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Chapter 2 accounting for housing in a cpi

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Chapter 2


W. Erwin Diewert and Alice O. Nakamura1

1. Introduction
Stephen Ceccheti (2007), a former Executive Vice President and Director of Research at the New York Federal Reserve Bank, writes that: “Price stability is about helping people make their long-term plans.” The Consumer Price Index (CPI) produced by the U.S. Bureau of Labor Statistics (the BLS), is the most widely used measure of inflation. The Federal Reserve uses the CPI in various forms, along with various forms of the Personal Consumption Expenditures (PCE) price index,2 in its efforts to achieve price stability. As Ceccheti also explains, the large expenditure share for owner occupied housing (OOH) means that the way OOH is accounted for in a price index makes a great deal of difference.3 We note too that the large share for housing in consumer expenditure means that inflation in the cost of housing services greatly affects people’s living costs and longer term plans.

The rental equivalency approach is used to account for the cost of OOH services in the CPI and in the PCE price index, including core and trimmed variants of these inflation measures. Poole, Ptacek and Verbrugge (2005) of the BLS explain that for renters, “rental equivalence” is easily measured as the amount of rent paid. For owners living in their owned homes --- i.e., for owner occupiers -- this cost is unobserved because owner occupiers, in effect, rent to themselves. Thus the BLS uses the rents of rental units in the same localities as the sampled owner occupied homes to compute the rental equivalence for owner occupied housing (OOH) services. This paper raises questions about, and suggests an alternative to, sole reliance on the rental equivalence approach for accounting for OOH in a CPI.

Bauer, Haltom, and Peterman (2004) with the Federal Reserve Bank of Atlanta argue that some of the observed post-2002 increases in rental vacancy rates were causally attributable to increases in the demand for owned homes. The belief is that rapid and sustained increases in the prices for housing in many localities led some renters who had planned on purchasing homes later to enter the housing market earlier for fear of being permanently priced out of the market if they did not do this. Behaviour of this sort would have helped sustain the increases in house prices while contributing to a softening in rental markets. Concerns as to how the treatment of owner occupied housing was affecting the movements of the CPI spilled over into the financial press. For example, in Market Watch, Robb (2006) wrote that:

“The way the government computes the CPI has created a distortion that made inflation look tame when home prices were soaring, but is now making inflation look worse as price gains moderate. It’s all because the government measures everyone’s housing costs -- renters and homeowners by looking at rents, not at the cost of owning.”

As Ceccheti explains, criticisms like those above led to arguments that OOH services should be priced more directly. Cecchetti (2007) notes that:

“There is an argument that, rather than including observed rents, the existing price of a home should be in the consumer price index....

Making this change in the consumer price index would make an enormous difference. To see how big, start with the fact that since 2000, the U.S. headline CPI has risen at an average annual rate of 2.75%, while the traditional core CPI has gone up 2.20% per year on average. If government statisticians had been using the price of homes sold rather than rents, consumer price inflation would have registered an annual increase of something like 4% per year – roughly one and one-quarter percentage points higher. And core CPI inflation would have been something like 3.8%; that’s more than one and one-half percentage points above the official reading. Had these been the inflation readings, it’s hard to imagine the Fed keeping their federal funds rate target below 2% for three years.”

Direct inclusion of home prices in the CPI has been resisted by the BLS on the grounds that it is the dwelling services of OOH that the BLS is trying to price; not investment services. Nevertheless, there is no way of living in a home without investing in housing. Also, a homeowner with a mortgage cannot continue living in their home and cannot rent it out without keeping their mortgage payments up to date. Nor can they sell the home without discharging their mortgage. Thus concern has grown that the rental equivalency approach is not properly measuring inflation for OOH services. Verbrugge (2008) notes that:

“Between 1995 and 2004, the owners-equivalent-rent (OER) subindex of the CPI rose by about 30%, but the Office of Federal Housing Enterprise Oversight (OFHEO) house price index rose by over 61%, a divergence which many commentators viewed as ‘perverse’ and unacceptable.”

We argue that the shelter services provided by otherwise equivalent owned and rented accommodations are different products, just as owned and rented cars and fine art and party dresses and suits are different products. Moreover, since so many more households have opted to live in owned rather than rented accommodations in the United States, we argue that there is no way of effectively monitoring inflation as experienced by households in a period like the post 2002 years without more directly accounting for the cost of OOH services.

In section 2, we take stock of how statistical agencies in different nations are currently accounting for housing in their CPIs. Of the four measures currently in use, the rental equivalence and user cost ones have been the favourites of economists. Both these approaches can be derived from the fundamental equation of capital theory, as outlined in section 3. This theoretical basis is not the only way of justifying these approaches, but it is the basis usually noted in the official statistics literature. However, because of the assumptions involved, the use of the fundamental equation of capital theory is on less firm ground in applications to housing than to financial asset markets. Also, there is empirical evidence for housing markets that conflicts with implications of the fundamental equation of capital theory. Concerns about these approaches are taken up in section 4.

In section 5, we argue that an opportunity cost approach is the correct theoretical framework for accounting for OOH in a CPI. This approach, first mentioned in Diewert (2006), is developed more fully here.4 We explore the relationship of this new approach to the usual rental equivalency approach and to the way in which the user cost approach is implemented by Verbrugge (2008). The new approach leads to an Owner Occupied Housing Opportunity Cost (OOHOC) index that is a weighted average of the rental and the financial opportunity costs. In section 6, we outline some of the broader reasons for favouring the proposed new approach.

2. Different Concepts of the Cost of Owner Occupied Housing (OOH)
Here we briefly review the four main existing approaches for accounting of housing in official statistics: the rental equivalence, user cost, acquisitions and payments approaches.5
2.1 The Rental Equivalence Approach

The rental equivalence approach values the services yielded by a dwelling using the observed market rent for the same sort of dwelling for the same period of time (if such a rental value exists). Here we outline the implementation of this approach by the BLS for accounting for OOH in the CPI.6 We then also examine the treatment of OOH services in the Personal Consumption Expenditure component of the National Income and Product Accounts (NIPAs) compiled by the Bureau of Economic Analysis (BEA) using data inputs from the Census Bureau.

The U.S. shelter index component of the CPI is the household expenditure weighted average of several components. The two main shelter index components are the Rent of Primary Residence Index, hereafter referred to as the rent index, and the Owners’ Equivalent Rent of Primary Residence Index (hereafter referred to as the rental equivalence index). Both price observations and expenditure weights are needed for compiling the rent index and the rental equivalence index. Johnson (2006) of the BLS explains that the expenditure share weights are computed using Consumer Expenditure Survey (CES) data. Sampled census renters are asked the following about the dwellings they occupy:

“What is the rental charge to your ... unit including any extra charges for garage & parking facilities? Do not include direct payments by local, state or federal agencies. What period of time does this cover?”

And owner occupiers are asked:

“If someone were to rent your home today, how much do you think it would rent for monthly, unfurnished, and without utilities?”

The CES information is used only for the CPI expenditure share weights and this is the only data used that is collected from owner occupiers as well as renters. In contrast, the price information for housing services is only collected from renters.

To determine housing price changes, the BLS first produces a sample of local area block groups. It is assumed that changes in owners’ equivalent rent in small geographic areas (3-4 city blocks per block group) will be similar to the changes in actual rents for renters in those localities. Hence, each rental unit that is priced does double duty: it represents the renters within the block group, and it represents owner occupiers. Adjustments are made for landlord provided utilities and for the different effects of aging on owned versus rented housing.7

The main focus of this chapter is on the CPI. However, here we also some pay attention to the treatment of OOH in the U.S. National Income and Product Accounts (NIPAs). That treatment is what often is being referred to when mention is made that the U.S. uses the rental equivalence approach, but the details of how rental equivalence is implemented differ from the CPI case. Of course, if incorrect estimates of inflation are used in compiling the NIPAs, this can result in incorrect estimates of output and productivity growth. Many nations benchmark their productivity against the U.S. case, which makes the possibility that the U.S. productivity numbers are biased due to the U.S. price treatment of OOH a serious concern for many other nations as well. Also, the data sets used in accounting for OOH in the NIPAs are potentially useful as well for the new opportunity cost approach we suggest in section 5.

Housing services are a component of Personal Consumption Expenditures (PCE), and consequently are also part of the Gross Domestic Product (GDP) in the NIPAs. The rental value of tenant occupied housing and the imputed rental value of OOH are both included in the PCE housing services component. Mayerhauser and Reinsdorf (2007) explain that treating owner occupiers as renting from themselves is viewed as necessary in order for GDP to be invariant when housing units shift between tenant occupancy and owner occupancy.

Garner at the BLS and Short at the U.S. Census Bureau explain in detail how the gross rental value of owner occupied units is operationally imputed for the NIPAs and the PCE price index and how this process differs from the BLS methods for the CPI program. Garner and Short (2008) write that, first, rent-to-value ratios are computed from data collected in the decennial Residential Finance Survey (RFS).8 The most recent Residential Finance Survey is the 2001 one. For the 2001 RFS, a sample of about 50,000 addresses was drawn from the address file for the Census 2000.9 Then questionnaires were mailed to a sample of property owners and to lenders who held mortgages on the sampled properties. The RFS provides a comprehensive view of mortgage finance in the United States, including information about loans and also demographic information about the property owners. Responding to the RFS is mandatory for those sampled. This is an important consideration for collecting information from mortgage lenders. The RFS is exempt from statutes prohibiting release of financial records by financial institutions.

The RFS-based rent-to-value ratios are applied to the mid-point market values of the owner occupied units within corresponding value classes, as reported in the American Housing Survey (AHS). The AHS collects data on the nation’s rental and owner occupied housing, including apartments, single-family homes, mobile homes, and vacant housing units. National AHS data are collected biannually for about 55,000 homes. The survey is conducted by the Census Bureau for the Department of Housing and Urban Development.10

Total rental services are the product of the RFS-based value ratios in a benchmark year times the number of sample units in each value class as determined from the AHS. The average OOH equivalent value over all value classes provides an average rent estimate in a benchmark year. Between benchmark years, this estimate must be updated taking into account inflation as well as improvements in the quality of owned dwellings and any inflation in rents for dwellings of a given quality. The inflation factors are based on the OOH rent component of the CPI, while the quality change adjustment is based on estimated BEA adjustment factors.
2.2 The User Cost Approach

It is often stated that the user cost for owner occupied housing can be thought of as the cost to a household of purchasing a home at the beginning of a unit time period, living in it during the period, and re-selling it at the end of the period. Like the rental equivalence approach, the user cost approach is routinely used for a variety of assets other than housing. For example, the approach is used in the capital asset pricing literature, in production function studies, in the measurement of total factor productivity growth, and in the analysis of tax depreciation rules.

The full ex ante user cost consists of normal maintenance expenditures plus property taxes plus depreciation expenses (loss of value of the dwelling unit due to the effects of aging and wear and tear that is not offset by normal maintenance expenditures)11 plus waiting costs (the costs of forgone interest due to the funds tied up in an owned dwelling) and anticipated capital gains or losses due to housing market specific inflation over the given time period. The full ex post user cost is defined the same way except that ex post (i.e., actual) capital gains or losses are used in place of ex ante anticipated gains or losses.

Official statistics agencies that have adopted user cost approaches have so far adopted simplifications rather than the full user cost approach. Here we report on two nations that use simplified variants of the user cost approach.

2.2.1 The Canadian case12

Statistics Canada states that they use a modified user cost for OOH services. The Statistics Canada OOH measure is very different from the user cost as defined above, or in recent international manuals. The Statistics Canada measure includes the loss of value due to physical depreciation plus the following sorts of household operating costs: (a) the cost of ongoing maintenance and repairs and upkeep; (b) the cost of homeowners’ insurance and property taxes; and (c) mortgage interest cost. This treatment of OOH omits both the waiting cost of foregone interest on funds tied up in an owned dwelling and also financial appreciation or depreciation. If the physical depreciation term were dropped from the Canadian treatment, this would be a variant of the payments approach (see section 2.4).

Baldwin, Nakamura and Prud’homme (2006, 2009) explain that the mortgage interest component of the official concept is intended to estimate price induced changes in the amount of mortgage interest owed by the target population on outstanding mortgages. The Statistics Canada practice is to hold the volume of mortgage loans, by age of mortgage, constant so that interest owed depends only on house prices and interest rates; not on the changes in lump sum payments or changes in the loan-to-value ratios or the amortization periods of the outstanding loans.13

Erdur and Prud’Homme (2007) note that data on house prices enter into five parts of the OOH component of the Canadian CPI: mortgage interest cost, replacement cost (without land), insurance, realtor commissions, and legal fees. Because of this, it is unfortunate that Statistics Canada has only been able to afford to collect new house price information. It is known that new house prices often move differently from prices for pre-owned homes. At least, however, the Statistics Canada treatment does use some direct evidence about house price movements.

2.2.2 The Icelandic case

Statistics Iceland labels the OOH component of their CPI as an “owner equivalent rent” index, but describes this as a simplified user cost, as Diewert (2003) defines this term.14 Copies of all sales deeds for residential housing are filed with the Icelandic Land Registry. The deeds state the purchase prices of the properties together with the buyer liabilities and details of the interest and scheduling of payments on the debt. The Land Registry evaluates all these details and computes the present discounted value for the sale. The Icelandic owner equivalent rent is intended to reflect changes in market prices of housing and also financing costs and depreciation.

2.3 The Acquisitions Approach

For both durable and nondurable goods, the acquisitions approach charges the entire price of a purchase to the period of the purchase. The approach can potentially be applied to OOH. This approach is the one used by all official statistics agencies for all goods and services covered by a CPI (other than OOH services in the case of the nations like the United States that use other approaches for accounting for the cost of OOH). With this approach, the objective is to measure the average change in prices of the products acquired by households each period, irrespective of whether they were wholly or even partially paid for (e.g., credit purchases) or used in that period.

Only goods that the household sector purchases from other sectors are in scope with the acquisitions approach. For most products, the direct sales by households to other households are negligible. Thus, limiting coverage to purchases from other sectors makes little difference. However, when the acquisitions approach is used for OOH, the housing related expenditures that enter the CPI are mostly expenditures on new dwellings excluding land. This is because most second hand dwellings, and even most of the land used for new home construction, are excluded. The acquisitions approach is used by Australia and New Zealand (Statistics New Zealand 2006). This approach has also been tentatively chosen for the European Union’s Harmonized Indices of Consumer Prices (HICPs), which is the euro area measure of consumer price inflation.15
2.4 The Payments Approach

The payments approach only measures actual cash outflows associated with OOH. Thus the consumption of OOH services gets very little weight from fully owned dwellings. When there is moderate or high general inflation, mortgage payments swell, but there is no offsetting benefit to the homeowner since the appreciation in the housing asset is ignored. The payments approach produces high values in periods of inflation: erroneously high values in our view.

The Central Statistics Office of Ireland (2003) uses the payments approach. For owner occupiers, the Irish CPI covers the costs for repairs and decorations and other home maintenance services; house insurance; local authority charges, and mortgage interest. Mortgage interest payments are measured using a fixed basket of mortgages up to twenty years in duration.
3. The Theory of Household User Costs
As noted above, no nation uses the full user cost approach. However, reports on the treatment of OOH in official statistics make ubiquitous reference to the shared theoretical underpinnings for the user cost and the rental equivalency approaches, and it is the full user cost that is relevant in that context. Hence here we consider the full user cost approach in fuller detail.

Diewert (1974, p. 504) sets out the following user cost principles for consumer durables:

“To form the rental price (or user cost) for the services of one unit of the nth good during period t, we imagine that the consumer purchases the good during period t and then sells it during the following period (possibly to himself). Then the discounted expected rental price for the nth consumer good during period t is given by the discounted cost of the purchase of the nth good during period t minus the discounted resale value of the depreciated good during period t + 1.”

The “resale value of the depreciated good during period ” referred to in the above quotation includes not only the loss of value due to physical depreciation but also the waiting costs (i.e., the costs of forgone interest) and financial capital gains or losses.16 Dougherty and van Order (1982) helped adapt and establish the user cost as a conceptual framework in the real estate literature. Bajari, Benkard, and Krainer (2003, p. 3) observe that:

“Dougherty and Van Order (1982) were among the first to recognize that the user cost ... should be equal to the rental price of a single unit of housing services charged by a profit-maximizing landlord. Thus, the inherently difficult task of measuring an unobservable marginal rate of substitution is replaced by the much easier task of measuring rents.”

Attention to timing matters. Realized prices are determined at points in time. Rates of interest are regarded as fixed at points in time. But rates of inflation are defined for time intervals. If there is inflation, money is less valuable when received at the end versus the beginning of a period. An end of period t value can be converted to its equivalent at the beginning of that same (not the next) period by discounting by , where is the period t nominal interest rate.

Katz (2009) reviews the theoretical framework that can be used to derive both user cost and rental equivalence measures from the fundamental equation of capital theory:

“The ‘user cost of capital’ measure is based on the fundamental equation of capital theory. This equation, which applies equally to both financial and non-financial assets ... states that in equilibrium, the price of an asset will equal the present discounted value of the future net income that is expected to be derived from owning it.”

The end of period t user cost for a durable that had already been used for v periods as of the start of period t is denoted by . In box 1, the derivation of the user cost measure by Katz (2009, appendix A) is shown, recast using the notation for our paper.17 We denote the value of a home that is v years old at the start of period t by . Given only the information available at the start of period t, the expected price a home could be sold for at the end of period t, which is the start of period , is denoted by . And denotes the anticipated operating costs, largely consisting of normal maintenance plus property taxes, that are treated as being paid at the end of the period. Katz explains that the traditional user cost measure is derived by assuming that flow transactions within a period actually occur at the end of the period. Thus he derives the following end of period user cost, shown in box 1 as equation (3-4):18


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