Semiparametric Estimation of Correlated Random Coefficient Models without Instrumental Variables

TL;DR

This paper introduces a semiparametric method for estimating effects in correlated random coefficient models without using instrumental variables, applicable to continuous treatments observed over time.

Contribution

It develops a novel estimator for average effects in correlated random coefficient models that does not require instrumental variables, expanding the toolkit for empirical researchers.

Findings

Estimator performs well in small samples

Compared favorably with control function methods

Applied successfully to malaria and economic development data

Abstract

We study a linear random coefficient model where slope parameters may be correlated with some continuous covariates. Such a model specification may occur in empirical research, for instance, when quantifying the effect of a continuous treatment observed at two time periods. We show one can carry identification and estimation without instruments. We propose a semiparametric estimator of average partial effects and of average treatment effects on the treated. We showcase the small sample properties of our estimator in an extensive simulation study. Among other things, we reveal that it compares favorably with a control function estimator. We conclude with an application to the effect of malaria eradication on economic development in Colombia.