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Estimation of Spatial Models with Endogenous Weighting Matrices and an Application to a Demand Model for Cigarettes

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Author Info

  • Harry H. Kelejian

    ()
    (Department of Economics, University of Maryland)

  • Gianfranco Piras

    ()
    (Regional Research Institute, West Virginia University)

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    Abstract

    Weighting matrices are typically assumed to be exogenous. However, in many cases this exogeneity assumption may not be reasonable. In these cases, typical model specifications and corresponding estimation procedures will no longer be valid. In this paper we specify a spatial panel data model which contains a spatially lagged dependent variable in terms of an endogenous weighting matrix. We suggest an estimator for the regression parameters, and demonstrate its consistency and asymptotic normality. We also suggest an estimator for the large sample variance-covariance matrix of that distribution. We then apply our results to an interstate panel data cigarette demand model which contains an endogenous weighting matrix. Among other things, our results suggest that, if properly accounted for, the bootlegging effect of buyers, or “agents” for them, crossing state borders to purchase cigarette turns out to be positive and significant.

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    Bibliographic Info

    Paper provided by Regional Research Institute, West Virginia University in its series Working Papers with number 201302.

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    Length: 29 pages
    Date of creation: Feb 2013
    Date of revision:
    Handle: RePEc:rri:wpaper:201302

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    Keywords: weighting matrices; econometrics; estimation;

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    1. Jeffrey P. Cohen & Catherine J. Morrison Paul, 2004. "Public Infrastructure Investment, Interstate Spatial Spillovers, and Manufacturing Costs," The Review of Economics and Statistics, MIT Press, vol. 86(2), pages 551-560, May.
    2. Olivier Parent & James P. LeSage, 2008. "Using the variance structure of the conditional autoregressive spatial specification to model knowledge spillovers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(2), pages 235-256.
    3. Nicolas Debarsy & Cem Ertur & James P. Lesage, 2012. "Interpreting Dynamic Space-Time Panel Data Models," Post-Print hal-00525740, HAL.
    4. 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.
    5. Case, Anne C. & Rosen, Harvey S. & Hines, James Jr., 1993. "Budget spillovers and fiscal policy interdependence : Evidence from the states," Journal of Public Economics, Elsevier, vol. 52(3), pages 285-307, October.
    6. Badi H. Baltagi & Peter Egger & Michael Pfaffermayr, 2005. "Estimating Models of Complex FDI: Are There Third-Country Effects?," Center for Policy Research Working Papers 73, Center for Policy Research, Maxwell School, Syracuse University.
    7. 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.
    8. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-65, July.
    9. Joris Pinkse & Margaret E. Slade & Craig Brett, 2002. "Spatial Price Competition: A Semiparametric Approach," Econometrica, Econometric Society, vol. 70(3), pages 1111-1153, May.
    10. Kelejian, Harry H. & Prucha, Ingmar R., 2004. "Estimation of simultaneous systems of spatially interrelated cross sectional equations," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 27-50.
    11. 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.
    12. Mukerji, Purba, 2009. "Ready for capital account convertibility?," Journal of International Money and Finance, Elsevier, vol. 28(6), pages 1006-1021, October.
    13. Kim, Min Seong & Sun, Yixiao, 2011. "Spatial heteroskedasticity and autocorrelation consistent estimation of covariance matrix," Journal of Econometrics, Elsevier, vol. 160(2), pages 349-371, February.
    14. Luc Anselin & Nancy Lozano-Gracia, 2008. "Errors in variables and spatial effects in hedonic house price models of ambient air quality," Empirical Economics, Springer, vol. 34(1), pages 5-34, February.
    15. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "HAC estimation in a spatial framework," Journal of Econometrics, Elsevier, vol. 140(1), pages 131-154, September.
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