Modeling Intertemporal and Contemporal Dependence in Binary TSCS Data: A Bayesian Model with Ar(P) Errors and Non-Nested Clustering

Abstract

I propose a Bayesian generalized linear multilevel model with pth-order autoregressive errors for modeling unbalanced binary time-series cross-sectional (TSCS) data by considering correlation in both the time and spatial dimensions. By controlling for heterogeneities in the two dimensions and modeling the dynamic error process, the proposed model handles the inefficiency and endogeneity problems resulting from the generic TSCS data structure. With the stationarity restriction on the error process, the model can also be used as a unit root and cointegration test on discrete TSCS data following the line of residual-based approaches. This is especially valuable since cointegration tests on discrete panel data are challenging and rarely conducted in practice. Methodologically, to handle the model estimation difficulties, I develop an efficient Markov Chain Monte Carlo algorithm by orthogonalizing the errors with the Cholesky decomposition and adding an auxiliary variable. I also apply the parameter expansion method, i.e., partial group move multigrid Monte Carlo updating, to further improve mixing and speed up convergence of the Markov chain. The paper also provides a computational scheme to approximate the Bayes Factor for the purpose of serial correlation diagnostics, lag order determination, and variable selection. Simulated and empirical examples are used to assess the performance of the model and techniques.

Keywords: Time-Series Cross-Sectional Data, Autoregressive Errors, Cholesky Decomposition, Multigrid Monte Carlo, Parameter Expansion, Cointegration

JEL Classification: C11