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Register a new userWelfare Analysis via Marginal Treatment Effects
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Consider a causal structure with endogeneity (i.e., unobserved confoundedness) in empirical data, where an instrumental variable is available. In this setting, we show that the mean social welfare function can be identified and represented via the marginal treatment effect (MTE, Bjorklund and Moffitt, 1987) as the operator kernel. This representation result can be applied to a variety of statistical decision rules for treatment choice, including plug-in rules, Bayes rules, and empirical welfare maximization (EWM) rules as in Hirano and Porter (2020, Section 2.3). Focusing on the application to the EWM framework of Kitagawa and Tetenov (2018), we provide convergence rates of the worst case average welfare loss (regret) in the spirit of Manski (2004).
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In nonlinear panel data models, fixed effects methods are often criticized because they cannot identify average marginal effects (AMEs) in short panels. The common argument is that the identification of AMEs requires knowledge of the distribution of unobserved heterogeneity, but this distribution is not identified in a fixed effects model with a short panel. In this paper, we derive identification results that contradict this argument. In a panel data dynamic logic model, and for T as small as four, we prove the point identification of different AMEs, including causal effects of changes in the lagged dependent variable or in the duration in last choice. Our proofs are constructive and provide simple closed-form expressions for the AMEs in terms of probabilities of choice histories. We illustrate our results using Monte Carlo experiments and with an empirical application of a dynamic structural model of consumer brand choice with state dependence.
We study the causal interpretation of regressions on multiple dependent treatments and flexible controls. Such regressions are often used to analyze randomized control trials with multiple intervention arms, and to estimate institutional quality (e.g. teacher value-added) with observational data. We show that, unlike with a single binary treatment, these regressions do not generally estimate convex averages of causal effects-even when the treatments are conditionally randomly assigned and the controls fully address omitted variables bias. We discuss different solutions to this issue, and propose as a solution anew class of efficient estimators of weighted average treatment effects.
The policy relevant treatment effect (PRTE) measures the average effect of switching from a status-quo policy to a counterfactual policy. Estimation of the PRTE involves estimation of multiple preliminary parameters, including propensity scores, conditional expectation functions of the outcome and covariates given the propensity score, and marginal treatment effects. These preliminary estimators can affect the asymptotic distribution of the PRTE estimator in complicated and intractable manners. In this light, we propose an orthogonal score for double debiased estimation of the PRTE, whereby the asymptotic distribution of the PRTE estimator is obtained without any influence of preliminary parameter estimators as far as they satisfy mild requirements of convergence rates. To our knowledge, this paper is the first to develop limit distribution theories for inference about the PRTE.
This paper discusses the problem of estimation and inference on the effects of time-varying treatment. We propose a method for inference on the effects treatment histories, introducing a dynamic covariate balancing method combined with penalized regression. Our approach allows for (i) treatments to be assigned based on arbitrary past information, with the propensity score being unknown; (ii) outcomes and time-varying covariates to depend on treatment trajectories; (iii) high-dimensional covariates; (iv) heterogeneity of treatment effects. We study the asymptotic properties of the estimator, and we derive the parametric convergence rate of the proposed procedure. Simulations and an empirical application illustrate the advantage of the method over state-of-the-art competitors.
In non-experimental settings, the Regression Discontinuity (RD) design is one of the most credible identification strategies for program evaluation and causal inference. However, RD treatment effect estimands are necessarily local, making statistical methods for the extrapolation of these effects a key area for development. We introduce a new method for extrapolation of RD effects that relies on the presence of multiple cutoffs, and is therefore design-based. Our approach employs an easy-to-interpret identifying assumption that mimics the idea of common trends in difference-in-differences designs. We illustrate our methods with data on a subsidized loan program on post-education attendance in Colombia, and offer new evidence on program effects for students with test scores away from the cutoff that determined program eligibility.
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