MCMC Conditional Maximum Likelihood for the two-way fixed-effects logit
2021
We propose a Markov chain Monte Carlo Conditional Maximum Likelihood
(MCMC-CML) estimator for two-way fixed-effects logit models for dyadic data. 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 a simulation study and three empirical applications,
where we also show that the MCMC-CML estimator can be applied to binary logit
models for panel data with both subject and time fixed effects. Results confirm the
expected theoretical advantage of the proposed approach, especially with small and
sparse networks or with rare events in panel data.
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