On Measuring the Welfare Gains from Trade under Consumer Heterogeneity

Transcription

1 On Measuring the Welfare Gains from Trade under Consumer Heterogeneity Sergey Nigai ETH Zurich and KOF September, 2012 Abstract I develop a multi-country model of international trade with heterogeneous consumers and non-homothetic preferences. The model provides structural link between real income per capita, income inequality and trade. Trade liberalization exerts heterogeneous income and price effects that are translated into consumer-specific welfare gains. The rich gain everywhere, but more than a half of the poor lose. I use these estimates to quantify the bias caused by the assumption of a representative consumer (ARC). First, I find that the model under ARC predicts the sign of the welfare gains incorrectly for 61% of consumers in the left tail of the income distribution, and for 15% of consumers overall. Second, the quantitative errors in the estimates of gains from trade under ARC are as large as 8.6 and -6.6 percentage points for the poorest and the richest consumer, respectively. Keywords: International trade; Income distribution; General equilibrium model. JEL-codes: F11; F14; Q43; Q48. ETH Zurich, KOF, Weinbergstrasse 35, 8092 Zurich, Switzerland; nigai@kof.ethz.ch; Telephone: This work is based on the main chapter of my Ph.D. dissertation. I am forever indebted to my advisor Peter Egger for his guidance and support. 1

2 1 Introduction An overwhelming majority of economists believe that free international trade is welfare enhancing. In fact, this conventional wisdom may have been the least disputable one in the profession. 1 The general public, however, seems to have mixed feelings towards globalization, with many people consistently opposing free trade policies. Surveys often indicate that up to half of the population views free trade as potentially harmful. 2 What is the reason for this large gap between one of the most robust theoretical and empirical results in economics and general perception of the public? I argue that the reason for this disparity stems from the assumption of a representative consumer (ARC). I show that this assumption is a source of large measurement errors in the estimates of welfare gains from trade for certain consumer groups. For that, I build a multi-country model of trade with non-homothetic preferences and heterogeneous consumers, and demonstrate that welfare gains from trade in a counterfactual global trade liberalization experiment largely differ both qualitatively and quantitatively across individuals. The model predicts that under trade liberalization consumer experience heterogeneous changes in their total nominal incomes and consumer price indices. This heterogeneity must be taken into account when evaluating welfare gains because measures based on ARC may (under)overstate the gains by up to (8.6) 6.6 percentage points depending on the consumer and the country. The extent of the quantitative bias is large, considering that total welfare gains range between -8.3% and 13.7%. The results also point to large qualitative bias, especially for consumers in the left tail of the income distribution. Welfare gains calculated under ARC are qualitatively wrong for 61% of the poor and for 15% of consumers overall. Differences in the consumption patterns across consumers are the first source of heterogeneity 3 in welfare gains from trade. The poor and the rich consume different bundles of goods. 1 The survey data among economists across different periods show that on average only about 5% of economists believe that tariffs do not reduce welfare. See Alston, Kearl and Vaughan (1992), Poole (2004) and others. 2 According to the survey conducted by the Pew Research Center in 2010, only 35% of respondents agreed that free trade agreements such as NAFTA and WTO policies are good for the United States. In fact, 44% of the respondents indicated that they consider free trade agreements to be bad for the United States. 3 Fajgelbaum, Grossman and Helpman (2011) formulate a model with non-homothetic preferences, horizontal and vertical product diffentiation. They show that income distribution, in terms of the numeraire good, remains unchanged after a trade liberalization episode but not in terms of real consumption. Two empirical case studies discuss the bias from calculating welfare gains using a price index common to all consumers. Porto (2006) calculates welfare gains for different consumer groups in Argentina from joining MERCOSUR. Recently, Broda and Romalis (2009) have argued that welfare gains for low-income groups in the US have been underestimated by using the price index of a representative consumer. The authors also argue that around 50% of the documented increase in income inequality in the US between 1994 and

3 For example, abolishment of import tariffs on luxury cars and premium wines will have positive price effects on the rich, but will offer no gains to the poor, whose consumption baskets do not include those goods. The non-homothetic preference structure that I employ here allows each consumer to have unique expenditure shares. Consumers also differ in terms of their nominal incomes. I assume that each country has a unique distribution of physical capital, so that the factor returns are distributed unevenly across individuals. 4 On the other hand, total government transfers such as foreign aid and tariff revenues are distributed equally among all consumers. Trade liberalization affects factor prices and government transfers which exert heterogeneous income effects. Depending on the relative shares of factor returns and government transfers in total income, each consumer faces a potential trade-off between change in factor prices and the size of tariff revenues in case of a trade liberalization. I use these two sources of heterogeneity and calculate consumer-specific welfare gains from a counterfactual global trade liberalization. The results of the experiment suggest that the rich gain everywhere. However, more than a half of the poor lose. Overall, 19% of the world population experience reduction in their welfare in the counterfactual experiment. Recently, non-homothetic preferences have been reintroduced into the models of international trade (for example see Markusen, 2010; Simonovska, 2010; Fieler, 2011). The authors show that non-homotheticity plays an important role in explaining bilateral trade patterns across several margins. However, these papers are mainly concerned with consumer heterogeneity across countries and not within a single country. In that sense, they still evaluate potential welfare gains through the lens of ARC which, as I argue, can be a source of large bias. I recognize the importance of large differences in the consumption patterns across countries in explaining bilateral trade flows. However, I also add an additional dimension differences in the consumption patterns within a single country. This contributes to the literature in two ways. First, relaxing ARC allows identifying differences in welfare gains from trade for consumers within each country. This heterogeneity in welfare effects is missing in recent is due to the problem of using a uniform price index. 4 Another way to introduce heterogeneity in incomes is to include labor market frictions (see Egger and Kreickermeier, 2009; Helpman, Itskhoki and Redding, 2010; Davis and Harrigan, 2011 and others). For example, Davis and Harrigan (2011) introduce labor market frictions into Melitz (2003) model and show that while trade liberalization raises average wage, it negatively impacts workers that had relatively high wages in the pre-trade equilibrium. Several empirical studies point to the heterogeneous income effects from trade liberalization. Artuc, Chaudhuri, McLaren (2010) use a dynamic labor adjustment model and estimate how trade liberalization affects different types of workers. McLaren and Hakobyan (2010) use US Census data to estimate local welfare effects for heterogenous workers from joining NAFTA. Helpman, Itskhoki and Redding (2008, 2010) explore the link between wages, income inequality and unemployment in general equilibrium models of trade with heterogenous firms and workers. 3

4 general equilibrium models that incorporate non-homotheticity into new trade models. The model also offers novel, often neglected, insights concerning the differences between welfare gains of the rich versus the poor. Second, non-homotheticity together with consumer heterogeneity delivers predictions documented in the empirical literature but currently missing in computable general equilibrium work. The model provides the missing two-way link between international trade and within-country income inequality (for example see Goldberg and Pavcnik 2004, 2007; Harrison, McLaren and McMillan, 2010). It also delivers clear predictions, consistent with the empirical literature, on the relationship between total labor force, real income per capita, within-country income distribution and bilateral trade flows. In the next section, I present the model and illustrate the fundamental problem with ARC under non-homothetic preference structure and heterogenous consumers. In Section 3, I estimate the parameters of the model and describe the calibration procedures. Section 4 discusses novel predictions of the model that are consistent with a number of empirically established facts. I conduct a counterfactual trade liberalization experiment to assess the validity of the predictions under ARC and evaluate consumer-specific welfare gains in Section 5. In Section 6, I test for sensitivity of the results. The final section offers a brief conclusion. 2 Model There are N countries in the world. Each country i = (1,..., N) is endowed with L i units of labor and K i units capital. Each country hosts a measure of heterogeneous firms in three sectors: agricultural, manufacturing and non-tradable. Manufacturing and agricultural goods can be traded subject to sector specific iceberg trade costs from n to i, τ m,in and τ a,in, respectively 5. The factors of production are assumed to be completely mobile across sectors but not countries. I introduce consumer heterogeneity in the spirit of Mayer (1984) by assuming that each household owns a unit of labor and d units of capital. Here, I interpret capital as physical capital without loss of generality. There are alternative ways to interpret heterogeneity in workers. For example, Blanchard and Willmann (2011) assume differences in abilities, Costinot and Vogel (2010) point to the importance of skill intensities. Capital may also be interpreted as human capital (see Bougheas and Riezman, 2007). I largely follow Mayer (1984) in modeling heterogeneity and find it natural to interpret capital accordingly. The solution of the model does not depend on the interpretation of capital. 5 The usual triangularity (no arbitrage) assumption applies. 4

5 Households vary according to their endowment of capital, k id and can be of type d = 1,..., D, where d stands for the decile in the capital distribution. The distribution of capital is assumed to be exogenous, stationary and country-specific. Hence, households are homogeneous within a decile in any country i but not across countries and/or deciles. 6 The preference structure is non-homothetic which ensures that differences in the level of real income are mapped into the differences in consumption patterns of consumers across deciles and countries. Depending on the level of real income, some consumers may choose not to consume (or consume little) of certain goods. Both extensive and intensive margins of import demand are important Households Households of type d = (1,..., D) in country i maximize consumption of the non-tradable good, c ni, the tradable manufacturing good, c mi and the tradable agricultural good, c ai, according to the following nested Stone-Geary utility function: U(c ni, c mi, c ai ) = (c β ni c1 β mi + µ) α c 1 α ai s.t. y id = c ni p ni + c mi p mi + c ai p ai, (2.1) where p ni, p mi and p ai are prices of the non-tradable, manufacturing, and agricultural goods, respectively. Let me denote labor as l i, then total per-capita income of a household of type d in i is y id = (l i w i + k id r i ) + v i, where w i is the wage rate, r i the capital rental rate, and v i total per capita transfers. The utility function in (2.1) captures non-homotheticity of preferences through the term µ, which can be interpreted as endowment of non-tradable and manufacturing goods. 8 As long 6 I use deciles to approximate the distribution of capital simply because no data are available on a more disaggregated level. On the other hand, I find that using less disaggregated measures such as quartiles or quintiles would convolute the differences between the poor and the rich to the point when income inequality is no longer as important (for example see Fieler, 2011). 7 A large class of general equilibrium models of trade deliver identical predictions in terms of welfare gains from trade (see Arkolakis, Costinot and Rodriguez-Clare, 2010). The two necessary conditions for this remarkable result are CES demand system and structural gravity equation. This model deviates in two major ways: consumer heterogeneity and non-homothetic preferences. The combination of these two guarantees that the predictions of the model here differ from the canonical models of trade (Eaton and Kortum, 2002; Anderson and van Wincoop, 2003; Bernard, Jensen, Eaton and Kortum, 2003; Melitz, 2003) and provides novel insights in terms of welfare gains from trade liberalization. 8 It is more customary to specify Stone-Geary preferences as U(c ni, c mi, c ai ) = (c β ni c1 β mi ) α (c ai µ) 1 α, where µ may be interpreted as a subsistence level of consumption of agricultural goods. However, this specification does not allow evaluating changes in welfare for consumers with initially binding subsistence level of income whose initial utility is zero. For further discussion of Stone-Geary preferences refer to 5

6 as consumer d in country i has income higher than cut-off level yi, which is sufficient to buy some positive amount of manufacturing and non-tradable aggregates 9, the value of his final demands are given by: c ni,d p ni = αβ (y id y i ), (2.2) c mi,d p mi = α(1 β) (y id y i ), (2.3) c ai,d p ai = (1 α)y id + αy i, (2.4) Otherwise, c ni,d p ni = c mi,d p mi = 0 and c ai p ai = y id. The demand equations in (2.2)-(2.4) can be normalized by total income of consumers of type d to get expenditure shares in that decile. For instance, consumer of type d in country i spends s ai,d c ai,dp ai on agricultural goods. For a given distribution of y id, I also derive country-level income shares spent on nontradables, tradables and agricultural goods s ni,s mi and s ai respectively. I aggregate demands of all consumers in i and normalize the sum by i s total income as follows: y id s ni = D d=1 s ni,dy id D d=1 y ; s mi = id D d=1 s mi,dy id D d=1 y ; s ai = id D d=1 s ai,dy id D d=1 y, (2.5) id Specifying income shares spent on non-tradable, manufacturing, and agricultural goods is vital for calculating aggregate bilateral trade flows. Let me also define y i as average real income per capita. This will turn out to be useful in subsequent sections. 2.2 Measuring welfare: basic idea One of the elemental questions in international economics is calculating welfare gains from trade. Until recently, much of theoretical and empirical work featured homothetic preferences and homogenous consumers. 10 Recent works relax the former assumption by combining non-homothetic preferences and new trade theories of Melitz (2003), and Eaton and Kortum (2002). For example, Simonovska (2010) shows that non-homothetic preference Markusen (2010). ( ) 1 β 9 Formally, yi µ(1 α) β p mi. αβ 1 β p ni 10 Notable exceptions are Jackson (1984), Hunter (1991) and Matsuyama (2000). 6

7 structure helps explaining pricing-to-market patterns across countries, while Fieler (2011) quantitatively shows that non-homotheticity is important for explaining North-South and South-South trade patterns. However, both models feature a representative consumer which effectively means that they are able to predict average (or aggregate) gains from trade only. This is not an issue as long as average gains from trade reflect welfare gains from trade of different consumer groups. I show below that non-homotheticity together with heterogeneity in real incomes rule out the case when this holds. Income of consumer d in country i is comprised of wage w i, capital rental rate multiplied by the amount of capital that d owns, k id r i, and government transfers, v i. The transfers subsume tariff and tax revenues, and transfers from other countries including foreign aid. Formally, v i = g i +cab i, where g i is total government transfers and cab i is balance of payment in the benchmark year (current account balance net of trade deficit). Most trade models ignore the issue of income transfers. However, share of v i in total income of some consumers is in no way negligible, hence including v i adds realism to the model. In Section 6, as a sensitivity check I exclude v i and show that the results of the model remain. 11 Because factors are domestically mobile and the production functions are Cobb-Douglas, introduced in the following section, the economy is largely Ricardian i.e. w i is proportional to r i. However, v i is comprised of tariff revenues and balance of payments which are divided equally among all consumers. In the benchmark, the poor get a larger share of their income from v i compared to the rich. This creates frictions that ensure that changes in w i, r i and/or v i affect income of different consumers disproportionately. The heterogeneity in income shares between the poorest and the richest consumer is most acute in developing countries. For instance, the share of tariff revenues and foreign transfers is more than 83% of the income of the poorest consumer in Zimbabwe. However, the same share is only 2.95% for the richest consumer. The difference between the poorest and the richest consumer is less severe in developed countries. Let V (y id, p ni, p mi, p ai ) be the indirect utility function corresponding to (2.1). Use Marshallian demands specified in (2.2)-(2.4) to get: ( ) B(y id yi ) α ( yid α(y id yi + µ ) p β V (y id, p ni, p mi, p ai ) = ni p1 β p mi ai ( µ α yid α(y id yi ) p ai ) 1 α if y id > y i ) 1 α if y id y i, (2.6) 11 I report the relative shares of g i and cab i in total y id for each decile in the Appendix (Tables 8 and 9). 7

8 where B = α(1 β) 1 β β β. Suppose that under a hypothetical trade liberalization wage rage in i, w i, becomes w i. This, in turn, means that income, y id, becomes y id. Because initial income shares are not the same across consumers, changes in their nominal incomes are disproportional such that y id y i d for y id y y id y i d. An immediate corollary is that income i d welfare effects related to an arbitrary trade liberalization are different across consumers: V (y id, p ni, p mi, p ai ) V (y id, p ni, p mi, p ai ) V (y i d, p ni, p mi, p ai) V (y i d, p ni, p mi, p ai ) y id y i d. (2.7) Second source of heterogeneity are the differences in the price effects. Suppose that under an arbitrary trade liberalization consumers in i face a new vector of prices {p ni, p mi, p ai}. It is trivial to prove using (2.6) that under non-homothetic preference structure and heterogenity in the initial level of income y id, arbitrary changes in prices {p ni, p mi, p ai} affect consumers differently, that is: V (y id, p ni, p mi, p ai) V (y id, p ni, p mi, p ai ) V (y i d, p ni, p mi, p ai) V (y i d, p ni, p mi, p ai ) y id y i d. (2.8) Trade liberalization is likely to affect both nominal incomes and prices, hence higher trade would exert heterogenous welfare effects on consumers. I am interested in quantifying the extent of this heterogeneity and, in particular, the difference between average (representative) and decile-specific welfare effects. 2.3 Production I model production in the spirit of Eaton and Kortum (2002) because multi-country Ricardian models calibrated to real data mimic both aggregate trade flows and average levels of real income per capita with high accuracy 12. This allows me to provide clear quantitative predictions in the counterfactual section that have straightforward interpretation relative to the benchmark data. Each country is endowed with a fixed measure of capital and labor. Besides these two factors of production, firms employ Spence-Dixit-Stiglitz (SDS hereafter) aggregates of the nontradable and manufacturing goods, and firms in the agricultural sector also employ the SDS 12 For example, see Alvarez and Lucas (2007); Egger and Nigai (2012). 8

9 aggregate of the agricultural goods. 13 Modeling production with three sectors is motivated by the data from aggregate input-output tables. Including intermediate inputs and a nontradable sector is important to identify welfare gains in case of a trade liberalization correctly (see Goldberg, Khandelwal, Pavcnik and Topalova, 2009; Caliendo and Parro, 2010). Non-tradable sector Let n i be the quantity of the non-tradable good, m i quantity of the manufacturing aggregate and a i quantity of the agricultural aggregate. I assume that each country has a measure of firms in the non-tradable sector producing identical non-tradable output using constantreturns-to-scale technology: n i = [ l i (n) ν k i (n) 1 ν] φ [ ni (n) ϱ m i (n) 1 ϱ] 1 φ, (2.9) accordingly the price of the non-tradable good is: where Γ n is a sector-specific constant. Manufacturing sector p ni = Γ n (wi ν r 1 ν i ) φ (p ϱ ni p1 ϱ mi )1 φ, (2.10) Each country hosts a measure of firms each producing a unique variety with a productivity drawn from a Frechèt distribution. The productivity is a realization of a random variable z mi distributed according to: F mi (z mi ) = exp( λ mi z θm mi ), (2.11) here λ mi is country-specific productivity parameter and θ m dispersion parameter common across all countries. Each firm in the sector employs labor, capital, non-tradable and manufacturing aggregates in the following way: m i (q) = z mi (q) [ l i (q) ν k i (q) 1 ν] ξ [ ni (q) ζ m i (q) 1 ζ] 1 ξ, (2.12) q denotes different varieties of the manufacturing goods. The probabilistic representation of 13 Consistent with the literature and the OECD classification I classify industries in three broad sectors: Agricultural goods, Manufacturing goods and Non-tradable goods. The SDS aggregates are produced according to conventional CES technology with the elasticity parameters 1 σ a and 1 σ m for the agricultural and manufacturing sectors, respectively. 9

10 technologies allows me to derive the average variable cost of a producer of a manufacturing variety in country i: κ mi = Γ m λ θm mi (wi ν r 1 ν i ) ξ (p ζ ni p1 ζ mi )1 ξ, (2.13) where Γ m is a sector-specific constant. The average variable cost, κ mi, along with the sectorspecific iceberg trade costs, τ m,il, and the ad-valorem tariff rate, t m,il, are sufficient to derive the aggregate price of tradables in i as follows: Agricultural sector ( N ) p mi = (κ ml τ m,il t m,il ) θm l 1 θm. (2.14) Similarly to the firms in the tradable sector, firms in the agricultural sector each produces a unique variety with a total factor productivity parameter drawn from a country-specific productivity distribution. 14 F ai(z ai) = exp( λ aiz θa ai ). (2.15) The respective expression of the production function of a producer of an agricultural variety h in i is: a i (h) = z ai (h) [ l(h) ν i k(h) 1 ν i ] γ [ ] n(h) ɛ i m(h) ρ 1 γ i a1 ɛ ρ i. (2.16) An important feature of the production of agricultural goods is their dependence on the aggregate agricultural input. This is not the case for the firms in the non-tradable and manufacturing sectors 15. This modeling choice is consistent with the data on the production inputs in the three sectors. The price of the agricultural aggregate can be expressed using average variable cost in i s partner countries, κ al, iceberg trade costs specific to that sector τ a,in and import tariff t a,in : 14 The productivity distributions of the tradable and the agricultural sectors are identical in terms of the family class but not the underlying parameters. I estimate the parameters for each of them in the following sections. 15 This approach is consistent with Caliendo and Parro (2011) who use input-output tables to account for the inter-dependence across industries. My formulation simply uses information from the input-output tables on a more aggregate level. 10

11 ( N ) p ai = (κ al τ a,il t a,in ) θa l 1 θa. (2.17) 2.4 International trade International trade occurs in the manufacturing and agricultural sectors. Firms producing identical varieties in different countries compete vis-à-vis each other given geographical and policy barriers to trade. Bilateral trade flows, X m,in and X a,in, can be decomposed into three components: X m,in = x m,in f mi Y i, and X a,in = x a,in f ai Y i, (2.18) here x m,in and x a,in are the supply side components of total trade flows. As in Eaton and Kortum (2002) they represent the share of i s total spending on manufacturing agricultural goods, respectively. x m,in = (κ mnτ m,in t m,in ) θm N l (κ mlτ m,il t m,il ) θm, and x a,in = (κ anτ a,in t a,in ) θa N l (κ alτ a,il t a,il ) θa (2.19) An important difference between the models based on the CES demand structure and the model here is that total spending on tradable goods is not proportional to i s total income. In other words, x mi and x ai are not sufficient to derive bilateral trade flows because country-level income shares spent on m and a vary across countries. I specify demand side components of trade, f mi and f ai, as the ratios of total manufacturing and agricultural absorption to total country-level income, Y i, respectively. These two variables are functions of s ni, s mi, s ai and parameters of the model, derived below. In a model without intermediate inputs f mi and f ai would be equal to s mi and s ai, respectively. Hence, the demand side does not disappear from total bilateral trade flow equations. Moreover, because f mi and f ai are functions of s mi and s ai, (2.5) implies that total bilateral trade depends on the distribution and the average level of income. To derive f ni, f mi and f ai, I first need to find sectoral absorption variables. Consistent with the literature, I define total absorption in a sector as total output plus net imports: A ni = Y ni, A mi = Y mi + D mi and A ai = Y ai + D ai, where Y ni, Y mi and Y ai are sectoral output values and D mi, D ai net imports in the respective sectors. The absorption, however, 11

12 is nothing but the sum of intermediate and final demands. Hence, the following identity must hold: Y ni 0 (1 φ)ϱ (1 φ)(1 ϱ) 0 Y ni s ni 0 0 Y i Y mi + D mi = (1 ξ)ζ (1 ξ)(1 ζ) 0 Y mi + 0 s mi 0 Y i, (2.20) Y ai D ai (1 γ)ɛ (1 γ)ρ (1 γ)(1 ɛ ρ) Y ai 0 0 s ai Y i } {{ } } {{ } } {{ } Sectoral Absorption Intermediate Demand Final Demand Given data on the sectoral trade deficits, I use (2.20) to pin down benchmark values of Y ni, Y mi and Y ai. Then f ni, f mi and f ai can be calculated as: f ni = A ni Y i, f mi = A mi Y i, f ai = A ai Y i, (2.21) To close the model, I assume that total imports, IM i, equal total exports, EX i up to a country-specific constant D i which is an exogenous deficit constant observed in the data: D i = EX i IM i, where (2.22) N IM i = (L i w i + K i r i + L i v i ) (f mi x m,in + f ai x a,in ), (2.23) n=1 N EX i = (L n w n + K n r n + L n v n ) (f mn x m,ni + f an x a,ni ). (2.24) n=1 Closing the model in this way is in the spirit of Dekle, Eaton and Kortum (2007). The central difference of (2.22) from the Ricardian models with homothetic preferences and/or homogeneous consumers is in the terms f mi and f ai. In models with homothetic preferences these two variables cancel out as they are constant across all countries. In models with non-homothetic preferences under ARC, these two shares differ across countries but are independent of income distribution. This contradicts the empirical evidence on the link between income inequality and trade. Here, f mi and f ai differ across countries and depend on the distribution of income in importer-country. I discuss the predictions of the model in terms of the link between total population, average income per capita, income distribution and bilateral trade in the next section. 3 Predictions of the model General equilibrium models of trade often fail to predict two stark relationships between trade and income that are evident in the data: (i) given a constant total income, trade increases 12

13 in income per capita rather than in population, and (ii) trade and within-country income inequality are correlated. Many recent papers have tackled the former issue by incorporating non-homothetic preferences into trade models. My approach is consistent with these works and provides predictions in line with the data. The latter issue, however, has been largely ignored in general equilibrium analysis of trade. Numerous empirical studies have suggested that trade liberalization episodes have been characterized by a substantial increase in income inequality. For an overview of recent advances in the research on trade and inequality refer to Goldberg and Pavcnik (2004, 2007). In addition, a number of empirical papers have found a considerable amount of evidence in support of Linder s (1961) hypothesis countries with similar income distributions tend to trade more. I introduce within-country differences in capital owned by households, which, together with a non-homothetic preference structure, link income inequality to total import demand. For brevity, I give predictions for the manufacturing sector only. It would be straightforward to extrapolate the predictions on the agricultural sector. Recall that X m,in is total trade flow from n to i which can be decomposed into the supply and the demand side components: X m,in = x } m,in {{ } f }{{} mi supply side Y i }{{} market size expenditure share } {{ } demand side. (3.1) Let ω id be the income distribution parameter of decile d such that y id = ω id y i, where y i is average real income per capita. Then, I derive the demand side from (2.20) as: f mi Y i = Z D 1 yid >yi L id (ω id y i yi ), (3.2) d where 1 yid >yi is an indicator function taking a value of unity whenever the income cut-off condition is satisfied and zero otherwise and Z is a constant. Hence, total import demand for manufacturing goods in country i depends on: (i) total population L i = D d=1 L id (ii) average real income per capita y i and (iii) income distribution parameters ω id. Let me keep aggregate Y i = L i D d=1 D ω idy i constant and examine how changes in L i, ω id and y i affect total import demand for manufacturing goods. Prediction 1 Total import demand for manufacturing goods in countries with min d (y id, y id ) > y i, increases in average real income per capita, y i, and decreases in population, L i, ceteris paribus. 13

14 Let L i, y i be counterfactual values of total labor force, per-capita real income, and income distribution parameters such that Y i = Y i = L i D d=1 D ω idy i. For countries where no consumer has total income below the cut-off level, min d (ω id y i) > yi, equation (3.2) collapses to the following: f mi Y i = ZL i (y i y i ), (3.3) Let b be a positive constant and define L i = L i b and y i = by i. Notice that L iy i = Y i = Y i, so that b governs division between per-capita real income and labor but keeps the total income constant. Equation (3.3) then becomes: ( ) f mi Y i = ZL i y i y i b Then the following two identities hold:,where Z is a constant, (3.4) (a) f mi Y i < f mi Y i for 0 < b < 1, if two countries have identical total income, total import demand for manufacturing is higher in the country with relatively higher income per capita. (b) f mi Y i f mi Y i for 1 < b, if two countries have identical total income, import demand demand for manufacturing is lower in the country with relatively higher population. Hence, division of total income, Y i, between L i and y i shapes total import demand of i. Two countries with identical total incomes may have highly heterogeneous total import demands. Prediction 2 There is a positive relationship between income inequality and total import demand for manufacturing goods ceteris paribus. For this thought experiment, keep Y i, L i and y i constant and vary distribution of ω id. Consider two extreme cases: (i) distribution G 1 : ω id = ω i d = 1 for all d and d, so that the income inequality is effectively zero and (ii) distribution G 2 : ω id with ω i10 = D and ω id = 0 for all d = 1,..., 9, so that one consumer owns everything. I consider two separate cases, one for poor countries and one for relatively rich countries. (a) Consider a poor country such that y i < yi and Dy i yi. Total import demand for manufacturing is lower under G 1 and higher under G 2. Under G 1, no consumer has income sufficient enough to demand positive amount of manufacturing goods. On the other hand, if all wealth in i belongs to consumers in the richest decile their demand for m i will be positive. Formally, f mi(g 1 )Y i = 0 < f mi(g 2 )Y i = ZL i10 (Dy i y i ) (3.5) 14

15 (b) Consider a rich country such that y i > yi, total import demand for manufacturing is higher under less equal distribution. In Prediction 1, I argued that total import demand is increasing in y i and decreasing in L i, here I observe similar mechanism. Formally, ( ) f mi(g 1 )Y i = ZL i (y i yi ) < f mi(g 2 )Y 2 = ZL i y i y i, (3.6) D Hence, the predictions of the model are consistent with empirical works that found positive relationship between income inequality and international trade. The relationship in Prediction 2, of course, provides insights about how income inequality affects import demand only. There is a backward link between international trade and income inequality. I demonstrate in the counterfactual exercise that trade liberalization is likely to increase income inequality. The predictions of the model here provide additional insights compared to the models with non-homothetic preferences and a representative consumer. For example, Fieler (2011) provides a brief discussion of the role of income distribution in shaping international trade flows. She finds that income inequality has a very small impact, if any, on import demand schedules. The reason for this is twofold. First, she uses quintiles of the income distribution so that the differences between the richest and the poorest consumer are not as pronounced as here. Second, Stone-Geary preferences have a discontinuity at the level of subsistence so that both the extensive and intensive margins of consumption are important. Preferences specified in Fieler (2011) are continuous in a sense that each consumer always spends some part of her income on each type of good Calibration I calibrate the model to 92 countries 17 in the world. The reference year for all the data is I describe the data sources in the Appendix. For the counterfactual experiment I need to calibrate the parameters of the utility function and the production functions in the three sectors. I also need to estimate θ m and θ a. I solve for the counterfactual values in the spirit of Dekle, Eaton and Kortum (2007) and do not have to estimate λ mi, λ ai, τ m,in, and τ a,in. The details of the solution method are in the Appendix. 16 This is a well-known property of any CES related demand system. 17 The limitations of the data do not allow me to extend the sample further. However, the 92 countries in the sample include all large countries in the world. Hence, the calibrated model is very close to reflecting the world in economic terms. 15

16 4.1 Parameters of the utility function Calculating β, which governs the ratio of the consumption of non-tradable to manufacturing goods, is straightforward given the data on households spending. This share is constant across countries and does not vary much with the average level of per capita income. This is confirmed in the left panel of Figure 1 where I plot the ratio of the total non-tradable consumption in each country to the total manufacturing consumption. It is then straightforward to infer the value of β from the following: β 1 β = 1 N N i=1 p ni d c ni,d p mi d c mi.d (4.1) The calculated average is (1.96) with standard deviation of (0.62) which implies β = Estimating the remaining two parameters α and µ is more challenging because, unlike β, the share of income spent on agricultural goods is not constant across countries and is consistently correlated with the real income of an average household in country i. The relationship 18 is seemingly non-linear as shown the right panel of Figure 1 where I plot the ratio of total consumption in agricultural goods to the remaining expenditures. Figure 1: Expenditure Ratios versus Average Real Income per Capita The reason for this starkly strong relationship is the non-homotheticity of household prefer- 18 This is the maximum number of observations of the data in Penn World Tables. Benchmark year

17 ences. This has been well documented in the literature. 19 Modeling this relationship using Stone-Geary preferences has two advantages. First, the utility function leads to tractable linear demand functions. Second, the parameters of the utility function have straightforward and intuitive interpretation. I calibrate α and µ to match the data on country level spending shares s ai. To estimate these parameters, I minimize the squared distance between country-level expenditure shares predicted by the model as described in (2.5) in Section 2.1 and data as follows: min α,µ N [s ai s ai (α, µ)] 2 s.t. α [0, 1], (4.2) i=1 where s ai are the data and s ai (α, µ) is the function of α and µ, which given the value of β and the data on y id and prices, is calculated as in (2.5). Solving (4.2) yields α = and µ = The fit of calibration is good 20, the correlation between the predicted and actual s ai is I use the calibrated parameters to calculate Marshallian demand for each consumer d in i and get consumer-specific spending shares. The calibrated model implies that the the average income cut-off condition is 1.08 US dollars per day. This estimate is extremely close to the 1996 poverty line of 1 dollar per day suggested by the World Bank. In Table 1, I report shares of income spent on agricultural goods, as predicted by the calibrated model, of the poorest and the richest decile in each country. The calibrated model suggests that the differences in the income shares spent on agricultural goods are extremely large for developing countries. The subsistence level is binding for the poorest consumers in a number of developing countries but never for the richest consumers. The differences are less acute, yet still substantial, for relatively rich countries. 4.2 Parameters of the production functions The only parameter common to all three production functions is the capital-labor ratio parameter ν. Consistent with the literature in macroeconomics and international trade (for example see Gollin, 2002), I set ν = Stone-Geary preferences have been used extensively in the international trade literature. Recently, Tombe (2012) used them to explain trade patterns in food products between poor and rich countries. A minor departure of this paper from the literature is in the specification of the utility function a nested functional form which is easier to calibrate and interpret. 20 For this calibration exercise and throughout the rest of this paper, all income values are normalized such that the average real income per capita in the USA is unity. 17

18 Table 1: Income shares spent on agricultural goods for d = 1 and d = 10 country s a,i1 s a,i10 country s a,i1 s a,i10 country s a,i1 s a,i10 country s a,i1 s a,i10 ARG DZA ITA PNG AUS ECU JAM PRT AUT EGY JPN PRY BDI ESP KEN ROM BEL ETH KOR RWA BEN FIN LKA SEN BFA FJI MAR SLE BGD FRA MDG SLV BOL GBR MEX SWE BRA GHA MLI SYR BRB GMB MOZ TCD CAF GRC MWI TGO CAN GTM MYS THA CHE GUY NER TUN CHL HND NGA TUR CHN HTI NIC TZA CIV HUN NLD UGA CMR IDN NOR URY COL IND NPL USA CYP IRL NZL VEN DEU IRN PAK ZAF DNK ISL PER ZMB DOM ISR PHL ZWE The rest of the production parameters are calculated using input-output tables as follows. Parameters {φ, ξ, γ} govern the share of value added in the non-tradable, manufacturing and agricultural sectors, respectively. I calculate them as a ratio of value added to the total output in the respective sector. Similarly, parameters {ϱ, ζ, ɛ, ρ} are calculated from the ratio of total non-tradable input to total manufacturing input. Cross-country averages and standard deviations of the production parameters are in Table 2. Table 2: Production parameters φ ξ γ ϱ ζ ɛ ρ mean std.deviation N Notes: The parameters were calculated using the data on Argentina, Australia, Austria, Belgium, Brazil, Canada, Chile, China, Czech Rep., Denmark, Estonia, Finland, France, Germany, Greece, Hungary, India, Indonesia, Ireland, Italy, Japan, Korea, Mexico, Netherlands, New Zealand, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey, UK, USA, Vietnam. The data for other countries in the sample were unavailable. I estimate the trade elasticities in the manufacturing and the agricultural sectors θ m and θ a using the data on trade flows and tariffs. Let X m,in denote manufacturing trade flow from n to i. Normalize trade flows by the value of domestic sales to get a familiar structural gravity equation: X m,in X m,ii = ( ) θm κn τ m,in t m,in where τ m,in = (τ m,i τ m,inτ m,n). (4.3) κ i I assume total trade costs τ m,in to be log-additive with tariffs and consist of an exporterspecific asymmetric component τ m,n, an importer specific asymmetric component τ m,i, 18

19 and a symmetric component τ m,in. Consistent with the literature, I proxy for the symmetric component of trade costs τ m,in using a distance measure and an adjacency dummy. 21 The two asymmetric trade cost components will be captured by the respective fixed effects. I estimate the following stochastic version of (4.3): X m,in X m,ii = exp[log(ex n ) + log(im i ) θ m log(t m,in ) θ m log( τ m,in )] + error in, (4.4) here im i and ex n are catch-all importer and exporter fixed effects respectively. Notice that the coefficient on tariffs between i and n identifies θ m. 22 I estimate θ a using the data on X a,in and t a,in in the same fashion. I choose to estimate (4.4) in levels rather than in logs to avoid the problem of zeros. 23 The trade data for the 92 countries include a considerable number of zeros and dropping those may lead to inconsistent marginal effects. In practice, I maximize the respective Poisson Pseudo Maximum Likelihood function as advocated by Santos Silva and Tenreyro (2006). The estimates are ˆθ m = 6.53(1.23) and ˆθ a = 12.07(1.16), standard errors in parenthesis are based on Eicker-White sandwich estimates and are robust to heteroskedasticity of an unknown form. The values of θ m and θ a suggest that the degree of heterogeneity in technology is relatively lower in the the agricultural sector. The result is consistent with Fieler (2010) who finds that the degree of heterogeneity in technology is less pronounced in less income elastic goods. The estimates are also consistent with Caliendo and Parro (2011) who estimate trade elasticity parameters for a number of different sectors. 4.3 Benchmark transfers and distribution of capital To calculate benchmark level of v i I use data on balance of payments, cab i, trade flows, X ij, and tariffs, t ij. The benchmark tariff revenues, g i, are calculated as follows: 21 The coefficients on distance and adjacency variables have the expected signs and due to the solution strategy are of no particular interest, hence not reported. 22 Caliendo and Parro (2011), Ramondo and Rodriguez-Claire (2009), Egger and Nigai (2011, 2012) use tariffs to identify the elasticity of trade. The critique of Simonovska and Waugh (2011) is not particularly pertinent to the methodology here because: (i) I do not use price data for identification of the trade elasticity and (ii) the results for manufacturing sector are reasonably close to Simonovska and Waugh (2011) and other estimates in the literature. For example see Donaldson, Costinot and Komunjer (2012). 23 For example, see Baldwin and Harrigan (2011), Chor (2010). 19

20 ( g i = 1 N ) (t a,ij 1)X a,ij + (t m,ij 1)X m,ij, (4.5) L i j=1 Then, v i is simply the sum of appropriately deflated g i and cab i (from data). Average real income y i is then calibrated as real GDP per capita plus total governmental transfers. I use the data on the distribution of income to calibrate the model to the observed levels of heterogeneity across consumers. The benchmark level of real income is: y id = (l i w i + r i k id ) + v i, (4.6) here capital ownership, k id, is the only source of heterogeneity. The data on income inequality correspond to the share of income held by consumers in decile d in country i. ω id = y id. I pin down the values of k id as follows: y i Recall, k id = (1 ν) (ω idy i v i ) r i. (4.7) 5 Counterfactual experiment For the counterfactual experiment, it is useful to express the model in relative changes. Let a denote benchmark and a - counterfactual value of some variable, then the relative change is â = a /a. This approach is particularly convenient 24 because one may assume that the primitives of the model τ in and λ i do not respond to indirect shocks and can conduct counterfactual experiments without having to estimate these unobservable fundamentals. In the counterfactual experiment, I globally eliminate all import tariffs to assess the effect of this hypothetical policy on real income, welfare and income distribution. Tariffs are asymmetric, hence for this counterfactual exercise I reduce tariffs in an asymmetric manner: t a,in = 1 and t m,in = 1 such that t a,in = (t a,in ) 1 ; t m,in = (t m,in ) 1 for all i, n. (5.1) which effectively means zero MFN-tariffs for all countries in both tradable sectors. I list expressions for the counterfactual values of all variables and describe the solution algorithm and the data in the Appendix. 24 see Dekle, Eaton and Kortum, 2007; Caliendo and Parro, 2011; Egger and Nigai,

21 5.1 Trade liberalization and heterogeneous welfare effects Conventional wisdom suggests that trade liberalization on average has positive effects when they are measured in terms of real income. The main goal of this work is to compare welfare gains from trade liberalization calculated under ARC versus those calculated under the heterogeneous consumers framework. To answer the question at stake, I conduct the counterfactual exercise twice. First, I adopt a representative consumer framework, keeping other elements of the model, so that in each country there is only one consumer with income y i. The second variant, corresponds to the model with heterogenous consumer where y id are different across d. I measure welfare using the indirect utility function specified in (2.6). Let V i denote welfare measure of a representative consumer in i and let V id denote welfare of consumer d in i. I plot the counterfactual percentage change 25 in welfare, V i, against the initial values of real income per capita in Figure 3. Figure 2: Trade Liberalization and Consumer Welfare under ARC With few exceptions, all countries gain but small countries gain relatively more. This result is consistent with the results of the models with homothetic (see Eaton and Kortum, 2002; Alvarez and Lucas, 2007) or non-homothetic (see Fieler, 2010) preferences and a representative consumer. Smaller countries gain relatively more for two reasons. First, they are able to specialize on the production of goods where productivity is relatively high. Second, ( ) a 25 Hereafter, denotes percentage change such that a = 100 a 1, where a is a variable and a is its counterfactual value. 21

22 in 1996 developing countries consistently faced higher import tariffs. Global trade liberalization lowers market access costs for them relatively more. In general, the results of the counterfactual exercise, as far as changes in the welfare of an average consumer go, are very much in line with both the empirical literature and other computable general equilibrium models of trade. Next, I calculate welfare gains from the global trade liberalization for consumers across different deciles. If ARC is generally harmless then the welfare effects of a representative consumer must be reasonably close to the welfare gains of consumers across deciles. I report decile-specific welfare gains in Table 3. It is immediately clear that the predictions under ARC are immensely different from the predictions of the model with heterogeneous consumers. The differences are especially large for d = 1 and d = 10, I plot welfare gains for these two deciles in Figure 3. Figure 3: Trade Liberalization and Consumer Welfare for d = 1 and d = 10 Figure 3 offers two major insights. First, the welfare gains of the richest and the poorest deciles are qualitatively different for vast majority of countries. This is true for all rich countries where average real income is at least 70% of the United States level. The relationship is a bit less clear for poor countries, although the general pattern carries through. Consumers in the richest decile gain everywhere except for Japan where welfare loss is negligible and amounts to only -0.03%. Rich consumers gain relatively more in developing than in developed countries. Rich consumers in Thailand (+13.7%), Guyana (+10.7%) and Egypt (+10.6%) experience the largest increase in welfare. 22