Essays on estimating distributional continuous treatment effects.

摘要

The unconditional distribution of potential outcomes with continuous treatments and the quantile structural function in a nonseparable triangular model can both be expressed as a partial mean process with generated regressors. In Chapter 1, I propose a multi-step nonparametric kernel-based estimator for this partial mean process. A uniform expansion reveals the influence of estimating the generated regressors on the final estimator. I focus on two examples of generated regressors (i) the generalized propensity score for a continuous treatment and (ii) the control variable in the nonseparable triangular models. By extending my results to Hadamard-differentiable functionals of the partial mean process, I am able to provide the limit distribution for estimating common inequality measures and various distributional features of the outcome variable.;In the second chapter, I estimate the density-weighted Average Quantile Derivative (AQD), defined as the expectation of the partial derivative of the conditional quantile function (CQF) weighted by the density function of the covariates. The proposed estimator achieves root-n-consistency and asymptotic normality by a first-step nonparametric kernel estimation for the unknown functions and a second-step sample analogue of a full- mean. Therefore, the AQD summarizes the average marginal response of the covariates on the CQF and can be viewed as a nonparametric quantile regression coefficient. Similar to the widely studied average derivative in mean regression, the AQD identifies the coefficients up to scale in semiparametric single-index and partial linear models.;In the third chapter, I allow for misspecification in the linear conditional quantile function (CQF) and calculate the semiparametric efficiency bound for the quantile regression (QR) parameter, the best linear predictor for a response variable under the asymmetric check loss function. As a result, the QR estimator developed by Koenker and Bassett (1978) semiparametrically efficiently estimates a pseudo-true parameter. The linear quantile projection model can be understood by the orthogonality condition of the covariates and the distribution error (i.e., the deviation of the true conditional distribution function, evaluated at the linearly approximated quantile, from the true probability).