Instrumental Variable Quantile Estimation of Spatial Autoregressive Models

We propose an instrumental variable quantile regression (IVQR) estimator for spatial autoregressive (SAR) models. Like the GMM estimators of Lin and Lee (2006) and Kelejian and Prucha (2006), the IVQR estimator is robust against heteroscedasticity. Unlike the GMM estimators, the IVQR estimator is also robust against outliers and requires weaker moment conditions. More importantly, it allows us to characterize the heterogeneous impact of variables on different points (quantiles) of a response distribution. We derive the limiting distribution of the new estimator. Simulation results show that the new estimator performs well in finite samples at various quantile points. In the special case of median restriction, it outperforms the conventional QML estimator without taking into account of heteroscedasticity in the errors; it also outperforms the GMM estimators with or without considering the heteroscedasticity.

[1]  fei Lee.  GMM and 2 SLS Estimation of Mixed Regressive , Spatial Autoregressive Models by Lung - , 2022 .

[2]  Lung-fei Lee,et al.  Best Spatial Two‐Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances , 2003 .

[3]  S. Lee.  Endogeneity in Quantile Regression Models: A Control Function Approach , 2004 .

[4]  D. Rubinfeld,et al.  Hedonic housing prices and the demand for clean air , 1978 .

[5]  R. Koenker,et al.  Robust Tests for Heteroscedasticity Based on Regression Quantiles , 1982 .

[6]  Tae-Hwan Kim,et al.  Two-Stage Quantile Regression When the First Stage is Based on Quantile Regression , 2003 .

[7]  Bo E. Honoré,et al.  On the Performance of Some Robust Instrumental Variables Estimators , 2004 .

[8]  D. Griffith.  Spatial Autocorrelation , 2020, Spatial Analysis Methods and Practice.

[9]  R. Koenker,et al.  Regression Quantiles , 2007 .

[10]  Takeshi Amemiya,et al.  Two Stage Least Absolute Deviations Estimators , 1982 .

[11]  Harvey S. Rosen,et al.  Budget spillovers and fiscal policy interdependence: Evidence from the states , 1993 .

[12]  V. Chernozhukov,et al.  Finite Sample Inference for Quantile Regression Models , 2006 .

[13]  M. Slade,et al.  A central limit theorem for endogenous locations and complex spatial interactions , 2007 .

[14]  L. Anselin,et al.  Fast maximum likelihood estimation of very large spatial autoregression models: a characteristic polynomial approach , 2001 .

[15]  D. Ruppert,et al.  Trimmed Least Squares Estimation in the Linear Model , 1980 .

[16]  L. Anselin.  Spatial Econometrics: Methods and Models , 1988 .

[17]  Christian Hansen,et al.  Inference approaches for instrumental variable quantile regression , 2007 .

[18]  Phillip Kostov,et al.  A Spatial Quantile Regression Hedonic Model of Agricultural Land Prices , 2009 .

[19]  Alberto Abadie.  Changes in Spanish Labor Income Structure During the 1980's:a Quantile Regression Approach , 1997 .

[20]  Stephen Portnoy,et al.  Censored Regression Quantiles , 2003 .

[21]  Harry H. Kelejian,et al.  A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model , 1999 .

[22]  D. Pollard,et al.  Simulation and the Asymptotics of Optimization Estimators , 1989 .

[23]  Donald W. K. Andrews,et al.  Empirical Process Methods in Econometrics , 1993 .

[24]  Roger Koenker,et al.  Conditional Quantile Estimation and Inference for Arch Models , 1996, Econometric Theory.

[25]  A. Case.  Spatial Patterns in Household Demand , 1991 .

[26]  Lung-fei Lee,et al.  GMM and 2SLS estimation of mixed regressive, spatial autoregressive models , 2007 .

[27]  Robert V. Hogg,et al.  Introduction to Mathematical Statistics. , 1966 .

[28]  P. Robinson.  Efficient estimation of the semiparametric spatial autoregressive model , 2006 .

[29]  J. Angrist,et al.  Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings , 1999 .

[30]  Joris Pinkse,et al.  Dynamic Spatial Discrete Choice Using One-step GMM: An Application to Mine Operating Decisions , 2006 .

[31]  K. Ord.  Estimation Methods for Models of Spatial Interaction , 1975 .

[32]  Lung-fei Lee,et al.  CONSISTENCY AND EFFICIENCY OF LEAST SQUARES ESTIMATION FOR MIXED REGRESSIVE, SPATIAL AUTOREGRESSIVE MODELS , 2002, Econometric Theory.

[33]  H. Koul.  A weak convergence result useful in robust autoregression , 1991 .

[34]  H. Kelejian,et al.  A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances , 1998 .

[35]  V. Chernozhukov,et al.  Instrumental variable quantile regression: A robust inference approach , 2008 .

[36]  J. Zietz,et al.  Department of Economics and Finance Working Paper Series @bullet Determinants of House Prices: a Quantile Regression Approach † , 2022 .

[37]  Joris Pinkse,et al.  Contracting in space: An application of spatial statistics to discrete-choice models , 1998 .

[38]  Christian Hansen,et al.  Instrumental quantile regression inference for structural and treatment effect models , 2006 .

[39]  R. Koenker.  Confidence Intervals for Regression Quantiles , 1994 .

[40]  A. Case.  Neighborhood influence and technological change , 1992 .

[41]  V. Chernozhukov,et al.  An IV Model of Quantile Treatment Effects , 2002 .

[42]  E. Tamer.  Inference in Censored Models with Endogenous Regressors , 2003 .

[43]  R. Koenker,et al.  Quantile regression methods for recursive structural equation models , 2004 .

[44]  Otis W. Gilley,et al.  On the Harrison and Rubinfeld Data , 1996 .

[45]  S. Sakata.  Instrumental variable estimation based on conditional median restriction , 2007 .

[46]  James L. Powell,et al.  THE ASYMPTOTIC NORMALITY OF TWO-STAGE LEAST ABSOLUTE , 1983 .

[47]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[48]  J. Powell,et al.  ESTIMATION OF MONOTONIC REGRESSION MODELS UNDER QUANTILE RESTRICTIONS , 1988 .

[49]  E. Glaeser,et al.  Crime and Social Interactions , 1995 .

[50]  James P. LeSage,et al.  “Theory and Practice of Spatial Econometrics” , 2015 .

[51]  Lung-fei Lee,et al.  Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models , 2004 .

[52]  J. Powell,et al.  Censored regression quantiles with endogenous regressors , 2007 .

[53]  B. Hansen.  Stochastic Equicontinuity for Unbounded Dependent Heterogeneous Arrays , 1996, Econometric Theory.

[54]  Jushan Bai,et al.  Weak Convergence of the Sequential Empirical Processes of Residuals in ARMA Models , 1994 .

[55]  Harry H. Kelejian,et al.  On the asymptotic distribution of the Moran I test statistic with applications , 2001 .