Bounding a Linear Causal Effect Using Relative Correlation Restrictions

Abstract This paper describes and implements a simple partial solution to the most common problem in applied microeconometrics: estimating a linear causal effect with a potentially endogenous explanatory variable and no suitable instrumental variables. Empirical researchers faced with this situation can either assume away the endogeneity or accept that the effect of interest is not identified. This paper describes a middle ground in which the researcher assumes plausible but nontrivial restrictions on the correlation between the variable of interest and relevant unobserved variables relative to the correlation between the variable of interest and observed control variables. Given such relative correlation restrictions, the researcher can then estimate informative bounds on the effect and assess the sensitivity of conventional estimates to plausible deviations from exogeneity. Two empirical applications demonstrate the potential usefulness of this method for both experimental and observational data.