Abstract
Spatial units typically vary over many of their characteristics, introducing potential unobserved heterogeneity which invalidates commonly used homoskedasticity conditions. In the presence of unobserved heteroskedasticity, methods based on the quasi-likelihood function generally produce inconsistent estimates of both the spatial parameter and the coefficients of the exogenous regressors. A robust generalized method of moments estimator as well as a modified likelihood method have been proposed in the literature to address this issue. The present paper constructs an alternative indirect inference (II) approach which relies on a simple ordinary least squares procedure as its starting point. Heteroskedasticity is accommodated by utilizing a new version of continuous updating that is applied within the II procedure to take account of the parameterization of the variance–covariance matrix of the disturbances. Finite-sample performance of the new estimator is assessed in a Monte Carlo study. The approach is implemented in an empirical application to house price data in the Boston area, where it is found that spatial effects in house price determination are much more significant under robustification to heterogeneity in the equation errors.
Highlights
In recent years, spatial models have stimulated growing interest and application in various areas in economics
We report the results of a set of Monte Carlo experiments to compare the finitesample performance of the continuously updated indirect inference (CUII) estimators with the standard QML (Lee, 2004) and 2SLS estimators (Kelejian and Prucha, 1998), as well as the Robust Generalized Method of Moments (RGMM) procedure of Lin and Lee (2010) and the modified QML (MQML) estimator of Liu and Yang (2015)
The new estimation method introduced in this paper directly addresses such heterogeneity, relying on an indirect inference (II) transformation of standard ordinary least squares (OLS) estimation that parameterizes the error covariance matrix in terms of the unknown spatial parameter
Summary
Spatial models have stimulated growing interest and application in various areas in economics. Common examples include real estate pricing data, R&D spillover effects, crime rates, unemployment rates, regional economic growth patterns, and environmental characteristics in urban, suburban, and rural areas Econometric modeling of such phenomena makes extensive use of formulations that accommodate spatial dependence through autoregressive specifications known as spatial autoregressions (SARs). ML/QML methods provide an obvious general approach to parameter estimation (Lee, 2004), in the presence of unobserved heterogeneity, they produce inconsistent estimates (e.g., Lin and Lee, 2010) This lack of robustness to heteroskedasticity is possibly the main shortcoming of ML/QML methods for spatial data. We show that our new CUII estimator is consistent and asymptotically normal, while simulation and empirical results confirm its satisfactory finite-sample properties under general spatial designs and heteroskedasticity structures.
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