Abstract
In this paper, I survey the recent theoretical literature that incorporates heterogeneous labor into models of international trade. The models with heterogeneous labor have been used to study how talent dispersion can be a source of comparative advantage, how the opening of trade affects the full distribution of wages, and how trade affects industry productivity and efficiency via its impact on sorting and matching in the labor market. Some of the most recent contributions also introduce labor market frictions to study the effects of trade on structural unemployment and on mismatch between workers and firms.
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Notes
Equivalently, there might be many dimensions of variation provided that these dimensions can be summarized in a single sufficient statistic for purposes of predicting labor market outcomes.
A more general specification of the production technology would be to write x k i = g k i (q L , q H , ℓ, h), where h is the quantity of the second factor whose quality is q H . This would allow, for example, for the possibility that the diminishing returns to the quantity of labor depends on the quality of labor that is employed. I do not write the technology this way, because little of the literature that I shall review has anything to say about this more general case. But see Eeckhout and Kircher (2012), who study the conditions for PAM in this more general environment.
Actually, log supermodularity need not be a stronger requirement than supermodularity for functions that are not monotone. But since the functions we consider here are all monotonically increasing in their arguments, we can consider log supermodularity as the more stringent condition.
Costinot allows for an arbitrary number (or a continuum) of workers, industries and countries. Ruffin assumes there are two countries that share common productivity for a given worker type in a given industry. Bougheas and Riezman focus on an economy with two sectors in which all workers are equally productive in one of them. Finally, Matsuyama analyzes a small country with two sectors in which newborn agents can choose their industry of lifetime employment after learning their individual comparative advantage. He studies the dynamics of resource allocation as workers die and are replaced by new generations.
Let V(q, k) be the supply of workers of type q in country k. Then if V is log supermodular, V(q 1, k 1)/V(q 0, k 1) > V(q 1, k 0)/V(q 0, k 0) whenever q 1 > q 0 and k 1 > k 0.
Actually, Costinot and Vogel allow for cross-country productivity differences provided they are Hicks-neutral; i.e., proportionately the same for all worker types and industries.
A function of three arguments is log supermodular if it is log supermodular as a function of any pair of arguments, holding the third argument constant. In our setting, this would mean that higher index workers are relatively more productive in higher-index industries in every country, higher-index workers are relatively more productive in higher-index countries in every industry, and higher-index countries have a relatively better technology in higher-index industries for every worker type.
Mussa (1982) has a similar model, except that his second factor—which he calls capital—is specific to an industry.
Note that (6) represents a generalization of the wage Eq. (11) in Costinot and Vogel (2010). In my notation, let ψ (q, i) be the productivity of a worker with ability q in industry i. Then, Costinot and Vogel prove in their Lemma 2 that
$$ \varepsilon_{\psi} [q, \iota (q)] =\varepsilon_{w}(q) $$where \(\iota (q)\) is the equilibrium sector of employment of a worker with ability q and \(\varepsilon_{\psi }\equiv q(\partial \psi /\partial q) /\psi\). Their model has constant returns to labor, so implicitly γ (i) = 1. Therefore, their Lemma 2 also implies that wages rise with an elasticity equal to the elasticity of productivity with respect to ability divided by the elasticity of output with respect to quantity (which, in their case, is equal to one).
Of course, if γ1 = γ2, then the sorting pattern reflects a comparison of \(\varepsilon_{\psi_{1}}\) and \(\varepsilon_{\psi_2}\). The better workers will sort to industry 1 if and only if productivity is a log supermodular function of ability and industry. This observation represents a generalization of the findings of Costinot (2009) to the case with diminishing returns when factor intensities are the same in all industries.
See also Bustos (2011).
In Yeaple (2005), there is also a homogeneous good, so there is both matching within the differentiated products sector and sorting between sectors. Here, I focus on the implications of his model for matching, and so I omit the homogeneous good from my discussion.
Given the costliness of search, it is not necessarily socially optimal for the high-ability workers to decline offers from firms with the basic technology. But the externalities associated with the employment decision suggest that cross-matching skill equilibrium will be inefficient for some parameter values.
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Based on the Bernhard Harms Prize Lecture delivered at the Kiel Institute of World Economics on October 31, 2012. Part of the work on this lecture was completed when I was visiting STICERD at the London School of Economics and Centre de Recerca en Economia Internacional (CREI) in Barcelona. I thank both institutions for their hospitality and support. I am grateful to Arnaud Costinot, Elhanan Helpman, Stephen Redding, and Esteban Rossi-Hansberg for their comments and suggestions.
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Grossman, G.M. Heterogeneous workers and international trade. Rev World Econ 149, 211–245 (2013). https://doi.org/10.1007/s10290-013-0152-7
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DOI: https://doi.org/10.1007/s10290-013-0152-7