The Paris OECD-IMF Workshop on Real Estate Price Indexes

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The Paris OECD-IMF Workshop on Real Estate Price Indexes

    Chapter 6




    1W. Erwin Diewert

1. Introduction

     This paper highlights some of the themes that emerged from the OECD-IMF Workshop on Real Estate Price Indexes which was held in Paris, November 6-7, 2006. The paper discusses possible uses and target indexes for real estate price indexes and notes that a major problem is that it is not possible to exactly match the quality of dwelling units over time due to the fact that the housing stock changes in quality due to renovations and depreciation. Four alternative methods for constructing real estate price indexes are discussed: the repeat sales model; the use of assessment information along with property sale information; stratification methods and hedonic methods. The paper notes that the typical hedonic regression method may suffer from specification bias and suggests a way forward. Problems with the user cost method for pricing the services of owner occupied housing are also discussed. The paper is organized as follows.

     Section 2 discusses the question: what are appropriate target indexes for Real Estate Prices? This section argues that the present System of National Accounts is a good starting point for a systematic framework for Real Estate Price indexes but the present SNA has to be augmented somewhat to meet the needs of economists who are interested in measuring consumption on a more comprehensive service flow basis and who are interested in measuring the productivity of an economy.

     Section 3 notes the fundamental problem that makes the construction of constant quality real estate price indexes very difficult: namely depreciation and renovations to structures make the usual matched model methodology for constructing price indexes inapplicable.

     Section 4 discusses four classes of methods that were suggested at the workshop to deal with the above problem and section 5 discusses some additional technical difficulties.

    1 This paper is an extended written version of my Discussion at the Concluding Overview session of the OECD-IMF Workshop on Real Estate Price Indexes held in Paris, November 6-7, 2006. The financial assistance of the OECD and the Australian Research Council is gratefully acknowledged, as is the hospitality of the Centre for Applied Economic Research at the University of New South Wales. The author thanks Paul Armknecht, Stephan Arthur, David Fenwick, Jan de Haan, Johannes Hoffmann, Anne Laferrère, Alice Nakamura, Marc Prud‟homme, David Roberts, Mick Silver, Paul Schreyer and Kam Yu for helpful comments. None of the above individuals or organizations is responsible for any opinions expressed in this paper.

Diewert, W.E. (2009), “The Paris OECD-IMF Workshop on Real Estate Price Indexes:

    Conclusions and Future Directions,” chapter 6, pp. 87-116 in

    W.E. Diewert, B.M. Balk, D. Fixler, K.J. Fox and A.O. Nakamura (2009),

    PRICE AND PRODUCTIVITY MEASUREMENT: Volume 1 -- Housing, Trafford Press.

    Also available as a free e-publication at and

    ? Alice Nakamura, 2009. Permission to link to, or copy or reprint, these materials is granted without restriction, including for use in commercial textbooks, with due credit to the authors and editors.

     Section 6 discusses the problems raised by Verbrugge‟s (2006) contribution to the

    Workshop; i.e., why do user costs diverge so much from rents?

     Finally, section 7 summarizes suggestions for moving the agenda forward, including a proposal for a new approach to accounting for real estate in measures of inflation.

2. What Are Appropriate Target Indexes?

     There are many possible target real estate price indexes that could be constructed. Thus it is useful to consider alternative uses for real estate price indexes that were suggested at the workshop since these uses will largely determine what type of indexes should be constructed.

     Fenwick (2006; 6) suggested the following list of possible uses for house price indexes: As a general macroeconomic indicator (of inflation);

     As an input into the measurement of consumer price inflation;

     As an element in the calculation of household (real) wealth, and

     As a direct input into an analysis of mortgage lender‟s exposure to risk of default.

     Arthur (2006) also suggested some (related) uses for real estate price indexes: Real estate price bubbles (and the subsequent collapses) have repeatedly been related to financial crises and thus it is important to measure these price bubbles accurately and in a way that is comparable across countries, and

     Real estate price indexes are required for the proper conduct of monetary policy.

     Fenwick also argued that various real estate price indexes are required for deflation purposes in the System of National Accounts (SNA):

    “The primary focus of a national accountant seeking an appropriate deflator for national accounts

    will be different. Real estate appears in the National Accounts in several ways;

     the imputed rental value received by owner occupiers for buildings, as opposed to land, is

    part of household final consumption,

     the capital formation in buildings, again as opposed to land, is part of gross fixed capital

    formation, depreciation, and the measurement of the stock of fixed capital,

     and land values are an important part of the National stock of wealth.”

    David Fenwick (2006; 7-8)


     Fenwick (2006; 6) also argued that it would be useful to develop a coherent conceptual 2framework for an appropriate family of real estate price indexes and he provides such a 3framework towards the end of his paper.

     Diewert, in his oral presentation to the Workshop, followed Fenwick and argued that in the first instance, real estate price statistics should serve the needs of the SNA. The reason for this is that (with one exception to be discussed later) the SNA provides a quantitative framework where value flows and stocks are systematically decomposed in an economically meaningful way into price and quantity (or volume) components. The resulting p‟s and q‟s are the basic building blocks which are used in virtually all macroeconomic models. Hence it seems important for price statisticians to do their best to meet the deflation needs of the SNA.

     Before the main problem area with the present SNA treatment of real estate is discussed, it is useful to review a bit of basic economics. There are two main paradigms in economics: Consumers or households maximizing utility subject to their budget constraints, and Producers maximizing profits subject to their production function (or more generally, their technology) constraints.

     There are one period “static” and many period “intertemporal” versions of the two paradigms. However, for our purposes, it suffices to say that the SNA provides the necessary data to implement both models except for the fact that the SNA does not deal adequately with the

    consumption of consumer durables for the needs of either consumer or producer modeling. The problem is that when a consumer or producer purchases a good that provides services over a number of years, it is not appropriate to charge the entire purchase cost to the quarter or month when the durable is purchased; the purchase cost should be spread out over the useful life of the durable. However, with the important exception of residential housing, the SNA simply charges 4the entire cost of the durable to the period of purchase. This is not an appropriate treatment of

    durables for many economic purposes. Thus, for the SNA household accounts, in addition to the usual acquisitions approach treatment of consumer durables (which simply charges the entire

    purchase cost to the period of purchase), it would be useful to have alternative measures of the service flows generated by household holdings of consumer durables. There are two alternative approaches to constructing such flow measures:

     An imputed rent approach which imputes market rental prices for the same type of

    service (if such prices are available), and

     A user cost approach which forms an estimate of what the cost would be of buying the

    durable at the beginning of the period, using the services of the durable during the period and then selling it at the end of the period. This estimated cost also includes the interest cost that is

    2 “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.” David Fenwick (2006, p. 8).

    3 See Fenwick (2006, pp. 8-11).

    4 More specifically, for owner occupied residential housing, the SNA incorporates estimates of the period by period flow of housing services. One reason this is done is to improve the comparability of the SNA between nations where the percentage of households living in owner occupied versus rental housing is very different.


    5associated with value of the capital that is tied up in the purchase of the durable. However, if

    most owners of some sort of durable, in fact, continue to hold it for multiple periods, then the buy-use-sell sequence might be priced out as a per-year average over the expected holding period, using the available information on the beginning and end of period prices and the transaction costs that would be involved in buying and then selling once over the expected holding period.

     We discuss the relative merits of the above two service flow methods for valuing housing services in section 6 below. For additional material on the various economic approaches to the treatment of durables and housing in particular, see Diewert (2002; 611-622), (2003), Verbrugge (2006), and Chapter 23, “Durables and User Costs”, in the International Labour Organization (ILO) Consumer Price Index Manual (2004).

     On the producer side of the SNA, the service flows generated by durable inputs that are used to produce goods and services are buried in Gross Operating Surplus. Jorgenson and Griliches (1967) (1972) showed how gross operating surplus could be decomposed into price and quantity components using the user cost idea and their work led directly to the first national 6statistical agency productivity program; see the Bureau of Labor Statistics (1983). Schreyer,

    Diewert and Harrison (2005) argued that this productivity oriented approach to the System of

    National Accounts could be regarded as a natural extension of the present SNA where the extended version provides a decomposition of a value flow (Gross Operating Surplus) into price and quantity (or volume) components.

     We will argue below that if the SNA is expanded to exhibit the service flows that are associated with the household and production sectors‟ purchases of durable goods, then the 7resulting Durables Augmented System of National Accounts (DASNA) provides a natural

    framework for a family of real estate price indexes.

     In this augmented system of national accounts, household wealth and consumption will be measured in real and nominal terms. This will entail measures of the household sector‟s stock of residential wealth and it will be of interest to decompose this value measure into price and quantity (or volume) components. It will also be useful to decompose the residential housing stock aggregate into various subcomponents such as:

     by type of housing,

     by location or region,

     by the proportion of land and structures in the aggregate value,

     by age (in particular, new housing should be distinguished), and

     by whether the residence is rented or owned.

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

    6 The list of countries that now have official productivity programs includes the United States, Canada, the United Kingdom, Australia, New Zealand and Switzerland. The EU KLEMS project (for the EU KLEMS database and related information, see 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).

    7 Such an accounting system is laid out and implemented for the United States by Jorgenson and Landefeld (2006).


     Each of these subaggregates should be decomposed into price and volume components if possible. The DASNA will also require a measure of the flow of services from households‟ consumption of the services of their long lived consumer durables such as motor vehicles and 8owner occupied housing. Thus it will be necessary to either implement the rental equivalence approach (as is currently recommended in the SNA) or the user cost approach (or some alternative) for valuing the services of Owner Occupied Housing in this extended system of 9accounts.

     Turning now to the producer side of the DASNA, for productivity measurement purposes, we will want user costs for owned commercial, industrial and agricultural properties. In order to form wealth estimates, we will require estimates for the value of commercial, industrial and agricultural properties and decompositions of the values into price and volume components. The price components can be used as basic building blocks to form user costs for the various types of property. It will also be useful to decompose the business property stock aggregates into various subcomponents such as:

     by type of structure,

     by location or region,

     by the proportion of land and structures in the aggregate value,

     by age (in particular, new structures should be distinguished), and

     by whether the structure is rented or owned.

     If we think back to the list of uses for real estate price indexes suggested by Fenwick and Arthur earlier in this section, it can be seen that if we had all of the price indexes for implementing the DASNA as suggested above, then virtually all of the user needs could be met by this family of national accounts type real estate price indexes. The Durables Augmented SNA is a natural framework for the development of real estate price indexes that would meet comprehensive user needs.

     We turn now to a discussion of the many technical issues that arise when trying to construct a property price index.

3. Failure of the Traditional Matched Model Methodology in the Real Estate Context

     Consider the problems involved in constructing a constant quality price index for a class of residential dwelling units or business structures. The starting point for constructing any price index between two time periods is to collect prices on exactly the same product or item for the 10two time periods under consideration; this is the standard matched model methodology.

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

    9 We will return to this topic in section 6 below.

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


     The fundamental problem that price statisticians face when trying to construct a real estate price index is that exact matching of properties over time is often not possible for two


     The property depreciates over time (the depreciation problem), and

     The property may have had major repairs, additions or remodeling done to it between the two time periods under consideration (the renovations problem).

     Because of the above two problems, some form of imputation or indirect estimation will be required. A third problem that faces many European countries is the problem of low turnover

    of properties; i.e., if the sales of properties are very infrequent, then even if the depreciation and renovations problems could be solved, there would still be a problem in constructing a 11satisfactory property price index because of the low incidence of resales.

     A fourth problem should be mentioned at this point. For some purposes, it is desirable to decompose the real estate price index into two separate constant quality components: A component that measures the change in the price of the structure, and A component that measures the change in the price of the underlying land.

     In the following section, we will look at some of the methods that were suggested by conference participants to construct constant quality real estate price indexes for the land and structures taken together. The problem of decomposing a real estate price index into its structure and land components is deferred until section 5 below.

    4. Suggested Methods for Constructing Constant Quality Real Estate Price Indexes 4.1 The Repeat Sales Method

     The repeat sales approach is due to Bailey, Muth and Nourse (1963), who saw their

    procedure as a generalization of the chained matched model methodology that was used by the

    early pioneers in the construction of real estate price indexes like Wyngarden (1927) and Wenzlick (1952). We will not describe the technical details of the method; we simply note that the method uses information on real estate properties which trade on the market more than once 12over the sample period. By utilizing information on properties that are legally the same that trade more than one period, the repeat sales method attempts to hold the quality of the properties constant over time.

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

    12 See Case and Shiller (1989) and Diewert (2003, pp. 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, Corrado and Doms (2001).


    13 We now discuss some of the advantages and disadvantages of the repeat sales method.

     The main advantages of the repeat sales model are:

     The availability of source data from administrative and real estate industry records on property sales, so that no imputations are involved (if no adjustments are made for renovations), and

     Reproducibility of the results; i.e., different statisticians given the same data on the sales 14of real estate properties will come up with the same estimate of quality adjusted price change.

     The main disadvantages of the repeat sales model are:

     It does not use all of the available information on property sales; it uses only information 15on properties that have sold more than once during the sample period.

     It cannot deal adequately with depreciation of the dwelling unit or structure.

    16 It cannot deal adequately with units that have undergone major repairs or renovations.

    In contrast, a general hedonic regression model for housing or structures can adjust for the

    13 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, pp. 2-6).

    14 Hedonic regression models suffer from a reproducibility problem; i.e., different statisticians will use different characteristics variables, different functional forms and different stochastic specifications, possibly leading to quite different results. However, in actual applied use, 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 or regression-based adjustments are made to try to allow for changes in properties in the intervals between resale. The exact methods for making these sorts of adjustments vary among analysts and over time to time, leading to a lack of reproducibility.

    15 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 if the pure repeat sales approach is used. For example, Erna van der Wal, Dick ter Steege and Bert Kroese (2006, p. 3) write that: “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.” Andrew Leventis (2006, p. 9) writes that: “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 goes on to cite material by Stephens, Li, Lekkas, Abraham, Calhoun and Kimner (2005) on this point. Finally, Gudnason and Jonsdottir (2006) observe that: “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. Furthermore, in Iceland, this method cannot be used because the numbers of housing transactions are too few and thus there are not enough repeated sales to enable calculation of the repeated sales index.”

    16 Case and Shiller (1989) used a variant of the repeat sales method with U.S. 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” (Karl E. Case and Robert J. Shiller, 1989, pp. 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.


effects of renovations and extensions if (real) expenditures on renovations and extensions are 17known and can be temporally matched with the data on property transactions.

     The method cannot be used if indexes are required for very fine classifications of the type of property, due to insufficient observations. For example, if monthly property price indexes are required, the method may fail due to a lack of market sales for smaller categories of property. In principle, estimates for past price change obtained by the repeat sales method should 18be updated as new transaction information becomes available. Thus the Repeat Sales property

    price index is subject to never ending revision.

     We turn now to another class of methods suggested by workshop participants for forming constant quality property price indexes.

4.2 The Use of Assessment Information

     Most countries tax real estate property. Hence, most countries have some sort of official valuation office that provides periodic appraisals of all taxable real estate property. The paper by van der Wal, ter Steege and Kroese (2006) presented at the Workshop describes how Statistics Netherlands uses appraisal information in order to construct a property price index. In particular, 19the SPAR (Sales Price Appraisal Ratio) Method is described as follows:

    “This method has been used in New Zealand since the early 1960s. It also uses matched pairs, but

    unlike the Repeat Sales method, the SPAR method relies on nearly all transactions that have

    occurred in a given housing market, and hence should be less prone to sample selection bias. The

    first measure in each pair is the official government appraisal of the property, while the second

    measure is the matching transaction price. The ratio of the sale price and the appraisal of all sold

    dwellings in the base period, , serves as the denominator. The numerator is the ratio of the t0

    selling price in the reference period, , and the appraisal price in the base period for all tt

    dwellings that were sold in the reference period,” van der Wal, ter Steege and Kroese (2006, p. 3).

     We will follow the example of van der Wal, ter Steege and Kroese and describe the SPAR method algebraically. Denote the number of sales of a certain type of real estate in the

    0000base period by N(0), let the sales prices be denoted as [S,S,;,S]S and denote the 12N(0)

    17 However, usually information on maintenance and renovation expenditures is not available in the context of estimating a hedonic regression model for housing. Malpezzi, Ozanne and Thibodeau (1987, pp. 375-376) 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).”

    18 “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,” Erna van der Wal, Dick ter Steege and Bert Kroese (2006, p. 3).

    19 van der Wal, ter Steege and Kroese (2006, p. 3) noted that this method is described in more detail in Bourassa, Hoesli and Sun (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 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, ter Steege and de Vries (2006).


    00000000corresponding official appraisal prices as . Similarly, denote the [A,A,;,A]A12N(0)

    number of sales of the same type of property in the current period by N(t), let the sales prices be

    0tttttdenoted as and denote the corresponding official appraisal A prices in [S,S,;,S]S12N(t)

    0t0t0t0tthe base period as . The reason for the double superscript on the [A,A,;,A]A12N(t)

    appraisals is that we are assuming here that the appraisals are only made periodically; i.e., in period 0 but not period t. Thus the first superscript 0 indicates that the appraisal was made in period 0 and the second superscript, 0 or t, indicates that the property was sold either in period 0 or t. The value weighted SPAR index defined by van der Wal, ter Steege and Kroese (2006; 4) in

    our notation is defined as follows:

    0t000tt0t000N(t)N(t)N(0)N(0)(1) . P(S,S,A,A)[S/A]/[S/A]????DSPARnnn1n1i1ii1i

     We have labeled the index defined by (1) as P where the D stands for Dutot, since DSPAR

    the index formula on the right hand side of (1) is closely related to the Dutot formula that occurs in the theory for the elementary price index components, which are the lowest level of 20aggregation for the components used in compiling a price index.

     What is the intuitive justification for formula (1)? One way to justify (1) is to suppose

    0that the value for each property transaction in period 0 is equal to a period 0 common price Sn

    00Plevel for the type of property under consideration, say, times a quality adjustment factor, Qn

    say, so that:

    000(2) , n1,2,;,N(0). SPQnn

    00 Next, we assume that the period 0 assessed value for transacted property n, , is equal An

    00Pto the common price level times the quality adjustment factor times an error term, which Qn

    2100we write as , and which is assumed to be independently distributed with zero mean. 1;n

    Thus we have

    000000(3) , n1,2,;,N(0), APQ(1;)nnn


    00n1,2,;,N(0)(4) , . E[]0n

    where E is the expectation operator.

    00020N(0)N(0)S/A If the term on the right hand side of (1) is equal to 1, then the index reduces to a Dutot ??nnn1k1

    index. For the properties of Dutot indexes, see Chapter 20, “Elementary Indices”, in ILO (2004) or IMF (2004).

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


     Turning now to a model for the period t property price transactions, we suppose that the

    tvalue for each property transaction in period t is equal to a period t common price level for Sn

    ttPthe given property type, say, times a quality adjustment factor, say, so that: Qi

    ttt(5) , . SPQi1,2,;,N(t)ii

     Next, we assume that the period 0 assessed value for property i transacted in period t,

    00ttP, is equal to the period 0 price level times the quality adjustment factor times an AQii

    220tindependently distributed error term, which we write as 1;. Thus we have: i

    0t0t0t(6) APQ(1;) i1,2,;,N(t). iii

     Our goal is to obtain an estimator for the level of property prices in period t relative to

    t0P/Pperiod 0, which is . Define the share of transacted property n in period 0 to the total value

    0of properties transacted in period 0, , as follows: sn

    000N(0)(7) sS/S n1,2,;,N(0). ?nnk1k

    Similarly, define the share of transacted property i in period t to the total value of properties

    tstransacted in period t, , as: i

    tttN(t)sS/S(8) i1,2,;,N(t). ?iik1k

    Substituting (2)-(6) into definition (1), and using definitions (7) and (8), and we obtain the following expression for the Dutot type SPAR price index:

    0t000t(9) P(S,S,A,A)DSPAR

    tt0t0t000000N(t)N(t)N(0)N(0)[PQ/PQ(1;)]/[PQ/PQ(1;)] ????nnnn1n1i1ii1ii

    t0000t0tN(0)N(t)P/P1;s][1;s] =[][/. ??nnn1i1ii

    t0P/PThus the Dutot type SPAR index will be unbiased for the “true” property price index, ,

    provided that the share weighted average of the period 0 and t quality adjustment errors are equal to zero; i.e., there will be no bias if

    000N(0)s0(10) and ?nnn1

    t0tN(t)s0(11) . ?nnn1

     It is likely that the weighted sum of errors in period 0 is equal to zero (at least approximately) because it is likely that the official assessed values for period 0 are

    0t22 It is no longer likely that the expected value of the error term is equal to 0 since the base period assessments i

    cannot pick up any depreciation and renovation biases that might have occurred between periods 0 and t.


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