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Unformatted text preview: Spatial Heteroskedasticity and Autocorrelation Consistent Estimation of Covariance Matrix Min Seong Kim and Yixiao Sun & Department of Economics, UC San Diego Abstract This paper considers spatial heteroskedasticity and autocorrelation consistent (spa- tial HAC) estimation of covariance matrices of parameter estimators. We generalize the spatial HAC estimators introduced by Kelejian and Prucha (2007) to apply to lin- ear and nonlinear spatial models with moment conditions. We establish its consistency, rate of convergence and asymptotic truncated mean squared error (MSE). Based on the asymptotic truncated MSE criterion, we derive the optimal bandwidth parameter and suggest its data dependent estimation procedure using a parametric plug-in method. The &nite sample performances of the spatial HAC estimator are evaluated via Monte Carlo simulation. Keywords : Asymptotic mean squared error, Heteroskedasticity and autocorrela- tion, Covariance matrix estimator, Optimal bandwidth choice, Robust standard error, Spatial dependence. JEL Classi&cation Number : C13, C14, C21 & Email: email@example.com and firstname.lastname@example.org. Correspondence to: Department of Economics, Univer- sity of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0508. We thank Tim Conley, Graham Elliott, Xun Lu, Dimitris Politis and Hal White for helpful comments. We appreciate the comments of Cheng Hsiao, the coeditor, an associate editor and two referees, which led to considerable improvements of the paper. Sun gratefully acknowledges partial research support from NSF under Grant No. SES-0752443. 1 Introduction This paper studies spatial heteroskedasticity and autocorrelation consistent (HAC) estima- tion of covariance matrices of parameter estimators. As heteroskedasticity is a well known feature of cross sectional data (e.g. White (1980)), spatial dependence is also a common property due to interactions among economic agents. Therefore, robust inference in the presence of heteroskedasticity and spatial dependence is an important problem in spatial data analysis. The &rst discussion of spatial HAC estimation is Conley (1996, 1999). He proposes a spatial HAC estimator based on the assumption that each observation is a realization of a random process, which is stationary and mixing, at a point in a two-dimensional Euclidean space. Conley and Molinari (2007) examine the performance of this estimator using Monte Carlo simulation. Their results show that inference is robust to the measurement error in locations. Robinson (2005) considers nonparametric kernel spectral density estimation for weakly stationary processes on a d-dimensional lattice. Kelejian and Prucha (2007, hereafter KP) also develop a spatial HAC estimator. As in many empirical studies, they model spatial dependence in terms of a spatial weighting matrix. The di/erence is that the weighting matrix is not assumed to be known and is not parametrized. Typical examples of this type of processes include the spatial autoregressiveparametrized....
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