Missing the Mark: House Price Index Accuracy and Mortgage Credit Modeling William Larson*,** with co-authors: Alex Bogin*, William Doerner* George Washington University, September 29, 2016 Federal Housing Finance Agency **The analysis and conclusions are those of the authors and do not
necessarily represent the views of the Federal Housing Finance Agency or the United States. * Summary Appreciation rates often vary for predictable reasons within cities, but precise measurement is difficult. A tension exists between aggregation bias and estimation error.
What index (or indices, or combinations) should be used? What are the consequences of using an inaccurate index? We estimate indices at 8 levels of geographic aggregation, and find patterns of highest fit: ZIP 5 indices in large cities; city indices in small cities; linear combinations may be best. Outline
Motivation House price index construction Muths Equation and the house price gradient New house price indices: stylized facts House price index accuracy Mortgage credit modeling implications
Motivation House price measurement is a challenge: Ideally, homes would be identical and transact every period. Then one could simply construct an average of the transaction prices (as with wheat, oil, or other commodities). Instead, housing is a heterogeneous composite commodity that transacts infrequently. Controlling for heterogeneity requires a large number of transactions.
Infrequent transactions require aggregation over time or geography. Motivation Previous house price measurement: Aggregation is almost exclusively on geographic dimensions. This has given us Case-Shiller, FHFA, CoreLogic, and other city and state HPIs at a quarterly frequency. Appreciation is expected to vary stochastically
within cities. A city index is acceptable in this case. But house price appreciation can also vary for predictable reasons within cities. Then a city index is subject to aggregation bias. Motivation Consequences of inaccurate house price measurement: Poor estimation of prices for individual homes.
Less accurate current loan-to-value ratio estimates for mortgages. Greater difficulty targeting at-risk borrowers through policy. More difficult to conduct impact analysis for stadiums, metro stations, crime, or other policies or events. In general: it limits our ability to use house price measures effectively.
Motivation Why not Zillows Home Value Index or the Census/ACS estimates of median home value? These are value measures. They are only valid as price measures under the strong assumption that average housing quality is identical in every period (i.e. no new construction).
Motivation What we do: In several papers, we are researching what can be done when aggregating transactions over space and time. Daily national house price indices (Chinloy and Larson, work in progress) Annual ZIP-3, ZIP-5, Census Tract, Census Block Group indices (Bogin, Doerner, and Larson , 2016a, 2016b, 2016c)
Many others have created indices of these types, and we benefit greatly from their prior work. See Bollerslev, Patton, and Wang, (2015) for daily HPIs. See Mian and Sufi (2009), Molloy and Shan (2011), and Guerrieri, Hartley, and Hurst (2013), for several recent examples of within-city HPIs. Motivation From Guerrieri, Hartley, and Hurst (2013), footnote
7: The zip code indices are not publicly available. Fiserv, the company overseeing the Case-Shiller index, provided them to us for the purpose of this research project. Unfortunately, we only have the data through 2008 and, as a result, we cannot systematically explore within-city house price patterns during the recent bust. We have been unsuccessful in our attempts to secure the post-2008 data from Fiserv.
Motivation What we do: We construct constant-quality, repeat-sales indices. They are estimated using consistent method and sample data. No imputation or smoothing we only use information within the area and time period in question. They are free and publicly available.
ZIP5 released in May; County (planned) in November. Currently, they are experimental and intended to be ad-hoc releases from the authors and not House Price Index Construction We use the standard repeat-sales method. Bailey, Muth, and Nourse (1963) pioneered the approach
Case and Shiller (1987) added holding period weights Data consist of purchase and refinance mortgages purchased by Fannie Mae and Freddie Mac. 97 million transactions (54 million same-unit pairs) between 1975 and 2015. After filtering out extreme appreciation rates and holding periods less than 1 year, we have 48 million pairs.
House Price Index Construction Suppose the value of a home consists of its property-specific characteristics, implicit prices, and a price level in each period: Assuming characteristics do not change, subtracting two sales of the same unit gives:
House Price Index Construction But a units characteristics may change! We perform 2 pre-filters: Sales within 12 months are excluded Sales where annual average rate of appreciation is >|40%| are excluded FGLS reduces weight on transactions with long holding periods. Despite these adjustments, there may still be
issues, but constant-quality is a necessary assumption in order to compute the index. House Price Index Construction The index is then calculated based on the estimated log-price levels in the FGLS specification: House Price Index Construction To produce an index for an area, we
require 100 paired post-filter transactions. Within the area, HPIs for years prior to the observation of 25 half pairs (either first or second sale) are set to null. Conditional on these criteria, withinsample years with less than 5 HPs are set to null. House Price Index Construction Muths Equation and the SUM
The standard urban model (SUM) of Alonso (1964), Mills (1967) and Muth (1969) is the canonical urban model. Assumes a monocentric city with exogenous employment at the central business district (CBD). Households commute to this center. Households are identical. Muths Equation and the SUM
In equilibrium, households are willing to trade-off housing consumption for reductions in commuting costs, resulting in a downward-sloped price gradient as a function of distance to the CBD. Muths equation gives the bid-rent curve for housing. It is decreasing in slope with t, and is affected by parameters related to desirability of the CBD, . Muths Equation and the SUM
Key takeaways: the iso-utility condition links house prices within all areas of a city, but that as t and change, prices may increase at different, monotonic rates as a function of distance to the CBD. Changes to the supply of housing anywhere in the city affect prices everywhere. Muths Equation and the SUM
Recent empirical literature related to SUM gradients: Robust evidence of increasing desirability of centercity vs suburbs by looking at millennials, education, median home values, etc. Florida (2004), Glaeser, Gottlieb, and Toibo (2012), Edlund, Machado, and Sviachi (2015), Couture and Handbury (2016) Explanations: transportation costs, crime, amenities, preferences for children. No prior study has established steepening price
gradients over a large cross-section of cities dating back to the mid 1980s. New House Price Indices: Stylized Facts New House Price Indices: Stylized Facts New House Price Indices: Stylized
Facts New House Price Indices: Stylized Facts New House Price Indices: Stylized Facts Takeaways: The suburbanization throughout most of the 20th century has reversed. We have
experienced 30 years of sustained increases in relative demand for center-city locations. Sustained price increases occur in the centers of large cities but not small cities. These changes are potentially caused by changes in economic conditions (transportation costs, reductions in crime, rising amenities) or preferences (children). New House Price Indices: Stylized
Facts Questions: We produce indices at a variety of different levels of aggregationwhich should be used: A tension: lower levels of aggregation have lower transaction counts (more estimation error) but less aggregation bias. Where: Large cities show within-city differences in appreciation, but small cities do not. When: Do within-city prices diverge more during
periods of national increases or decreases? At what horizon: Holding periods of 1 year vs later. How might this affect models of mortgage performance? House Price Index Accuracy To evaluate accuracy, we estimate indices using an 80% sample of housing units. For the 20% hold-out sample, we predict a
2nd-sale price based on a 1st sale and a price index path and compute various metrics and statistical tests. House Price Index Accuracy Housing unit ID is in 20% hold-out sample. Transactions for this unit are not
used to calculate index. state: 11 cbsa: 47900 county: 11001 zip3: 200 zip5: 20002 tract:11001008100 blockgrp: 110010081003
House Price Index Accuracy Base metric: Theils U statistic: RMSE1/ RMSE2 U2 ~ F(N-1,N-1) Encompassing tests House Price Index Accuracy House Price Index Accuracy
House Price Index Accuracy House Price Index Accuracy Index encompassing tests: Chong and Hendry (1986), Ericsson and Marquez (1993) Estimate the actual house value as a function of a vector of predicted values.
Insignificant predictions are index encompassed. We attribute negative predictions to high collinearity and classify these as encompassed as well. House Price Index Accuracy House Price Index Accuracy Takeaways: In small cities, use ZIP 5 if available, but
CBSA indices are not statistically different at short horizons. In large cities, use ZIP 5 indices. When national prices are declining, its even more important to use disaggregated indices. Index encompassing tests suggest a linear combination of several indices may offer superior fit. Mortgage Credit Modeling
Implications Predicting mortgage defaults is valuable for policymakers and investors. Of the many determinants (credit score, income, etc.), the ratio of the current mortgage balance to the value of the house is of primary concern. This is called the Current Loan-toValue Ratio, or CLTV
Mortgage Credit Modeling Implications Accurate CLTV calculations require accurate estimates of the value of the house. Korteweg and Sorensen (2016) find city-level indices under-report underwater borrowers by up to 80%. What are the gains from using a more accurate index? Gains may be large: CLTV is an important determinant.
LTV-default relationship is convex. Gains may be small: If true CLTVs are correlated with other measures (current income or employment status, for instance), explanatory power may be captured by the other measures. Mortgage Credit Modeling Implications Competing options credit model: multinomial
logit model with options: make payment, fully pay outstanding balance (pre-pay), or default. Covariates include: Credit score, debt/income, loan purpose, number of borrowers, current UPB, yield curve, CLTV, and FEs for cohort. Model is estimated using an 80% loan sample. Accuracy is calculated using the
20% hold-out sample. Mortgage Credit Modeling Implications Freddie Mac Data: stratified random sample of 35,000 loans per year, with annual observations of loan outcomes between 1999 and 2014. 420,000 loans. 1.7 million loan-year observations.
Mortgage Credit Modeling Implications Mortgage Credit Modeling Implications CLTV effect attenuates with less accurate indices. Mortgage Credit Modeling Implications
Over the entire sample, Census Block through City levels of aggregation are statistically indistinguishable. State and National indices give worse fit. Mortgage Credit Modeling Implications But in center-cities of large cities, a negative relationship exists between aggregation level and fit. Concluding Remarks Estimates suggest a steepening of the
house price gradient over the last 30 years. There are consequences of missing the mark (using the wrong price index). Here, we show that it affects the performance of mortgage credit models. In work in progress, Carrillo and Larson show positive price anomalies at origination are predictors of eventual default and loss-givendefault. Concluding Remarks
Our new indices are freely and publicly available. New possibilities for urban economics and real estate research, allowing us to rely on within-city differences for identification, and measure current loan-to-value ratios much more accurately. Policy applications include targeting distressed borrowers, distributing housing credits, local impact analysis, or creating affordability measures.
Thank you! Sources: with William Doerner and Alex Bogin: Local House Price Dynamics: New Indices and Stylized Facts (2016a) Local House Price Growth Accelerations (2016b) Missing the Mark: House Price Index Accuracy and Mortgage Credit Modeling (2016c)
with Peter Chinloy Housing Market Efficiency, Volatility, and Risk-Adjusted Returns: Evidence from a Daily U.S. House Price Index (work in progress) with Paul Carrillo Transaction Price Anomalies: Mortgage Performance and Price Index Consequences (work in progress) Data are available at http://
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