Abstract
This paper is motivated by two common challenges in hedonic price modeling: nonlinear price functions, which require flexible modeling approaches, and the inherent spatial heterogeneity in real estate markets. We apply additive mixed regression models (AMM) to estimate hedonic price equations for rents in Vienna. Non-linear effects of continuous covariates as well as a smooth time trend are modeled non-parametrically through P-splines. Unobserved district-specific heterogeneity is modeled in two ways: First, by location specific intercepts with the postal code serving as a location variable. Second, in order to permit spatial variation in the nonlinear price gradients, we introduce multiplicative scaling factors for nonlinear covariates. This allows highly nonlinear implicit price functions to vary within a regularized framework, accounting for district-specific spatial heterogeneity, which leads to a considerable improvement of model quality and predictive power. Our findings provide insight into the spatially heterogeneous structure of price gradients in Vienna, showing substantial spatial variation. Accounting for spatial heterogeneity in a very general way, this approach permits higher accuracy in prediction and allows for location-specific nonlinear rent index construction.
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References
Anglin, P., & Gençay, R. (1996). Semiparametric estimation of a hedonic price function. Journal of Applied Econometrics, 11(6), 633–648.
Anselin, L. (1988). Spatial econometrics: Methods and models. Dordrecht: Kluwer.
Anselin, L. (2003). Spatial externalities, spatial multipliers and spatial econometrics. International Regional Science Review, 26, 153–166.
Anselin, L., Florax, R., & Rey, S. (2004). Advances in spatial econometrics: Methodology, tools and applications (Advances in Spatial Sciences). Berlin: Springer.
Basu, S., & Thibodeau, T. (1998). Analysis of spatial autocorrelation in house prices. Journal of Real Estate Finance and Economics, 17(1), 61–85.
Besag, J., & Kooperberg, C. (1995). On conditional and intrinsic autoregressions. Biometrika, 82, 733–746.
Brezger, A., & Lang, S. (2006). Generalized structured additive regression based on Bayesian P-splines. Computational Statistics and Data Analysis, 50, 967–991.
Brezger, A., Kneib, T., & Lang, S. (2005a). Bayesx: analyzing Bayesian structured additive regression models. Journal of Statistical Software, 14, 1–22.
Brezger, A., Kneib, T., Lang, S. (2005b). Bayesx manuals. Technical Report, Department of Statistics, University of Munich. Available at: http://www.stat.uni-muenchen.de/~bayesx.
Clapp, J. M. (2003). A semiparametric method for valuing residential locations: application to automated valuation. Journal of Real Estate Finance and Economics, 27(3), 303–320.
Clapp, J. M. (2004). A semiparametric method for estimating local house price indices. Real Estate Economics, 32(1), 127–160.
Clapp, J. M., Kim, H.-J., & Gelfand, A. E. (2002). Predicting spatial patterns of house prices using LPR and Bayesian smoothing. Real Estate Economics, 30(4), 505–532.
Court, A. T. (1939). Hedonic price indexes with automotive examples. The Dynamics of Automobile Demand. New York: General Motors.
De Boor, C. (2001). A practical guide to splines. New York: Springer.
Diggle, P. J., & Ribeiro, P. J. (2007). Model-based geostatistics. New York: Springer.
Eilers, P., & Marx, B. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11(2), 89–121.
Fahrmeir, L., Kneib, T., & Lang, S. (2004). Penalized additive regression for space-time data: a Bayesian perspective. Statistica Sinica, 14, 731–761.
Fahrmeir, L., Kneib, T., & Lang, S. (2007). Regression. Modelle, Methoden und Anwendungen. Berlin: Springer.
Follain, J., & Jimenez, E. (1985). Estimating the demand for housing characteristics: a survey and critique. Regional Science and Urban Economics, 15(1), 77–107.
Fotheringham, A. S., Brundson, C., & Charlton, M. E. (2002). Geographically weighted regression: The analysis of spatially varying relationships. Chichester: Wiley.
Griliches, Z. (1971). Price indexes and quality change: Studies in new methods of measurement. Cambridge, MA: Harvard University Press.
Kamman, E. E., & Wand, M. P. (2003). Geoadditive models. Journal of the Royal Statistical Society C, 52, 1–18.
Lancaster, K. (1966). A new approach to consumer theory. Journal of Political Economy, 74, 132–157.
Lang, S., & Brezger, A. (2004). Bayesian P-Splines. Journal of Computational and Graphical Statistics, 13, 183–212.
LeSage, J. P. (1999). The theory and practice of spatial econometrics. University of Toledo: Unpublished Manuscript.
LeSage, J. P., & Pace, R. K. (eds). (2004). Spatial and spatiotemporal econometrics (Advances in Econometrics). Oxford: Elsevier.
Malpezzi, S. (2002). Hedonic pricing models: A selective and applied review. Prepared for: Housing Economics: Essays in Honor of Duncan Maclennan.
Martins-Filho, C., & Bin, O. (2005). Estimation of hedonic price functions via additive nonparametric regression. Empirical Economics, 30, 93–114.
Mason, C., & Quigley, J. M. (1996). Non-parametric hedonic housing prices. Housing Studies, 11(3), 373–385.
McMillen, D. P. (2003). Spatial autocorrelation or misspecification? International Regional Science Review, 26, 591–612.
MRG. (1981). Bundesgesetz vom 12. November 1981 über das Mietrecht – MRG. BGBI. Nr. 520/1981 i.d.F. BGBI. Nr. I/124/2006.
Pace, R. K. (1995). Hedonic prices and public goods: an argument for weighting locational attributes in hedonic regressions by lot size. Journal of Urban Economics, 12, 177–201.
Pace, R. K. (1998). Appraisal using generalized additive models. Journal of Real Estate Research, 15, 77–99.
Parmeter, C. F., Henderson, D. J., & Kumbhakar, S. C. (2007). Nonparametric estimation of a hedonic price function. Journal of Applied Econometrics, 22(3), 695–699.
Rosen, S. (1974). Hedonic prices and implicit markets: product differentiation in pure competition. Journal of Political Economy, 82(1), 34–55.
Ruppert, D., Wand, M.P. and Carroll, R.J. (2003). Semiparametric regression. Cambridge University Press.
Sheppard, S. (1999). Hedonic analysis of housing markets. In: Paul C. Chesire and Edwin S. Mills (eds.). Handbook of Regional and Urban Economics, 3, 1595–1635.
Sirmans, G., Macpherson, D., & Zietz, E. (2005). The composition of hedonic pricing models. Journal of Real Estate Literature, 13(1), 3–43.
Wallace, N. (1996). Hedonic-based price indexes for housing: theory, estimation, and index construction. Federal Reserve Bank of San Francisco Economic Review, 3, 34–48.
Wood, S. (2006a). An Introduction to Generalized Additive Models with R. Taylor & Francis Ltd.
Wood, S. (2006b). Low-Rank scale-invariant tensor product smooths for generalized additive mixed models. Biometrics, 62(4), 1025–1036.
Wood, S. N., Bravington, M. V., & Hedley, S. L. (2008). Soap film smoothing. Journal of the Royal Statistical Society B, 70(5), 931–955.
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We gratefully acknowledge the financial support by Tiroler Wissenschaftsfonds (TWF) and thank the ERES NETconsulting-Immobilien.NET GmbH for the provision of the data.
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Brunauer, W.A., Lang, S., Wechselberger, P. et al. Additive Hedonic Regression Models with Spatial Scaling Factors: An Application for Rents in Vienna. J Real Estate Finan Econ 41, 390–411 (2010). https://doi.org/10.1007/s11146-009-9177-z
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DOI: https://doi.org/10.1007/s11146-009-9177-z