Slicing the Pie: Quantifying the Aggregate and Distributional Effects of Trade

Transcription

1 Slicing the Pie: Quantifying the Aggregate and Distributional Effects of Trade Simon Galle BI Norwegian Business School Moises Yi US Census Bureau Andrés Rodríguez-Clare UC Berkeley & NBER June 2017 Preliminary and incomplete - Please do not circulate Abstract This paper develops a framework to analyze the effect of trade on aggregate welfare as well as the distribution of this aggregate effect across different groups of workers. The framework combines a multi-sector gravity model of trade with a Roy-type model of the allocation of workers across sectors. By opening to trade, a country reaps aggregate gains by specializing according to its comparative advantage, but the distribution of these gains is unequal as labor demand increases (decreases) for groups of workers specialized in export-oriented (import-oriented) sectors. Generalizing the specific-factors intuition to a setting with labor reallocation, the model predicts an unequal distribution of the gains from trade while maintaining analytical tractability for any number of groups and countries. We bring the model to the data using China s growth as a trade shock, where we define groups on the basis of geography and education. We then structurally estimate the model s parameter that governs the distributional effects of the model. Counterfactual simulations show that this parameter implies a coefficient of variation for the group-level welfare effects from the China shock of 51.4%. Furthermore, the inequality-adjusted welfare effect of this shock, which captures the full cross-group distribution of welfare changes in one measure, is smaller than the standard effect. We are grateful to seminar participants at BI, Columbia, Edinburgh, Fed Board of Governors, LSE, Mannheim, Oslo, Paris-Sud, Rochester, Stockholm, UC Berkeley, UC Merced, USC and the World Bank for helpful comments and suggestions. We also benefited from useful comments from Dominick Bartelme, Arnaud Costinot, Kerem Coşar, Pablo Fajgelbaum, Patrick Kline, Stephen Redding and Jonathan Vogel. Daniel Haanwinckel Junqueira, Yusuf Mercan, Preston Mui, Mathieu Pedemonte and Román Zárate provided excellent research assistance. We are grateful for financial support from the National Science Foundation and from the Clausen Center for International Business and Policy. All errors are our own.

2 SLICING THE PIE 1 1 Introduction Since Eaton and Kortum (2002) s seminal work, gravity models have become the workhorse models for examining the aggregate welfare effects of trade. The gravity structure is appealing as it nests a wide range of models with different microfoundations (Arkolakis et al. (2012) - henceforth ACR; Costinot and Rodríguez-Clare (2014)), and fits well with empirical reduced-form estimates of the gains from trade (see e.g. Donaldson (2012)). But in spite of their empirical and theoretical prominence, gravity models remain silent on the associated distributional effects of trade. 1 This shortcoming of the existing gravity literature stands in stark contrast with vast empirical evidence: as we discuss below, a large body of empirical studies demonstrates sharply disparate effects of trade on various groups of agents. In this paper, we present an integrated ACR-type gravity framework to quantify the effect of trade on the size of the pie, and on the way it is sliced and divided across different groups of workers. In principle, these worker groups can be defined based on several dimensions (e.g. age, gender, location), and in our main empirical application for the United States, we choose to define groups based on education and geographic location (i.e., commuting zone) This way, our theoretical framework provides a general equilibrium structure for the empirical literature on the distributional effects of trade across local labor markets (e.g. Autor et al. (2013) - ADH). The distributional effects in our model arise from a Roy (1951) structure of the labor market. Workers differ in their pattern of comparative advantage across sectors, and therefore sector-specific import-competition shocks will generate distributional effects. At the heart of the analysis is a simple expression for the change in real income due to a foreign shock (i.e. a change in trade costs or foreign technology levels) for group g in country i, Ŵ ig = s ˆλ β is/θ s iis }{{} Multi sector ACR s ˆπ β is/κ ig igs }{{} Group level Roy, (1) where we use hat change notation ˆx x /x. The first term on the right-hand side cap- 1 Notable exceptions are Fajgelbaum and Khandelwal (2016), which studies the differential effect of trade on rich and poor households, and Burstein and Vogel (2016), which analyzes the effect of trade on the skill premium. Both these theoretical frameworks are not nested by the ACR structure.

3 2 GALLE - RODRíGUEZ-CLARE - YI tures the change in prices given wages and is standard in the literature. As in ACR, this term is a geometric average of the changes in the sector-level domestic trade shares elevated to the negative of the inverse of the trade elasticity, 1/θs ˆλ iis. The second term captures the effect on the real income of group g caused by the movement in sector-level wages. It is given by a geometric average of changes in sectoral employment shares elevated to the negative of the inverse of the labor-supply elasticity to each sector, ˆπ 1/κ igs. In our Roy model, the elasticity of labor supply to each sector, κ ig, is equal to the shape parameter of the Fréchet distribution that we assume governs the productivity levels that each worker draws for each sector. For both the first and second terms in Equation (1), the averaging weights are the Cobb-Douglas expenditure shares β is. This framework extends the existing analysis of Ricardian sector-level comparative advantage in Costinot et al. (2012) - henceforth CDK - to incorporate an upward-sloping labor supply curve to each sector. 2 In fact, as κ ig, our model collapses to CDK. With a finite κ ig, workers are heterogeneous in their sector-level productivities, so trade shocks that lead to the expansion of some sectors and the contraction of others have effects that vary across workers. 3 The intuition here is similar to the one in the specificfactors model. In fact, as κ ig are perfectly immobile across sectors. 4 1 our model is equivalent to one in which workers The fact that our model nests CDK and the specific-factors model as κ ig moves from infinity to one implies that κ ig is a key parameter in the determination of the welfare effects of trade. Indeed, as we can see from Equation (1), given changes in sectoral employment shares, ˆπ igs, a lower κ ig implies a higher between-group variance in the welfare effects of trade shocks. The case κ ig 1 2 CDK extend the seminal Eaton and Kortum (2002) framework to a multi-sector environment. As shown in ACR, a multi-sector version of the Armington model would be a workable substitute for the CDK-side of the model. The Krugman (1980) model or the Melitz (2003) model with a Pareto distribution (as in Chaney (2008)) would also work, though these models would introduce extra terms because of entry effects. 3 This paper belongs to the Ricardian revival in international trade, surveyed by Costinot and Vogel (2014). Their terminology of Ricardo-Roy models succinctly summarizes the framework of our model: Ricardo on the trade-side and Roy on the labor-side, capturing the source of comparative advantage at the country and worker-level respectively. 4 For the specific-factors model (i.e., the model in which labor is sector specific), the formula in Equation (1) is valid for κ ig 1 if we define π igs as the share of earnings of group g that comes from sector s. In the Roy-Fréchet model with κ > 1, thinking of π igs as employment shares or earning shares is equivalent. However, for κ ig 1, the equivalence between our model and the specific-factors model does not extend to the number of workers across sectors in particular, for κ ig 1 the elasticity of labor supply to any particular sector with respect to the wage in that sector goes to 1 in our model but is zero in the specific-factors model.

4 SLICING THE PIE 3 is noteworthy because then the group-level change in welfare is equal to the aggregate welfare effect multiplied by the inverse of the change in a Bartik-style index of grouplevel import competition; a relationship that we will examine in the empirical section. The term labeled Group-level Roy in Equation (1) is equal to the change in the degree of specialization of each group elevated to the power 1/κ ig, Ŝ1/κ ig, with the grouplevel degree of specialization S ig defined as the exponential of the Kullback-Leibler divergence of the employment shares (π igs, s = 1,..., S ) from the expenditure shares (β is, s = 1,..., S ). 5 Thus, shocks that reduce a group s specialization have less beneficial welfare effects. As an example, the removal of import quotas on apparel imports from China would likely reduce the degree of specialization for a US group that specializes in apparel, exerting downward pressure on the group s welfare. Moreover, since the United States is a net importer of apparel, this group would gain from an increase in specialization if the US were to move to autarky. This formalizes the idea that groups that are specialized in import-competing sectors gain less from trade. We use the concept of inequality-adjusted welfare in Jones and Klenow (2016) to measure the aggregate welfare effect of a shock that has heterogeneous effects across groups when there is no compensation for losers. 6 One interpretation of this measure is that it captures the utility of a risk-averse agent who is behind the veil of ignorance regarding the group to which she belongs. Loosely speaking, if a shock increases inequality then the inequality-adjusted welfare effect is less favorable than the one implied by the standard aggregation, which corresponds to our measure when the coefficient of inequality aversion goes to zero. Our methodology can be applied to several different categorizations of workers into groups (e.g., education, age or gender), and our empirical application categorizes workers by geographic region and education. The geographic categorization is motivated by a growing body of empirical work documenting substantial variation in local labor-market outcomes in response to national-level trade shocks (ADH, Dauth et al. (2014), Dix-Carneiro and Kovak (2016), Hakobyan and McLaren (2016), Kovak (2013), Yi et al. (2016), Topalova (2010)). 7 5 Formally, S ig exp D KL(π ig β i ) exp s βis ln(βis/πigs). 6 Our inequality-adjusted welfare measure is closely related to the Atkinson (1970) inequality index, which is also employed in recent work by Antras et al. (2016), Carrère et al. (2015). 7 Autor et al. (2016) and Dippel et al. (2015) demonstrate that increased local import competition also has substantial political-economy consequences.

5 4 GALLE - RODRíGUEZ-CLARE - YI Our model provides a tractable general-equilibrium framework to analyze this heterogeneous impact of trade shocks, which makes our paper a structural complement to the existing set of empirical papers. 8 We demonstrate the empirical relevance and validity of our model with data on the US, where we split each of 722 commuting zones into groups of workers with or without a minimum of college education. On this data, we examine if the impact of an ADH-style China shock is in line with the model s theoretical predictions. We first demonstrate that trade shocks indeed lead to labor reallocation across sectors at the regional level, as implied by the model. Second, we show that our model s Bartik-style measure for changes in regional import-competition effectively captures the distributional effects of the China shock across groups. Finally, we exploit the relationship between sectoral reallocation and group-level income changes to structurally estimate κ ig, which results in a preferred point estimate of κ ig = 2.2 for groups in the US. Given this value for κ ig, we perform counterfactual analysis using the approach proposed by Dekle et al. (2008). Our first exercise is to compute the welfare effects of the rise of China for each group and for the country as a whole (with the standard aggregation as the population-weighted mean of group-level gains), as well as the inequalityadjusted welfare effects. As expected, the dispersion of the welfare effects is higher for low values of κ ig. Importantly, we demonstrate that the Bartik-style index of regionlevel import competition, which was theoretically derived for the case κ ig 1, continues to perfectly predict the ranking across groups in the gains from trade for κ ig > 1. We also find that the inequality-adjusted welfare effects from the rise of China are lower than the aggregate gains, as income levels become more dispersed due to the China shock. In our second exercise, we focus on the gains from trade and their distribution across groups. 9 We confirm that the distributional impact of trade falls with κ ig, and so do the aggregate gains from trade. For this counterfactual scenario, the inequality- 8 In the theory section of his paper, Kovak (2013) proposes a small-economy model to understand, up to a first-order approximation, the differential effect of tariff changes across regions. Compared to that, ours is a general equilibrium model for the world economy that connects to the gravity literature and yields tractable expressions for aggregate and group-level welfare effects in terms of changes in trade and employment shares, which in turn can be computed for counterfactual shocks using the techniques in Dekle et al. (2008). 9 As in ACR, the gains from trade are computed as the negative of the proportional welfare change caused by the country moving to autarky.

6 SLICING THE PIE 5 adjusted welfare gain again tends to be lower than the aggregate gain. This is a reflection of a negative cross-group correlation in the data between earnings per worker and import competition (in manufacturing). These results suggest that trade is pro-rich in the United States, at least from our between-group distributional perspective. Hence, both international trade in general as well as the recent exposure to the rise of China are found to be pro rich in our simulations. Our paper is related to several research areas in international trade. In addition to the above-mentioned research on trade and local labor markets, there is a large theoretical and empirical literature on the unequal effects of trade on labor-market outcomes see for example Autor et al. (2014), Burstein and Vogel (2016), Costinot and Vogel (2010), Dauth et al. (2016), Helpman et al. (2012), Krishna et al. (2012). A literature focusing specifically on the effect of trade shocks on the reallocation of workers across sectors finds significant effects for developed countries (Artuç et al. 2010, Revenga 1992), 10 which is the focus of our analysis. 11 Artuç et al. (2010) and Dix-Carneiro (2014) use a Roy model of the allocation of workers across sectors to offer a structural analysis of the dynamic adjustment to trade liberalization in a small economy. We complement these papers by linking the Roy model for the labor market with a gravity model of trade and by using the resulting framework to provide a simple and transparent way to quantify the aggregate and distributional welfare effects of trade. 12 Other structural analyses of trade liberalization and labor market adjustments are Coşar (2013), Coşar et al. (2013), Kambourov (2009) and Ritter (2012). 13 While all these papers focus on the differential impact of trade through the earnings channel, another set of papers focuses on the expenditure channel, as in Atkin and Donaldson (2015), Faber (2014), Fajgelbaum and Khandelwal (2016) 10 See also Gourinchas (1999) and Kline (2008) for evidence of substantial reallocation in response to sectoral (but not trade) price shocks. 11 In contrast, the evidence for developing countries suggests that reallocation in response to trade shocks is at best very sluggish see Goldberg et al. (2007), Menezes-Filho and Muendler (2011)), and Dix-Carneiro (2014). 12 Adão (2015) and Lee (2016) develop models similar to ours, where the former focuses on relaxing the parametric assumptions on the distribution of worker productivity and the latter puts the emphasis on the quantification of trade s impact on inequality across multiple countries and types of worker groups. 13 There is also a broad literature on the impact of trade on poverty and the income distribution using a Computable General Equilibrium (CGE) methodology. Savard (2003) offers an overview of the different approaches for counterfactual analysis of the income distribution within this CGE literature, while Cockburn et al. (2008) integrate multiple chapters on methodology and empirical findings of the CGE approach into a book-length discussion.

7 6 GALLE - RODRíGUEZ-CLARE - YI and Porto (2006). 14 Our paper also relates to the renewed attention to Roy models in various fields of economics see for example Lagakos and Waugh (2013) for a recent application to development, and Young (2014) and Hsieh et al. (2013) for the productivity literature. Closer to our paper, Burstein et al. (2016) utilize a Roy model with a Fréchet distribution of worker abilities across occupations to decompose the changes in between-group earnings inequality into various channels, focusing on the role of technological change in explaining the evolution of the skill premium. Finally, it is worth commenting on how our model relates to the one in ADH. They present a multi-sector gravity model of trade with homogeneous and perfectly mobile workers across sectors (as in CDK), but with each local economy (our groups) modeled as a separate economy. In this case all the variation in the effects of a shock across regions arises because of different terms of trade effects. In our model technologies are national and there are no trade costs among groups within countries, so terms of trade are the same for all groups. Instead, heterogeneity of workers implies that some groups of workers are more closely attached to some sectors, and it is this that generates variation in the effect of trade shocks across groups. The rest of this paper is structured as follows. Section 2 describes the baseline model. The data is described in Section 3, and Section 4 discusses the empirical findings for the baseline model, including a structural estimation of κ ig and a validation of the model s Bartik-style measure for import competition. Then, Section 5 presents our counterfactual analysis of the rise of China and a US return to autarky. The final sections of the paper consider extensions of the baseline model. Section 6 adds intermediate goods to the model, and Section 7 introduces within-country trade costs. Section 8 concludes. 2 Theory We present a multi-sector, multi-country, Ricardian model of trade with heterogeneous workers. There are N countries and S sectors. Each sector is modeled as in Eaton and Kortum (2002) - henceforth EK; there is a continuum of goods, preferences across 14 Heins (2016) also studies the unequal gains from trade through the expenditure channel, while at the same time endogenizing the quality-differentiation decision on the supply side.

8 SLICING THE PIE 7 goods within a sector s are CES with elasticity of substitution σ s, and technologies have constant returns to scale with productivities that are distributed Fréchet with shape parameter θ s > σ s 1 and level parameters T is in country i and sector s. Preferences across sectors are Cobb-Douglas with shares β is. There are iceberg trade costs τ ijs 1 to export goods in sector s from country i to country j. On the labor side, we assume that there are G i groups of workers in country i. A worker from group g in country i (henceforth simply group ig) has a number of efficiency units Z in sector s drawn from a Fréchet distribution with shape parameter κ ig > 1 and scale parameters (Γ(1 1/κ ig )) κ ig A igs, where Γ(.) is the Gamma function. 15 Thus, workers within each group are ex-ante identical but ex-post heterogeneous due to different ability draws across sectors, as in Roy (1951), while workers across groups also differ in that they draw their abilities from different distributions. The number of workers in a group is fixed and denoted by L ig. In the baseline model labor supply is inelastic workers simply choose the sector to which they supply their entire labor endowment. If κ ig for all ig and A igs = 1 for all igs, the model collapses to the multi-sector EK model developed in CDK. On the other hand, if τ ijs for all j i and G i = 1 then economy i is in autarky and collapses to the Roy model in Lagakos and Waugh (2013) (see also Hsieh et al. (2013)) Equilibrium To determine the equilibrium of the model, it is useful to separate the analysis into two parts: the determination of labor demand in each sector in each country as a function of wages, which comes from the EK part of the model; and the determination of labor supply to each sector in each country as a function of wages, which comes from the Roy part of the model. Since workers are heterogeneous in their sector productivities, the supply of labor 15 This normalization by (Γ(1 1/κ ig)) κ ig allows us later on to take the limit as κ ig 1 without having terms blow up to infinity. 16 There are two sources of comparative advantage in this model: first, as in CDK, differences in T is drive sector-level (Ricardian) comparative advantage; second, differences in A igs lead to factor-endowment driven comparative advantage. Given the nature of our comparative statics exercise, however, the source of comparative advantage will not matter for the results only the actual sector-level specialization as revealed by the trade data will be relevant.

9 8 GALLE - RODRíGUEZ-CLARE - YI to each sector is upward sloping, and hence wages can differ across sectors. However, since technologies are national, wages cannot differ across groups. Let wages per efficiency unit in sector s of country i be denoted by w is. From EK we know that the demand for efficiency units in sector s in country i is 1 λ ijs β js X j, w is j where X j is total expenditure by country j and λ ijs are sectoral trade shares given by λ ijs = T is (τ ijs w is ) θs l T. (2) θs ls (τ ljs w ls ) For future purposes, also note that the price index in sector s in country i is P js = γ 1 s where γ s Γ(1 σs 1 θ s ) 1/(1 σs). ( ) 1/θs T is (τ ijs w is ) θs, (3) i Labor supply is determined by workers choices regarding which sector to work in. Let Z = (Z 1, Z 2,..., Z S ) and let Ω s {Z s.t. w is Z s w ik Z k for all k}. A worker with productivity vector Z in country i will choose sector s iff Z Ω s. Let F ig (z) be the joint probability distribution of Z for workers of group ig. From Lagakos and Waugh (2013) and Hsieh et al. (2013) we know that the share of workers in group ig that choose to work in sector s is where Φ κ ig ig sector s is given by k A igkw κ ig ik.17 π igs df ig (z) = A igsw Ω s Φ κ ig E igs L ig ig κ ig is, (4) In turn, the supply of efficiency units by this group to Ω s z s df ig (z) = Φ ig w is π igs L ig. (5) One implication of this result is that income levels per worker are equalized across sec- 17 This result and the ones below generalize easily to a setting with correlation in workers ability draws across sectors. In this case, the dispersion parameter κ ig is replaced by κ ig/(1 ρ ig), where ρ ig measures the correlation parameter of ability draws across sectors for each worker.

10 SLICING THE PIE 9 tors. That is, for group ig, we have w is E igs π igs L ig = Φ ig. This is a special implication of the Fréchet distribution and it implies that the share of income obtained by workers of group ig in sector s (i.e., w is E igs / w ik E igk ) is also given by π igs. Note also that total income of group ig is Y ig s w ise igs = L ig Φ ig, while total income in country i is Y i g G i Y ig. Combining the supply and demand sides of the economy, the excess demand for efficiency units in sector s of country i is ELD is 1 λ ijs β js X j E igs. (6) w is g G i j Allowing for trade imbalances via transfers as in Dekle et al. (2008), we also have X j = Y j + D j, (7) with j D j = 0. Since λ ijs, Y j and E igs are functions of the whole matrix of wages w {w is }, the system ELD is = 0 for all i and s is a system of equations in w whose solution gives the equilibrium wages for some choice of numeraire. 2.2 Comparative Statics Consider some change in trade costs or technology parameters. We proceed as in Dekle et al. (2008) and solve for the proportional change in the endogenous variables. Formally, using notation ˆx x /x, we consider shocks ˆτ ijs for i j, ˆDj, Â igs and ˆT is. The counterfactual equilibrium entails ELD is = 0 for all i, s. Noting that w is E igs = ˆπ igsŷigπ igs Y ig, equation ELD is = 0 can be written as ˆλ ijs λ ijs β js Ŷ jg Y jg + ˆD j D j = ˆπ igs Ŷ ig π igs Y ig (8) j g G j g Gi

11 10 GALLE - RODRíGUEZ-CLARE - YI with Ŷ ig = ( k π igk  igk ŵ κ ig ik ) 1/κig, (9) ˆλ ijs = ˆT is (ˆτ ijs ŵ is ) θs k λ kjs ˆT, (10) θs ks (ˆτ kjs ŵ ks ) and ˆπ igs =  igs ŵ κ ig is k π igkâigkŵ κ ig ik. (11) Given values for parameters θ s and κ ig ; data on income levels, Y ig, trade imbalances, D j, trade shares, λ ijs, expenditure shares, β is, labor allocation shares π igs, and labor endowments, L ig ; and the shocks to trade costs, ˆτ ijs, trade imbalances, ˆDj, and productivity levels,  igs and ˆT is, we can solve for changes in wages, ŵ is, from the system of equations associated with (8)-(11), and then solve for all other relevant changes, including changes in trade shares using (10) and changes in employment shares using (11). 2.3 Group-Level Welfare Effects Our measure of welfare of individuals in group ig is ex-ante real income, W ig Y ig/l ig P i. We are interested in the change in W ig caused by a shock to trade costs or foreign technology levels, henceforth simply referred to as a foreign shock. Cobb-Douglas preferences imply that Ŵ ig = Ŷig s ˆP β is is. (12) From (3) and (10) and given ˆT is = 1 for all s in domestic country i, we have ˆP is = ŵ isˆλ1/θ s iis while from (9) and (11) we have Ŷig = ŵ isˆπ 1/κ ig igs. Combining these two results with (12) we arrive at the following proposition: Proposition 1 Given some shock to trade costs or foreign technology levels, the ex-ante percentage change in the real wage of group g in country i is given by Ŵ ig = s ˆλ β is/θ s iis s ˆπ β is/κ ig igs. (13) The RHS of the expression in (13) has two components: s ˆλ β is/θ s iis and s ˆπ β is/κ ig igs,

12 SLICING THE PIE 11 with all variation across groups coming from the second term. If κ ig for all g G i then the gains for all groups in country i are equal to ˆλ β is/θ s s iis, which is the multisector formula for the welfare effect of a trade shock in ACR. It is easy to show that the term s s ˆπ β is/κ ig igs ˆλ β is/θ s iis corresponds to the change in real income given wages while the term corresponds to the change in real income for group ig coming exclusively from changes in wages ŵ is for s = 1,..., S. 18 The term s ˆπ β is/κ ig igs is related to the change in the degree of specialization of group ig. We use the Kullback-Leibler (KL) divergence as a way to define the degree of specialization of a group. Formally, the KL divergence of π ig {π ig1, π ig2,..., π igs } from β i {β i1, β i2,..., β is } is given by D KL (π ig β i ) s β is ln(β is /π igs ). Note that if group ig was in full autarky (i.e., not trading with any other group or country) then π igs = β is. Thus, D KL (π ig β i ) is a measure of the degree of specialization as reflected in the divergence of the actual distribution π ig relative to β i. We can now write s ˆπ β is/κ ig igs ( 1 [ = exp DKL (π ig β κ i ) D KL (π ig β i ) ] ). ig This implies that, apart from the common term ˆλ β is/θ s s iis, the welfare effect of a trade shock on a particular group in country i is determined by the change in the degree of specialization of that group as measured by the KL divergence interacted with the degree of heterogeneity in worker productivity across sectors as captured by 1/κ ig. Consider a group ig that happens to have efficiency parameters (A ig1,..., A igs ) that give it a strong comparative advantage in a sector s for which the country as a whole has 18 The result in Proposition 1 can alternatively be derived by first applying the envelope theorem to the consumption and labor allocation problem at the group level, d ln W jg = s π jgsd ln w js i,s β jsλ ijsd ln(w isτ ijs). We can then proceed as in ACR to substitute for d ln w js and d ln(w isτ ijs) in this expression. From the trade side of the model we have d ln(λ ijs/λ jjs) = θs, while from the labor side we have d ln(π jgs/π jgk) = κjg. d ln(w is τ ijs /w js) d ln(w js /w jk) Solving for d ln(w isτ ijs) and d ln w js from these two equations, respectively, and then plugging back into the expression for d ln W jg above yields d ln W jg = [ d ln πjgs s βjs κ jg result in (13). + d ln λ jjs θ s ]. Integration leads to the

13 12 GALLE - RODRíGUEZ-CLARE - YI a comparative disadvantage, as reflected in positive net imports in that sector. Group ig would be highly specialized in s when the country is in autarky (but groups trade among themselves) but that specialization would diminish as the country starts trading with the rest of the world. As a consequence, the KL degree of specialization falls with trade for group ig, implying lower gains relative to other groups in the economy. 2.4 Aggregate Welfare Effects The aggregate welfare effect can be obtained from Proposition 1 as Ŵi Ŷi/ ˆP i = g G i (Y ig /Y i ) Ŵig. Using (13), this can be written explicitly as Ŵ i = s ˆλ β is/θ s iis g G i ( Yig Y i ) s ˆπ β is/κ ig igs. (14) The aggregate welfare effect of a trade shock is no longer given by the multi-sector ACR term (i.e., Ŵ i s ˆλ β is/θ s iis ). This is because a trade shock will in general affect wages w is, and this in turn will affect welfare through its impact on income and sector-level prices. 2.5 Aggregate and Group-Level Gains from Trade Following ACR, we define the gains from trade as the negative of the proportional change in real income for a shock that takes the economy back to autarky: GT i 1 Ŵ A i and GT ig 1 Ŵ A ig. A move to autarky for country i entails ˆτ ijs = for all s and all i j and ˆD i = 0. Conveniently, solving for changes in wages in country i (i.e., solving for ŵ is for s = 1,..., S) from Equation (8) only requires knowing the values of employment shares, income levels and expenditure shares for country i, namely β is for all s and π igs and Y ig for all g, s. This can be seen by letting ˆτ ijs in Equation (8), which yields β is g G i Ŷ ig Y ig = g G i ˆπ igs Ŷ ig π igs Y ig. (15) Let r is g G i π igs Y ig /Y i be the share of sector s in total output in country i and note that there is inter-industry trade in country i as long as r is β is for some s. Proposition 2 Assume that κ ig = κ i for all g G i. If κ i < and there is inter-industry

14 SLICING THE PIE 13 trade in country i then the aggregate gains from trade are strictly higher than those that arise in the limit as κ i. Appendix B has the proof. To understand this result, it is useful to consider the simpler case with a single group of workers, G i = 1. For a move back to autarky, in this case we would have Ŵ A i = s λ β is/θ s iis [ exp 1 ] D KL (r i β κ i ). i If there is inter-industry trade then D KL (r i β i ) > 0 so (given r i ) a lower κ i implies a lower Ŵi. Intuitively, a finite κ i introduces more curvature to the PPF, making it harder for the economy to adjust as it moves to autarky. This implies higher losses if the economy were to move to autarky, and hence higher gains from trade see Costinot and Rodríguez-Clare (2014). Proposition 2 establishes that this result generalizes to the case G i > 1. Turning to the group-specific gains from trade, we again use the KL measure of specialization to understand whether a group gains more or less than the economy as a whole. The results of the previous section imply that the gains from trade for group ig are GT ig = 1 s λ β is/θ s iis ( 1 [ exp DKL (π A ig β κ i ) D KL (π ig β i ) ] ). ig The term D KL (π A ig β i) D KL (π ig β i ) could be positive or negative, depending on whether group g in country i becomes more or less specialized with trade as measured by the KL divergence. Intuitively, if a group happens to be specialized in industries that face strong import competition, this would imply that D KL (π ig β i ) < D KL (π A ig β i), and hence lower gains from trade. 2.6 A Limit Case An interesting case arises in the extreme case in which κ ig = 1 for all g G i, where the model becomes isomorphic (for country i) to one in which labor cannot move across sectors (i.e., where E igs is fixed for all gs). For this case, equation (9) implies that for a foreign shock Ŷ ig = π igs ŵ is. (16) s

15 14 GALLE - RODRíGUEZ-CLARE - YI Recalling that r is g π igsy ig /Y i, equation (16) implies that Ŷi = k r ikŵ ik, and together with equation (11) this further implies that ˆr is = ŵ is /Ŷi. Combining these results we get that Ŷ ig /Ŷi = s π igsˆr is. (17) The benefit of this result is that ˆr is is observable in the data. Thus, if we can identify the impact of a foreign shock on output shares, then we can compute the implied relative income changes across groups. To perform that exercise, Section 4.4 will outline a strategy to identify trade-induced ˆr is, based on the instrumental-variables procedure in Autor et al. (2013), and then test the following relationship ln Ŷig = ln Ŷi + ln s π igsˆr is If κ ig was indeed very close to 1 for all g G i then such a regression should yield a coefficient close to one. In the counterfactual simulations in Section 5, we will see that the relationship between s π igsˆr is and Ŷig continues to be log-linear when κ ig = κ i > 1 for all g G i, but that the slope of their relationship falls with κ i. The case κ ig = 1 for all g G i also leads to a sharp result for the change in relative income levels across groups in a move back to autarky. Noting that ˆr is = β is /r is and plugging into (17) yields Ŷ A ig Ŷ A i = I ig s π igs β is r is. (18) We can think of β is /r is as an index of the degree of import competition in industry s and I ig as an index of import competition faced by group g. Thus, in the extreme case in which κ ig = 1 for all g G i, the change in relative income levels across groups is simply given by the index of import competition that we can directly observe in the data. Things are more complicated in the general case with κ ig = κ i > 1 for all g G i, but we will see that I ig remains a good proxy for ranking Ŷ ig A/Ŷ i A across g and that the variance of Ŷ ig A/Ŷ i A falls with κ. Of course, one can also use the result in (18) to rewrite the result in (17) and get an expression for Ŷig/Ŷi for any foreign shock (not just moving to autarky) as Ŷ ig Ŷ i = 1 Î ig. (19)

16 SLICING THE PIE Inequality-Adjusted Welfare Effects We follow Atkinson (1970) and think about social welfare as a (geometric) average of welfare across all individuals with a constant inequality aversion parameter ρ > 0 (with ρ 1 to simplify the exposition below). Since the Z s for workers in group ig is distributed Frechet with scale and shape parameters parameter (Γ(1 1/κ ig )) κ ig A igs and κ ig, then income max s w s Z s for workers in group ig is distributed Frechet with scale and shape parameters Γ(1 1/κ ig ) κ ig s A igsw κ ig s then where l ig L ig /L i. that U i = g l ig ( Γ ( Γ ) 1 1 ρ κ ig ( 1 1 and κ ig. Social welfare in country i is κ ig )) 1 ρ W 1 ρ ig In the quantitative section below we will focus on the case κ ig = κ i, which implies ( where η i Γ ) 1 1 ρ 1 1 ρ κ i Γ U i = η i ( g l ig W 1 ρ ig ) 1 1 ρ (1 1 κi ). The inequality-adjusted welfare effect of a foreign shock is defined as Ûi 1 whereas the inequality-adjusted gains from trade are defined as IGT i 1 Û A i. If ρ = 0 then these measures correspond to those defined above, namely Ŵi 1 and GT i 1 Ŵ i A. To write these results in terms of observables and the endogenous group-level welfare changes Ŵig, let ξ ig l ig(y ig /L ig ) 1 ρ be a modified weight for h l ih(y ih /L ih ) 1 ρ group ig in country i welfare that appropriately accounts for the social value of income accruing to groups with different income levels. Then simple algebra reveals that Û i = ( g ξ ig Ŵ 1 ρ ig ) 1 1 ρ., 1 1 ρ, 3 Data For our quantitative analysis, we define groups based on geographic location and education. We follow Autor et al. (2013), henceforth ADH, in using Commuting Zones (CZs) as geographic units to define local labor markets, and further separate each CZ into two

17 16 GALLE - RODRíGUEZ-CLARE - YI groups based on whether workers hold at least an Associate s degree. 19 Our sectors are based on the 1987 SIC classification codes. We aggregate all manufacturing industries into 13 sectors which roughly correspond to two-digit ISIC Rev. 3 codes. 20 The remaining sectors, excluding public administration, are aggregated to one non-manufacturing sector. This leaves us with a total of 1,444 groups (722 CZs x 2 skill groups) and 14 sectors. 21 All countries other than the U.S. are assumed to have a single group. We restrict our analysis to the period National figures on bilateral trade flows, sectoral output and employment shares come from the World Input-Output Database (WIOD). 22 For wages and labor shares across our U.S. groups, we rely on data from the 2000 Census and American Community Survey (ACS). 23 In the regression analysis, we define labor shares π igs based on share of workers, share of labor hours or share of earnings in sector s. 24 For the simulation analysis, we focus on π igs as shares of earnings. Appendix D describes in detail the construction of our dataset and the definition of our variables. It also details the supplementary data employed in our model extensions and robustness tests. 4 Empirics We bring the model to the data with a set of empirical exercises. First, we apply the ADH China shock to our setting, and examine the reduced-form impact of the China shock on income and on expansion of the non-manufacturing sector, both at the group level. Next, we impose κ g,us = κ US for all groups in the US and estimate κ US. In this 19 Our assumption of fixed groups applied to this setting implies no mobility across local labor markets and education categories. We view this as a reasonable assumption in light of existing literature that finds little evidence of trade exposure causing population shifts across local labor markets. See, for example, ADH for the US, Dauth et al. (2014) for Germany, and Dix-Carneiro and Kovak (2016) for Brazil. Moreover, except for the very long run, it seems reasonable to ignore the effect of trade on workers acquiring an Associate s degree. 20 Table?? in the Appendix shows the list of manufacturing sectors. 21 In cases where π igs = 0, we imputed a small value to make the data consistent with our model. 22 The WIOD dataset is discussed in Timmer et al. (2015). 23 The Census and ACS Public Use Microdata Areas (PUMAs) are mapped into commuting zones using a crosswalk provided by David Dorn. 24 Ou Roy-Frechet framework implies that the share of workers and the share of earnings in group g, sector s, is identical.

18 SLICING THE PIE 17 structural estimation, we exploit the theoretical link between trade-induced expansion of the non-manufacturing sector and changes in group-level income. As such, this estimation strategy nicely structures and synthesizes our reduced-form analysis. Finally, we test the model-based prediction on how changes in our Bartik measure of import competition affect group-level income levels. Throughout the regression analysis, we restrict our sample to full-time workers. In Appendix C we perform a robustness analysis for the full sample of workers, including part-time workers, and the results are highly similar. 4.1 The rise of China as a trade shock Throughout our empirical analysis, we follow ADH and focus on the China shock to US manufacturing. Specifically, we use changes in sector-level exports from China to a group of countries similar to the US to proxy for changes in sectoral importcompetition from China in the US. 25 The assumption behind this identification strategy is that increased Chinese exports to these other advanced economies are driven by the exogenous rise of China, which consists of Chinese productivity growth in manufacturing and reductions in export costs for Chinese producers. 26 Our specific measure of the China import-penetration shock in sector s is IP China Other st M China Other st L US, st 0 where L US st 0 denotes US employment in sector s in year 2000, M China Other st are imports from China by the above-defined set of countries for year t, and refers to the change over the period 2000 to below, we henceforth suppress the t subindex. Since we use this same period in all the regressions 25 This set of countries consists of Australia, Denmark, Finland, Germany, Japan and Spain. Except for Switzerland and New Zealand, which are not included in the WIOD data, this set of Other countries is identical to the set in ADH. Countries are selected based on having a similar income level as the US, but direct neighbors are excluded. 26 For an extensive discussion on the exogeneity restrictions and the robustness of this identification strategy, see ADH. 27 Our version of the import-penetration shock differs from the one in ADH due to different sector definitions and a different time period. We chose to have more aggregated sectors to reduce the share of zeros in π igs, λ ijs, which is important for the simulation. Compared to the ADH time period ( ), our choice of time horizon ( ) resulted from the constraints imposed by our different trade and labor datasets.

19 18 GALLE - RODRíGUEZ-CLARE - YI 4.2 Reduced-form impact of the China shock We first explore the impact of the China shock in our setting by examining its reducedform effect on group-level income. This cross-sectional relationship links directly to the distributional impact of trade shocks across groups that we are capturing in our model. ln ŷ g = α + β ln s M π M gs IP China Other s + ε g, (20) where ŷ g Ŷg/ˆL g is measured as average labor income per worker and πgs M π gs /π gm is the share of labor employed in manufacturing sector s relative to total manufacturing employment. The set of manufacturing sectors is denoted by M. We also check the impact of the China shock on the change in the share of the non-manufacturing sector, denoted by π gnm. Trade-induced changes in π gnm feature prominently in the ADH analysis, and will be central to our structural estimation of κ US. In the reduced-form regression analysis, we update equation (20) to have ln ˆπ gnm as the dependent variable. Throughout the entire regression analysis, we will calculate Conley (1999) standard errors, to account for spatial correlation in the error term. 28 As expected from the ADH analysis, we find that higher exposure to the China shock negatively affects groups income, and leads to an expansion of the non-manufacturing sector (Table 1). Both findings are strongly significant. In the next section, we will integrate these reduced-form findings in our structural estimation of κ. 4.3 Estimation of κ As is evident from equation (1), the κ ig parameter is central to our model as it jointly affects the aggregate and the distributional welfare effects from trade. In this subsection we estimate κ ig by exploiting the relationship between trade-induced expansion of the non-manufacturing sector and income changes across groups. Imposing κ ig = κ and using ŷ g = ˆΦ g ˆL g that ŷ g = Â1/κ gs together with equations (9) and (11) implies ŵ sˆπ gs 1/κ. Since this holds for all sectors, we can focus on reallocation to non-manufacturing, which is where we know from the previous section that the China 28 For the OLS regressions we use code from Hsiang (2010), and for the IV the original code from Conley (1999).

20 SLICING THE PIE 19 Table 1: Reduced-form impact of the rise of China (a) Dependent variable: ln ŷ g (1) (2) (3) Definition of π gs Workers Hours Earnings ln s M πm gs IP China Other st ( ) ( ) ( ) P-value Observations (b) Dependent variable: ln ˆπ gnm (1) (2) (3) Workers Hours Earnings ln s M πm gs IP China Other st ( ) ( ) ( ) P-value 2.76e e e-09 Observations Estimation results for specification (20), where y g, the dependent variable in panel (a), is measured as average earnings per worker. The dependent variable in panel (b) is ln ˆπ gnm, the log change in the labor share of the non-manufacturing sector. Labor shares π gs are measured as the share of workers, share of labor hoursand share of earnings for columns 1, 2 and 3 respectively. Standard errors (in parentheses) are calculated as in Conley (1999), with a cutoff for the spatial correlation at 500km.

21 20 GALLE - RODRíGUEZ-CLARE - YI shock offers a strong instrument. After taking logs, we obtain: ln ŷ g = ln ŵ NM 1 κ ln ˆπ gnm + ln Â1/κ gnm This gives rise to the following regression equation: 29 ln ŷ g = α + β ln ˆπ gnm + ε g. (21) Because our theory implies that the error term is correlated with the regressor, we instrument ln ˆπ gnm with the China shock variable Z g s M πm gs IPs China Other. ] The exclusion restriction E [ε g Z g ] = 0 is satisfied as long as E [ÂgNM π gs = 0 and ] E [ÂgNM IPs China Other = 0 for all g and s M. Table 2 presents the results for the IV regression described above. The first row shows our second-stage results, while the fourth row has the corresponding estimate ˆκ = 1/ ˆβ, and the sixth row displays the F-statistic from the first stage. As implied by our reduced-form results for the impact of the China shock on the expansion of the non-manufacturing sector, the first-stage F-statistics are sufficiently high. The second stage estimate is always significantly different from zero, and the values for ˆκ range from 2.03 to For the next section, where we will run simulations to analyze the quantitative role of κ in our framework, we will set our preferred value at κ = 2.2. In addition, we will also show results for κ 1, i.e. the theoretical lower bound for κ, and for κ = 4. The latter value is an upper bound of the 95% confidence intervals for the κ estimates. 29 In principle, one can also estimate this equation for each of the 13 manufacturing sectors, but there the first-stage F-statistic is typically much lower than in the current IV-strategy. 30 The structural estimation for the sample including part-time workers in Appendix Table A.4 yields lower point estimates, with values centered around κ = 1.6. These values are within the 95% confidence intervals of the estimations in the current table, but would imply stronger distributional effects from the China shock.

22 SLICING THE PIE 21 Table 2: Esimation of κ Dependent variable: ln ŷ g (1) (2) (3) Definition of π gs Workers Hours Earnings ln ˆπ gnm (0.164) (0.171) (0.177) P-value Implied κ (0.849) (0.772) (0.732) First-stage F-Statistic Observations IV-estimation results for specification (21), where y g is measured as average earnings per worker, and π gnm is the labor share employed in non-manufacturing. Labor shares π gs are measured as the share of workers, share of labor hoursand share of earnings for columns 1, 2 and 3 respectively. Standard errors (in parentheses) are calculated as in Conley (1999), with a cutoff for the spatial correlation at approximately 500km. The first row shows the second-stage results, while the fourth row has the corresponding κ estimates implied by the model and the sixth row displays the F-statistic from the first stage.

23 22 GALLE - RODRíGUEZ-CLARE - YI 4.4 Import competition and income In this subsection we explore the empirical relationship between group-level income changes and our model-based measure of changes in group-level import competition. As will become clear, this exploration will also provide an indirect inference strategy to estimate κ, which we will use as a robustness check on our structural estimation results. From Equation (17) we can obtain that, in the extreme case with κ ig = 1 for all g, ln ŷ g = ln ŷ + ln s π gsˆr s. (22) Moreover, the simulation-based analysis in Section 5 will confirm that if κ ig = κ for all ig and κ > 1 the relationship between ŷ g and s π gsˆr s remains close to log-linear, but with an elasticity lower than one. We test this approximately log-linear relationship in the data by running the following regression: ln ŷ g = α + β ln s π gsˆr s + ε g. (23) In our empirical analysis, Y g, y g and π gs are measured as before, and r s g π gsy g /Y. Through the lens of our model, the error term ε g could be driven by changes in A gs, measurement error or a deviation of the log-linear relationship in (22) for values of κ > 1. We instrument for ln s π gsˆr s with s π gs IPst China Other. The exclusion restriction in this IV regression is that sector-level growth in China affects group-level incomes only through its effect on US sectoral output and a group s initial pattern of specialization. The theoretical analysis from Section 2.6 and the simulations in Section 5.1 (below) imply that this regression should yield an estimate ˆβ < 1. Intuitively, as κ increases and workers comparative advantage becomes more homogeneous, the variation across groups in the impact of the China shock fades away. Table 3 presents the results. The first stage has the expected sign and has sufficient statistical power. In the second stage, the estimated coefficient is positive and strongly statistically significant in all specifications. This result corroborates the theoretical prediction that regional income changes depend positively on trade-induced changes in s π gsˆr s. In addition, the confidence intervals for all the estimated coefficients are contained within zero and one, as required by the theory (see discussion in Section 2.6).