# Inequality, nonhomothetic preferences, and trade: a gravity approach.

1. Introduction

One basic tenet of the standard theory of international trade is that tastes are homothetic. For a long time this was a convenient simplification because, along with the assumption that tastes are also identical across countries, it allowed trade theorists to concentrate on the supply side as an explanation for the causes of international trade. However, what started out as a convenient modeling technique propagated into virtually all empirical work in international trade, regardless of whether the assumption on homotheticity is empirically tenable or not. This is problematic because, as we review in more detail below, there is consistent and robust evidence that tastes cannot properly be considered to be homothetic. In particular, one conclusion from accepting the nonhomotheticity of tastes is that income distribution and income per capita become arguments for the aggregate demand function. Because one country's international trade is given by its aggregate supply minus its aggregate demand, we conclude that income distribution and income per capita are important determinants of international trade from the demand side. (1) This effect has been almost completely absent from the empirical trade literature. (2) In particular, as we argue further on, the standard gravity model, which has been used widely to explain trade flows among countries, can only be considered to be complete if it does include income distribution and income per capita as explanatory variables.

Specifically, we propose in this paper to demonstrate the role that income distribution plays in international trade, while also controlling for income per capita. To enhance the persuasiveness of our results, it is crucial that we rely on the most standard and successful empirical model of trade, the gravity model previously mentioned. Thus, we are quite purposeful in excluding the possibility that our results stem in any way from an innovation in the methodology. The gravity model, which explains the volume of trade by the economic masses of the trading partners and the distance between them, has been remarkably successful. In practical applications, researchers sometimes call its use the "modified gravity methodology" because, depending on the question that the researcher intends to ask, she modifies the basic model with some variable or variables of interest. For example, in the first paper (to our knowledge) to look at the impact of the Internet on trade, Freund and Weinhold (2004) include variables on the number of Web hosts in each country to show that they have a positive impact on trade. Dunlevy (2006) asks the question: What is the impact of the immigrant population in the United States on state-level trade with foreign nations? Naturally, he uses the stock of immigrants in each state as his main explanatory variable. Hutchinson (2005) wants to study the impact of language differences on trade, taking the interesting stance that what matters most is how much languages differ from one another. Therefore, he modifies the gravity model with a measure of linguistic distance (Japanese being more distant from English than Dutch from English, for example). As a final recent example of this methodology, Rose (2004) augments the gravity model with membership in the World Trade Organization/General Agreement on Tariffs and Trade (WTO/ GATT) to ask whether the WTO enhances trade. Surprisingly, he is unable to find any significant effect of membership in the WTO/GATT on trade.

We begin our argument with the empirical fact that tastes cannot be considered to be homothetic. The evidence that all goods do not have unit income elasticity of demand abounds in the literature. In particular, the papers by Hunter and Markusen (1988) and Hunter (1991) specifically test for nonhomotheticity of preferences by estimating linear income-expansion paths that have intercepts significantly different from zero. Their model is consistent with a minimum subsistence level for one good (N), causing consumers at very low levels of income to consume good N only, purchasing the other good (L) only at higher levels of income. Good N is a necessity and good L is a luxury, in the sense that their income elasticities of demand are below and above 1, respectively. The strongest prediction of Hunter and Markusen's and Hunter's models is that income per capita is a determinant of aggregate demand. If income per capita increases in a perfectly equal country with a representative consumer, she increases her budget share of the luxury good in response. Note that while the positive intercepts of the income-expansion paths make budget shares a function of per capita income, the linearity of the paths imply that income redistribution, holding per capita income constant, has no impact on the demand for each good, as long as everyone's income is sufficiently high to consume both goods.

Further empirical evidence is provided by Thursby and Thursby (1987). They estimate a gravity model augmented with income per capita, finding that countries with more similar incomes per capita trade more. They ascribe this result to countries with similar GDP per capita having similar consumption patterns, which is an indication of nonhomothetic tastes, and stems directly from the Linder (1961) theory that they are trying to test. Note that this paper is closer to our framework than the aforementioned pieces by Hunter and Hunter, and Markusen, because, like us, Thursby and Thursby also estimate a gravity model. However, their paper differs from our approach in that they also do not allow for a role for income distribution.

The empirical work mentioned in the preceding paragraphs shows that income per capita plays an important role in the determination of expenditure shares, thereby establishing the importance of nonhomotheticity in tastes. But only Francois and Kaplan (1996) look at the effect of income distribution, and in particular of inequality, on trade. However, note that they perform this in a nongravity setting. More specifically, they look at inequality in developing countries as a determinant of the shares of imports of manufactured goods from developed countries. They find that these shares increase with the inequality of the developing country (and with its per capita income), and more so in product categories that are more differentiated, according to their classification of product differentiation.

Having established from previous work that tastes should properly be considered to be nonhomothetic, we consider in the next section the possibility that they are so in a way that makes income-expansion paths have some curvature. As has already been pointed out, this is different from the work of Hunter (1991) and Hunter and Markusen (1988). See also the seminal contribution of Markusen (1986), who also considers income-expansion paths that are linear but with an intercept. When the income-expansion path is actually curved, income distribution becomes a determinant of aggregate demand and therefore of trade flows. The intuition is simple. Imagine that income is redistributed in a country, by taking one dollar from the poor and giving it to the rich. Given curved income-expansion paths, the same dollar will be used by the rich to buy proportionately more luxuries than before. Then, aggregate demand for luxuries increases, and aggregate demand for necessities decreases. All else being equal (including the country's total income, its income per capita, and the income of all other countries), this country will import more luxuries. Therefore, a country pair's GDPs and the distance between them, which constitute the backbone of the gravity model, cannot be considered to be a complete model to determine world trade flows. At a minimum the gravity model must be augmented with income per capita and a measure of income distribution.

We use these insights to set up our own modified gravity model. We then ask whether these measures perform according the theoretical predictions. But to do that we need to identify which goods are necessities and which goods are luxuries. In our main approach, we use consumer data from the Bureau of Labor Statistics (BLS), along with a concordance that we created between BLS product categories and Standard International Trade Classification (SITC) codes, to categorize goods into luxuries and necessities at the four-digit SITC level. We then use our classification to reaggregate trade flows into luxuries and necessities, and estimate the gravity model separately for imports of either type of good.

A summary of our results follows. From the cross-country regressions for the 1990s, (3) we find strong support for imports of luxuries being positively related to importing country inequality, and imports of necessities being negatively related to it, exactly as our theory predicts. We also find (qualified) support from our panel estimation spanning the last three decades. Here the composition of trade also switches toward luxuries and away from necessities as inequality goes up, as we would have predicted. However, for full sample estimations, despite the presence of this relationship between trade composition and inequality, trade volume in both kinds of goods seems to increase with inequality. This is perhaps not as surprising as it might at first seem. Note that our necessity-luxury classification is based on U.S. household data for 2001. Even with identical tastes (an assumption that we maintain throughout), many goods are likely to be luxuries for low income consumers and necessities for consumers at higher incomes. Therefore we conjectured that the necessity-luxury classification is more valid for more developed countries, whose populations are at approximately the same income levels as that of United States. One way to check this was to restrict our panel to include only country pairs in which the importing country is developed, while keeping the exporting country unrestricted. There we find strong evidence for our theoretical predictions not only regarding the composition of imports (the proportion of luxuries and necessities) but also regarding the levels of luxury imports and necessity imports separately. Thus, our preferred explanation for why we find stronger results from the 1990s cross-sectional regressions with the full sample and from the panel regressions with only developed importing countries is that the goods classification is more appropriate in both cases, in the sense that the importing country (whose inequality, as the demander, is the one that matters) is most akin to the United States in 2001: either because it is richer, or because it was closer in time. Note that with economic growth, we should be seeing a convergence across countries in the way goods are classified into luxuries and necessities. Of course, other explanations are also possible. An example of a plausible, alternative explanation is the following: In developing countries, because in the past the actual or the perceived quality of domestically produced goods was lower than that of goods produced in developed countries, the elite preferred consuming the latter to the former. This meant inequality could have shifted consumption in developing countries toward imported goods coming from developed countries, increasing the consumption of both luxury and necessity imports at the same time (with the former increasing proportionally more than the latter). This kind of perception about quality of goods produced in developing countries, with increasing globalization, has been diminishing over time, and, as a consequence, by the 1990s developing countries were already buying luxuries and necessities in accordance with what more developed countries were doing.

Partly motivated by Francois and Kaplan's (1996) identification of luxuries as being differentiated goods, we then turn to a classification of product differentiation constructed by Rauch (1999). We check whether inequality matters differently for trade in differentiated goods, as compared with trade in homogenous goods. We find only weak evidence of systematic differences in the inequality coefficient, thus not lending support to one of Francois and Kaplan's assumptions. We conclude that the assumed relationship between product differentiation and income elasticity of demand is not very strong.

In our third approach, we look at a classification of trade flows based on the income levels of the country of origin (while controlling for the country of destination). We find that, holding everything else constant, an increase in the inequality of the importing country leads to higher imports from rich countries and a reduction of imports from poor countries. This result clearly shows that on average high income countries produce luxuries and low income countries produce necessities, thus validating one key assumption in Markusen (1986), which is also used by Mitra and Trindade (2005): High income elasticity goods are on average capital intensive. Note that in our second and third approaches, we use our full sample (allowing less developed countries to be importers) because we are no longer relying on consumer data from U.S. sources.

We consider our paper complementary to Francois and Kaplan (1996), while departing from it in a number of dimensions. First, quite importantly, we choose the most successful and widely employed model of empirical trade, the gravity model. We then are able to pinpoint precisely how much inequality matters for trade, as compared with the standard results. For example, our calculations show that if income distribution in the United States became as equal as Canada, the United States would import about 9-13% less in luxury goods and 13-19% more in necessity goods. Second, and equally as important, note that Francois and Kaplan in their first approach rely on two crucial assumptions to identify goods that are luxuries (we mention their second and third approaches further on). First, they assume that luxuries are differentiated goods. Second, they assume that differentiated goods are those that have higher indices of intra-industry trade. While both links in this chain of assumptions are justified by Linder's story (which is ultimately what Francois and Kaplan are trying to test), it remains an empirical question to decide whether they are valid. We break open both links with the use of the first direct classification of luxuries and necessities that is compatible with international trade data. Therefore we can test directly the effect of income inequality on trade of luxuries and necessities.

Note that in our panel analysis, the observations are country pairs at various points in time in the 1970s, 1980s, and 1990s, while in our cross-sectional analysis, we have one observation per country pair, using 1990s decade averages for the variables used. Therefore, we make use of much more information than Francois and Kaplan, whose study aggregates imports to each developing country across different exporters and does not have a time component. The structure of our data allows us to control for country-specific effects, expunging the results from any such effects that might contaminate the impact of inequality. (4) Furthermore, using income distribution data from developing countries only, as Francois and Kaplan (1996) do, can be problematic because of potential measurement problems in those countries. (5) Importantly, we will be able to state what trade looks like for different pairs of countries (such as between two high income countries, between a high and a low income country, and so on), and will argue that the patterns of trade with respect to luxuries and necessities are different for different pair types, which to our knowledge is a new empirical effect (see the theories in Markusen 1986 and Mitra and Trindade 2005).

In sum, the paper makes three contributions to the literature. First, we examine the role of inequality (through nonhomotheticity of preferences) in determining the composition of trade. We emphasize that this effect occurs from the demand side, which has been an understudied aspect of international trade flows. Second, we document novel patterns of trade between different pairs of countries. Third, we hope that our classification of four-digit industries into luxuries and necessities will be useful to researchers interested in the role of income elasticity in trade.

2. Theoretical Considerations

If tastes are homothetic, the income expansion path is a straight line starting from the origin. (6) If tastes are nonhomothetic, then some goods are luxuries and others are necessities, meaning that they have income elasticities of demand higher and lower than 1, respectively. The empirical investigations of Hunter and Markusen (1988) and Hunter (1991) find that, in contrast to the standard assumption in trade models, tastes are nonhomothetic in a statistically and economically significant way. According to Hunter, for example, restricting preferences to be homothetic causes an overestimation of the total volume of trade by approximately 25%.

In this paper, we take the stance that if tastes are nonhomothetic, there is a case for studying the effects of income distribution on trade flows. To our knowledge, ours is the first gravity-based paper to do so. Suppose that there are n individuals in an economy with two goods, which we call L and N (luxuries and necessities). It is well-known that if we assume preferences to be homothetic and identical, we can write the aggregate demand function for L as follows:

L = D(p, I), (1)

in which p is the price ratio (= [p.sub.L]/[p.sub.N]) between the two goods, and I = [[SIGMA].sup.n.sub.j=1] [I.sub.j] is total income in the economy, [I.sub.j] being the jth individual's income. There is an analogous demand function for N. Now let us relax the assumption of homothetic tastes, which we do in two steps. First, suppose that the income expansion path is a straight line that does not pass through the origin (see the line labeled E in Figure 1). This is usually called quasi-homothetic tastes. This path is consistent, for example, with assuming that good N is food, which has a minimum subsistence level that every consumer tries to reach before she buys any good L.

Let us first note that with quasi-homothetic tastes aggregate demand no longer is simply a function of aggregate income. Even with a perfectly equal economy where all consumers have the same income (and consume say at point [C.sub.0]), we must now know where along line E each consumer is: the richer he gets, the more proportion of good L he consumes. Thus, income per capita matters. However, note that income distribution still does not matter as long as all consumers are rich enough to consume both goods. Suppose for example that the economy has two consumers, both consuming at [C.sub.0]. Redistribute income from one consumer to the other, such that they end up consuming at points [C.sub.1] and [C.sub.2], respectively. Because [C.sub.1] + [C.sub.2] = 2[C.sub.0], aggregate demand remains unchanged. In conclusion, with quasi-homothetic tastes, Equation 1 is replaced by

L = D(p, I, I/n), (2)

that is, we add income per capita I/n as an argument of aggregate demand.

Second, suppose that preferences are strictly nonhomothetic in such a way that the income expansion path is curved (see Figure 2). Income per capita still matters here, of course. But now, performing the same income redistribution experiment as above, we see that aggregate demand changes. In particular, note that aggregate demand for good L increases ([L.sub.1] + [L.sub.2] > 2[L.sub.0]), while it decreases for good N ([N.sub.1] + [N.sub.2] < 2[N.sub.0]). Thus, aggregate demand now depends on the income of each consumer in the economy: As inequality in the country rises, aggregate demand for luxuries increases and aggregate demand for necessities decreases. Equations 1 and 2 are amended as follows:

L = D(p, [I.sub.1], [I.sub.2], ..., [I.sub.n]). (3)

[FIGURE 1 OMITTED]

One problem with this specification is that we do not have data on every single consumer. What we do have are various summary measures of income distribution. More precisely we have several moments of the distribution. Consequently, we work with an approximation of Equation 3 by including those moments:

L = D(p, I, I/n, [sigma]),

where [sigma] is the measure of income dispersion, that is of income inequality.

We make use of these insights to modify the gravity equation. Let the value of country i's production of luxuries and necessities be denoted by [X.sup.i.sub.L] and [X.sup.i.sub.N], respectively. Country i's values of exports of luxuries and necessities to country j are then given by [X.sup.ij.sub.L] = [s.sup.j.sub.L][X.sup.i.sub.L], [X.sup.ij.sub.N] = [s.sup.j.sub.N][X.sup.i.sub.N], respectively, where [s.sup.j.sub.L] and [s.sup.j.sub.N] represent country j's shares of world expenditure on luxuries and necessities, respectively. Further, letting [[alpha].sup.i.sub.L] and [[alpha].sup.i.sub.N] = (1 - [[alpha].sup.i.sub.L]) denote the shares of luxuries and necessities, respectively, in the overall GDP of country i, and taking logs,

we have

log [X.sup.ij.sub.L] = log [s.sup.j.sub.L] + log [[alpha].sup.i.sub.L] + log [GDP.sup.i],

log [X.sup.ij.sub.L] = log [s.sup.j.sub.N] + log [[alpha].sup.i.sub.N] + log [GDP.sup.i]. (4)

[FIGURE 2 OMITTED]

With nonhomothetic preferences, we can write

[s.sup.j.sub.L] = [phi]([GDP.sup.j]/[GDP.sup.W], [(GDP/capital).sup.j], [[sigma].sup.j], [[sigma].sup.W]),

[s.sup.j.sub.N] = [psi]([GDP.sup.j]/[GDP.sup.W], [(GDP/capital).sup.j], [[sigma].sup.j], [[sigma].sup.W]),

where [(GDP/capita).sup.j] denotes GDP per capita of country j, [GDP.sup.W] is world GDP, [[sigma].sup.j] is the inequality measure of country j, and [[sigma].sup.W] is the inequality measure for the world. Here, all countries face a common world relative price of luxuries to necessities, and therefore this variable is absorbed into a year fixed effect in our regressions. A first-order Taylor expansion yields:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Here, the coefficients of per capita GDP and inequality are positive in the case of luxuries and negative in the case of necessities. Plugging into Equation 4, we have:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)

We estimate equations similar to Equation 5. They are of course the well-known gravity equations, in that exports from country i to country j depend on the logarithms of the GDP of each country. However, the equations are modified by the inclusion of GDP per capita and inequality for the importing country. Note that according to the gravity literature, the GDP per capita plays a dual role in the estimation, in that the stage of development of the trading countries may capture trade barriers. (7) Therefore, its role through nonhomotheticity will be virtually impossible to identify. The effect of nonhomothetic preferences through the inequality measure is more clear-cut and less contaminated. As is traditional in the gravity literature, we also allow for natural barriers to trade, proxied by distance. One last modification is that we expect from the model that the coefficients on luxuries and necessities to be different, and therefore for our main model we will estimate two different equations, one for luxuries and one for necessities.

In deciding how to classify goods as necessities and luxuries, we need to address the fact that nothing guarantees that a good is only a necessity or a luxury. In fact, the opposite is likely to occur often; for example, a good may at low levels of income be a luxury, while at higher levels of income it becomes a necessity. We will use U.S. household data to classify goods into luxuries and necessities because those are the most readily available household data, and also the most likely to be accurate. The data we use are from the year 2001. Note that we maintain the assumption of identical preferences throughout this paper. Therefore, our use of U.S. data is a less severe problem when we use our classification to study other developed countries' demands over the last three decades because the populations in developed countries during this period will be in the same approximate region of the income expansion path as the U.S. population in 2001. But it may be a problem when we use the classification for less developed countries over the entire period of the past three decades. Being attuned to this difficulty will have the consequence that we shall have to drop observations in which a less developed country is the importer (but not when it is the exporter) in our panel regressions for the entire three-decade period. However, even for this three-decade period, across all country pairs (developed and developing, importing and exporting countries) we find that our classification is consistent with a less strict (milder) hypothesis related to luxury and necessity imports, purely based on composition of overall imports. Furthermore, we find that in the case of the cross-sectional regressions using decade averages for the 1990s, our results, relating to both the strong and the mild version of our hypothesis, across all country pairs (developed and developing, importing and exporting countries), are consistent with our classification of goods into luxuries and necessities.

3. Empirical Strategy

Direct Measure: Luxuries versus Necessities

The standard gravity model estimates the volume of trade between two countries, as determined by the product of their GDPs, and some factors that may stimulate or impede trade. Among the latter factors, it is standard to include the distance between the two countries (a proxy for trade costs). As discussed in the previous section, we add per-capita GDP and a measure for the second moment of income distribution (income inequality), both of which also matter if preferences are nonhomothetic. We have already noted that GDP per capita will perform a dual role, and its interpretation should be treated with care. This is one further reason to include inequality, because its interpretation is more straightforward. (8)

We expect that the impact of the different variables, especially GDP per capita and inequality, on the international trade of some good will depend on the nature of the good being transacted. If the good is considered a luxury, then the impact of importing country inequality should be positive, while the converse is true of necessities. We must therefore classify goods as luxuries or necessities in a manner that is compatible with the trade data and aggregate trade flows according to these two categories. We describe in the next section and in the Appendix how we constructed our classification. We then estimate the following model:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (6)

where the variables are defined as follows:

* [X.sub.ijkt]: exports from country i to country j in category k (luxuries or necessities) in year t

* [GDP.sub.it]: country i's GDP in year t

* [(GDP/capita).sub.it]: country i's GDP per capita in year t

* [Distance.sub.ij]: great circle distance between principal cities of countries i and j

* [Inequality.sub.jt]: income inequality in (importing) country j in year t

* [v.sub.ijkt], [u.sub.ijkt]: error terms, with assumed normal independent and identically-distributed distributions

We use country fixed effects ([A.sub.ik] and [A.sub.jk]) throughout, which stand for country-specific factors that may affect differently trade of luxuries and trade of necessities. These might include differences in tastes, comparative advantage in one of the two types of goods, country-specific trade barriers, or multilateral resistance effects. (9) Finally, we also use "fixed time effects," [A.sub.kt], to account for such things as business cycles, systematic currency fluctuations, changes in price levels, worldwide rise or fall in protectionism, and so on. Also, these time effects are added to control for variables that, although they change with time, are common to all countries at a given time. Examples of such variables are world GDP and world inequality ([GDP.sup.W] and [[sigma].sup.W] in our previous section).

In addition to the previously discussed regressions, we run a regression of the ratio of luxury exports from country i to country j in year t to necessity exports from country i to country j in year t exactly on the same right-hand side variables as used in Equation 6. This provides a test of a milder hypothesis that the composition of imports moves toward luxuries with greater inequality. Also, it is hard to think of any endogeneity problems associated with this regression.

Finally, we run gravity regressions as in Equation 6, using cross-sectional decade averages for the 1990s. Because inequality only varies across importing countries and there is no time dimension, the importing country fixed effects for these cross-sectional regressions are modeled as random rather than fixed.

Homogeneous versus Differentiated Goods

Next we use a classification devised by Rauch (1999), which separates goods at the four-digit SITC level according to three different types: goods that are traded in organized exchanges; goods that are not traded in organized exchanges but for which there is a published reference price; and goods that fall under neither of the two previous categories. Rauch argues that the last type is more differentiated than the first two types. We estimate Equation 6 for two categories of goods. The first, k = w + r, is the category that aggregates trade in all goods with organized exchanges (w) plus goods with reference prices (r). This is the category of homogeneous goods. The second category, k = n, denotes trade in all other goods, that is, in differentiated goods. We are motivated to separate trade into these two categories motivated by the following two reasons: (1) Linder's (1961) book, which also motivated previous empirical work, and which argued that luxuries are manufactured, differentiated goods; and (2) Francois and Kaplan's (1996) evidence that works in the same direction. It is certainly plausible that differentiated goods such as automobiles and toys tend to be bought by consumers who have considerable disposable income after the bare necessities of life are met. Because, unlike Francois and Kaplan, we have at our disposal a direct measure of product differentiation, it seems worthwhile to compare our results with theirs.

Source Country

We next attempt to correlate the country of origin of a given good to whether that good is a necessity or a luxury. Here, the working hypothesis is that a country will either produce luxuries or necessities but not both. Because this is an obvious approximation of reality, it is surprising how strong the results come out. Specifically, we reestimate the models in Equation 6 differently. The first difference is that we use total exports from country i to country j. Second, we include the variables [HighIncome.sub.i] and [MidIncome.sub.i], which are dummies for whether the exporting country i is high or midincome. Third, we also include [HighIncome.sub.j] and [MidIncome.sub.j], which perform the analogous role for the importing country. These dummy variables are introduced both in levels and interacted with Inequality for the importing country.

We then estimate the average impact of inequality on bilateral trade for the different combinations of income levels of the importing and the exporting countries. Because we allow three income levels (high income, medium income, or low income), there will be nine combinations in all.

Robustness Checks

Starting with the estimation that uses our direct classification of luxuries and necessities, note that the dependent variable [X.sub.ijkt] is bounded below by zero, and the bound is observed for a large number of bilateral observations. Therefore, besides estimating the models in Equation 6 with OLS, we also estimate a corresponding Tobit model. The equation is changed to:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (7)

where the estimation is performed with maximum likelihood methods. Note that for all models we replaced the (logs of) missing trade flows with zeros. (10) This is because typically missing trade flows happen between small countries that are far apart, and the most likely reason for no trade to be recorded is absent or negligible trade between them.

We also perform median regressions as robustness. This is a type of regression that attempts to estimate the median of the dependent variable (as opposed to the mean), conditional on the independent variables. Therefore, it is quite robust to outliers and bunching of zeros in the dependent variable.

We then try further ways to check the robustness of the results. First, because it is possible that the impact of inequality is nonlinear, we experiment with the inclusion of the square of inequality. Second, apart from using the Gini coefficient, the most widely used summary measure of inequality, we also experiment with the ratio of the income of the top quintile in the income distribution to the income of the bottom quintile. In this way, we hope to capture various aspects of income inequality. This also has the advantage that it responds to a possible criticism of the Gini index, namely that it is a measure that is relatively insensitive to changes in the extremes of the distribution.

One further issue may be the possible endogeneity of the inequality variable. This may occur through a Stolper-Samuelson effect, in which a country's trade has a direct impact on its factor rewards, and thus an indirect impact on inequality. (11) We handle such concerns by restricting the sample in two ways: First, we exclude all observations in which the exporting country represents more than 1% of the importing country's trade; second, we exclude all observations in which the exporting country has one of the five largest GDPs for that year. The goals of both restrictions are the same. By excluding each country's major trading partners, we are restricting ourselves to imports that will have no or at most a negligible impact on inequality, but on which inequality will, according to theory, most definitely have an impact.

Our final robustness check uses country-pair fixed effects. This will take into account effects of common border, language, culture, etc.

4. Data

One contribution of this paper was the creation of a classification of goods as luxuries or necessities that is compatible with the most widely used trade classification in manufactures, namely the Standard International Trade Classification (SITC). In this section we briefly describe our procedure, leaving to the Appendix a more complete documentation of our methodology to create this data set and of some data issues that arose in the process. First, we obtained data from the Bureau of Labor Statistics (BLS) on U.S. households' expenditure layouts in 2001. The BLS separates the U.S. household population into five income quintiles and for each quintile lists the average expenditure share of about 100 consumption categories. These data are then used to extract information about which goods are luxuries and necessities. The next step was matching goods categories from the BLS with categories in international trade data in manufactures, which are coded in the SITC. We used this concordance between the two classifications to aggregate bilateral exports according to whether they are necessities or luxuries. At the end of this process, for any exporter i, importer j, and year t, we have two trade flows: exports by i to j in luxuries and exports by i to j in necessities.

The trade data come from the World Trade Analyzer (WTA), which is a panel covering trade flows from 1970 to 1997 for most countries of the world, organized by the SITC, Revision 2, at the four-digit aggregation level. The WTA was compiled by Statistics Canada using bilateral trade data from the United Nations Statistical Office, and it has been made widely available by Robert Feenstra (2000). The usefulness of this data set comes from its two main characteristics. First, Statistics Canada took special care to match import and export data between any two countries. Second, imports from one country to another are reported in quite a disaggregated manner. The latter feature is important for our purposes because we must aggregate trade data according to our luxury-necessity classification, and according to the Rauch commodity categories.

We also use Raueh's (1999) classification, which divides four-digit SITC goods into three groups: goods that are traded on organized exchanges (denoted by w), goods that have reference prices (r), and finally those goods that fall into none of these categories, and therefore can be thought of as differentiated (n). We aggregated w and r goods into w + r, and, following Rauch, take this aggregate to be homogeneous goods.

Table 1 presents the list of countries in the sample. For the purpose of defining income level dummies, we separated countries into high, medium, and low income countries in each year according to the World Bank's cutoffs to designate high income, middle income, and low income countries. Note that countries can change their income classifications over time. For each country the last three columns of Table 1 represent how many years the country belonged to the low, medium, or high income group.

Inequality data come from Dollar and Kraay (2002), according to whom theirs is the largest data set on inequality available to date. It is largely a recompilation of the UN-WIDER data set that was also used by Deininger and Squire (1996) to construct what they call "a high quality dataset." These data contain a panel of 137 countries, spanning the years from 1955 to 1999. For the main part of the analysis, we use the Gini coefficient as the summary measure of inequality.

Real GDP and real per capita GDP (in 1995 constant U.S. dollars) come from the World Bank's Worm Development Indicators. We obtained the logarithm of the great circle distance data from Rose (2004).

5. Estimation Results

Direct Measure of Luxuries and Necessities

We begin by aggregating bilateral exports into luxuries and necessities, and we then estimate Equation 6 separately for each category. The estimation of our gravity equations separately for luxuries and necessities with an unrestricted sample of all importing countries fails to get results that are economically meaningful and robust to inclusion and exclusion of country dummies, econometric techniques, and measures of inequality. However, one result using that same sample that makes economic sense is that as importing country inequality increases, the composition of imports moves toward luxuries and away from necessities:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the subscript "lux" stands for luxuries and the subscript "nec" stands for necessities. (12) We have explained in the Introduction why we feel that the weak, composition version of our hypothesis holds universally, but the strong version applied separately to luxury and necessity imports does not hold for the early decades. In light of the likelihood that some goods switch from necessities to luxuries or from luxuries to necessities at different income levels and because we used U.S. household data to classify goods, we restrict the sample spanning all of the last three decades to high income importing countries only, keeping exporting countries unrestricted. The results of such a model are presented in the first two columns of Table 2. We also experimented with a model slightly different from Equation 6, in that it restricts the importer and exporter GDP elasticities to be the same, as well as the importer and exporter GDP per capita elasticities to be the same. (13) That model--which is sometimes taken to be the standard gravity model--is reported in columns 4 and 5 of Table 2 for ease of comparison. Columns 3 and 6 show us how the ratio of luxury to necessity imports behaves with respect to the standard gravity variables and inequality.

We first note from either set of estimations that the gravity model works well, as countless numbers of papers have shown before us. All gravity variables enter with the right sign and roughly with magnitudes comparable with other gravity papers (note that in columns 1 and 2, the parameters on log mGDP and log (mGDP/capita) need to be added to get the total effect of the importing country's GDP).

It is remarkable that only one variable changes sign between the two categories, and that is precisely the variable that the theory predicts. In particular, the main prediction of the model is strongly confirmed: Imports of luxuries go up with importing country inequality, and imports of necessities go down. A percentage point increase in importing country inequality causes an increase of luxury imports by 0.9% and a reduction of necessity imports by 1.3%. (14) Thus, for example, if the United States changed from its Gini index of 45 to Canada's Gini index of roughly between 30 and 35 (depending on year), the United States would see a 9-13% reduction in luxury imports and a 13-18% increase in necessity imports. These are surely nontrivial numbers. Inequality seems to have not only a statistically significant but also an economically significant impact on the structure of trade.

From columns 4 and 6, we see that the ratio of imports of luxuries to necessities changes between 0.3 to 0.4% in response to a percentage point change in inequality. This response is three to four times the response in the case of the overall sample. These results are important because they show how the composition of imports changes with inequality. Also, the ratio estimates are less likely to have an endogeneity bias. We therefore illustrate these results with the help of scatter plots. We drop the variable Inequality (the Gini coefficient for the importing country) from the ratio regression in column 4, then generate residuals and plot the residuals against Inequality. Figures 3 and 4 show these plots for the exports of two major high income economies, namely the United States and Japan (with its various trading partners). (15) In both cases, the fitted line is positively sloped as predicted by theory. The plots are similar (with upward sloping fitted lines) for a large number of exporting countries, including the largest low income economies of China and India.

We next run a set of purely cross-sectional regressions (across country pairs). These regressions are useful because our variables are decade averages for the 1990s, thus making our luxury-necessity classification (originating from 2001 U.S. data) more applicable even to developing countries as explained earlier in this paper. Therefore, these cross-sectional regressions use all country pairs with developed and developing countries on both sides of the trade flow. In other words, no restriction has been placed on the set of importing or exporting countries. Because the data set does not have a time dimension, we cannot have importing country inequality and importing country fixed effects at the same time. Therefore, we use random effects. (16)

We present these cross-sectional results in Table 3. The signs of the inequality coefficients are exactly as expected (based on our theory). While the size of the inequality coefficient for luxuries is about a third larger than the luxury coefficients from the panel results presented in Table 2, the cross-sectional inequality coefficient for necessities gets reduced to half the value in Table 2. The inequality coefficient in the luxury-necessity ratio regression in Table 3 is also only 50% of the value in Table 2. This ratio rises by 0.2% as a result of a percentage point increase in inequality.

[FIGURE 3 OMITTED]

Homogeneous versus Differentiated Goods

The results that are most easily comparable with the work of Francois and Kaplan (1996) are shown in Table 4. They are the estimation of Equation 6 for the Rauch differentiated and homogeneous categories, presented in columns 1 and 5 and columns 2 and 6, respectively. We obtain at best only modest support for Francois and Kaplan's approach. In two of their three approaches, the identifying assumption is that luxuries are differentiated goods. (17) Here we use a more recent, and arguably better, classification of product differentiation than the one they used. (18) When using the full sample, we do not find that imports of homogeneous goods (identified as necessities) decrease with inequality. When we restrict the sample as we did in the previous subsection to high income importing countries only, we do find that imports of homogeneous goods decrease with the importing country's inequality, but the coefficient for the differentiated goods (identified as luxuries) loses significance and enters with the wrong sign. These results are perhaps not on the whole surprising because we are after all positing that the definition of differentiated goods (ultimately a combination of technological and taste characteristics, as defined by Rauch) somehow maps to the definition of luxuries (purely a taste characteristic).

[FIGURE 4 OMITTED]

Overall, no specification shows a statistically significant pattern that agrees with the strong theoretical prediction, separately for differentiated and homogeneous goods. This stands in contrast with the results of the previous subsection, in which by using a direct classification of luxuries and necessities, and thus avoiding any identifying assumptions, we do find such a statistically and economically significant pattern. Note that the contrast in Table 4 between the two samples (the full sample and the restricted sample) alerts us once more to the importance of considering demand, and nonhomothetic tastes in particular, for the empirical study of international trade. If tastes were homothetic, and each country's demand were simply proportional to world supply, then restricting the sample of importing countries should not matter, as long as we do not restrict the sample of exporting countries.

It must be noted however that the weaker hypothesis on the ratio variable is verified (columns 3 and 6). The ratio of differentiated to homogeneous imports increases with inequality both in the restricted and in the unrestricted sample. This may mean that the degree of love for variety increases with income.

Source Country

We now turn our attention to whether luxuries and necessities differ according to the income level or the stage of development of the source (exporting) country. Once again we find economically and statistically significant results. The main message we find is: Developing countries export necessities and developed countries export luxuries. We conjecture that this may be due to systematic technological differences between luxuries and necessities, which cause necessities to be labor-intensive goods. But it may also be due to differences in technological advancement of less developed versus more developed countries. (19) The result here is also consistent with the Markusen (1986) conjecture implying that the share of luxury production is higher in countries with higher per-capita income. This is also posited in Mitra and Trindade (2005). Then, if the exporting country i is high income, it will have a higher [[alpha].sub.L] in Equation 4, which in turn leads to a higher predicted [X.sup.ij.sub.L] than if the exporting country were low or middle income.

To thoroughly investigate this issue (and to see the roles of the country of origin versus that of the destination country), we created four additional dummy variables: [HighIncome.sub.i] and [MidIncome.sub.i] take value one if the exporting country i is high or mid-income, respectively, with two analogous variables for the importing country. Table 5 presents the regression results. All gravity variables enter with the right sign and most are significant at the 1% level.

Note that because we interact the dummy variables with our measure of inequality for the importing country, we need to calculate the partial effect of inequality on imports. Because there are three types of countries (high, medium, and low income), there are nine types of country pairs for one-way trade. Table 6 presents the partial effects of inequality on imports, arranged in a matrix with all nine possibilities. Again, these partial effects can be fairly large in magnitude. (20) One can discern a fair amount of structure. Note that because the different rows let the income level of the exporting country vary, this is the variation of greatest interest. The results provide a fairly strong confirmation of the presumption that whether a good is a luxury or a necessity is mostly determined by country of origin, not country of destination. To see this, consider each row one by one. For the first and the third rows, whenever the results are statistically significant, the row determines the sign of the partial effect of inequality on trade. In particular, by moving through the first row (barring the import demand from middle income countries, which has a positive sign but is statistically insignificant), one can see that import demand from all income levels behaves as if the exports of low income countries are necessities. Analogously from the last row, exports from high income countries behave as luxuries, irrespective of the income level of the importing country.

Only for middle income exporters does the rule break down. Here, we have a result similar to something that we have already encountered: What is a luxury for one person may be a necessity for someone else at a different income level. In particular, the pattern of signs in the middle row is reasonable: As the importer grows richer, it sees middle income countries more and more as low income, and therefore it sees middle income exports more and more as necessities--the sign of the coefficient starts out positive and ends as negative. Note that a sign pattern that would be the reverse of this would be unexpected.

The results in this subsection are consistent with the so-called Linder's hypothesis. Linder posited that similarity in tastes is tied to per capita incomes. He argued that producers first produce goods that home consumers demand and only then export these to other markets. This would then result in poor countries being exporters of necessities and rich countries exporters of luxuries. (21)

In sum, we provide strong support for the following stylized fact, to our knowledge not known to the empirical economics literature: Poor countries export necessities, and rich countries export luxuries.

Robustness Checks

We have performed several robustness checks, a selection of which are reported in Table 7. First, we checked for nonlinearities with respect to inequality, with results reported in columns 1 and 2. Introduction of an additional squared inequality term does not qualitatively (or even quantitatively) change the results. The partial derivatives of imports with respect to inequality remain preserved in terms of sign and magnitude. Furthermore they remain preserved in significance if one accepts an 11% significance level. (22)

One may argue that the Gini index, which we have used throughout, is relatively insensitive to the extremes of the income distribution. As a further robustness check, we use the ratio of the income share of the fifth quintile to that of the first quintile (Q51) as an alternative measure of inequality (columns 3, 4). Q51 has the right signs--negative in the case of necessities and positive in the case of luxuries. While it is insignificant in the case of necessities, it is highly significant (at the 1% level) in the case of luxuries.

Columns 5-8 report Tobit and median regressions. This is done because, as mentioned before, the dependent variable is bounded below by zero, and the bound is observed for a large number of bilateral observations. The results are very robust for the median regressions, and for necessities with Tobit, while the coefficient of interest loses significance for the Tobit regression in luxuries. Note that the interpretation of the Tobit results is affected by the likely existence of heteroskedasticity in our panel data, for which, to our knowledge, there is no adequate econometric treatment in Tobit.

Columns 9 and 10 report the results when we exclude from the sample each country's main trading partners. In particular, we exclude observations in which the exporting country represents more than 1% of the importer's import flows. As explained in section 3, this is done to allay the worry that Inequality is endogenous. For the remaining (smaller) exporters, most likely the chain of causality runs unambiguously from inequality to imports, not the other way around. An inspection of columns 9 and 10 reveals the essential robustness of the main results in Table 2. Columns 11 and 12 can be used to perform the analogous analysis when we exclude the largest five economies each year from the exporting side. While in columns 13 and 14, we include the remoteness variable, in columns 15 and 16, we try country-pair fixed effects to capture the effects of variables like common border, common language, common culture, remoteness, etc. The results are qualitatively unchanged. (23)

6. Conclusion

In this paper, we are mostly concerned with the question of how the variation in income distribution among countries affects the volume and pattern of trade. In the framework of established trade theory, the assumption of homothetic and identical tastes rules out that the distribution of income has any effect on trade. In our framework, we drop the assumption of homothetic preferences, which allows us to empirically pursue an investigation on the effect of inequality on trade with the use of a gravity model.

Overall, our findings show that inequality affects the structure and the origin of trade flows. In almost every regression, inequality variables are both economically and statistically significant. When we separate goods according to whether they are luxuries or necessities, based on consumer surveys, we see that a product's characteristic is a major predictor of the impact of inequality on trade. This provides a tighter link with the theory. Furthermore, we document another pattern in the relationship between inequality and trade: As inequality increases in the importing countries, we observe that imports from rich countries increase while imports from poor countries decrease. We note that most standard variables of the gravity model remain qualitatively the same, in the presence of inequality, as in the existing gravity literature.

Appendix

This appendix describes how we classified four-digit SITC goods as necessities or luxuries. (24) First, we obtained data from the Bureau of Labor Statistics on household expenditure shares in the United States in 2001. The BLS separates household population into five income quintiles and, for each quintile, lists the average expenditure share of about 100 expenditure categories. For example, the BLS category labeled "APM1" is "apparel and services, men, 16 and over." For this category, expenditure shares of the different quintiles, from the bottom quintile to the top quintile, are 0.8, 0.8, 0.8, 0.9, and 1.0%, respectively. We defined any category in which expenditure share is weakly rising (as in this example) as a luxury. Conversely, any category in which expenditure share weakly decreases is classified as a necessity. We did not classify either as luxuries or necessities those BLS categories in which shares vary in a nonmonotonic way, or in which shares do not vary at all.

The second part of our procedure was to match the BLS categories to SITC codes. To do so, we went through the description of each four-digit SITC, and matched it with a BLS description. Some judgment calls were needed, as we now detail. To use the example above, we matched the BLS category APM1, "apparel and services, men, 16 and over," to the following SITC codes:

* 8421: overcoats and other coats, men's

* 8422: suits, men's, of textile fabrics

* 8423: trousers, breeches, etc., of textile fabrics (25)

* 8424: jackets, blazers, of textile fabrics

* 8429: other outer garments of textile fabrics

* 842A: outer garments, men's, of textile fabrics

* 842X: outer garments, men's, of textile fabrics

* 8441: shirts, men's, of textile fabrics

These eight SITCs were therefore assigned as luxuries, and many other SITC codes were in this way assigned as either luxuries or necessities. We also assigned as luxuries less than 10 SITC categories for which there was no direct BLS correspondence, but that clearly are luxuries: for example, SITC 8973, "jewelry of gold, silver, or platinum." Of course, many SITCs remained unclassified either as luxuries or necessities because there was no clear BLS correspondence.

Some of the judgment calls had to do with the wording describing the BLS codes and the SITCs did not correspond to each other in a clean way. Furthermore, generally speaking, the BLS categories are at a fairly more aggregated level than the SITC. To illustrate these problems, take SITC categories 0573 "bananas, fresh or dried," and 0579 "fruit, fresh or dried, not elsewhere specified." We matched both to the BLS category FHF1 "fresh fruits," on the following two assumptions: Consumer tastes for most fruits are similar, therefore consumer behavior for a more disaggregated fruit (bananas) should closely match the consumer behavior for aggregate fruit; furthermore, most trade is likely to be in fresh fruit, the part in which the BLS and SITC descriptions coincide.

The SITC, as revised by Statistics Canada, includes some codes ending in X or XX, which for our purposes can be interpreted as aggregate, or "unallocated," trade (for more details, see Feenstra 2000, p. 5). The criterion to match these codes to the BLS codes was a modified majority rule. Generally, if the BLS supplied a closely corresponding aggregate code (those codes ending in 0 or 00), we simply matched the corresponding aggregates; otherwise, if over half the disaggregated SITC codes were assigned to a single BLS code, we also assigned the aggregate SITC code to the same BLS code. (26)

Another issue was posed by the so-called rolled-up codes, also created by Statistics Canada, many of which end with the letter A. These codes were the result of combining two or more SITC codes (for details the reader is referred again to the Feenstra paper). We checked all rolled-up codes for consistency. Generally, we forced consistency by letting the rolled-up code dictate its assigned BLS code to all the original SITCs that were rolled up into it. In some cases, we used judgment to make exceptions to this rule. For example, Statistics Canada rolled up code 7631 "gramophones & record players, electric," into 7649 "parts of apparatus of division 76." We left 7649 unassigned to any BLS code. (27) However, we decided to still assign 7631 to the BLS category that clearly corresponds to it: ENT0, "televisions, radios, audio equipment."

To summarize, at the end of this procedure, we had three types of SITC: luxuries, necessities, and unassigned. We dropped all unassigned trade, and separately aggregated the luxuries and the necessities. Thus, for exporter i, importer j, and year t, we had two trade flows: exports in luxuries and exports in necessities.

Received May 2006; accepted January 2007.

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(1) Mitra and Trindade (2005) work out a theory of this effect. They also discuss intra-industry trade and international transmission of inequality, which are outside the scope of the present paper.

(2) We discuss further on the few exceptions to this general statement, and their relation to our work.

(3) This is the most recent decade in our data set, and it is the one for which the classification of goods into luxuries and necessities that is drawn from 2001 U.S. data as just described is more likely to be relevant.

(4) In the case of our panel regressions, we are able to use exporting country and importing country fixed effects, while in our cross-sectional regressions, because inequality varies across importing countries (and there is no time dimension), we are able to use only random effects (the second best thing to do) for importing countries but still have fixed effects (the first best) for exporting countries. We perform our cross-sectional regressions with and without the importing country random effects, and the results are qualitatively unchanged and quantitatively close.

(5) This would be the case, for example, if a large proportion of asset ownership and of economic transactions in developing countries is informal.

(6) The income expansion path is the locus of consumption bundles for varying income levels at constant prices.

(7) Frankel (1997) argues that per-capita GDPs capture formal and informal barriers to trade and are therefore negatively correlated with trade barriers not directly measured by distance.

(8) It needs to be noted that introducing aggregate GDP and population in the gravity regressions (as done in many papers in the recent past) is not more restrictive than having aggregate GDP and GDP per capita as two different variables as we do in this paper. In fact, the two specifications are equivalent because a(ln GDP) + b(ln GDP--In Population) = (a+b)(ln GDP)--b(ln Population).

(9) For a discussion of the latter, see Anderson and van Wincoop (2003). The case for using country fixed effects to capture multilateral resistance is made by Feenstra (2003). Gravity models with country fixed effects have been estimated by Dunlevy (2006) and Feenstra (2002), among others. Note that this paper is not about trade barriers, or about how they interact, which is Anderson and van Wincoop's true contribution to the literature. In other words, the effects that we test here would still be present even if all trade barriers were zero. Any attempt to use Anderson and van Wincoop's full approach would suffer the difficulty that their model was deduced with the assumption of homothetic tastes, and therefore would not be immediately relevant for our purposes. Using fixed country-year effects also does not solve the problem because the fixed effects would absorb our inequality variable.

(10) This is done by replacing missing trade flows with 0, then adding 1 to all trade flows, and finally taking logs.

(11) A country with a leftist government that wishes to enhance equality may well use trade policy to do so.

(12) The regression where we used the logs of GDP and GDP per capita of the importing and exporting countries separately in place of using the logs of products of GDPs of the two countries gives us exactly the same coefficient on inequality, but the statistical significance of this term is somewhat reduced. We later explain the relationship between these two alternative specifications. Note that * indicates significance at 10%, ** at 5%, and *** at 1%.

(13) Here we have two very similar specifications, namely one in which we use the log of the product of the GDPs of the exporting and importing countries, and another where the logs of the GDPs of the two different countries (exporting and importing) are treated as two different variables. Since In AB = In A + In B, the two specifications are related. However, the specification that uses the product of the two GDPs is more restrictive because it imposes the restriction that the coefficient of the importing country GDP exactly equals the coefficient of the exporting country GDP. Even though one version is more restrictive than the other, we present results using both specifications because they are both used in the literature and we want to show that our results are not driven by any one specification.

(14) Note that the Gini coefficient in our data set is measured on a scale of 0 to 100 (not 0 to 1).

(15) A scatter plot with all pairs of exporting and importing countries is not useful because it would have overcrowded the chart with more than 26,000 observations and would therefore not have a great deal of illustrative power. The scatter plots with one exporting country at a time are much more powerful.

(16) Dropping these random effects keeps the results virtually unchanged.

(17) These are their first and third approach. Their second approach assumes that luxuries are goods that industrial countries trade more. We have something of this flavor in the next subsection, in which we divide trade according to the income per capita of the trading partners.

(18) In their first approach they use the further assumption that differentiated goods have high indices of intra- industry trade. In their third approach, they simply count the number of subindustries that the industrial classification provides for each industry. Rauch's measure is arguably an improvement on both of these approaches because it relies on market responses to each good (for example, are there reference prices widely available for the good?), not on the decisions of the officials that create industrial classifications.

(19) In other words, the reason for more developed countries to have comparative advantage in luxuries may be Heckscher-Ohlin: Luxuries such as automobiles (but also leather bags and fashion clothing) systematically use capital more intensively than necessities. But the reason may also be Ricardian: Simply because luxuries are consumed more as the world is getting richer, it is likely that luxuries are newer goods, with whose technology less developed countries have not yet caught up.

(20) Note that the partial derivative here is that of the log of imports with respect to importing country inequality. In other words, we are looking at the percentage change in imports due to a percentage point change in the Gini coefficient. One has to be careful in interpreting the partial effects because a 1% change in imports might be much more in the case of developed countries that are much richer and are much more open in trade than other countries.

(21) We are grateful to an anonymous referee for having made this point.

(22) Even though inequality and inequality squared are individually insignificant in column 2 for necessities, they are jointly significant leading to the low p-value for the partial effect of inequality.

(23) Some additional robustness tests were performed. We tried adding the inequality of the exporting country, which for the bilateral trade sample we are focusing on, enters insignificantly, in all cases with a t-ratio less than 1. This is understandable because in deriving the gravity model, we find that the country that produces a tradable good will consume a negligible share of the output of that good in a world with many countries. Bilateral imports should then be a function of, in addition to the other gravity variables, the importing country's inequality and the inequality of the rest of the world, which in turn can be expressed as a function of importing country inequality and overall world inequality. Our year dummies capture variations in world inequality from one year to another. In one set of regressions (columns 13 and 14), we include a variable for "remoteness" of the country pair, which is sometimes used in the gravity literature, without affecting the main conclusion. We also tried to combine some of the tests, for example, including the square of the inequality measure in a Tobit regression. We also tried dropping all the OPEC countries and our results and conclusions remain fully preserved. Finally, for the Rauch categories, we tried to separate regressions for the w and for the r goods, in all cases getting no qualitative changes.

(24) A file with our classification is posted online at http://web.missouri.edu/~trindadev/.

(25) Even though "men's" is not explicitly mentioned in this category 8423, or in 8424 and 8429, it can be inferred from the "X" and "A" categories, as explained later.

(26) An exception to this general rule was SITC 1XXX, "beverages and tobacco," which we assigned to BLS AB00 "alcoholic beverages," rather than TB00, "tobacco products and smoking supplies." Note that for our purposes this choice does not matter, since both AB00 and TB00 are necessities according to expenditure shares.

(27) This was also the result of a general criterion. Because the BLS expenditure categories refer to final consumer expenditures, there is no information regarding parts or components. Therefore, all SITCs that refer specifically to parts were left unassigned, and therefore were dropped out of all estimations. Also unassigned were all machinery, except when these are household appliances. Finally, we left unassigned codes that mix machinery with both industrial and household applications (e.g., SITC 7412, "furnace burners for liquid fuel and parts").

Muhammed Dalgin, * Vitor Trindade, ([dagger]) and Devashish Mitra ([double dagger])

* Kania School of Management, University of Scranton, Scranton, PA 18510, USA, E-mail sufHallumDalgin@ gmail.com.

([dagger]) Department of Economics, University of Missouri, Columbia, MO 65211, USA; E-mail trindadev@missouri. edu; corresponding author.

([double dagger]) Department of Economics, Syracuse University, Syracuse, NY 13244-1090, USA; E-mail dmitra@maxwell.syr. edu.

We are indebted to Neville Francis, Gordon Hanson, Duke Kao, Nuno Limbo, Joaquim Silvestre, Mark Vancauteren, and seminar participants at the University of Maryland, University of Texas at Austin, the Universities of California at Berkeley, Davis, Irvine, San Diego, and Santa Cruz, and the Midwest Trade Meetings (Michigan State University) for useful discussions and comments. We also thank Natalia Trofimenko for excellent research assistance. Finally and most importantly, this paper has benefited enormously from comments made by two anonymous referees. The standard disclaimer applies.

One basic tenet of the standard theory of international trade is that tastes are homothetic. For a long time this was a convenient simplification because, along with the assumption that tastes are also identical across countries, it allowed trade theorists to concentrate on the supply side as an explanation for the causes of international trade. However, what started out as a convenient modeling technique propagated into virtually all empirical work in international trade, regardless of whether the assumption on homotheticity is empirically tenable or not. This is problematic because, as we review in more detail below, there is consistent and robust evidence that tastes cannot properly be considered to be homothetic. In particular, one conclusion from accepting the nonhomotheticity of tastes is that income distribution and income per capita become arguments for the aggregate demand function. Because one country's international trade is given by its aggregate supply minus its aggregate demand, we conclude that income distribution and income per capita are important determinants of international trade from the demand side. (1) This effect has been almost completely absent from the empirical trade literature. (2) In particular, as we argue further on, the standard gravity model, which has been used widely to explain trade flows among countries, can only be considered to be complete if it does include income distribution and income per capita as explanatory variables.

Specifically, we propose in this paper to demonstrate the role that income distribution plays in international trade, while also controlling for income per capita. To enhance the persuasiveness of our results, it is crucial that we rely on the most standard and successful empirical model of trade, the gravity model previously mentioned. Thus, we are quite purposeful in excluding the possibility that our results stem in any way from an innovation in the methodology. The gravity model, which explains the volume of trade by the economic masses of the trading partners and the distance between them, has been remarkably successful. In practical applications, researchers sometimes call its use the "modified gravity methodology" because, depending on the question that the researcher intends to ask, she modifies the basic model with some variable or variables of interest. For example, in the first paper (to our knowledge) to look at the impact of the Internet on trade, Freund and Weinhold (2004) include variables on the number of Web hosts in each country to show that they have a positive impact on trade. Dunlevy (2006) asks the question: What is the impact of the immigrant population in the United States on state-level trade with foreign nations? Naturally, he uses the stock of immigrants in each state as his main explanatory variable. Hutchinson (2005) wants to study the impact of language differences on trade, taking the interesting stance that what matters most is how much languages differ from one another. Therefore, he modifies the gravity model with a measure of linguistic distance (Japanese being more distant from English than Dutch from English, for example). As a final recent example of this methodology, Rose (2004) augments the gravity model with membership in the World Trade Organization/General Agreement on Tariffs and Trade (WTO/ GATT) to ask whether the WTO enhances trade. Surprisingly, he is unable to find any significant effect of membership in the WTO/GATT on trade.

We begin our argument with the empirical fact that tastes cannot be considered to be homothetic. The evidence that all goods do not have unit income elasticity of demand abounds in the literature. In particular, the papers by Hunter and Markusen (1988) and Hunter (1991) specifically test for nonhomotheticity of preferences by estimating linear income-expansion paths that have intercepts significantly different from zero. Their model is consistent with a minimum subsistence level for one good (N), causing consumers at very low levels of income to consume good N only, purchasing the other good (L) only at higher levels of income. Good N is a necessity and good L is a luxury, in the sense that their income elasticities of demand are below and above 1, respectively. The strongest prediction of Hunter and Markusen's and Hunter's models is that income per capita is a determinant of aggregate demand. If income per capita increases in a perfectly equal country with a representative consumer, she increases her budget share of the luxury good in response. Note that while the positive intercepts of the income-expansion paths make budget shares a function of per capita income, the linearity of the paths imply that income redistribution, holding per capita income constant, has no impact on the demand for each good, as long as everyone's income is sufficiently high to consume both goods.

Further empirical evidence is provided by Thursby and Thursby (1987). They estimate a gravity model augmented with income per capita, finding that countries with more similar incomes per capita trade more. They ascribe this result to countries with similar GDP per capita having similar consumption patterns, which is an indication of nonhomothetic tastes, and stems directly from the Linder (1961) theory that they are trying to test. Note that this paper is closer to our framework than the aforementioned pieces by Hunter and Hunter, and Markusen, because, like us, Thursby and Thursby also estimate a gravity model. However, their paper differs from our approach in that they also do not allow for a role for income distribution.

The empirical work mentioned in the preceding paragraphs shows that income per capita plays an important role in the determination of expenditure shares, thereby establishing the importance of nonhomotheticity in tastes. But only Francois and Kaplan (1996) look at the effect of income distribution, and in particular of inequality, on trade. However, note that they perform this in a nongravity setting. More specifically, they look at inequality in developing countries as a determinant of the shares of imports of manufactured goods from developed countries. They find that these shares increase with the inequality of the developing country (and with its per capita income), and more so in product categories that are more differentiated, according to their classification of product differentiation.

Having established from previous work that tastes should properly be considered to be nonhomothetic, we consider in the next section the possibility that they are so in a way that makes income-expansion paths have some curvature. As has already been pointed out, this is different from the work of Hunter (1991) and Hunter and Markusen (1988). See also the seminal contribution of Markusen (1986), who also considers income-expansion paths that are linear but with an intercept. When the income-expansion path is actually curved, income distribution becomes a determinant of aggregate demand and therefore of trade flows. The intuition is simple. Imagine that income is redistributed in a country, by taking one dollar from the poor and giving it to the rich. Given curved income-expansion paths, the same dollar will be used by the rich to buy proportionately more luxuries than before. Then, aggregate demand for luxuries increases, and aggregate demand for necessities decreases. All else being equal (including the country's total income, its income per capita, and the income of all other countries), this country will import more luxuries. Therefore, a country pair's GDPs and the distance between them, which constitute the backbone of the gravity model, cannot be considered to be a complete model to determine world trade flows. At a minimum the gravity model must be augmented with income per capita and a measure of income distribution.

We use these insights to set up our own modified gravity model. We then ask whether these measures perform according the theoretical predictions. But to do that we need to identify which goods are necessities and which goods are luxuries. In our main approach, we use consumer data from the Bureau of Labor Statistics (BLS), along with a concordance that we created between BLS product categories and Standard International Trade Classification (SITC) codes, to categorize goods into luxuries and necessities at the four-digit SITC level. We then use our classification to reaggregate trade flows into luxuries and necessities, and estimate the gravity model separately for imports of either type of good.

A summary of our results follows. From the cross-country regressions for the 1990s, (3) we find strong support for imports of luxuries being positively related to importing country inequality, and imports of necessities being negatively related to it, exactly as our theory predicts. We also find (qualified) support from our panel estimation spanning the last three decades. Here the composition of trade also switches toward luxuries and away from necessities as inequality goes up, as we would have predicted. However, for full sample estimations, despite the presence of this relationship between trade composition and inequality, trade volume in both kinds of goods seems to increase with inequality. This is perhaps not as surprising as it might at first seem. Note that our necessity-luxury classification is based on U.S. household data for 2001. Even with identical tastes (an assumption that we maintain throughout), many goods are likely to be luxuries for low income consumers and necessities for consumers at higher incomes. Therefore we conjectured that the necessity-luxury classification is more valid for more developed countries, whose populations are at approximately the same income levels as that of United States. One way to check this was to restrict our panel to include only country pairs in which the importing country is developed, while keeping the exporting country unrestricted. There we find strong evidence for our theoretical predictions not only regarding the composition of imports (the proportion of luxuries and necessities) but also regarding the levels of luxury imports and necessity imports separately. Thus, our preferred explanation for why we find stronger results from the 1990s cross-sectional regressions with the full sample and from the panel regressions with only developed importing countries is that the goods classification is more appropriate in both cases, in the sense that the importing country (whose inequality, as the demander, is the one that matters) is most akin to the United States in 2001: either because it is richer, or because it was closer in time. Note that with economic growth, we should be seeing a convergence across countries in the way goods are classified into luxuries and necessities. Of course, other explanations are also possible. An example of a plausible, alternative explanation is the following: In developing countries, because in the past the actual or the perceived quality of domestically produced goods was lower than that of goods produced in developed countries, the elite preferred consuming the latter to the former. This meant inequality could have shifted consumption in developing countries toward imported goods coming from developed countries, increasing the consumption of both luxury and necessity imports at the same time (with the former increasing proportionally more than the latter). This kind of perception about quality of goods produced in developing countries, with increasing globalization, has been diminishing over time, and, as a consequence, by the 1990s developing countries were already buying luxuries and necessities in accordance with what more developed countries were doing.

Partly motivated by Francois and Kaplan's (1996) identification of luxuries as being differentiated goods, we then turn to a classification of product differentiation constructed by Rauch (1999). We check whether inequality matters differently for trade in differentiated goods, as compared with trade in homogenous goods. We find only weak evidence of systematic differences in the inequality coefficient, thus not lending support to one of Francois and Kaplan's assumptions. We conclude that the assumed relationship between product differentiation and income elasticity of demand is not very strong.

In our third approach, we look at a classification of trade flows based on the income levels of the country of origin (while controlling for the country of destination). We find that, holding everything else constant, an increase in the inequality of the importing country leads to higher imports from rich countries and a reduction of imports from poor countries. This result clearly shows that on average high income countries produce luxuries and low income countries produce necessities, thus validating one key assumption in Markusen (1986), which is also used by Mitra and Trindade (2005): High income elasticity goods are on average capital intensive. Note that in our second and third approaches, we use our full sample (allowing less developed countries to be importers) because we are no longer relying on consumer data from U.S. sources.

We consider our paper complementary to Francois and Kaplan (1996), while departing from it in a number of dimensions. First, quite importantly, we choose the most successful and widely employed model of empirical trade, the gravity model. We then are able to pinpoint precisely how much inequality matters for trade, as compared with the standard results. For example, our calculations show that if income distribution in the United States became as equal as Canada, the United States would import about 9-13% less in luxury goods and 13-19% more in necessity goods. Second, and equally as important, note that Francois and Kaplan in their first approach rely on two crucial assumptions to identify goods that are luxuries (we mention their second and third approaches further on). First, they assume that luxuries are differentiated goods. Second, they assume that differentiated goods are those that have higher indices of intra-industry trade. While both links in this chain of assumptions are justified by Linder's story (which is ultimately what Francois and Kaplan are trying to test), it remains an empirical question to decide whether they are valid. We break open both links with the use of the first direct classification of luxuries and necessities that is compatible with international trade data. Therefore we can test directly the effect of income inequality on trade of luxuries and necessities.

Note that in our panel analysis, the observations are country pairs at various points in time in the 1970s, 1980s, and 1990s, while in our cross-sectional analysis, we have one observation per country pair, using 1990s decade averages for the variables used. Therefore, we make use of much more information than Francois and Kaplan, whose study aggregates imports to each developing country across different exporters and does not have a time component. The structure of our data allows us to control for country-specific effects, expunging the results from any such effects that might contaminate the impact of inequality. (4) Furthermore, using income distribution data from developing countries only, as Francois and Kaplan (1996) do, can be problematic because of potential measurement problems in those countries. (5) Importantly, we will be able to state what trade looks like for different pairs of countries (such as between two high income countries, between a high and a low income country, and so on), and will argue that the patterns of trade with respect to luxuries and necessities are different for different pair types, which to our knowledge is a new empirical effect (see the theories in Markusen 1986 and Mitra and Trindade 2005).

In sum, the paper makes three contributions to the literature. First, we examine the role of inequality (through nonhomotheticity of preferences) in determining the composition of trade. We emphasize that this effect occurs from the demand side, which has been an understudied aspect of international trade flows. Second, we document novel patterns of trade between different pairs of countries. Third, we hope that our classification of four-digit industries into luxuries and necessities will be useful to researchers interested in the role of income elasticity in trade.

2. Theoretical Considerations

If tastes are homothetic, the income expansion path is a straight line starting from the origin. (6) If tastes are nonhomothetic, then some goods are luxuries and others are necessities, meaning that they have income elasticities of demand higher and lower than 1, respectively. The empirical investigations of Hunter and Markusen (1988) and Hunter (1991) find that, in contrast to the standard assumption in trade models, tastes are nonhomothetic in a statistically and economically significant way. According to Hunter, for example, restricting preferences to be homothetic causes an overestimation of the total volume of trade by approximately 25%.

In this paper, we take the stance that if tastes are nonhomothetic, there is a case for studying the effects of income distribution on trade flows. To our knowledge, ours is the first gravity-based paper to do so. Suppose that there are n individuals in an economy with two goods, which we call L and N (luxuries and necessities). It is well-known that if we assume preferences to be homothetic and identical, we can write the aggregate demand function for L as follows:

L = D(p, I), (1)

in which p is the price ratio (= [p.sub.L]/[p.sub.N]) between the two goods, and I = [[SIGMA].sup.n.sub.j=1] [I.sub.j] is total income in the economy, [I.sub.j] being the jth individual's income. There is an analogous demand function for N. Now let us relax the assumption of homothetic tastes, which we do in two steps. First, suppose that the income expansion path is a straight line that does not pass through the origin (see the line labeled E in Figure 1). This is usually called quasi-homothetic tastes. This path is consistent, for example, with assuming that good N is food, which has a minimum subsistence level that every consumer tries to reach before she buys any good L.

Let us first note that with quasi-homothetic tastes aggregate demand no longer is simply a function of aggregate income. Even with a perfectly equal economy where all consumers have the same income (and consume say at point [C.sub.0]), we must now know where along line E each consumer is: the richer he gets, the more proportion of good L he consumes. Thus, income per capita matters. However, note that income distribution still does not matter as long as all consumers are rich enough to consume both goods. Suppose for example that the economy has two consumers, both consuming at [C.sub.0]. Redistribute income from one consumer to the other, such that they end up consuming at points [C.sub.1] and [C.sub.2], respectively. Because [C.sub.1] + [C.sub.2] = 2[C.sub.0], aggregate demand remains unchanged. In conclusion, with quasi-homothetic tastes, Equation 1 is replaced by

L = D(p, I, I/n), (2)

that is, we add income per capita I/n as an argument of aggregate demand.

Second, suppose that preferences are strictly nonhomothetic in such a way that the income expansion path is curved (see Figure 2). Income per capita still matters here, of course. But now, performing the same income redistribution experiment as above, we see that aggregate demand changes. In particular, note that aggregate demand for good L increases ([L.sub.1] + [L.sub.2] > 2[L.sub.0]), while it decreases for good N ([N.sub.1] + [N.sub.2] < 2[N.sub.0]). Thus, aggregate demand now depends on the income of each consumer in the economy: As inequality in the country rises, aggregate demand for luxuries increases and aggregate demand for necessities decreases. Equations 1 and 2 are amended as follows:

L = D(p, [I.sub.1], [I.sub.2], ..., [I.sub.n]). (3)

[FIGURE 1 OMITTED]

One problem with this specification is that we do not have data on every single consumer. What we do have are various summary measures of income distribution. More precisely we have several moments of the distribution. Consequently, we work with an approximation of Equation 3 by including those moments:

L = D(p, I, I/n, [sigma]),

where [sigma] is the measure of income dispersion, that is of income inequality.

We make use of these insights to modify the gravity equation. Let the value of country i's production of luxuries and necessities be denoted by [X.sup.i.sub.L] and [X.sup.i.sub.N], respectively. Country i's values of exports of luxuries and necessities to country j are then given by [X.sup.ij.sub.L] = [s.sup.j.sub.L][X.sup.i.sub.L], [X.sup.ij.sub.N] = [s.sup.j.sub.N][X.sup.i.sub.N], respectively, where [s.sup.j.sub.L] and [s.sup.j.sub.N] represent country j's shares of world expenditure on luxuries and necessities, respectively. Further, letting [[alpha].sup.i.sub.L] and [[alpha].sup.i.sub.N] = (1 - [[alpha].sup.i.sub.L]) denote the shares of luxuries and necessities, respectively, in the overall GDP of country i, and taking logs,

we have

log [X.sup.ij.sub.L] = log [s.sup.j.sub.L] + log [[alpha].sup.i.sub.L] + log [GDP.sup.i],

log [X.sup.ij.sub.L] = log [s.sup.j.sub.N] + log [[alpha].sup.i.sub.N] + log [GDP.sup.i]. (4)

[FIGURE 2 OMITTED]

With nonhomothetic preferences, we can write

[s.sup.j.sub.L] = [phi]([GDP.sup.j]/[GDP.sup.W], [(GDP/capital).sup.j], [[sigma].sup.j], [[sigma].sup.W]),

[s.sup.j.sub.N] = [psi]([GDP.sup.j]/[GDP.sup.W], [(GDP/capital).sup.j], [[sigma].sup.j], [[sigma].sup.W]),

where [(GDP/capita).sup.j] denotes GDP per capita of country j, [GDP.sup.W] is world GDP, [[sigma].sup.j] is the inequality measure of country j, and [[sigma].sup.W] is the inequality measure for the world. Here, all countries face a common world relative price of luxuries to necessities, and therefore this variable is absorbed into a year fixed effect in our regressions. A first-order Taylor expansion yields:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Here, the coefficients of per capita GDP and inequality are positive in the case of luxuries and negative in the case of necessities. Plugging into Equation 4, we have:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)

We estimate equations similar to Equation 5. They are of course the well-known gravity equations, in that exports from country i to country j depend on the logarithms of the GDP of each country. However, the equations are modified by the inclusion of GDP per capita and inequality for the importing country. Note that according to the gravity literature, the GDP per capita plays a dual role in the estimation, in that the stage of development of the trading countries may capture trade barriers. (7) Therefore, its role through nonhomotheticity will be virtually impossible to identify. The effect of nonhomothetic preferences through the inequality measure is more clear-cut and less contaminated. As is traditional in the gravity literature, we also allow for natural barriers to trade, proxied by distance. One last modification is that we expect from the model that the coefficients on luxuries and necessities to be different, and therefore for our main model we will estimate two different equations, one for luxuries and one for necessities.

In deciding how to classify goods as necessities and luxuries, we need to address the fact that nothing guarantees that a good is only a necessity or a luxury. In fact, the opposite is likely to occur often; for example, a good may at low levels of income be a luxury, while at higher levels of income it becomes a necessity. We will use U.S. household data to classify goods into luxuries and necessities because those are the most readily available household data, and also the most likely to be accurate. The data we use are from the year 2001. Note that we maintain the assumption of identical preferences throughout this paper. Therefore, our use of U.S. data is a less severe problem when we use our classification to study other developed countries' demands over the last three decades because the populations in developed countries during this period will be in the same approximate region of the income expansion path as the U.S. population in 2001. But it may be a problem when we use the classification for less developed countries over the entire period of the past three decades. Being attuned to this difficulty will have the consequence that we shall have to drop observations in which a less developed country is the importer (but not when it is the exporter) in our panel regressions for the entire three-decade period. However, even for this three-decade period, across all country pairs (developed and developing, importing and exporting countries) we find that our classification is consistent with a less strict (milder) hypothesis related to luxury and necessity imports, purely based on composition of overall imports. Furthermore, we find that in the case of the cross-sectional regressions using decade averages for the 1990s, our results, relating to both the strong and the mild version of our hypothesis, across all country pairs (developed and developing, importing and exporting countries), are consistent with our classification of goods into luxuries and necessities.

3. Empirical Strategy

Direct Measure: Luxuries versus Necessities

The standard gravity model estimates the volume of trade between two countries, as determined by the product of their GDPs, and some factors that may stimulate or impede trade. Among the latter factors, it is standard to include the distance between the two countries (a proxy for trade costs). As discussed in the previous section, we add per-capita GDP and a measure for the second moment of income distribution (income inequality), both of which also matter if preferences are nonhomothetic. We have already noted that GDP per capita will perform a dual role, and its interpretation should be treated with care. This is one further reason to include inequality, because its interpretation is more straightforward. (8)

We expect that the impact of the different variables, especially GDP per capita and inequality, on the international trade of some good will depend on the nature of the good being transacted. If the good is considered a luxury, then the impact of importing country inequality should be positive, while the converse is true of necessities. We must therefore classify goods as luxuries or necessities in a manner that is compatible with the trade data and aggregate trade flows according to these two categories. We describe in the next section and in the Appendix how we constructed our classification. We then estimate the following model:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (6)

where the variables are defined as follows:

* [X.sub.ijkt]: exports from country i to country j in category k (luxuries or necessities) in year t

* [GDP.sub.it]: country i's GDP in year t

* [(GDP/capita).sub.it]: country i's GDP per capita in year t

* [Distance.sub.ij]: great circle distance between principal cities of countries i and j

* [Inequality.sub.jt]: income inequality in (importing) country j in year t

* [v.sub.ijkt], [u.sub.ijkt]: error terms, with assumed normal independent and identically-distributed distributions

We use country fixed effects ([A.sub.ik] and [A.sub.jk]) throughout, which stand for country-specific factors that may affect differently trade of luxuries and trade of necessities. These might include differences in tastes, comparative advantage in one of the two types of goods, country-specific trade barriers, or multilateral resistance effects. (9) Finally, we also use "fixed time effects," [A.sub.kt], to account for such things as business cycles, systematic currency fluctuations, changes in price levels, worldwide rise or fall in protectionism, and so on. Also, these time effects are added to control for variables that, although they change with time, are common to all countries at a given time. Examples of such variables are world GDP and world inequality ([GDP.sup.W] and [[sigma].sup.W] in our previous section).

In addition to the previously discussed regressions, we run a regression of the ratio of luxury exports from country i to country j in year t to necessity exports from country i to country j in year t exactly on the same right-hand side variables as used in Equation 6. This provides a test of a milder hypothesis that the composition of imports moves toward luxuries with greater inequality. Also, it is hard to think of any endogeneity problems associated with this regression.

Finally, we run gravity regressions as in Equation 6, using cross-sectional decade averages for the 1990s. Because inequality only varies across importing countries and there is no time dimension, the importing country fixed effects for these cross-sectional regressions are modeled as random rather than fixed.

Homogeneous versus Differentiated Goods

Next we use a classification devised by Rauch (1999), which separates goods at the four-digit SITC level according to three different types: goods that are traded in organized exchanges; goods that are not traded in organized exchanges but for which there is a published reference price; and goods that fall under neither of the two previous categories. Rauch argues that the last type is more differentiated than the first two types. We estimate Equation 6 for two categories of goods. The first, k = w + r, is the category that aggregates trade in all goods with organized exchanges (w) plus goods with reference prices (r). This is the category of homogeneous goods. The second category, k = n, denotes trade in all other goods, that is, in differentiated goods. We are motivated to separate trade into these two categories motivated by the following two reasons: (1) Linder's (1961) book, which also motivated previous empirical work, and which argued that luxuries are manufactured, differentiated goods; and (2) Francois and Kaplan's (1996) evidence that works in the same direction. It is certainly plausible that differentiated goods such as automobiles and toys tend to be bought by consumers who have considerable disposable income after the bare necessities of life are met. Because, unlike Francois and Kaplan, we have at our disposal a direct measure of product differentiation, it seems worthwhile to compare our results with theirs.

Source Country

We next attempt to correlate the country of origin of a given good to whether that good is a necessity or a luxury. Here, the working hypothesis is that a country will either produce luxuries or necessities but not both. Because this is an obvious approximation of reality, it is surprising how strong the results come out. Specifically, we reestimate the models in Equation 6 differently. The first difference is that we use total exports from country i to country j. Second, we include the variables [HighIncome.sub.i] and [MidIncome.sub.i], which are dummies for whether the exporting country i is high or midincome. Third, we also include [HighIncome.sub.j] and [MidIncome.sub.j], which perform the analogous role for the importing country. These dummy variables are introduced both in levels and interacted with Inequality for the importing country.

We then estimate the average impact of inequality on bilateral trade for the different combinations of income levels of the importing and the exporting countries. Because we allow three income levels (high income, medium income, or low income), there will be nine combinations in all.

Robustness Checks

Starting with the estimation that uses our direct classification of luxuries and necessities, note that the dependent variable [X.sub.ijkt] is bounded below by zero, and the bound is observed for a large number of bilateral observations. Therefore, besides estimating the models in Equation 6 with OLS, we also estimate a corresponding Tobit model. The equation is changed to:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (7)

where the estimation is performed with maximum likelihood methods. Note that for all models we replaced the (logs of) missing trade flows with zeros. (10) This is because typically missing trade flows happen between small countries that are far apart, and the most likely reason for no trade to be recorded is absent or negligible trade between them.

We also perform median regressions as robustness. This is a type of regression that attempts to estimate the median of the dependent variable (as opposed to the mean), conditional on the independent variables. Therefore, it is quite robust to outliers and bunching of zeros in the dependent variable.

We then try further ways to check the robustness of the results. First, because it is possible that the impact of inequality is nonlinear, we experiment with the inclusion of the square of inequality. Second, apart from using the Gini coefficient, the most widely used summary measure of inequality, we also experiment with the ratio of the income of the top quintile in the income distribution to the income of the bottom quintile. In this way, we hope to capture various aspects of income inequality. This also has the advantage that it responds to a possible criticism of the Gini index, namely that it is a measure that is relatively insensitive to changes in the extremes of the distribution.

One further issue may be the possible endogeneity of the inequality variable. This may occur through a Stolper-Samuelson effect, in which a country's trade has a direct impact on its factor rewards, and thus an indirect impact on inequality. (11) We handle such concerns by restricting the sample in two ways: First, we exclude all observations in which the exporting country represents more than 1% of the importing country's trade; second, we exclude all observations in which the exporting country has one of the five largest GDPs for that year. The goals of both restrictions are the same. By excluding each country's major trading partners, we are restricting ourselves to imports that will have no or at most a negligible impact on inequality, but on which inequality will, according to theory, most definitely have an impact.

Our final robustness check uses country-pair fixed effects. This will take into account effects of common border, language, culture, etc.

4. Data

One contribution of this paper was the creation of a classification of goods as luxuries or necessities that is compatible with the most widely used trade classification in manufactures, namely the Standard International Trade Classification (SITC). In this section we briefly describe our procedure, leaving to the Appendix a more complete documentation of our methodology to create this data set and of some data issues that arose in the process. First, we obtained data from the Bureau of Labor Statistics (BLS) on U.S. households' expenditure layouts in 2001. The BLS separates the U.S. household population into five income quintiles and for each quintile lists the average expenditure share of about 100 consumption categories. These data are then used to extract information about which goods are luxuries and necessities. The next step was matching goods categories from the BLS with categories in international trade data in manufactures, which are coded in the SITC. We used this concordance between the two classifications to aggregate bilateral exports according to whether they are necessities or luxuries. At the end of this process, for any exporter i, importer j, and year t, we have two trade flows: exports by i to j in luxuries and exports by i to j in necessities.

The trade data come from the World Trade Analyzer (WTA), which is a panel covering trade flows from 1970 to 1997 for most countries of the world, organized by the SITC, Revision 2, at the four-digit aggregation level. The WTA was compiled by Statistics Canada using bilateral trade data from the United Nations Statistical Office, and it has been made widely available by Robert Feenstra (2000). The usefulness of this data set comes from its two main characteristics. First, Statistics Canada took special care to match import and export data between any two countries. Second, imports from one country to another are reported in quite a disaggregated manner. The latter feature is important for our purposes because we must aggregate trade data according to our luxury-necessity classification, and according to the Rauch commodity categories.

We also use Raueh's (1999) classification, which divides four-digit SITC goods into three groups: goods that are traded on organized exchanges (denoted by w), goods that have reference prices (r), and finally those goods that fall into none of these categories, and therefore can be thought of as differentiated (n). We aggregated w and r goods into w + r, and, following Rauch, take this aggregate to be homogeneous goods.

Table 1 presents the list of countries in the sample. For the purpose of defining income level dummies, we separated countries into high, medium, and low income countries in each year according to the World Bank's cutoffs to designate high income, middle income, and low income countries. Note that countries can change their income classifications over time. For each country the last three columns of Table 1 represent how many years the country belonged to the low, medium, or high income group.

Inequality data come from Dollar and Kraay (2002), according to whom theirs is the largest data set on inequality available to date. It is largely a recompilation of the UN-WIDER data set that was also used by Deininger and Squire (1996) to construct what they call "a high quality dataset." These data contain a panel of 137 countries, spanning the years from 1955 to 1999. For the main part of the analysis, we use the Gini coefficient as the summary measure of inequality.

Real GDP and real per capita GDP (in 1995 constant U.S. dollars) come from the World Bank's Worm Development Indicators. We obtained the logarithm of the great circle distance data from Rose (2004).

5. Estimation Results

Direct Measure of Luxuries and Necessities

We begin by aggregating bilateral exports into luxuries and necessities, and we then estimate Equation 6 separately for each category. The estimation of our gravity equations separately for luxuries and necessities with an unrestricted sample of all importing countries fails to get results that are economically meaningful and robust to inclusion and exclusion of country dummies, econometric techniques, and measures of inequality. However, one result using that same sample that makes economic sense is that as importing country inequality increases, the composition of imports moves toward luxuries and away from necessities:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the subscript "lux" stands for luxuries and the subscript "nec" stands for necessities. (12) We have explained in the Introduction why we feel that the weak, composition version of our hypothesis holds universally, but the strong version applied separately to luxury and necessity imports does not hold for the early decades. In light of the likelihood that some goods switch from necessities to luxuries or from luxuries to necessities at different income levels and because we used U.S. household data to classify goods, we restrict the sample spanning all of the last three decades to high income importing countries only, keeping exporting countries unrestricted. The results of such a model are presented in the first two columns of Table 2. We also experimented with a model slightly different from Equation 6, in that it restricts the importer and exporter GDP elasticities to be the same, as well as the importer and exporter GDP per capita elasticities to be the same. (13) That model--which is sometimes taken to be the standard gravity model--is reported in columns 4 and 5 of Table 2 for ease of comparison. Columns 3 and 6 show us how the ratio of luxury to necessity imports behaves with respect to the standard gravity variables and inequality.

We first note from either set of estimations that the gravity model works well, as countless numbers of papers have shown before us. All gravity variables enter with the right sign and roughly with magnitudes comparable with other gravity papers (note that in columns 1 and 2, the parameters on log mGDP and log (mGDP/capita) need to be added to get the total effect of the importing country's GDP).

It is remarkable that only one variable changes sign between the two categories, and that is precisely the variable that the theory predicts. In particular, the main prediction of the model is strongly confirmed: Imports of luxuries go up with importing country inequality, and imports of necessities go down. A percentage point increase in importing country inequality causes an increase of luxury imports by 0.9% and a reduction of necessity imports by 1.3%. (14) Thus, for example, if the United States changed from its Gini index of 45 to Canada's Gini index of roughly between 30 and 35 (depending on year), the United States would see a 9-13% reduction in luxury imports and a 13-18% increase in necessity imports. These are surely nontrivial numbers. Inequality seems to have not only a statistically significant but also an economically significant impact on the structure of trade.

From columns 4 and 6, we see that the ratio of imports of luxuries to necessities changes between 0.3 to 0.4% in response to a percentage point change in inequality. This response is three to four times the response in the case of the overall sample. These results are important because they show how the composition of imports changes with inequality. Also, the ratio estimates are less likely to have an endogeneity bias. We therefore illustrate these results with the help of scatter plots. We drop the variable Inequality (the Gini coefficient for the importing country) from the ratio regression in column 4, then generate residuals and plot the residuals against Inequality. Figures 3 and 4 show these plots for the exports of two major high income economies, namely the United States and Japan (with its various trading partners). (15) In both cases, the fitted line is positively sloped as predicted by theory. The plots are similar (with upward sloping fitted lines) for a large number of exporting countries, including the largest low income economies of China and India.

We next run a set of purely cross-sectional regressions (across country pairs). These regressions are useful because our variables are decade averages for the 1990s, thus making our luxury-necessity classification (originating from 2001 U.S. data) more applicable even to developing countries as explained earlier in this paper. Therefore, these cross-sectional regressions use all country pairs with developed and developing countries on both sides of the trade flow. In other words, no restriction has been placed on the set of importing or exporting countries. Because the data set does not have a time dimension, we cannot have importing country inequality and importing country fixed effects at the same time. Therefore, we use random effects. (16)

We present these cross-sectional results in Table 3. The signs of the inequality coefficients are exactly as expected (based on our theory). While the size of the inequality coefficient for luxuries is about a third larger than the luxury coefficients from the panel results presented in Table 2, the cross-sectional inequality coefficient for necessities gets reduced to half the value in Table 2. The inequality coefficient in the luxury-necessity ratio regression in Table 3 is also only 50% of the value in Table 2. This ratio rises by 0.2% as a result of a percentage point increase in inequality.

[FIGURE 3 OMITTED]

Homogeneous versus Differentiated Goods

The results that are most easily comparable with the work of Francois and Kaplan (1996) are shown in Table 4. They are the estimation of Equation 6 for the Rauch differentiated and homogeneous categories, presented in columns 1 and 5 and columns 2 and 6, respectively. We obtain at best only modest support for Francois and Kaplan's approach. In two of their three approaches, the identifying assumption is that luxuries are differentiated goods. (17) Here we use a more recent, and arguably better, classification of product differentiation than the one they used. (18) When using the full sample, we do not find that imports of homogeneous goods (identified as necessities) decrease with inequality. When we restrict the sample as we did in the previous subsection to high income importing countries only, we do find that imports of homogeneous goods decrease with the importing country's inequality, but the coefficient for the differentiated goods (identified as luxuries) loses significance and enters with the wrong sign. These results are perhaps not on the whole surprising because we are after all positing that the definition of differentiated goods (ultimately a combination of technological and taste characteristics, as defined by Rauch) somehow maps to the definition of luxuries (purely a taste characteristic).

[FIGURE 4 OMITTED]

Overall, no specification shows a statistically significant pattern that agrees with the strong theoretical prediction, separately for differentiated and homogeneous goods. This stands in contrast with the results of the previous subsection, in which by using a direct classification of luxuries and necessities, and thus avoiding any identifying assumptions, we do find such a statistically and economically significant pattern. Note that the contrast in Table 4 between the two samples (the full sample and the restricted sample) alerts us once more to the importance of considering demand, and nonhomothetic tastes in particular, for the empirical study of international trade. If tastes were homothetic, and each country's demand were simply proportional to world supply, then restricting the sample of importing countries should not matter, as long as we do not restrict the sample of exporting countries.

It must be noted however that the weaker hypothesis on the ratio variable is verified (columns 3 and 6). The ratio of differentiated to homogeneous imports increases with inequality both in the restricted and in the unrestricted sample. This may mean that the degree of love for variety increases with income.

Source Country

We now turn our attention to whether luxuries and necessities differ according to the income level or the stage of development of the source (exporting) country. Once again we find economically and statistically significant results. The main message we find is: Developing countries export necessities and developed countries export luxuries. We conjecture that this may be due to systematic technological differences between luxuries and necessities, which cause necessities to be labor-intensive goods. But it may also be due to differences in technological advancement of less developed versus more developed countries. (19) The result here is also consistent with the Markusen (1986) conjecture implying that the share of luxury production is higher in countries with higher per-capita income. This is also posited in Mitra and Trindade (2005). Then, if the exporting country i is high income, it will have a higher [[alpha].sub.L] in Equation 4, which in turn leads to a higher predicted [X.sup.ij.sub.L] than if the exporting country were low or middle income.

To thoroughly investigate this issue (and to see the roles of the country of origin versus that of the destination country), we created four additional dummy variables: [HighIncome.sub.i] and [MidIncome.sub.i] take value one if the exporting country i is high or mid-income, respectively, with two analogous variables for the importing country. Table 5 presents the regression results. All gravity variables enter with the right sign and most are significant at the 1% level.

Note that because we interact the dummy variables with our measure of inequality for the importing country, we need to calculate the partial effect of inequality on imports. Because there are three types of countries (high, medium, and low income), there are nine types of country pairs for one-way trade. Table 6 presents the partial effects of inequality on imports, arranged in a matrix with all nine possibilities. Again, these partial effects can be fairly large in magnitude. (20) One can discern a fair amount of structure. Note that because the different rows let the income level of the exporting country vary, this is the variation of greatest interest. The results provide a fairly strong confirmation of the presumption that whether a good is a luxury or a necessity is mostly determined by country of origin, not country of destination. To see this, consider each row one by one. For the first and the third rows, whenever the results are statistically significant, the row determines the sign of the partial effect of inequality on trade. In particular, by moving through the first row (barring the import demand from middle income countries, which has a positive sign but is statistically insignificant), one can see that import demand from all income levels behaves as if the exports of low income countries are necessities. Analogously from the last row, exports from high income countries behave as luxuries, irrespective of the income level of the importing country.

Only for middle income exporters does the rule break down. Here, we have a result similar to something that we have already encountered: What is a luxury for one person may be a necessity for someone else at a different income level. In particular, the pattern of signs in the middle row is reasonable: As the importer grows richer, it sees middle income countries more and more as low income, and therefore it sees middle income exports more and more as necessities--the sign of the coefficient starts out positive and ends as negative. Note that a sign pattern that would be the reverse of this would be unexpected.

The results in this subsection are consistent with the so-called Linder's hypothesis. Linder posited that similarity in tastes is tied to per capita incomes. He argued that producers first produce goods that home consumers demand and only then export these to other markets. This would then result in poor countries being exporters of necessities and rich countries exporters of luxuries. (21)

In sum, we provide strong support for the following stylized fact, to our knowledge not known to the empirical economics literature: Poor countries export necessities, and rich countries export luxuries.

Robustness Checks

We have performed several robustness checks, a selection of which are reported in Table 7. First, we checked for nonlinearities with respect to inequality, with results reported in columns 1 and 2. Introduction of an additional squared inequality term does not qualitatively (or even quantitatively) change the results. The partial derivatives of imports with respect to inequality remain preserved in terms of sign and magnitude. Furthermore they remain preserved in significance if one accepts an 11% significance level. (22)

One may argue that the Gini index, which we have used throughout, is relatively insensitive to the extremes of the income distribution. As a further robustness check, we use the ratio of the income share of the fifth quintile to that of the first quintile (Q51) as an alternative measure of inequality (columns 3, 4). Q51 has the right signs--negative in the case of necessities and positive in the case of luxuries. While it is insignificant in the case of necessities, it is highly significant (at the 1% level) in the case of luxuries.

Columns 5-8 report Tobit and median regressions. This is done because, as mentioned before, the dependent variable is bounded below by zero, and the bound is observed for a large number of bilateral observations. The results are very robust for the median regressions, and for necessities with Tobit, while the coefficient of interest loses significance for the Tobit regression in luxuries. Note that the interpretation of the Tobit results is affected by the likely existence of heteroskedasticity in our panel data, for which, to our knowledge, there is no adequate econometric treatment in Tobit.

Columns 9 and 10 report the results when we exclude from the sample each country's main trading partners. In particular, we exclude observations in which the exporting country represents more than 1% of the importer's import flows. As explained in section 3, this is done to allay the worry that Inequality is endogenous. For the remaining (smaller) exporters, most likely the chain of causality runs unambiguously from inequality to imports, not the other way around. An inspection of columns 9 and 10 reveals the essential robustness of the main results in Table 2. Columns 11 and 12 can be used to perform the analogous analysis when we exclude the largest five economies each year from the exporting side. While in columns 13 and 14, we include the remoteness variable, in columns 15 and 16, we try country-pair fixed effects to capture the effects of variables like common border, common language, common culture, remoteness, etc. The results are qualitatively unchanged. (23)

6. Conclusion

In this paper, we are mostly concerned with the question of how the variation in income distribution among countries affects the volume and pattern of trade. In the framework of established trade theory, the assumption of homothetic and identical tastes rules out that the distribution of income has any effect on trade. In our framework, we drop the assumption of homothetic preferences, which allows us to empirically pursue an investigation on the effect of inequality on trade with the use of a gravity model.

Overall, our findings show that inequality affects the structure and the origin of trade flows. In almost every regression, inequality variables are both economically and statistically significant. When we separate goods according to whether they are luxuries or necessities, based on consumer surveys, we see that a product's characteristic is a major predictor of the impact of inequality on trade. This provides a tighter link with the theory. Furthermore, we document another pattern in the relationship between inequality and trade: As inequality increases in the importing countries, we observe that imports from rich countries increase while imports from poor countries decrease. We note that most standard variables of the gravity model remain qualitatively the same, in the presence of inequality, as in the existing gravity literature.

Appendix

This appendix describes how we classified four-digit SITC goods as necessities or luxuries. (24) First, we obtained data from the Bureau of Labor Statistics on household expenditure shares in the United States in 2001. The BLS separates household population into five income quintiles and, for each quintile, lists the average expenditure share of about 100 expenditure categories. For example, the BLS category labeled "APM1" is "apparel and services, men, 16 and over." For this category, expenditure shares of the different quintiles, from the bottom quintile to the top quintile, are 0.8, 0.8, 0.8, 0.9, and 1.0%, respectively. We defined any category in which expenditure share is weakly rising (as in this example) as a luxury. Conversely, any category in which expenditure share weakly decreases is classified as a necessity. We did not classify either as luxuries or necessities those BLS categories in which shares vary in a nonmonotonic way, or in which shares do not vary at all.

The second part of our procedure was to match the BLS categories to SITC codes. To do so, we went through the description of each four-digit SITC, and matched it with a BLS description. Some judgment calls were needed, as we now detail. To use the example above, we matched the BLS category APM1, "apparel and services, men, 16 and over," to the following SITC codes:

* 8421: overcoats and other coats, men's

* 8422: suits, men's, of textile fabrics

* 8423: trousers, breeches, etc., of textile fabrics (25)

* 8424: jackets, blazers, of textile fabrics

* 8429: other outer garments of textile fabrics

* 842A: outer garments, men's, of textile fabrics

* 842X: outer garments, men's, of textile fabrics

* 8441: shirts, men's, of textile fabrics

These eight SITCs were therefore assigned as luxuries, and many other SITC codes were in this way assigned as either luxuries or necessities. We also assigned as luxuries less than 10 SITC categories for which there was no direct BLS correspondence, but that clearly are luxuries: for example, SITC 8973, "jewelry of gold, silver, or platinum." Of course, many SITCs remained unclassified either as luxuries or necessities because there was no clear BLS correspondence.

Some of the judgment calls had to do with the wording describing the BLS codes and the SITCs did not correspond to each other in a clean way. Furthermore, generally speaking, the BLS categories are at a fairly more aggregated level than the SITC. To illustrate these problems, take SITC categories 0573 "bananas, fresh or dried," and 0579 "fruit, fresh or dried, not elsewhere specified." We matched both to the BLS category FHF1 "fresh fruits," on the following two assumptions: Consumer tastes for most fruits are similar, therefore consumer behavior for a more disaggregated fruit (bananas) should closely match the consumer behavior for aggregate fruit; furthermore, most trade is likely to be in fresh fruit, the part in which the BLS and SITC descriptions coincide.

The SITC, as revised by Statistics Canada, includes some codes ending in X or XX, which for our purposes can be interpreted as aggregate, or "unallocated," trade (for more details, see Feenstra 2000, p. 5). The criterion to match these codes to the BLS codes was a modified majority rule. Generally, if the BLS supplied a closely corresponding aggregate code (those codes ending in 0 or 00), we simply matched the corresponding aggregates; otherwise, if over half the disaggregated SITC codes were assigned to a single BLS code, we also assigned the aggregate SITC code to the same BLS code. (26)

Another issue was posed by the so-called rolled-up codes, also created by Statistics Canada, many of which end with the letter A. These codes were the result of combining two or more SITC codes (for details the reader is referred again to the Feenstra paper). We checked all rolled-up codes for consistency. Generally, we forced consistency by letting the rolled-up code dictate its assigned BLS code to all the original SITCs that were rolled up into it. In some cases, we used judgment to make exceptions to this rule. For example, Statistics Canada rolled up code 7631 "gramophones & record players, electric," into 7649 "parts of apparatus of division 76." We left 7649 unassigned to any BLS code. (27) However, we decided to still assign 7631 to the BLS category that clearly corresponds to it: ENT0, "televisions, radios, audio equipment."

To summarize, at the end of this procedure, we had three types of SITC: luxuries, necessities, and unassigned. We dropped all unassigned trade, and separately aggregated the luxuries and the necessities. Thus, for exporter i, importer j, and year t, we had two trade flows: exports in luxuries and exports in necessities.

Received May 2006; accepted January 2007.

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(1) Mitra and Trindade (2005) work out a theory of this effect. They also discuss intra-industry trade and international transmission of inequality, which are outside the scope of the present paper.

(2) We discuss further on the few exceptions to this general statement, and their relation to our work.

(3) This is the most recent decade in our data set, and it is the one for which the classification of goods into luxuries and necessities that is drawn from 2001 U.S. data as just described is more likely to be relevant.

(4) In the case of our panel regressions, we are able to use exporting country and importing country fixed effects, while in our cross-sectional regressions, because inequality varies across importing countries (and there is no time dimension), we are able to use only random effects (the second best thing to do) for importing countries but still have fixed effects (the first best) for exporting countries. We perform our cross-sectional regressions with and without the importing country random effects, and the results are qualitatively unchanged and quantitatively close.

(5) This would be the case, for example, if a large proportion of asset ownership and of economic transactions in developing countries is informal.

(6) The income expansion path is the locus of consumption bundles for varying income levels at constant prices.

(7) Frankel (1997) argues that per-capita GDPs capture formal and informal barriers to trade and are therefore negatively correlated with trade barriers not directly measured by distance.

(8) It needs to be noted that introducing aggregate GDP and population in the gravity regressions (as done in many papers in the recent past) is not more restrictive than having aggregate GDP and GDP per capita as two different variables as we do in this paper. In fact, the two specifications are equivalent because a(ln GDP) + b(ln GDP--In Population) = (a+b)(ln GDP)--b(ln Population).

(9) For a discussion of the latter, see Anderson and van Wincoop (2003). The case for using country fixed effects to capture multilateral resistance is made by Feenstra (2003). Gravity models with country fixed effects have been estimated by Dunlevy (2006) and Feenstra (2002), among others. Note that this paper is not about trade barriers, or about how they interact, which is Anderson and van Wincoop's true contribution to the literature. In other words, the effects that we test here would still be present even if all trade barriers were zero. Any attempt to use Anderson and van Wincoop's full approach would suffer the difficulty that their model was deduced with the assumption of homothetic tastes, and therefore would not be immediately relevant for our purposes. Using fixed country-year effects also does not solve the problem because the fixed effects would absorb our inequality variable.

(10) This is done by replacing missing trade flows with 0, then adding 1 to all trade flows, and finally taking logs.

(11) A country with a leftist government that wishes to enhance equality may well use trade policy to do so.

(12) The regression where we used the logs of GDP and GDP per capita of the importing and exporting countries separately in place of using the logs of products of GDPs of the two countries gives us exactly the same coefficient on inequality, but the statistical significance of this term is somewhat reduced. We later explain the relationship between these two alternative specifications. Note that * indicates significance at 10%, ** at 5%, and *** at 1%.

(13) Here we have two very similar specifications, namely one in which we use the log of the product of the GDPs of the exporting and importing countries, and another where the logs of the GDPs of the two different countries (exporting and importing) are treated as two different variables. Since In AB = In A + In B, the two specifications are related. However, the specification that uses the product of the two GDPs is more restrictive because it imposes the restriction that the coefficient of the importing country GDP exactly equals the coefficient of the exporting country GDP. Even though one version is more restrictive than the other, we present results using both specifications because they are both used in the literature and we want to show that our results are not driven by any one specification.

(14) Note that the Gini coefficient in our data set is measured on a scale of 0 to 100 (not 0 to 1).

(15) A scatter plot with all pairs of exporting and importing countries is not useful because it would have overcrowded the chart with more than 26,000 observations and would therefore not have a great deal of illustrative power. The scatter plots with one exporting country at a time are much more powerful.

(16) Dropping these random effects keeps the results virtually unchanged.

(17) These are their first and third approach. Their second approach assumes that luxuries are goods that industrial countries trade more. We have something of this flavor in the next subsection, in which we divide trade according to the income per capita of the trading partners.

(18) In their first approach they use the further assumption that differentiated goods have high indices of intra- industry trade. In their third approach, they simply count the number of subindustries that the industrial classification provides for each industry. Rauch's measure is arguably an improvement on both of these approaches because it relies on market responses to each good (for example, are there reference prices widely available for the good?), not on the decisions of the officials that create industrial classifications.

(19) In other words, the reason for more developed countries to have comparative advantage in luxuries may be Heckscher-Ohlin: Luxuries such as automobiles (but also leather bags and fashion clothing) systematically use capital more intensively than necessities. But the reason may also be Ricardian: Simply because luxuries are consumed more as the world is getting richer, it is likely that luxuries are newer goods, with whose technology less developed countries have not yet caught up.

(20) Note that the partial derivative here is that of the log of imports with respect to importing country inequality. In other words, we are looking at the percentage change in imports due to a percentage point change in the Gini coefficient. One has to be careful in interpreting the partial effects because a 1% change in imports might be much more in the case of developed countries that are much richer and are much more open in trade than other countries.

(21) We are grateful to an anonymous referee for having made this point.

(22) Even though inequality and inequality squared are individually insignificant in column 2 for necessities, they are jointly significant leading to the low p-value for the partial effect of inequality.

(23) Some additional robustness tests were performed. We tried adding the inequality of the exporting country, which for the bilateral trade sample we are focusing on, enters insignificantly, in all cases with a t-ratio less than 1. This is understandable because in deriving the gravity model, we find that the country that produces a tradable good will consume a negligible share of the output of that good in a world with many countries. Bilateral imports should then be a function of, in addition to the other gravity variables, the importing country's inequality and the inequality of the rest of the world, which in turn can be expressed as a function of importing country inequality and overall world inequality. Our year dummies capture variations in world inequality from one year to another. In one set of regressions (columns 13 and 14), we include a variable for "remoteness" of the country pair, which is sometimes used in the gravity literature, without affecting the main conclusion. We also tried to combine some of the tests, for example, including the square of the inequality measure in a Tobit regression. We also tried dropping all the OPEC countries and our results and conclusions remain fully preserved. Finally, for the Rauch categories, we tried to separate regressions for the w and for the r goods, in all cases getting no qualitative changes.

(24) A file with our classification is posted online at http://web.missouri.edu/~trindadev/.

(25) Even though "men's" is not explicitly mentioned in this category 8423, or in 8424 and 8429, it can be inferred from the "X" and "A" categories, as explained later.

(26) An exception to this general rule was SITC 1XXX, "beverages and tobacco," which we assigned to BLS AB00 "alcoholic beverages," rather than TB00, "tobacco products and smoking supplies." Note that for our purposes this choice does not matter, since both AB00 and TB00 are necessities according to expenditure shares.

(27) This was also the result of a general criterion. Because the BLS expenditure categories refer to final consumer expenditures, there is no information regarding parts or components. Therefore, all SITCs that refer specifically to parts were left unassigned, and therefore were dropped out of all estimations. Also unassigned were all machinery, except when these are household appliances. Finally, we left unassigned codes that mix machinery with both industrial and household applications (e.g., SITC 7412, "furnace burners for liquid fuel and parts").

Muhammed Dalgin, * Vitor Trindade, ([dagger]) and Devashish Mitra ([double dagger])

* Kania School of Management, University of Scranton, Scranton, PA 18510, USA, E-mail sufHallumDalgin@ gmail.com.

([dagger]) Department of Economics, University of Missouri, Columbia, MO 65211, USA; E-mail trindadev@missouri. edu; corresponding author.

([double dagger]) Department of Economics, Syracuse University, Syracuse, NY 13244-1090, USA; E-mail dmitra@maxwell.syr. edu.

We are indebted to Neville Francis, Gordon Hanson, Duke Kao, Nuno Limbo, Joaquim Silvestre, Mark Vancauteren, and seminar participants at the University of Maryland, University of Texas at Austin, the Universities of California at Berkeley, Davis, Irvine, San Diego, and Santa Cruz, and the Midwest Trade Meetings (Michigan State University) for useful discussions and comments. We also thank Natalia Trofimenko for excellent research assistance. Finally and most importantly, this paper has benefited enormously from comments made by two anonymous referees. The standard disclaimer applies.

Table 1. List of Countries Middle High Country Name Low Income Income Income 1 Algeria 0 28 0 2 Argentina 0 28 0 3 Australia 0 0 28 4 Austria 0 0 28 5 Bahamas 0 3 25 6 Bangladesh 28 0 0 7 Barbados 0 28 0 8 Belgium 0 0 28 9 Bolivia 0 28 0 10 Brazil 0 28 0 11 Bulgaria 0 18 0 12 Burkina Faso 28 0 0 13 Burundi 28 0 0 14 Cambodia 11 0 0 15 Cameroon 18 10 0 16 Canada 0 0 28 17 Central African Republic 28 0 0 18 Chad 28 0 0 19 Chile 0 28 0 20 China 28 0 0 21 Colombia 0 28 0 22 Costa Rica 0 28 0 23 Cote d'Ivoire 6 22 0 24 Czech Republic 0 8 0 25 Denmark 0 0 28 26 Djibouti 0 11 0 27 Dominican Republic 0 28 0 28 Ecuador 0 28 0 29 Egypt Arab Republic 12 16 0 30 El Salvador 0 28 0 31 Ethiopia 17 0 0 32 Fiji 0 28 0 33 Finland 0 0 28 34 France 0 0 28 35 Gabon 0 28 0 36 Gambia 28 0 0 37 Germany 0 0 26 38 Ghana 28 0 0 39 Greece 0 4 24 40 Guatemala 0 28 0 41 Guinea 12 0 0 42 Guinea-Bissau 28 0 0 43 Guyana 13 15 0 44 Honduras 28 0 0 45 Hong Kong, China 0 7 21 46 Hungary 0 28 0 47 India 28 0 0 48 Indonesia 20 8 0 49 Iran 0 25 0 50 Iraq 0 0 0 51 Ireland 0 5 23 52 Israel 0 1 27 53 Italy 0 0 28 54 Jamaica 0 28 0 55 Japan 0 0 28 56 Jordan 0 23 0 57 Kenya 28 0 0 58 Korea 0 23 5 59 Laos 14 0 0 60 Lebanon 0 10 0 61 Madagascar 28 0 0 62 Malawi 28 0 0 63 Malaysia 0 28 0 64 Mali 28 0 0 65 Mauritania 28 0 0 66 Mauritius 0 28 0 67 Mexico 0 28 0 68 Mongolia 17 0 0 69 Morocco 0 28 0 70 Mozambique 18 0 0 71 Myanmar 0 0 0 72 Nepal 28 0 0 73 Netherlands 0 0 28 74 New Zealand 0 0 28 75 Nicaragua 19 9 0 76 Niger 28 0 0 77 Nigeria 28 0 0 78 Norway 0 0 28 79 Pakistan 28 0 0 80 Panama 0 28 0 81 Papua New Guinea 0 28 0 82 Paraguay 0 28 0 83 Peru 0 28 0 84 Philippines 0 28 0 85 Poland 0 16 0 86 Portugal 0 19 9 87 Russian Federation 0 28 0 88 Rwanda 28 0 0 89 Senegal 28 0 0 90 Seychelles 0 28 0 91 Sierra Leone 28 0 0 92 Singapore 0 8 20 93 South Africa 0 28 0 94 Spain 0 2 26 95 Sri Lanka 27 1 0 96 Sudan 28 0 0 97 Suriname 1 27 0 98 Sweden 0 0 28 99 Switzerland 0 0 28 100 Tanzania 10 0 0 101 Thailand 1 27 0 102 Trinidad and Tobago 0 28 0 103 Tunisia 0 28 0 104 Turkey 0 28 0 105 Uganda 16 0 0 106 United Kingdom 0 0 28 107 United States 0 0 28 108 Uruguay 0 28 0 109 Venezuela 0 28 0 110 Vietnam 14 0 0 111 Yemen 8 0 0 112 Zambia 28 0 0 113 Zimbabwe 28 0 0 Countries were divided into income groups in each of the 28 years of the sample (1970-1997). For each country the numbers in the last three columns denote how many years the country belonged in the low, medium, or high income group, respectively (for some countries the total is less than 28 because of missing income data). Table 2. Panel OLS Estimations with Direct Measure of Necessities and Luxuries (Sample Restricted to Developed Importing Countries, Unrestricted on the Exporting Side) Regressand Luxuries Necessities Lux/Nec Regressors (l) (2) (3) Inequality 0.009 ** -0.013 *** 0.004 *** (0.005) (0.005) (0.001) lxGdp 1.319 *** 1.045 *** 0.221 *** (0.287) (0.357) (0.074) lmGdp -2.162 *** -0.216 -0.247 ** (0.521) (0.586) (0.122) lxGdpPc 0.405 0.224 -0.074 (0.280) (0.360) (0.073) lmGdpPc 3.815 *** 1.705 *** 0.359 *** (0.572) (0.660) (0.139) ldist -1.449 *** -1.487 *** 0.031 ** (0.059) (0.070) (0.013) lGdp lGdpPc Observations 26,644 26,644 26,644 R-squared 0.84 0.75 0.35 Regressand Luxuries Necessities Lux/Nec Regressors (4) (5) (6) Inequality 0.008 * -0.013 *** 0.003 *** (0.005) (0.005) (0.001) lxGdp lmGdp lxGdpPc lmGdpPc ldist -1.448 *** -1.487 *** 0.031 ** (0.059) (0.069) (0.013) lGdp 0.669 *** 0.821 *** 0.132 ** (0.258) (0.303) (0.064) lGdpPc 0.977 *** 0.447 0.002 (0.255) (0.309) (0.063) Observations 26,644 26,644 26,644 R-squared 0.84 0.75 0.35 Regressand: log of bilateral exports, in luxuries in columns 1 and 4 and in necessities in columns 2 and 5, and the log of the ratio of luxury to necessity exports in columns 3 and 6. The column title shows the commodity category. x is the exporting country, m is the importing country. Year, exporting, and importing country dummies not shown. Robust standard errors in parentheses. Standard errors clustered for country pairs. * p < 10%. ** p < 5%. *** p < 1%. Table 3. Cross-Sectional Random Effects Regressions (Full Sample) Regressand Luxuries Necessities Lux/Nec Regressors (1) (2) (3) Inequality 0.012 *** -0.006 ** 0.002 *** (0.002) (0.003) (0.001) lxGdp -0.048 * -0.194 *** 0.014 * (0.028) (0.032) (0.008) lmGdp 0.528 *** 0.772 *** 0.016 *** (0.012) (0.014) (0.003) lxGdpPc 0.633 *** 0.950 *** -0.083 *** (0.080) (0.094) (0.022) lmGdpPc 0.361 *** 0.374 *** 0.027 *** (0.017) (0.019) (0.005) ldist -1.290 *** -1.574 *** 0.011 (0.026) (0.031) (0.007) Observations 10,120 10,120 10,120 Number of mcs 92 92 92 R-squared 0.77 0.75 0.32 Regressand: log of bilateral exports, in luxuries or in necessities in columns 1 and 2, respectively, and the log of the ratio of luxury to necessity exports in column 3. The column title shows the commodity category. x is the exporting country, m (or mc) is the importing country. Exporting country dummies not shown. Importing-country random effects used. * p < 10%. ** p < 5%. *** p < 1%. Table 4. OLS Regressions (Panel) using Rauch Categories Regressand n r + w n/(r + w) Regressor (1) (2) (3) Inequality 0.011 *** 0.008 *** 0.002 ** (0.002) (0.003) (0.001) lxGdp 0.349 ** 0.458 ** 0.045 (0.168) (0.214) (0.059) lmGdp -1.105 *** 0.506 ** -0.516 *** (0.l69) (0.2l1) (0.058) lxGdpPc 1.375 *** 0.981 *** 0.341 *** (0.l64) (0.213) (0.056) lmGdpPc 2.551 *** 1.256 *** 0.562 *** (0.175) (0.219) (0.061) ldist -1.488 *** -1.617 *** 0.003 (0.036) (0.039) (0.0l0) Observations 67,956 67,956 67,956 R-squared 0.82 0.72 0.39 Regressand n r + w n/(r + w) Regressor (4) (5) (6) Inequality -0.003 -0.013 *** 0.003 * (0.004) (0.005) (0.002) lxGdp 0.488 * 0.872 ** 0.141 (0.268) (0.356) (0.098) lmGdp -0.636 1.266 ** -0.556 *** (0.483) (0.590) (0.l74) lxGdpPc 1.152 *** 0.350 0.341 *** (0.269) (0.362) (0.098) lmGdpPc 2.446 *** 0.771 0.664 *** (0.548) (0.646) (0.l89) ldist -1.338 *** -1.510 *** 0.108 *** (0.057) (0.07l) (0.0l9) Observations 26,644 26,644 26,644 R-squared 0.85 0.74 0.43 w shows goods that are traded on organized exchanges, r shows goods that have reference prices, and n shows differentiated goods. Robust standard errors in parentheses. Column title shows commodity categories. Year, exporting, and importing country dummies not shown. While the first three columns pertain to the full sample, the next three columns are for the restricted sample (where the imported countries are developed, but no restrictions are placed on exporting countries). * p < 10%. ** p < 5%. *** p < 1%. Table 5. Regressions with Interactions of Source Country Income Level Regressand Total Exports Total Exports Regressors (1) (2) Inequality -0.009 -0.007 (0.006) (0.007) log xGDP 0.493 ** (0.194) log mGDP -0.073 (0.198) log xGDP/capita 1.210 *** (0.196) log mGDP/capita 1.999 *** (0.208) log Distance -1.597 *** -1.598 *** (0.038) (0.038) log (xGDP mGDP) 0.287 ** (0.137) log (xGDP/capita mGDP/capita) 1.485 *** (0.137) mHighIncome 1.555 *** 1.704 *** (0.302) (0.320) mMidIncome -0.483 * -0.377 (0.275) (0.301) xHighIncome -2.673 *** -2.750 *** (0.251) (0.246) xMidIncome -0.651 *** -0.685 *** (0.225) (0.224) mlnequality x mHighIncome -0.035 *** -0.037 *** (0.007) (0.007) mlnequality x mMidIncome 0.016 ** 0.014 * (0.007) (0.008) mlnequality x xHighIncome 0.077 *** 0.077 *** (0.005) (0.005) mlnequality x xMidIncome 0.022 *** 0.022 *** (0.005) (0.005) Observations 67,956 67,956 R-squared 0.77 0.77 x refers to exporting country variables; m refers to importing country variables. Robust standard errors in parentheses. Standard errors clustered for country pairs. mHighIncome, mMidIncome: dummies for the importing country being high or mid-income. xHighIncome, xMidIncome: analogous dummies for the exporting country. * p < 10%. ** p < 5%. *** p < 1%. Table 6. Partial Effects of Inequality on Imports, by the Income Levels of Importers and Exporters Importer Exporter Low Income Medium Income Low income -0.0089 0.0069 (0.154) (0.188) Medium income 0.0135 ** 0.0293 *** (0.031) (3.31 x [10.sup.-8]) High income 0.0682 *** 0.0839 *** (1.28 x [10.sup.-26]) (0) Importer Exporter High Income Low income -0.0441 *** (1.14 x [10.sup.-16]) Medium income -0.0217 *** (1.25 x [10.sup.-5]) High income 0.0330 *** (4.26 x [10.sup.-10]) Partial effects of importer's inequality on total imports, calculated from Table 5, column 1. p-values in parentheses * p < 10%. ** p < 5%. *** p < 1%. Table 7. Robustness Checks for the Direct Measure of Luxuries and Necessities (Panel) Regressand Lux. Nec. Lux. Regressors (1) (2) (3) Inequality (Gini) -0.099 *** -0.030 (0.032) (0.033) Square inequality 0.002 *** 0.000 (Gini) (0.001) (0.001) Inequality (Q51) 0.046 *** log xGDP 1.319 *** 1.045 *** 1.984 *** (0.285) (0.357) (0.335) log mGDP -2.384 *** -0.250 -2.668 *** (0.497) (0.575) (0.622) log xGDP/capita 0.405 0.224 -0.386 (0.278) (0.360) (0.328) log mGDP/capita 3.971 *** 1.729 *** 4.466 *** (0.555) (0.654) (0.614) log Distance -1.450 *** -1.487 *** -1.479 *** (0.059) (0.070) (0.061) Partial effect of 0.007 -0.013 *** inequality at mean (0.11) (0.004) inequality (p-values) Observations 26,644 26,644 21,757 R-squared 0.84 0.75 0.84 Regressand Nec. Lux. Tobit Nec. Tobit Regressors (4) (5) (6) Inequality (Gini) -0.002 -0.017 *** (0.005) (0.005) Square inequality (Gini) Inequality (Q51) -0.021 log xGDP 1.174 *** 2.963 *** 1.667 *** (0.405) (0.246) (0.250) log mGDP -0.341 -2.402 *** 0.273 (0.697) (0.544) (0.542) log xGDP/capita 0.057 -1.023*** -0.414 * (0.408) (0.242) (0.243) log mGDP/capita 1.426 ** 4.860 *** 1.256 ** (0.710) (0.642) (0.636) log Distance -1.477 *** -1.754 *** -1.591 *** (0.073) (0.030) (0.031) Partial effect of inequality at mean inequality (p-values) Observations 21,757 26,644 26,644 R-squared 0.75 Regressand Lux. Median Nec. Median Lux. Regressor (7) (8) (9) Inequality (Gini) 0.015 *** -0.013 *** 0.019 *** (0.003) (0.003) (0.006) log xGDP 0.523 *** 0.237 1.112 *** (0.146) (0.155) (0.376) log mGDP -3.015 *** 0.166 -1.778 *** (0.303) (0.322) (0.491) log xGDP/capita 0.986 *** 1.005 *** -0.649 * (0.142) (0.151) (0.373) log mGDP/capita 4.568 *** 0.861 ** 3.030 *** (0.348) (0.370) (0.513) log Distance -1.295 *** -1.372 *** -0.789 *** (0.018) (0.020) (0.084) Observations 26,644 26,644 15,320 R-squared 0.54 Regressand Nec. Lux. Nec. Regressor (10) (11) (12) Inequality (Gini) -0.021 *** 0.010 ** -0.013 *** (0.007) (0.005) (0.005) log xGDP 2.417 *** 1.274 *** 1.139 *** (0.598) (0.306) (0.380) log mGDP -2.815 *** -2.147 *** -0.222 (0.839) (0.543) (0.613) log xGDP/capita -2.050 *** 0.453 0.157 (0.573) (0.301) (0.383) log mGDP/capita 5.129 *** 3.764 *** 1.717 ** (0.883) (0.594) (0.688) log Distance -1.045 *** -1.499 *** -1.558 *** (0.153) (0.062) (0.075) Observations 12,782 25,339 25,339 R-squared 0.65 0.81 0.74 Regressand Lux. Nec. Regressor (13) (14) Inequality (Gini) 0.008 * -0.013 *** (0.005) (0.005) log xGDP 1.217 *** 1.083 *** (0.290) (0.366) log mGDP -2.428 *** -0.117 (0.526) (0.590) log xGDP/capita 0.458 0.205 (0.281) (0.363) log mGDP/capita 3.955 *** 1.653 ** (0.571) (0.659) log Distance -1.450 *** -1.487 *** (0.059) (0.070) log Remote -9.810 ** 3.645 -4.201 -4.091 Observations 26,644 26,644 R-squared 0.84 0.75 Regressand Lux. Nec. Regressor (15) (16) Inequality (Gini) 0.012 *** -0.010 *** (0.003) (0.003) log xGDP 1.397 *** 1.073 *** (0.137) (0.161) log mGDP -2.167 *** -0.663 ** (0.269) (0.315) log xGDP/capita 0.310 ** 0.185 (0.133) (0.156) log mGDP/capita 4.048 *** 2.229 *** (0.308) (0.361) log Distance log Remote Observations 26,644 26,644 R-squared 0.24 0.13 Robust standard errors in parentheses. Column title shows commodity categories. Year, exporting, and importing country dummies not shown. * p < 10%. ** p < 5%. *** p < 1%.

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Title Annotation: | theory of international trade studies income distribution pattern |
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Comment: | Inequality, nonhomothetic preferences, and trade: a gravity approach.(theory of international trade studies income distribution pattern) |

Author: | Dalgin, Muhammed; Trindade, Vitor; Mitra, Devashish |

Publication: | Southern Economic Journal |

Article Type: | Author abstract |

Geographic Code: | 1USA |

Date: | Jan 1, 2008 |

Words: | 14094 |

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