Spatial and Non-Spatial Panel Data Estimators: Simulation Study and Application to Personal Income in U.S. States

Abstract

The spatial analysis aims to understand and explore the nature of entanglements and interactions between spatial units’ locations. The analysis of models involving spatial dependence has received great attention in recent decades. Because ignoring the presence of spatial dependence in the data is very likely to lead to biased or inefficient estimates if we use traditional estimation methods. Therefore, this paper is an attempt to assess the risks involved in ignoring the spatial dependence that characterizes the panel data by using a Monte Carlo simulation (MCS) study for two of the most common spatial panel data (SPD) models; Spatial lag model (SLM) and spatial error model (SEM), by comparing the performance of two estimators; i.e., spatial maximum likelihood estimator (MLE) and non-spatial ordinary least squares (OLS) within-group estimator, across two levels of analysis; Parameter-level in terms of bias and root mean square error (RMSE), and model-level in terms of goodness of fit criteria under different scenarios of spatial units N, time-periods T, and spatial dependence parameters, by using two different structures of spatial weights matrix; inverse distance, and inverse exponential distance. The results show that the non-spatial bias and RMSE of β ̂ are functions of the degree of spatial dependence in the data for both models, i.e., SLM and SEM. If the spatial dependence is small, then the choice of the non-spatial estimator may not lead to serious consequences in terms of bias and RMSE of β ̂. On the contrary, the choice of the non-spatial estimator always leads to has disastrous consequences if the spatial dependence is large. On the other hand, we provide a general framework that shows how to define the appropriate model from among several candidate models through application to a dataset of per capita personal income (PCPI) in U.S. states during the period from 2009 to 2019, concerning three main aspects: educational attainment, economy size, and labour force type. The results confirm that PCPI is spatially dependent lagged correlated.