ARTICLE
ABSTRACT
In this paper an alternative procedure to partial regression is introduced. The presented procedure can be used in maximum likelihood estimation of spatial autoregressive model. Under certain assumptions on the dimension of certain invariant space associated with spatial weight matrix a feasible procedure is formulated, which can be used to handle large class of fixed effect designs. This is done at the expense of possibly decreased number of degrees of freedom in the Gaussian log likelihood function. Additionally, a statement on asymptotic behaviour of presented estimator is given.
KEYWORDS
partial regression, maximum likelihood estimation, spatial autoregressive model, fixed effects model
REFERENCES
Anselin L., (1988), Spatial Econometrics: Methods and Models, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Anselin L., Le Gallo J., Jayet H., (2006), Spatial Panel Econometrics, in: Matyas L., Sevestre P., (eds.), The Econometrics of Panel Data, Fundamentals and Recent Developments in Theory and Practice, 3rd edition, Kluwer, Dordrecht.
Baltagi B. H., (2005), Econometric Analysis of Panel Data, John Wiley & Sons, Chichester West Sussex, England.
Elhorst J. P., (2014), Spatial Econometrics: From Cross-Sectional Data to Spatial Panels, Springer, Heidelberg.
Elhorst J. P., Fréret S., (2009), Evidence of Political Yardstick Competition in France Using a Two-Regime Spatial Durbin Model with Fixed Effects, Journal of Regional Science, 49 (5), 931–951.
Fiebig D. G., Bartels R., (1996), The Frisch-Waugh Theorem and Generalized Least Squares, Econometric Reviews, 15 (4), 431–443.
Frisch R., Waugh F. V., (1933), Partial Time Regressions as Compared with Individual Trends, Econometrica, 1 (4), 387–401.
Greene W. H., (2008), Econometric Analysis, 6th edition, Prentice Hall, Upper Saddle River, N. J.
Kelejian H. H., Prucha I. R., (2001), On the Asymptotic Distribution of the Moran I Test Statistic with Applications, Journal of Econometrics, 104, 219–257.
Lee L.-F., (2004), Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models, Econometrica, 72 (6), 1899–1925.
Lee L.-F., Yu J., (2010), Estimation of Spatial Autoregressive Panel Data Models with Fixed Effects, Journal of Econometrics, 154 (2), 165–85.
Liesen J., Strakoš Z., (2013), Krylov Subspace Methods: Principles and Analysis, Oxford University Press, Oxford UK.
Olejnik A., Olejnik J., (2017), Increasing Returns to Scale, Productivity and Economic Growth – A Spatial Analysis of the Contemporary EU Economy, submitted to Argumenta Oeconomica.
Olejnik A., Özyurt S., (2016), Multi-Dimensional Spatial Auto-regressive Models: How Do They Perform in an Economic Growth Framework?, working paper.
Pace R. K., (2014), Maximum Likelihood Estimation, in: Fisher M. M., Nijkamp P., (eds.), Handbook of Regional Science, Springer-Verlag, Berlin Heidelberg.
Pötscher B. M., Prucha I., (1997), Dynamic Nonlinear Econometric Models, Springer-Verlag, Berlin Heidelberg.
Yamada H., (2016), The Frisch–Waugh–Lovell Theorem for the Lasso and the Ridge Regression, Communications in Statistics – Theory and Methods, Available online at: http://dx.doi.org/10.1080/03610926.2016.1252403.
