Endogeneity bias in the absence of unobserved heterogeneity

Purpose To demonstrate that endogeneity bias can still arise even when no unobserved heterogeneity exists. Methods A formal mathematical proof and a Monte Carlo simulation are used to demonstrate that ordinary estimation techniques will generate biased parameter estimates. Results The Monte Carlo results support the formal proof. Even in the absence of unobserved heterogeneity, ordinary least squares estimation that does not account for the endogenous nature of an explanatory variable resulted in a parameter estimate for the endogenous variable that was significantly biased (by a factor of 1.42 for the simple model and 1.98 for the saturated model). Alternatively, controlling for endogeneity using the instrumental variables approach led to an unbiased parameter estimate. Conclusions Endogeneity bias can still occur even when unobserved heterogeneity is not present.