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Markov Chain Monte Carlo estimation of spatial dynamic panel models for large samples

LeSage, James P., Chih, Yao-Yu, Vance, Colin
Computational statistics & data analysis 2019 v.138 pp. 107-125
Markov chain, covariance, models, space and time
Focus is on efficient estimation of a dynamic space–time panel data model that incorporates spatial dependence, temporal dependence, as well as space–time covariance and can be implemented where there are a large number of spatial units and time periods. Quasi-maximum likelihood (QML) estimation in cases involving large samples poses computational challenges because optimizing the (log) likelihood requires: (1) evaluating the log-determinant of a large matrix that appears in the likelihood, (2) imposing stability restrictions on parameters reflecting space–time dynamics, and (3) simulations to produce an empirical distribution of the partial derivatives used to interpret model estimates that require numerous inversions of large matrices.A Markov Chain Monte Carlo (MCMC) estimation procedure is set forth that produces estimates equivalent to those from QML along with a Monte Carlo integrated estimate of the log-marginal likelihood, useful for model comparison. An applied illustration is based on over six million observations. The MCMC estimation procedure uses: (1) a Taylor series approximation to the log-determinant based on traces of matrix products calculated prior to MCMC sampling, (2) block sampling of the spatiotemporal parameters, which allows imposition of the stability restrictions, and (3) a Metropolis–Hastings guided Monte Carlo integration of the log-marginal likelihood. In addition, an efficient approach to simulations needed to produce the empirical distribution of the partial derivatives for model interpretation is set forth.