Ruhr Economic Papers

Ruhr Economic Papers #769

Markov Chain Monte Carlo Estimation of Spatial Dynamic Panel Models for Large Samples

by James P. LeSage, Chih Yao-Yu and Colin Vance

RWI, 09/2018, 56 S./p., 8 Euro, ISBN 978-3-86788-897-4 DOI: 10.4419/86788897

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Abstract

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 in large N and T situations, where N is the number
of spatial units and T the number of time periods. Quasi-maximum likelihood (QML)
estimation in cases involving large N and T poses computational challenges because
optimizing the (log) likelihood requires: 1) evaluating the log-determinant of an NT x NT
matrix that appears in the likelihood, 2) imposing stability restrictions on parameters
reflecting space-time dynamics, as well as 3) simulations to produce an empirical
distribution of the partial derivatives used to interpret model estimates that require
numerous inversions of large matrices. We set forth a Markov Chain Monte Carlo
(MCMC) estimation procedure capable of handling large problems, which we illustrate
using a sample of T = 487 daily fuel prices for N = 12, 435 German gas stations, resulting
in N x T over 6 million. The procedure produces estimates equivalent to those from
QML and has the additional advantage of producing a Monte Carlo integrated estimate
of the log-marginal likelihood, useful for purposes of model comparison. Our MCMC
estimation procedure uses: 1) a Taylor series approximation to the logdeterminant
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 logmarginal
likelihood. We also provide an efficient approach to simulations needed to
produce the empirical distribution of the partial derivatives for model interpretation.

JEL-Classification: C23, D40

Keywords: Dynamic panel models; spatial dependence; Markov Chain Monte Carlo estimation

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