In eq u a lity an d U n e mp loy ment in a G lo b a l E co n o my∗Elhanan HelpmanHarvard U niversity and CIFAROleg Itskhok iPrinceton UniversityStephen ReddingLondon Sc hool of EconomicsFebruary 9, 2010AbstractThis paper develops a new framework for examining the determinants of wage distribu-tions that emphasizes within-industry reallocation, labor market frictions, and differences inworkforce composition across firms. More productive firms pay higher wages and exportingincreases the wage paid by a firm with a given productivity. The opening of trade enhanceswage inequality and can either raise or reduce unemployment. While wage inequality ishigher in a trade equilibrium than in autarky, gradual trade liberalization first increases andlater decreases inequality.Key words: Wage Inequality, In ternational Trade, Risk, UnemploymentJEL classification: F12, F16, E24∗This paper is a combined version of Helpman, Itskhoki and Redding (2008a, 2008b). Work on these papersstarted when Redding was a Visiting Professor at Harvard University. We thank the National Science Foundationfor financial support. Redding thanks the Centre for Economic Performance a t the London School of Econom icsand the Yale School of Management for financial support. We are grateful to Daron Acemoglu, four anonymousreferees, Pol Antràs, Matilde Bombardini, Arnaud Costinot, Gilles Duranton, Gene Grossman, James Harrigan,Larry Katz, Marc Melitz, Guy M ichaels, Steve Pischke, E steban Rossi-Hansberg, Peter Schott, Dan Trefler andconference and seminar participants at AEA , Berkeley, CEPR, Chicago, Columbia, Harvard, LSE, NBER, NYU,Northwestern, Penn State , Princeton, Stanford , Stockholm, Tel Aviv, UCLA and Yale for helpful comments. Theusual disc laimer applies.1IntroductionTwo core issues in international trade are the allocation of resources across economic activitiesand the distribution of incomes across factors of production. In this paper, we dev elop a newframework for examining the determinants of resource allocation and income distribution, inwhich both wage inequality and unemployment respond to trade. Our framework encompassesa number of important features of product and labor markets, as a result of which it generatespredictions that match features of the data. This framework is rich, flexible and tractable, as wedemonstrate by deriving a number of interesting results on trade, inequality and unemployment.And we show how this framework can be extended in various ways and how it can accommodatedifferent general equilibrium structures. Moreover, our framework fits squarely in to the newview of foreign trade that emphasizes firm heterogeneity in differentiated product sectors.We introduce standard Diamond-Mortensen-Pissarides searc h and matching frictions intoa Melitz (2003) model, but unlike previous work in this area, such as Helpman and Itskhoki(2009a), we also introduce ex post match-specific heterogeneity in a worker’s ability. Becausea worker’s ability is not directly observable by his employer, firms screen workers in order toimprov e the composition of their employees. Complementarities between workers’ abilities andfirm productivity imply that firms have an incentive to screen workers to exclude those withlowe r abilities. As larger firms ha ve higher returns to screening and the screening technologyisthesameforallfirms, more productive firms screen more intensively and have workforces ofhigher average ability than less productive firms. Search frictions induce multilateral bargainingbetween a firm and its w ork ers, and since higher-ability workforces are more costly to replace,more productive firms pa y higher wages. When the economy is opened to trade, the selectionof more productive firms into exporting increases their revenue relative to less productive firms,which further enhances their incentive to screen workers to exclude those of lower ability. Asa result, exporters have workforces of higher average ability than non-exporters and hence payhigher wages. This mec hanism generates a wage-size premium and implies that exporting in-creases the w age paid by a firm with a given productivity. Both features of the model haveimportant implications for wage inequality within sectors and within groups of workers with thesame ex ante characteristics.Our first main result is that the opening of a closed economy to trade raises wage inequality.The intuition for this result is that larger firms pay higher wages and the opening of tradeincreases the dispersion of firm revenues, which in turn increases the dispersion of firm wages.This result is more general than our model in the sense that it holds in a wider class of models inwhic h firm wages are increasing in firm revenue and there is selection into export markets. Weprovide a proof that the opening of trade raises wage inequality for any inequality measure thatrespects second-order stochastic dominance, and this result holds for a class of models satisfyingthe following three sufficien t conditions: firm wages and employmen t are power functions of firmproductivity, exporting increases the wage paid by a firm with a given productivity, and firm1productivity is Pareto distributed.1,2Our second main result is that once the econom y is open to trade the relationship betweenwage inequality and trade openness is at first increasing and later decreasing. As a result, agiven change in trade frictions can either raise or reduce w age inequality, depending on the initiallevel of trade openness. The intuition for this result stems from the increase in firm wages thatoccurs at the productivity threshold above which firmsexport,whichisonlypresentwhensomebut not all firms export. When no firm exports, a small reduction in trade costs increases wageinequality, because it induces some firms to export and raises the wages paid by these exportingfirms relative to domestic firms. When all firms export, a small rise in trade costs increaseswage inequality, because it induces some firms to cease exporting and reduces the wages paidby these domestic firms relative to exporting firms.Another key prediction of our framework is that these two results hold regardless of gen-eral equilibrium effects. To demonstrate this, we derive these results from comparisons acrossfirms that hold in sectoral equilibrium irrespective of how the sector is embedded in generalequilibrium. It follows that our results for sectoral wage inequality do not depend on the im-pact of