Trading Off the Income Gains and the Inequality Costs of Trade Policy

This paper characterizes the trade-off between the income gains and the inequality costs of trade using survey data for 54 developing countries. Tariff data on agricultural and manufacturing goods are combined with household survey data on detailed income and expenditure patterns to estimate the first-order effects of the elimination of import tariffs on household welfare. The paper assesses how these welfare effects vary across the distribution by estimating impacts on the consumption of traded goods, wage income, farm and non-farm family enterprise income, and government transfers. For each country, the income gains and the inequality costs of trade liberalization are quantified and the trade-offs between them are assessed using an Atkinson social welfare index. The analysis finds average income gains from import tariff liberalization in 45 countries and average income losses in nine countries. Across countries in the sample, the gains from trade are 1.9 percent of real household expenditure on average. We find overwhelming evidence of a trade-off between the income gains (losses) and the inequality costs (gains), which arise because trade tends to exacerbate income inequality: 45 countries face a trade-off, while only nine do not. The income gains typically more than offset the increase in inequality. In the majority of developing countries, the prevailing tariff structure thus induces sizable welfare losses.


Policy Research Working Paper 8825
This paper characterizes the trade-off between the income gains and the inequality costs of trade using survey data for 54 developing countries. Tariff data on agricultural and manufacturing goods are combined with household survey data on detailed income and expenditure patterns to estimate the first-order effects of the elimination of import tariffs on household welfare. The paper assesses how these welfare effects vary across the distribution by estimating impacts on the consumption of traded goods, wage income, farm and non-farm family enterprise income, and government transfers. For each country, the income gains and the inequality costs of trade liberalization are quantified and the trade-offs between them are assessed using an Atkinson social welfare index. The analysis finds average income gains from import tariff liberalization in 45 countries and average income losses in nine countries. Across countries in the sample, the gains from trade are 1.9 percent of real household expenditure on average. We find overwhelming evidence of a trade-off between the income gains (losses) and the inequality costs (gains), which arise because trade tends to exacerbate income inequality: 45 countries face a trade-off, while only nine do not. The income gains typically more than offset the increase in inequality. In the majority of developing countries, the prevailing tariff structure thus induces sizable welfare losses. This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at brijkers@worldbank.org, eartuc@worldbank.org, and guido.porto@depeco.unlp.edu.ar.

Introduction
The recent wave of 'new' trade models has rekindled interest in the gains from trade. The results and theorems on the aggregate gains from trade in Dixit and Norman (1980,1986) have been extended by Arkolakis, Costinot and Rodriguez-Clare and Gonzalez-Navarro (2018). 2 In this paper, we combine these two questions and assess the income gains relative to the inequality costs of trade policy. Using survey data for 54 developing countries, we explore the potential trade-off between the gains from trade and the distribution of those gains and we provide a quantification of the inequality-adjusted welfare gains from trade. The evaluation of this trade-off is important, especially because free trade is often opposed on inequality grounds.
We develop a comprehensive model that describes how trade policy affects the real income of different households. Tariffs determine domestic prices which affect households both as consumers and as income earners. As consumers, households are affected through the cost of the entire bundle of traded consumption goods. Similarly, household income is affected through changes in the returns to household production activities, crop growing, family businesses, labor earnings, and government transfers. Our model encompasses all these mechanisms. Following Deaton (1989), we use a first-order approximation to measure how changes in tariffs impact real income.
We then combine tariff data on various goods with household survey data on detailed income and expenditure patterns to estimate these first order welfare effects for 54 low and middle income countries. With estimates of the welfare effects of import tariff liberalization for each household, we study the aggregate gains from trade (as in Arkolakis, Costinot and Rodriguez-Clare, 2012) and the distribution of the gains from trade (as in Porto, 2006). Using A distinctive feature of this paper is that we merge these two approaches by looking at both average gains from trade and their distributional impacts. As is standard in the literature, we rely on first order approximations. We offer a flexible model with extensive household heterogeneity in incomes and expenditures. As in Nicita, Olarreaga and Porto (2014), we allow for a more comprehensive set of sources of income heterogeneity than in most other papers. As in Fajgelbaum and Khandelwal (2015), we allow for non-homothetic preferences and heterogeneity in expenditure patterns. To operationalize this flexible framework, we need to impose some structure on our model. Our setting is compatible with perfect competition, constant returns to scale, and homogeneous products.
We find average income gains from import tariff liberalization in 45 countries and average income losses in the remainder 9 countries. On average, the developing countries in our study enjoy gains from trade equivalent to 1.9 percent of real household expenditure. This is mostly because the consumption gains from lower prices dominate the income losses from reduced protection.
The distributional impacts of import tariff liberalization are highly heterogeneous, across both countries and households. We find that the equality gains, the change in social welfare associated with these distributional impacts, are negatively correlated with the average income gains. Inequality costs arise primarily because trade exacerbates nominal income inequality, while the consumption gains tend to be more evenly spread. This creates trade-offs between the income gains and the equality gains in 45 of the 54 countries in our sample. The income gains typically more than offset the increase in inequality. In 39 countries, liberalization of import tariffs would result in inequality-adjusted welfare gains for a wide range of empirically plausible values of inequality aversion (between 1 and 2). In 9 countries that face trade-offs, protectionism would instead be welfare enhancing for plausible values of inequality aversion. Finally, there are 6 countries where the trade-offs are acute, in which the presence of welfare gains or losses depends crucially on the presumed level of inequality aversion and policy prescriptions are consequently more equivocal. These results imply that in the majority of developing countries in our study, the prevailing pattern of protection induces sizeable welfare losses.
The rest of the paper is organized as follows. Section 2 sets up the model and derives the formulas for the welfare effects of trade policy. Section 3 uses the tariff data and the survey data to estimate those welfare effects in 54 countries. Section 4 discusses the gains from trade and their distribution. Section 5 evaluates and quantifies the trade-off between income gains and inequality costs of trade. It also decomposes equality gains into consumption equality gains and income equality gains, presents robustness tests, and assesses the trade-offs that would arise if countries were to undertake protectionist trade reforms instead of liberalizing.

2 Tariffs and Household Welfare
In this section, we develop a model to study the welfare effects of tariff changes. We adopt an extended agricultural household model to define household welfare (Singh, Squire and Strauss, 1986; Benjamin, 1993) and we derive the welfare effects using first order approximations (Deaton, 1989;Porto, 2006; Nicita, Olarreaga and Porto, 2014).
We begin by discussing production decisions. We assume that households are endowed with a fixed amount of resources v h , which include land or capital, and labor L h . There is no leisure choice but households can differ in the labor endowment because of differences in family size and composition. Assume for now that these factors can be allocated to the production of one (composite) agricultural good or to the labor market. The agricultural good i is produced with a constant return to scale production function F i (v h , L h ). The household takes goods prices p i and wages w as exogenous. There is no market for land or capital v, but labor can be traded, i.e., it can be hired in-farm, sold off-farm, or sold to the labor market. These different types of labor are perfect substitutes. Agricultural profit maximization requires using labor in-farm (own or hired) up to a point where p i ∂F i /∂L = w. The profit function associated with this optimization problem is π i (p i , w, v). In this formulation, household income y h is the sum of maximized profits π h i and the value of the labor endowment wL h . To simplify the exposition that follows, let w h be the labor income that household h derives only from the labor market and let π h be maximized profits defined net of hired off-farm labor only. 3 Allowing for many goods (Singh, Squire and Strauss, 1986), total maximized household income y h is where p is the vector of prices p i , π h i are farm enterprise profits obtained from the sales of good i (such as cotton, tobacco, beans or maize), and T h are taxes paid to (or transfers received from) the government. All other potential sources of income, such as remittances, gifts, other types of public transfers (e.g. pensions) and income from non-traded household enterprises are included in Ω h . 4 Household h maximizes a utility function defined over a vector of consumer goods c, u h = u(c), subject to a vector of given prices p and total household income. Assuming households are price takers in consumer markets, in production and in the labor market, the optimization problem is recursive because production decisions are independent of consumption decisions.
Thus, households maximize u(·), subject to p and maximized income y h . The solution to this optimization problem delivers a demand function for each good. Optimal consumption of good i is c h i and, given required utility u h , the household expenditure function is To derive the welfare effects of trade, we use the concept of compensating variation CV h . For price changes, this is generally done using the expenditure function e h . In our case, we need to consider the fact that trade affects nominal income y h as well. Consequently, we follow Dixit and Norman (1980) and Anderson and Neary (1996) and use the trade expenditure function, V h : which depends on prices p via the maximized nominal income function y h (·) and the expenditure function e(·). Note that the trade expenditure function is usually defined in the Hicksian tradition as e h − y h but we work with (3) instead so as we can interpret the results as changes in real household income (Porto, 2006).
We proceed in two steps. We first derive general welfare effects of price changes in Proposition 1. Then, in proposition 2, we derive estimable welfare effects of trade policy.
In particular, we list additional assumptions that we need to impose in order to obtain estimates of the welfare effects that are compatible with our data. This proposition imposes restrictions on the price changes and on household impacts that we can accommodate in our data. Changes in these assumptions allow for different responses and different welfare effects.
We discuss below some salient alternative model formulations, and present robustness tests in section 5.6.
Proposition 1 Assume the household is a price taker in consumer, producer and labor markets. Given the income generating function y(p, v h ) in equation (1) and the expenditure function e(p, u h ) in equation (2), the impact of a price change on household welfare dV h i (as a share of household initial expenditure e h ) is given by where s h i is the share of traded good i in the consumption bundle of household h, φ h i is the income share derived from the sales of good i, and φ h w is the share of labor income. dV h i is the negative of the compensating variation CV h , the monetary transfer that would allow household h to attain the same utility u h before the trade shock and the price change.
Equation (4) follows from taking the derivative of (3) with respect to p i and expressing the resulting expression in proportional terms. Thus, the proportional price change is d ln p i = dp i /p i . Hotelling's Lemma (i.e., the envelope theorem applied to the profit function) implies that (∂π i /∂p i )dp i = q h i dp i , where q h i is the quantity produced of good i. Multiplying and dividing by p i and expressing the result relative to total income y h gives ( Shephard's Lemma, the derivative of the expenditure function with respect to p i is the quantity consumed c h i so that (∂e/∂p i )dp i = c h i dp i and (p i c h i /e h )d ln p i = s h i d ln p i . 5 This accounts for the first term within brackets in (4). The second term captures the labor income impacts, which are given by the product of the share of income derived from labor, φ h w , and the wage elasticity with respect to the price (∂w h /∂p i )/(p i /w h ). This formulation allows for different assumptions about the functioning of labor markets that determine the nature of the labor income elasticities. 6 The last term in (4) accounts for any impacts on government transfers received or on taxes paid by household h.
Proposition 2 Let τ i be the level of tariff protection in sector i. Assume: (i) goods are homogeneous; (ii) the country is small and thus faces exogenously given international prices p * i ; (iii) perfect price transmission from tariffs to domestic prices; (iv) labor is specific, that is, labor is perfectly immobile across sectors; (v) the loss of public revenue due to tariff cuts is compensated with increases in income taxes. Then, the estimable welfare effects are given by: where now φ h wi is the share of labor income derived only from wages in sector i (and not other sectors) and Ψ h i is the increase in income tax accrued by the household.
This expression is the welfare effect of a simulated full unilateral tariff liberalization. This means that the country reduced its own tariffs individually. Under full import tariff liberalization, so that dτ i = −τ i , the perfect pass-through assumption implies that The unitary pass-through elasticity requires constant returns to scale in the production of the traded goods and perfect competition. 7 This is a simplification of our analysis that is rooted in the lack of data needed to estimate the pass-through elasticities for a broad range of products and countries (see Nicita (2009), Ural Marchand (2012), Atkin, Faber and 6 Since we do not have information on input use, equation (4) omits the indirect effects of wages to hired in-farm labor, L hired on farm profits. See Porto (2005) for a study of those effects in Moldova.
7 See Goldberg and Knetter (1997) for a exhaustive discussion of the conditions needed for perfect pass-through. Note also that there is no role for entry and exit in our model. Gonzalez-Navarro (2018), for estimates of imperfect pass-through for selected countries).
Note that by simulating cases of own unilateral tariff liberalization, we are not accounting for the effects of foreign tariff reductions and market access effects.
The sector specificity of labor allows us to derive a simple wage-price elasticity, because with fixed labor d ln w = d ln p i for wages in sector i and d ln w = 0 for wages in all sectors j = i. It is in principle possible to accommodate different assumptions on how labor markets work. Under full labor mobility, for example, labor would reallocate until a new equilibrium is reached. In the literature, such a model has been estimated by Porto (2006), Nicita (2009) and Nicita, Olarreaga, and Porto (2014). In our model, furthermore, labor is homogeneous and, in particular, there is no skill differentiation. Nicita, Olarreaga and Porto (2014) estimate wage-price elasticities for skilled and unskilled labor separately. Another possibility is to assume imperfect labor mobility and equilibrium inter-industry wage differences. In this case, a price shock can trigger labor reallocation responses across sectors and, consequently, there can be sector-specific wages elasticities. Artuc, Lederman, and Porto (2015) provide estimates of such a model for a wide range of countries. In section 5.6 we assess how our results change if we do not account for labor market responses to tariff changes.
The interpretation of equation (5) is straightforward. After a price change caused by tariff cuts d ln p i = −τ i /(1 + τ i ), the first order effects on real income can be well-approximated with the corresponding expenditure and income shares. In the language of Deaton (1989), because we are working with tariff cuts and price declines, net-consumers benefit while net-producers suffer. In our setting, the net position of a household is defined in an extended model including not only consumption and production of traded goods but also labor income and government transfers.
As in Nicita, Olarreaga and Porto (2014), we want a measure of the welfare effects generated by the entire structure of tariff protection. To obtain it, we sum the changes in welfare in (5) over all traded goods i to get: where V h is the proportional change in household real income. In the remainder of the paper, we estimate the different components of equation (7) and study them in detail. We also use equation (7) to build ex-post counterfactual distributions. Let x h 0 be the observed, ex-ante level of real household income (from the data compiled in the household surveys).
The counterfactual real income x h 1 is Much of what we do below hinges on the comparison of the ex-ante and ex-post distributions of income. Our results also have interesting implications for trade theory. We argue that the most innovative feature of our approach is household heterogeneity, which is often missing in standard trade models. Heterogeneity takes two forms. One is consumption heterogeneity and non-homothetic preferences. In particular, since the poor and the rich allocate their expenditure very differently across goods (most notably, food), this can have implications for the overall gains from trade as well as for the inequality costs of trade. These differences and their implications are not captured by standard models based on homothetic preferences.
There are, of course, papers that rely on non-homothetic preferences, and the conclusions from those models are consistent with the conclusions from our paper.
The other important dimension of heterogeneity is income heterogeneity. In our model, households earn income from various sources not limited to labor markets. In particular, income from sales of different agricultural products plays a crucial role in agrarian economies and these sales include returns to non-labor household factors such as land and assets such as tractors, ploughs, and more humble tools such as shovels, carts, and wheelbarrows. The "distribution" of these factors across households in the surveys is highly heterogeneous.
Households thus have very different sources of incomes and this matters for welfare and inequality. This income heterogeneity is missing in many neoclassical models.

Estimating the Welfare Impacts of Trade Policy
To estimate the welfare impacts of trade policy, we need to measure the different components of equations (5)

Trade Policy and Price Changes
In the empirical application that follows, good i represents one of the product classifications from the expenditure, income and home-consumption templates modules of the household surveys. Each of these classifications includes many finer product groups from the HS classification. We compute weighted average tariff rates τ i for each of our survey categories: where n is an HS-category that belongs to survey-category i and m c,n are imports of good n from country c. The results are shown in Table 1. We report the average tariff for our 2-digit classification, Staple Agriculture, Non-Staple Agriculture, and Manufactures.
Average tariffs are highest for non-staple agricultural goods (14.4 percent). They are lower for staple agricultural goods (10.8 percent) and manufactures (10.9 percent). These averages mask substantial variation in trade barriers across countries. Average tariffs on non-staple agricultural goods range from as high as 46.1 percent in Bhutan to as low as 1.9 percent in Indonesia. Countries with higher tariffs in agriculture (staple and non-staple) tend to have higher tariffs on manufactures as well.
Using the full price transmission assumption (equation 6), we calculate the price changes induced by the elimination of tariffs as follows:

Expenditure and Income Shares
To measure the first order welfare effects we retrieve the expenditure shares s h i and the income shares φ h i and φ h w from the household surveys. Appendix Table A1 lists the countries included in the analysis, together with the corresponding household survey, the year of the survey and the sample size. Our analysis covers all low income countries for which appropriate household survey data were available, as well as the majority of lower middle income countries. To minimize the role of measurement error, we exclude households in the top and bottom 0.5% of the status quo expenditure distribution in all our analyses.
All statistics derived from household surveys presented in the remainder of the paper are weighted using survey weights. For the relatively few surveys for which survey weights are not available, we simply assume each household has the same weight.
Expenditure shares are reported in Table 2. We show averages for six major expenditure

Labor Income and Transfers
As established in Proposition 2, we assume that labor is sector specific. This is consistent with a short-run model, in which households do not adjust labor to the trade shock. To implement this assumption empirically, we consider 10 different sectors (see the Income Template in the Appendix). This is convenient because in this setting the changes in prices transmit one to one to nominal wages and the elasticity of the wage in sector i with respect to its own price p i is one, while the elasticities with respect to other prices j is zero. In robutsness tests, we also consider a model without labor income responses (as in Deaton, 1989). 8 Lastly, we need to derive the cost of tax payments needed to compensate for the tariff revenue loss, Ψ h i . We assume that the government imposes a proportional income tax to do so at the moment it liberalizes. Denoting import quantity by m i , we can approximate the loss of tariff revenue as dR i = −τ i p * i m i (ignoring production and consumption responses). With a proportional income tax, the change in income tax paid by household h is dT h = dψy h , where dψ is the compensatory change in the tax rate. Consequently, In the robustness exercises, we consider two additional cases, one where there is no compensation of the revenue losses via the income tax and another where there is progressivity in the income tax system.

Income Gains and Inequality Costs of Trade Policy
In this section, we investigate the potential income gains (or losses) and the potential inequality costs (or gains) from import tariff liberalization. The next section (section 5) investigates the potential trade-off between the two.

Income Gains from Trade
To be consistent with the literature (e.g., Arkolakis, Costinot and Rodriguez-Clare, 2012), the gains from trade G are defined as the proportional change in aggregate household real expenditures, after import tariff liberalization: where V h is the proportional change in real expenditures of household h which we estimate with equation (7). Thus, G is a weighted average of the welfare effects V h . Table 4 reports G for 45 countries with positive aggregate gains from trade (G > 0). On average, the net gain from import tariff liberalization is a 2.5 percentage point increase in real expenditures. The highest gains accrue to Cameroon and Zambia (6.9 and 5.9 percent of real expenditure, respectively). The smallest gains, for Bangladesh, Burundi, and Mongolia, are about 0.5, 0.4 and 0.1 percent of initial expenditures, respectively. Table 5 reports 10 countries in which import tariff liberalization causes losses (G < 0) which average -0.9 percent of real expenditures. In Cambodia, the country with the largest loss, households are estimated to lose 3.1 percentage points of real expenditure. There are also instances of very small, almost negligible, losses as in Rwanda.
Across all countries in the sample, the average gain from trade liberalization is equal to 1.9 percent of real expenditures. The developing world seems to gain from trade.
To establish the sources of the gains from trade, we decompose the average gains into different channels in columns 2-8 of Tables 4 and 5. Households gain on the expenditure side, but they lose on the income side. The consumption gains come from lower prices of tradables, which on average result in (gross) real income gains of 6.4 percent for the winners (Table 4) and 5.3 percent for the losers (Table 5). About two-thirds of these gains, on average, are due to lower prices of agricultural goods and one-third to lower prices of manufacturing goods. This is a consequence both of the higher expenditure shares on food items in developing countries, and the comparatively high tariffs on agricultural products.
Households lose nominal income. Agricultural income losses account for average real income 14 declines of 1.5 percent across countries with gains and 2.0 percent across countries with losses.
Wage income effects create losses of 0.6 percent in countries with gains and 1.1 percent in countries with losses. The reduction in income from enterprises producing tradable goods is small on average; -0.2 percent of income among winners and -0.1 percent among countries that lose. The biggest driver of income losses is the reduction in government revenue: this channel accounts for 1.6 of the 3.9 percentage points loss in income among winners and 3.2 of the 6.4 percentage point loss among losers.

The Distributional Effects of Trade
We now turn to the distribution of the gains from the trade, which have been the focus of the average impacts just discussed mask significant heterogeneity across households. This is because the net welfare impact is determined by a combination of initial tariffs as well as income and consumption portfolios. We combine two techniques to explore the distributional effects. We estimate kernel averages of the gains from trade, conditional on household initial well-being (per capita expenditure), and we estimate bivariate kernel densities of the joint distribution of the gains from trade and household per capita expenditure.
For the sake of exposition, we divide countries into two groups using the pro-poor index of Nicita, Olarreaga and Porto (2014). In our application, the pro-poor index is the difference between the average gains for the poor-the bottom 20 percent of the income distribution-and the rich-the top 20 percent. If the index is positive the poor gain proportionately more (or lose proportionately less) than the rich, while the opposite happens when the index is negative. According to this classification, import tariff liberalization would be pro-poor in 17 countries, while it would be pro-rich in the remaining 37 countries.
We illustrate the case of pro-poor bias in Figure 1 for the cases of the Central African Republic (panel (a)) and Mauritania (panel (b)). Appendix B provides figures for all countries. In the Central African Republic, the kernel average is positive everywhere, so that there are average gains from trade across the income distribution, but the slope of the kernel regression is negative (so that the poor gain proportionately more than the rich). This pro-poor bias with positive kernel average gains also appears in Azerbaijan, Central African Republic, Ecuador, Indonesia, Moldova, Nepal, Pakistan, Papua New Guinea, Rwanda, the Republic of Yemen and Zambia (see Appendix B). In these countries, import tariff liberalization raises incomes across the income distribution and may reduce inequality. Lanka (see Appendix B). In all these countries, import tariff liberalization raises average income and may reduce inequality significantly.
We illustrate the pro-rich bias in Figure 2. In Uzbekistan (panel (a)), the kernel average is always positive at all levels of per capita expenditure, and the slope of the kernel regression is positive, indicating that, on average, the rich gain proportionately more than the poor.
Again, some individual households stand to lose, as the underlying bivariate kernel density graph shows. Import tariff liberalization lifts incomes throughout the income distribution, but at the expense of potentially higher inequality. This pattern is found in Armenia, Bolivia, Cameroon, Côte d'Ivoire, the Arab Republic of Egypt, Ethiopia, Georgia, Guatemala, Guinea, Iraq, Kyrgyz Republic, Liberia, Malawi, Mozambique, Nicaragua, Niger, Sierra Leone, South Africa, Tajikistan, Tanzania, Uganda, and Ukraine (see Appendix B). The case of pro-rich bias with average gains for the richest households and losses for the poorest is illustrated in panel (b) for Togo. Import tariff liberalization is strongly pro-rich and inequality significantly exacerbated. Similar patterns arise in Bangladesh, Benin, Burkina Faso, Burundi, The Gambia, Kenya, Nigeria, and Vietnam. In panel (c), we show the case of average losses and a pro-rich bias for Ghana. In this country, as well as in Bhutan, Cambodia, Comoros and Madagascar, the poor lose proportionately more than the rich. This is a scenario with average losses as well as increased inequality.

The Trade-Off between Income Gains and Inequality
Costs Given the patterns of gains from trade and of the distribution of those gains, we now assess whether there is a trade-off between the income gains and the inequality costs of import tariff liberalization. This necessarily involves value judgments because different societies, individuals or policy makers may value the gains or losses of some households differently. A tool to describe the trade-off between income inequality and average incomes is the Atkinson social welfare function (Atkinson, 1970): where W is social welfare and ε = 1 is a parameter that measures the dislike for inequality. 9 When ε=0, every household counts the same and social welfare is just the sum (average) of per capita expenditures. As ε increases, the weight attached to the well-being of poorer households increases. In the limit, as ε approaches infinity social welfare is determined by the well-being of the very poorest household (as in a Rawlsian social welfare function). It is very important to interpret the Atkinson social welfare function correctly. As Deaton (1997) explains, W in (13) is not necessarily (and more precisely, it seldom is) the object that policy makers maximize when choosing among policy options. Rather, it provides a means of quantifying potential tensions between mean income and its distribution across households.
An important property of the Atkinson social welfare function is that it can be decomposed in a way that is conducive to the assessment of this trade-off. Concretely, we can write For completeness, when ε = 1, we define ln where µ is mean income and , is an implicit measure of income inequality. Social welfare thus depends on average income µ and on the aggregate level of "equality" (1 − I(ε)). This measure of inequality I(ε) (or the measure of equality (1−I(ε))) depends on ε and nests a whole family of inequality measures.
Using W (ε), we can define a measure of the gains from trade that includes a correction for the inequality costs: where W 0 is the ex-ante social welfare, calculated with the observed (x h 0 ) income distribution in the presence of trade protection and W 1 (ε) is the counterfactual social welfare under import tariff liberalization ( x h 1 ). Given the initial situation and the post-liberalization situation, we can compare W 0 and W 1 using (16). For ε = 0, this is a comparison of mean income, For ε > 0, this comparison involves the calculation of the gains from trade with an implicit correction for inequality (Antras, de Gortari, Itskhoki, 2017; and Galle, Rodriguez-Clare, and Yi, 2017). With estimates of G(ε) for different ε, we can establish whether there is a trade-off between the gains in average incomes and the costs of inequality in its distribution, we can quantify this trade-off, and we can assess it.
For the discussion that follows, we exploit the decomposition of W in equation (14). Note that we can write The inequality-adjusted gains from trade are thus equal to the income gains from trade G(0) plus a correction for changes in inequality, which we will refer to as equality gains.
The gains from trade G(0) can be positive or negative, as shown in section 4.1. The correction for inequality is governed by the Atkinson inequality index I(ε), which may depend non-monotonically on ε. If inequality increases for some ε a > 0 so that then G(ε a ) incorporates a downward correction for these inequality costs. Conversely, if , then the gains from trade are amplified. Note that G(ε) > 0 does not imply no inequality costs per se but rather that their welfare impacts are dominated by the income gains.
Trade-offs arise when income gains and equality gains move in opposite directions, i.e.
when G(0) and µ 1 µ 0 have opposite signs. This is the case in countries where trade exacerbates inequality but improves average income, and in countries where it reduces inequality at the expense of lowering mean income. In some countries, these trade-offs can even result in reversals of trade policy preferences, in the sense that for certain levels of inequality aversion ε, the inequality adjusted gains from trade may be negative (positive) even though import tariff liberalization leads to an increase (reduction) in average income.
Since the sign and magnitude of the equality gains can vary with ε both the existence and acuteness of the trade-offs depend on the level of inequality aversion. No trade-offs occur in countries where import tariff liberalization leads to both income and equality gains (for all ε) or in countries where it leads to lower income and higher inequality (for all ε).
One of the main findings of our paper is the high prevalence of trade policy trade-offs between average incomes and income inequality in the developing world. Among the 54 countries in our sample, 45 face a trade-off and only 9 do not. In 27 of the 45 countries the trade-offs can be severe enough to generate (potential) reversals in the ranking of trade policy preferences. We present countries without trade-offs (section 5.1), countries with trade-offs but without trade policy preference reversals (section 5.2) and with reversals (section 5.3).
Sections 5.4 and 5.5 evaluate such trade-offs and some of the underlying factors. Finally, we run robustness tests in section 5.6 and we explore protectionists scenarios in section 5.7.

No Trade-off Countries
When average income gains emerge together with equality gains, there is no trade-off.
The case of the Central African Republic is shown in Figure 3, which plots G(ε) for ε ∈ [0, 10]. 10 To obtain confidence intervals for G(ε) we resample from the observed distribution and bootstrap using 1000 replications. In the Central African Republic, import tariff liberalization leads to average welfare gains with a pro-poor bias (see Figure 1). The gains in average incomes of 4.2 percent are independent of ε and the pro-poor bias implies that liberalization also leads to equality gains. As ε increases and more weight is put on the poor, these equality gains actually get bigger. As a result, the inequality adjusted welfare gains are increasing in the inequality aversion parameter ε, and exceed 6 percent for large ε. Other countries in which import tariff liberalization yields both equality gains and lifts average incomes are Guinea-Bissau, Jordan and Yemen. In these countries, import tariff liberalization is unambiguously social welfare enhancing.
At the other end of the spectrum lie 4 countries, Comoros, Ghana, Madagascar and Rwanda, which are characterized by average income losses and inequality costs for all ε. In these countries import tariff liberalization would be unambiguously social welfare depressing.

Reversals
There are 45 countries with evidence of a trade-off. In 18 countries, this trade-off is not strong enough to generate reversals of trade policy preferences because import tariff liberalization dominates protection at all levels of inequality aversion (in 16 countries) or because protection dominates liberalization (in only 2 countries, notably Bhutan and Cambodia). Figure 5 illustrates the case of Uzbekistan, where liberalization creates average income gains at the expense of inequality costs. In Uzbekistan inequality increases smoothly with ε and, as a consequence, the inequality adjusted welfare gains G(ε) decrease as inequality aversion rises. The gains from trade are G(0) = 3.5 percent, while the inequality-adjusted gains for large ε can go down to about 1.1 percent. Other countries exhibiting a similar pattern are Armenia, Azerbaijan, Cameroon, the Arab Republic of Egypt, Guinea, Indonesia, Iraq, the Kyrgyz Republic, Moldova, Pakistan, Tajikistan, Uganda, Ukraine, Uzbekistan, South Africa, and Zambia. Since G(ε) is positive and statistically significant for all ε, import tariff liberalization would unambiguously lead to higher social welfare.
Plots of G(ε) for all these countries are given in Appendix C. We summarize the information contained in Figures 3, 4 and 5 in Table 6, which reports the income gains from trade G(0) (column 1) as well as the equality gains (( for several values of inequality aversion ε. To illustrate, consider the case of Guinea-Bissau The table reports many other interesting patterns.

Trade-off Countries with Trade Policy Preference Reversals
In the remaining 27 countries in our sample, we find evidence of a stronger trade-off which may induce a potential reversal of the ranking of trade policy preferences. This reversal occurs when G(ε) changes sign, going from positive to negative or from negative to positive, as ε increases. This means that, depending on the value judgement parameter ε, the social welfare function points to welfare gains associated with import tariff liberalization or with trade protection. Figures 6 and 7 show two examples of the existence of such trade-offs.
In Benin (Figure 6), there are significant average income gains of 2.2 percent so that To quantify these policy preference reversals, we define the cutoff value ε * such that G(ε * ) = 0. The cutoff ε * , which we refer to as trade-ε * , is a measure of the inequality aversion to import tariff liberalization. It is a sufficient statistic to describe the trade-off between mean income and inequality in the presence of trade policy preference reversals.
Defining the trade-off in terms of the gains, the value of ε * shows how intolerant towards inequality a society would have to be in order to make the gains from trade not worthwhile from a social welfare perspective. 12 A high value of ε * implies a soft trade-off: a society needs to put a heavy weight on the cost of higher inequality to be willing to forgo the gains (always in a social welfare function sense). In the limit case, when trade-ε * tends to infinity or when trade-ε * does not exist (as in the countries discussed in sections 5.1 and 5.2), there is no reversal in trade policy preference rankings and, given gains from trade, import tariff liberalization leads to higher social welfare for any ε. By contrast, a low trade-ε * implies a very hard trade-off because relatively light weights on the inequality costs are enough to offset the gains from trade. It is important to note that while the value of ε * describes the nature of the trade-off, it is silent about whether this trade-off is socially acceptable. Table 7 presents estimates of the trade-ε * (column 1) and its 95% confidence interval There are countries with trade-offs where the evidence on trade policy reversals is not so compelling. This occurs when the inequality-adjusted gains from trade are not statistically indistinguishable from zero, that is the null hypothesis that G(ε) = 0 cannot be rejected for a range of ε. We report these cases in columns 4 and 5 of Table 7. In Sierra Leone, for instance, for ε > 4.0, there are inequality adjusted gains from trade (G(ε) > 0) that are not statistically different from 0. Consequently, we cannot rule out a potential reversal (from preferring liberalization to preferring protection). Similar scenarios emerge in Bolivia Nepal (ε > 9.3), Tanzania (ε > 8.9), and Ecuador (ε > 9.9). In all these countries, however, the trade policy preference reversal would come about only for levels of inequality aversion that are arguably implausibly large.
Among the countries with aggregate losses (Panel (b)) of Table 7), the estimated trade-ε * tend to be low. For instance, we get ε * = 0.3 in Sri Lanka (at the first reversal) and ε * = 0.4 in Mali. Note that the interpretation in these cases is different because for low ε, trade protection is preferred to liberalization, and, conversely, liberalization is preferred to protection for higher ε. In these countries, a low ε * thus implies a presumption in favor of lower tariffs, too. In Mauritania (ε * = 1.6), trade protection would be preferred under more moderate values of inequality aversion making it harder to infer trade policy prescriptions.

Assessment
While our results attest to highly heterogeneous welfare impacts of trade liberalization across households and countries, overall the analysis provides overwhelming evidence of a trade-off between income gains and inequality costs of trade policy. In most cases, however, the income gains outweigh the inequality costs, suggesting countries are better off with freer trade. We summarize these observations and results in Figure 8. We plot the value of the inequality-adjust gains from trade G(ε) against the gains from trade G(0). For our assessment, we use ε = 1.5 because it is in the middle of the empirically plausible interval Mauritania jumps from orthant III to orthant II (thus preferring liberalization).
A fundamental conclusion of this analysis is therefore that many of the countries that face a trade-off between mean income and its distribution are better off with lower tariffs (liberalization) than with higher tariffs (protection). Concretely, for empirically plausible levels of inequality aversion, liberalization is expected to enhance welfare in 39 countries and to reduce it in 9 countries. Only in the remaining 6 countries are the policy implications more equivocal.
These results raise questions about why these countries protect their economies. Perhaps countries are not maximizing the Atkinson social welfare function when setting tariffs.
Alternatively, they may be maximizing this function, but subject to constraints. These could include political economy considerations such as rent re-distribution to non-labor income

Underlying Factors: Expenditure and Income Household Heterogeneity
How do the gains from trade and trade-offs described above emerge? We argue that a distinctive element of our approach is the vast heterogeneity in household expenditures and incomes. We showed in section 4.1 that this heterogeneity helps explain the gains from trade. Across-household differences in the consumption gains and in the income losses of the elimination of tariffs show that countries are more likely to benefit from liberalization if food expenditure shares are large, relative to agricultural production income shares.
Household heterogeneity underlies the patterns of trade-offs as well. In Table 8 1−I 0 (ε) ). 13 As much as there is heterogeneity in the trade-offs, there is a marked heterogeneity in the income and consumption equality components. Note, however, that the consumption equality gains are positive yet small in the majority of countries. As consumers, the poor seem to benefit disproportionately from liberalization, in part because they spend a larger share of their budget on food items, which are subject to comparatively high tariffs. By contrast, the income component is overwhelmingly negative across countries, reflecting the fact that trade liberalization creates income inequality costs that are disproportionately borne by poorer households. Whereas the consumption equality gains on average increase only slightly as inequality aversion rises, the average income inequality costs tend to increase sharply (i.e., become more negative) with ε. The trade-offs between the aggregate gains and aggregate 13 Consumption and income impacts may interact, such that the total equality gains from trade are not simply equal to the sum of the consumption equality gains and income equality gains; to assess the importance of these types of interaction effects, we calculated "residual" equality gains as the difference between total equality gains and the sum of income and consumption equality gains. The residual was typically very small and is therefore not presented here.
inequality costs are thus predominantly driven by nominal income inequality. This finding shows that the income losses associated with trade liberalization are borne disproportionately by the poorer segment of the income distribution, whereas the consumption gains are more widely spread.
The role of household heterogeneity is typically underplayed in much of trade theory.
There are theories that postulate non-homothetic preferences and expenditure heterogeneity, but income heterogeneity is often ignored. This can help rationalize potential discrepancies between our results and the intuitions regarding the gains from trade and their distributive impacts that stem from many trade models. For example, the Stolper-Samuelson result could imply a reduction in inequality for low-income, unskilled intensive countries that integrate with the world. Our model shows that this effect can be offset and fully dominated by impacts on other sources of income also affected by trade. 14

Robustness
To assess the robustness of our results, we use two different permutations of our model.

Protectionist Scenarios
Thus far, we have analyzed the inequality-adjusted gains from liberalization, but our framework also lends itself to evaluating trade-offs that might arise if countries become more protectionist. To explore this, we evaluate the welfare impacts associated with three protectionist scenarios that move the economy closer to autarky: (i) a uniform increase in tariffs of 10 percentage points (i.e. adding 10% to all existing tariffs); (ii) a relative increase in tariffs of 10 percent (i.e. multiplying all pre-existing tariffs by 1.1); and (iii) increasing all tariffs to 62.4%. 16 The aim of this exercise is to establish whether the trade-offs that may arise under protectionist scenarios are in general consistent with those derived when countries liberalize. Accordingly, we summarize the results in Table 10 which presents estimates of the (inequality adjusted) gains from trade, the number of countries that exhibit trade-offs, and the trade policy reversals. Country-specific estimates of the gains from trade are presented in Appendix F. 17 As expected, the average gains from these protectionist trade reforms are now negative in the vast majority of countries. While there are 45 winners under liberalization, we find between 43 and 48 losers with increased protection. The estimated average income gains (G(0)) across countries in the three scenarios are, respectively -0.2%, -1.3% and -5.7% (Panel A of Table 10). More importantly, the prevalence of trade-offs is widespread (Panel B). There are only 8-10 countries without trade-offs and, of these, between 6 and 9 prefer the status quo to more protection. There are between 44 and 46 countries with trade-offs.
The resolution of these trade-offs is fairly stable in favor of the status quo for plausible levels of ε (1, 1.5 or 2). That is, in all three protectionist scenarios the vast majority of countries attain higher levels of welfare with the pre-existing structure of trade protection rather than with more protection. Most countries would be hurt by protectionist trade reforms, even after inequality impacts are taken into consideration.

Conclusion
Using household survey data for 54 low and middle income countries harmonized with trade and tariff data, this paper offers a quantitative assessment of the income gains and inequality costs of trade liberalization and the potential trade-off between them.
A stylized yet comprehensive model that allows for a rich range of first-order effects on household consumption and income is used to quantify welfare gains or losses for households in different parts of the expenditure distribution. These welfare impacts are subsequently explored by deploying the Atkinson social welfare function that allows us to decompose inequality adjusted gains into aggregate gains and equality (distributional) gains.
Liberalization is estimated to lead to income gains in 45 countries in our study, and to income losses in 9 countries. The developing world as a whole would enjoy gains of about 1.9 percent of real household expenditures, on average. These income gains are negatively correlated with equality gains, such that liberalization typically entails a trade-off between average incomes and income inequality. In fact, such trade-offs arise in 45 out of 54 different impacts on prices and because the household heterogeneity noted above implies that the inequality implications of a positive welfare effect may be quite different from those of negative effects. countries, and are primarily the result of trade exacerbating income inequality. By contrast, consumption gains tend to be more evenly spread across households.
While trade-offs are prevalent, our findings also suggest that liberalization would be welfare enhancing in the vast majority of countries in our study: in a large part of the developing world, the current structure of tariff protection is inducing sizable welfare losses.
Explaining what drives these patterns is beyond the scope of this paper but an interesting avenue for future research.                Notes: Authors' calculations. The table presents the decomposition of the inequality-adjusted gains from trade G(ε). The first column reports the average income gains from trade (the proportional change in real household expenditures). The three remaining columns show the equality gains (due to changes in inequality) for different values of inequality aversion (ε = 0.5,ε = 1, and ε = 10). The inequality-adjusted gains from trade is the sum of the income gains and the equality gains.   Notes: The table presents the decomposition of the equality gains from trade G(ε) − G(0). The first three column report the average consumption equality gains from trade for different values of inequality aversion (ε = 0.5, ε = 1, and ε = 10). These consumption equality gains are calculated by assuming that liberalization only impacts consumption and not income. The three remaining columns report the income equality gains from trade for different values of inequality aversion (ε = 0.5, ε = 1, and ε = 10), calculated by assuming that liberalization only impacts income but not consumption. Notes: The table presents the decomposition of the equality gains from trade G(ε) − G(0). The first three column report the average consumption equality gains from trade for different values of inequality aversion (ε = 0.5, ε = 1, and ε = 10). These consumption equality gains are calculated by assuming that liberalization only impacts consumption and not income. The three remaining columns report the income equality gains from trade for different values of inequality aversion (ε = 0.5, ε = 1, and ε = 10), calculated by assuming that liberalization only impacts income but not consumption. Notes: The table summarizes the results of various alternative models to assess the robustness of the results obtained using our baseline model present in column 1. The alternative model presented in column 2 does not allow for labor market responses. Column 3 shows the results of a model without tariff redistribution, i.e. in which governments do not increase taxes to make up for the loss of government revenue. Column 4 shows the results of model in which the government makes up the loss in tariff revenue by means of progressive taxes. Both of these last two models are discussed in greater detail in the Appendix, which also presents country specific results for all these models.                Notes: The red curve is the non-parametric kernel regression of the welfare effects and the initial level of per capita household expenditure. The contour lines are level curves of the non-parametric kernel bivariate density of these two variables. Liberalization is classified as having a pro-rich bias if the average proportional real income gains accruing to households in the the top 20% of the pre-liberalization income distribution exceed the average proportional real income gains accruing to households in the bottom 20% of the pre-liberalization real income income distribution.
Appendix C: Inequality Adjusted Welfare Gains                 Notes: this table shows the gains from trade G(0), the inequality adjusted gains from trade, G(0.5), G(1), G(1.5), G(2) and G(10), and trade-when wages do not respond to the tariff liberalization.
Appendix E: Robustness to Alternative Tariff

Redistribution Schemes
To assess the robustness of our results we consider two alternative tariff redistribution scenarios: (1) the government does not make up the budget loss (i.e. tariff redistribution is ignored) and (2)  For each country we calculate the increase in segment j specific tax rates τ j required to balance the budget to compensate for the revenue loss resulting from liberalization. To do so, we first calculate the scaling factor λ where dT is the anticipated tariff revenue loss associated with the liberalization, I ij is a dummy variable that takes the value 1 if household i belongs to tax segment j and 0 otherwise, y i is a measure of (pre-additional tax) income, and r j is the average tax rate paid by households in segment j. After solving for λ we can calculate the "segment" specific tax increase as τ j = λ * r j . These tax increases in turn are part of the income losses associated with liberalization imposing that the progressivity of the tax system is respected. 19 .
Tables E1 and E2 presents estimates of the inequality adjusted gains from trade using 18 These measures are adjusted for allowances/deductions, tax credits, significant local taxes and other main rules of the tax code. They are not, however, adjusted for deductions, exemptions, and credits that depend on taxpayer specific characteristics (for example, no adjustment is made for child credits). They also do not account for evasion and/or avoidance. 19 This formula can be thought of as a crude approximation to the tax function T (y) = y − λy 1−τ .  Notes: this table shows the gains from trade G(0), the inequality adjusted gains from trade, G(0.5), G(1), G(1.5), G(2) and G(10), and trade-when the loss in tariff revenue incurred when countries liberalize and the welfare consequences of the attendant loss in tariff revenue is not taken into consideration. Notes: this table shows the gains from trade G(0), the inequality adjusted gains from trade, G(0.5), G(1), G(1.5), G(2) and G(10), and trade-when the loss in tariff revenue incurred when countries liberalize and the welfare consequences of the attendant loss in tariff revenue is not taken into consideration. Notes: this table shows the gains from trade G(0), the inequality adjusted gains from trade, G(0.5), G(1), G(1.5), G(2) and G(10), and trade-when the loss in tariff revenue incurred when countries liberalize is compensated for by an increase in income taxes that respects the progressivity of the existing labor income tax system. Notes: this table shows the gains from trade G(0), the inequality adjusted gains from trade, G(0.5), G(1), G(1.5), G(2) and G(10), and trade-when the loss in tariff revenue incurred when countries liberalize is compensated for by an increase in income taxes that respects the progressivity of the existing labor income tax system.

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Appendix F: Protectionist Scenarios Notes: this table shows the gains from trade G(0), the inequality adjusted gains from trade, G(0.5), G(1), G(1.5), G(2) and G(10), and trade-when all tariffs are increased by 10% in absolute terms terms. Notes: this table shows the gains from trade G(0), the inequality adjusted gains from trade, G(0.5), G(1), G(1.5), G(2) and G(10), and trade-when all tariffs are increased by 10% in absolute terms terms.  Tariffs  (Table continues on Tariffs  (continued from previous   Notes: this table shows the gains from trade G(0), the inequality adjusted gains from trade, G(0.5), G(1), G(1.5), G(2) and G(10), and trade-when all tariffs are increased by 10% in relative terms (i.e. then tariffs are pre-multiplied by 1.1). Notes: this table shows the gains from trade G(0), the inequality adjusted gains from trade, G(0.5), G(1), G(1.5), G(2) and G(10), and trade-when all tariffs are increased to 62.4%, with tariffs already in excess of 62.4% left unaltered. Notes: this table shows the gains from trade G(0), the inequality adjusted gains from trade, G(0.5), G(1), G(1.5), G(2) and G(10), and trade-, when all tariffs are increased to 62.4%, with tariffs already in excess of 62.4% left unaltered.