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Register a new userEfficient Treatment Effect Estimation in Observational Studies under Heterogeneous Partial Interference
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In many observational studies in social science and medical applications, subjects or individuals are connected, and one units treatment and attributes may affect another units treatment and outcome, violating the stable unit treatment value assumption (SUTVA) and resulting in interference. To enable feasible inference, many previous works assume the ``exchangeability of interfering units, under which the effect of interference is captured by the number or ratio of treated neighbors. However, in many applications with distinctive units, interference is heterogeneous. In this paper, we focus on the partial interference setting, and restrict units to be exchangeable conditional on observable characteristics. Under this framework, we propose generalized augmented inverse propensity weighted (AIPW) estimators for general causal estimands that include direct treatment effects and spillover effects. We show that they are consistent, asymptotically normal, semiparametric efficient, and robust to heterogeneous interference as well as model misspecifications. We also apply our method to the Add Health dataset and find that smoking behavior exhibits interference on academic outcomes.
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In the recent literature on estimating heterogeneous treatment effects, each proposed method makes its own set of restrictive assumptions about the interventions effects and which subpopulations to explicitly estimate. Moreover, the majority of the literature provides no mechanism to identify which subpopulations are the most affected--beyond manual inspection--and provides little guarantee on the correctness of the identified subpopulations. Therefore, we propose Treatment Effect Subset Scan (TESS), a new method for discovering which subpopulation in a randomized experiment is most significantly affected by a treatment. We frame this challenge as a pattern detection problem where we efficiently maximize a nonparametric scan statistic over subpopulations. Furthermore, we identify the subpopulation which experiences the largest distributional change as a result of the intervention, while making minimal assumptions about the interventions effects or the underlying data generating process. In addition to the algorithm, we demonstrate that the asymptotic Type I and II error can be controlled, and provide sufficient conditions for detection consistency--i.e., exact identification of the affected subpopulation. Finally, we validate the efficacy of the method by discovering heterogeneous treatment effects in simulations and in real-world data from a well-known program evaluation study.
We develop new semiparametric methods for estimating treatment effects. We focus on a setting where the outcome distributions may be thick tailed, where treatment effects are small, where sample sizes are large and where assignment is completely random. This setting is of particular interest in recent experimentation in tech companies. We propose using parametric models for the treatment effects, as opposed to parametric models for the full outcome distributions. This leads to semiparametric models for the outcome distributions. We derive the semiparametric efficiency bound for this setting, and propose efficient estimators. In the case with a constant treatment effect one of the proposed estimators has an interesting interpretation as a weighted average of quantile treatment effects, with the weights proportional to (minus) the second derivative of the log of the density of the potential outcomes. Our analysis also results in an extension of Hubers model and trimmed mean to include asymmetry and a simplified condition on linear combinations of order statistics, which may be of independent interest.
In this study, we develop a novel estimation method of the quantile treatment effects (QTE) under the rank invariance and rank stationarity assumptions. Ishihara (2020) explores identification of the nonseparable panel data model under these assumptions and propose a parametric estimation based on the minimum distance method. However, the minimum distance estimation using this process is computationally demanding when the dimensionality of covariates is large. To overcome this problem, we propose a two-step estimation method based on the quantile regression and minimum distance method. We then show consistency and asymptotic normality of our estimator. Monte Carlo studies indicate that our estimator performs well in finite samples. Last, we present two empirical illustrations, to estimate the distributional effects of insurance provision on household production and of TV watching on child cognitive development.
The ill-posedness of the inverse problem of recovering a regression function in a nonparametric instrumental variable model leads to estimators that may suffer from a very slow, logarithmic rate of convergence. In this paper, we show that restricting the problem to models with monotone regression functions and monotone instruments significantly weakens the ill-posedness of the problem. In stark contrast to the existing literature, the presence of a monotone instrument implies boundedness of our measure of ill-posedness when restricted to the space of monotone functions. Based on this result we derive a novel non-asymptotic error bound for the constrained estimator that imposes monotonicity of the regression function. For a given sample size, the bound is independent of the degree of ill-posedness as long as the regression function is not too steep. As an implication, the bound allows us to show that the constrained estimator converges at a fast, polynomial rate, independently of the degree of ill-posedness, in a large, but slowly shrinking neighborhood of constant functions. Our simulation study demonstrates significant finite-sample performance gains from imposing monotonicity even when the regression function is rather far from being a constant. We apply the constrained estimator to the problem of estimating gasoline demand functions from U.S. data.
This paper considers fixed effects estimation and inference in linear and nonlinear panel data models with random coefficients and endogenous regressors. The quantities of interest -- means, variances, and other moments of the random coefficients -- are estimated by cross sectional sample moments of GMM estimators applied separately to the time series of each individual. To deal with the incidental parameter problem introduced by the noise of the within-individual estimators in short panels, we develop bias corrections. These corrections are based on higher-order asymptotic expansions of the GMM estimators and produce improved point and interval estimates in moderately long panels. Under asymptotic sequences where the cross sectional and time series dimensions of the panel pass to infinity at the same rate, the uncorrected estimator has an asymptotic bias of the same order as the asymptotic variance. The bias corrections remove the bias without increasing variance. An empirical example on cigarette demand based on Becker, Grossman and Murphy (1994) shows significant heterogeneity in the price effect across U.S. states.
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