Are Instrumental Variables Really That Instrumental? Endogeneity Resolution in Regression Models for Comparative Studies

TL;DR

This paper presents a new approach to address endogeneity in regression models for comparative studies, offering conditions under which bias can be avoided without solely relying on instrumental variables.

Contribution

It introduces a technique that can replace or complement instrumental variables by ensuring unbiased coefficient interpretation under specific covariance conditions.

Findings

Endogeneity may not bias coefficients if covariance conditions are met.

The method applies across different systems and time periods.

It provides an alternative to traditional instrumental variable approaches.

Abstract

We provide a justification for why, and when, endogeneity will not cause bias in the interpretation of the coefficients in a regression model. This technique can be a viable alternative to, or even used alongside, the instrumental variable method. We show that when performing any comparative study, it is possible to measure the true change in the coefficients under a broad set of conditions. Our results hold, as long as the product of the covariance structure between the explanatory variables and the covariance between the error term and the explanatory variables are equal, within the same system at different time periods or across multiple systems at the same point in time.