Relationship between the Variants of the User Cost Approach. By Andrew Baldwin. January 11, 2017

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1 Relationship between the Variants of the User Cost Approach By Andrew Baldwin January 11, 2017 [I am very grateful to Terry Schau, Managing Editor for BLS s Monthly Labor Review, for kindly providing me with a copy of Robert Gillingham s 1980 paper in the MLR.] Our view is that neither mortgage payments nor house prices are a good measure of housing costs. Mortgage payments mix up how houses are financed with the price of housing. On the other hand, house prices partly reflect that houses are an asset as well as a provider of housing services. Rising asset prices makes people better off, compared to rising costs of goods and services which make people worse off. Rental equivalence allows us to separate out the asset price from the price of the housing services provided. The fact that rental equivalence measures have diverged from house prices reflects the fact that the asset and housing services components of houses have moved differently. This is an advantage of the rental equivalence methodology, not a weakness. Letter from John Pullinger to Tony Cox, 9 December, 2016 The quote above provides the justification by the National Statistician to the chair of our RPI CPI User Group for discontinuing the RPIJ series after the publication of its January 2017 update in February. It cannot be taken seriously as a critique of the accounting approach used to measure owner-occupied housing (OOH) in the RPI/RPIJ as that approach is never explicitly mentioned. (The accounting approach is also used to measure OOH costs in the Canadian CPI.) Pace Mr. Pullinger, the accounting approach does not incorporate mortgage payments, only mortgage interest payments. Changes in current housing prices are reflected in the RPI/RPIJ mainly in housing depreciation. In fact, the housing depreciation component in the accounting approach is conceptually the same as the same component in an opportunity cost approach for which the rental equivalence approach Mr. Pullinger favours serves as a lower bound. The mortgage interest payments that Mr. Pullinger finds distasteful in the accounting approach are also conceptually part of the opportunity cost approach, and so one doesn t eliminate them, conceptually speaking, by the use of imputed rents. Conceptually speaking, both the accounting approach and the rental equivalence approach measure housing services; the biggest difference between them is that the accounting approach excludes the opportunity cost of owner s equity and the capital appreciation of a home that are implicitly part of the rental equivalence measure, and the accounting approach, but not the rental equivalence approach, treats transaction costs like estate agent fees as being in scope. 1

2 In what follows the discussion is always in terms of consumer price indices as cost-of-living indices or indices to be used for upratings and not as macroprudential indicators. I have argued elsewhere that for central bank use a consumer price series should use a consumer price series with an OOH component based on the net acquisitions approach. The conceptual model described below is taken from a 1980 paper by Robert Gillingham of the US Bureau of Labor Statistics, written to endorse the upcoming move of the US CPI-U and CPI-W to a rental equivalence approach to measuring OOH; for clarity I have broken out depreciation as a separate component, which Gillingham made part of his other costs component. In a simple form of the opportunity cost approach: CC tt= rr tt PP tt + δδpp tt AA tt + ZZ tt (1) where C is the user cost, r is the interest rate applicable to the house price, δ is the depreciation rate and A is the appreciation in the house price and Z are all other costs. Note that it is assumed that the house is owned outright, or at least that there is no difference between the mortgage rate and the rate of interest used to calculate the opportunity cost of owner s equity In the home. In what Gillingham(1980) describes as a world of perfect rental and resale markets and no uncertainty the rent received for the dwelling if it were rented would equal the opportunity cost of the homeowner, which would equal the rent paid by the tenant: RR tt LL = CC tt = RR tt TT (2) It can readily be seen that the interest rate appropriate to calculating the opportunity cost of owner s equity can be derived from the rent received by the landlord and the terms on the right hand side of (1): rr tt = (RR tt LL δδpp tt + AA tt ZZ tt )/PP tt (2a) This is an interest rate that Gillingham has designated an internal rate of return. Although this would seem to be about as simple an opportunity cost model as one could imagine, Iceland has actually implemented a simpler approach in its CPI, where: CC tt= rr tt PP tt + δδpp tt + ZZ tt (2b) i.e. appreciation of the house price is ignored. (See Guðnason and Jónsdóttir (2009).) 2

3 Adopting a more realistic opportunity cost model, one obtains instead: CC tt= rr eeee EE tt + rr mmmm MM tt + δδpp tt AA tt + ZZ tt (3) where rr ee is the interest rate used to calculate the opportunity cost of owner s equity, rr mm is the mortgage interest rate, E is the equity portion of the value of the home and M is the mortgage portion. Now, rather than being defined by an equality the relationship between the opportunity cost is defined by inequalities and there Is a difference between rent received by the landlord and rent paid by the tenant: RR tt LL CC tt RR tt TT (5) Gillingham ascribes the difference between rents paid by tenants and rents received by landlords to the value of a management function. One could also imagine a tax wedge between the two rents. (Here in Ontario, the Harmonised Sales Tax, a Canadian version of VAT applies to rents at the same rate as other goods and services.) If one assumes that RR tt LL = CC tt so that there is an equality rather than an inequality relationship between opportunity cost and the rent received by a landlord, then one can solve for rr ee as the internal rate of return: rr eeee = (RR tt LL rr mmmm MM tt δδpp tt + AA tt ZZ tt )/EE tt (5a) As Gillingham notes, while this is not the only way one might calculate the rate of return on owner s equity, it is in a sense, the logical and preferred one, since otherwise the measured opportunity cost may go out of bounds, exceeding the rent paid by the tenant or lying below the rent received from the landlord. Gillingham emphasizes the use of the internal rate of return as the appropriate interest rate in a footnote, writing: In measuring the (presumably current) user cost of owner-occupied housing, one might question whether current or historical mortgage interest rates are the appropriate rate with which to measure mortgage costs. The framework developed in this paper makes it clear that this issue is not important. Because the services of a house have an (implicit) market value, this value, along with whatever mortgage rate is chosen, will determine the appropriate return on equity as a residual. Thus, ceteris paribus, higher (one might read "more current" though not necessarily) mortgage interest rates result in lower equity returns and vice versa. 3

4 The appreciation term in equation (3) should be considered an ex ante projection of what the increase in house prices will be, not an ex post evaluation of what they were. The posited correspondence between rents received by a landlord and the opportunity cost of the homeowner only works in an ex ante sense, since actual market rents depend on a forward-looking evaluation of where house prices are going. Also, as a practical matter, any opportunity cost index that was based on ex-post changes in house prices on a monthly, quarterly or annual basis, would be hopelessly volatile. The ex ante forecasts are usually based on previous history. Gillingham, in his empirical work, settled on a 15-year weighted backward moving average of appreciation rates to obtain an index that was not hopelessly volatile. Sabourin and Dion (2015), in calculating an OOH series for Canada based on the opportunity cost approach, actually use an unchanging appreciation rate of 4.0% to measure it, the average annual rate of change of house prices over the period of the inflation-targeting regime ( ). (The Bank of Canada actually adopted an inflation-targeting regime in February 1991.) They are apparently unconcerned about using a constant value to measure a temporal variable in a monthly price index, or that the average rate of house price change over this period was double the target inflation rate for most of it, the Bank of Canada having a two percent target rate from 1995 forward. The appreciation term is frequently left out of opportunity cost measures of OOH. The Icelandic CPI was already mentioned. The Swedish CPI uses an opportunity cost approach for houses but not for rented flats, where a rental equivalence approach is adopted. Unlike the Icelandic CPI, the Swedish CPI includes a mortgage interest component in its opportunity cost measure, but the appreciation term is excluded. The Bank of England published a Housing-Adjusted RPI or a HARP Index in its Inflation Report through most of the 1990s. It was also an opporutunity cost index with a component for owner s equity but none for capital appreciation. (Details on it are provided in Baldwin (2015).) Whether it is there or not, there is still a link between the rental equivalence approach and the opportunity cost approach: one can always equalize the two indices by calculating the interest rate for owner s equity as an internal rate of return. Under a rental equivalence approach, transaction costs such as legal fees, estate agents fees are excluded. In National Accounting terms these are part of the residential construction component of gross fixed capital formation, and do not relate to consumption. For the most part, they have also been excluded from official series (Swedish and Icelandic CPI) and experimental series (the Bank of England s HARP index) based on the opportunity cost approach. The so-called narrow user cost index calculated as part of CPAC s research into an appropriate methodology for OOH in the CPIH was an opportunity cost index that did include all important transaction costs, even stamp duty. Sabourin and Duguay calculate their opportunity cost index including transaction costs, not excluding land transfer taxes. This is possibly just due to neglect as these are subsumed in an other owned accommodation expenses basic aggregate in the Canadian CPI that they would have had to decompose to exclude transaction costs. 4

5 My own view is that anyone serious about calculating an opportunity cost index for OOH has to exclude such transaction costs. It ill becomes an economic statistician to insist that it is the consumption of dwelling services that must be measured and then incorporate components that the SNA decided long ago were not related to consumption expenditures. Also, excluding transaction costs is consistent with the idea that the opportunity cost approach should give the same result as the rental equivalence approach. There has never been any proposal by the ONS to calculate an OOH component based on opportunity cost for the CPIH in parallel with the already published component based on rental equivalence. If the interest rate on owner s equity were calculated using an internal rate of return it would give the same result, however it would provide a detailed breakdown of where the OOH movements were coming from. This would provide either useful analysis of what was causing changes in OOH costs or such unexplainable results as to discredit the estimates. The second scenario seems more probable to me, and possibly to ONS senior management as well, which might explain why this has never been discussed. Equation (6) below shows how user costs would be redefined in an OOH series based on the accounting approach, as opposed to the schema for the opportunity cost approach given in (3): CC tt= rr mmmm MM tt + δδpp tt + ZZ tt + TTTT tt (6) Here TC indicates TC transaction costs that were not part of the opportunity cost measure. The other differences relate to exclusions: neither the opportunity cost of owner s equity nor housing appreciation are included since these are not accounting costs. To call this a limited user cost approach as the CPAC did, conflating it with the quite different opportunity cost approaches adopted by Iceland and Sweden, is simply wrong. Neither is it, as Sabourin and Duguay claim a truncated version of the user cost [meaning opportunity cost ] approach speaking of the owned accommodation component of the Canadian CPI. As shown, the opportunity cost approach differs from the opportunity cost approach not only in what it chooses to exclude, but also in what it chooses to include. It treats transaction costs as being in scope where the opportunity cost approach excludes them. This paper does not attempt to discuss at all John Astin and Jill Leyland s proposal for a Household Inflation Index, but it is worth noting that their approach to measuring OOH is much closer to the accounting approach than the opportunity cost approach. It is essentially the same as the accounting approach except that the depreciation component is replaced with a component for net equity payments towards owneroccupied homes and a component for renovations. Conceptually speaking the rental equivalence approach Mr. Pullinger favours for measuring OOH is equivalent to the opportunity cost approach and shares its disadvantages. It doesn t, or at least shouldn t, include transaction costs, but this makes it less relevant to the experience of UK homeowners who don t understand why the measurement of their living costs should be based on a national accounting manual. Again, 5

6 conceptually speaking, the rental equivalence approach does not ignore housing prices either. Even in the most dumbed-down version of an opportunity cost approach one always has a depreciation component and a component for the opportunity cost of owner s equity and the rental equivalence index, is, by construction, equivalent to an opportunity cost index where the interest rate on owner s equity is defined as an internal rate of return. So his objection to the accounting approach has no merit. This is not to say that the accounting approach, as it is currently implemented in the RPI/RPIJ, does not have defects. It omits stamp duty although it is a transaction cost like any other and should be in scope. It uses an index for houses (i.e. dwelling and lot) rather than dwellings only to measure the replacement cost of depreciation, although arguably a dwelling index would be more appropriate. (Its Canadian counterpart does use a dwelling index to measure depreciation costs, and based on the Canadian data, it would seem that the error entailed by this procedure, if that is what it is, is not large.) There is an exponential smoothing of the housing index used to calculate depreciation which does not appear to be justified. Also, arguably, transaction costs would be overstated for a cost-of-living index basing it on actual costs as is done if the UK population were stable and the stock of owner-occupied housing were increasing. Of course, the UK population is increasing, and not stable, so it is hard to know if there is any weighting problem here. If there is one, it would appear to be a second- or third-order problem. It was a terrible decision to discontinue the RPIJ after the January 2017 CPI update. It should be revoked, and the February 2017 update should introduce commodity detail for the RPIJ. It should also add stamp duty to the scope of the RPIJ, something that should have been done in March 2013, when the index was introduced. References: Baldwin, Andrew (2015), The Accounting Approach to Measuring Owner-Occupied Housing in Consumer Price Indices, RPI CPI User Group document Central Statistical Office _ Retail Prices Index Advisory Committee (1994), Treatment of Owner Occupiers Costs in the Retail Prices Index (Cm 2717) Consumer Prices Advisory Committee (2010), The Narrow User Cost Approach to Owner Occupiers Housing Costs, CPAC (10)02 Flower, Tanya (2016), Understanding the different approaches of measuring owner occupiers housing costs(ooh): Quarter 2 (Apr to June) 2016, Office of National Statistics Gillingham, Robert (1980), Estimating the user cost of owner-occupied housing, Monthly Labor Review, February, pp

7 Guðnason, R. and G.R. Jónsdóttir (2009), Owner Occupied Housing in the Icelandic CPI, chapter 9, pp in Diewert, W.E., B.M. Balk, D. Fixler, K.J. Fox and A.O. Nakamura (2009), Price and Productivity Measurement: Volume 1 -- Housing. Trafford Press. Also available at and Sabourin, Patrick and Pierre Duguay (2015), Measuring Durable Goods and Housing Prices in the CPI: An Empirical Assessment, Bank of Canada Review, fall 2015, pp