MCMC conditional maximum likelihood for the two-way fixed-effects logit

We propose a Markov Chain Monte Carlo Conditional Maximum Likelihood (MCMC-CML) estimator for the two-way fixed-effects logit model for dyadic data, typically used in network analyses. The proposed MCMC approach, based on a Metropolis algorithm, allows us to overcome the computational issues of evaluating the probability of the outcome conditional on nodes in- and out-degrees, which are sufficient statistics for the incidental parameters. Under mild regularity conditions, the MCMC-CML estimator converges to the exact CML one and is asymptotically normal. Moreover, it is more efficient than the existing pairwise CML estimator. We study the finite sample properties of the proposed approach by means of an extensive simulation study and three empirical applications, where we also show that the MCMC-CML estimator can be applied to logit models for binary panel data with both subject and time-fixed effects. Results confirm the expected theoretical advantage of the proposed approach, especially with small, concentrated, and sparse networks or with rare events in panel data.