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Regional Housing Prices in the USA: An Empirical Investigation of Nonlinearity

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Abstract

Existing literature on housing prices is predominantly in a linear framework, and an important question that has not been addressed is whether housing prices exhibit nonlinearity. We examine Smooth Transition Autoregressive (STAR) model based nonlinear properties of housing prices over the 1969–2004 period for the entire US and the four regions. Our main findings are (1) housing price for the entire US and all regions except for the Midwest show non-linearity, (2) the dynamic properties implied by the nonlinear estimation explain the typical patterns that have characterized each housing market, and (3) results of Granger causality tests look more plausible in the nonlinear framework where we find stronger evidence of Granger causality from housing price to employment and also from mortgage rates to housing price.

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Notes

  1. McHugh et al. (2004). “A Smooth-Transition Model of the Australian Unemployment Rate.” Retrieved from the world wide web at http://www.svt.ntnu.no/iso/WP/2002/10ausu.pdf.

  2. Seslen, T. (2004). “Housing Price Dynamics and Household Mobility Decisions.” Retrieved from the world wide web at http://www.usc.edu/schools/sppd/lusk/research/pdf/wp_2005.

  3. For example, Tversky and Kahneman (1991).

  4. This steeper rise and milder fall also holds in real terms (Abraham and Hendershcott 1996; Angell and Williams 2005, please see footnote 5).

  5. Angell and Williams (2005). “Home Prices: Does Bust Always Follow Boom?” Retrieved from the world wide web at http://www.fdic.gov/bank/analytical/fyi/2005/050205fyi_table1.pdf.

  6. We use the growth rate of housing price so that r t will be stationary.

  7. Engelhardt (2001) shows that households can lever nominal capital gains to purchase larger homes, but they became constrained by nominal capital losses.

  8. See Teräsvirta and Anderson (1992), Sarantis (2001) and the references therein for a similar transformation of various macro time series.

  9. Results of the unit root tests are not reported for the sake of brevity and may be obtained from the first author.

  10. It should be noted that if \(H_{02} :\phi _{2i} = 0\,given\,\phi _{3i} = \phi _{4i} = 0\) is accepted then it implies that the hypothesis of linearity is accepted, implying that the linear AR model is appropriate.

  11. We perform Ljung Box and ARCH-LM tests to check for misspecification. These results, which can be available from the authors on request, indicate no evidence of misspecification.

  12. In the case of explosive roots, the modulus of the root is greater than 1.

  13. The outer regime in all cases includes roots with modulus values that are as low as 0.8, but are not reported in Table 7 for the sake of brevity.

  14. Housing at the Tipping Point (2006), Moody’s Economy.com.

  15. Under the null, the test statistic has an F-distribution with degrees of freedom \({{q\left( {q + 1} \right)} \mathord{\left/ {\vphantom {{q\left( {q + 1} \right)} {2 + 2q}}} \right. \kern-\nulldelimiterspace} {2 + 2q}}\) in the numerator and \({{{\text{T}} - n - q\left( {q + 1} \right)} \mathord{\left/ {\vphantom {{{\text{T}} - n - q\left( {q + 1} \right)} {2 - 2q}}} \right. \kern-\nulldelimiterspace} {2 - 2q}}\) in the denominator, where T is the number of observatiuns and n is the dimension of the gradient vector, y t-i , y t-i y t-j , and \(y_{t - i}^3 ,\).

  16. The nonlinear estimation results on regional employment are available on request from the first author.

  17. We were not able to break down the testing of the Ganger causality results into sub periods of economic booms and recessions because the method of testing for nonlinearity calls for large data sets.

  18. When the variable y Granger causes variable r, the sum of significant coefficients (the θs below) of the “causing” variable (y) shows ‘net effect of y on r’. In the following equation for the Granger causality test, the sum of θs represents the size of net effect from y to r. \(r_t = \left[ {\phi _0 + \sum\limits_{i = 1}^p {\phi _i r_{t - i} } } \right] + \left[ {\theta _0 + \sum\limits_{i = 1}^q {\theta _i y_{t - i} } } \right] + \varepsilon _t \) Details of the Granger causality estimation can be obtained from the first author on request.

  19. This does not imply that employment is not an important determinant of home prices, but only that this relationship may not be evident in the short run.

  20. The mortgage rate data is available from April 1972 onwards only.

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Authors and Affiliations

  1. Department of Economics, Ewha Womans University, Seoul, Korea

    Sei-Wan Kim

  2. Department of Economics, California State University at Fullerton, Fullerton, CA, 92834, USA

    Radha Bhattacharya

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  1. Sei-Wan Kim
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  2. Radha Bhattacharya
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Correspondence to Radha Bhattacharya.

Appendix

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Table 8 Definitions of Regions
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Kim, SW., Bhattacharya, R. Regional Housing Prices in the USA: An Empirical Investigation of Nonlinearity. J Real Estate Finan Econ 38, 443–460 (2009). https://doi.org/10.1007/s11146-007-9094-y

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