pnj Pn

!θ−σ

(29)

αj

j

−θ .

Substituting into (8) gives that Xni

Yn Yi = Y



dni P n Πi

−θ ,

(30)

where Pn and Πi , defined by equations (22), (27), and (28), are implicit functions of aggregate variables.

21

B

Product Level Gravity in an Eaton-Kortum Model

B.1

Production

There are constant returns to scale in the production of each product. Following the standard Ricardian framework, the factors of production are perfectly mobile across products but immobile across countries. Labor is the only factor of production, and workers in each country are paid a country specific wage wi .13 Combined with country i’s level of efficiency at producing product (j, k), denoted zij (k), the cost of producing a unit of product (j, k) in country i is

wi . zij (k)

Barriers to trade take the standard “iceberg” form. Delivering one unit of a product from country i to country n requires shipping dni > 1 units of the products for n 6= i. By assumption, dii = 1. The cost of producing a unit of product (j, k) in country i and delivering it to country n is then pjni (k) =

wi dni zij (k)

.

(31)

Assuming perfect competition,14 this is also equal to the price that consumers in n would pay for product (j, k) if they chose to purchase it from country i. Since consumers are indifferent among the various potential suppliers of a particular product, the price actually paid for product (j, k) in country i is equal to pji (k) = min{pjni (k)} n

B.2

(32)

Technology

The efficiency with which product (j, k) is produced in country i is made up of both a deterministic component common to all products in the same product category and an idiosyncratic, product-specific component that is the realization of a random variable, U . Specifically, zij (k) is given by ln(zij (k)) = ln(zij ) + uji (k).

(33)

If U is distributed Gumbel(0, θ),15 then zij (k) is a draw from a Fr´echet distribution (as in Eaton and Kortum (2002)), but here the shift parameter of the distribution varies across 13 This assumption is for notational simplicity. The analysis that follows easily generalizes to multiple factors of production which may be used in different proportions for different products. For example, see Costinot and Komunjer (2008). 14 This assumption is for expositional simplicity. It can be shown that all of the results that follow are identical under both Bertrand competition (as in French (2009)) and monopolistic competition with constant markups. −θu+γ 15 That is, F (u) = e−e , where γ ' 0.5772 is Euler’s constant.

22

product categories (as in Costinot and Komunjer (2008) and French (2009)). Following the analysis of Eaton and Kortum (2002), it can be shown that the probability that country n buys product (j, k) from country i is (z j )θ (wi dni )−θ j j πni (k) = πni =P i j θ −θ i (zi ) (wi dni )

(34)

Since this expression is independent of the identity of the product (k) within product catej gory j, πni is also the expected fraction of products in j that country n buys from country

i. Further, since the distribution of prices in country n for each product in category j is independent of the country from which the product actually originates – due to a convenient j property of the Gumbel distribution – two key results obtain: (a) πni also represents the

expected fraction of country n’s total expenditure on products in j from country i, and (b) the expected price index for product category j is ! −1 Pnj = ξ

X

(zij )θ (wi dni )−θ

θ

(35)

i

where ξ is a function of constants. It must be the case that θ + 1 > σ for Pnj to be well-defined, and this condition will be assumed henceforth. Combining, (34) and (35) with (2), country n’s total expenditure on products in category j from country i is j Xni

B.3

=ξ

(zij )θ (wi dni )−θ (Pnj )−θ

Pnj Pn

!1−σ Xn

(36)

Product Level Gravity

Using the market clearing condition that total production by country i in product category P j j is equal to total sales (Yij = n Xni ), it is easy to verify that (36) can be rewritten in the following form: j Xni

where Πji

Xnj Yij = Yj

dni

!−θ (37)

Pnj Πji

X  dni −θ Xnj = Yj Pnj n

and Pnj =

X

dni

i

Πji

23

!−θ

Yij Yj

(38)

(39)

and Y j is total world expenditure on products in category j.16 16

Pnj is also the same value as that defined in (2) and (35) above, and Πji =

24

j

Yi /Y j j

ξ(zi )θ (wi dni )−θ

.

References Anderson, James E., “A Theoretical Foundation for the Gravity Equation,” The American Economic Review, 1979, 69 (1), 106–116. and Eric van Wincoop, “Gravity with Gravitas: A Solution to the Border Puzzle,” The American Economic Review, 2003, 93 (1), 170–192. and

, “Trade Costs,” Journal of Economic Literature, 2004, 42 (3), 691–751.

Armenter, Roc and Miklos Koren, “A Balls-in-Bins Model of Trade,” 2008, Working Paper. Balassa, Bela, “Trade Liberalization and ’Revealed’ Comparative Advantage,” The Manchester School of Economic and Social Studies, 1965, 33, 99–123. Broda, Christian and David E. Weinstein, “Globalization and the Gains from Variety*,” Quarterly Journal of Economics, 2006, 121 (2), 541–585. Chaney, Thomas, “Distorted Gravity: the Intensive and Extensive Margins of International Trade,” American Economic Review, 2008, 98 (4), 1707–1721. Chor, Davin, “Unpacking Sources of Comparative Advantage: A Quantitative Approach,” Journal of International Economics, 2010, 82 (2), 152–167. Costinot, Arnaud and Ivana Komunjer, “What Goods do Countries Trade?: A Structural Ricardian Model,” 2008, Working Paper. Eaton, Jonathan and Samuel Kortum, “Technology, Geography, and Trade,” Econometrica, 2002, 70 (5), 1741–1779. Fieler, Anna C., “Nonhomotheticity and Bilateral Trade: Evidence and a Quantitative Explanation,” 2010, Working Paper. French, Scott, “Innovation and Product Level Trade,” 2009, Working Paper. Helpman, Elhanan, Marc Melitz, and Yona Rubinstein, “Estimating Trade Flows: Trading Partners and Trading Volumes*,” Quarterly Journal of Economics, 2008, 123 (2), 441–487.

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Waugh, Michael E., “International Trade and Income Differences,” Federal Reserve Bank of Minneapolis, 2009, Reserach Department Staff Report 435.

26