We study inference in shift-share regression designs, such as when a regional outcome is regressed on a weighted average of observed sectoral shocks, using regional sector shares as weights. We conduct a placebo exercise in which we estimate the effect of a shift-share regressor constructed with randomly generated sectoral shocks on actual labor market outcomes across U.S. Commuting Zones. Tests based on commonly used standard errors with 5% nominal significance level reject the null of no effect in up to 55% of the placebo samples. We use a stylized economic model to show that this overrejection problem arises because regression residuals are correlated across regions with similar sectoral shares, independently of their geographic location. We derive novel inference methods that are valid under arbitrary cross-regional correlation in the regression residuals. We show that our methods yield substantially wider confidence intervals in popular applications of shift-share regression designs.
Supplemental Material: Online Appendix
How do shocks to economic fundamentals in the world economy affect local labor markets? In a framework with a flexible structure of spatial linkages, we characterize the model-consistent shock exposure of a local market as the exogenous shift in its production revenues and consumption costs. In general equilibrium, labor outcomes in any market respond directly to the market’s own shock exposure, and indirectly to other markets shocks exposures. We show how spatial linkages control the size and the heterogeneity of these indirect effects. We then develop a new estimation methodology – the Model-implied Optimal IV (MOIV) – that exploits quasi-experimental variation in economic shocks to estimate spatial linkages and evaluate their counterfactual implications. Applying our methodology to US Commuting Zones, we find that difference-in-difference designs based on model-consistent measures of local shock exposure approximate well the differential effect of international trade shocks across CZs, but miss around half of the aggregate effect, partly due to the offsetting action of indirect effects.
This paper proposes a new approach to quantify the distributional effects of international trade. The starting point of my analysis is a Roy-like model where workers are heterogeneous in terms of their comparative and absolute advantage. In this environment, I show that the schedules of comparative and absolute advantage (i) determine changes in the average and the variance of the log-wage distribution, and (ii) are nonparametrically identified from the cross-regional variation in the sectoral responses of employment and wages to observable shifters of sector labor demand. I then use these theoretical results to quantify the distributional consequences of the recent movements in world commodity prices in Brazil. I find that shocks to world commodity prices account for 5-10% of the fall in Brazilian wage inequality between 1991 and 2010.
Work in Progress
American Economic Review, 107(3): 633-89. (Lead Article)
We develop a methodology to construct nonparametric counterfactual predictions, free of functional form restrictions on preferences and technology, in neoclassical models of international trade. First, we establish the equivalence between such models and reduced exchange models in which countries directly exchange factor services. This equivalence implies that, for an arbitrary change in trade costs, counterfactual changes in the factor content of trade, factor prices, and welfare only depend on the shape of a reduced factor demand system. Second, we provide sufficient conditions under which estimates of this system can be recovered nonparametrically. Together, these results offer a strict generalization of the parametric approach used in so-called gravity models. Finally, we use China's recent integration into the world economy to illustrate the feasibility and potential benefits of our approach.