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Register a new userBootstrap Inference for Quantile Treatment Effects in Randomized Experiments with Matched Pairs
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This paper examines methods of inference concerning quantile treatment effects (QTEs) in randomized experiments with matched-pairs designs (MPDs). Standard multiplier bootstrap inference fails to capture the negative dependence of observations within each pair and is therefore conservative. Analytical inference involves estimating multiple functional quantities that require several tuning parameters. Instead, this paper proposes two bootstrap methods that can consistently approximate the limit distribution of the original QTE estimator and lessen the burden of tuning parameter choice. Most especially, the inverse propensity score weighted multiplier bootstrap can be implemented without knowledge of pair identities.
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In this paper, we study the estimation and inference of the quantile treatment effect under covariate-adaptive randomization. We propose two estimation methods: (1) the simple quantile regression and (2) the inverse propensity score weighted quantile regression. For the two estimators, we derive their asymptotic distributions uniformly over a compact set of quantile indexes, and show that, when the treatment assignment rule does not achieve strong balance, the inverse propensity score weighted estimator has a smaller asymptotic variance than the simple quantile regression estimator. For the inference of method (1), we show that the Wald test using a weighted bootstrap standard error under-rejects. But for method (2), its asymptotic size equals the nominal level. We also show that, for both methods, the asymptotic size of the Wald test using a covariate-adaptive bootstrap standard error equals the nominal level. We illustrate the finite sample performance of the new estimation and inference methods using both simulated and real datasets.
Analyses of environmental phenomena often are concerned with understanding unlikely events such as floods, heatwaves, droughts or high concentrations of pollutants. Yet the majority of the causal inference literature has focused on modelling means, rather than (possibly high) quantiles. We define a general estimator of the population quantile treatment (or exposure) effects (QTE) -- the weighted QTE (WQTE) -- of which the population QTE is a special case, along with a general class of balancing weights incorporating the propensity score. Asymptotic properties of the proposed WQTE estimators are derived. We further propose and compare propensity score regression and two weighted methods based on these balancing weights to understand the causal effect of an exposure on quantiles, allowing for the exposure to be binary, discrete or continuous. Finite sample behavior of the three estimators is studied in simulation. The proposed methods are applied to data taken from the Bavarian Danube catchment area to estimate the 95% QTE of phosphorus on copper concentration in the river.
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.
Datasets from field experiments with covariate-adaptive randomizations (CARs) usually contain extra baseline covariates in addition to the strata indicators. We propose to incorporate these extra covariates via auxiliary regressions in the estimation and inference of unconditional QTEs under CARs. We establish the consistency, limiting distribution, and validity of the multiplier bootstrap of the regression-adjusted QTE estimator. The auxiliary regression may be estimated parametrically, nonparametrically, or via regularization when the data are high-dimensional. Even when the auxiliary regression is misspecified, the proposed bootstrap inferential procedure still achieves the nominal rejection probability in the limit under the null. When the auxiliary regression is correctly specified, the regression-adjusted estimator achieves the minimum asymptotic variance. We also derive the optimal pseudo true values for the potentially misspecified parametric model that minimize the asymptotic variance of the corresponding QTE estimator. We demonstrate the finite sample performance of the new estimation and inferential methods using simulations and provide an empirical application to a well-known dataset in education.
In nonseparable triangular models with a binary endogenous treatment and a binary instrumental variable, Vuong and Xu (2017) show that the individual treatment effects (ITEs) are identifiable. Feng, Vuong and Xu (2019) show that a kernel density estimator that uses nonparametrically estimated ITEs as observations is uniformly consistent for the density of the ITE. In this paper, we establish the asymptotic normality of the density estimator of Feng, Vuong and Xu (2019) and show that despite their faster rate of convergence, ITEs estimation errors have a non-negligible effect on the asymptotic distribution of the density estimator. We propose asymptotically valid standard errors for the density of the ITE that account for estimated ITEs as well as bias correction. Furthermore, we develop uniform confidence bands for the density of the ITE using nonparametric or jackknife multiplier bootstrap critical values. Our uniform confidence bands have correct coverage probabilities asymptotically with polynomial error rates and can be used for inference on the shape of the ITEs distribution.
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