Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-17T01:40:45.677Z Has data issue: false hasContentIssue false
  • English
  • Français

RANDOM EFFECTS AND SPATIAL AUTOCORRELATION WITH EQUAL WEIGHTS

Published online by Cambridge University Press:  30 August 2006

Badi H. Baltagi
Badi H. Baltagi
Affiliation:
Syracuse University
Get access Rights & Permissions [Opens in a new window]

Abstract

This note considers a panel data regression model with spatial autoregressive disturbances and random effects where the weight matrix is normalized and has equal elements. This is motivated by Kelejian, Prucha, and Yuzefovich (2005, Journal of Regional Science, forthcoming), who argue that such a weighting matrix, having blocks of equal elements, might be considered when units are equally distant within certain neighborhoods but unrelated between neighborhoods. We derive a simple weighted least squares transformation that obtains generalized least squares (GLS) on this model as a simple ordinary least squares (OLS). For the special case of a spatial panel model with no random effects, we obtain two sufficient conditions where GLS on this model is equivalent to OLS. Finally, we show that these results, for the equal weight matrix, hold whether we use the spatial autoregressive specification, the spatial moving average specification, the spatial error components specification, or the Kapoor, Kelejian, and Prucha (2005, Journal of Econometrics, forthcoming) alternative to modeling panel data with spatially correlated error components.I thank Paolo Paruolo and an anonymous referee for helpful comments and suggestions.

Type
NOTES AND PROBLEMS
Information
Econometric Theory , Volume 22 , Issue 5 , October 2006 , pp. 973 - 984
Copyright
© 2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Anselin, L. (1988) Spatial Econometrics: Methods and Models. Kluwer Academic Publishers.
Anselin, L. (2003) Spatial externalities, spatial multipliers and spatial econometrics. International Regional Science Review 26, 153–166.Google Scholar
Baltagi, B.H. (2005) Econometric Analysis of Panel Data. Wiley.
Baltagi, B.H., S.H. Song, & W. Koh (2003) Testing panel data regression models with spatial error correlation. Journal of Econometrics 117, 123–150.Google Scholar
Case, A.C. (1991) Spatial patterns in household demand. Econometrica 59, 953–965.Google Scholar
Fuller, W.A. & G.E. Battese (1973) Transformations for estimation of linear models with nested error structure. Journal of the American Statistical Association 68, 626–632.Google Scholar
Holtz-Eakin, D. (1994) Public-sector capital and the productivity puzzle. Review of Economics and Statistics 76, 12–21.Google Scholar
Kapoor, M., H.H. Kelejian, & I.R. Prucha (2005) Panel data models with spatially correlated error components. Journal of Econometrics, forthcoming.Google Scholar
Kelejian, H.H. & I.R. Prucha (2002) 2SLS and OLS in a spatial autoregressive model with equal spatial weights. Regional Science and Urban Economics 32, 691–707.Google Scholar
Kelejian, H.H., I.R. Prucha, & Y. Yuzefovich (2005) Estimation problems with spatial weighting matrices which have blocks of equal elements. Journal of Regional Science, forthcoming.Google Scholar
Kelejian, H.H. & D.P. Robinson (1995) Spatial correlation: A suggested alternative to the autoregressive model. In L. Anselin & R.J. Florax (eds.), New Directions in Spatial Econometrics, pp. 75–95. Springer-Verlag.
Lee, L.F. (2002) Consistency and efficiency of least squares estimation for mixed regressive, spatial autoregressive models. Econometric Theory 18, 252–277.Google Scholar
Magnus, J.R. (1982) Multivariate error components analysis of linear and nonlinear regression models by maximum likelihood. Journal of Econometrics 19, 239–285.Google Scholar
Milliken, G.A. & M. Albohali (1984) On necessary and sufficient conditions for ordinary least squares estimators to be best linear unbiased estimators. American Statistician 38, 298–299.Google Scholar
Wansbeek, T.J. & A. Kapteyn (1982) A simple way to obtain the spectral decomposition of variance components models for balanced data. Communications in Statistics A11, 2105–2112.Google Scholar
Zyskind, G. (1967) On canonical forms, non-negative covariance matrices and best and simple least squares linear estimators in linear models. Annals of Mathematical Statistics 36, 1092–1109.Google Scholar