1. International Policy Discussion in Property Price Indices

It can be seen that user needs will vary and that in some instances, more than one measure of house price or real estate inflation may be required. It can also be seen that coherence between different measures and with other economic statistics is important and that achieving this will be especially difficult as statisticians are unlikely to have an ideal set of price indicators available to them. Fenwick (2006; 8).

See Fenwick (2006; 8–11).

The one exception is residential housing, where estimates of the period by period flow of housing services are made in the SNA.

The user cost idea can be traced back to Walras in 1874; see Walras (1954).

The list of countries who now have official productivity programs includes the U.S., Canada, the UK, Australia, New Zealand and Switzerland. The EU KLEMS project is developing productivity accounts for many European countries using the Jorgenson and Griliches methodology, which is described in more detail in Schreyer (2001). For recent extensions and modifications, see Schreyer (2006).

Such an accounting system is laid out in great detail and implemented for the U.S. by Jorgenson and Landefeld (2006).

For short lived household durables, it is not worth the bother of capitalizing these stocks and so the usual acquisitions approach will suffice for these assets.

We will return to this topic in Sect. 1.6 below.

For a detailed description of how this methodology works, see Chap. 20, “Elementary Indices”, in the ILO (2004).

Related problems are that the mix of transactions can change over time and in fact entirely new types of housing can enter the market.

See Case and Shiller (1989) and Diewert (2013a, b, c; 31–39) for detailed technical descriptions of the method. Diewert showed how the repeat sales method is related to Summers’ (1973) country product dummy model used in international price comparisons and the product dummy variable hedonic regression model proposed by Aizcorbe et al. (2001).

Throughout this section, we will discuss the relative merits of the different methods that have been suggested for constructing property price indexes. For a similar (and perhaps more comprehensive) discussion, see Hoffmann and Lorenz (2006; 2–6).

Hedonic regression models suffer from a reproducibility problem; i.e., different statisticians will use different characteristics variables, use different functional forms and make different stochastic specifications, possibly leading to quite different results. However, the repeat sales model is not as reproducible in practice as indicated in the main text because in some variants of the method, houses that are “flipped” (sold very rapidly) and houses that have not sold for long periods are excluded from the regressions. The exact method for excluding these observations may vary from time to time leading to a lack of reproducibility.

Some of the papers presented at the workshop suggested that the repeat sales method might lead to estimates of price change that were biased upwards, since often sellers of properties undertake major renovations and repairs just before putting their properties on the market, leading to a lack of comparability of the unit from its previous sale. “The repeat sales method does not entirely adjust for changes in quality of the dwellings. If a dwelling undergoes a major renovation or even an extension between two transaction moments, the repeat sales method will not account for this. The last transaction price may in that case be too high, which results in an overestimation of the index.” van der Wal et al. (2006; 3). “Research has suggested that appreciation rates for houses that sell may not be the same as appreciation rates for the rest of the housing stock.” Leventis (2006; 9). Leventis cites Stephens et al. (1995) on this point. Finally, Gudnason and Jonsdottir made the following observations on the method: “The problem with this method is the risk for bias; e.g., when major renovation and other changes have been made on the house which increases the quality or if the wear of the house has been high, causing a decrease in the quality. Such changes are not captured by this method. In Iceland, this method cannot be used because the number of housing transactions are too few and thus there are not enough repeated sales to be able to calculate the repeated sales index.” Gudnason and Jonsdottir (2006; 2).

Case and Shiller (1989) used a variant of the repeat sales method using US data on house sales in four major cities over the years 1970–1986. They attempted to deal with the depreciation and renovation problems as follows: “The tapes contain actual sales prices and other information about the homes. We extracted from the tapes for each city a file of data on houses sold twice for which there was no apparent quality change and for which conventional mortgages applied.” Case and Shiller (1989; 125–126). It is sometimes argued that renovations are approximately equal to depreciation. While this may be true in the aggregate, it certainly is not true for individual dwelling units because over time, many units are demolished.

However, usually information on maintenance and renovation expenditures is not available in the context of estimating a hedonic regression model for housing. Malpezzi et al. (1987; 375–6) comment on this problem as follows: “If all units are identically constructed, inflation is absent, and the rate of maintenance and repair expenditures is the same for all units, then precise measurement of the rate of depreciation is possible by observing the value or rent of two or more units of different ages. ... To accurately estimate the effects of aging on values and rents, it is necessary to control for inflation, quality differences in housing units, and location. The hedonic technique controls for differences in dwelling quality and inflation rates but cannot control for most differences in maintenance (except to the extent that they are correlated with location).”

Another drawback on the RS method is the fact that previously published index numbers will be revised when new data are added to the sample. van der Wal et al. (2006; 3).

van der Wal et al. (2006; 3) noted that this method is described in more detail in Bourassa et al. (2006). The conference presentation by Statistics Denmark indicated that a variant of this method is also used in Denmark. Jan de Haan brought to my attention that a much more comprehensive analysis of the SPAR method (similar in some respects to the analysis in this section) may be found in de Haan, van der Wal et al. (2006).

If the term \(\sum _{n=1}^{N(0)}S_{n}^{0}/\sum _{n=1}^{N(0)}A_{n}^{00}\) on the right hand side of (1.1) is equal to 1, then the index reduces to a Dutot index. For the properties of Dutot indexes, see Chap. 20, “ Elementary Indices”, in ILO (2004) or IMF (2004).

This stochastic specification reflects the fact that the errors are more likely to be multiplicative rather than additive.

It is no longer likely that the expected value of the error term \(\varepsilon _{i}^{0t}\) is equal to 0 since the base period assessments cannot pick up any depreciation and renovation biases that might have occurred between periods 0 and t.

For the properties of Carli indexes, see Chap. 20, “Elementary Indices”, in ILO (2004).

See Chap. 20, “Elementary Indices”, in ILO (2004).

For the properties of Jevons indexes, see Chap. 20, “Elementary Indices”, in the ILO (2004) Manual.

Using second order Taylor series approximation techniques, it can be shown that the upward bias in the Jevons type SPAR index will be less than in the corresponding Carli type SPAR index.

The Manual does not recommend the use of the Carli formula since it fails the time reversal test with an upward bias.

These indexes should be further adjusted to take into account depreciation and renovations bias.

Leventis (2006) discussed some of the problems with U.S. private sector assessment techniques when he discussed the work of Chinloy et al. (1997) as follows: “Using a sample of 1993 purchase price data for which they also had the appraisal information, they compared purchase prices against appraisals to determine whether there were systematic differences. They estimated an upward bias of two percent and found that appraisals exceeded purchase price in approximately 60% of the cases. ... That appraisers ‘extrapolate’ valuations from recent results and have a vested interest in ensuring that their valuations appear reasonable (and perhaps consistent) to the originators suggest that the volatility of appraised values may be lower. At the same time, the authors believe that the appraisals’ reliance on a small number of comparables ‘almost surely’ leads to ‘more volatility than marketwide prices’. Leventis (2006; 5–6).

If the assessments are used for taxation purposes and they are supposed to be based on market valuations, then the assessed values cannot be too far off the mark since the government has an incentive to make the assessments as large as possible (to maximize tax revenue) and taxpayers have the opposite incentive to have the assessments as small as possible.

This is not really a major problem since the base period assessment information can be used to obtain satisfactory weights. When a new official assessment takes place, superlative indexes can be formed between any two consecutive assessment periods and interpolation techniques can be used to form approximate weights for all intervening periods. For descriptions of superlative indexes and their properties, see Diewert (1976, 1978) or Chaps. 15–20 of ILO (2004).

The paper presented by Girouard et al. (2006; 26) showed that there are regional differences in the rate of housing price change. This paper also showed that real estate bubbles were quite common in many OECD countries. In many countries, bubbles lead to differential rates of housing price increase; i.e., in the upward phase of the bubble, expensive properties tend to increase in price more rapidly than cheaper ones and then in the downward phase, the prices of more expensive properties tend to fall more rapidly. A single index will not be able to capture these differential rates of price change.

We show later in Sect. 1.5.1 that the hedonic method can deal with this problem.

A bit of caution is called for here: sometimes official assessments are not very accurate for various reasons.

However, the monthly index is produced as a moving average: “The calculation of price changes for real estate is a three month moving average, with a one month delay.” Gudnason and Jonsdottir (2006; 4). Gudnason and Jonsdottir (2006; 3) also note that each year about 8–10% of all the housing in the country is bought and sold.

However, Prasad and Richards (2006) show that the stratification method applied to Australian house price data gave virtually the same results as a hedonic model that had locational explanatory variables.

If no information on housing characteristics is used, then the method is subject to tremendous unit value bias.

The standard assessment method leads to only a single price index whereas the stratification method leads to a family of subindexes. However, if stratification variables are available, the assessment method can also produce a family of indexes.

See Diewert (2003b) who showed that stratification techniques or the use of dummy variables can be viewed as a nonparametric regression technique. In the statistics literature, these partitioning or stratification techniques are known as analysis of variance models; see Scheffé (1959).

An alternative approach to the hedonic method is to estimate separate hedonic regressions for both of the periods compared; i.e., for the base and current period. Predicted prices can then be generated in each period using the estimated hedonic regressions based on a constant characteristics set, say the characteristics of the base period. A ratio of the geometric means of the estimated prices in each period would yield a pure price comparison based on a constant base period set of characteristics. A hedonic index based on a constant current period characteristic could also be compiled, as could such indexes based on a symmetric use of base and current period information. Heravi and Silver (2007) outline alternative formulations and Silver and Heravi (2007) provide a formal analysis of the difference between this approach and that of the time dummy method. The French method also does not use the time dummy method but is too complex to explain here.

This property of the hedonic regression method also applies to the stratification method. The main difference between the two methods is that continuous variables can appear in hedonic regressions (like the area of the structure and the area of the lot size) whereas the stratification method can only work with discrete ranges for the independent variables in the regression.

Basically, this recent literature makes connections between weighted hedonic regressions and traditional index number formula that use weights; see Diewert (2003c, 2004, 2005a, b), de Haan (2003, 2004), Silver (2003) and Silver and Heravi (2005). It is worth noting that a perceived advantage of the stratification method is that median price changes can be measured as opposed to arithmetic mean ones, that are implicit in a say ordinary least squares estimator. However, regression estimates can also be derived from robust estimators from which the parameter estimates for the price change will be similar to a median.

Note that the same criticism can be applied to stratification methods; i.e., different analysts will come up with different stratifications.

For example, the dependent variable could be the sales price of the property or its logarithm or the sales price divided by the area of the structure and so on.

This evaluation agrees with that of Hoffmann and Lorenz: “As far as quality adjustment is concerned, the future will certainly belong to hedonic methods.” Hoffman and Lorenz (2006; 15).

Multiplicative errors with constant variances are more plausible than additive errors with constant variances; i.e., it is more likely that expensive properties have relatively large absolute errors compared to very inexpensive properties. The multiplicative specification for the errors will be consistent with this phenomenon.

However, note that this model is not linear in the unknown parameters to be estimated.

Of course, in practice, some of the land or location variables could act as proxies for unobserved structure quality variables. There are also some interesting conceptual problems associated with the treatment of rental apartments and owner occupied apartments or condominiums. Obviously, separate hedonic regressions would be appropriate for apartments since their structural characteristics are quite different from detached housing. For rental apartments, the sale price of the apartment can be the dependent variable and there will be associated amounts of structure area and land area. For a condo sale, the price of the single unit is the dependent variable while the dependent variables in the bare bones model would be structure area of the apartment plus the apartment’s share of commonly owned facilities plus the apartment’s share of the lot area. In the end, we want to be able to impute the value of the property into land and structure components and so the hedonic regression should be set up so as to accomplish this task.

Of course, large data sets can be transformed into smaller data sets if we run separate hedonic regressions for various property strata!

From Hoffmann and Kurz (2002; 3–4), about 60% of German households live in rented dwellings whereas only about 11% of Spaniards rent their dwellings in 1999 (private communication).

Hoffmann and Kurz-Kim (2006) provide some recent evidence of seasonality in German prices.

See Hill (1996) and Diewert (1998) for a discussion of these problems.

The usual CPI methodology is to never revise the index.

For an update on how thinking is progressing on the treatment of Owner Occupied Housing in the HICP, see Makaronidis and Hayes (2006).

For a description and further references to the Canadian program on estimating depreciation rates, see Baldwin et al. (2005).

Actually, since 1991, the Dutch have a separate (mail) survey for enterprises with more than 100 employees to collect information on discards and retirements: The Survey on Discards; see Bergen et al. (2005; 8) for a description of the Dutch methods.

The Economic and Social Research Institute (ESRI), Cabinet Office of Japan, with the help of Koji Nomura is preparing a new survey to be implemented as of the end of 2006.

See formula (1) in Verbrugge (2006; 11). We have not followed his notation exactly.

Verbrugge (2006; 11) used either the current 30 year mortgage rate or the average one year Treasury bill rate and noted that the choice of interest rate turned out to be inconsequential for his analysis.

Verbrugge (2006; 13) assumed that \(\delta \) was approximately equal to 7%. Note that the higher the volatility in house prices is, the higher the risk premium would be for a risk averse consumer.

\(\pi _{i}^{t}\) is the actual 4 quarter (constant quality) home price appreciation between the beginning of period t and one year from this period.

Diewert (2003a) noted that there would be a few differences between a user cost formula for an owner occupier as compared to a landlord but these differences are not important for Verbrugge’s analysis.

Hoffmann and Kurz-Kim find that German rents are changed only once every 4 years on average: “In Germany, as in other euro area countries, prices of most products change infrequently, but not incrementally. Pricing seems to be neither continuous nor marginal. In our sample, prices last on average more than two years—if price changes within a month are not considered—but then change by nearly 10%. The longest price durations are found for housing rents, which, on average, are for more than four years.” Hoffmann and Kurz-Kim (2006; 5).

The paper by Girouard, Kennedy, van den Noord and André nicely documents the length of housing booms and busts: “To qualify as a major cycle, the appreciation had to feature a cumulative real price increase equalling or exceeding 15%. This criterion identified 37 such episodes, corresponding to about two large upswings on average per 35 years for English speaking and Nordic countries and to \(1\frac{1}{2}\) for the continental European countries.” Girouard et al. (2006; 6). Thus one could justify taking 10 to 20 year (annualized) average rates of property price inflation in the user cost formula rather than one year rates.

See Gudnason (2004) and Gudnason and Jonsdottir (2006; 11).

Verbrugge (2006; 35) assumed that the transactions costs in the U.S. were approximately 8–10% of the sales price.

Woolford (2006) shows that different treatments of Owner Occupied Housing in the Australian context generate very different aggregate consumer price indexes.

As was noted above in Sect. 1.2, it is necessary to look beyond the present SNA to the next version which will probably have a more detailed treatment of durable goods in it so that consumer service flows can be better measured and so that productivity accounts can be constructed for the business sector. A natural family of real estate price indexes emerges from this expanded SNA.

Johannes Hoffmann made this point.