A note on difference-in-difference estimation by Fixed Effects and OLS when there is panel non-response

In this note, we show that the OLS and fixed-effects (FE) estimators of the popular differ-ence-in-differences model may deviate when there is time varying panel non-response. If such non-response does not affect the common-trend assumption, then OLS and FE are consistent, but OLS is more precise. However, if non-response is affecting the common-trend assumption, then FE estimation may still be consistent, while OLS will be inconsistent. We provide simulation as well as empirical evidence for this phenomenon to occur. We conclude that in case of unbalanced panels, any evidence of deviating OLS and FE estimates should be considered as evidence that non-response is not ignorable for the differences-in-differences estimation.