Causal inference with endogenous price response

We study the estimation of causal treatment effects on demand when treatment is randomly assigned but prices adjust in response to treatment. We show that regressions of demand on treatment or on treatment and price lead to biased estimates of the direct treatment effect. The bias in both cases depends on the correlation of price with treatment and points in the same direction. In most cases including an endogenous price control reduces bias but does not remove it. We show how to test whether bias from an endogenous price response arises and how to recover an unbiased treatment effect (holding price constant) using a price instrument. We apply our approach to the estimation of the impact of feature advertising across several product categories using supermarket scanner data and show that the bias when not instrumenting for price can be substantial.