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17-09-2022

Non-linear structures, chaos, and bubbles in U.S. regional housing markets

Authors: Benjamas Jirasakuldech, Riza Emekter, Thuy Bui

Published in: Journal of Economics and Finance

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Abstract

This study analyzes the nonlinear price pattern and its underlying source of nonlinearity for U.S. housing markets along with the plausible explanations of chaos and bubble-like characteristics during 1987 to 2019. The results from the BDS test show evidence of nonlinear dependence in overall U.S. housing markets along with home markets in twenty cities. The K-map Z-map analysis shows that nonlinear dependence in all cities is consistent with chaotic behavior. The nonlinear dependence is also substantiated with the use of Markov chain test where nonlinearity is due to the persistence of either positive or negative returns. Applying the duration dependence test on positive runs confirms that housing markets in all five regions experience some episodes of bubbles, except for home markets in Detroit and Minneapolis in Midwest region. A time reversibility test further provides supporting evidence that the mechanism generating nonlinear dependence in housing markets in all four cities in Midwest region comes from non-Gaussian innovations. Similar finding is reported in housing markets in other regions including Atlanta, Charlotte, Dallas, San Diego, and San Francisco, suggesting that a linear function with non-Gaussian error terms is appropriate for modelling these housing markets.
Footnotes
1
According to Devaney (1989), chaos process has three conditions. The chaos dynamics are highly dependent on the initial starting point and topologically transitive with many periodic orbits close to each other.
 
2
The study period for K-map and Z-map analysis is different from other tests due to the limited data on economic condition index variable. The study period runs from February 1990 to March 2019 for all cities except for Detroit (1991:01), Atlanta (1991:01), and Dallas (2000:01).
 
3
The 15 variables used in economic condition index calculation include average weekly hours worked, unemployment rate, all goods-producing employees, all private service-producing employees, all government employees, real average hourly earnings, construction permits for new private residential buildings, real average quarterly wages per employee, total real personal income per capita, industrial availability rate, office vacancy rate, return on average assets, net interest margin, loan loss reserve ratio, and gross metropolitan product.
 
4
As indicated by Evans (1991), the finding of bubble could be the result of omitting the important fundamental variables. Therefore, the empirical results from the use of cointegration test for bubbles is questionable as it is subject to testing joint null hypothesis of bubbles and model specification.
 
5
Prior studies implemented duration dependence technique include Jirasakuldech et al. (2006), Lehkonen (2010), Emekter et al. (2012), Nartea and Cheema (2014), Nartea et al. (2017), and Watanapalachaikul (2021).
 
6
The standard deviations of housing returns for 20 cities in our study are about 82%. However, if we average the returns of housing in 20 cities across each month, the standard deviation is reduced to 61%, which is close to standard deviation of U.S. National Home Price Index of 65%. This verifies that standard deviation decreases significantly in aggregate data, which can be attributable to the loss of information when data is aggregated. This is expected because the correlations among home price indexes from different cities are not perfectly positive. The highest correlation between home price index of Los Angeles and San Diego is 0.88, while the average correlation of home price index is 0.51 between two random cities.
 
7
The duration dependence showed a negative hazard rate in negative runs across all cities except for Denver, CO and San Francisco, CA, suggesting that negative returns tend to persist. This result substantiated the findings of persistence in negative returns by Markov Chain test. To conserve space, the results are available from authors upon request.
 
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Metadata
Title
Non-linear structures, chaos, and bubbles in U.S. regional housing markets
Authors
Benjamas Jirasakuldech
Riza Emekter
Thuy Bui
Publication date
17-09-2022
Publisher
Springer US
Published in
Journal of Economics and Finance
Print ISSN: 1055-0925
Electronic ISSN: 1938-9744
DOI
https://doi.org/10.1007/s12197-022-09598-4

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