We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.

Evolution and Rationality Some Recent Game-Theoretic Results. Identification and Estimation of Local Average Treatment Effects

We study the pro-competitive effects of international trade, or lack thereof, in models with monopolistic competition, firm-level heterogeneity, and variable markups. Under standard restrictions on consumers’ demand and the distribution of firms’ productivity, we derive two theoretical results. First, although markups vary acrossfirms, the distribution of markups and the share of aggregate profits in revenues are invariant to changes in openness to trade. Second, although the distribution of markups and the share of aggregate profits in revenues are unaffected by trade, gains from trade liberalization are weakly lower than those predicted by the models with constant markups considered in Arkolakis, Costinot, and Rodriguez-Clare (2012).

/pdf/the-elusive-pro-competitive-effects-of-trade-41jgsz5vq0.pdf

The Elusive Pro-Competitive Effects of Trade

Many studies use shift-share (or ``Bartik'') instruments, which average a set of shocks with exposure share weights. We provide a new econometric framework for shift-share instrumental variable (SSIV) regressions in which identification follows from the quasi-random assignment of shocks, while exposure shares are allowed to be endogenous. The framework is motivated by an equivalence result: the orthogonality between a shift-share instrument and an unobserved residual can be represented as the orthogonality between the underlying shocks and a shock-level unobservable. SSIV regression coefficients can similarly be obtained from an equivalent shock-level regression, motivating shock-level conditions for their consistency. We discuss and illustrate several practical insights of this framework in the setting of Autor et al. (2013), estimating the effect of Chinese import competition on manufacturing employment across U.S. commuting zones.

Quasi-Experimental Shift-Share Research Designs

Many studies use shift-share (or "Bartik") instruments, which average a set of shocks with exposure share weights. We provide a new econometric framework for shift-share instrumental variable (SSIV) regressions in which identification follows from the quasi-random assignment of shocks, while exposure shares are allowed to be endogenous. The framework is motivated by an equivalence result: the orthogonality between a shift-share instrument and an unobserved residual can be represented as the orthogonality between the underlying shocks and a shock-level unobservable. SSIV regression coefficients can similarly be obtained from an equivalent shock-level regression, motivating shock-level conditions for their consistency. We discuss and illustrate several practical insights of this framework in the setting of Autor, Dorn, and Hanson (2013), estimating the effect of Chinese import competition on manufacturing employment across U.S. commuting zones.

This paper uses factor analytic methods to decompose industrial production (IP) into components arising from aggregate shocks and idiosyncratic sector-specific shocks. An approximate factor model finds that nearly all (90%) of the variability of quarterly growth rates in IP are associated with common factors. Because common factors may reflect sectoral shocks that have propagated by way of input-output linkages, we then use a multisector growth model to adjust for the effects of these linkages. In particular, we show that neoclassical multisector models, of the type first introduced by Long and Plosser (1983), produce an approximate factor model as a reduced form. A structural factor analysis then indicates that aggregate shocks continue to be the dominant source of variation in IP, but the importance of sectoral shocks more than doubles after the Great Moderation (to 30%). The increase in the relative importance of these shocks follows from a fall in the contribution of aggregate shocks to IP movements after 1984.

/pdf/sectoral-vs-aggregate-shocks-a-structural-factor-analysis-of-3af9josp3y.pdf

Sectoral vs. Aggregate Shocks: A Structural Factor Analysis of Industrial Production : Supplementary Material

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.

Shift-Share Designs: Theory and Inference

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. (JEL C51, D51, F11, F14, O19, P33)

/pdf/nonparametric-counterfactual-predictions-in-neoclassical-448lar51ih.pdf

Nonparametric counterfactual predictions in neoclassical models of international trade

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, independent 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.

/pdf/shift-share-designs-theory-and-inference-2g1bfvxfeq.pdf

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.

/pdf/general-equilibrium-effects-in-space-theory-and-measurement-2xn131jrwc.pdf

Rodrigo Adao

Papers

Shift-Share Designs: Theory and Inference

Shift-Share Designs: Theory and Inference

Nonparametric counterfactual predictions in neoclassical models of international trade

Shift-Share Designs: Theory and Inference

General Equilibrium Effects in Space: Theory and Measurement