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.
We analyze the impact of trade and productivity shocks in a generalized spatial model with aggregate elasticities controlling cross-market links in productivity, labor supply, and trade flows. We show how spatial linkages determine the effect on a local labor market of its direct shock exposure, as well as its indirect general equilibrium exposure to adjustment in other markets. We propose a class of consistent estimators for the model’s aggregate elasticities based on cross-market variation in exposure to observed trade shocks and actual changes in trade and labor outcomes. The “optimal” estimator in this class uses the local responses to the trade shock predicted by our general equilibrium model – the Model-implied Optimal IV (MOIV). Applying our methodology to US states, we find a limited role for indirect effects in the response to trade shocks, implying that the model’s general equilibrium predictions are well approximated by difference-in-difference designs based on simple measures of local shock exposure.
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.
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.