Robust outer product of gradients tests for testing spatial dependence
Yıl 2021,
Cilt: 13 Sayı: 3, 120 - 141, 31.12.2021
Osman Doğan
,
Suleyman Taspinar
,
Bulent Guloglu
Öz
In this paper, we suggest outer-product-of-gradient (OPG) variants of the Lagrange multiplier (LM) test statistic for testing spatial dependence under the local parametric misspecification in spatial models. Our OPG statistic for testing the presence of a spatial lag in the disturbance term remains valid irrespective of whether or not there is spatial dependence in the dependent variable. Similarly, our suggested OPG statistic for testing the presence of a spatial lag in the dependent variable is robust to the presence of spatial dependence in the disturbance term. We also suggest the OPG variants that are robust to the presence of an unknown form of heteroskedasticity in the disturbance terms. The computations of all suggested tests only require the least squares estimates from a linear regression model. In a Monte Carlo simulation, we investigate the finite sample properties of our tests and some alternative tests suggested in the literature. The simulation results show that our tests work well in finite samples.
Kaynakça
- Anselin, L. (1998). Spatial Econometrics: Methods and Models. Springer, New York.
- Anselin, L., Bera, A.K., Florax, R. and Yoon, M.J. (1996). Simple diagnostic tests for spatial dependence.
Regional Science and Urban Economics, 26(1), 77-104.
- Baltagi, B.H., Chang, Y.J. and Li, Q. (1992). Monte Carlo results on several new and existing tests for
the error component model. Journal of Econometrics, 54(1), 95-120.
- Baltagi, B.H. and Yang, Z. (2013a). Heteroskedasticity and non-normality robust LM tests for spatial
dependence. Regional Science and Urban Economics, 43(5), 725-739.
- Baltagi, B.H. and Yang, Z. (2013b). Standardized LM tests for spatial error dependence in linear or panel
regressions. The Econometrics Journal, 16(1), 103-134.
- Bera, A.K. and Yoon, M.J. (1993). Specification testing with locally misspecified alternatives. Econometric Theory, 9(4), 649-658.
- Born, B. and Breitung, J. (2011). Simple regression-based tests for spatial dependence. The Econometrics
Journal, 14(2), 330-342.
- Burridge, P. (1980). On the Cliff-Ord test for spatial correlation. Journal of the Royal Statistical Society,
Series B: Methodological, 42, 107-108.
- Davidson, R. and MacKinnon, J.G. (1987). Implicit alternatives and the local power of test statistics.
Econometrica, 55(6), 1305-1329.
- Do˘gan, O. (2015). Heteroskedasticity of unknown form in spatial autoregressive models with a moving
average disturbance term. Econometrics, 3(1), 101-127.
- Elhorst, J.P. (2014). Spatial Econometrics: From Cross-Sectional Data to Spatial Panels. Springer,
Berlin.
- Jin, F. and Lee, L. (2018). Outer-product-of-gradients tests for spatial autoregressive models. Regional
Science and Urban Economics, 72, 35-57.
- Kelejian, H.H. and Prucha, I.R. (2001). On the asymptotic distribution of the Moran I test statistic
with applications. Journal of Econometrics, 104(2), 219-257.
- Kelejian, H.H. and Prucha, I.R. (2010). Specification and estimation of spatial autoregressive models
with autoregressive and heteroskedastic disturbances. Journal of Econometrics, 157, 53-67.
- Koenker, R. (1981). A note on studentizing a test for heteroscedasticity. Journal of Econometrics, 17(1),
107-112.
- Lee, L. (2004). Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica, 72(6), 1899-1925.
- LeSage, L. and Pace, R.K. (2009). Introduction to Spatial Econometrics. Chapman and Hall/CRC,
Londo
- Lin, X. and Lee, L. (2010). GMM estimation of spatial autoregressive models with unknown heteroskedasticity. Journal of Econometrics, 157(1), 34-52.
- Liu, S.F. and Yang, Z. (2014). Modified QML estimation of spatial autoregressive models with unknown
heteroskedasticity and nonnormality. Regional Science and Urban Economics, 52, 50-70.
- Moulton, B.R. and Randolph, W.C. (1989). Alternative tests of the error components model. Econometrica, 57(3), 685-693.
- Pace, R.K. and Barry, R. (1997). Quick computation of spatial autoregressive estimators. Geographical
Analysis, 29(3), 232-247.
- Qu, X. and Lee, L. (2015). Estimating a spatial autoregressive model with an endogenous spatial weight
matrix. Journal of Econometrics, 184(2), 209-232.
- Saikkonen, P. (1989). Asymptotic relative efficiency of the classical test statistics under misspecification.
Journal of Econometrics, 42(3), 351-369.
- White, H. (1994). Estimation, Inference and Specification Analysis. Cambridge University Press, Cambridge.
- Yang, Z. (2018). Unified M-estimation of fixed-effects spatial dynamic models with short panels. Journal
of Econometrics, 205(2), 423-447.
Yıl 2021,
Cilt: 13 Sayı: 3, 120 - 141, 31.12.2021
Osman Doğan
,
Suleyman Taspinar
,
Bulent Guloglu
Kaynakça
- Anselin, L. (1998). Spatial Econometrics: Methods and Models. Springer, New York.
- Anselin, L., Bera, A.K., Florax, R. and Yoon, M.J. (1996). Simple diagnostic tests for spatial dependence.
Regional Science and Urban Economics, 26(1), 77-104.
- Baltagi, B.H., Chang, Y.J. and Li, Q. (1992). Monte Carlo results on several new and existing tests for
the error component model. Journal of Econometrics, 54(1), 95-120.
- Baltagi, B.H. and Yang, Z. (2013a). Heteroskedasticity and non-normality robust LM tests for spatial
dependence. Regional Science and Urban Economics, 43(5), 725-739.
- Baltagi, B.H. and Yang, Z. (2013b). Standardized LM tests for spatial error dependence in linear or panel
regressions. The Econometrics Journal, 16(1), 103-134.
- Bera, A.K. and Yoon, M.J. (1993). Specification testing with locally misspecified alternatives. Econometric Theory, 9(4), 649-658.
- Born, B. and Breitung, J. (2011). Simple regression-based tests for spatial dependence. The Econometrics
Journal, 14(2), 330-342.
- Burridge, P. (1980). On the Cliff-Ord test for spatial correlation. Journal of the Royal Statistical Society,
Series B: Methodological, 42, 107-108.
- Davidson, R. and MacKinnon, J.G. (1987). Implicit alternatives and the local power of test statistics.
Econometrica, 55(6), 1305-1329.
- Do˘gan, O. (2015). Heteroskedasticity of unknown form in spatial autoregressive models with a moving
average disturbance term. Econometrics, 3(1), 101-127.
- Elhorst, J.P. (2014). Spatial Econometrics: From Cross-Sectional Data to Spatial Panels. Springer,
Berlin.
- Jin, F. and Lee, L. (2018). Outer-product-of-gradients tests for spatial autoregressive models. Regional
Science and Urban Economics, 72, 35-57.
- Kelejian, H.H. and Prucha, I.R. (2001). On the asymptotic distribution of the Moran I test statistic
with applications. Journal of Econometrics, 104(2), 219-257.
- Kelejian, H.H. and Prucha, I.R. (2010). Specification and estimation of spatial autoregressive models
with autoregressive and heteroskedastic disturbances. Journal of Econometrics, 157, 53-67.
- Koenker, R. (1981). A note on studentizing a test for heteroscedasticity. Journal of Econometrics, 17(1),
107-112.
- Lee, L. (2004). Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica, 72(6), 1899-1925.
- LeSage, L. and Pace, R.K. (2009). Introduction to Spatial Econometrics. Chapman and Hall/CRC,
Londo
- Lin, X. and Lee, L. (2010). GMM estimation of spatial autoregressive models with unknown heteroskedasticity. Journal of Econometrics, 157(1), 34-52.
- Liu, S.F. and Yang, Z. (2014). Modified QML estimation of spatial autoregressive models with unknown
heteroskedasticity and nonnormality. Regional Science and Urban Economics, 52, 50-70.
- Moulton, B.R. and Randolph, W.C. (1989). Alternative tests of the error components model. Econometrica, 57(3), 685-693.
- Pace, R.K. and Barry, R. (1997). Quick computation of spatial autoregressive estimators. Geographical
Analysis, 29(3), 232-247.
- Qu, X. and Lee, L. (2015). Estimating a spatial autoregressive model with an endogenous spatial weight
matrix. Journal of Econometrics, 184(2), 209-232.
- Saikkonen, P. (1989). Asymptotic relative efficiency of the classical test statistics under misspecification.
Journal of Econometrics, 42(3), 351-369.
- White, H. (1994). Estimation, Inference and Specification Analysis. Cambridge University Press, Cambridge.
- Yang, Z. (2018). Unified M-estimation of fixed-effects spatial dynamic models with short panels. Journal
of Econometrics, 205(2), 423-447.