Housing Price Cycle Interdependencies and Comovement: A Markov-Switching Approach

Abstract

This paper uses a Markov-switching approach to examine why there is house price cycle comovement across some U.S. metropolitan areas (MSAs) but not others, and which MSAs cluster together for each of these reasons. Past studies have attributed common housing downturns in different regions as possible explanations for comovement. We explore other channels, and find some clusters based on common industry concentration (such as information technology), house price elasticity, as well as a cluster of MSAs that are desirable for retirees (in the sun belt). We find seven clusters of MSAs, where each cluster experiences idiosyncratic house price downturns, plus one distinct national house price cycle. Notably, only the housing downturn associated with the Great Recession spread across all the MSAs in our sample; all other house price downturns remained contained to a single cluster. We also identify MSA economic and geographic characteristics that correlate with housing price cluster membership, which implies comovement due to mobility of residents. In addition, while prior research has found housing and business cycles to be related closely at the national level, we find very different house price comovement and employment comovement across clusters and across MSAs.

Keywords:

• Housing price cycles
• comovement
• Markov-switching
• spatial dependence

JEL CODES:

• R30
• C3

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Although used in a different context than in our paper, the concept of regional clusters in some industries was used in Hamilton and Owyang (2012).

2 See, for example, Cohen (2010).

3 See Leamer (2015) for discussion of the “volume cycle” and the “price cycle”.

4 The Hamilton and Owyang (2012) Markov-switching model is a prime example of the basis of our generalization.

5 See: https://www.pewtrusts.org/en/research-and-analysis/blogs/stateline/2022/07/22/investors-bought-a-quarter-of-homes-sold-last-year-driving-up-rents (accessed 3/4/2023).

6 Another related paper focused on MSAs, is by Arias et al. (2016). Based on a dynamic factor model, they highlight the heterogeneity of business cycles at the metropolitan level. In a related paper, Owyang et al. (2013) find much heterogeneity in employment cycles across 57 large U.S. cities.

7 A voluminous literature exists with Dubin (1988) and Can (1992) are frequently cited as the first papers to apply spatial econometric techniques in the context of real estate prices. More recently, Baltagi et al. (2014), Baltagi and Bresson (2011), Besner (2002), and Basu and Thibodeau (1998) developed more rigorous approaches to estimate spatial econometrics in the context of hedonic housing price models.

8 In contrast, Wong et al. (2013), using spatial econometric techniques, argue that the price discovery process is the economic explanation for the spatially correlated prices of Hong Kong apartments.

9 Fischer et al. (2021) focus on comovement at a very micro level (the New York City borough of Manhattan) and find that comovement is very local over the period of 2004-2015.

10 For a recent example of the latter, see Cohen and Zabel (2020).

11 Closely related to studies on comovement are studies on long-run convergence. One recent example is Barros et al. (2012). Using U.S. state housing price indices and overall U.S. housing prices and fractional integration and cointegration techniques, they raise doubts about long-run convergence in U.S. state housing prices and the presence of the ripple effect. On the other hand, Holmes et al. (2011) focus on long-run convergence across states and MSAs. Using pairwise unit root rejections, they find evidence supporting long-run convergence, with a speed of adjustment inversely related to distance.

12 They identified a number of other cross-country studies that have explored the impact of synchronized monetary policy, integrated financial markets, financial liberalization, and global business cycle linkages on the comovement of house prices.

13 The role of housing in business cycles is analyzed by Álvarez et al. (2009). They found that GDP cycles among Germany, France, Italy, and Spain showed a high degree of comovement, much higher than the comovement of housing prices.

14 See Apergis and Payne (2012) for an extensive list of references exploring convergence in regional housing markets outside the United States, frequently in the United Kingdom.

15 This model assumes constant transition probabilities across time. Francis et al. (2022) allows various global shocks to influence the transition probabilities, so they are time varying. Because our study is primarily on which entities comove and not on the proximate shocks causing common downturns, we opted for the more parsimonious framework of constant transition probabilities.

16 Francis et al. (2022) show that this assumption can be loosened by estimating the full covariance matrix using the method outlined by Carriero et al. (2019), but the full covariance model is dominated by our more parsimonious framework due to substantially fewer parameters and more intuitive cluster compositions.

17 See Hamilton and Owyang (2012).

18 The approach we follow below parallels Hamilton and Owyang (2012) and Frühwirth-Schnatter and Kaufmann (2008).

19 To maintain comparability to Hamilton and Owyang (2012), autoregressive terms of $y$ were left out of the model. However, the model could be further generalized to allow for AR terms on the right-hand-side.

20 Full sample statistics for the house price data are available from the authors upon request. The mean of the growth rates for each MSA are approximately in the range of 1% to 6% per quarter. MSAs on the higher end include Los Angeles (6.66%) and San Francisco (7.09%), with the lower end being comprised of Toledo, OH (2.7%) and Youngstown, OH (3.04%). MSAs with the highest standard deviation of house price growth include those in California, Florida, and Nevada. On the other hand, the most stable markets include those in the Midwest and South (such as Columbus, OH and Chattanooga, TN).

21 See https://www.nber.org/cycles.html.

22 We should note that this refers to the model’s regime of “national house-price expansion” when all MSAs are jointly in an expansion state. We acknowledge the difference with the more common usage of national expansion wherein most MSAs are in expansion, but not all. This state is similar to the “idiosyncratic cluster recession” where a downturn is isolated to a specific set of MSAs.

23 Full results (e.g., parameter estimates, cluster membership, etc.) for the model with a population spatial similarity matrix are available from the authors upon request.

24 Note that this assumption is necessary for identification and is arbitrary. Any other cluster could be the reference cluster and the results would be unchanged.

25 A helpful referee suggested we try including a control for whether or not an MSA was a “coastal” city. We tried this and found the coastal variable was insignificant for all clusters except for Cluster 2. That cluster consists of several MSAs in Tennessee, which does not seem to correlate with coastal locations. Therefore, we decided not to include a control for coastal cities in the results in Table 7.

26 See Leamer (2007, 2015) and Hernández-Murillo et al. (2017), among others.

27 Our finding also differs from Hernández-Murillo et al. (2017), who conclude that the national cycle for housing starts mimics the NBER recession dates for economic activity.

28 We should note a number of caveats. The first is that cluster membership is held constant throughout the entire sample. Allowing for time-varying cluster membership would capture interesting changes in house price linkages between MSAs across time. Second, our framework uses simple fixed transition probabilities. Future work could include macroeconomic (or even regional) shocks in a time-varying transition probability framework as in Francis et al. (2022) to diagnose the proximate causes of aggregate or regional downturns.