Matching and Sorting in the Global Economy (議事概要)


    • Time and Date: 15:30-17:00, Friday, April 4, 2014
    • Venue: RIETI's seminar room #1121 (METI Annex 11th Floor)
    • Language: English
    • Host: Research Institute of Economy, Trade and Industry (RIETI)


Professor Elhanan Helpman of Harvard University presented a paper entitled "Matching and Sorting in a Global Economy" at RIETI on April 4, 2014. This paper was written together with Professor Gene Grossman of Princeton University and Professor Philipp Kircher of the University of Edinburgh. Among the questions that the paper addresses is how trade affects the distribution of income.

Traditional international trade theory yields differing conclusions concerning how a change in the relative price of goods will redistribute income. In the Heckscher-Ohlin model with two factors and complete factor mobility, the Stolper-Samuelson theorem implies that a decrease in the relative price of the import competing good (due, for instance, to trade liberalization) would benefit the abundant factor and harm the scarce factor. For the United States, this would imply that trade liberalization would increase the return to capital and decrease the return to labor. In the Ricardo-Viner model with two industry-specific factors, on the other hand, trade liberalization would benefit the export industry and harm the import-competing industries.

These models assume homogeneous factors of production. Professor Helpman noted that workers and managers are heterogeneous. Workers differ in physical attributes, in cognitive abilities, and in their education, training, and experience. Firms in the same industry differ in size, in the compositions of their workforces, in the technologies and capital goods they use, and in the wages they pay to their workers. Further, industries differ in factor intensities and in the marginal contributions of workers and managerial ability to firm productivity. A model with heterogeneous factors allows a more complete analysis of the distributional effects of trade than is possible in one with homogeneous factors.

Professor Helpman examined how workers sort to sectors and how workers match with managers within a sector. To do this he presented a model with two countries, two competitive industries, and two heterogeneous factors of production. One of the factors he called labor and the other managers. The quantity of labor is given exogenously and workers' abilities are represented by a probability density function (pdf). Managers' abilities are represented by a different pdf. Firms in both countries employ identical, constant returns to scale technologies. Output is a function of one manager of a given ability and l workers of a given ability. There are assumed to be diminishing returns to combining more workers with a given manager. The rest of the model (e.g., consumers share homothetic preferences, firms hire factors in frictionless national markets) is familiar from the neoclassical trade theory.

If the productivity of a production unit is a strictly supermodular function of the ability levels of the managers and workers, Professor Helpman showed that there would be positive assortative matching. This implies that, for the workers and managers that sort to a sector, better workers will be teamed with better managers. When there are strong complementarities between workers' and managers' abilities, the forces guiding the sorting of factors to sectors and the matching of factors within sectors become inextricably linked.

Even when strong complementarities dictate positive assortative matching within every sector, the economy-wide pattern of factor assignments can be subtle and complex. Professor Helpman examined in detail the factors that determined how workers and managers sorted to different sectors.

What does the model say for the effect of trade on wages and salaries? Considering first the case of homogeneous managers and heterogeneous workers, when trade causes the relative price of a country's export good to rise, the resulting expansion of the export sector benefits all types of the factor used intensively in that sector and harms the factor used intensively in the import-competing sector. This is familiar from the Heckscher-Ohlin economy. When a factor is heterogeneous, trade benefits all types of the factor that have comparative advantage in the export industry and harms those types that have comparative advantage in the import-competing industry. This is familiar from the Ricardo-Viner economy.

When both workers and managers are heterogeneous and there are complementarities between their abilities, there is the additional question of how trade affects the individual's match with other factors of production. If a change in trade conditions causes a worker to re-match with a better manager than before, then his productivity will improve and his wage will receive an upward boost. If instead a worker's match deteriorates, then his wage may suffer. The effects of trade on wage or salary inequality across sectors may also run counter to the effects on inequality within a sector.

Professor Helpman's findings imply that the Heckscher-Ohlin theorem extends to a setting with heterogeneous factors provided that the countries share similar distributions of worker and managerial talent. But his results also indicate that differences in the distributions of talent can be an independent source of comparative advantage. A country that has more able workers than another in the sense of a rightward shift in the pdf for talent will produce relatively more of the good for which productivity responds more elastically to ability.

Professor Helpman concluded his stimulating talk by noting that much work remains to be done to clarify the connection between trade and the efficiency of matching.