Price Indices Based on the Hedonic Repeat-Sales Method: Application to the Housing Market

Shiller (1993) proposes the hedonic repeated-measures (HRM) approach to measuring constant quality price indices for heterogeneous assets such as some bonds and real estate. We derive a mathematical relationship between the coefficients of the HRM model and those from the standard repeat-sales model, and we demonstrate how hedonic characteristics should be chosen for inclusion in the HRM model. Empirical estimates using Fairfax, Virginia, housing transactions data show that the HRM price index evaluated at the mean of the hedonic variable is virtually identical to the standard repeat sales index, just as predicted by our mathematical relationship. But the HRM allows estimation of different price paths for heterogeneous assets. We demonstrate that use of assessed value as the only hedonic characteristic allows parsimonious HRM estimates.     

Estimating price trends for residential property: A comparison of repeat sales and assessed value methods

The repeat sales methodology for estimating residential price indices is based on actual appreciation of individual properties. On the other hand, the repeat sales method wastes data, typically discarding a large percentage of all sales. This article explores two issues related to the subsample of repeat sales. First, are paired sales representative of the entire population of properties that sold? Second, is there evidence that sample selectivity biases the price trend estimates? Evidence from five metropolitan areas supports a negative answer to the first question and the second question. It appears that a “lemon” or “starter home” effect causes repeat residential sales to be a biased subsample of all transactions. Cumulative price trends for the repeat subsamples can differ from the full samples over periods ranging from two to ten quarters. While short-term price trends can differ widely, there are no systematic differences among the samples over long periods of time (e.g., three years or more).     

The Choice of Methodology for Computing Housing Price Indexes: Comparisons of Temporal Aggregation and Sample Definition

Housing transactions are executed and recorded daily, but are routinely pooled into longer time periods for the measurement and analysis of housing price trends. We utilize an unusually rich data set, covering essentially all arm's length housing sales in Sweden for a dozen years, in an attempt to understand the effect of temporal aggregation upon estimates of housing prices and their volatilities. This rich data set also provides a unique opportunity to compare the results using the conventional weighted repeat sales model (WRS) to those based on a research strategy which incorporates all available information on house sales. The results indicate the clear importance of temporal disaggregation in the estimation of housing prices and volatilities—regardless of the model employed.The appropriately disaggregated model is then used as a benchmark to compare estimates of the course of housing prices produced by the two models during the twelve year period 1981–1993. These results indicate that much of the difference between estimates of price movements can be attributed to the data limitations which are inherent in the repeat sales approach. The results, thus, suggest caution in the interpretation of government-produced price indices or those produced by private firms based on the repeated sales model.     

Alternative Methods of Increasing the Precision of Weighted Repeat Sales House Prices Indices

Weighted repeat sales house price indices have become one of the primary indicators used to identify housing market conditions and to estimate the amount of equity homeowners have gained through house price appreciation. The primary reason for the acceptance of this methodology is that it derives a location specific (typically, census division, state or metropolitan area) average change in house prices from repeated observations of individual house prices. It is this repeat attribute that allows repeat sales price indices to claim that it is a preferable index which does a better job of holding quality constant. The amount of time between the two observed prices for a single property is determined by when the home transacts. Some homes transact twice in a period of months and others do not transact for decades. It is likely that individual house price appreciation rates vary from the mean appreciation rate, as estimated by the index, in a systematic fashion. In general, the longer the time between transactions the more variance there is in individual house price appreciation. This paper extends this concept to include new dimensions. For instance, houses that appreciate faster than the mean, as estimated by the index for that location, may experience a different variation structure than homes that appreciate slower. This process can be viewed as an asymmetric treatment of the variance of house price appreciation around the estimated index. In addition, the variance of expensive and affordable homes may also be different and time varying. This paper finds evidence that adding the dimensions of price tiers and asymmetry to the variance estimate has merit and does affect the estimated index as well as homeowner equity estimates. Homeowner equity estimates are especially sensitive to these added dimensions because they depend on both the revised index and the estimated variances, which are specific to each dimension considered—time between transaction, asymmetry, and price tier.     

Evaluating the Usefulness of the American Housing Survey for Creating House Price Indices

The American Housing Survey (AHS) is a valuable source of information on houses and occupants over time. The AHS has several advantages over sales data for use in the creation of price indices: it is readily available, has frequent observations over time and space, has data from the late 1970s through the mid-1990s, includes houses that do not sell, as well as those that do, and has information on the occupants. The drawbacks include: a time lag between the interview and the release of the data, data suppression issues, owner-stated house values, and a lack of neighborhood information. In this study, we use the metropolitan version of the AHS, which has been supplemented with the original survey data as well as Census tract data for three cities over 14 years to examine whether the AHS can be used to create indices. Indices are estimated using hedonic, repeat valuation, and hybrid techniques, overcoming some of the problems inherent in the estimation of indices. We find that the data-suppression issues and the owner-stated house values are not problematic. The biggest drawback of the AHS is its lack of objective information on neighborhood quality.     

Selectivity,Quality Adjustment and Mean Reversion in the Measurement of House Values*

This paper develops a model of price formation in the housing market which accounts for the non-random selection of those dwellings sold on the market from the stock of existing houses. The model we develop also accounts for changes in the quality of dwellings themselves and tests for mean reversion in individual house prices. The model is applied to a unique body of data representing all dwellings sold in Sweden's largest metropolitan area during the period 1982–1999. The analysis compares house price indices that account for selectivity, quality change and mean reversion with the conventional repeat sales models used to describe the course of metropolitan housing prices. We find that the repeat sales method yields systematically large biased estimates of the value of the housing stock. Our comparison suggests that the more general approach to the estimation of housing prices or housing wealth yields substantially improved estimates of the course of housing prices and housing wealth.     

Repeat Sales Index for Thin Markets

The repeat sales model is commonly used to construct reliable house price indices in absence of individual characteristics of the real estate. Several adaptations of the original model by Bailey et al. (J Am Stat Assoc 58:933–942, 1963) are proposed in literature. They all have in common using a dummy variable approach for measuring price indices. In order to reduce the impact of transaction price noise on the estimates of price indices, Goetzmann (J Real Estate Finance Econ 5:5–53, 1992) used a random walk with drift process for the log price levels instead of the dummy variable approach. The model that is proposed in this article can be interpreted as a generalization of the Goetzmann methodology. We replace the random walk with drift model by a structural time series model, in particular by a local linear trend model in which both the level and the drift parameter can vary over time. An additional variable—the reciprocal of the time between sales—is included in the repeat sales model to deal with the effect of the time between sales on the estimated returns. This approach is robust can be applied in thin markets where relatively few selling prices are available. Contrary to the dummy variable approach, the structural time series model enables prediction of the price level based on preceding and subsequent information, implying that even for particular time periods where no observations are available an estimate of the price level can be provided. Conditional on the variance parameters, an estimate of the price level can be obtained by applying regression in the general linear model with a prior for the price level, generated by the local linear trend model. The variance parameters can be estimated by maximum likelihood. The model is applied to several subsets of selling prices in the Netherlands. Results are compared to standard repeat sales models, including the Goetzmann model.     

Aggregation Bias in Repeat-Sales Indices

The repeat-sales methodology has become a standard approach for estimating real estate price indices. This article examines the underlying assumptions inherent in the repeat sales model and provides an empirical test for both included and omitted variables as sources of aggregation bias. The results indicate that virtually all price indices may be biased, the degree of bias being dependent upon the number of variables examined and the instability of their parameters over time.     

Is It Possible to Construct Derivatives for the Paris Residential Market?

Index-based derivatives markets are fast developing in Europe, the US and Asia. Both valuation based and transactions based indices are used as bases for these derivatives contracts. This paper addresses the issue of revision effects on key index parameters, and their implications for derivatives pricing and questions whether these indices may be suitable for derivatives. More specifically, we address the issue of the robustness of the price level, mean, and volatility estimates for two repeat sales real estate price indices: the classical Weighted Repeat Sales (WRS) method and a Principal Component Analysis (PCA) factorial method, as elaborated in Baroni et al. (J Real Estate Res, 29(2):137–158, 2007). Our work is an extension of Clapham et al. (Real Estate Econ, 34(2):275–302, 2006), with the aim of helping judge the efficiency of such indices in designing real estate derivatives. We use an extensive repeat sales database for the Paris (France) residential market. We describe the dataset used and compute the parameters (index price level, trend and volatility) of the indices produced over the period 1982–2005. We then test the sensitivity of these two indices to revisions due to additional repeat-sales transactions information. Our analysis is conducted on the overall Paris market as well as on sub-markets. Our main conclusion is that even if the revision problem may cause substantial concern for the stability of key parameters that are used as inputs in the pricing of derivatives contracts, the order of magnitude of revision on derivatives pricing is not sufficient to deter market participants when it comes to products such a swap contract or insurance contracts against severe losses. We also show that WRS and PCA react differently to revision. The impact of index revision is non negligible in estimating the index price level for both indices. This result is consistent with existing literature for the US and Swedish markets. Price level revision causes moderate concern when trading products such as index futures or price insurance contracts, but could deter option like products. We show that managing this price level revision risk is similar to delta hedging in standard option pricing theory. We also find that although revision impact on index trend can be important, the WRS method seems more robust than PCA. However, the trend revision impact order of magnitude for contracts such as total return swaps is low. Finally, revision influence on volatility estimates seems to have a modest impact on derivatives, and according to the robustness of the volatility estimate, the PCA factorial index seems to fare relatively better than the WRS index. Hence, our findings show that the factorial index could better sustain volatility based derivatives. We also show that whatever the index, managing this volatility revision risk is similar to vega hedging in option pricing theory.

The Hierarchical Repeat Sales Model for Granular Commercial Real Estate and Residential Price Indices

This paper concerns the estimation of granular property price indices in commercial real estate and residential markets. We specify and apply a repeat sales model with multiple stochastic log price trends having a hierarchical additive structure: One common log price trend and cluster specific log price trends in deviation from the common trend. Moreover, we assume that the error terms potentially have a heavy tailed (t) distribution to effectively deal with outliers. We apply the hierarchical repeat sales model on commercial properties in the Philadelphia/Baltimore region and on residential properties in a small part of Amsterdam. The results show that the hierarchical repeat sales model provides reliable indices on a very detailed level based on a small number of observations. The estimated degrees of freedom for the t-distribution is small, largely rejecting the commonly made assumption of normality of the error term.     

Controlling for Quality in House Price Indices

Given the importance of house prices it is not surprising that house price indices are used for many purposes. One of the factors that differentiates these indices is the house price determinants (such as structural characteristics and neighborhood quality) that are accounted for—that is, held constant. Indices are usually generated from house price regressions. It is shown that, regardless of the desired level of accounting, it is necessary to control for all significant determinants of house prices in these regressions to obtain unbiased estimates of the growth in house prices. An empirical example shows that not controlling for neighborhood quality can lead to substantial biases in estimates of house price appreciation rates even if the index does not account for this factor.     

The Construction of Residential Housing Price Indices: A Comparison of Repeat-Sales,Hedonic-Regression,and Hybrid Approaches

This article examines a number of hypotheses that underpin the repeat-sales and hedonic approaches to the construction of housing price indices, as well as the practical problems associated with the implementation of either approach. We also examine a hybrid procedure that combines elements of both the repeat-sales and hedonic-regression techniques. For our sample of individual home sales in Oakland and Fremont California over an 18-year period, repeat-sales methods are subject to sample selection bias; the maintained assumption of time constancy of implicit prices of housing attributes is violated; the repeat-sales estimator is extremely sensitive to influential observations; and the usual method used to correct for heteroskedasticity in repeat-sale housing returns is inappropriate in our sample. Hedonic techniques are better suited to contend with index number problems per se, as they can accommodate changing attribute prices over time. They also appear to give rise to more reliable estimates of price indices, as unusual observations have less effect on estimated price indices. Drawbacks of the hedonic approach include the usual concern with omitted attributes, and their effect on the estimated price index.     

Constructing Indices of the Price of Multifamily Properties Using the 1991 Residential Finance Survey

Indices of the price of constant-quality, owner-occupied single-family housing are widely available and have been instrumental in learning about the operations of the market for owner-occupied housing. Such is not the case for multifamily rental housing. The purpose of this article is to provide information about movements in the price of multifamily properties during the 1980s and early 1990s using the 1991 Residential Finance Survey (RFS). Several conclusions are drawn from the development and analysis of indices of the price of multifamily housing for the nation and four large states (California, Florida, New York, and Texas). First, indices for the period 1983--1991 generate similar patterns among the various methods employed; furthermore, movements in the index during the period 1983--1991 seem reasonable. Second, much regional variation exists. Prices in Texas were particularly hard hit, falling by over 25% in nominal terms between 1983 and 1991. Third, the impact of the Tax Reform Act of 1986 does not appear to have been as dramatic as some have suggested. Indeed, price declines do not show up in either the 1986 or 1987 indices for the nation, California, or New York.     

Adjusting for Non-Linear Age Effects in the Repeat Sales Index

A true constant quality real estate price index should measure the general change in price level free from any change in quality over time. In recent years, the repeat-sales method has been widely used to construct constant quality property price indices. Since buildings depreciate over time, a simple repeat-sales index would underestimate the growth in property prices. The major problem of controlling the effects of age constant in a repeat-sales model arises from the exact multicollinearity between the age variable and the time dummy variables. In this study, we derive a solution that is theoretically sound and practical by allowing the age effects to be non-linear. In case of leasehold properties, we further incorporated interest rates into the model because the effects of age on real estate prices depend theoretically on interest rates. A sample of residential units in Hong Kong sold more than once from Quarter 2 of 1991 to Quarter 1 of 2001 (more than 11,000 repeat sales pairs) are used for the empirical analysis.     

Appraisal Quality and Residential Mortgage Default: Evidence from Alaska

We empirically examine the effect of appraisal quality on subsequent mortgage loan performance using data from the high volatility housing market of Alaska in the 1980s. We develop measures of appraisal quality by computing the residual between a hedonic estimate of house value using available information from other appraisals compared to actual ex ante appraised value. We then estimate proportional hazard models of mortgage default and find that several measures of appraisal quality, particularly appraised value in excess of hedonic estimates, are significantly related to default risk. Using valuations subsequent to loan default, we are also able to evaluate how well house price indices perform in terms of estimating current loan-to-value and offer some additional evidence on the controversy over the role of net equity versus trigger events as determinants of mortgage default. We also show that defaults are related to ex ante measures of housing market conditions, with additional implications for underwriting policies and the current industry trend away from traditional appraisal and toward automated valuation.     

A Pricing Framework for Real Estate Derivatives

New methods are developed here for pricing the main real estate derivatives — futures and forward contracts, total return swaps, and options. Accounting for the incompleteness of this market, a suitable modelling framework is outlined that can produce exact formulae, assuming that the market price of risk is known. This framework can accommodate econometric properties of real estate indices such as predictability due to autocorrelations. The term structure of the market price of risk is calibrated from futures market prices on the Investment Property Databank index. The evolution of the market price of risk associated with all five futures curves during 2009 is discussed.     

Developing a House Price Index for The Netherlands: A Practical Application of Weighted Repeat Sales

This paper describes the development of a house price index that has been introduced in May 2005 in The Netherlands. This monthly index, called Woningwaarde Index Kadaster (House Price Index Kadaster), is designed to detect changes in the price of the overall stock of owner-occupied homes. Fifty-five indices are calculated: one overall index, four regional indices, 12 provincial indices and 38 indices based on combinations of region/province and dwelling type. We used Case and Shiller’s geometric Weighted Repeat Sales Model to calculate monthly house price indices. We used recorded data on the sales of over 500,000 owner-occupied homes in The Netherlands, all representing repeat sales between January 1993 and December 2006. The accuracy of the index was determined using the 95% confidence interval. We observed that accuracy might become a problem in smaller sub samples. Revision volatility was explored by comparing the index values computed from all available data until December 2005 with the index values computed from the data available until December 2006. Our analysis showed that revision volatility does not seem to be a major problem to the index. We also explored heteroskedasticity in the Repeat Sales method but did not find conclusive evidence for the proposed heteroskedasticity. Given our target (a geometric mean index value) and the characteristics of the dataset (very large but without property characteristics) the Repeat Sales Method seems to be adequate for calculating a house price index for The Netherlands.

The accuracy of real estate indices: Repeat sale estimators

Simulation techniques allow us to examine the behavior and accuracy of several repeat sales regression estimators used to construct real estate return indices. We show that the generalized least squares (GLS) method is the maximum likelihood estimator, and we show how estimation accuracy can be significantly improved through a Baysian approach. In addition, we introduce a biased estimation procedure based upon the James and Stein method to address the problems of multicollinearity common to the procedure.     

A Bayesian Approach to the Construction and Comparison of Alternative House Price Indices

Several repeat-sales models have been advanced over the years for estimating real estate price indices. This article proposes a general model which incorporates earlier works as special cases and compares the alternative repeat-sales models using posterior odds ratios as criteria. While the existing literature estimates the real estate indices from the sampling point of view, in this article indices are constructed and then compared using a Bayesian approach. In general, the two-error term models outperform the one-error models. The model with a nontemporal component proposed by Goetzmann and Spiegel is found to be superior in three out of four cities. There is a significant discrepancy among the returns and indices obtained from different models.     

What drove the mid-2000s explosiveness in alternative energy stock prices? Evidence from U.S., European and global indices

Soaring prices in European alternative energy stocks and their subsequent tumble have attracted attention both from investors and academics. We extend recent research to an international setting and analyze whether the explosive price behavior of the mid-2000s was driven by rising crude oil prices and overall bullish market sentiment. Inflation-adjusted U.S. alternative energy stock prices do not exhibit signs of explosiveness. By contrast, we find strong evidence of explosive price behavior for European and global sector indices, even after controlling for a set of explanatory variables. Interestingly, while the sector indices plunged with the outbreak of the global financial crisis, idiosyncratic components continued to rise and did not start to decline until after world equity markets had already begun to recover in 2009. This finding suggests a substantial revaluation of alternative energy stock prices in light of intensifying sector competition and shrinking sales margins and casts some doubts on the existence of a speculative bubble. Nevertheless, we observe temporary episodes of explosiveness between 2005 and 2007 followed by rapid collapses, indicating the presence of some irrational exuberance among investors.