Price Equalization Theory

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Factor price equalization is an economic theory, by Paul A. Samuelson (1948), which states that the prices of identical factors of production, such as the wage rate, or the return to capital, will be equalized across countries as a result of international trade in commodities. The theorem assumes that there are two goods and two factors of production, for example capital and labour. Other key assumptions of the theorem are that each country faces the same commodity prices, because of free trade in commodities, uses the same technology for production, and produces both goods. Crucially these assumptions result in factor prices being equalized across countries without the need for factor mobility, such as migration of labour or capital flows. Whichever factor receives the lowest price before two countries integrate economically and effectively become one market will therefore tend to become more expensive relative to other factors in the economy, while those with the highest price will tend to become cheaper. Economic theory suggests two powerful mechanisms promoting factor price convergence across regions and countries — goods trade and factor mobility. Within a country, goods markets are more highly integrated, and factors of production are more mobile, than they are across countries. As a result, factor price equalization, to the extent it exists anywhere, is more likely to occur within nations than internationally Absolute factor price equality implies that identical factors of production are paid the same wage across regions. Relative factor price equality, on the other hand, allows absolute wages to vary so long as relative wages (i.e. the skill premium) remain constant. An obvious potential explanation for a violation in absolute factor price equality is the existence of regional Hicks-neutral productivity differences: regions with higher Hicks-neutral Productivity can offer higher wages to both skilled and unskilled workers even while relative wages remain uniform. Rejection of factor price equality can also arise for more complicated reasons. For example, both absolute and relative factor price equality can fail due to unobserved variation in regional factor quality.


Analyzing the effect of such variation on output and wages has a long history in the international trade literature, including the classic paper by Leontief (1953) and the more recent cross-country study by Trefler (1993). A key advantage of the methodology that we develop is its robustness to unobserved differences in factor quality. Indeed, our tests control for factor quality differences across pairs of regions and industries.

Our approach is based upon extremely general conditions for producer equilibrium and builds upon techniques developed by Bernard and Schott (2001) to test for factor price equality in the US. We generalize that theoretical framework from the case of the CES production technology to any constant returns to scale technology, to allow for unobserved factor quality differences that are region-industry specific rather than just region-specific, and to the case of imperfect competition. Our methodology exploits the fact that, although an empirical researcher will not typically observe factor quality or quality-adjusted factor prices, observed factor prices contain information about the quality of observed factors when firms minimize costs. This approach does not make any assumptions regarding the preferences and costs of living faced by different types of workers. As a result, it is robust to unobserved variation in consumer price indices specific to types of workers or locations. Nonetheless, the analysis has implications for the value of real wages and the degree of factor mobility across locations. Though our technique is...
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