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Journal of Geographical Systems

, Volume 15, Issue 1, pp 51–69 | Cite as

Empirical likelihood estimation of the spatial quantile regression

  • Philip KostovEmail author
Original Article

Abstract

The spatial quantile regression model is a useful and flexible model for analysis of empirical problems with spatial dimension. This paper introduces an alternative estimator for this model. The properties of the proposed estimator are discussed in a comparative perspective with regard to the other available estimators. Simulation evidence on the small sample properties of the proposed estimator is provided. The proposed estimator is feasible and preferable when the model contains multiple spatial weighting matrices. Furthermore, a version of the proposed estimator based on the exponentially tilted empirical likelihood could be beneficial if model misspecification is suspect.

Keywords

Empirical likelihood Quantile regression Spatial data 

JEL Classification

C21 C26 

Supplementary material

10109_2012_162_MOESM1_ESM.zip (9 kb)
Supplementary material 1 (ZIP 9 kb)

References

  1. Aoki M (1996) New approaches to macroeconomic modelling. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  2. Blundell R, Powell JL (2003) Endogeneity in semiparametric and nonparametric regression models. In: Dewatripont M, Hansen LP, Turnovsky SJ (eds) Advances in economics and econometrics: theory and applications, eighth world congress, vol II. Cambridge University Press, Cambridge, pp 312–357Google Scholar
  3. Borjas GJ (1995) Ethnicity, neighborhoods, and human-capital externalities. Am Econ Rev 86(3):365–390Google Scholar
  4. Brueckner JK (2003) Strategic interaction among governments: an overview of empirical studies. Int Reg Sci Rev 26(2):175–188CrossRefGoogle Scholar
  5. Chen SX, Wong CM (2009) Smoothed block empirical likelihood for quantiles of weakly dependent processes. Statistica Sinica 19(1):71–81Google Scholar
  6. Chernozhukov V, Hansen C (2006) Instrumental quantile regression inference for structural and treatment effect models. J Econom 132(2):491–525CrossRefGoogle Scholar
  7. Chernozhukov V, Hansen C (2008) Instrumental variable quantile regression: a robust inference approach. J Econom 142(1):379–398CrossRefGoogle Scholar
  8. Chernozhukov V, Hong H (2003) An MCMC approach to classical estimation. J Econom 115(2):293–346CrossRefGoogle Scholar
  9. Durlauf SN (1994) Spillovers, stratification and inequality. Eur Econ Rev 38(3–4):836–845CrossRefGoogle Scholar
  10. Durlauf SN (1997) Statistical mechanics approaches to socioeconomic behaviour. In: Arthur BW, Durlauf SN, Lane DA (eds) The economy as an evolving complex system II. Addison-Wesley, Reading, MA, pp 81–104Google Scholar
  11. Fujita M, Krugman P, Venables A (1999) The spatial economy: cities, regions and international trade. MIT Press, Cambridge, MAGoogle Scholar
  12. Glaeser EL, Sacerdote B, Scheinkman J (1996) Crime and social interactions. Quart J Econ 111(2):507–548CrossRefGoogle Scholar
  13. Hansen LP, Heaton J, Yaron A (1996) Finite sample properties of some alternative GMM estimators. J Bus Econ Stat 14(3):262–280Google Scholar
  14. Imbens GW (1997) One-step estimators for over-identified generalized method of moments models. Rev Econ Stud 64(3):359–383CrossRefGoogle Scholar
  15. Imbens GW, Spady RH, Johnson P (1998) Information theoretic approaches to inference in moment condition models. Econometrica 66(2):333–358CrossRefGoogle Scholar
  16. Kelejian HH, Prucha IR (1998) A generalized spatial two stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances. J Real Estate Financ Econ 17(1):99–121CrossRefGoogle Scholar
  17. Kim TH, Muller C (2004) Two-stage quantile regression when the first stage is based on quantile regression. Econom J 7(1):218–231CrossRefGoogle Scholar
  18. Kitamura Y (1997) Empirical likelihood methods with weakly dependent processes. Ann Stat 25(5):2084–2102CrossRefGoogle Scholar
  19. Kitamura Y, Stutzer M (1997) An information-theoretic alternative to generalized method of moment’s estimation. Econometrica 65(5):861–874CrossRefGoogle Scholar
  20. Kitamura Y, Tripathi G, Ahn H (2004) Empirical likelihood-based inference in conditional moment restriction models. Econometrica 72(6):1667–1714CrossRefGoogle Scholar
  21. Koenker R (2005) Quantile regression. Econometric society monograph series. Cambridge University Press, CambridgeGoogle Scholar
  22. Koenker R, Bassett G (1978) Regression quantiles. Econometrica 46(1):33–50CrossRefGoogle Scholar
  23. Kostov P (2009) A spatial quantile regression hedonic model of agricultural land prices. Spat Econ Anal 4(1):53–72CrossRefGoogle Scholar
  24. Kwak D (2010) Implementation of instrumental variable quantile regression (IVQR) methods. Working Paper, Michigan State UniversityGoogle Scholar
  25. Lahiri SN (2003) Resampling methods for dependent data. Springer Series in Statistics. Springer, LondonGoogle Scholar
  26. Lancaster T, Jun SJ (2010) Bayesian quantile regression methods. J Appl Econom 25(2):287–307CrossRefGoogle Scholar
  27. Lee S (2007) Endogeneity in quantile regression models: a control function approach. J Econom 141(2):1131–1158CrossRefGoogle Scholar
  28. LeSage JP, Fischer MM (2008) Spatial growth regressions: model specification, estimation and interpretation. Spat Econ Anal 3(3):275–304CrossRefGoogle Scholar
  29. LeSage JP, Fischer MM (2012) Estimates of the impact of static and dynamic knowledge spillovers on regional factor productivity. Int Reg Sci Rev 35(1):103–127Google Scholar
  30. Newey WK, Smith RJ (2004) Higher order properties of GMM and generalized empirical likelihood estimators. Econometrica 72(1):219–255CrossRefGoogle Scholar
  31. Nordman DJ (2008) A blockwise empirical likelihood for spatial lattice data. Statistica Sinica 18(3):1111–1129Google Scholar
  32. Otsu T (2003) Empirical likelihood for quantile regression, Manuscript, Department of Economics, University of WisconsinGoogle Scholar
  33. Otsu T (2008) Conditional empirical likelihood estimation and inference for quantile regression models. J Econom 142(1):508–538CrossRefGoogle Scholar
  34. Owen A (1988) Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75(2):237–249CrossRefGoogle Scholar
  35. Owen A (1990) Empirical likelihood ratio confidence regions. Ann Stat 18(1):90–120CrossRefGoogle Scholar
  36. Owen A (1991) Empirical likelihood for linear models. Ann Stat 19(4):1725–1747CrossRefGoogle Scholar
  37. Politis DN, Romano JP, Wolf M (1999) Subsampling. Springer, New YorkGoogle Scholar
  38. Qin J, Lawless J (1994) Empirical likelihood and general estimating equation. Ann Stat 22(1):300–325Google Scholar
  39. Ramalho JS (2005) Small sample bias of alternative estimation methods for moment condition models: Monte Carlo evidence for covariance structures. Stud Nonlinear Dynamics Econom 9(1), Art no. 3. http://www.bepress.com/snde/vol9/iss1/art3
  40. Reich BJ, Fuentes M, Dunson DB (2011) Bayesian spatial quantile regression. J Am Statist Assoc 106(493):6–20Google Scholar
  41. Schennach SM (2005) Bayesian exponentially tilted empirical likelihood. Biometrika 92:31–46Google Scholar
  42. Schennach SM (2007) Point estimation with exponentially tilted empirical likelihood. Econometrica 35(2):634–672Google Scholar
  43. Smith RJ (1997) Alternative semi-parametric likelihood approaches to generalized method of moments estimation. Econ J 107(441):503–519Google Scholar
  44. Su L, Yang Z (2011) Instrumental variable quantile estimation of spatial autoregressive models. Working paper, School of Economics, Singapore Management University. Available at http://www.mysmu.edu/faculty/ljsu/Publications/ivqr_sar20110505.pdf, last accessed 5 Sep 2011
  45. Whang Y-J (2006) Smoothed empirical likelihood methods for quantile regression models. Econom Theory 22(2):173–205Google Scholar
  46. Zietz J, Zietz E, Sirmans S (2008) Determinants of house prices: a quantile regression approach. J Real Estate Finance Econ 37(4):317–333Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Lancashire Business SchoolUniversity of Central LancashirePreston, LancashireUK

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