Estimation and Inference in Functional-Coefficient Spatial Autoregressive Panel Data Models with Fixed Effects

Sun, Yiguo and Malikov, Emir (2017): Estimation and Inference in Functional-Coefficient Spatial Autoregressive Panel Data Models with Fixed Effects.

Abstract

This paper develops an innovative way of estimating a functional-coefficient spatial autoregressive panel data model with unobserved individual effects which can accommodate (multiple) time-invariant regressors in the model with a large number of cross-sectional units and a fixed number of time periods. The methodology we propose removes unobserved fixed effects from the model by transforming the latter into a semiparametric additive model, the estimation of which however does not require the use of backfitting or marginal integration techniques. We derive the consistency and asymptotic normality results for the proposed kernel and sieve estimators. We also construct a consistent nonparametric test to test for spatial endogeneity in the data. A small Monte Carlo study shows that our proposed estimators and the test statistic exhibit good finite-sample performance.

• Item Type: MPRA Paper
• Language: English
• Keywords: First Difference, Fixed Effects, Hypothesis Testing, Local Linear Regression, Nonparametric GMM, Sieve Estimator, Spatial Autoregressive, Varying Coefficient
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C23 - Panel Data Models ; Spatio-temporal Models

References

Anselin, L. (1988). Spatial Econometrics: Methods and Models. Dordrecht: Kluwer.

Anselin, L. & Lozano-Gracia, N. (2009). Spatial hedonic models. In K. Patterson & T. C. Mills (Eds.), Palgrave Handbook of Econometrics, 2. Basingstoke: Palgrave Macmillan.

Belloni, A., Chernozhukov, V., Chetverikov, D., & Kato, K. (2015). Some new asymptotic theory for least squares series: Pointwise and uniform results. Journal of Econometrics, 186, 345-366.

Brueckner, J. K. (2003). Strategic interaction among governments: An overview of empirical studies. International Regional Science Review, 26, 175-188.

Du, P., Parmeter, C. F., & Racine, J. S. (2013). Nonparametric kernel regression with multiple predictors and multiple shape constraints. Statistica Sinica, 23 (3), 1347-1371.

Dzyadyk, V. K. & Shevchuk, I. A. (2008). Theory of Uniform Approximation of Functions by Polynomials. New York: Walter de Gruyter & GmbH Co.

Ertur, C. & Koch, W. (2007). Growth, technological interdependence and spatial externalities: Theory and evidence. Journal of Applied Econometrics, 22, 1033-1062.

Fan, Y. & Li, Q. (1999). Central limit theorem for degenerate U-statistics of absolutely regular processes with applications to model specification testing. Journal of Nonparametric Statistics, 10, 245-271.

Hall, P. (1984). Central limit theorem for integrated square error of multivariate nonparametric density estimators. Annals of Statistics, 14, 1-16.

Hall, P. & Heyde, C. C. (1980). Martingale Limit Theory and Its Applications. New York: Academic Press.

Hall, P. & Huang, L.-S. (2001). Nonparametric kernel regression subject to monotonicity constraints. Annals of Statistics, 29 (3), 624-647.

Henderson, D. J., Carroll, R. J., & Li, Q. (2008). Nonparametric estimation and testing of fixed effects panel data models. Journal of Econometrics, 144 (1), 257-275.

Jin, F. & Lee, L.-f. (2015). On the bootstrap for Moran’s I test for spatial dependence. Journal of Econometrics, 184, 295-314.

Kelejian, H. H., Murrell, P., & Shepotylo, O. (2013). Spatial spillovers in the development of institutions. Journal of Development Economics, 101, 297-315.

Kelejian, H. H. & Prucha, I. R. (1999). A generalized moment estimator for the autoregressive parameter in a spatial model. International Economic Review, 40, 509-533.

Kelejian, H. H. & Prucha, I. R. (2010). Speci_cation and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. Journal of Econometrics, 157, 53-67.

Lee, L.-F. (2007). GMM and 2SLS estimation of mixed regressive, spatial autoregressive models. Journal of Econometrics, 137, 489-514.

Lee, L.-F. & Yu, J. (2010a). Estimation of spatial autoregressive panel data models with fixed effects. Journal of Econometrics, 154, 165-185.

Lee, L.-F. & Yu, J. (2010b). Some recent developments in spatial panel data models. Regional Science and Urban Economics, 40, 255-271.

Lee, L.-F. & Yu, J. (2012). Spatial panels: Random components versus fixed effects. International Economic Review, 53, 1369-1412.

Lee, L.-F. & Yu, J. (2014). Effcient GMM estimation of spatial dynamic panel data models with fixed effects. Journal of Econometrics, 180, 174-197.

Li, C. & Liang, Z. (2015). Asymptotics for nonparametric and semiparametric fixed effects panel models. Journal of Econometrics, 185, 420-434.

Li, Q. (1999). Consistent model specification tests for time series econometric models. Journal of Econometrics, 92, 101-147.

Li, Q. & Wang, S. (1998). A simple consistent bootstrap test for a parametric regression functional form. Journal of Econometrics, 87, 145-165.

Lin, Z., Li, Q., & Sun, Y. (2014). A consistent nonparametric test of parametric regression functional form in fixed effects panel data models. Journal of Econometrics, 178, 167-179.

Liu, X., Lee, L.-f., & Bollinger, C. T. (2010). An efficient GMM estimator of spatial autoregressive models. Journal of Econometrics, 159, 303-319.

Malikov, E., Kumbhakar, S., & Sun, Y. (2016). Varying coefficient panel data model in the presence of endogenous selectivity and fixed effects. Journal of Econometrics, 190 (2), 233-251.

Malikov, E. & Sun, Y. (2017). Semiparametric estimation and testing of smooth coefficient spatial autoregressive models. Journal of Econometrics, 199 (1), 13-34.

Mammen, E., St_ve, B., & Tjostheim, D. (2009). Nonparametric additive models for panels of time series. Econometric Theory, 25, 442-481.

Martins-Filho, C. & Yao, F. (2009). Nonparametric regression estimation with general parametric error covariance. Journal of Multivariate Analysis, 100, 309-333.

Masry, E. (1996). Multivariate local polynomial regression for time series: Uniform strong consistency and rates. Journal of Time Series Analysis, 17, 571-599.

Newey, W. K. (1997). Convergence rates and asymptotic normality for series estimators. Journal of Econometrics, 79, 147-168.

Pinkse, J., Slade, M. E., & Brett, C. (2002). Spatial price competition: A semiparametric approach. Econometrica, 70, 1111-1153.

Qian, J. & Wang, L. (2012). Estimating semiparametric panel data models by marginal integration. Journal of Econometrics, 167, 483-493.

Seber, G. A. F. (2008). A Matrix Handbook for Statisticians. Wiley Series in Probability and Statistics. John Wiley & Sons, Inc.

Su, L. (2012). Semiparametric GMM estimation of spatial autoregressive models. Journal of Econometrics, 167, 543-560.

Su, L. & Jin, S. (2010). Profile quasi-maximum likelihood estimation of partially linear spatial autoregressive models. Journal of Econometrics, 157, 18-33.

Su, L. & Qu, X. (2017). Specification test for spatial autoregressive models. Journal of Business and Economic Statistics (online). forthcoming.

Su, L., Ullah, A., & Wang, Y. (2013). Nonparametric regression estimation with general parametric error covariance: A more efficient two-step estimator. Empirical Economics, 45, 1009-1024.

Sun, Y. (2016). Functional-coe_cient spatial autoregressive models with nonparametric spatial weights. Journal of Econometrics, 195, 134-153.

Sun, Y., Cai, Z., & Li, Q. (2015). A consistent nonparametric test on semiparametric smooth coefficient models with integrated time series. Econometric Theory. forthcoming.

Sun, Y., Carroll, R. J., & Li, D. (2009). Semiparametric estimation of fixed-effects panel data varying coefficient models. Advances in Econometrics, 25, 101-129.

Sun, Y. & Malikov, E. (2015). Estimation and inference in functional-coefficient spatial autoregressive panel data models with fixed effects. Manuscript.

Sun, Y., Yan, H., Zhang, W., & Lu, Z. (2014). A semiparametric spatial dynamic model. Annals of Statistics, 42, 700-727.

Sun, Y., Zhang, Y., & Li, Q. (2015). Nonparametric panel data regression models. In B. H. Baltagi (Ed.), The Oxford Handbook on Panel Data chapter 10. Oxford University Press.

Wang, Q. & Phillips, P. C. B. (2012). A specification test for nonlinear nonstationary models. Annals of Statistics, 40, 727-758.

Yu, J., de Jong, R., & Lee, L.-f. (2012). Estimation for spatial dynamic panel data with fixed effects: The case of spatial cointegration. Journal of Econometrics, 167, 16-37.

Zhang, Z. (2013). A pairwise difference estimator for partially linear spatial autoregressive models. Spatial Economic Analysis, 8, 176-194.

Zheng, J. X. (1996). A consistent test of function form via nonparametric estimation techniques. Journal of Econometrics, 75, 263-289.