## Research

### Working Papers

**Not-Parametric Gravity: Measuring the Aggregate Implications of Firm Heterogeneity**** **(Joint with Costas Arkolakis and Sharat Ganapati)

**New paper - April 2020**

How does firm heterogeneity affect the aggregate consequences of international trade shocks? In the workhorse monopolistic competition model, we show that the distribution of firm fundamentals affects aggregate equilibrium outcomes only through the shape of two univariate functions of the exporter firm share. These functions determine semiparametric gravity equations for the extensive and intensive margins of firm exports, yielding bilateral elasticities of trade flows to trade costs that vary with the exporter firm share. We show that the shape of these elasticity functions is sufficient to compute (i) counterfactual changes in aggregate outcomes and (ii) expressions for welfare gains. We estimate these elasticity functions using the model-implied semiparametric gravity equations of firm exports. Our estimates imply that bilateral trade is less sensitive to trade shocks when the exporter firm share is high. Firm heterogeneity leads to a 15% change in the gains from trade (compared to the constant elasticity gravity benchmark) that are higher in countries with a higher exporter firm share

**Technological Transition with Skill Heterogeneity Across Generations**** *** *(Joint with Martin Beraja and Nitya Pandalai-Nayar)

Supplemental Material: Online Appendix

**Updated on February 2020**

Why are some technological transitions particularly unequal and slow to play out? We develop a theory to study transitions after technological innovations driven by worker reallocation within a generation and changes in the skill distribution across generations. The economy’s transitional dynamics have a representation as a q-theory of skill investment. We exploit this in two ways. First, to show that technology-skill specificity and the cost of skill investment determine how unequal and slow transitions are by affecting the two adjustment margins in the theory. Second, to connect these determinants to measurable, short-horizon changes in labor market outcomes within and between generations. We then empirically analyze the adjustment to recent cognitive-biased innovations in developed economies. Strong responses of cognitive-intensive employment for young but not old generations suggest that cognitive-skill specificity is high and that the supply of cognitive skills is more elastic for younger generations. This evidence indicates that cognitive-biased transitions slowly unfold over many generations. As such, naively extrapolating from observed changes at short horizons leads to overly pessimistic views about their welfare and distributional implications.

**General Equilibrium Effects in Space: Theory and Measurement**** ** (Joint with Costas Arkolakis and Federico Esposito)

Supplemental Material: Online Appendix

**Updated on June 2020**

How do international trade shocks affect spatially connected regional markets? We answer this question by extending shift-share empirical specifications to incorporate general equilibrium effects that arise in spatial models. In partial equilibrium, regional shock exposure has a shift-share structure: it is the average shock weighted by regional exposure shares in revenue and consumption. General equilibrium responses of employment and wages in each market are the sum, across all regions, of these shift-share measures times bilateral reduced-form elasticities determined by the economy's spatial links. We use this reduced-form representation of the model to efficiently estimate the bilateral elasticities exploiting exogenous variation in shock exposure across markets. Finally, we study the general equilibrium impact of the ``China shock’’ on U.S. CZs using our model-consistent generalization of the specification in Autor et al. (2013). We find that indirect effects from the shock exposure of other markets reinforce the negative impact of the market’s own shock exposure, leading to employment and wage losses that are significantly larger than those reported in the existing literature.

**Worker Heterogeneity, Wage Inequality, and International Trade: Theory and Evidence from Brazil**__ __

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

**How Large is the Impact of Trade on Inequality? A New Factor Content of Trade Approach ***Version coming soon! *(Joint with Paul Carrillo, Arnaud Costinot, Dave Donaldson and Dina Pomeranz)

### Refereed Publications

**Shift-Share Designs: Theory and Inference**** **(Joint with Michal Kolesàr and Eduardo Morales)

Supplemental Material: Stata Code; Matlab Code; R Code; Online Appendix

*The Quarterly Journal of Economics, *134(4): 1949-2010, 2019

We study inference in shift-share regression designs, such as when a regional outcome is regressed on a weighted average of 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 using popular applications of shift-share designs that our methods may lead to substantially wider confidence intervals in practice.

**Nonparametric Counterfactual Predictions in Neoclassical Models of International Trade** (Joint with Arnaud Costinot and Dave Donaldson)

*American Economic Review*, 107(3): 633-89, 2017. (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.