Wage and Industry Effects in U.S. Regional Incomes, 1840 to 1987: A CES Wage Index Method

The Solow growth and the Heckscher-Ohlin trade models describe two competing processes through which regional incomes converge over time. Solow's model attributes rising productivity of labor to additional regional capital investments. Heckscher-Ohlin's trade model ascribes the relocation of high value industries to regions with low wage rates. On the other hand Paul Krugman expects incomes to diverge over time as regions with an initial advantage maintain it through ever increasing external economies of scale. The Solow and Heckscher-Ohlin models imply that incomes converge through the movement of high quality labor and capital and high value goods and services into low income regions respectively. In 1951 Frank Hanna recognized that an index of average income per worker of a region compared to the same average for the nation equals the sum of the region's wage and industry effects.1 A Hanna wage index compares the sum of average wage per worker per sector between the region and the nation weighted by the relative importance of the sectors in the region. The Hanna industry index compares the sum of the relative importance of each sector between the region and the nation weighted by the average wage per worker per sector for the nation. The industry index measures the effect on average wages from some sectors consistently paying higher wages than others. For example, the aggregate "nonagricultural sector" pays higher wages than the agricultural sector. Ceterus paribus, a region with a larger portion of its economy devoted to the nonagricultural sector will have relatively higher average income. In 1998 Sukkoo Kim applied Hanna's income index to measuring the relative importance of the wage and industry effects. In particular, he measured the contribution of these effects for each of nine census regions of the United States at five points in time between 1840 and 1987. If the Solow theory were right, Kim would find no industry effect and decreasing wage effects over time. If the Heckscher-Ohlin theory were right, he should observe the opposite. Were the Hanna indices more consistent with those predicted by the Solow or the Heckscher-Ohlin theory? From this research, Kim drew six conclusions about the convergence of wages across the regions of the United States. In a note, Sumner La Croix used Kim's data and applied his own index number approach. La Croix's wage and industry indices resulted in some contradictions to those developed by Kim using the Hanna index approach. More importantly, La Croix's results cast doubt on three of the six conclusions stated by Kim. La Croix and Kim both accepted the following three conclusions: First, "the most significant cause of income divergence between 1840 and 1900 was the sharp relative decline in Southern income per capita caused by the region's growing unfavorable industry mix and lower wages relative to other regions."2 Second, "for all regions in 1954 the income differences that can be attributed to the industry-mix effects were considerably lower than they were in 1900."3 Third, "the favorable industry-mix income effect for the New England and Middle Atlantic regions fell from 25 percent to less than 10 percent between 1900 and 1954."4