Essays on causal mediation analysis

This dissertation consists of three chapters on causal mediation analysis. The first two chapters propose new estimation approaches for direct and indirect effects in a semiparametric model, and the third chapter studies regression discontinuity design that incorporates indirect effects. In the first chapter, we consider a unifying framework to test for direct and indirect treatment effects in nonlinear models. Specifically, we extend a generalized linear-index model to incorporate endogenous treatments and endogenous mediators. We propose a kernel-weighted Kendall's tau statistics, which is a nonparametric rank correlation estimator, to test the significance of the direct and indirect effects of endogenous treatments on the outcome variable mediated by endogenous mediators. The proposed semiparametric model allows for treatments and mediators to be discrete, continuous, or neither of these two (e.g., censored or truncated). For the indirect effect, we construct two distinct kernel-weighted Kendall's tau statistics that capture the effect of (i) the treatment on the mediator, and (ii) the mediator on the outcome. In the second chapter, we address the issue of testing indirect effects in the generalized regression model. Also, we suggest Monte Carlo simulation results and empirical results using the new method. Unfortunately, standard joint hypothesis tests using these statistics are severely under-sized, a problem that has been noted for linear causal mediation models. To address the problem, we apply a new testing method (van Garderen and van Giersbergen (2020)) that has correct size. As an empirical illustration, we assess the effect of education level on social functioning mediated by individual income, using the British Household Panel Survey data. In the third chapter, we suggest a sharp regression discontinuity model that allows an indirect effect from the intermediate characteristics. These characteristics are determined by the treatment status and random type of each individual. We analyze RD treatment effect represented as a weighted average form and the mean expected outcome at the cutoff in the presence of intermediate characteristics. Especially, we derive bounds on the treatment effect under inequality restrictions on expected outcomes conditioned on the intermediate characteristics. Finally, we suggest a simple extension of the estimation method that incorporates the indirect effect based on local linear regression. Monte Carlo experiments validate the finite sample performance of the suggested estimation method.