HB consider U.S. product prices to be endogenous and thus require instruments for consistent estimation. For domestic prices their instrument set includes a set of domestic variables such as factor supplies, tfp, and government demand. For tradables prices HB use a set of international variables meant to capture the effect of developments abroad communicated to the United States through changes in our product prices. More specifically, they construct variables aimed at measuring “the presence of each country’s labor supply in the international market” (p. 9). To do this, for each year HB separate all countries into four income quartiles and then sum across all countries in each quartile the product of each country’s labor force multiplied by its ratio of gross trade to GDP. Thus, HB are the first researchers to try to model the effect on U.S. prices of “international trade” in terms of foreign changes in productive capacity communicated to the United States through changes in our product prices.
The main results from their wage decomposition are reported in Table 5. HB find that the most important relative-price change contributing to rising wage inequality was the large increase in the price of nontraded skill-intensive products relative to tradables and to the other nontraded sector. The effects of changes in tradables relative prices are less clear: parameter estimates for these variables are relatively imprecise. This suggests that the international instruments might be weak.