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

Difference-in-Differences with multiple time periods

To estimate the dynamic effects of an absorbing treatment, researchers often use two-way fixed effects regressions that include leads and lags of the treatment. We show that in settings with variation in treatment timing across units, the coefficient on a given lead or lag can be contaminated by effects from other periods, and apparent pretrends can arise solely from treatment effects heterogeneity. We propose an alternative estimator that is free of contamination, and illustrate the relative shortcomings of two-way fixed effects regressions with leads and lags through an empirical application.

Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects

To the extent that students benefit from high-achieving peers, tracking will help strong students and hurt weak ones. However, all students may benefit if tracking allows teachers to present material at a more appropriate level. Lower-achieving pupils are particularly likely to benefit from tracking if teachers would otherwise have incentives to teach to the top of the distribution. We propose a simple model nesting these effects. We compare 61 Kenyan schools in which students were randomly assigned to a first grade class with 60 in which students were assigned based on initial achievement. In non-tracking schools, students randomly assigned to academically stronger peers scored higher, consistent with a positive direct effect of academically strong peers. However, compared to their counterparts in non-tracking schools, students in tracking schools scored 0.14 standard deviations higher after 18 months, and this effect persisted one year after the program ended. Furthermore, students at all levels of the distribution benefited from tracking. Students near the median of the pre-test distribution benefited similarly whether assigned to the lower or upper section. A natural interpretation is that the direct effect of high-achieving peers is positive, but that tracking benefited lower-achieving pupils indirectly by allowing teachers to teach at a level more appropriate to them.

Replication data for: Peer Effects, Teacher Incentives, and the Impact of Tracking: Evidence from a Randomized Evaluation in Kenya

Difference-in-differences analysis with staggered treatment timing is frequently used to assess the impact of policy changes on corporate outcomes in academic research. However, recent advances in econometric theory show that such designs are likely to be biased in the presence of treatment effect heterogeneity. Given the pronounced use of staggered treatment designs in applied corporate finance and accounting research, this finding potentially impacts a large swath of prior findings in these fields. We survey the nascent literature and document how and when such bias arises from treatment effect heterogeneity. We apply recently proposed methods to a set of prior published results, and find that correcting for the bias induced by the staggered nature of policy adoption frequently impacts the estimated effect from standard difference-in-difference studies. In many cases, the reported effects in prior research become indistinguishable from zero.

How Much Should We Trust Staggered Difference-In-Differences Estimates?

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.

Revisiting Event Study 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 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.

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 delivered by this framework in the setting of Autor et al (2013)

/pdf/quasi-experimental-shift-share-research-designs-f02j4o87n2.pdf

We develop new tools for estimating the causal effects of treatments or instruments that combine multiple sources of variation according to a known formula. Examples include treatments capturing spillovers in social and transportation networks, simulated instruments for policy eligibility, and shift-share instruments. We show how exogenous shocks to some, but not all, determinants of such variables can be leveraged while avoiding omitted variables bias. Our solution involves specifying counterfactual shocks that may as well have been realized and adjusting for a summary measure of non-randomness in shock exposure: the average treatment (or instrument) across such counterfactuals. We further show how to use shock counterfactuals for valid finite-sample inference, and characterize the valid instruments that are asymptotically efficient. We apply this framework to address bias when estimating employment effects of market access growth from Chinese high-speed rail construction, and to boost power when estimating coverage effects of expanded Medicaid eligibility.

/pdf/non-random-exposure-to-exogenous-shocks-theory-and-3po6dsr8ig.pdf

Kirill Borusyak

Papers

Revisiting Event Study Designs

Quasi-Experimental Shift-Share Research Designs

Quasi-Experimental Shift-Share Research Designs

Quasi-Experimental Shift-Share Research Designs

Non-Random Exposure to Exogenous Shocks: Theory and Applications