Direct and Indirect Effects under Sample Selection and Outcome Attrition

Martin Huber,Anna Solovyeva

doi:10.3390/econometrics8040044

Abstract

This paper extends the evaluation of direct and indirect treatment effects, i.e., mediation analysis, to the case that outcomes are only partially observed due to sample selection or outcome attrition. We assume sequential conditional independence of the treatment and the mediator, i.e., the variable through which the indirect effect operates. We also impose missing at random or instrumental variable assumptions on the outcome attrition process. Under these conditions, we derive identification results for the effects of interest that are based on inverse probability weighting by specific treatment, mediator, and/or selection propensity scores. We also provide a simulation study and an empirical application to the U.S. Project STAR data in which we assess the direct impact and indirect effect (via absenteeism) of smaller kindergarten classes on math test scores. The estimators considered are available in the ‘causalweight’ package for the statistical software ‘R’.

Highlights

Mediation analysis, i.e., the evaluation of direct and indirect causal effects, is widespread in social sciences, following the seminal papers (Baron and Kenny 1986; Judd and Kenny 1981; Robins and Greenland 1992)
The estimators considered in the simulation study and the empirical application are available in the ‘causalweight’ package by (Bodory and Huber 2018) for the statistical software ‘R’
We proposed an approach for disentangling a total causal effect into a direct component and a indirect effect operating through a mediator in the presence of outcome attrition or sample selection

Summary

Introduction

I.e., the evaluation of direct and indirect causal effects, is widespread in social sciences, following the seminal papers (Baron and Kenny 1986; Judd and Kenny 1981; Robins and Greenland 1992). We extend mediation analysis to account for the complication of outcome nonresponse and sample selection, implying that outcomes are only observed for a subset of the initial population of interest. Such problems frequently occur in empirical applications like wage gap decompositions, where wages are only observed for those who work. We combine the evaluation of average natural direct and indirect effects based on sequential conditional independence with specific MAR or IV assumptions about sample selection. We identify the parameters of interest in the total as well as the selected population (whose outcomes are observed) by inverse probability weighting (IPW) based on propensity scores for treatment and selection.

Parameters of Interest

Assumptions and Identification Results under MAR

Estimation

Simulation Study

Empirical Application

Conclusions