Bias in instrumental-variable estimators of fixed-effect models for count data

This note looks at the properties of instrumental-variable estimators of models for non-negative outcomes in the presence of individual effects. We show that fixed-effect versions of the estimators of Mullahy (1997) and Windmeijer and Santos Silva (1997) are inconsistent under conventional asymptotics, in general, and that inference based on them in long panels requires bias correction. Such corrections are derived and their effectiveness is investigated in numerical experiments. Consistent estimation in short panels is nonetheless possible in the setting underlying Mullahy’s (1997) approach using a differencing strategy along the lines of Wooldridge (1997) and Windmeijer (2000). •Instrumental-variable estimators of fixed-effect models for non-negative outcomes are asymptotically-biased under rectangular-array asymptotics.•Bias corrections are proposed.•For multiplicative-error specifications an alternative estimator is suggested.•Simulations illustrate the relevance of these procedures.