Mynbaev, Kairat (2006): Asymptotic Distribution of the OLS Estimator for a Mixed Regressive, Spatial Autoregressive Model.
Download (401kB) | Preview
We find the asymptotics of the OLS estimator of the parameters $\beta$ and $\rho$ in the spatial autoregressive model with exogenous regressors $Y_n = X_n\beta+\rho W_nY_n+V_n$. Only low-level conditions are imposed. Exogenous regressors may be bounded or growing, like polynomial trends. The assumption on the spatial matrix $W_n$ is appropriate for the situation when each economic agent is influenced by many others. The asymptotics contains both linear and quadratic forms in standard normal variables. The conditions and the format of the result are chosen in a way compatible with known results for the model without lags by Anderson (1971) and for the spatial model without exogenous regressors due to Mynbaev and Ullah (2006).
|Item Type:||MPRA Paper|
|Institution:||Kazakh-British Technical University|
|Original Title:||Asymptotic Distribution of the OLS Estimator for a Mixed Regressive, Spatial Autoregressive Model|
|Keywords:||mixed regressive spatial autoregressive model; OLS estimator; asymptotic distribution|
|Subjects:||C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C21 - Cross-Sectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions
C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C31 - Cross-Sectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions ; Social Interaction Models
|Depositing User:||Kairat Mynbaev|
|Date Deposited:||15. Aug 2007|
|Last Modified:||24. Feb 2013 06:13|
Bibliography Amemiya, T. (1985) Advanced Econometrics. Blackwell, Oxford, UK. Anderson, T. W. (1971) The Statistical Analysis of Time Series. Wiley, New York. Anderson, T.W. and D. A. Darling (1952) Asymptotic theory of certain ”goodness of fit” criteria based on stochastic processes. Ann. Math. Stat. 23, 193-212. Anselin, L. (1988) Spatial Econometrics: Methods and Models. Kluwer Academic Publishers, The Netherlands. Anselin, L. (1992) Space and Applied Econometrics. Anselin, ed. Special Issue, Regional Science and Urban Economics 22. Anselin, L. and R. Florax (1995) New Directions in Spatial Econometrics. Springer- Verlag, Berlin. Anselin, L. and S. Rey (1997) Spatial Econometrics. Anselin, L. and S. Rey, ed. Special Issue, International Regional Science Review 20. Billingsley, P. (1968) Convergence of Probability Measures. Wiley & Sons, New York. Cressie, N. (1993) Statistics for Spatial Data. Wiley, New York. Gohberg, I.C. and M.G. Kre\˘ın (1969) Introduction to the Theory of Linear Nonselfadjoint Operators. American Mathematical Society, Providence, Rhode Island. Hamilton, J. D. (1994) Time Series Analysis. Princeton University Press, Princeton, New Jersey. Kelejian, H.H. and I.R. Prucha (1998) A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances. Journal of Real Estate Finance and Economics 17, 99-121. Kelejian, H.H. and I.R. Prucha (1999) A generalized moments estimator for the autoregressive parameter in a spatial model. International Economic Review 40, 509-533. Kelejian, H.H. and I.R. Prucha (2001) On the asymptotic distribution of the Moran I test statistic with applications. Journal of Econometrics 104, 219-257. Lee, L.F. (2001) Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models I: Spatial autoregressive processes. Manuscript, Department of Economics, The Ohio State University, Columbus, Ohio. Lee, L.F. (2002) Consistency and efficiency of least squares estimation for mixed regressive, spatial autoregressive models. Econometric Theory 18, 252-277. Lee, L.F. (2003) Best spatial two-stage least squares estimators for a spatial autoregressive model with autoregressive disturbances. Econometric Reviews 22, No. 4, 307-335. Lee, L.F. (2004) Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica 72, No. 6, 1899-1925. Milbrodt, H. (1992) Testing stationarity in the mean of autoregressive processes with a nonparametric regression trend. Ann. Statist. 20, 1426-1440. Millar, P. W. (1982) Optimal estimation of a general regression function, Ann. Statist. 10, 717-740. Moussatat, M. W. (1976) On the Asymptotic Theory of Statistical Experiments and Some of Its Applications. Ph.D. dissertation, Univ. of California, Berkeley. 24 Mynbaev, K.T. (2001) Lp-approximable sequences of vectors and limit distribution of quadratic forms of random variables. Advances in Applied Mathematics 26, 302-329. Mynbaev, K.T. (2006) Asymptotic properties of OLS estimates in autoregressions with bounded or slowly growing deterministic trends. Communications in Statistics 35, No. 3, 499-520. Mynbaev, K.T. and A. Lemos (2004) Econometrics (in Portuguese). Funda\,cao Get\´ulio Vargas, Brazil. Mynbaev, K.T. and I. Castelar (2001) The Strengths and Weaknesses of L2-approximable Regressors. Two Essays on Econometrics. Express˜ao Gr´afica, Fortaleza, v.1. Mynbaev, K.T. and Ullah, A. (2006) A remark on the asymptotic distribution of the OLS estimator for a purely autoregressive spatial model. The North American Summer Meetings of the Econometric Society, Minneapolis, MN, June 22 - June 25. P\¨otscher, B.M. and I.R. Prucha. (1991) Basic structure of the asymptotic theory in dynamic nonlinear econometric models, Part I: Consistency and approximation concepts. Econometric Reviews 10, 125-216 Ord, J.K. (1975) Estimation methods for models of spatial interaction. Journal of American Statistical Association 70, 120-126. Paelinck, J. and L. Klaassen (1979) Spatial Econometrics. Saxon House, Farnborough. Schmidt, P. (1976) Econometrics. Marcel Dekker, New York and Basel. Varberg, D.E. (1966) Convergence of quadratic forms in independent random variables. Ann. Math. Stat. 37, 567-576. Whittle, P. (1954) On stationary processes in the plane. Biometrika 41, 434-449. 25
- Mynbaev, Kairat Asymptotic Distribution of the OLS Estimator for a Mixed Regressive, Spatial Autoregressive Model. (deposited 15. Aug 2007) [Currently Displayed]