Smoothed estimators for Markov Chains with sparse spatial observations

Authors: Wei Kang*, Arizona State University, Sergio Rey, University of California, Riverside
Topics: Spatial Analysis & Modeling, Economic Geography
Keywords: Economic growth, Spatial econometrics, Monte Carlo simulation
Session Type: Paper
Day: 4/12/2018
Start / End Time: 5:20 PM / 7:00 PM
Room: Astor Ballroom II, Astor, 2nd Floor
Presentation File: No File Uploaded

Empirical applications of the Markov chain model and spatial Markov chain model can suffer from issues induced by the sparse transition probability matrix which is usually estimated by adopting maximum likelihood estimation techniques. The sparsity arises from the generally short length of time series employed in empirical work using spatial data. We propose two discrete kernel estimators with cross validation-based smoothing parameters selection, which are a modification of the smoothing techniques for high-order contingency tables, to address the sparsity issue.

Based on the Monte Carlo experiments, we find the performance of discrete kernel estimators offers an improvement over traditional approaches when the sample size is small compared to the number of categories in the classic and spatial Markov chain models. Although the performance of the kernel estimators is not superior to MLEs in every aspect, they do produce estimates which give rise to a better recovery of the true underlying dynamics.

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