Bayesian Estimation of Fixed Effects Models with Large Datasets*

In hierarchical prior longitudinal models, random effects are estimated by the Gibbs sampler. We show that fixed effects can be handled by a similar Gibbs sampler under a diffuse prior on the unobserved heterogeneity. The dummy variable approach for fixed effects is computationally intensive and has the out‐of‐memory risk, while the Gibbs sampler can reproduce the dummy variable estimator without creating dummy variables, and therefore avoids the memory burden. Compared to alternating projections and other classical approaches, our method simplifies both inference and estimation of the limited dependent variable models with fixed effects. The proposed method is applied to a real‐world mortgage dataset for classification with three‐way fixed effects on banks, regions, and loan purposes.