Control Variables, Discrete Instruments, and Identification of Structural Functions

TL;DR

This paper develops identification results for structural functions in econometrics using control variables and discrete instruments, applicable to various treatment effects, with an empirical Engel curve application.

Contribution

It introduces new identification methods accommodating discrete instruments and multiple structural objects in models with control variables.

Findings

Identification of average and quantile treatment effects.

Applicable to models with nonseparable and multidimensional heterogeneity.

Empirical illustration with Engel curve estimation.

Abstract

Control variables provide an important means of controlling for endogeneity in econometric models with nonseparable and/or multidimensional heterogeneity. We allow for discrete instruments, giving identification results under a variety of restrictions on the way the endogenous variable and the control variables affect the outcome. We consider many structural objects of interest, such as average or quantile treatment effects. We illustrate our results with an empirical application to Engel curve estimation.