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Nonlinearity of housing price structure: Assessment of three approaches to nonlinearity in the previously owned condominium market of Tokyo

Chihiro Shimizu (Department of Economics, Reitaku University, Kashiwa, Japan)
Koji Karato (Faculty of Economics, University of Toyama, Toyama, Japan)
Kiyohiko Nishimura (Department of Economics, University of Tokyo, Tokyo, Japan)

International Journal of Housing Markets and Analysis

ISSN: 1753-8270

Article publication date: 30 September 2014




The purpose of this article, starting from linear regression, was to estimate a switching regression model, nonparametric model and generalized additive model as a semi-parametric model, perform function estimation with multiple nonlinear estimation methods and conduct comparative analysis of their predictive accuracy. The theoretical importance of estimating hedonic functions using a nonlinear function form has been pointed out in ample previous research (e.g. Heckman et al. (2010).


The distinctive features of this study include not only our estimation of multiple nonlinear model function forms but also the method of verifying predictive accuracy. Using out-of-sample testing, we predicted and verified predictive accuracy by performing random sampling 500 times without replacement for 9,682 data items (the same number used in model estimation), based on data for the years before and after the year used for model estimation.


As a result of estimating multiple models, we believe that when it comes to hedonic function estimation, nonlinear models are superior based on the strength of predictive accuracy viewed in statistical terms and on graphic comparisons. However, when we examined predictive accuracy using out-of-sample testing, we found that the predictive accuracy was inferior to linear models for all nonlinear models.

Research limitations/implications

In terms of the reason why the predictive accuracy was inferior, it is possible that there was an overfitting in the function estimation. Because this research was conducted for a specific period of time, it needs to be developed by expanding it to multiple periods over which the market fluctuates dynamically and conducting further analysis.

Practical implications

Many studies compare predictive accuracy by separating the estimation model and verification model using data at the same point in time. However, when attempting practical application for auto-appraisal systems and the like, it is necessary to estimate a model using past data and make predictions with respect to current transactions. It is possible to apply this study to auto-appraisal systems.

Social implications

It is recognized that housing price fluctuations caused by the subprime crisis had a massive impact on the financial system. The findings of this study are expected to serve as a tool for measuring housing price fluctuation risks in the financial system.


While the importance of nonlinear estimation when estimating hedonic functions has been pointed out in theoretical terms, there is a noticeable lag when it comes to testing based on actual data. Given this, we believe that our verification of nonlinear estimation’s validity using multiple nonlinear models is significant not just from an academic perspective – it may also have practical applications.



Shimizu, C., Karato, K. and Nishimura, K. (2014), "Nonlinearity of housing price structure: Assessment of three approaches to nonlinearity in the previously owned condominium market of Tokyo", International Journal of Housing Markets and Analysis, Vol. 7 No. 4, pp. 459-488.



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