Approximated likelihood and root estimators for spatial interaction in spatial autoregressive models
In this paper, we first generalize an approximate measure of spatial dependence, the APLE statistic (Li et al., 2007), to a spatial Durbin (SD) model. This generalized APLE takes into account exogenous variables directly and can be used to detect spatial dependence originating from either a spatial autoregressive (SAR), spatial error (SE) or SD process. However, that measure is not consistent. Secondly, by examining carefully the first order condition of the concentrated log likelihood of the SD (or SAR) model, whose first order approximation generates the APLE, we construct a moment equation quadratic in the autoregressive parameter that generalizes an original estimation approach in Ord (1975) and yields a closed-form consistent root estimator of the autoregressive parameter. With a specific moment equation constructed from an initial consistent estimator, the root estimator can be as efficient as the MLE under normality. Furthermore, when there is unknown heteroskedasticity in the disturbances, we derive a modified APLE and a root estimator which can be robust to unknown heteroskedasticity. The root estimators are computationally much simpler than the quasi-maximum likelihood estimators.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 42 (2012)
Issue (Month): 3 ()
|Contact details of provider:|| Web page: http://www.elsevier.com/locate/regec|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Kelejian, Harry H. & Prucha, Ingmar R., 2010.
"Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances,"
Journal of Econometrics,
Elsevier, vol. 157(1), pages 53-67, July.
- Harry H. Kelejian & Ingmar R. Prucha, 2008. "Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances," CESifo Working Paper Series 2448, CESifo Group Munich.
- Liu, Xiaodong & Lee, Lung-fei & Bollinger, Christopher R., 2010. "An efficient GMM estimator of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 159(2), pages 303-319, December.
- Kelley Pace, R., 1997. "Performing large spatial regressions and autoregressions," Economics Letters, Elsevier, vol. 54(3), pages 283-291, July.
- J. Barkley Rosser, 2009. "Introduction," Chapters, in: Handbook of Research on Complexity, chapter 1 Edward Elgar Publishing.
- Lee, Lung-Fei, 2002. "Consistency And Efficiency Of Least Squares Estimation For Mixed Regressive, Spatial Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 18(02), pages 252-277, April.
- H. Kelejian, Harry & Prucha, Ingmar R., 2001.
"On the asymptotic distribution of the Moran I test statistic with applications,"
Journal of Econometrics,
Elsevier, vol. 104(2), pages 219-257, September.
- Harry H. Kelejian & Ingmar R. Prucha, 1999. "On the Asymptotic Distribution of the Moran I Test Statistic with Applications," Electronic Working Papers 99-002, University of Maryland, Department of Economics.
- Li, Hongfei & Calder, Catherine A. & Cressie, Noel, 2012. "One-step estimation of spatial dependence parameters: Properties and extensions of the APLE statistic," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 68-84.
- Lee, Lung-fei & Liu, Xiaodong, 2010. "Efficient Gmm Estimation Of High Order Spatial Autoregressive Models With Autoregressive Disturbances," Econometric Theory, Cambridge University Press, vol. 26(01), pages 187-230, February.
- Smirnov, Oleg A. & Anselin, Luc E., 2009. "An O(N) parallel method of computing the Log-Jacobian of the variable transformation for models with spatial interaction on a lattice," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2980-2988, June.
- Helms, Andrew C., 2012. "Keeping up with the Joneses: Neighborhood effects in housing renovation," Regional Science and Urban Economics, Elsevier, vol. 42(1-2), pages 303-313.
- Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
- Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
- Lee, Lung-fei, 2007. "The method of elimination and substitution in the GMM estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 140(1), pages 155-189, September.
- Kelejian, Harry H & Prucha, Ingmar R, 1998.
"A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances,"
The Journal of Real Estate Finance and Economics,
Springer, vol. 17(1), pages 99-121, July.
- Harry H. Kelejian & Ingmar R. Prucha, 1997. "A Generalized Spatial Two Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," Electronic Working Papers 97-002, University of Maryland, Department of Economics, revised Aug 1997.
- Harry H. Kelejian & Ingmar R. Prucha, 1995.
"A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model,"
Electronic Working Papers
95-001, University of Maryland, Department of Economics, revised Mar 1997.
- Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-33, May.
- Lee, Lung-fei, 2007. "GMM and 2SLS estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 137(2), pages 489-514, April.
- Martellosio, Federico, 2010. "Power Properties Of Invariant Tests For Spatial Autocorrelation In Linear Regression," Econometric Theory, Cambridge University Press, vol. 26(01), pages 152-186, February.
- Smirnov, Oleg & Anselin, Luc, 2001. "Fast maximum likelihood estimation of very large spatial autoregressive models: a characteristic polynomial approach," Computational Statistics & Data Analysis, Elsevier, vol. 35(3), pages 301-319, January.
- Irani Arraiz & David M. Drukker & Harry H. Kelejian & Ingmar R. Prucha, 2010.
"A Spatial Cliff-Ord-Type Model With Heteroskedastic Innovations: Small And Large Sample Results,"
Journal of Regional Science,
Wiley Blackwell, vol. 50(2), pages 592-614.
- Irani Arraiz & David M. Drukker & Harry H. Kelejian & Ingmar R. Prucha, 2008. "A Spatial Cliff-Ord-type Model with Heteroskedastic Innovations: Small and Large Sample Results," CESifo Working Paper Series 2485, CESifo Group Munich.
- R. Pace & James LeSage, 2009. "A sampling approach to estimate the log determinant used in spatial likelihood problems," Journal of Geographical Systems, Springer, vol. 11(3), pages 209-225, September.
- Kelley Pace, R. & Barry, Ronald, 1997. "Sparse spatial autoregressions," Statistics & Probability Letters, Elsevier, vol. 33(3), pages 291-297, May.
When requesting a correction, please mention this item's handle: RePEc:eee:regeco:v:42:y:2012:i:3:p:446-458. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.