Large Sample Properties of Bayesian Estimation of Spatial Econometric Models

Abstract

This paper studies asymptotic properties of a posterior probability density and Bayesian estimators of spatial econometric models in the classical statistical framework. We focus on the high-order spatial autoregressive model with spatial autoregressive disturbance terms, due to a computational advantage of Bayesian estimation. We also study the asymptotic properties of Bayesian estimation of the spatial autoregressive Tobit model, as an example of nonlinear spatial models. Simulation studies show that even when the sample size is small or moderate, the posterior distribution of parameters is well approximated by a normal distribution, and Bayesian estimators have satisfactory performance, as classical large sample theory predicts.

Economic Growth Modelling in West Nusa Tenggara Using Bayesian Spatial Model Approach

“…The data that becomes the object of research are data on the value of GRDP, labor, and the electrification ratio. Several stages of research can be described through the following steps : (1) Determine the response variable and predictor variable from the data that has been obtained, (2) Describe each variable in the study as an illustration of the economy in West Nusa Tenggara and the factors that are thought to influence it, (3) Identifying the relationship pattern between response variables and predictor variables through the Scatter Plot, (4) Assign a spatial weighting matrix for each area using the Queen Contiquity weight, (5) Testing the spatial aspects (spatial dependency and spatial heterogeneity) (Liu & Zhu, 2017), (6) Test the appropriate spatial model using the Lagrange Multiplier (Chica-Olmo et al, 2020), (7) Determine the likelihood function, (8) Set prior, (9) Get a joint distribution function (Joint Distribution) (Han et al, 2020), ( 10) Form a full conditional posterior distribution, (11) Carry out the Markov Chain Monte Carlo (MCMC) process (Seya et al, 2012), ( 12) Evaluating the model that has been formed , and ( 13) Interpret the model that has been obtained .…”

Efficient closed-form estimation of large spatial autoregressions

“…Modern network data sets are amenable to modelling via SAR techniques and can feature, or accommodate, large parameter spaces but computation remains a serious challenge. Han et al (2020) provide a discussion of the problems and propose a Bayesian solution.…”

Consistent Specification Testing Under Spatial Dependence

“…As noted above, these links may form for a variety of reasons, so the "spatial" terminology represents a very general notion of space, such as social or economic space. Key papers on the estimation of SAR models and their variants include Kelejian and Prucha (1998) and Lee (2004), but research on various aspects of these is active and ongoing (see, e.g., Robinson and Rossi, 2015;Martellosio, 2018a, 2018b;Hahn, Kuersteiner, and Mazzocco, 2020;Kuersteiner and Prucha, 2020;Han, Lee, and Xu, 2021).…”