Trade with Correlation∗ Nelson Lind Natalia Ramondo Emory University

UCSD and NBER

November 28, 2017

Abstract We develop a theory of trade that allows for arbitrary patterns of correlation in technology between countries. Our framework captures a key insight of Ricardo that is absent in the canonical Ricardian trade model—a country gains the most from trading with those countries that are technologically dissimilar. We show that calculating the gains from trade in the presence of heterogenous correlation entails a simple correction to the gains associated with CES demand systems. The theory also relates macro substitutability patterns to underlying micro-structures, and our aggregation results provide guidance on incorporating micro estimates into macro counterfactual exercises. We apply our framework to a multi-sector model of trade, and estimate that countries specialized in sectors with low cross-country correlation have 40 percent higher gains from trade relative to countries specialized in high correlation sectors. JEL Codes: F1. Key Words: international trade; generalized extreme value; Fréchet distribution; gains from trade; gravity. ∗

TBA.

1

Introduction

Two hundred years ago, David Ricardo (1818) put forward the idea that cross-country differences in production technologies can lead to gains from trade. Ricardo’s work, which extended Adam Smith (1776)’s idea on comparative advantage to international trade, had two basic insights. First, if two countries have production possibility frontiers with different slopes (i.e., the ratio of productivity across sectors), then there is scope for engaging in mutually profitable trade. Second, the gains are higher when trade occurs between more dissimilar partners. Eaton and Kortum (2002, henceforth, EK) capture the first insight of Ricardo’s idea by treating technologies as random variables, giving rise to a rich theoretical and quantitative literature. Their results are based on a useful property of Fréchet distributions: The maximum of Fréchet-distributed random variables is also Fréchet, 

P[max{Z1 , . . . , ZN } ≤ z] = exp −

X

Ti z

−θ



.

i

Under independence with a common shape parameter of θ, the location of the maximum is the sum of the underlying location parameters, Ti . This symmetry across countries gives tractability to the EK model of trade, but imposes that all trading partners are indistinguishable in generating gains from trade. As a result, the EK model of trade does not capture the second aspect of the old Ricardian idea—which may be important to understand why countries choose certain trading partners and not others.1 In this paper, we develop a theory of trade that allows for arbitrary patterns of correlation in technology between countries. Relaxing the independence assumption implies that the distribution of the maximum of Fréchet random variables is   P[max{Z1 , . . . , ZN } ≤ z] = exp − G(T1 , . . . , TN )z −θ , for some correlation function G. Countries can now have different weight on the location of the maximum due to the correlation structure of technology across countries. In this way, our main theoretical result generalizes EK—while maintaining its tractability— and captures the second aspect of the Ricardian idea. In turn, this result represents a 1

Costinot et al. (2015) analyze the relation between the patterns of comparative advantage and optimal trade taxes schemes. They perform the analysis using the canonical Ricardian model of trade, but notice that their analysis carries to more general environments with non-CES utility and arbitrary neoclassical production functions.

1

generalization of the results of Arkolakis et al. (2012) (henceforth, ACR). Our quantitative application to a multi-sector model of trade shows that even a small departure from symmetry produces large changes in the gains from trade. We start by relating the technology structure of countries to a Fréchet process for productivity with an unrestricted correlation structure. Our key innovation is that, for each good, there is an (unbounded) collection of production technologies available. Each technology has a global productivity component and a bilateral-specific applicability component. The former component is common to all countries and captures the fundamental efficiency of the technology. The later component is unique to each country pair and captures idiosyncratic factors—such as trade frictions, domestic inefficiencies, and country endowments—that lead to differences in productivity. While for each good the global component follows a Poisson process, the applicability component is correlated across countries and i.i.d. across goods and technologies. We apply the spectral representation theorem for max-stable processes (De Haan, 1984; Penrose, 1992; Schlather, 2002) and establish that this structure for technology is necessary and sufficient for productivity to follow a Fréchet process.2 The effective productivity that a given origin presents to a given destination country is distributed Fréchet across the continuum of goods, while dependence across countries is unrestricted. Even with this generalization, we can calculate the gains from trade as a simple adjustment to the case of a CES demand system. In this way, we show that the results of ACR generalize, after a simple correction, to the class of models whose demand systems fit into the generalized extreme value (GEV) form, as in McFadden (1978). In the Ricardian context, this correction adjusts a country’s self-trade share to account for correlation in technology with the rest of the world and formalizes Ricardo’s insight that more dissimilar countries have higher gains from trade. Moreover, for any given pattern of correlation across countries, the adjusted self-trade share is calculated using only data on expenditure shares across countries, preserving the simplicity of ACR. Perhaps not surprisingly, our general correlation structure also entails a different estimate of the trade elasticity. In fact, our model provides guidance on how to relate the macro substitution patterns implied by the observable trade flows to a given underlying micro-structure. In this way, we get guidance on how to use the micro data to discipline the estimates of macro parameters that capture the aggregate correlation 2

The spectral representation theorem for max-stable processes has previously been used in the decision theory context by Dagsvik (1994) to propose behavioral assumptions that justify max-stable random utility processes.

2

structure. This is possible because our structure is able to accommodate models based on EK that have a richer layer of interactions across countries, such as sectoral models (Costinot et al., 2012; Costinot and Rodrìguez-Clare, 2014; Caliendo and Parro, 2015; Ossa, 2015; Levchenko and Zhang, 2016), multinational production models (Ramondo and Rodríguez-Clare, 2013; Tintelnot, 2017), global value chains models (Antràs et al., 2017), and models of trade with domestic geography (Fajgelbaum and Redding, 2014; Ramondo et al., 2016; Redding, 2016). To quantitatively evaluate the relevance of the correlation adjustment for the gains from trade, we use a multi-sector model of trade, and we assume that the macro correlation function takes a cross-nested CES form. We show that, in this case, key elasticities can be estimated by a simple two-step Ordinary Least Square (OLS) procedure using data on sectoral bilateral trade and bilateral tariffs. This is due to the fact that, after some adjustments, gravity holds at the sector level. It is worth noting that multi-sector extensions of the EK model of trade (e.g., Caliendo and Parro, 2015; Ossa, 2015) assume that the shape parameter θ is sector specific. The combination of independence with heterogenous shape parameters implies that the distribution of productivity across traded goods is not Frechet. As a result, these sectoral models do not aggregate to an equivalent macro model with Frechet distributed productivity. Accounting for correlation in productivity can have substantial effects on estimates of the gains from trade—up to 30 percent higher relative to ACR. Crucially, the correlation correction delivers gains from trade that are much more heterogenous across countries with the same self trade share—and within countries across time. We calculate that countries specialized in low correlations sectors have 40 percent higher gains from trade relative to countries specialized in high correlation sectors. This result captures the second aspect of Ricardo’s idea and is a reflection of the ever-evolving pattern of comparative advantage of countries, documented by Hanson et al. (2015). Our benchmark model is based on technology determining the patterns of trade across countries. From this supply-side point of view, substitution patterns come from the degree of technological (dis)similarity—i.e., correlation—between countries. More broadly, comparative advantage may come from demand-side factors as in the Armington model of trade (Anderson, 1979), and from entry of heterogenous firms (Krugman, 1980; Melitz, 2003). We introduce a general framework that encompasses these micro foundations and generates the same class of GEV demand systems as the Ricardian benchmark. These results also make clear which assumptions on economic fundamentals are equivalent to a

3

large and useful class of models that feature an invertible demand system. Our work relates to several strands of the literature. First, we naturally make contact with the large trade literature using the Ricardian-EK framework in its various forms (see Eaton and Kortum, 2012, for a survey). More generally, our approach can be applied to any environment that requires Fréchet tools, with the potential of changing some of their quantitative conclusions. In particular, it can be applied to selection models used in the growth literature (such as Hsieh et al., 2013), and the macro development literature (such as Lagakos and Waugh, 2013), as well as to recent trade models used in the urban literature (such as Ahlfeldt et al., 2015; Monte et al., 2015; Caliendo et al., 2017). Second, we relate to papers in the international trade literature that use non-CES demand systems.3 In particular, a recent paper by Adao et al. (2017) shows how to calculate macro counterfactual exercises in neoclassical trade models with invertible factor demand systems. In our paper, we provide necessary and sufficient conditions for a model’s fundamentals to be distributed Fréchet, and, therefore, to fit into the GEV class—a subclass of models with the invertibility property. Our aggregation results allow us to relate various microstructures to the kind of macro counterfactuals they study. Finally, papers such as Caron et al. (2014), Brooks and Pujolas (2017), Lashkari and Mestieri (2016), and Bas et al. (2017), among others, estimate non-CES demands systems at the micro level. They aim, as we do, at showing the consequences of abandoning the assumptions that lead to linear gravity systems, and at incorporating more detailed micro data (i.e., sectoral trade) to estimate key model’s elasticities. They all notice the failure of aggregate theories to incorporate the richness of the micro data (e.g., heterogeneous price and income elasticities across trade goods), and "fix it" by departing from CES demand systems.4 By linking various possible micro structures to common primitives of technology, our general framework provides guidance on how to incorporate the micro estimates in this literature into macro counterfactual exercises. 3

A related trade literature departs from CES with the goal of analyzing endogenous mark-ups and their effects on the gains from trade. See DeLoecker et al. (2016), Feenstra and Weinstein (2017), Bertoletti et al. (2017), and Arkolakis et al. (2017), among others. 4 Caron et al. (2014) use a constant-relative-elasticity-of-income utility functions to link characteristics of goods in production to their characteristics in preferences, and in this way explain some "puzzles" observed in the data on trade patterns. Lashkari and Mestieri (2016) uses constant-relative-elasticity-of-income-andsubstitution (CREIS) utility functions that allows for general patterns of correlations between income and price elasticity. Brooks and Pujolas (2017) analyze the expression for gains from trade arising from models with unrestricted utility functions (typically non-homothetic) that generate a non-constant trade elasticity. Finally, Bas et al. (2017) break the Pareto assumption in the Melitz model of trade to get country-pair specific aggregate elasticities, which they estimate using sectoral-level trade data.

4

2

Ricardian Model

Consider a global economy consisting of N countries. Countries produce and trade in a continuum of product varieties v ∈ [0, 1]. Consumers in all countries have identical CES preferences with elasticity of substitution σ > 0. Given total expenditure of Xd by destination country d, their expenditure on variety v is Xd (v) = (Pd (v)/Pd )1−σ Xd where σ R  σ−1 σ−1 1 Pd (v) is the cost of the variety in terms of numeraire and Pd = 0 Pd (v) σ dv is the price level in country d. For each variety there exists a collection of constant returns to scale technologies indexed by i = 1, 2, . . . . Each technology produces a single variety and uses labor as input. We assume that the marginal product of labor of the i’th technology can be factored into a global total factor productivity component and a destination-market and origin-country specific component: Yiod (v) = Z¯i (v)Aiod (v)Liod (v)

(1)

Here o denotes the origin country, d the destination country, and Liod (v) is the amount of labor used to produce variety v via the i’th technology. Productivity can be divided into two factors. The global total factor productivity component Z¯i (v) captures the overall productivity of the technology, while the origin-destination specific component Aiod (v) captures the effect of idiosyncratic country-specific factors that influence a origin country’s ability to produce goods and then deliver them to a given destination market. Our key result comes from two assumptions. First, we assume that realizations of the origin-destination component of productivity are iid across technologies and varieties. Assumption 1. For each origin-destination pair (o, d), Aiod (v) is identically and independently distributed across (i, v). Importantly, this assumption does not impose independence across origin-destination pairs. We allow for arbitrary patterns of correlation in productivity across countries. When delivering goods to market d, country o will use the most efficient technology. Define effective productivity as A∗od (v) ≡ max Z¯i (v)Aiod (v). i=1,2,...

(2)

This random variable summarizes the production possibilities for producing goods in country o and delivering them to market d given the globally available technologies for 5

producing variety v. Our second assumption puts structure on the global component of productivity. Assumption 2. For each v ∈ [0, 1], the collection {Z¯i (v)θ }i=1,2,... is a Poisson process with intensity measure g −2 dg that is independent of {{Aiod (v)}N o,d=1 }i=1,2,... . This assumption implies that the global component of productivity is Pareto. Remark 1. Let Assumption 2 hold. Then for any b > a > 0 we have P[a < Z¯i (v) ≤ b] = a−θ − b−θ . In particular, Z¯i (v) has a Pareto tail with parameter θ. One can interpret Assumption 2 as arising from a random discovery process for new technologies as in Eaton and Kortum (1999, 2010). The number of technologies for producing variety v is Poisson and the global component of productivity for the i’th technology is drawn from a Pareto distribution. The key distinction here is that the overall productivity of individual technologies is not country specific — Z¯i (v) is a global outcome. However, the applicability of each individual technology may be country specific. The random variable Aiod (v) captures how countryspecific factors influence the ultimate productivity of technology i. This random variable will determine correlation in productivity across countries, while the global productivity component ensures that the marginal distribution of productivity is Fréchet. Specifically, effective productivity will have Fréchet marginals and an arbitrary correlation structure across origin-destination pairs. Lemma 1. For each origin-destination pair (o, d), effective productivity A∗od (v) is a Fréchet random variable across varieties with shape parameter θ if and only if Assumption 1 and Assumption 2 hold for some global productivity process {Z¯i (v)}i=1,2,... and some origin-destination productivity process {{Aiod (v)}N o,d=1 }i=1,2,... . In this case, the joint distribution of productivity across origin countries when delivering to destination market d is " P[A∗1d (v) ≤ a1 , . . . , A∗N d (v) ≤ aN ] = exp −E max

o=1,...,N



Aiod (v) ao

θ # .

(3)

Proof. See Appendix A. This lemma completely characterizes when productivity can be taken as a Fréchet process across countries. It is useful because it leads to closed form expressions for import 6

price distributions and expenditure shares — just like in Eaton and Kortum (2002) — while also allowing for rich patterns of correlation in productivity across countries. These closed forms are analogous to results for choice specific probabilities in generalized extreme value discrete choice models (McFadden, 1978). Moreover, this characterization establishes primitive assumptions on global technology that are necessary and sufficient for Fréchet distributed productivity. The equivalence result is a consequence of the spectral representation theorem for max-stable processes—see De Haan (1984), Penrose (1992), and Schlather (2002)—and has been previously used in economics by Dagsvik (1994) to propose behavioral assumptions that justify max-stable random utility processes used in decision theory. The marginal distributions are Fréchet because   P[A∗od (v) ≤ ao ] = lim P[A∗1d (v) ≤ x, . . . , A∗od (v) ≤ ao , . . . , A∗N d (v) ≤ x] = exp −EAiod (v)θ a−θ . o x→∞

This lemma will allow us to develop models of trade built on Fréchet distributed productivity in the spirit of Eaton and Kortum (2002) while allowing for arbitrary patterns of correlation in technology across countries. We now proceed to characterize import price distributions and expenditure shares. First, we setup some convenient notation that separates out interpretable components of bilateral productivity. Define origin country o’s productivity index and their iceberg trade costs to country d as Ao ≡ E[Aioo (v)θ ]1/θ

and τod ≡

E[Aioo (v)θ ]1/θ . E[Aiod (v)θ ]1/θ

Ao measure a country’s ability to produce goods in their domestic market, while τod measures efficiency losses associated with delivering goods to market d. Finally, define the idiosyncratic component of productivity as Ziod (v) ≡

Aiod (v) . E[Aiod (v)θ ]1/θ

This quantity is a centered measure of productivity satisfying EZiod (v)θ = 1. This notation maps our setup into standard notation in the trade literature. For instance,

7

we can write the minimum marginal cost to deliver a particular variety to d as Wo τod Wo /Ao M Cod (v) ≡ min ¯ = . i=1,2,... Zi (v)Aiod (v) maxi=1,2,... Z¯i (v)Ziod (v) Marginal cost equals the wage deflated by the marginal product of labor. The second equality re-writes the minimum marginal cost in terms of iceberg trade costs and the unit labor cost of Wo /Ao . The denominator is effective productivity after centering. With perfect competition, potential import prices equal marginal cost Pod (v) = M Cod (v) and the joint distribution of potential import prices follows from Lemma 1. The following proposition summarizes this result. Proposition 1. Let Assumption 1, and Assumption 2 hold. Suppose that markets are perfectly competitive. Then the joint distribution of prices presented to destination market d is 
 P[P1d (v) ≥ p1 , . . . , PN d (v) ≥ pN ] = exp −Gd Φ1d pθ1 , . . . , ΦN d pθN where  Φod ≡

τod Wo Ao

−θ and



d

G (x1 , . . . , xN ) = E

θ



max Ziod (v) xo .

o=1,...,N

Proof. See appendix C. The idiosyncratic component of productivity, {Ziod (v)}N o=1 , determines the joint distribution of potential import prices presented to d. The correlation structure of prices is summarized by the correlation function, Gd , while the marginal price distribution has its location captured by the competitiveness index, Φod . Competitiveness depends on bilateral trade costs, a origin’s overall productivity of Ao , and their wage Wo . The function, Gd , corresponds to the social surplus function in generalized-extreme value (GEV) models (McFadden, 1978). In the trade context, it will relate closely to a country’s price level, and, in analogy to the discrete choice literature, welfare calculations will depend crucially on the specification of the correlation function.5 5

Note that, unlike the discrete choice literature, the central distributional restriction captured in Assumption 2 is on a cardinal rather than an ordinal quantity. Unlike latent utility, productivity is, in principle, a measurable quantity.

8

Given the distribution of potential import prices, a country will import at the lowest possible price for each variety. The previous characterization of the import price distribution leads to the following closed form results — which generalize Eaton and Kortum (2002). Proposition 2. Let Assumption 1, and Assumption 2 hold. Suppose that markets are perfectly competitive. Then: 1. The share of varieties that destination d imports from o is πod =

Φod God d G (Φ1d , . . . , ΦN d )

(4)

where God is the partial derivative of Gd in its o’th argument: God ≡

∂Gd (Φ1d , . . . , ΦN d ) . ∂Φod

2. The distribution of prices among goods imported into country d from o is P[Pod (v) ≥ p | Pod (v) ≤ Po0 d (v)

  ∀o0 6= o] = exp −Gd (Φ1d , . . . , ΦN d ) pθ

3. Total expenditure by country d on goods from country o is (5)

Xod = πod Xd . and the price index in country d is 1

Pd = γGd (Φ1d , . . . , ΦN d )− θ where γ = Γ

θ+1−σ θ

1
1−σ

(6)

and Γ(·) is the gamma function.

Proof. See appendix D The formula for the expenditure share, πod , takes the same form as choice probabilities in GEV discrete choice models. Here, the competitiveness index takes the place of choice specific utility. As a result, this model is observationally equivalent at the aggregate level to any trade model whose implied demand system is in the GEV class. It turns out that many existing trade models imply GEV demand systems—a connection we explore with the examples in Section 3.2.

9

As in EK, the distribution of prices among goods actually imported into market d is identical to the distribution of potential import prices. As a result, we get that expenditures shares are equal to the share of varieties imported into d from o. Finally, the price level in each destination market is determined by the function Gd . We can interpret this function as an aggregator that defines the welfare relevant price index. The key point is that the gains from trade will depend crucially on the functional form of Gd . It is through this correlation function that we will be able to capture Ricardo’s second insight tying the degree of technological similarity to the gains from trade.

3

Gains From Trade

What are the consequences of correlation in technology for the gains from trade? Intuitively, if who countries have identical idiosyncratic productivity draws across varieties, then, with their average productivity determining the cost of labor, they will offer each other identical prices across varieties, and there is no scope for trade between the two countries. This intuition captures the second part of Ricardo’s insight — countries with similar production possibilities gain less from trade with each other. We show that heterogeneity in correlation leads to heterogeneity in the gains from trade. In fact, the necessary adjustment for correlation relative to the EK model is a simple correction to the gains from trade formula of Arkolakis et al. (2012, henceforth ACR) for CES trade models. Importantly, this correlation correction only requires data on expenditure shares across countries, preserving the simplicity of the ACR gains from trade calculation. In our model, the real wage in each country can be written as 1 Wd = γ −1 Wd Gd (Φ1d , . . . , ΦN d ) θ . Pd

Note that the self-trade share is πdd =

(Wd /Ad )−θ Gdd Gd (Φ1d , . . . , ΦN d )

Therefore, we can write real wages as Wd = γ −1 Ad Pd



10

πdd Gdd

− θ1 .

(7)

The shape parameter, θ, a country’s productivity, and their self-trade share deflated by the derivative of the correlation function, Gdd , are sufficient statistics to compute real wages. In autarky, all countries only purchase their own goods and so πdd = 1. Also, as τod → ∞ we have Φod → 0 for o 6= d. As a result Gdd = Gdd (Φ1d , . . . , ΦN d ) → Gdd (0, . . . , 0, Φdd , 0, . . . , 0) = 1. Intuitively, correlation with other countries is irrelevant in autarky. Therefore, real wages in autarky are 

Wd Pd



= γ −1 Ad .

Autarky

Comparing the real wage in Equation 7 to this counterfactual autarky real wage gives the following result for the gains from trade. Proposition 3 (Gains From Trade). Let Assumption 1, and Assumption 2 hold. Suppose that markets are perfectly competitive. Then the gains from trade relative to autarky are: Wd /Pd GTd ≡ = (Wd /Pd )Autarky



πdd Gdd

− θ1 .

This proposition generalizes the results of ACR to the class of models with GEV demand systems. The results in ACR rely on a constant elasticity of substitution (CES) demand system. With CES demand—such as in the EK model with zero correlation in technology—the denominator inside the brackets is equal to 1 and Proposition 3 simplifies to the expression for the gains from trade in ACR. The model introduced in this paper allows for much richer demand systems, and includes CES demand as a special case. This proposition shows that the basic spirit of ACR holds in the class of models with GEV demand, after an adjustment for correlation in technology. This result captures the second aspect of Ricardo’s idea. If a country has very similar technology to all other countries—the case of high correlation—the gains from trade will be small. In contrast if their technology is very dissimilar—with low correlation—then the gains from trade will be large. The influence of correlation on the gains from trade relative to ACR leads to a simple adjustment to a country’s self trade. This correlation correction equals the derivative of country d’s correlation function with respect to their own competitiveness index. 11

From Proposition 2, we know that the correlation function acts as a price aggregator and determines a country’s price level. This connection will help us interpret the correlation correction. First, note that expenditure shares equal the elasticity of a destination’s price level to an origin country’s production costs: πod =

Φod God ∂ ln Gd (Φ1d , . . . , ΦN d ) ∂ ln Pd−θ ∂ ln Pd = = = Gd (Φ1d , . . . , ΦN d ) ∂ ln Φod ∂ ln(τod Wo /Ad )−θ ∂ ln Wo

In the case of self-trade, this elasticity is linked to the real marginal cost of production, and the correction term, Gdd . ∂ ln Pd Φdd Gdd = πdd = d = ∂ ln Wd G (Φ1d , . . . , ΦN d )

 −θ Wd /Pd γ Gdd Ad

In the Eaton-Kortum special case with zero correlation, Gdd = 1. The restriction to uncorrelated technology imposes a structural relationship between a country’s real marginal cost of

Wd /Pd Ad

and its elasticity of prices to wages. It is this restriction — as summarized

by the condition that Gdd = 1 — which leads to the usual ACR result for the gains from trade. Allowing for correlation in technology breaks this tight link. Proposition 3 shows that Gdd is precisely the quantity needed to calculate the gains from trade without imposing this structural relationship between the elasticity of prices to wages and a country’s real marginal cost of production. The following example illustrates the consequences of this correlation correction. We consider a three country world where two countries have correlated technology. Example 1 (Three-Country Nested CES). Suppose that the correlation function is d

G (x1 , x2 , x3 ) =



1/(1−ρ) x1

+

1/(1−ρ) x2

1−ρ

+ x3

We can interpret country 1 and country 2 as technological peers with the parameter ρ measuring the degree of correlation in their technology. We have God =

Gdo (Φ1d , Φ2d , Φ3d )

=



1/(1−ρ) Φ1d

+

1/(1−ρ) Φ2d

−ρ

while G3d = Gd3 (Φ1d , Φ2d , Φ3d ) = 1. 12

ρ/(1−ρ)

Φod

for s = 1, 2

(8)

Given that πod = Φod God /Gd (Φ1d , Φ2d , Φ3d ), we can take the ratio of Equation (8) for o = 1 and for o = 2 to get G1d = G2d



π1d π2d

ρ

 =⇒

God =

πod π1d + π2d

ρ for o = 1, 2.

As a result the gains from trade are − θ1



  1−ρ (π1d + π2d )ρ  GTd = πdd | {z }

for d = 1, 2

−1

and, GT3 = π33θ .

πdd /Gdd

In Example 1, the gains from trade for countries 1 and 2 depend on the degree of correlation in technology between the two countries, while the gains from trade for country 3 are pinned down by their self-trade share. The corrected self-trade shares for country 1 and 2 end up as a convex combination of each country’s expenditure share on their own goods and their expenditure share on both their own goods and their peer’s goods. The later can be interpreted as their self-trade if they were combined into a single country with their peer. Indeed, if they have perfectly correlated technology, so that ρ = 1, then the two countries are effectively a single country, so the relevant self-trade share is their combined expenditure. The correlation coefficient is the weight in the convex combination. When there is zero correlation in technology (ρ = 0), a correction is unnecessary. For positive correlation, the correction increases effective self-trade, implying lowers the gains from trade. For perfect correlation (ρ = 1), the two countries are effectively a single country and it is their combined self trade that is relevant for calculating the gains from trade. This example illustrates how heterogenous correlation in technology implies heterogeneity in the gains from trade. Our framework accommodates arbitrary correlation patterns and captures Ricardo’s second insight—countries gain more when trading with countries who have dissimilar technology.

3.1

Calculating the Gains From Trade

To make the necessary adjustment for correlated technology, we need to know the correlation structure across countries — which requires estimation of Gd . Given the correlation function, we can then calculate the gains from trade directly from expenditure data. The 13

procedure requires solving a system of equations in the correlation-adjusted expenditures shares of πod /God for given expenditure share data, πod . For each destination d, this calculation comes from the following system of N equations. God = Gdo (Φ1d , . . . , ΦN d ) for o = 1, . . . , N. Each equation in this system is the definition of the correlation correction—God equals the partial derivative of the correlation function in its o’th argument evaluated at the competitiveness in destination d of all origins. Note that from Equation 4 in Proposition 2 we get that Φod ∝ πod /God across o for each d. Since Gdo (x1 , . . . , xN ) is homogenous of degree zero, we can use this proportionality to re-write the system in terms of correlation-adjusted expenditure shares as πod

πod d = G God o



πN d π1d ,..., G1d GN d

 for o = 1, . . . , N

(9)

This expression is an identity. When we evaluate the derivative of the correlation function at the correlation-adjusted expenditure shares, we get the correlation correction. The product of the correlation correction with the corresponding correlation-adjusted expenditure share then removes the correlation adjustment and gives the un-adjusted expenditure share. Writing the system in this way is useful because, for observed expenditure share data, it gives us a system of N equations in the N unknown correlation-adjusted expenditure shares. Performing the adjustment for correlation amounts to solving this system. N Note that the correlation adjustment is well defined. The mapping from RN + to R+ defined

by the right hand side of System 9 satisfies strict gross substitutability, and is homogenous of degree one. As a result, it is injective (see, for instance, Berry et al., 2013) and there is N a unique solution for {πod /God }N o=1 given expenditure share data of {πod }o=1 . After solv-

ing this system to adjust observed expenditure shares for correlation, we can then apply Proposition 3 to calculate GTd . This result establishes that—up to knowing the structure of correlations as captured by Gd —calculating the gains from trade only requires expenditure share data. We can relax the assumption of independence, depart from CES demand systems, and calculate the gains from trade using the same data as ACR.

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3.2

Examples

Next, we consider several specifications related to models in the trade literature and derive expenditure share formulas and the gains from trade. In many parametric specifications for Gd , we can solve for correlation-adjusted expenditure shares in closed form. When closed forms are not available, the invertibility of system 9 ensures that we can numerically solve for the adjusted shares. Additionally, we can often take advantage of dissaggregated data to calculate the gains from trade when closed forms based on aggregated expenditure shares are unavailable. First consider models with CES demand systems, such as the standard Ricardian model as outlined in Eaton and Kortum (2002). Example 2 (Constant Elasticity of Substitution (CES)). Suppose that Ziod (v) is iid unit Fréchet with shape θ over (i, v). Then Gd is identical across destination markets and 

d

G (x1 , . . . , xN ) = E

θ



max Ziod (v) xo =

o=1,...,N

N X

xo .

o=1

In this case, the joint distribution of import prices is " P[P1d (v) ≥ p1 , . . . , PN d (v) ≥ pN ] = exp −

N X

# Φod pθo

o=1

Expenditure shares and prices satisfy: Φod

πod = PN

o0 =1

Φo0 d

,

and

Pd = γ

N X

!− θ1 Φod

.

o=1

Since God = 1, the gains from trade are −1

GTdCES = πddθ . The EK model corresponds to specifying an additive correlation function. This functional form implies a high degree of symmetry across countries — the competitiveness of each origin country influences a destination’s price level identically. The implication is that any two countries with the same self-trade share have identical gains from trade because all countries gain equally from each of their trading partners, and we get the CES gains from trade, GTdCES . The symmetry coming from independence means that there is no 15

heterogeneity coming from the degree of similarity in technology across countries. To account for Ricardo’s second insight, we must relax the independence assumption and allow for heterogeneous correlations in technology. For example, we can introduce heterogeneity but take a small departure from CES by specifying the correlation function as an implicit function following Hanoch (1975) and Sato (1977). This specification leads to isoelastic expenditure shares. Example 3 (Isoelastic). Specify Gd (x1 , . . . , xN ) as an implicit function satisfying 1=

N  X o=1

xo d G (x1 , . . . , xN )

1  1−ρ

o

.

Define bi-lateral price indices as −1/θ

Pod ≡ Φod . Then expenditure shares and the price level satisfy θ − 1−ρ o γ PPodd  − 1−ρθ Po0 d 1 o0 γ 1−ρ 0 Pd

1 1−ρo

πod = PN

o0 =1



θ

and

− 1−ρ N  X o Pod 1= γ . P d o=1

o

The system for correlation-adjusted expenditure shares has the following closed form solution: πod = God where ρ¯d =

PN

n=1

πod ρo πod



1−¯ ρd 1−ρo

1−ρo .

ρd πnd is d’s expenditure-weighted exposure to the correlation of its trading

partners. The implied gains from trade are GTdIsoelastic =



1 − ρd πdd 1 − ρ¯d

− 1−ρ d θ .

This specification of the correlation function implies an isolastic demand system and leads to a correlation adjustment with two components. First, expenditure by d on o gets adρo justed to account for o’s correlation with the rest of the world—the term πod in the denom-

inator. The correlation correction term, God , decreases and the expenditure share of d on goods from o gets adjusted upwards when origin o has higher correlation with the rest of the world.

16

Second, there is an adjustment that accounts for relative correlations across exporters.  1−ρo 1−¯ ρd This second component—the term 1−ρo — decreases the correlation correction and revises the expenditure share upward when a destination has more exposure to correlation from its average trading partner than from the origin. These two components of the correlation correction lead to an expression for the gains from trade that incorporates an elasticity adjustment and a level adjustment relative to ACR. First, a country’s overall correlation with the rest of the world makes their effective trade elasticity equal to

θ . 1−ρd

When a country has more correlation with the rest of world,

their effective trade elasticity increases (their goods become more substitutable) because it is less likely that they will be the lowest cost supplier of a given variety. This increased elasticity due to higher correlation reduces the gains from trade. d Second, relative correlations create a level adjustment of 1−ρ to the self-trade share. When 1−¯ ρd

a country’s average trading partner has higher correlation relative to their own correlation, it is as-if they have a higher self-trade share. That is, higher correlation among a country’s trading partners relative their own correlation reduces the gains from trade. Together, both the elasticity adjustment and the level adjustment imply that more correlation in technology reduces the gains from trade—formalizing Ricardo’s second insight. An important consequence is that the gains from trade can be heterogenous across countries with the same self-trade share. The elasticity adjustment implies that a country’s own correlation introduces heterogeneity relative to ACR by changing the effective substitutability of their goods. The level adjustment introduces heterogeneity in the gains from trade relative to ACR through the correlations of the country’s trading partners relative to their own correlation. The isoelastic specification shows how correlation and relative correlations can introduce heterogeneity in the gains from trade for a given self-trade share. It also implies that gravity holds at the aggregate level but with heterogenous trade elasticities. As a result, it is straightforward to estimate the isoelastic model using standard gravity regressions and data on aggregate trade shares, tariffs, and geography. To link to trade models where gravity may fail to hold at the aggregate level, we also consider a cross-nested CES functional form for the correlation function. In this case, the setup is analogous to cross-nested logit discrete-choice models—see Train (2009). This specification leads to a demand system that can be linked to existing trade models that incorporate sectors and multinational production.

17

Example 4 (Cross-Nested (CN) CES). Specify the correlation function as Gd (x1 , . . . , xN ) =

M X

N X

m=1

o=1

!1−ρm (ωmod xo )1/(1−ρm )

.

Here the outer sum captures latent factors that induce correlation across origins. The parameter ρm measures the strength of the correlation induced by the m’th latent factor and ωmod measures the extent to which factor m matters for trade flows from o to d. For the correlation function to be P well defined, it must satisfy Gd (0, . . . , 0, 1, 0, . . . , 0) = 1, so we must normalize N m=1 ωmod = 1. Define price indices as

Pmod = (ωmod Φod )−1/θ

and

Pmd =

N X

θ − 1−ρ m Pmod

!− 1−ρθ m

o=1

Then expenditure shares and price levels are

πod

− 1−ρθ  −θ M  X m Pmd Pmod γ = P Pd md m=1

and

Pd = γ

M X

!−1/θ −θ Pmd

.

m=1

We cannot get a closed form for correlation-adjusted expenditure shares in terms of aggregate trade shares. However, if we relate the latent factor m to some observable disaggregated expenditure shares so that  πmod =

Pmod Pmd

− 1−ρθ  −θ m Pmd γ Pd

holds, then correlation-adjusted trade shares and the gains from trade are M X πod = π 1−ρm God m=1 mod

N X

!ρm πmod

and

GTdCN =

o=1

M X

1−ρm πmod

m=1

N X

!ρm !− θ1 πmod

.

o=1

The latent factors in the cross-nested CES can be related to various micro-foundations underlying aggregate trade flows. To illustrate this idea, our empirical application in Section 5 interprets the latent factor as the sector producing a good. More generally, latent factors can correspond to any observable or theoretical characteristics of traded goods. Beyond sectoral classification, they might include the home country of the firm producing the good, the sub-region of the country where the good is produced, or the series of locations (value chain) along which the good gets produced. For example, we can get a version of the multinational production model of Ramondo and 18

Rodríguez-Clare (2013) if we interpret m as the home country of the multinational firm that produces a given product. In their framework, multinational firms have correlated productivity across production locations and this correlation does not differ by the home country of the firm. We can generalize their model and allow for heterogeneity across home countries.6 Example 5 (Multinational Production With Heterogenous Correlation). Relabel the latent factor dimension m of the cross-nested CES model in Example 4 to correspond to the home country n of the multinational producing a given good. Define productivity and multinational production inefficiency indices Tn and hno such that ωnod ≡ Tn1−ρn (hno Ao )−θ . Then the correlation function becomes N X

Gd (x1 , . . . , xN ) =

Tn

N X

n=1

!1−ρn (hno Ao )−θ/(1−ρn ) xo1/(1−ρn )

.

o=1

Define a cost index for goods produced by multinationals from home country n as N X (hno Wo τod )−θ/(1−ρn )

cnd =

!−(1−ρn )/θ .

o=1

Then d’s expenditure share on goods produces in o by multinationals from home country n is Tn c−θ nd

πnod = PN

n0 =1

(hno Wo τod )−θ/(1−ρn )

Tn0 c−θ n0 d

PN

−θ/(1−ρn ) o0 =1 (hno0 Wo0 τo0 d )

.

Aggregate expenditure shares and price levels are

πod =

N X

πnod

and

Pd = γ

n=1

N X

!−1/θ Tn c−θ nd

.

n=1

This example illustrates how our framework can accommodate and help to generalize many existing trade models. To explore this connection further, we now introduce a trade model which incorporates many possible micro foundations and establish that, after aggregation, it is observationally equivalent to the macro Ricardian model of Section 2. 6 For simplicity, we abstract from intermediates goods in production so we consider a limiting case of their setup where only labor is used as an input.

19

4

Micro to Macro: Consumers and Firms

We now consider a model of trade that incorporates micro-foundations from standard trade models. After aggregation, this model is observationally equivalent to the Ricardian model of Section 2 for a correlation function that depends on the underlying micro structure. This connection provides interpretation for aggregate correlation patterns and also justifies the use of micro level data to estimate the macro correlation function. Variety v is produced by a single firm in origin country o(v) and their product has characteristics of m(v) ∈ {1, . . . , M }. The set of products with characteristics of m produced in o is Vmo and V = ∪mo Vmo is the set of all varieties. Characteristics can capture many micro observables—e.g. the classification of a product into a specific sector, the home country of a multinational operating the firm, a sub-region of the country where the variety is produced, or the sequence of locations (value chain) along which the good is produced. Firms choose to enter destination markets, and, after entry, the set of destinations where v delivers is D(v). The set of all varieties available to consumers in d is Vd = {v ∈ V | d ∈ D(v)}. Denote the set of products with characteristic m produced in origin o and available in destination d as Vmod = {v ∈ Vd | m(z) = m, o(v) = o}. Consumers in each country have random utility over varieties and are endowed with a unit of time that they supply inelastically in a competitive labor market. The set of consumers in destination d is Id . Let Wd denote the wage in d and T (i) any lump sump transfers to the household (e.g., from firm profits). Household i ∈ Id then solves Z max

U (v, i)C(v, i)dv

C(·,i)≥0

Vd

Z s.t.

~ d + T (i) Pd (v)C(v, i)dv ≤ W

Vd

where Pd (v) is the price that firm v ∈ Vd charges for their product in destination d. Heterogeneity in preferences for products will be a source of comparative advantage in the spirit of Armington models of trade (such as Anderson, 1979). We can interpret the random quantity U (v, i) as consumer i’s perception of the quality of variety v. Since varieties are perfect substitutes, individual consumers will purchase whichever variety they perceive to have the lowest quality-adjust price. C(v, i) > 0

=⇒

Pd (v) Pd (v) = inf . U (v, i) v∈Vd U (v, i) 20

We can break this decision into first choosing product characteristics m and origin o and then choosing a product in Vmod : C(v, i) > 0

=⇒

Pd (v) Pd (v) = min min inf . m=1,...,M o=1,...,N v∈V U (v, i) mod U (v, i)

We assume that for a given v ∈ Vmod , U (v, i) | v is identically and independently distributed Fréchet across i ∈ Id with shape mod − 1 and location Qd (v). Then the density of consumers in d that purchase variety v is  πmod (v) = R

Pd (v) Qd (v)

 Vmod

1−mod

Pd (v) Qd (v)

1−mod

πmod dv

with the share of expenditure by of consumers in d on type-m goods from country o equal to



πmod

 Pd (v) Pd (v) = P inf = min min inf | i ∈ Id . v∈Vmod U (v, i) s=1,...,S o=1,...,N v∈Vsod U (v, i)

We interpret the quantity Qd (v) as an index of the perception of product v’s quality among consumers in market d. Faced with a CES demand curve, firm v will set their price in destination d as a constant markup over marginal cost.7 Production requires labor and may require labor inputs from ~ = (W1 , . . . , WN ) denote the global wage vector. We assume that multiple countries. Let W firms have constant returns to scale production and take wages as given. The marginal cost function of firm v ∈ Vd with m(v) = m and o(v) = o when delivering to d is ~) M Cmod (W ~ 0 L(v) ~ = min W ~ Ad (v) L(v) ~ s.t. 1 ≤ Ad (v)Fmod (L(v)) ~ where L(v) = (L1 (v), . . . , Ln (v)) is a vector of labor used in production. The production ~ is constant returns to scale and common across varieties with the same function, Fmod (L), ~ ) is homogenous of degree product characteristics, origin, and destination, so M Cmod (W one in the global wage vector. By allowing for dependence on factors of production in multiple countries, this produc7

The CES demand curve at the variety level comes from our assumed process for household utility. A different distribution will generate non-CES demand and variable markups. See Footnote 3 for citations.

21

tion structure accommodates models incorporating global value chains (Antràs et al., 2017). For example, if an individual variety is associated with production along a particular value chain, then the product characteristic m(v) would include the list of countries where factors of production get used, and the production function and marginal cost function for v would depend on inputs from those countries. Their price in d is then Pd (v) =

~) mod M Cmod (W mod − 1 Ad (v)

∀ v ∈ Vmod

and they have profit of 1 mod

R

(Ad (v)Qd (v))mod −1 Xmod . mod −1 (A (v)Q (v)) dv d d Vmod

where Xmod = πmod Xd

with Xd = Wd Ld + Td

is expenditure by consumers in d on type-m goods from o. Here, Ld is the measure of R Id (total labor endowment in d) and Td = Id T (i)di is the total transfers to d from firm profits. By incorporating the choice to export to specific destination markets, the model accommodates standard models of trade based on monopolistic competition and heterogenous ~ ) denote the cost of introducing a variety with characterfirms (Melitz, 2003). Let κmod (W istics of m produced in o into destination market d. The threshold level of quality-adjusted productivity at which varieties begin to enter d is the quantity χmod satisfying ~ )= κmod (W

mod −1 χmod Xmod . R mod V (Ad (v)Qd (v))mod −1 dv mod

1

As a result, the set of entering varieties, Vmod , satisfies ( Vmod =

v ∈ Vmo | Ad (v)Qd (v) > χmod

1

  −1 ~ ) Z mod mod κmod (W mod −1 = (Ad (v)Qd (v)) dv Xmod Vmod

Following Chaney (2008), we assume that Ad (v)Qd (v) is distributed Pareto with shape αmod > mod − 1 among varieties in v ∈ Vmo independently across d. We additionally assume that not all v ∈ Vmo enter each destination market. Under this assumption we can

22

) .

calculate that

χmod =

~) mod κmod (W Xmod

−1 ! mod αmod 

αmod Mmo αmod − mod + 1

α 1

mod

χmod

where χmod is the lower bound of the distribution of Ad (v)Qd (v). Then the measure of varieties after entry is χmod χmod

Mmod =

!−αmod Mmd .

Given the pricing of varieties, the quality-adjusted price faced by individual i for variety v ∈ Vmod is

~) Pd (v) mod M Cmod (W = . U (v, i) mod − 1 Ad (v)U (v, i)

The quality-adjusted price faced by each individual consumer is a markup over qualityadjusted marginal cost. We assume that for each d, Ad (v)U (v, i) is a θ-Fréchet process on (m, o) with correlation function H d .8 As a result the expenditure share of consumers in d who purchase type-m goods from o is πmod =

d ~ 1d , . . . , Ψ ~ N d) Ψmod Hmo (Ψ ~ 1d , . . . , Ψ ~ N d) H d (Ψ

~ od = (Ψ1od , . . . , ΨM od ) is a vector of competitiveness indices across product charwhere Ψ acteristics, and each competitiveness index is defined as

Ψmod

" " # #  1 −1 1−mod mod Pd (v) = E | v ∈ Vmod Mmod Qd (v) !−θ !ηmod ~) M Cmod (W πmod = τmod µmod Mmo ~) Amo κmod (W

8

More precisely—to be consistent with our previous assumption for U (v, i) | v—we assume that for each d, U (v, i) is a θ-Fréchet process on v with location E[U (v, i)θ ]1/θ = Qd (v) and a nested correlation functional of the form   ~ 1d (x), . . . Ψ ~ N d (x) {x(v)}v∈Vd 7→ H d Ψ ~ od (x) = (Ψ1od (x), . . . , ΨM od (x)) and each functional Ψmod (x) is defined as where Ψ Z {x(v)}v∈Vd 7→

x(v)

mod −1 θ

θ mod −1

 dv

.

Vmod

Note that this leaves the distribution of the location of Ad (v)U (v, i) unrestricted, justifying our assumption that Ad (v)Qd (v) is Pareto across v ∈ Vmo .

23

for productivity and iceberg indices of 1 θ

Amo = χmoo

and

τmod =

χmoo

! θ1

χmod

and parameters ηmod

mod − 1 ≡1− αmod

 and µmod ≡

mod mod − 1

−θ/ηmod

−1/ηmod

mod ηmod

.

Note that since αmod > mod − 1, we have 0 < ηmod < 1.

4.1

Selection Effects

This micro model incorporates selection effects — here showing up as the endogenous dependence of competitiveness on the expenditure share. This feedback—where more expenditure induces more firms to enter a destination market, expand variety, and increase expenditure further—represents a strategic complementarity that can possibly move the model outside the class of GEV demand systems. However, by a continuity argument for ηmod not too large, the effect of this complementarity will not dominate the substitution patterns associated with a GEV demand system. ˜ d (Φ ~ 1, . . . , Φ ~ N) Even for large 0 < ηmod < 1, there is a homogenous of degree one function H such that πmod =

d ~ ˜ mo ~ N d) Φmod H (Φ1d , . . . , Φ ˜ d (Φ ~ 1d , . . . , Φ ~ N d) H

where selection-adjusted competitiveness is

Φmod =

~) M Cmod (W Amo

!−θ

~) κmod (W µmod

!−ηmod Mmo

~ od = (Φ1od , . . . , ΦM od ). If selection effects are strong this system may not fit into and Φ the GEV class. That case corresponds to relaxing sign restrictions related to substitution ˜ d and interpret effects (see Train, 2009). In general, we can specify a functional form for H patterns of complementarity as potentially coming from heterogenous firms choosing to export to destination markets.

24

4.2

Aggregation

We next map this micro model to the Ricardian model in Section 2 by finding the macro correlation function which rationalizes aggregated trade flows. This correlation function takes the GEV form so long as complementarities from selection and production are not too strong. In this case, this micro model is observationally equivalent—after aggregation—to the Ricardian macro model. Define a macro index of origin-destination monopolistic-competition-adjusted efficiency as Aod =

−θ M  X τmod m=1

Amod

! θ1 mod Mmo µηmod

.

and decompose into trade costs (which measure relative inefficiencies of both actual trade costs and due to monopolistic competition) and productivity as

τod

Ao = Aod

and

Ao =

N X

! θ1 Aθod

.

d=1

We then can de-compose competitiveness after removing selection effects as

Φmod =

~) mod M Cmod (W τmod mod − 1 Amo

!−θ

~) κmod (W µmod

!−ηmod Mmo

= Φod Cmod (Φ1d , . . . , ΦN d ) for Cmod the unique homogenous of degree zero function satisfying  −θ ! WN , . . . , τN d AN !−θ !−ηmod ~) ~) mod M Cmod (W κmod (W τmod Mmo mod − 1 Amo µmod

−θ  Wo τod Cmod Ao =



W1 τ1d A1

−θ

This function captures how the structure of production across countries creates dependence of bilateral trade flows on global labor costs (e.g. due to global value chains). Aggregating over product characteristics, we get M X m=1

πmod ≡ πod =

Φod Gdo (Φ1d , . . . , ΦN d ) Gd (Φ1d , . . . , ΦN d ) 25

for   ˜ d Φ1d C ~ 1d (Φ1d , . . . , ΦN d ), . . . , ΦN d C ~ N d (Φ1d , . . . , ΦN d ) . Gd (Φ1d , . . . , ΦN d ) ≡ H ~ od = (C1od , . . . , CM od ) is the vector across product-characteristics of the functions, where C Cmod . This micro structure implies aggregate trade flows that take the GEV form so long as the ˜ d , takes the GEV form and cost function selection-adjusted micro correlation function, H Cmod is consistent with labor being substitutable in production. Generally, complementarity generated by selection effects or complementarity in production may lead to a nonGEV demand system at the aggregate level. Provided that these sources of complementarity are not too strong, we can directly link the aggregate predictions of this model to the Ricardian model of Section 2. This result provides interpretation for macro correlation patterns. They may arise from latent product characteristics (capturing sectors, multinational production, sub-regions, and global value chains), and selection effects from heterogenous firms choosing where to export. Generally, we can relax the restriction of Gd to the GEV class with the interpretation that complementarities arise from these micro-foundations.9 This aggregation result allows us to use micro level estimates to calculate the macro correlation function. Then we can use the implied correlation function to do macro counterfactual analysis.

5

Empirical Application: Multi-Sector Model of Trade

We now proceed to present an empirical application of our framework with a general correlation structure. We choose the multi-sector model of trade as our application because it represents a common extension of the EK model of trade in the literature. Alternative applications refer to extensions of the EK model of trade to multinational production; this application, however, would be more challenging in terms of its data requirements. We specify the correlation function as a cross-nested CES function, as in Example 4, and we interpret the latent factors, which induce correlation across origins, as sectors.10 The 9

Note that the results of Section 2 for counterfactuals do not rely on the specific restrictions inherent to the GEV class 10 If our application referred to multinational production, latent factors m would represent the potential countries of origin of multinational production, origin countries o would be the countries of production, and destination countries d the countries where consumers are located. The data needed would refer to triangular flows: exports of multinational firms from m located in o and exporting to d. If, instead, we

26

aggregate correlation function is S N X X d d G (Φ ) = (ωsod Φod )1/(1−ρs ) s=1

with

PN

s=1

!1−ρs ,

o=1

ωsod = 1. The parameter ρs measures the degree of correlation across origin

countries, in each sector s, while ωsod reflects sectoral trade costs and comparative advantage. In this model, gravity fails to hold at the aggregate level due to correlation, but it holds at the sector level. As a result, we can run gravity at the micro level in order to calibrate the aggregate correlation function that rationalizes the aggregated sector-level data.

5.1

Sectoral Gravity

Using the expressions in Example 4, the expenditure share on sector s and origin o by destination d is  πsod =

Psod Psd

−σs 

Psd Pd

−θ .

Taking logs, we get a sectoral gravity equation, ln πsod = −σs ln

Psd Wo − θ ln − σs ln τsod = aso + bsd − σs ln τsod , Aso Pd

(10)

where aso ≡ −σs ln AWsoo , bsd ≡ −θ ln PPsdd are, respectively, sector-origin and sector-destination fixed effects, and σs ≡ θ/(1 − ρs ). In a first step, we estimate the sectoral elasticity of substitution, σs , by OLS, using bilateral sectoral data on trade flows and bilateral sectoral measures of trade costs, such as freight costs and tariffs and other geography covariates, ln τsod = ln(1 + tsod ) + δ 0 Geood + usod

(11)

In a second step, given our estimates of σs , we estimate θ using the expressions that relate relative prices to trade shares, we can use the observed expenditure shares to identify relative prices, Psod = Psd

πsod PN

o=1 πsod

!− σ1

s

Psd and = Pd

N X

!−1/θ πsod

.

o=1

interpreted m as a sub-region of the country, then we would need data on trade between sub-regions.

27

Within-sector relative prices across origins are related to observed expenditure shares and the elasticity of substitution within the sector. Further, N

Psod Psod Psd Wo 1 X ln = ln − ln = ln − ln Pd + ln τsod + ln πsod . Psd Pd Pd Aso θ o=1 After adjusting relative prices for trade costs, we can identify θ by estimating the following gravity equation, ln ysod

N 1 X = aso + bd + δ Geood + ln πsod + usod , θ o=1 0

where ln ysod ≡ ln

(12)

!− σ1

s

πsod PN

o=1 πsod

− ln(1 + tsod ),

and we use the assumption on trade costs in (11).

5.2

Estimates and Macro Counterfactuals

We use the two-step procedure described above and sectoral bilateral data on trade flows and trade costs to calculate the gains from trade for each country and infer the underlying correlation structure across countries. The data for trade flows and freight costs are the ones used in Adao et al. (2017). The data contain 36 countries plus the rest of the world, and 16 sectors. Data for freight costs are available for two importers only, Australia and the United States. We restrict the period to 1995-2006. Gravity covariates are from CEPII. Pooling the data over years, we estimate, by OLS, the following sectoral gravity equation ∆d ln πsodt = ∆d βsdt − σs ∆d ln(1 + tsodt ) − σs δ 0 ∆d Geood + ∆d sodt ,

(13)

where ∆d denotes the difference between d = AU S and d = U SA. Figure 1 summarizes the estimates for the sectoral elasticity of substitution, σs . Next, we get the trade elasticity, θ, by estimating through OLS the following gravity equa-

28

−10

Sectoral Elasticity 0 10

20

Figure 1: Estimates of Sectoral Elasticities, σs , OLS.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Sector

Notes: Results from estimating (13) by OLS. Point estimates and 95% confidence intervals shown.

tion, pooling again the data over years, X 1 πsod + ∆d usodt , ∆d ln ysodt = ∆d βdt + δ 0 ∆d Geood + ∆d ln θ o

(14)

for differences between d = AU S and d = U SA. Results in Table 1 imply that θ = 2.56. Sectoral correlations are simply calculated using the definition of σs , and the restriction that ρs ≥ 0, ρs = max(0, 1 −

θ ), σs

for all s.

Armed with estimates for θ and ρs , we use the bilateral sectoral data for the 36 countries in the sample, for each year, and construct estimates of the gains from trade, P GTd =

πsdd Gdd s

− θ1 ,

(15)

and the correlation-correction term, P Gdd = P

πsdd . P ( o πsod )ρs

s

1−ρs s πsdd

(16)

Figure 2 shows the results, by country, for 2006. Panel (2a) compares the gains from trade calculated under our cross-nested CES specification against the gains from trade 29

Table 1: Estimates of the Trade Elasticity θ, OLS. ln ysot,AU S − ln ysot,U SA (1) .393

1/θ

(.032)∗∗

Share Border

-.909

(.051)∗∗

Log Distance

.049

(.021)∗

Year Effects Year-Covariate Interactions Observations R-squared

5,589 0.113

(2) .391

(.032)∗∗

-.909

(3) .391

(.032)∗∗

-.828

(.051)∗∗

(.178)∗∗

.049

.070

(.021)∗

(.073)

X

X X

5,589 0.114

5,589 0.114

Notes: Results from estimating (14) by OLS. Standard errors in parenthesis with levels of significance denoted by ** p < 0.01, and * p < 0.05.

−1/

calculated using CES. That is, we compare GTdCN = (πdd /Gdd )−1/θ and GTdCES = πdd , with θ = 2.56—our estimate—and  = 5—as commonly used in the trade literature for the trade elasticity. Correcting the gains from trade by correlation implies gains that do not have a one-to-one mapping to self trade shares; two countries with the same level of openness can now have very different gains from trade. Panel (2b) makes this point even clearer: For instance, while under CES, Ireland (IRL) and Lithuania (LTU) would have the same gains from trade, correcting those gains for correlation entails gains that are 40 percent higher for Lithuania. Additionally our calculations suggest that, for individual countries, the corrected gains from trade can be 30 percent larger than without the correction. Appendix Figures H.1 and H.2 show the results by year, for all years. The heterogeneity observed in the gains from trade, and that is not captured by self trade, relates precisely to Ricardo’s insight: Countries with higher gains should be countries that are specialized in sectors that present low correlation with —i.e., more dissimilar to—the ones of their trading partners. We explore the source of heterogeneity in the gains from trade by linking it the to specialization patterns of countries. To such end, we use Balassa revealed-comparative-advantage (RCA) indices, constructed at the sector-country-year level, RCAsot

P P Xsodt / sdt Xsodt d P =P , X / sodt od sod Xsodt

(17)

and use them as weights to aggregate, by country and year, our sectoral estimates of the 30

Figure 2: Gains from Trade, 2006. (a) level SVK

Gains From Trade 1.05 1.075

HUN

LTU

Percent Difference in Gains From Trade −10 0 10 20 30

1.1

40

(b) percent difference

BLX SVN BGR BAL NLD TWN CZE AUT DNK

IRL

ROU PRT SWEPOL GRC DEU FIN CAN

BGR NLD

TUR JPN IDN RUS ROU ESP IND ITA FRA CAN KOR GBR POL USABRA DEU AUS FIN GRC

PRT

SVN BLX

BAL AUT DNK

SVK TWN

SWE

HUN

CZE

MEX CHN

IRL

1

−20

1.025

ESP KOR TUR FRA MEXGBR ITA IDN RUS IND AUS CHN USA JPN BRA

LTU

.6

.65

.7

.75 .8 .85 Self Trade Share

Notes: (2a) Black data: GTdCN = (

.9

P

s

.95

1

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

P 1 ρ 1−ρs P πsdd ( o πsod ) s )− θ . Red line: GTdCES = ( s πsdd )−1/ε for ε = 5.

(2b): Percent difference calculated as 100 ×

GTd −GTdCES . GTdCES −1

correlation parameters, ρs , ρRCA = dt

X s

RCAsdt ρs P . s RCAsdt

(18)

We call the expression in (18) the RCA-weighted correlation index. The interpretation is very intuitive: High RCAsot indices in high correlation sectors (i.e., high ρs ) implies a high ρRCA . dt Figure 3 shows our RCA-weighted correlation index against self trade, by country, for 1996 and 2006. First, consider again the case of Ireland (IRL) and Lithuania (LTU). These two countries have very similar self trade shares, which under a CES demand system would imply very similar gains. However, their sectoral trade patterns are very different: While Ireland specializes in sectors which are correlated with those of its trading partners (ρRCA IRL,2006 = 0.48), Lithuania specializes in sectors with a much lower correlation (ρRCA LT U,2006 = 0.28). The lower correlation index for Lithuania materializes in gains from trade that are 40 percent higher than the gains observed for Ireland. Appendix Figure H.3 shows the results by year, for all years. Differences in specialization patterns imply not only differences in the gains from trade— that go beyond differences captured by self trade—in the cross section of countries, but also differences in the gains from trade across time, for each country. The presence of correlation represents a key channel through which the gains from trade change with a country’s comparative advantage patterns. As documented by Hanson et al. (2015), 31

Figure 3: RCA-Weighted Correlation Index, selected years. (a) 1996 .55

.55

(b) 2006

JPN

DEU IRL SVN

AUT TWN DNK CZE CAN

BLX

SVK NLD BAL HUN

GBR FRA KOR ITA ESP

PRT MEX POL AUS IDN

BGR

ROUGRC TURRUS

USA

BRA CHN IND

JPN

CZE AUT TWN HUN SVK

SVN BALDNK

BLX

NLD

KOR GBR FRA ITA POL CAN ESP PRT ROU

MEX

USA CHN AUS BRA

GRC

LTU

IDNRUS IND BGR

TUR

.15

.15

LTU

SWE FIN DEU

IRL

RCA−Weighted Correlation Index .25 .35 .45

RCA−Weighted Correlation Index .25 .35 .45

SWE FIN

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

.6

.65

.7

.75 .8 .85 Self Trade Share

Notes: Revealed-Comparative-Advantage (RCA)-weighted correlation index: ρRCA = dt

P

s

.9

.95

1

sdt ρs PRCA RCAsdt . s

the churning in comparative advantage for individual countries across time is extremely dynamic. In the same vein, Figure 4 links the evolution of specialization patterns, for selected countries, to our RCA-weighted correlation index. Reflecting the ever-evolving pattern of comparative advantage, a country’s correlation structure with trading partners can drastically change year by year, and with it, the gains from trade. Appendix Figure H.4 shows the results by country, for all countries. While Figure 3 shows the link between the RCA-weighted correlation index and self trade for the cross of countries in our sample, Figure 5 shows that relation across time, for selected countries. Appendix Figure H.5 presents the results for each country in our sample. While for a country like the United States, the changes in the gains from trade are captured fairly well by the changes in self trade shares, for the Baltic Republics, for instance, changes in their sectoral specialization patterns, which is reflected in changes in the correlation index, can have large impacts in the calculations of their gains from trade. Heterogeneity in the gains from trade across time, coming from the correlation channel, seems to be quite important. The negative correlation between the RCA-weighted correlation index and the gains from trade is confirmed by running an OLS regression of the gains from trade, GTdt and the correlation correlation, Gddt , alternately, on the RCA-weighted correlation index, ρRCA and dt self trade shares, πddt . Results in Table 2 confirm that the correlation index is significantly and negatively related to the correlation-correction term and to the gains from trade, re32

Figure 4: Evolution of RCA-Weighted Correlation Index, selected countries. (a) Baltic Republics

1995

2000 Year

2005

.5 RCA−Weighted Correlation Index .3 .35 .4 .45 .25

RCA−Weighted Correlation Index .3 .35 .4 .45

.5

(c) China

.25

.25

RCA−Weighted Correlation Index .3 .35 .4 .45

.5

(b) Brazil

1995

2005

2005

2005

.5 .25

RCA−Weighted Correlation Index .3 .35 .4 .45

.5 RCA−Weighted Correlation Index .3 .35 .4 .45 2000 Year

2000 Year

(f) United States

.25

RCA−Weighted Correlation Index .3 .35 .4 .45 .25 1995

1995

(e) Korea

.5

(d) Indonesia

2000 Year

1995

2000 Year

2005

1995

Notes: Revealed-Comparative-Advantage (RCA)-weighted correlation index: ρRCA = dt Republics are Estonia, Latvia, and Lithuania.

2000 Year

P

s

2005

sdt ρs PRCA RCAsdt . Baltic s

spectively, both across countries and within a country across time.

6

Conclusions

This paper is motivated by the old Ricardian idea that a country gains the most from trading with those countries that are technologically less similar. We argue that Ricardo’s insight is absent from the canonical Ricardian model of trade and develop a theory of trade that allows for arbitrary patterns of correlation in technology between countries. We start from technology primitives that generate a Fréchet process with a general correlation structure and yet preserves all the tractability of EK-type tools. We show that the gains from trade in the presence of heterogenous correlation can be written as a simple correction to self trade shares. The theory, by relating macro substitutability patterns to underlying micro-structures, provides guidance on using standard micro estimates into macro counterfactual exercises. Our empirical application to a multi-sector model of trade reveals that the adjustment implied by our correlation structure matters: Gains are much 33

Figure 5: RCA-Weighted Correlation Index and Self Trade Shares, selected countries. (a) Baltic Republics

1999

1998 1997 1996

2004 2002

2001

2003

2005 2006 2000

1995 1996 1997 1998

1999

.2

.2

1995

.73

.74 Self Trade Share

.75

.76

.925

.93

.945

.95

1996 1997

2003 1999

.84

.86 Self Trade Share

.88

.9

2001 2000

1999 1997 1996

1995

1998

.89

.9

.91 .92 Self Trade Share

.93

.94

.5

.5 RCA−Weighted Correlation Index .25 .3 .35 .4 .45

.82

2002

(f) United States

2006 2004

2005 2003

2002

2001

2000

1997 1998

1999

1996

.2

2006 2002

.2

1998

2004

2003

1995

2000 2006

2004

2005

2003

1998 2001 1999 2002 1997 1996 1995

.2

.5

1995 2005 2001 2000

2006 2005 2004

(e) Korea

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

(d) Indonesia

.935 .94 Self Trade Share

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

.72

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

2000

.2

2002

.5

(c) China

.5 2001 2004

2005 2003

2006

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

.5

(b) Brazil

.845

.85

.855 .86 Self Trade Share

.865

.87

.92

.925

Notes: Revealed-Comparative-Advantage (RCA)-weighted correlation index: ρRCA = dt Republics are Estonia, Latvia, and Lithuania.

.93 Self Trade Share

P

s

.935

sdt ρs PRCA RCAsdt . Baltic s

more heterogeneous across countries, and within countries across time, than without the correlation adjustment. By capturing Ricardo’s insight, our approach has the potential of changing other quantitative results in literatures that apply Fréchet tools.

34

.94

Table 2: Comparative Advantage and the Gains from Trade, OLS. Correlation correction, ln Gddt (1) RCA-weighted correlation, ρRCA dt Self trade share, ln πddt

(2)

-.079

-.139

(.007)∗∗

(.014)∗∗

.445

.454

(.005)∗∗

(.009)∗∗

Country Effects Year Effects Observations R-squared

Gains from trade, ln GTdt (3) -.031

(.003)∗∗

-.217

(.002)∗∗

X X 444 0.947

444 0.995

(4) -.054

(.005)∗∗

-.213

(.004)∗∗

X X 444 0.961

444 0.996

P PRCAsdt Notes: Revealed-Comparative-Advantage (RCA)-weighted correlation index: ρRCA = dt s ρs s RCAsdt . Standard errors in parenthesis with levels of significance denoted by ** p < 0.01, and * p < 0.05.

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A

Proof of Lemma 1 1

Normalize by Aod ≡ E[Aiod (v)θ ] θ and transform by a power of θ to define A˜od (v) ≡



A∗od (v) Aod

θ

= max Z¯i (v)

θ



i=1,2,...

Aiod (v) Aod

θ .

By theorem 2 of De Haan (1984), theorem 3 of Penrose (1992), or, most directly, theorem 2 of Schlather (2002), we get that A˜od (v) is a Fréchet process with standard Fréchet marginals if and only if we can take {Z¯i (v)θ , i}i=1,2,... as a Poisson point process on [0, ∞) with intensity measure g −2 dg and E[(Aiod (v)/Aod )θ ] = 1.

B

Properties of Fréchet Processes

Fréchet random variables have the following useful properties. Lemma 2. Let X be distributed as an Fréchet random variable with location T > 0 and shape α > 0 so that it has cumulative distribution function of −α

P[X ≤ x] = e−T x . Then it has mean E[X] = Γ(1 − 1/α)T 1/α . and for any S > 0 and β > 0 (S 1/α X)β is Fréchet with location ST and shape α/β. In particular, P[(S 1/α X)β ≤ z] = e−ST z

38

−α/β

.

Proof. Z

∞

∂ P [X ≤ z] dz ∂z 0 Z ∞ ∂ −α = z e−T z dz ∂z Z0 ∞ −α ze−T z αT z −α−1 dz = Z0 ∞ t−1/α e−t dtT 1/α =

E[X] =

z

0

= Γ(1 − 1/α)T 1/α . and P[(S 1/α X)β ≤ z] = P[X ≤ S −1/α z 1/β ] = e−T (S

−1/α z 1/β )−α

= e−ST z

−α/β

.

Let {Xi }i=1,...,N be an α-Fréchet process with correlation function G : R+N → R+ . That is, the joint distribution of {Xi }i=1,...,N is −α P[Xi ≤ xi , i = 1, . . . , N ] = exp[−G(x−α 1 , . . . , xN )].

Lemma 3. Let {Xi }i=1,...,N be an α-Fréchet process with given correlation function G. Then maxi=1,...,N Ti Xi is a Fréchet random variable with location G(T1α , . . . , TNα ) and shape α. Moreover, let {Ij }M j=1 be any partition of {1, . . . , N } and define the process {Y1 , . . . , YM } as Yj = max Ti Xi . i∈Ij

Let j : {1, . . . , N } → {1, . . . , M } be the unique mapping such that j = j(i) if and only if i ∈ Ij . Then: 1. {Y1 , . . . , YM } is an α-Fréchet process with correlation function H : RM + → R+ satisfying H(z1 , . . . , zM ) = G(T1α zj(1) , . . . , TNα zj(N ) ). 2. h

P

i

P Yj = max Ti Xi =

i∈Ij

i

where Gi (x1 , . . . , xN ) ≡ ∂G(x1 , . . . , xN )/∂xi . 39

Tiα Gi (T1α , . . . , TNα )

G(T1α , . . . , TNα )

.

3. For any j = 1, . . . , M , the distribution of maxi=1,...,N Ti Xi conditional on the event Yj = maxi=1,...,N Ti Xi is identical to the distribution of maxj=1,...,N Tj Xj :  P



−G(T1α ,...,Tnα )y −α

max Ti Xi ≤ y | Yj = max Ti Xi = e i

i=1,...,N

 =P

 max Ti Xi ≤ y .

i=1,...,N

Proof. We first prove part (1). Let {Ij }M j=1 be a partition of {1, . . . , N } and define Yj = maxi∈Ij Ti Xi . Let the function j : {1, . . . , N } → {1, . . . , M } satisfy i ∈ Ij(i) for all i = 1, . . . , N . Note that there is a unique function satisfying this condition since {Ij }M j=1 is a partition of {1, . . . , N }. Then   P [Yj ≤ yj , ∀j = 1, . . . , M ] = P Xi ≤ Ti−1 yj , ∀i ∈ Ij , ∀j = 1, . . . , M α −α

α −α

= e−G(T1 yj(1) ,...,TN yj(N ) ) Therefore {Y1 , . . . , YM } is an α-Fréchet process with correlation function (z1 , . . . , zM ) 7→ G(T1α zj(1) , . . . , TNα zj(N ) ). Note that if we take M = 1 so that I1 = {1, . . . , N } we get:  P

 max Ti Xi ≤ y = P [Y1 ≤ y]

i=1,...,N

= P [Yj ≤ y, ∀j = 1, . . . , M ] α −α ,...,T α y −α ) N

= e−G(T1 y α

α

= e−G(T1 ,...,TN )y

−α

That is, maxi=1,...,N Ti Xi is a Fréchet random variable with location G(T1α , . . . , TNα ) and shape α.

40

Next we prove part (2). We have h i P max Ti Xi ≤ y and Yj = max Ti Xi i i h i = P Yj ≤ y and Yj = max Ti Xi i

= P [Yj ≤ y and Ti Xi ≤ Yj , ∀i = 1, . . . , N ] = P [Yj ≤ y and Ti Xi ≤ Yj , ∀i ∈ / Ij ] Z y ∂ = P [Ti Xi ≤ t, ∀i ∈ / Ij | Yj = t] P[Yj ≤ t]dt ∂t Z0 y ∂ P [Ti Xi ≤ z, ∀i ∈ / Ij , and Ti Xi ≤ t, ∀i ∈ Ij ]|z=t dt = 0 ∂t Z yX ∂ −G(T1α y1−α ,...,Tnα yN−α ) dt = e yi =t,∀i=1,...,N 0 i∈I ∂yi j Z yX α −α α −α −α e−G(T1 y1 ,...,Tn yN ) Gi (T1α y1−α , . . . , Tnα yN = )Tiα αyi−α−1 0

Z

i∈Ij y

=

α

α

−α

e−G(T1 ,...,Tn )t

0

X

yi =t,∀i=1,...,N

dt

Tiα Gi (T1α , . . . , Tnα )αt−α−1 dt

i∈Ij

α α α Z y α α −α i∈Ij Ti Gi (T1 , . . . , Tn ) e−G(T1 ,...,Tn )t G(T1α , . . . , Tnα )αt−α−1 dt α α G(T1 , . . . , Tn ) 0 P α α α T G (T , . . . , T ) i 1 α α −α n i∈Ij i e−G(T1 ,...,Tn )y α α G(T1 , . . . , Tn )

P

= =

where Gi (x1 , . . . , xN ) = ∂G(x1 , . . . , xN )/∂xi . Let y → ∞ to get h

i

Tiα Gi (T1α , . . . , Tnα )

P

i∈Ij

P Yj = max Ti Xi =

G(T1α , . . . , Tnα )

i

.

Finally, we can prove part (3) using the previous results: h i P [max T X ≤ y and Y = max T X ] i i i j i i i P max Ti Xi ≤ y | Yj = max Ti Xi = i i P [Yj = maxi Ti Xi ] P

=

Tiα Gi (T1α ,...,Tnα )

α α −α e−G(T1 ,...,Tn )z G(T1α ,...,Tnα ) P α α α i∈I Ti Gi (T1 ,...,Tn )

i∈Ij

j

G(T1α ,...,Tnα ) α

α

−α

= e−G(T1 ,...,Tn )z h i = P max Ti Xi ≤ y . i

41

C

Proof of Proposition 1

Perfect competition implies that potential import prices are Wo Wo Wo . Pod (v) = min ¯ = = ∗ ¯ i=1,2,... Zi (v)Aiod (v) Aod (v) maxi=1,2,... Zi (v)Aiod (v) Then P[P1d (v) ≥ p1 , . . . , PN d (v) ≥ pN ] = P[P1d (v)/W1 ≥ p1 /W1 , . . . , PN d (v)/WN ≥ pN /WN ] = P[1/A∗1d (v) ≥ p1 /W1 , . . . , 1/A ∗N d (v) ≥ pN /WN ] = P[A∗1d (v) ≤ W1 /p1 , . . . , A∗N d (v) ≤ WN /pN ] By Lemma 1, " P[A∗1d (v) ≤ W1 /p1 , . . . , A∗N d (v) ≤ WN /pN ] = exp −E max

o=1,...,N



Aiod (v) Wo /po

θ #

"

 θ # Aiod (v)θ p o = exp −E max E[Aiod (v)θ ] o=1,...,N E[Aiod (v)θ ] Wo "  θ # p o = exp −E max Ziod (v)θ o=1,...,N τod Wo /Ao   −θ θ θ = exp −E max Ziod (v) (τod Wo /Ao ) po . o=1,...,N

Since Gd (x1 , . . . , Xn ) = E max Ziod (v)θ xo o=1,...,N

we have   P[A∗1d (v) ≤ W1 /p1 , . . . , A∗N d (v) ≤ WN /pN ] = exp −Gd (Φ1d pθ1 , . . . , ΦN d pθn ) for Φod = (τod Wo /Ao )−θ . Then P[P1d (v) ≥ p1 , . . . , PN d (v) ≥ pN ] = P[A∗1d (v) ≤ W1 /p1 , . . . , A∗N d (v) ≤ WN /pN ]   = exp −Gd (Φ1d pθ1 , . . . , ΦN d pθn ) .

42

D

Proof of Proposition 2

The proof of Proposition 2 follows directly from the properties of Fréchet random variables and processes. The probability that variety v is imported by destination d from origin o is ∀o0 6= o]

πod ≡ P[Pod (v) ≥ Po0 d (v) =

Φod Gdo (Φ1d , . . . , ΦN d ) Gd (Φ1d , . . . , ΦN d )

using Proposition 1 and Lemma 3. The distribution of prices among those goods imported by destination d from country o satisfies  P Pod (v) ≥ p | Pod (v) =

   min Po0 d (v) = P 0 min Po0 d (v) ≥ p 0

o =1,...,N

o =1,...,N

= e−G(Φ1d ,...,ΦN d )p

θ

by Proposition 1 and Lemma 3. The price index in destination d is then Z Pd =

1

min M Cod (v)1−σ dv

1  1−σ

0 o=1,...,N

1    1−σ 1−σ = E min M Cod (v)

o=1,...,N

1

= γGd (Φ1d , . . . , ΦN d )− θ where γ = Γ

θ+1−σ θ

1
1−σ

, Γ(·) is the gamma function, and the last follows from the fact

that mino=1,...,N Pod (v)1−σ = (maxo=1,...,N 1/Po d(v))σ−1 is a Fréchet random variable with location Gd (Φ1d , . . . , ΦN d ) and shape θ/(σ − 1) due to Lemma 2.

E

Equilibrium Existence and Uniqueness

Due to the gross substitutes property of the implied factor demand system and homogeneity, the existence and uniqueness of equilibrium follows from standard results in

43

general equilibrium theory. To establish this result we assume balanced trade. Assumption 3 (Balanced Trade). For each country n = 1, . . . , N , total expenditure on imports from countries equals total income from exports to other countries: X

Xon =

o6=n

X

Xnd .

d6=n

Let Ld denote the endowment of labor in country d. From zero profits, total income is then Wd Ld . Under balanced trade, the equilibrium conditions are then Wo Lo =

N X

πod Wd Ld

for each o = 1, . . . , N.

d=1

~ = (W1 , . . . , WN ) denote the vector of wages, define the implied excess demand Letting W N function as E : RN + → R with

~ ) = −Wo Lo + Eo (W

N X

πod Wd Ld

for each o = 1, . . . , N.

d=1

To get a uniqueness result, we assume that countries are technologically distinct so that comparative advantage always exists. Assumption 4 (Differentiated Technology). For each o, d = 1, . . . , N , and each x ∈ RN + with xo > 0



θ

θ



P Ziod (v) xo = max Zind (v) xn > 0. n=1,...,N

This assumption states that each origin country will have a comparative advantage at delivering some goods to each destination market. In particular, the assumption implies that all countries trade. Remark 2. Assume that Φod is finite for each o, d = 1, . . . , N . Then under Assumption 4, each origin country will trade with each destination market. Specifically, 

θ

θ



πod = E Ziod (v) Φod = max Zind (v) Φon > 0. n=1,...,N

Under this assumption, the excess demand system satisfies strict gross substitutability. 44

Since it is homogenous of degree one and satisfies Walras’ law, we get existence and uniqueness of equilibrium using standard results from general equilibrium theory. Proposition 4 (Existence and Uniqueness). Let Assumption 1, Assumption 2, and Assump~ at which global goods markets clear. tion 3 hold. Then there exists an equilibrium wage vector W If Assumption 4 also holds, then the equilibrium is unique up to a single global normalization (choice of numeraire). Proof. Define the event that country o has a comparative advantage in delivering variety v to d as Ωdo (v)

  θ θ ≡ Ziod (v) xo = max Zind (v) xn . o=1,...,N

Assumption 4 implies that P[Ωdo (v)] > 0. As a result, Gdo

=

Gdo (x1 , . . . , xN )

    θ θ θ = E 1 Ziod (v) xo = max Zind (v) xn Ziod (v) o=1,...,N

   = E Ziod (v)θ | Ωdo P Ωdo > 0. 

The implication is that the excess demand system satisfies strict gross substitutability. For each o = 1, . . . , N and each n 6= o we have N

∂Eo (W ) X ∂ Φod Gdo = W d Ld ∂Wn ∂Wn Gd d=1   N X ∂Φnd Φon Gno Φod Gdo Gdn d W L = + Ln G − d d on d d d G G ∂W G n d=1 | {z } {z } | ≤0

≥

Φon Gno Ln Gd

<0

> 0.

The first inequality of the last line follows from the general properties of the social surplus function in generalized extreme value models that Gdo ≥ 0 and Gdon ≤ 0 (see McFadden, 1978; Train, 2009). The final strict inequality follows from the result that Gdo > 0 under Assumption 4. Given that excess demand is homogenous of degree one and satisfies strict gross substitutability, we can apply Proposition 17.F.3 of Mas-Collell et al. (1995) to establish existence and uniqueness.

45

F

Solving for Equilibrium via Exact-Hat Algebra

To solve for equilibrium we can use precise-hat algebra methods (see Costinot and RodrìguezClare, 2014). Let a hat denote the percent change in an equilibrium outcome due to some percent change in fundamentals. As a preliminary step, we need to use the structure of Gd to adjust observed trade shares for correlation in comparative advantage. That is, solve for {πod /God }N o,d=1 given expenditure share data of {πod }N o,d=1 , as in the previous section Then, the procedure to calculate a change in expenditure shares consistent with a given change in fundamentals and wages is as follows. First, we have ˆ od = (ˆ ˆ o /Aˆo )−θ Φ τod W Then since ˆ od God = Gdo (Φ ˆ 1d Φ1d , . . . Φ ˆ N d ΦN d ) G and Φod ∝ πod /God we have ˆ od G ˆ od πod Φ

  π π π od 1d N d d ˆ od ˆ 1d ˆ Nd =Φ G Φ ,...Φ God o G1d GN d

for o, d = 1, . . . , N.

we can calculate the change in expenditure shares as ˆ od G ˆ od πod Φ . π ˆod πod = PN ˆ o0 d G ˆ o0 d π Φ 0 od o =1 ˆ n }N such that To find a change in equilibrium wages, we must find {W n=1 ˆ oL ˆ o Yo = W

N X

ˆ dL ˆ d Yd π ˆod πod W

for each s = 1, . . . , N

d=1

given observed production of {Yn }N n=1 (where Yn = Wn Ln ). From Proposition 4, we have a unique equilibrium and a tatonnment process can be used to solve for the unique equilibrium wage vector. As a result, we can apply a version of the tatonnment algorithm in Alvarez and Lucas (2007) based on this sequence of calculations and numerically solve for the change in wages.

46

G

General Estimation

We can perform structural estimation as follows. For given Gd , we first adjust observed trade share data to correct for correlation in technology. Gravity holds after this adjustment and we run gravity on the correlation-adjusted expenditure shares. We can then estimate parameters of Gd by choosing them to minimize the sum of squared gravity residuals. The first key result we use comes from Equation 9 in Section 3.1. That is, we can use observed expenditure shares and the structure of Gd to solve for πod /God . Next, the expenditure condition implies that gravity holds for these adjusted expenditure shares because

πod Φod = d God G (Φ1d , . . . , ΦN d )

and so ln

πod Ao + ln Gd (Φ1d , . . . , ΦN d )−1 −θ ln τod = θ ln {z } God Wo | | {z } bd ao

Assume that −θ ln τod = −θ ln(1 + tod ) + β 0 Geood + od for tariff data of tod , geography covariates Geood , and residuals od . Then: ln

πod = ao + bd − θ ln(1 + tod ) + β 0 Geood + od God

That is, gravity holds after we adjust observed trade shares to account for correlation in comparative advantage. Let γ denote parameters of the correlation function and let ϑ denote the parameters of this gravity regression. For example, for the cross-nested CES model, we have γ = M {{ρm , {ωmod }N o,d=1 }m=1 }. For given γ we get implied adjusted trade shares. For these

adjusted trade shares we use OLS to estimate the gravity equation and get the sum of squared residuals: RSSGravity (γ) = min ϑ

X

od (γ)2

od

where dependence on γ captures the dependence of the gravity regression on the preliminary adjustment for correlation in comparative advantage. We can then estimate γ by minimizing RSSGravity (γ).

47

H

Additional figures

48

Figure H.1: Gains from Trade, levels, by year. 1995

1.1

1997

1.1

1.1

1996 LTU BLX

Gains From Trade 1.05 1.075

SVK

BAL NLD SVN SVK

BGR HUN DNK CZE AUT TWN CANPRT SWE FINROU GBR GRC MEX KOR DEU POL TUR ESP FRA IDN ITA RUS AUS

1.025

BGR DNK CZE HUN TWN AUT CAN PRT SWE FIN ROU GBR GRC KOR RUS MEX DEU ESP ITA IDN FRA POL TUR AUS CHN IND USA BRA JPN

IRL

.7

.75 .8 .85 Self Trade Share

.9

.95

NLD SVNBGR SVK HUNAUT CZE DNK TWN CAN PRT SWE ROU FIN GRC KOR POL MEX DEU GBR ESP TUR FRA IDN ITA RUS AUS IND CHN USA BRA JPN

1 .65

BAL

IND CHN USA BRA JPN

1 .6

IRL

1.025

BAL NLD SVN

LTU

1

1

Gains From Trade 1.05 1.075

IRL

1.025

BLX

Gains From Trade 1.05 1.075

LTU

BLX

.6

.65

.7

.75 .8 .85 Self Trade Share

.95

1

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

1.1

2000

1.1

1999

1.1

1998

.9

IRL

BLX

SVN SVK NLD HUN

BGR

LTU SVN NLD BAL SVK HUN AUT CANDNK CZE TWN PRT SWE

1.025

1.025

AUT IDN CAN DNK CZE TWN PRT SWE ROU POL FIN GRC MEX KOR DEU ESP GBR RUS FRA TUR ITA AUS

ROU GRC RUS FIN POL ESP IDN MEX DEU KOR GBR FRA ITATUR AUS IND BRA USA CHN

IND USA CHN BRA JPN

.7

.75 .8 .85 Self Trade Share

.9

.95

SVK BGR SVN NLD BAL CZEAUT DNK TWN CANPRT ROU SWE GRC IDN FIN DEU ESP POL KOR MEX FRA RUS GBRITA TUR AUS IND CHN USA BRA JPN

1

1

1 .65

HUN

JPN

1 .6

LTU

Gains From Trade 1.05 1.075

BAL

BGR BLX

1.025

BLX LTU

Gains From Trade 1.05 1.075

Gains From Trade 1.05 1.075

IRL IRL

.6

.65

.7

.75 .8 .85 Self Trade Share

.95

1

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

1.1

2003

1.1

2002

1.1

2001

.9

IRL BLX BGR SVN BAL HUN NLD AUT CZE DNK ROU TWN CAN PRT GRC SWE POL DEU FIN ESP IDN RUS KOR GBR FRA MEX TUR ITA AUS

AUS

IND CHN BRA USA JPN

1

1

IND BRA CHN USA JPN

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

BLXLTU SVK BGR IRL HUN

.6

.65

.7

.75 .8 .85 Self Trade Share

ROU TWN DNK PRT CAN GRC SWEPOL DEU FIN ESP KOR MEX GBR RUS FRA IDN TUR ITA AUS CHN IND BRA USA JPN

.9

.95

1

.6

.65

.7

1.1

1.1

IRL HUN NLD BAL BGR CZE TWNAUT DNKROU SWE PRT CAN GRC POL DEU FIN IDN KOR ESP MEXGBR FRA TUR ITA RUS IND AUS CHN

1.025

1.025

PRT POL CAN GRC SWE DEU FIN KOR IDN ESP MEX TUR GBR FRA RUS ITA IND AUS CHN

Gains From Trade 1.05 1.075

ROU DNK

HUN

.7

.75 .8 .85 Self Trade Share

.9

.95

BGR

IRL

BAL NLD TWN CZE AUT DNK ROU PRT SWEPOL GRC DEU FIN CAN ESP KOR TUR FRA MEXGBR ITA IDN RUS IND AUS CHN USA JPN BRA

1

1

1

1

.65

1

LTU

USA JPN BRA

USA BRA JPN

.6

.95

BLX SVN

1.025

HUN

LTU BLX SVN

Gains From Trade 1.05 1.075

Gains From Trade 1.05 1.075

BGR LTU SVN

.9

2006 SVK

SVK

SVKBLX

NLD CZE BAL TWNAUT

.75 .8 .85 Self Trade Share

2005

1.1

2004

IRL

SVN BAL NLD AUT CZE

1

1.025

1.025

IDN DEUESP FIN POL KOR FRARUS GBR MEX TUR ITA

LTU

Gains From Trade 1.05 1.075

DNK ROU CAN PRT TWN GRC SWE

SVK

1.025

BGR SVN NLD BAL CZEAUT

HUN

IRL

Gains From Trade 1.05 1.075

Gains From Trade 1.05 1.075

BLX SVK LTU

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

.6

.65

.7

.75 .8 .85 Self Trade Share

P 1−ρs P P 1 ρ Notes: Black data: GTdCN = ( s πsdd ( o πsod ) s )− θ . Red line: GTdCES = ( s πsdd )−1/ε for ε = 5.

49

.9

.95

1

Figure H.2: Gains from Trade, percentage changes, by year. 1997

LTU

40

1996 40

40

1995

IND

ESP POL ITA FRA KOR DEU GBR IDN

SVK

HUN AUT CAN CZE TWN SWEFIN

BRA

CHN AUS USA

BGR BLX BAL

GRC RUS ROU TUR

SVN NLD

JPN IND

DNK PRT

ESP BRA POLITA FRA KOR HUN AUT DEUIDN CAN CHN FINGBR CZE AUS USA TWN SWE MEX

SVK IRL

−20

MEX

−20

IRL

JPN

TUR

Percent Difference in Gains From Trade −10 0 10 20 30

ROU RUS GRC

DNK PRT

NLD SVN

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

DNK PRT

ROU RUS GRC TUR

IND

ESP POL KORFRAITA DEU GBR AUS FIN CZE SWE MEX TWN AUT CAN

JPN

BRA

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

IND IDN RUS ROU

BGR BLX

DNK PRT

SVN BAL NLD

ESP ITA POL FRA DEU KOR GBR AUS FIN

CAN AUT

CZE SWE HUN

IRL

JPN

TUR

GRC

SVK

BRA

CHN USA

MEX

TWN

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

SWE TWN

AUS

BRA USA

FIN CHN

MEX

HUN

.6

.65

.7

.75 .8 .85 Self Trade Share

IDN RUS TUR

ROU BLX

PRT GRC

SVN NLD BAL

SVK

AUTDNK

CZE

CAN

SWE

JPN

ESP ITA POL FRA KOR GBR DEU AUS

BRA USA

FIN MEX

TWN

HUN

CHN IRL

.9

.95

1

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

ROU NLD

TUR RUS

PRT GRC

SVN

IND

JPN

BRA CAN ESP ITA FRA BAL AUT DNK POL GBR USA DEU KOR AUS FIN CZE SWE MEX TWN

SVK

HUN CHN

.65

.7

HUN IRL

BGR RUS ROU TUR NLD PRT GRC SVN SVK BAL DNK ESP ITA AUT CAN FRA POL KOR DEU GBR AUS CZE FIN SWE MEX TWN

.75 .8 .85 Self Trade Share

.9

.95

1

JPN

BRA USA CHN

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

LTUBGR IDN TUR RUS

ROU BLX

GRC PRT

SVN NLD BAL

SVK

AUT DNK

CAN POL

ESP ITA FRA

GBR DEUKOR FIN SWE MEX

CZE

IND JPN

BRA USA

AUS

TWN HUN CHN

IRL

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

40

2006

BGR

LTU

NLD

BLX SVN

ROU BAL AUTDNK

SVK

CZE TWN

JPN GRCIDN TUR PRT RUS ESP ITA FRA CAN IND USA GBR BRA POL KOR DEU AUS

SWE FIN MEX

HUN CHN IRL

−20

−20

IRL

.6

BLX

Percent Difference in Gains From Trade −10 0 10 20 30

IDN

1

LTU

BGR NLD

TUR JPN IDN RUS ESP IND ITA FRA CAN KOR GBR POL USABRA DEU AUS FIN GRC

PRT

SVN BLX

BAL AUT DNK

SVK TWN

ROU

SWE

HUN

CZE

MEX CHN

IRL

−20

LTU

.95

IND

.6

1

40 Percent Difference in Gains From Trade −10 0 10 20 30

Percent Difference in Gains From Trade −10 0 10 20 30

BGR

.9

IDN

2005

40

2004

BLX

.75 .8 .85 Self Trade Share

40 IND BGR LTU

−20

−20

IRL

.7

LTU

Percent Difference in Gains From Trade −10 0 10 20 30

ESP ITA KOR FRA POL

DEU GBR CZE

.65

−20

GRC CAN AUT DNK BAL

JPN

USA

2003

40 TUR RUS

PRT

SVNNLD

SVK

Percent Difference in Gains From Trade −10 0 10 20 30

Percent Difference in Gains From Trade −10 0 10 20 30

IND IDN

ROU BLX

.6

2002

40

2001

LTU BGR

JPN

BRA CHN

40 LTU

−20

CHN USA

−20

IRL

IRL

Percent Difference in Gains From Trade −10 0 10 20 30

BGR BLX

HUN

ESP ITA POLFRA IDN AUT KOR DEU CAN GBR FIN CZE AUS SWE MEX HUN TWN

SVK

−20

IDN

SVK

RUS GRC TUR

DNK PRT

SVN NLD

2000

40 Percent Difference in Gains From Trade −10 0 10 20 30

Percent Difference in Gains From Trade −10 0 10 20 30

LTU

IND

ROU BAL

1999

40

1998

BAL SVN NLD

BGR BLX

−20

BGR

BAL

BLX

Percent Difference in Gains From Trade −10 0 10 20 30

Percent Difference in Gains From Trade −10 0 10 20 30

LTU LTU

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

P 1−ρs P P 1 ρ Notes: Black data: GTdCN = ( s πsdd ( o πsod ) s )− θ . Red line: GTdCES = ( s πsdd )−1/ε for ε = 5. Percent difference calculated as 100 ×

GTd −GTdACR . GTdACR −1

50

Figure H.3: RCA-Weighted Correlation Index, by year. 1995

GBR FRA KOR ITA ESP

NLD SVK CZE HUN

BAL

AUS POL MEXIDN CHN

PRT

GRC ROU TUR

BGR

LTU

BRA

IND

AUT TWN DNK

SVN BLX

USA

GBR FRA KOR ITA ESP

CZE CAN SVK NLD BAL HUN

PRT MEX POL AUS IDN ROUGRC TURRUS

BGR

BRA CHN IND

LTU

.15

.15

RUS

IRL

RCA−Weighted Correlation Index .25 .35 .45

USA

AUT TWNDNK CAN

JPN

DEU

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

USA

GBR

DNK CZE CAN

FRA ITA

KOR ESP POL PRT MEX

GRC RUS ROU TUR

IDN LTU

AUS

BRA CHN IND

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

JPN

AUT TWN SVN

GBR FRA KOR ITA ESP

DNK CAN CZE

HUN BAL SVK NLD

BLX

POL PRT MEX

AUS

RUS GRC ROU IDN

LTU

TUR

USA

CHN BRA

IND

BGR

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

ROU GRC

AUS CHN BRA RUS

IDN

IND

TUR

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

HUN

JPN

SVNCZE BAL

SVK BLX

ITA

CAN

ESP POL

NLD PRT

AUS CHN BRA

MEX

ROU GRC

LTU

USA

GBR KOR FRA

DNK

RUS IDN

BGR

.6

.65

.7

TUR

.75 .8 .85 Self Trade Share

IND

.9

.95

PRT ROU

CHN AUS MEX

GRC

BRA

IDN RUS

BGR

IND

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

IDN

BRA CHN

RUS IND

TUR

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

DEU IRL

TWN AUT HUN SVNCZE DNK BAL SVK

JPN

KOR GBR FRA

USA

ITA BLX

CAN POL

NLD

PRT

ESP CHN AUS MEX

BRA

ROU

LTU

GRC

RUS IDN

BGR

TUR

IND

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

.55

2006

IRL SVK

DEU TWNAUT HUN CZE SVN BAL DNK BLX

NLD

JPN

KOR GBR FRA ITA POL ESP CAN PRT MEX

USA

CHN AUS

BRA

ROU GRC

LTU

IDN

BGR

RUS IND TUR

.15

.15

TUR

AUS

ROU GRC

SWE FIN DEU

IRL

JPN

CZE AUT TWN HUN SVK

KOR GBR FRA ITA POL CAN ESP

SVN BALDNK

BLX

NLD

PRT ROU LTU

MEX

USA CHN AUS BRA

GRC IDNRUS IND TUR

BGR

.15

CAN POL

USA

ITA ESP POL MEX

BGR

RCA−Weighted Correlation Index .25 .35 .45

RCA−Weighted Correlation Index .25 .35 .45

GBR FRA ITA ESP

DNK CAN

LTU

.6

1

.55

.55 RCA−Weighted Correlation Index .25 .35 .45

KOR DNK

NLD

LTU

JPN

USA

GBR KORFRA

PRT

SWE FIN

DEU

BLX

BLX

SVN CZE BAL SVK NLD

2005

SWE FIN TWNAUT CZE HUN SVN BAL SVK

HUN

SWE FIN

DEU IRL

2004

IRL

1

JPN

TWN AUT

FIN

TWN AUT

.15

.15

BGR

.95

DEU

IRL

RCA−Weighted Correlation Index .25 .35 .45

ESP POL MEX

.9

.15

USA

ITA

CAN

PRT

.6

.75 .8 .85 Self Trade Share

.55

.55 JPN

GBR FRA KOR

NLD

LTU

RCA−Weighted Correlation Index .25 .35 .45

AUT TWN BAL SVN CZE DNK

SVK BLX

.7

2003

SWE

FIN DEU

HUN

.65

2002

.55 RCA−Weighted Correlation Index .25 .35 .45

SWE

.6

SWE FIN

DEU

2001

IRL

IND

BGR

FIN

IRL

.15

.15

BGR

CHN

TURRUS ROUGRC LTU

RCA−Weighted Correlation Index .25 .35 .45

AUT TWN

JPN

BRA

AUS IDN

.15

HUN NLD BLXBALSVK

POL PRT MEX

.55

.55 DEU

JPN USA

GBR FRA ITA KOR ESP

2000

SWE

FIN

RCA−Weighted Correlation Index .25 .35 .45

RCA−Weighted Correlation Index .25 .35 .45

SWE

SVN

AUT TWN DNK CZECAN HUN SVK BAL NLD BLX SVN

1999

.55

1998

IRL

DEU IRL

.15

BLX

RCA−Weighted Correlation Index .25 .35 .45

RCA−Weighted Correlation Index .25 .35 .45

JPN

DEU SVN

SWE FIN

SWE FIN

SWE FIN

IRL

.55

1997

.55

.55

1996

.6

.65

.7

.75 .8 .85 Self Trade Share

.9

.95

1

.6

.65

Notes: Revealed-Comparative-Advantage (RCA)-weighted correlation index: ρRCA = dt

51

.7

P

s

.75 .8 .85 Self Trade Share

sdt ρs PRCA RCAsdt . s

.9

.95

1

1995

2000 Year

2005

1995

2000 Year

2005 1995

Slovenia

1995

2000 Year

2000 Year

2005

52 2005 1995

Poland

1995

Sweden

1995 2000 Year

2000 Year

2000 Year 2005

2005

2005

2005 .5

Italy 2000 Year

RCA−Weighted Correlation Index .3 .35 .4 .45

1995 .25

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45

.5

.5

2005

.25

.25

Great Britain 2000 Year

.5

.5

1995 .25

.25

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45

.5

.5

.5

.5

.5

.5

2005

RCA−Weighted Correlation Index .3 .35 .4 .45

2005 RCA−Weighted Correlation Index .3 .35 .4 .45

.25

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45

Czech Rep

2000 Year

.25

Netherlands 2000 Year

1995

.5

1995 2005

.25

Ireland 2000 Year

.5

1995 2005

RCA−Weighted Correlation Index .3 .35 .4 .45

France 2000 Year

.25

.5

1995

2005

RCA−Weighted Correlation Index .3 .35 .4 .45

2005 RCA−Weighted Correlation Index .3 .35 .4 .45

.25

.25

.25

.25

.25

.25

.25

.25

.25

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45

.5

.5

.5

.5

.5

.5

Baltic Rep

.25

Slovakia 2000 Year 2005 .25

.5

.5

.5

China 2000 Year

.5

1995 1995

RCA−Weighted Correlation Index .3 .35 .4 .45

Mexico 2000 Year .5

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45

Austria

.25

1995 2005

RCA−Weighted Correlation Index .3 .35 .4 .45

India 2000 Year

.25

1995 2005

.5

.25

.25

.25

Finland 2000 Year

RCA−Weighted Correlation Index .3 .35 .4 .45

.5

.5

.5

1995 2005

.25

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45

Canada 2000 Year

.5

2005 .25

.25

.25

1995

RCA−Weighted Correlation Index .3 .35 .4 .45

2000 Year 2005

.5

.5

.5

Australia

.25

1995 2000 Year 2005

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45 1995 2000 Year 2005

.25

.25

.25 1995 2000 Year 2005

.5

.5

.5 1995 2000 Year

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45

RCA−Weighted Correlation Index .3 .35 .4 .45 1995

.25

.25

.25

Figure H.4: Evolution of RCA-Weighted Correlation Index, by country. Bulgaria Benelux

1995

Germany

1995

Greece

1995

Japan

1995

Portugal

1995

Turkey

1995

2000 Year

2000 Year

2000 Year

2000 Year

2000 Year

2000 Year

Brazil

2005

2005

1995

Denmark

2005 1995

Hungary

2005 1995

Korea

2005 1995

Romania

2005 1995

Taiwan

1995

2000 Year

2000 Year

2000 Year

2000 Year

2000 Year

2000 Year

2005

Spain

2005

Indonesia

2005

Lithuania

2005

Russia

2005

United States

2005

P PRCAsdt Notes: Revealed-Comparative-Advantage (RCA)-weighted correlation index: ρRCA = dt s ρs s RCAsdt . Baltic Republics are Estonia, Latvia, and Lithuania; Benelux is Belgium, Luxembourg, and Netherlands.

Figure H.5: RCA-Weighted Correlation Index and Self Trade Shares, by country.

.76

.72

.74

1998

.88

.89

.92

.94

.62

.64

1997 1996 1995

.66 Self Trade Share

.68

.7

.84

.85

.86

.87

2004

2002

2003

.75

.76

.77

.65

.7

.75 Self Trade Share

.8

2001 2000

.7

.72

.74 Self Trade Share

.5 .84

2003 2002

1999 1998 1997 1995 1996

.76

.86

.88

2005 2004

2003

1998 1997 1999 1995

.88 Self Trade Share

2003

1996

.89

.9

2001 19981999

1997

1996 1995

.8

.82

.84 .86 Self Trade Share

.88

2005

.93

.9

2006

2005

1999 1998 200020012004 2002 2003

1996

.78

.8

.82

.84

Self Trade Share

2004

.94

2006

.81

1995

.96

.97

1997 2006

.87

2004

2005

.88

1997

1996 1995

.83

.5 RCA−Weighted Correlation Index .25 .3 .35 .4 .45

1997 1996 1995

.7

.75

.8

1995 1999

.9

.91

1998

1996

1997

.87 Self Trade Share

.88

1995

.89

1996 1997

1995 2004

2005 2001 2000

1998

.82

2006 2002

2003 1999

.84

.86 Self Trade Share

.88

.9

Lithuania

2005

2006 2004

2003

2002

2001

2000

1996

1999

1997 1998

1995

.85

.855 .86 Self Trade Share

.865

2006

2003 2002 2001

2005

2004 1999

2000 1998

1997

.87

.7

1996

1995

.72 Self Trade Share

.74

.76

Russia

2006 2005 2004

2003 2002 2001

2000

1996 1997 1999 1998

1995

.78

.8

.82 Self Trade Share

.84

2000

1999

20022003

2001

2006 2004 2005 1998

1997 1996

1995

.86

.87

Taiwan

1996 1998

.95

Indonesia

1998

.845

.84

20012002 2000 2003

.89 Self Trade Share

.86

Romania

2003

.82 Self Trade Share

.85

Korea

.95 Self Trade Share

20052004 2002 2001 1999 1998

2000

2005 2004 20021999 2003

Self Trade Share

2003 20001996 20011997 2002 1998 1999

.945

.5 .82

1999

Turkey 1997 1995

.8

2003 2002

2000 2001

Portugal

2002 2000

.78 Self Trade Share

2005 2004

2006

.65

.5 2006

.5 2004

1996 1995

.5 2004 2002

.2

1995

2005

.2

1997 1996

2006

.82

Sweden

.5 RCA−Weighted Correlation Index .25 .3 .35 .4 .45

.5 RCA−Weighted Correlation Index .25 .3 .35 .4 .45

1999 1998

.2

2000

1997

.2

1998 2005 2001 1996 1995

Slovenia

2003 2002

.87

Self Trade Share

2006

2001

2005 2001 2000

.76

Japan

.5 .74

Slovakia 2004

.86

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

1999 1997

2006

Self Trade Share

2005

2006

.74

Self Trade Share

.2

2000

.2

.2

1995

.868

Poland

.5 19972002 1996

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

2001 2003

1999 1998

.866

2006

2003 1998

1998

1999

2000

.2

2005 2004

Netherlands

.5

Mexico

2006 2005 2004

.862 .864 Self Trade Share

.2

1999 2002

Self Trade Share

2000

.86

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

.9

.858

.5 2000 2001

2004 2005 2002 2003

2001

.935 .94 Self Trade Share

2006 2001

2000

Hungary

2006

Italy

.5 .88

1998 2003 1999

2002

2006

.2

.2

1999 20002001 2003 2002

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

19981996 1997 1995

2004

2004

.88

Greece

1995

Ireland

.5 RCA−Weighted Correlation Index .25 .3 .35 .4 .45

2005

2005 1997

2000 2001

Self Trade Share

India

2006

2006 1996

.86

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

19961995

1997

.84 Self Trade Share

.5

.87

.82

.2

2003 1999 1998

1998 1995 1997 1999 1996

2003

.2

.86

.8

.2

2002 2004

2005 2001

2004 2002 2001 2000

.5

.85

.8

2005

.2

.84

.78

2006

.88

.89 Self Trade Share

.9

.91

United States

.5

.82 .83 Self Trade Share

.76 Self Trade Share

.2

2006 2000

1996 1995

.2

.81

.74

Great Britain

.2

RCA−Weighted Correlation Index .25 .3 .35 .4 .45 .2 .8

.72

France

2001 2003 2000 2004 2002 1998 1999 1997 1996 1995

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

.5

.94

.5

2005

.93

.5

Finland 2006

.91 .92 Self Trade Share

.93

Spain

2006

2005 2004

2003

2002

2000

20011999 1998 1997

1996 1995

.2

.9

19991998 1997

.5

.89

2004 2003 2002 2001 2000

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

.83

2005

.925

Denmark

.5

.82

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

.81 Self Trade Share

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

.8

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

.79

1996

1995

.72

.2

1999 1997 1996

1998 1997

1999

.71

.2

2001 2000 1995

2003 2002 2001 2000

.7 Self Trade Share

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

2002

.69

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

2003

2005 2004

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

2005 2004

.8

.2

2006

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

2006

.2

2002

2006

.2

1995 1996 2004 2005 2003

.2

2001

1997

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

2006

1998 1999 2000

.78

Germany

.5

.5

Czech Rep

.76 Self Trade Share

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

.75

.5

.74 Self Trade Share

.2

.73

.2

.2 .72

.5

.82

1998

.2

.8

China

.5

Canada

.78 Self Trade Share

1995 1996 1997 1999

.5

.76

2005 2006 2000

.2

.74

2003

.5

.91

2004 2002

2001

2000 2006

2004

2005

2003

1998 2001 1999 2002 1997 1996 1995

.2

.905

1998

1997

.5

.9 Self Trade Share

1995

.5

.895

.2

.2

.2 .89

2002

2000 2001

1999

1996

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

2003

1995 1998 1996 1999

2003

1997

.2

2005

2004 2006

2004 2002 2005

2001

2006 2000

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

1999

1995

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

2000

Brazil

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

2002

1996

.5

2001 2004

2005 2003

2006

1998 1997

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

1995

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

1996

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

1997 1998

1999

1997

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

1995 1996

19991998

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

2003

2003 2002 2000

Benelux

.5

2000

2004 2001

2004 2001

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

2002

Bulgaria

.5

Baltic Rep

.5 2006 2005

20062005

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

.5

Austria

RCA−Weighted Correlation Index .25 .3 .35 .4 .45

Australia

.72

.74

.76 Self Trade Share

.78

.8

.92

.925

.93 Self Trade Share

.935

.94

P PRCAsdt Notes: Revealed-Comparative-Advantage (RCA)-weighted correlation index: ρRCA = dt s ρs s RCAsdt . Baltic Republics are Estonia, Latvia, and Lithuania; Benelux is Belgium, Luxembourg, and Netherlands.

53