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Modeling House Prices using Multilevel Structured Additive Regression

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  • Wolfgang Brunauer

    ()

  • Stefan Lang

    ()

  • Nikolaus Umlauf

    ()

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    Abstract

    This paper analyzes house price data belonging to three hierarchical levels of spatial units. House selling prices with associated individual attributes (the elementary level-1) are grouped within municipalities (level-2), which form districts (level-3), which are themselves nested in counties (level-4). Additionally to individual attributes, explanatory covariates with possibly nonlinear effects are available on two of these spatial resolutions. We apply a multilevel version of structured additive regression (STAR) models to regress house prices on individual attributes and locational neighborhood characteristics in a four level hierarchical model. In multilevel STAR models the regression coefficients of a particular nonlinear term may themselves obey a regression model with structured additive predictor. The framework thus allows to incorporate nonlinear covariate effects and time trends, smooth spatial effects and complex interactions at every level of the hierarchy of the multilevel model. Moreover we are able to decompose the spatial heterogeneity effect and investigate its magnitude at different spatial resolutions allowing for improved predictive quality even in the case of unobserved spatial units. Statistical inference is fully Bayesian and based on highly efficient Markov chain Monte Carlo simulation techniques that take advantage of the hierarchical structure in the data.

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    File URL: http://eeecon.uibk.ac.at/wopec2/repec/inn/wpaper/2010-19.pdf
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    Bibliographic Info

    Paper provided by Faculty of Economics and Statistics, University of Innsbruck in its series Working Papers with number 2010-19.

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    Length: 29
    Date of creation: Jul 2010
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    Handle: RePEc:inn:wpaper:2010-19

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    Keywords: Bayesian hierarchical models; hedonic pricing models; multilevel models; MCMC; P-splines;

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    References

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    1. Carlos Martins-Filho & Okmyung Bin, 2005. "Estimation of hedonic price functions via additive nonparametric regression," Empirical Economics, Springer, Springer, vol. 30(1), pages 93-114, January.
    2. Andrea M. Leiter & Gerald J. Pruckner, . "Proportionality of willingness to pay to small changes in risk - The impact of attitudinal factors in scope tests," Working Papers, Faculty of Economics and Statistics, University of Innsbruck 2007-30, Faculty of Economics and Statistics, University of Innsbruck.
    3. Frühwirth-Schnatter, Sylvia & Wagner, Helga, 2010. "Stochastic model specification search for Gaussian and partial non-Gaussian state space models," Journal of Econometrics, Elsevier, Elsevier, vol. 154(1), pages 85-100, January.
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