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Open Access 23-12-2017

# Local House Price Paths: Accelerations, Declines, and Recoveries

Authors: Alexander N. Bogin, William M. Doerner, William D. Larson

## Abstract

Mortgage credit risk measurement hinges on the choice of a house price stress path, which is used to project loan losses and determine financial capital requirements. House price paths are commonly constructed at national or state levels and shock scenarios are created to mimic historical adverse market conditions. We provide evidence that this level of geographic aggregation is not granular enough in many cases—collateral risk often varies within cities. Using local house price indices that cover the United States from 1975 to 2016, we focus on house price performance in the years immediately following sustained periods of rapid acceleration. Price accelerations tend to exhibit temporal clustering and occur with greater frequency in large versus small cities. We exploit within-city variation in price dynamics to provide evidence that price initially overshoot sustainable levels but, in some areas, dynamics may reflect positive underlying economic fundamentals and can be sustained. After accelerating, price reach their trough after 4 or 5 years. Small cities show uniform declines whereas large cities exhibit greater price decreases farther away from city centers. These findings suggest differential collateral risk exists in large cities, financial losses can be predictable based on real estate location theory, and localized house price paths could aid credit risk management.

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Footnotes
1
After last decade’s crisis and the passage of the Dodd-Frank Wall Street Reform and Consumer Protection Act, large banks and regulated financial institutions have been required to estimate capital sufficiency using scenarios provided by the Federal Reserve Board as part of their annual Comprehensive Capital Analysis and Review (CCAR) report. These scenarios include a national house price stress path which is based upon the historical decline between 2007 and 2009. Recent press release announcements suggest that a more dynamic methodology might be used in the future.

2
Both Mian and Sufi (2009) and Guerrieri et al. (2013) rely on data from the Case-Shiller ZIP code-level house price indices. This data series is proprietary and begins in the late 1980s, with coverage including 1498 ZIP codes beginning in 1990 (see Column 3 of Table 2 in Guerrieri et al. 2013). The data used in our study is the Bogin et al. (2017) dataset, which is publicly available and spans nearly six times as many ZIP codes beginning in 1990 (nearly 9000). This dataset has coverage dating back to the mid-1980s, with over 4400 beginning before 1980 and over 6000 before 1985, making it ideal to study within-city house price cycles over a 40 year period. It was first released in May 2016 and updated with new data in February 2017.

3
Following the seminal results of Case and Shiller (1989), Glaeser et al. (2014) find that a $1 increase in house price is correlated with a$0.60 to $0.80 price increase the following year, but a$0.16 to \$0.28 price decline over the next five years.

4
House price paths have important practical uses for financial valuation. To provide a few examples, portfolio managers might need to know how quickly house price could accelerate to determine interest rate risk from prepayments or to place non-housing investments in shorter-term durations to later purchase more mortgage assets, modelers might be interested in how far house price could fall to compute potential losses and either sell off certain risky assets or purchase adequate hedges, or mortgage security issuers might want to know how quickly house price could accelerate to better estimate prepayment speeds that will affect reference pools and trigger events that alter investor payouts and security price.

5
CBSAs are metropolitan and micropolitan geographic areas defined by the White House’s Office of Management and Budget using Census data. We rely on the February 2013 definitions that were revised on July 2015. Nominal price are converted into real terms using the all items consumer price index for all urban consumers produced by the Bureau of Labor Statistics.

6
Robustness tests for these and other criteria are presented in Table 3. The results are qualitatively similar to our primary findings.

7
These measures may be vulnerable to estimation error in the indices during the first or fourth year of the acceleration. This may cause inappropriate classifications of acceleration episodes, and may bias findings towards mean reversion.

8
While these two cases are clearly confounded by contemporaneous economic events, necessitating control variables, they serve to illustrate two of the more common dynamic responses to an acceleration episode.

9
Since it takes 4 years to identify episodes, we drop ZIP codes before 1980 and where the end of the acceleration is undefined. To preserve data observations, the second criterion is not treated as binding in the first 8 years that an index is observed.

10
To focus on unique acceleration episodes, once a ZIP code has been identified as accelerating it cannot be identified again for another 4 years.

11
The CBD ZIP code is calculated as the maximum value within the CBSA of the inverse of the standardized land area plus the standardized share of housing units in 20+ unit structures. Land area data are from the Census’ TIGER line shapefiles, and structure type is from the 1990 Decennial Census, the earliest census for which ZIP code data are available. Distance to the CBD is calculated as the distance between a ZIP code’s centroid and the CBD ZIP code’s centroid.

12
Per a referee’s suggestion, we also created this figure for high regulation and low regulation cities. High regulation, or relatively inelastic, cities exhibit far more acceleration episodes. Low regulation cities, though, have seen a rise in acceleration episodes mainly during last decade’s boom and over the last several years.

13
An exception to this finding is the period between 1999 and 2003, when accelerations are found primarily in the centers of large cities.

14
The SUM of Alonso (1964), Mills (1967), and Muth (1969) assumes that households can freely migrate within a city. This results in a house price gradient within a city as a function of commuting costs, often represented as a function of distance to the CBD. A positive demand shock for housing in a city therefore results in a shift of house price in all areas of the city. The SUM with one household type and linear transportation costs is incompatible with differential appreciation rates within the city because of Muth’s Equation. However, household heterogeneity may give multiple bid rent curves and housing construction in a congested city may cause rotations of the bid-rent curve. Thus, differential dynamics are consistent with simple extensions of the model.

15
We thank a referee for asking about how episodes vary across market elasticities and include Figure 5 as evidence.

16
Davis and Weinstein (2002) examine distinct changes in population demographics in Japan in the years following Allied bombings in World War II. In a similar manner, we adapt their approach to study the after-effects of a rapid appreciation of house price. We deliberately pick out very quick and large price increases because their speed and size suggest a delayed supply response. These appreciation episodes are likely to be transitory as new construction increases and existing stock turns over. The Davis and Weinstein approach is attractive because it studied the mean reversion after such a kind of shock and, with our data, it can offer information about both the amplitude (mean reversion) and frequency (how long it takes to get back to the same level) of house price cycles. Admittedly, house price shocks may not be completely exogenous. We test the robustness of our results against endogeneity concerns and discuss the results in footnote 21.

17
There is a large body of empirical literature on house price as mean-reverting series. This is based on the idea that a bubble exists if a price level is in excess of a long-run price/income ratio (Malpezzi 1999), house price/rental price ratio (Gallin 2006), or a long-run trend (Smith et al. 2015). These studies focus on MSAs or states, implicitly assuming that all submarkets within the region behave in the same manner. While these models may be predictive at the city or state level, they are unable to determine conditions related to differential rates of mean reversion within cities.

18
The table results include interactions of all four location groups with city size for consistency with earlier figures. Some areas, like the exurbs, might seem better defined without the interaction. However, we do find different point estimates and report them to encourage researchers who are interested in the dynamics of rural areas (particularly as that relates to mortgage collateral risk of the USDA and VA).

19
Note that a real decline in house price of 25% over four years will be due, in part, to inflation. Therefore, in periods with positive inflation, nominal price declines are lower. For instance, with an annual average rate of inflation of 2% per year, a real decline of 25% gives a nominal decline of approximately 17%.

20
While the hypothesis β =  − 1 cannot be rejected for most parameters individually, a parsimonious but less illustrative model can reject the null of no effect of distance from the CBD interacted with city size. This model with clustered standard errors by year in parentheses is:
$$\Delta {p}_{t,t+4}={\alpha}_t-3.70(0.32)\Delta {p}_{t-4,t}-0.01(0.01)k-0.07(0.01)n+0.21(0.02)n\Delta {p}_{t-4,t}+0.09(0.03)k\Delta {p}_{t-4,t}-0.009(0.002) nk\Delta {p}_{t-4,t}$$
where n is the log population and k is the log distance to the CBD.

21
Per a referee’s suggestion, we also performed these estimations while instrumenting for post-2000 acceleration episodes using the percentage of subprime borrowers in each ZIP code as of December 1996. Our approach mirrors Mian and Sufi (2011) who use the same instrument to identify exogenous variation in ZIP code-level house price appreciation between 2002 and 2006. Our IV passes all the standard tests and we observe qualitatively similar results between the OLS and 2SLS specifications.

22
Two potential sources of bias should be noted that are both related to estimation error in the house price indices. The first biases results towards the finding of mean reversion, and is due to left-censoring of episodes classified as accelerations. The second biases results towards the finding of permanent effects, and is caused by attenuation in β.

23
This possibility is highlighted by Lee et al. (2015), who develop a model where the house price level is correlated with future appreciation. They argue that a high price level indicates strong current and future expectations of economic fundamentals. In this context, an acceleration in price could represent a permanent shift of housing demand in an area.

24
We caution against interpreting this as large cities having less credit risk or lower severity of predicted losses given default. As we will show later, the post-acceleration decline and recovery of price can vary by location in large cities. A singular shock path might be appropriate for small cities but could grossly overstate or understate the extent of mortgage losses in large cities where price and appreciations are more strongly related to location.

25
The adjustments are described in terms of mean reversion of house price levels because the literature takes that approach. We would prefer to frame these movements as a sinusoidal pattern (although not always symmetric house price have persistence and do not result from independent draws of shocks in each period) where column 3 includes episodes with lower amplitudes and column 6 stretches out the periodicity without also increasing the amplitude. Both effects serve to dampen the waves, leaving smaller average increases to be accompanied by muted decreases, and reducing the absolute magnitudes in the estimated coefficients.

26
The regulation and topography predictions are intuitive at first glance, but the decline prediction may not be. The logic for a lower elasticity of housing supply in a declining area is as follows. Cities in long-run decline often face home values far below the replacement cost of structures. Increases to demand for housing do not often increase the value of the existing housing stock above replacement cost. This demand shock results in limited housing construction, giving a low elasticity of housing supply.

27
Our long-run urban decline index is the standardized change in the aggregate value of the housing stock between 1970 and 1990. Positive values indicate decline. The housing stock value incorporates both price and quantity changes, making the measure both reflective of demand and invariant to differences in the elasticity of housing supply across areas. This is in contrast to quantity measures such as population and housing stock, which fail to identify demand in inelastic areas.

28
Acceleration episodes tend to occur more frequently in inelastic areas, i.e. high regulation or high topographic interruptions. Slightly more acceleration episodes fall in high regulation categories than in high topographic interruption. Comparing between the elasticity measures, over 3/4 of observed episodes fall in both inelastic categories, which results in similar magnitudes and patterns when comparing between those inelastic categories (Columns 2 and 4).

29
As a referee aptly pointed out, unlike their inelastic counterparts, the elastic subsamples exhibit dissimilar results and we believe there are two main causes. First, half as many episodes happen in low regulation areas, which leaves a small sample size and one that is concentrated with post-2000 episodes. Second, the two elastic subsamples flip their distributions across small and large city size—nearly 70% of low regulation areas are in small cities while nearly 70% of low topographic areas are in large cities. This is a stark contrast that is worth noting by researchers and policy makers when considering between elasticity measures.

30
Note this procedure does not impose any functional form or even mean reversion on the house price paths. We alter the dependent variable to different lengths since the peak and then construct time series with the estimated coefficients of different model samples to show the evolution.

31
Panel (d) shows exurbs do not follow traditional patterns for low regulation cities. Future research could explore whether these dynamics are an artifact of a small sample size or unique behavior in those rural areas.

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Title
Local House Price Paths: Accelerations, Declines, and Recoveries
Authors
Alexander N. Bogin
William M. Doerner
William D. Larson
Publication date
23-12-2017
Publisher
Springer US
Published in
The Journal of Real Estate Finance and Economics / Issue 2/2019
Print ISSN: 0895-5638
Electronic ISSN: 1573-045X
DOI
https://doi.org/10.1007/s11146-017-9643-y

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