On the Nuisance of Control Variables in Regression Analysis

TL;DR

This paper argues that control variables in regression analyses often lack causal interpretability due to endogeneity and complex causal mechanisms, recommending focus on main variables and clear reporting practices.

Contribution

It highlights the limitations of interpreting control variable effects causally and provides guidelines for better reporting and interpretation in regression studies.

Findings

Control variable effects are unlikely to have causal interpretation.

Researchers should focus on main variables with clear identification.

Coefficients of controls should be marked as non-causal or omitted.

Abstract

Control variables are included in regression analyses to estimate the causal effect of a treatment on an outcome. In this paper, we argue that the estimated effect sizes of controls are unlikely to have a causal interpretation themselves, though. This is because even valid controls are possibly endogenous and represent a combination of several different causal mechanisms operating jointly on the outcome, which is hard to interpret theoretically. Therefore, we recommend refraining from interpreting marginal effects of controls and focusing on the main variables of interest, for which a plausible identification argument can be established. To prevent erroneous managerial or policy implications, coefficients of control variables should be clearly marked as not having a causal interpretation or omitted from regression tables altogether. Moreover, we advise against using control variable estimates for subsequent theory building and meta-analyses.