Semiparametric Model of Hedonic Housing Prices in Japan

• Published date: 01 December 2015
• Author: Chihiro Shimizu,Koji Karato,Oleksandr Movshuk
• DOI: http://doi.org/10.1111/asej.12077
• Date: 01 December 2015

Semiparametric Model of Hedonic Housing

Prices in Japan*

Koji Karato, Oleksandr Movshuk and Chihiro Shimizu

Received 27 August 2013; accepted 26 May 2015

We propose a semiparametric hedonic model of housing prices with nonlinearity in

age and cohort effects. The model avoids the simultaneity problem among age,

cohort and year effects, which is a common problem in linear hedonic models.

Applying the model to housing prices in Tokyo between 1990 and 2008 revealed

significant nonlinearities in both the age and cohort effects, and significant inter-

actions between these effects, with the shape of the age effect differing across

housing cohorts. Estimates of the year effect indicated a declining trend in prices

that was more pronounced compared with those of conventional linear hedonic

models.

Keywords: age effect, cohort effect, generalized additive model, hedonic price

index.

JEL classification codes: C14, R21, R31.

doi: 10.1111/asej.12077

I. Introduction

Japan experienced a dramatic decline in housing prices following the collapse of

the bubble economy in the early 1990s. Recently, the revival of the moribund

housing market has become an important policy goal of the Japanese Govern-

ment, particularly in a set of policy measures of Prime Minister Abe, which are

also known as ‘Abenomics’. The key goals of Abenomics can be summarized as

follows: (i) fiscal stimulus; (ii) more aggressive monetary easing by the Bank of

Japan; and (iii) various structural reforms to boost the competitiveness of the

Japanese economy. By applying aggressive monetary policy, the government

aimed to stimulate domestic demand, mainly through the wealth effect from rising

asset prices, including stock market, real estate and land prices.

Abenomics has been particularly successful in the revival of stock market

prices. In addition, the Bank of Japan has aggressively purchased government

debt, aiming to reduce long-term interest rates. This, in turn, should lower Japan’s

mortgage rates, and stimulate the real estate demand. The effect on long-term

mortgage rates has already been noticeable, with major Japanese banks offering

* Karato: Faculty of Economics, University of Toyama, 3190 Gofuku, Toyama 930-8555, Japan.

Movshuk (corresponding author): Faculty of Economics, University of Toyama, 3190 Gofuku,

Toyama 930-8555, Japan. Email: movshuk@eco.u-toyama.ac.jp. Shimizu: Institute of Real Estate

Studies, National University of Singapore, 21 Heng Mui Keng Terrace,#04-02, 119613, Singapore.

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35-year fixed mortgages (so-called ‘Flat 35’ loans) at only 1.6–1.9 percent in May

2015 (Japan Housing Finance Agency, 2015).

As for the revival of Japan’s real estate market, it could be judged by hedonic

price indices that adjust for quality differences across houses (such as housing age,

land area, location and similar factors). In practice, the impacts of quality factors are

estimated using various hedonic models for housing prices, and the hedonic price

index is obtained after accounting for the impact of the quality differences on prices.

Hedonic models of housing prices commonly include three time-related

factors: age of house, time of sale, and cohort or year of construction. Perfect

collinearity exists between these time, age and cohort terms because the year

during which the house is sold equals the age of the house plus the construction

year.1This identification problem results in the multicollinearity among indepen-

dent variables when the model is estimated.

This paper addresses the simultaneity problem by estimating the time, age and

cohort effects using a nonparametric generalized additive model that allows for

nonlinearity in the age and cohort effects. To break the collinearity, the typical solution

is to omit either the age or cohort effect. Another solution is provided by nonlinearizing

these variables in the functional form of the ‘parametric’ regression model. However,

nonlinearizing may not perfectly solve the problem and may leave a high correlation

among year of sale, age of house and year of construction. Furthermore, the functional

form that should be used to specify the cohort effect is unclear.

As an alternative method, Coulson and McMillen (2008) disentangle the year,

age and cohort effects on housing price using the second difference approach of

McKenzie (2006). This method allows for simultaneous unrestricted estimations

of the age, time of sale and cohort effects. As a nonparametric estimator, it

removes the problem of imposing structure on a model when little information

exists on likely functional forms. The only restriction to this method is that some

two-neighboring age effects are equal to some known constant, which in practice

is set to zero. However, having too many alternative restrictions on the neigh-

boring parameters of the age, cohort and year effects is common. Fu (2008)

reports evidence that the estimates can be dramatically changed with different

combinations of neighboring effects that are assumed to be equal.

Compared with these previous studies, our paper makes three major contribu-

tions. First, we propose a different solution to the identification problem, with a

relatively mild restriction for the age effect, and the unrestricted cohort and year

effects. Specifically, we assume that the age effect is represented by a smooth

nonlinear function, which we estimated using a nonparametric effect in a

semiparametric regression model2. Second, by specifying a nonparametric age

effect, we were able to keep all three major effects on housing in the same model,

1 In other words, time of sale =housing age +housing cohort.

2 We choose nonlinear age effects not just for solving the perfect multicollinearity among age,

cohort and period effects. Another reason was the lack of theoretical justification for a particular

functional form of the age effect, and we considered the nonlinear specification to be flexible enough

to capture the essentially unknown effect of age on housing prices.

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