Transformations and moment conditions for dynamic fixed effects logit models

This study proposes transformations for dynamic fixed effects logit models. First, these transformations construct valid moment conditions for the case with neither explanatory variables nor time dummies. Using valid moment conditions, we can obtain the first-order condition of the conditional maximum likelihood estimator proposed by Chamberlain (1985). Next, we derive valid moment conditions based on the transformations for the cases with strictly exogenous continuous explanatory variables and/or time dummies when the number of time periods is four or more. Transformations of these moment conditions exactly coincide with a subset of those obtained by Honore and Weidner (2020) using the functional differencing approach proposed by Bonhomme (2012). (C) 2021 The Author(s). Published by Elsevier B.V.

Automated summary

This study proposes transformations for dynamic fixed effects logit models. Valid moment conditions are constructed for cases without explanatory variables or time dummies, and the first-order conditions of the conditional maximum likelihood estimator are obtained. Valid moment conditions are also derived for cases with strictly exogenous continuous explanatory variables and/or time dummies when the number of time periods is four or more. These moment conditions coincide with a subset of those obtained using the functional differencing approach proposed by Bonhomme (2012) and Honore and Weidner (2020).