This paper examines regression-adjusted estimation and inference of unconditional quantile treatment eﬀects (QTEs) under covariate-adaptive randomizations (CARs). Datasets from ﬁeld experiments 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. We establish the consistency, limit distribution, and validity of the multiplier bootstrap of the QTE estimator under CARs. 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. Our estimation and inferential methods can be implemented without tuning parameters and they allow for common choices of auxiliary regressions such as linear, probit and logit regressions despite the fact that these regressions may be misspeciﬁed. Finite-sample performance of the new estimation and inferential methods is assessed in simulations and an empirical application studying the impact of child health and nutrition on educational outcomes is included.
This paper examines methods of inference concerning quantile treatment eﬀects (QTEs) in randomized experiments with matched-pairs designs (MPDs). We derive the limit distribution of the QTE estimator under MPDs, highlighting the diﬀiculties that arise in analytical inference due to parameter tuning. We show that the naïve weighted bootstrap fails to approximate the limit distribution of the QTE estimator under MPDs because it ignores the dependence structure within the matched pairs.To address this diﬀiculty we propose two bootstrap methods that can consistently approximate the limit distribution: the gradient bootstrap and the weighted bootstrap of the inverse propensity score weighted (IPW) estimator. The gradient bootstrap is free of tuning parameters but requires knowledge of the pair identities. The weighted bootstrap of the IPW estimator does not require such knowledge but involves one tuning parameter. Both methods are straightforward to implement and able to provide pointwise conﬁdence intervals and uniform conﬁdence bands that achieve exact limiting coverage rates. We demonstrate their ﬁnite sample performance using simulations and provide an empirical application to a well-known dataset in microﬁnance.
This paper develops a new hedonic method for constructing a real estate price index that utilizes all transaction price information that encompasses both single-sale and repeat-sale properties. The new method is less prone to speciﬁcation errors than standard hedonic methods and uses all available data. Like the Case-Shiller repeat-sales method, the new method has the advantage of being computationally eﬀicient. In an empirical analysis of the methodology, we ﬁt the model to all transaction prices for private residential property holdings in Singapore between Q1 1995 and Q2 2014, covering several periods of major price fluctuation and changes in government macroprudential policy. Two new indices are created, one from all transaction prices and one from single-sales prices. The indices are compared with the S&P/Case-Shiller index. The result shows that the new indices slightly outperform the S&P/Case-Shiller index in predicting the price of single-sales homes out-of-sample. However, they underperform the S&P/Case-Shiller index in predicting the price of repeat-sales homes out-of-sample. The empirical ﬁndings indicate that speciﬁcation bias can be more substantial than the sample selection bias when constructing a real estate price index. In a further empirical application, the recursive method of Phillips, Shi and Yu (2014) is used to detect explosive periods in real estate prices of Singapore. The results conﬁrm the existence of an explosive period from Q4 2006 to Q1 2008. No explosive period is found after 2009, suggesting that the ten successive rounds of cooling measures implemented by the Singapore government have been eﬀective in changing price dynamics and preventing a subsequent outbreak of explosive behavior in the Singapore real estate market.