1 Introduction

Jan de Haan and Rens Hendriks

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When attempting to construct constant-quality house price indexes, statistical agencies face a number of problems. First, exact matching of properties over time is problematic as their quality will likely have changed; houses depreciate and they may also have had major repairs, additions or remodelling done to them. In other words, every property in each period can be viewed as a unique good. Second, the turnover of houses is generally low compared to the housing stock and the mix of properties sold changes over time, so a quality mix problem arises. Third, there is often a lack of data on characteristics. Data availability issues have implications for the choice of measurement method.

Three main types of house price indexes can be found in the literature: median or mean indexes, repeat sales indexes and hedonic indexes. A median (mean) index tracks the change in the price of the median (mean) house traded from one period to the next. This method is problematic in that the characteristics of, e.g., the median house changes over time. The problem is often tackled by stratifying the samples according to region, type of dwelling, etc., a procedure which is also known as mix adjustment. Stratification obviously requires additional data.

Repeat sales methods address the quality mix problem by restricting the data set to houses that have been sold twice or more during the sample period. This ensures that 'like is compared with like', assuming that the quality of the individual houses remains unchanged. Repeat sales methods are based on regressions where the repeat sales data pertaining to different periods are pooled. A potential drawback is revision; when new data is added to the sample, previously computed index numbers will change. The repeat sales method is originally due to Bailey, Muth and Nourse (1963). Case and Shiller (1987, 1989) argue that changes in house prices include components whose variances increase with the interval of sales and propose a Weighted Least Squares approach to adjust for this type of heteroskedasticity. An alternative weighted method has been suggested by Calhoun (1996). Jansen, de Vries, Coolen, Lamain and Boelhouwer (2008), using Dutch data, compare the unweighted repeat sales method with various weighted methods and conclude that the unweighted method performs satisfactorily.

Unlike repeat sales methods, hedonic regression methods can in principle adjust for quality changes of individual properties (in addition to quality mix changes). These methods utilize information on housing characteristics, such as number of bedrooms, lot size and location, to estimate quality adjusted price indexes using regression techniques. Today, hedonic house price indexes are computed in many countries. For example, the French statistical agency (INSEE), jointly with Conseil Supérieur du Notariat, compiles a hedonic index (Gouriéroux and Laferrère 2009) as does Statistics Finland (Saarnio 2006). The UK has three hedonic house price indexes, compiled by different institutes. RPData-Rismark computes hedonic indexes for the capital cities in Australia (Hardman 2011). Hedonic indexes come in two main varieties. The time dummy method models the log of price as a function of property characteristics and a set of dummy variables indicating the time periods. Since the data of all periods are pooled, this method suffers from revision as well. Hedonic imputation methods, which estimate the 'missing prices', do not have this drawback. Hill and Melser (2008) discuss numerous hedonic imputation methods in the housing context. Diewert, Heravi and Silver (2009) and de Haan (2010) provide a comparison between time dummy and hedonic imputation price indexes.

A fourth approach to estimating house price indexes is the use of assessment or appraisal data. One option is to augment a repeat sales dataset by using assessment data as estimates for past or current values of properties that have not been resold during the sample period. Some of the data on which the repeat sales index is based would then be pseudo rather than genuine repeat data. For more on the use of assessment information in a repeat sales price index and the removal of appraisal bias, see e.g., Geltner (1996), Edelstein and Quan (2006), and Leventis (2006). Another option, which also controls for quality-mix changes, is to combine current selling prices with appraisals from an earlier period to compute price relatives in a standard matched-model framework. An advantage over the repeat sales approach is that index numbers will not be revised. This so-called Sale Price Appraisal Ratio (SPAR) method has been applied in New Zealand for a long time now and is currently also being used in the Netherlands and a few other European countries. Bourassa, Hoesli and Sun (2006) describe the New Zealand SPAR index which is compiled by Quotable Value, a state-owned property valuation company. Other studies into the SPAR method include Rossini and Kershaw (2006), van der Wal, ter Steege and Kroese (2006), de Vries, de Haan, van der Wal and Mariën (2009), de Haan, van der Wal and de Vries (2009), Shi, Young and Hargreaves (2009), and Grimes and Young (2010).

In this paper we outline an alternative appraisal-based method to measure house price change. The appraisals serve as auxiliary information in a generalized regression (GREG) estimation framework. GREG is a model-assisted technique that can be used to increase efficiency as compared to simpler estimators such as sample means (Särndal, Swensson and Wretman 1992), provided that population information is known for one or more variables that exhibit a strong linear correlation with the variable under study. In our case we regress selling prices in each time period on appraisals. Appraised values are available in the Netherlands for all properties in stock in some reference period, and we expect them to be highly collinear with selling prices. Although the method is based on regression, the resulting price index is not a hedonic index as the regression model is descriptive rather than explanatory.

The paper is organized as follows. To set the stage, in Section 2 we describe the SPAR method and its relation to the sample means of sale prices and appraisals. Due to compositional change and the relatively low number of transactions, the Dutch SPAR series exhibits strong volatility, especially for small market segments. In Section 3 we outline a simple GREG estimator of house price change and two alternatives. The first alternative is a stratified version of the original index whereas the second one uses an alternative model specification. Section 4 contains empirical evidence using Dutch data. The GREG index numbers turn out to be very similar to the SPAR index numbers and are equally volatile. In Section 5 we explain this result by showing that the SPAR index is in fact an estimator of the GREG index and almost as efficient. Section 6 concludes and suggests a topic for further research in this field.

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