We quantify the distributional effects of trade shocks in the U.S. through consumer prices (expenditure channel) and wages (earnings channel). A quantitative trade model links these channels to compositional differences in expenditures and earnings across household groups. New data reveal that spending shares on imports are similar across education and income groups, implying a neutral expenditure channel. Estimated differences in workers’ exposure to import competition, exporting, and income effects indicate that the earnings channel favors college graduates. Overall, a uniform trade cost reduction generates welfare gains that are 25% larger for college graduates. Similar results apply to trade with China.
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 such designs in which identification follows from the quasi-random assignment of shocks, allowing exposure shares to be endogenous. This framework is centered around a numerical equivalence: conventional shift-share instrumental variable (SSIV) regression coefficients are equivalently obtained from a transformed regression where the shocks are used directly as an instrument. This equivalence implies a shock-level translation of the SSIV exclusion restriction, which holds when shocks are as-good-as-randomly assigned and large in number, with sufficient dispersion in their average exposure. We discuss and illustrate several practical insights delivered by this framework.
A broad empirical literature uses "event study" research designs for treatment effect estimation, a setting in which all units in the panel receive treatment but at random times. We make four novel points about identification and estimation of causal effects in this setting and show their practical relevance. First, we show that in the presence of unit and time fixed effects, it is impossible to identify the linear component of the path of pre-trends and dynamic treatment effects. Second, we propose graphical and statistical tests for pre-trends. Third, we consider commonly-used "static" regressions, with a treatment dummy instead of a full set of leads and lags around the treatment event, and we show that OLS does not recover a weighted average of the treatment effects: long-term effects are weighted negatively, and we introduce a different estimator that is robust to this issue. Fourth, we show that equivalent problems of under-identification and negative weighting arise in difference-in-differences settings when the control group is allowed to be on a different time trend or in the presence of unit-specific time trends. Finally, we show the practical relevance of these issues in a series of examples from the existing literature, with a focus on the estimation of the marginal propensity to consume out of tax rebates.
We study the properties of “shock-exposure instruments,” constructed from a set of quasi-experimental shocks and endogenous measures of heterogeneous exposure. Validity of these instruments generally requires a simple but non-standard correction, derived from knowledge of counterfactual shocks that might have been realized. Such design knowledge can also be used for exact randomization inference and specification tests that are valid in finite samples. We further characterize the shock-exposure instruments that are asymptotically efficient. This framework has practical implications for the use of shift-share instruments, simulated eligibility instruments, model-implied instruments, and for other designs. We illustrate these implications in two applications.
Slides can be shared by request. Draft is coming soon.
Are diversified firms mere collections of independent assets, or is there anything that glues together different businesses? We explore this question by looking at segment level growth of multi-segment (i.e., producing in several 6-digit industries at the same time) manufacturing firms in Japan. We find substantial co-movement between such segments and show that it can be driven by plant-wide but not firm-wide shocks. Our findings suggest that inputs that are shared firm-wide, such as brand and organizational routines, are not too important for production.
The fraction of a population that is affected by a treatment (the “responders”) may be as important to identify as the average magnitude of the treatment effect. I show that if the distributions of potential outcomes with and without treatment are identified, then the total variation distance between them serves as the sharp lower bound on the share of responders. It can be computed for randomized control trials, instrumental variables, and other empirical designs. I demonstrate the usefulness of the approach in three examples of economic interest, related to behavioral biases in retirement savings, electoral fraud, and student cheating.