Estimating Fixed Effects Logit Models with Large Panel Data

For the parametric estimation of logit models with individual time-invariant effects the conditional and unconditional fixed effects maximum likelihood estimators exist. The conditional fixed effects logit (CL) estimator is consistent but it has the drawback that it does not deliver estimates of the fixed effects or marginal effects. It is also computationally costly if the number of observations per individual T is large. The unconditional fixed effects logit estimator (UCL) can be estimated by including a dummy variable for each individual (DVL). It suffers from the incidental parameters problem which causes severe biases for small T. Another problem is that with a large number of individuals N, the computational costs of the DVL estimator can be prohibitive. We suggest a pseudo-demeaning algorithm in spirit of Greene (2004) and Chamberlain (1980) that delivers the identical results as the DVL estimator without its computational burden for large N. We also discuss how to correct for the incidental parameters bias of parameters and marginal effects. Monte-Carlo evidence suggests that the bias-corrected estimator has similar properties as the CL estimator in terms of parameter estimation. Its computational burden is much lower than the CL or the DVL estimators, especially with large N and/or T.