ESTIMATION OF UNIT ROOT SPATIAL DYNAMIC PANEL DATA MODELS

This paper examines the asymptotics of the QMLE for unit root dynamic panel data models with spatial effect and fixed effects. We consider a unit root dynamic panel data model with spatially correlated disturbances and a unit root spatial dynamic panel data model. For both models the estimate of the dynamic coefficient is $\root \of {nT^3 }$ consistent and the estimates of other parameters are $\root \of {nT}$ consistent, and all of them are asymptotically normal. For the latter model the sum of the contemporaneous spatial effect and dynamic spatial effect converges at $\root \of {nT^3 }$ rate. We also propose a bias-correction procedure so that the asymptotic biases of those estimates are eliminated as long as n/T3 → 0.

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

[2]  Mudit Kapoor,et al.  Panel data models with spatially correlated error components , 2007 .

[3]  Zhenlin Yang,et al.  QML estimation of dynamic panel data models with spatial errors , 2015 .

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

[5]  M. Arellano,et al.  Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations , 1991 .

[6]  Cheng Hsiao,et al.  Analysis of Panel Data , 1987 .

[7]  J. Stock,et al.  INFERENCE IN LINEAR TIME SERIES MODELS WITH SOME UNIT ROOTS , 1990 .

[8]  M. Arellano,et al.  Another look at the instrumental variable estimation of error-components models , 1995 .

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

[10]  Luc Anselin,et al.  Space and applied econometrics: Introduction , 1992 .

[11]  C. Kao,et al.  On the Estimation and Inference of a Cointegrated Regression in Panel Data , 1997 .

[12]  Harry H. Kelejian,et al.  A suggested method of estimation for spatial interdependent models with autocorrelated errors, and an application to a county expenditure model , 1993 .

[13]  J. Ligthart,et al.  GMM Estimation of Fixed Effects Dynamic Panel Data Models with Spatial Lag and Spatial Errors , 2014 .

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

[15]  Elisa Tosetti,et al.  Large Panels with Common Factors and Spatial Correlations , 2007, SSRN Electronic Journal.

[16]  M. Arellano,et al.  The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators , 2003 .

[17]  J. Kiviet,et al.  The Effects of Dynamic Feedbacks on Ls and Mm Estimator Accuracy in Panel Data Models , 2002 .

[18]  Wolfgang Kellera,et al.  The origin of spatial interaction , 2007 .

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

[20]  N. Cressie,et al.  Statistics for Spatial Data. , 1992 .

[21]  P. Phillips,et al.  Linear Regression Limit Theory for Nonstationary Panel Data , 1999 .

[22]  Lung-fei Lee,et al.  Some recent developments in spatial panel data models , 2010 .

[23]  Jinyong Hahn,et al.  JACKKNIFE AND ANALYTICAL BIAS REDUCTION FOR NONLINEAR PANEL MODELS , 2003 .

[24]  fei Lee,et al.  Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Econometric Models II : Mixed Regressive , Spatial Autoregressive Models by Lung - , 2001 .

[25]  Lung-fei Lee,et al.  CONVERGENCE: A SPATIAL DYNAMIC PANEL DATA APPROACH , 2012 .

[26]  Cheng Hsiao,et al.  Formulation and estimation of dynamic models using panel data , 1982 .

[27]  In Choiy.  Nonstationary Panels , 2004 .

[28]  Erich Novak,et al.  Special issue , 2006, J. Complex..

[29]  Cheng Hsiao,et al.  Estimation of Dynamic Models with Error Components , 1981 .

[30]  Christopher A. Sims,et al.  Advances in Econometrics , 1996 .

[31]  Hyungsik Roger Moon,et al.  Testing For A Unit Root In Panels With Dynamic Factors , 2002 .

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

[33]  Kerry Patterson,et al.  Palgrave Handbook of Econometrics , 2009 .

[34]  P. Pedroni.  Fully Modified OLS for Heterogeneous Cointegrated Panels and the Case of Purchasing Power Parity , 1996 .

[35]  J. Neyman,et al.  Consistent Estimates Based on Partially Consistent Observations , 1948 .

[36]  Badi H. Baltagi,et al.  Testing for Serial Correlation, Spatial Autocorrelation and Random Effects , 2004 .

[37]  Alain Pirotte,et al.  Estimating and Forecasting with a Dynamic Spatial Panel Data Model , 2014 .

[38]  Gianfranco Piras,et al.  splm: Spatial Panel Data Models in R , 2012 .

[39]  Luc Anselin,et al.  New Directions in Spatial Econometrics , 2011 .

[40]  R. Blundell,et al.  Initial Conditions and Moment Restrictions in Dynamic Panel Data Models , 1998 .

[41]  Luc Anselin,et al.  Spatial Dependence in Linear Regression Models with an Introduction to Spatial Econometrics , 1995 .

[42]  Lung-fei Lee,et al.  Estimation for spatial dynamic panel data with fixed effects: The case of spatial cointegration , 2012 .

[43]  Jinyong Hahn,et al.  Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects When Both N and T are Large , 2000 .

[44]  Lung-fei Lee,et al.  Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large , 2008 .

[45]  Nick Paulson,et al.  Spatial Approaches to Panel Data in Agricultural Economics: A Climate Change Application , 2011, Journal of Agricultural and Applied Economics.

[46]  Lung-fei Lee,et al.  Quasi-Maximum Likelihood Estimators For Spatial Dynamic Panel Data With Fixed Eects When Both n and T Are Large: A Nonstationary Case , 2007 .

[47]  Maurice J.G Bun,et al.  Bias-Corrected Estimation in Dynamic Panel Data Models , 2005 .

[48]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[49]  Badi H. Baltagi,et al.  Testing Panel Data Regression Models with Spatial Error Correlation , 2002 .