Evaluation of Price Indices by a Cohort Method

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1 Journal Evaluation of Housing of Price Research Indices by Volume a Cohort 6, Method Issue Fannie Mae All Rights Reserved. Evaluation of Price Indices by a Cohort Method Dowell Myers and John R. Pitkin* Abstract Census data are used to cross-validate housing price indices over 10-year periods, guided by demographic theory related to housing life cycles. Homeowners estimated house values are deflated by alternative price indices, creating real average house prices. These and other measures of real consumption are traced over a decade, and the indicators are compared. The criterion for evaluating the accuracy of price indices used as deflators is that cohorts passing through late middle age would be expected to have constant real average house prices over a 10-year interval. There is no confirming evidence that from 1980 to 1990 cohorts traded up to higher quality housing than they did from 1970 to However, using some indices, the cohorts real average house prices show an upturn in the 1980s versus the 1970s, casting doubt on those indices. The findings are discussed in light of potential sources of measurement error. Keywords: house price indices; census data; age cohorts Introduction This article presents a new criterion for evaluating housing price indices over long time intervals. Most price indices that seek to measure longitudinal trends are constructed from continuous series of sales data. It is assumed that these transactions are representative of the entire housing inventory at all times so that the series of transactions represents the historical movement of house prices without cumulative bias. We propose an alternative approach that can serve as a cross-check on continuous salesor appraisal-based price indices. Use of census data permits observation at widely spaced points in time, extending over several decades, thus permitting greater historical depth. Census data also afford virtually complete coverage of all homes in the nation, avoiding biases of sample selectivity. The specific method introduced here uses the cohort membership of householders as a marker to allow longitudinal analysis of large segments of the housing stock. Cohort populations can be used to define quasi-panels of homeowners whose housing can be compared between successive censuses. Cohorts in late middle age are best suited for this purpose. Their mortality rates are moderate and their home purchases and sales are infrequent, so the composition of a cohort and the housing it occupies are relatively * Dowell Myers is Associate Professor of Urban and Regional Planning at the University of Southern California and Codirector for Market Studies of the Lusk Center for Real Estate Development. John R. Pitkin is President of Analysis and Forecasting, Inc., in Cambridge, MA. The authors gratefully acknowledge the comments of two anonymous reviewers and the comments and encouragement provided by Isaac Megbolugbe. Also noted is Jesse Abraham s kind provision of two price index series. A portion of the research was supported by the Herbert U. Nelson Memorial Fund of the National Association of Realtors. Myers also acknowledges research support provided by the National Science Foundation through a grant on The Temporal Structure of Urban Residence (SES ).

2 498 Dowell Myers and John R. Pitkin stable. Rates of mobility and trading up are much higher at younger ages, and mortality is much greater in old age. What deaths and exchanges in units do occur in late middle age have little net effect on the average consumption of householders belonging to particular birth cohorts. When cohorts pass through late middle age between two censuses and their nominal house values are deflated by any price index, we would expect to see only slight changes in the cohort s real average house prices. The valuation of a late-middle-age cohort s housing consumption at different points in time can thus be used as a benchmark for evaluating price indices. This study emerged from a prior effort to model the future housing consumption of the baby boom generation (Pitkin and Myers 1994). In contrast to Mankiw and Weil (1989), cohort consumption was traced longitudinally from 1960 to 1990 and projected to The hypothesis of the Pitkin-Myers study was that cohorts per capita housing consumption continued to rise long after age 45, rather than falling as predicted for the baby boom by Mankiw and Weil. In fact, the consumption of cohorts during the 1980s, after deflation by alternative price indices, rose so much more sharply than in prior decades as to be implausible. It seemed that at least part of the explanation for the anomaly lay with price deflators that understated appreciation in house values between 1980 and In this manner, the cohort perspective on long-term trends in housing valuation was discovered to offer a potential cross-check on price indices cumulated from continuous transactions or other data. Evidence presented in this article shows that upward shifts in cohort consumption implied by certain indices during the 1980s stood in marked contrast to the situation in the 1960s and 1970s. Review of the record of other indicators of these cohorts housing consumption provides no indication that 50- and 60-year-old homeowners, on average, moved into larger or newer homes certainly not more so in the 1980s than in the 1970s. Therefore, the implication is either that these price indices did not deflate sufficiently or that the relationship between owners mean valuations and sales prices shifted between 1980 and The article begins with a review of theory that supports demographic insight into housing price indices. We also review the range of potential sources of error, both in the price indices and in our cohort-based validation instrument. Following that, we review a number of indicators of housing consumption that provide a foundation for our expectations about house value trends. Next, we address the construction of intertemporal data on cohorts house values and the selection of alternative price deflators. Results are presented graphically for all cohorts, with a particular focus on the cohort aged 60 to 64 in In the conclusion we suggest some useful further steps toward improved measurement of trends in cohort housing consumption.

3 Evaluation of Price Indices by a Cohort Method 499 Demographic Insight into Housing Price Indices A Demographic Perspective on Housing Consumption Numerous studies have shown the importance of age effects in shaping housing demand (e.g., Campbell 1966; Haurin, Hendershott, and Ling 1988; Hendershott 1988). To date, these demographic factors have not been used in the construction of price indices, except by Calhoun (1992). In explaining house value, information about the occupants may augment information on housing attributes alone. Demography is often considered to be the study of demographic characteristics, or more classically the study of fertility. However, the fundamental structure of demography has broader application to age and cohort effects on all kinds of behavior, including housing demand. The essence of demography is time and how changes can be measured and projected over time. The major dimensions are all temporal: age, period of history, and cohort membership. A research focus known as housing demography has been proposed for the study of temporally contingent behavior linking population cohorts, housing vintages, and residential mobility processes and their changes over time (Myers 1990). The temporal perspective of demography can assist with many research problems, including questions related to housing demand and, as a corollary, intertemporal price indices. Previous research has shown the role of cohort inertia to be distinct from age effects in housing consumption (Pitkin 1990). Once established in housing careers, cohorts have followed life-cycle progressions that parallel those of preceding cohorts. Parallel cohort progressions have been observed for homeownership and household headship, two measures of real housing consumption (Pitkin and Myers 1993, 1994). Modal Life-Cycle Path of House Values From birth, members of a cohort move together through an age-graded housing life cycle. Although personal variations can be extreme, the typical path is fairly similar among cohorts: leaving home, setting up separate living quarters, and then moving from renting to homeownership. Net transitions to ownership are rapid in the 20s and 30s and progressively slower in late middle age and the elderly years. Peak per capita ownership rates are not attained until around age 70. Early in the life cycle, at the same time as cohorts are acquiring homes, the average value of their housing also increases. Upward Influences on Average Values. The average size and quality of housing units owned and occupied by members of particular cohorts are observed to have increased as a result of trading up and remodeling during the life cycle. This tendency is greatest in the 30s and tapers off by age 60. An additional factor tends to raise average house values over the life cycle of a cohort: Mortality is higher among less wealthy members of a cohort and therefore probably reduces the number of renters and owners of lower priced homes. 1 1 No direct evidence of mortality differentials by housing type is known to exist. The closest evidence pertains to mortality in relation to wealth (which includes housing assets). Analysis of attrition from panel surveys, cross-referenced by the wealth of the initial respondent and cause of final nonresponse, indicates that mortality rates are three times as large among men in the bottom quintile of wealth as in the top quintile.

4 500 Dowell Myers and John R. Pitkin The effect of mortality on the proposed criterion can be mitigated by indexing married couples by the age of females the more likely survivors of spousal deaths and by avoiding ages above 65, when mortality effects are greatest. (There would be a similar influence on average values from the withdrawal from home owning by persons with more marginal circumstances and lower priced homes. However, such an effect does not appear to have been significant because ownership rates have been stable or increasing in the relevant part of the life course.) Downward Influences on Average Values. Offsetting the effects of remodeling and home improvement activities, depreciation pulls down the value of all structures. The net effect of depreciation minus remodeling may be greater on homes that have not turned over in a decade or more, because they have not been fixed up for sale or improved after possession by new owners (Myers 1984). Without remodeling and maintenance, a home occupied for more than 20 years by the same owner would be exposed to substantial depreciation due to both aging and obsolescence, but see the comments about the nonlinear declines in depreciation by Do and Grudnitski (1993) and Goodman and Thibodeau (1994). In addition, in late middle age, mortality leaves increasing numbers of surviving spouses who have an incentive to trade down to smaller and less valuable housing units. 2 Equilibrium in Late Middle Age. The maintained hypothesis of this analysis is that an equilibrium point is reached in late middle age when upward and downward influences on house values balance out. This turning point is approached slowly over a fairly wide age span, providing a period when a cohort s housing consumption remains stable. The exact age span when this equilibrium occurs can be discovered through analysis of consumption indicators reported in successive census years or in the American Housing Survey (AHS). Demographic Perspectives on Repeat-Sales Indices The housing demographic model also affords fresh perspective on biases in price indices that have been identified in the literature. In particular, we address selection bias, refinancing transaction bias, and the uncertainty about quality changes due to remodeling and depreciation. Selection Bias. Homes that are sold often and so are overrepresented in the repeat-sales database may differ systematically from the universe of all houses. For example, Case, Pollakowski, and Wachter (1991, 302 3) conclude that repeat transacting properties constitute a largely separate segment of the market with lower average rates of price Mortality rates over five years time, between ages and 65 69, were calculated as 18 percent for the bottom quintile, 11 percent for the middle, and 5 percent for the top. (This analysis is based on data reported in Jianakopolos, Ammon, Menchik, and Irvine 1989, table Their definition of wealth includes the sum of all assets and debts but excludes the capitalized value of income streams from pensions and annuities.) 2 However, mortality has declined markedly in recent decades, thus moderating the effects of this downward pressure on average housing consumption, and the sex differential in mortality has also narrowed. In 1990, mortality rates at age were only 65.3 percent as high for males as in 1960 and 73.4 percent as high for females. The decline was sharpest for males between 1980 and 1990: 17.0 percent, versus 6.1 percent for females. As a result the excess of male over female death rates declined from nearly double (94 percent) in 1980 to 72 percent in 1990 (National Center for Health Statistics 1991, table 5).

5 Evaluation of Price Indices by a Cohort Method 501 appreciation. High-turnover homes are likely to be less pleasing to their occupants and may command lower values because of visible defects or their occupants eagerness to sell (the so-called lemon effect). Additionally, high-turnover homes are more likely to be owned by young persons (whose mobility rates are typically higher), to be so-called starter homes, or simply to be newer homes that have not aged enough to acquire older, settled residents. The effect of selection bias is likely greatest for the most recent years covered in the index series, when the sample is typically very thin and composed disproportionately of highturnover houses. Homes that do transact in such a short interval are more likely to diverge from the stock as a whole, leading to subsequent revision volatility in the index as a larger, more representative sample enters the database in subsequent years. 3 Indeed, Clapp, Giaccotto, and Tirtiroglu (1991) report from a sample of Hartford properties that the slower rate of appreciation inferred from repeat sales converges on that estimated hedonically from one-time sales after a few years time. The interaction of selection bias with age of housing is especially important if units of different ages appreciate at different rates. Recent research suggests that the aging effect on house values is nonlinear, with steep depreciation in the first 15 years of dwelling life, followed by increases in value due to growing site values (Do and Grudnitski 1993; Goodman and Thibodeau 1994). Data presented below show that older cohorts are more likely to have occupied homes that have not sold in more than 20 years, and those homes are necessarily at least 20 years old. Although one reviewer has termed these nontransacting homes jewels, the opposite of lemons, the immobility is more likely a result of the cohorts age rather than of the character of the homes. In sum, the disparity between price trends based on repeat sales and those of the complete market might be exacerbated by lower turnover among older owners whose houses are appreciating relatively rapidly. Refinancing Appraisals. An additional concern is that the most representative national repeat-sales price index is actually based largely on refinancing transactions, rather than actual sales. Abraham and Schauman (1991) report that nearly 70 percent of their sample observations are based on appraisals conducted during mortgage refinancings. Concluding that more work needs to be done to evaluate the price effects of using refinancing data, Abraham and Schauman (1991, 340) speculate about whether the appraisals would boost appreciation in the index because borrowers would have an interest in receiving a higher appraised value. We suspect that the opposite effect is at work: The appraiser is hired by the lender, whose interest is to place a conservative value on the property. In practice, the appraiser need not determine the most probable selling price of the property, merely whether the property meets a threshold criterion required by the loan-to-value terms of the requested loan. This could have the effect of systematically censoring values on the high side, thereby yielding a lower rate of price appreciation. The degree of censoring would likely be greater for homeowners who have held their 3 Stephens et al. (1995) discuss revision volatility but reach an opposite conclusion about the direction of revision, finding in their inductive analysis a somewhat greater tendency toward downward than upward revision. They suspect this tendency is due to two factors: (1) 1990 was a transition year with sharp deceleration in price appreciation, and (2) initial transactions were composed of high-turnover houses that were better performers and appreciated more rapidly. The latter interpretation, of course, is the opposite of that ventured in our analysis.

6 502 Dowell Myers and John R. Pitkin homes longer (hence with more time for equity appreciation) and less for high-turnover homes. 4 However, owners who purchased their homes before 1980 may be less likely to refinance and enter the database at all. Depreciation and Remodeling. The literature on price indices discloses widespread lack of agreement about the proper measurement of two offsetting factors shaping housing quality. The repeat-sales method measures prices from a sample that is older at the second transaction than the first, and the aging effect could dampen the estimated rate of appreciation. To correct for this, one recommendation has been to apply a hybrid model mixing hedonic controls for age of structure with repeat-sales observations (Case, Pollakowski, and Wachter 1991). At the same time, remodeling inputs likely reduce the depreciation effect, although in practice these improvements in quality are very difficult to estimate. Researchers have proposed a series of rough adjustments based on average homeowner expenditures on alterations and improvements as a percentage of the value of the median-priced existing house, assumptions of unpaid labor investment (sweat equity), and assumptions of the value returns for remodeling inputs (Abraham and Schauman 1991; Peek and Wilcox 1991). These average remodeling improvements to quality are assumed implicitly to override any depreciation effects due to aging; however, it is certain that remodeling and depreciation are not randomly distributed across the stock. On balance, it is clear that the measurement of quality changes over time in the existing stock remains very uncertain and is a weak point in the construction of all price indices that are derived from repeated valuations of that stock. Demographic and Housing Data in the Census and AHS Measures of demographic characteristics and housing consumption are observable for the complete universe of households in both the decennial census and the biennial AHS. We make use of the following census and AHS variables. Definition of Variables Age is an indicator of life-cycle stage and membership in a birth cohort, since the same people who were age a in year y were age a + 10 in year y A second demographic variable, year last moved for householders, is used as an indicator of housing market participation and possible changes in housing consumption. Among homeowners this variable also indicates the length of time since the home was sold or purchased. Three objective housing unit characteristics number of rooms in housing unit, type of housing structure, and year structure was built are at once closely linked with the quality of the housing unit and invariant over time with respect to their respective numeraires. Unlike house values, these objective indicators are not subject to inflation 4 Conversely, censoring is also likely on the low side: Homes with inadequate appreciation would fail the appraisal test required for the loan and hence not enter the database, or the owners of lower valued homes would not even attempt to refinance for fear of not qualifying. In general, we assert that the effect of censoring on the high side outweighs that of censoring on the low side, although in markets suffering a general downturn in housing prices, such as California, low-side censoring may predominate because only exceptional homes qualify for refinancing and enter the transaction database. Much more research is needed on the refinancing issue.

7 Evaluation of Price Indices by a Cohort Method 503 from decade to decade, although the physical characteristics of the housing stock do change over time. 5 Respondents estimates of house value form the census s (and AHS s) measure of current house prices. Like all observations of current prices, these are heavily influenced by changes in the price level and must be deflated before they can be used as meaningful measures of real price changes. In addition, their subjective nature raises questions about their accuracy for measuring changes over time. Our research assumes that respondents estimates of home value are on average unbiased or, if not, that the bias remains constant over time. There is empirical evidence to support this assumption. Repeated investigations over the years have found respondents self-estimates to be unbiased relative to estimates by professional appraisers or actual sales prices (Kain and Quigley 1972; Kish and Lansing 1954). However, Goodman and Ittner (1993), using a much larger sample of AHS data from the late 1980s, found that respondents consistently overestimated the value of their homes relative to eventual sale prices by about 10 percent. Nevertheless, these overestimates were unbiased in the sense that they were found to bear no systematic relation to characteristics of the respondent, the home, or the market. Thus respondents estimates of house value remain a useful measurement for comparative purposes. Bias would be injected into our analysis only if respondents inflated their value estimates more in one year than in another; however, the fact that market differences do not explain the degree of overstatement of house values suggests that differences would not occur over time because of market changes. The validity of our use of respondents value estimates for measuring changes over time depends on the assumption that any such differences remain constant on average. Source of Data The demographic and housing data used in this article are drawn from the 1-in-1,000 Public Use Microdata Sample (PUMS) for the censuses of 1960, 1970, and 1980, supplemented by the 1989 AHS and the 1-in-100 PUMS for the censuses of 1980 and The larger samples for 1980 and 1990 are needed to analyze intertemporal changes for relatively small subpopulations with a minimum of sampling variability. The AHS contains all the relevant variables in the census and has the great advantage that its demographic indicators are much more current than those in the decennial census. The 1989 AHS is used as our principal estimate of 1990 house values. Dating from six months before the census, the AHS data are adjusted to an April 1990 date. We prefer these data over the census for two reasons. First, the 1990 census reports data in very broad categories in the upper range of house values (e.g., $300,000 to $399,999), whereas the AHS retains the exact estimate by the homeowner. 6 Second, AHS data are reported more frequently and allow us to extend our data series into the 1990s. 5 The year a structure was built remains constant, but the age of the structure changes continually. 6 The top 3 percent or so of observations in the AHS are grouped into an open-ended category.

8 504 Dowell Myers and John R. Pitkin Nonprice Measures of Consumption Change and Stability Before testing the different price index series against the implied changes in cohort housing consumption, we examine the evidence on the basic demographics of stability and changes in housing consumption using the invariant indicators from the census. The findings on changes that involve purchasing a home have implications also for the representativeness of all samples of market transactions. The results on changes in housing consumption will inform our subsequent consideration of the real price measures of consumption changes over time and inferences about the deflators on which they are based. The central question about cohort benchmarks for evaluating housing price indices is whether homeowners in specific birth cohorts changed their housing consumption level from one decade to the next. The data that follow support the notion that average housing consumption by these homeowners has been more stable in late middle age than at other points in the life cycle. This pattern is found to have been consistent since 1970 or longer. Homeowners Mobility and Stability of Consumption Mobility of homeowners is the first of three indicators of consumption change that are summarized and cross-classified by age, for 1980 and 1990, in table 1. The mobility behavior of homeowners is key to the demographic perspective on price indices because mobility is a primary mechanism for adjusting housing consumption. How frequently do homeowners change their residences, and how does this vary by age of households? A low rate of sales is presumed by our proposed cohort method, with the expectation that most middle-aged owners will stay in the same home. Mobility is defined here as having moved from a different home within 10 years of the census. This time interval was selected to correspond to the consumption period implicit in the use of intercensal changes. Age and homeowner status are as of census day in 1980 and In the great majority of cases, the date of purchase for this group is the same as the date of moving in, exceptions being inheritances, homes purchased after a period of rental occupancy, and absentee ownership prior to occupancy. As expected, mobility rates sharply diminish with age, in 1990 falling from 87.4 percent at ages to 27.4 percent at ages to a low of 12.0 percent at ages 85 and over. The age profile in 1980 is similar, but the rates are lower at all ages in 1990 than in In spite of the relatively low mobility in late middle age, a sizable fraction of 60- to 64-year-old homeowners in fact have occupied their homes for less than the 10-year interval. This mobility creates potential for 10-year changes in the average value of units owned by cohort members if there was net trading up or down by movers in this cohort over the period. Homeowners Mobility and Representativeness of Purchases Conversely, the evidence on mobility bears on a central assumption of transaction-based price indices: that the transaction prices are indicative of price movements in the entire

9 Evaluation of Price Indices by a Cohort Method 505 Table 1. Mobility and Housing Consumption, by Age of Homeowner, 1980 versus 1990 Age of Homeowner Percent of Owners That Moved in Last 10 Years Percent of Owner-Movers Selecting a Home Built in Last 10 Years Difference in Mean Rooms Occupied between Movers and Stayers (years)* Difference Difference Difference Total Source: PUMS B, 1 percent sample of the 1980 and 1990 censuses, U.S. total. * Age is defined by the wife in married couple households.

10 506 Dowell Myers and John R. Pitkin stock of housing units. If all homes sell on average with equal frequency, this assumption is warranted. However, if large blocks of homes are systematically underrepresented in the repeat-sales sample and are systematically different in their value trends, the derived indices would be biased. 7 As shown in table 1, fully 49.8 percent of all owner-occupants have moved into their homes within the preceding 10 years. However, if new homes constructed in that time interval are excluded, the figure drops to 37.6 percent (data not shown). With few exceptions, these occupancies represent purchases of homes that were sold by previous occupants; hence, we infer that little more than a third of all existing owner-occupied homes have turned over in a decade. It is clear from the mobility data that indices based on repeat sales exclude most homes occupied by the owners. Exclusion from repeat-sales samples is biased by age. The great majority of owners over age 55 have not moved in 10 years, even if occupants of new homes are included. In fact, further analysis of the mobility data (not shown) reveals that 49.0 percent of the homeowners in the age group have occupied their homes for 20 years or longer. By definition, these long-occupied homes have aged, and been subject to two or more decades worth of depreciation, since their apparent date of purchase. Such houses may well have special attributes that are otherwise unmeasured. For instance, Do and Grudnitski (1993) and Goodman and Thibodeau (1994) have estimated that depreciation rates decline markedly and may even become negative after houses are over 15 years old. Invariant Indicators of Changed Housing Consumption by Movers By itself, mobility does not guarantee a change in housing consumption: The move may be simply to a house of similar quality in a different location. However, a move to a new house is far more often than not associated with an increase in housing quality. Rates of mobility to new homes, defined as those built in the decade preceding the census, are shown in the middle set of columns in table 1. The specific measure is the percentage of recent-mover homeowners who occupy new houses. The new-home destination rates are remarkably similar across all age groups, in spite of the sharp decline of the underlying mobility propensity at older ages; the overall rate is 39.4 percent for This can be taken as evidence that the result of mobility among homeowners is similar at different life-cycle stages. Note that the proportion of movers buying new homes fell between 1980 and If new homes represent higher quality units, this decline suggests that homeowners moved up in the market somewhat less in the 1980s than in the 1970s. Size of home is a second invariant indicator of higher house values among owner-movers. Have owners who moved been occupying larger units than those who stayed in the same house for more than 10 years? To address this question, we calculated, by age, the 7 Not addressed here is the question of how the probability of refinancing transactions may vary by age of householder or by length of occupancy. It seems probable that homeowners who purchased their homes in the high-interest years of the 1980s would be the most likely to seek refinancing. We suspect that longer settled residents, often older, would be less likely to refinance and thereby enter the database of repeat transactions. That question deserves further research.

11 Evaluation of Price Indices by a Cohort Method 507 difference in the mean number of rooms between units occupied by movers and those occupied by stayers (last set of columns in table 1). The life-cycle profiles for 1980 and 1990 are similar. In 1990, movers occupy larger homes than stayers in the age range, but after age 44, movers occupy substantially smaller homes on average than stayers. Comparing 1980 and 1990, the last column of table 1 shows that the difference is increasingly unfavorable for movers. Only above age 69 has the gap in average home size between movers and stayers been reduced. Overall, this evidence suggests that cohorts at ages over 39 decrease, rather than increase, their housing consumption by moving. However, the data do not trace movers before and after their moves, so it is possible that the movers occupied units smaller than average both before and after moving, while the stayers occupied larger homes all along. The net effect of mobility on a cohort s housing consumption can be measured only with data on both premove and postmove housing consumption. 8 Net Changes in Cohorts Ownership of Large Single-Family Homes Many moves at all ages are no doubt lateral, between units of equal price, and, for a cohort population, trade-up moves for some members can be canceled by trade-down moves by others. Indeed, other changes over time can also affect the measurement of housing consumption by cohorts: not only mobility, but also remodeling, differential mortality, and other events. What is really desired is information on the net change in consumption after taking account of all factors. There is an alternative approach to measuring the net effects on average housing quality. A more inclusive measure is the net intercensal change in consumption experienced by all householders in specific cohorts. The proposed measure is based on the universe of all householders, including movers and stayers, owners and renters. A standard housing unit type is specified that represents the upper end of the housing consumption distribution: owner-occupied single-family units with seven or more rooms. (Attached as well as detached units are included, while mobile homes and condominiums are excluded.) Rates of large ownership, as a percentage of all householders, were calculated for five-year age groups in the United States using the censuses of 1960, 1970, 1980, and 1990 (figure 1). 9 Cohorts are traced from decade to decade as they grow 10 years older (see arrows), reflecting the net change in large single-family ownership for each cohort. The major point to observe is that during the 1980s, all cohorts older than 39 and younger than 75 exhibited little net change in ownership of large single-family homes. (The increase in large ownership after age 75 is likely a reflection of the mortality effect discussed above.) 8 Although these data are not available from the census, they could be gained from the longitudinal aspect of the AHS that records the housing origins of movers into the AHS sample. However, the use of data from the biennial AHS, with its much smaller sample size, to extrapolate 10-year net changes for cohort population groups is problematic. 9 For husband-wife households, we have consistently assigned the householder status to the wife because she is more likely to survive her husband in the home over time. For more detailed discussion, see Myers (1992) and Pitkin and Myers (1994).

12 % of Householders 508 Dowell Myers and John R. Pitkin Figure 1. Cohort Trajectories of Ownership per Householder of Single-Family Units with Seven or More Rooms Age of Householder (Years) Rapid increases are apparent in the younger portion of the housing life cycle. After age 39 the cohorts exhibit little net change from decade to decade, with few exceptions. 85+ Summary One conclusion to be reached from this review of invariant consumption indicators is that the most stable period of housing consumption is late middle age. Mobility rates are much lower than at younger ages, and overall cohort ownership of large single-family homes remains fairly constant as cohorts age from 50 to 65. The differences observed between late middle age and the next 10 years of the life cycle are modest, and mobility declines further at older ages. However, the largely unobserved effects of differential mortality and depreciation net of remodeling at older ages argue for the selection of late middle age as the age interval where cohorts have their most stable average housing consumption over a decade. It is also noteworthy that late-middle-age and elderly cohorts have not traded up to a greater degree in the 1980s than in the 1970s. Changes in average consumption by birth

13 Evaluation of Price Indices by a Cohort Method 509 cohorts appear to be stable or slightly lower in the 1980s than in the 1970s. Mobility rates of owners have declined, and the proportion of owners selecting new homes has decreased, suggesting if anything that net trading up in the market has decreased over time. Cohort Changes under Alternative Price Indices In light of the findings on invariant indicators of housing consumption of homeowners in late middle age, one would expect that real average consumption remained nearly constant in the 1980s relative to the 1970s. Net of price appreciation, it therefore seems that the average values of houses owned by members of the cohort aged in 1970 should have remained the same in 1980, and those of the following cohort aged in 1980 should have remained the same in When average respondents estimates of their homes values in current dollars are deflated by an appropriate index, the result is an estimate of real average house values. If the chosen index is an accurate measure of price movements net of quality change, then the deflated house values should represent the change in quality enjoyed by homeowners. Ten-year changes in this measure of real consumption for members of particular cohorts would be expected to be consistent with the invariant indicators of consumption reviewed above. Since none of these measures rose in late middle age during the 1980s, it also seems that any deviation from zero change during that decade is much more likely to have been negative than positive. Alternative Price Indices Used as Deflators Only a handful of housing price indices can cover a long historical record. These are briefly described here. The implicit price deflator for the residential investment component of the gross national product (GNP-Res) is based on the value costs of new construction put in place (President of the United States 1991). The cost index currently used for this purpose is the U.S. Bureau of the Census Single-Family Homes under Construction. It is based on the characteristics of current housing construction and the hedonic characteristic prices in the base year. Its validity for use as a deflator for house values depends on the accuracy of the hedonic model. In addition, there must be an assumption that quality-adjusted price differences between new and existing homes are constant that is, that differences in land values between new and existing houses and profits for producers of new housing are constant over time. 10 The Federal Housing Administration (FHA) median value of single-family homes purchased and financed with mortgages insured under the Section 203 program does encompass a mix of new and existing houses and includes land as well as structure value. However, the sample is restricted to homes falling below the upper limit for the Section 10 The Bureau of Economic Analysis has since issued a new composite fixed-weight price index to supplement the implicit deflator. Except for a somewhat smaller increase between 1980 and 1990, the 10-year changes in this index are similar to those in GNP-Res.

14 510 Dowell Myers and John R. Pitkin 203 program and thus excludes the highest value homes. The sample is also not adjusted for the changing quality of houses over time. The FHA series is valuable because it reaches back further in time than the more recently developed indices. The Freddie Mac national matched sale index developed by Abraham and Schauman (1991) was, at the time of development, the only national index including both new and existing structures and controlling for changes in the quality mix of houses sold in different periods. These controls were achieved by observing repeated transactions of the same houses and excluding those that received major remodeling improvements, although depreciation and minor remodeling effects are not controlled for. The main drawback to the Freddie Mac series is that it excludes higher priced transactions for which mortgages exceed the limit for standard conforming loans. This conforming loan limit was raised in the late 1980s, but Abraham and Schauman conclude that the change has little effect on appreciation in their derived index. This index is reported only for years after 1970; before that the Freddie Mac Index has been spliced to the FHA series to cover the complete period. Peek and Wilcox (1991) have proposed a modification of the Freddie Mac Index to account for changes in the quality of existing units between sales. This adjustment measures the effects of depreciation, net of expenditures for materials used in repairs, maintenance, and improvements and net of an assumed value of labor inputs (one equal to the expenditures for materials). On balance, the Peek-Wilcox adjustment (Adjusted Freddie Mac Index) indicates that the quality of the existing stock of residential structures has significantly increased over time and that the unadjusted Freddie Mac Index is biased upward. Most recently, Stephens et al. (1995) report a newly developed index that pools transaction data from Freddie Mac and Fannie Mae and so is termed the Agency Index. 11 This index shares the qualities of the earlier index described by Abraham and Schauman (1991) but benefits from both a larger sample size and a greater number of years for revision of the time series to reflect accumulated transactions. This index is reported only for years after 1975; before that the Agency Index has been spliced to the Freddie Mac and FHA series to cover the complete period. The values for the alternative deflator series are listed in table 2 (1980 = 1.0). It is clear from this table that the GNP-Res deflator makes the least adjustment to nominal house value increases from 1980 to 1990, while the Agency Index indicates the greatest inflation in values. It is noteworthy that the Agency Index shows greater inflation than the Freddie Mac Index, likely reflecting revisions for sample enlargement (and implicitly correction for selection biases that may depress value estimates in the most recent years when the sample is thinnest). Also noteworthy is the divergence of the Peek-Wilcox adjustments revisions for remodeling and depreciation that suggest substantially slower appreciation than either the Freddie Mac or the Agency Index. 11 The analysis that follows is based on the I-LGRS (interval-weighted linearized geometric repeat-sales estimator) series that is preferred among alternative formulations by Stephens et al. (1994).

15 Evaluation of Price Indices by a Cohort Method 511 Table 2. Alternative Housing Price Deflators Deflator 1990* GNP-Res Unadjusted Freddie Mac Adjusted Freddie Mac Freddie Mac Fannie Mae (Agency Index) * The 1990 deflator is designed for use with the fall 1989 American Housing Survey, which is six months out of phase with the spring decennial censuses. Accordingly, we have averaged the 1989 and 1990 values from each deflator series, creating a 1990 deflator that is six months short of the annual observation for Real Average House Values, by Year and Owners Cohort The required data on house values are derived from estimates by the respondents in the decennial censuses of 1960, 1970, 1980, and 1990 and the AHS of For reasons of comparability, and because of limitations in earlier surveys, we select only single-family homes on less than 10 acres with no farm or business on the property. Average house value is computed for classes of homeowners defined by five-year age groups. For married couples, the wife s age is used. The nominal house value data reported in each survey year have been deflated by the alternative price deflators, expressed now in 1990 dollars, and then assembled into time series of real average house prices for each cohort. Four price indices are compared first by graphically displaying the cohort trajectories implied when the alternative price deflators are applied. These trajectories represent the estimated quality of homes occupied by single-family homeowners as the cohort passes through its life cycle. The general pattern is that the upward trajectories are very steep for cohorts under age 40 and begin to level off toward late middle age and the elderly years. However, different decades exhibit different slopes over the same age range either because of true changes in housing quality or because of differences in the deflators. As shown earlier, our expectation is that real housing consumption should be approximately constant (flat trajectories) as cohorts pass through late middle age. GNP-Res Index. The cohort time series resulting from application of deflators defined by the GNP-Res component is shown in figure 2. Cohorts passing from 1980 to 1990 reveal sharp upward turns relative to their prior trajectories from 1970 to 1980 or the trajectories of cohorts passing through the same age range in earlier decades. As shown in table 2, this series estimates much less inflation in house values over the 1980s than the others; accordingly, the 1990 nominal house values are less deflated by this index, and the cohort trajectories of real average house prices rise sharply. The upward kink in this time series is implausible, especially in view of the stability of invariant indicators reported above. Freddie Mac Index. The cohort time series produced with deflators from the unadjusted Freddie Mac series is shown in figure 3. At all ages, trajectories of cohorts are much flatter in this series, especially in the period; values even decline for the cohort passing from age to 60 64, as homeowners begin to trade down to lower priced

16 512 Dowell Myers and John R. Pitkin Figure 2. Cohort Trajectories of Mean House Value Deflated by GNP-Res Index Value per Householder (Thousand $) Age of Householder (Years) homes. However, during the 1970s and 1980s, householders in the middle-aged and elderly cohorts sustained steady upward changes in real housing quality. For example, homeowners in the cohort aged in 1990 reached a real average house value of $109, percent higher than in 1980 at age In the preceding decade, homeowners in the cohort aged in 1980 occupied homes with a real value of $89,660, an increase of 6.0 percent from 1970 at age The implied increases in housing quality are inconsistent with the stability of the invariant indicators of consumption reported above. Adjusted Freddie Mac Index. As described above, Peek and Wilcox (1991) adjusted the Freddie Mac Index to correct for presumed changes in quality due to depreciation and remodeling. As shown in table 2, their Adjusted Freddie Mac Index estimates lower rates of appreciation and deflates nominal house values less severely. The result in figure 4 is that the cohort trajectories of real average house prices are no longer so flat in the period, but the slopes in the period are even steeper. The homeowners in the cohort passing from age to evidence real increases in house values of 13 percent in both the 1970s and the 1980s. This makes the real average price record even less consistent with the invariant indicators of housing consumption. 85+

17 Value per Householder (Thousand $) Evaluation of Price Indices by a Cohort Method 513 Figure 3. Cohort Trajectories of Mean House Value Deflated by Unadjusted Freddie Mac Index Age of Householder (Years) Agency Index. The last deflator series is derived from the recently developed, joint Freddie Mac Fannie Mae Agency Index of house prices. Of particular advantage, this series affords a larger and more representative sample of transactions for As depicted in table 2, the Agency Index records stronger appreciation during the 1980s and acts as a stronger deflator of nominal house values in Under this index, increases in housing quality during the 1980s were very small for cohorts over age 40. For example, homeowners in the cohort aged in 1990 reached a real average house value of $108,302, only 2.2 percent higher than in 1980 at age (figure 5). However, in the preceding decade, homeowners in the cohort aged in 1980 occupied homes with a real value of $91,656, an increase of 6.6 percent from 1970 at age The apparent slowdown in quality increase between the 1970s and 1980s in part reflects the fact that the Agency Index does not report a 1970 data point; that was estimated by splicing the Agency Index with the Freddie Mac and FHA series. Moreover, the evidence from the consumption indicators suggests that cohorts may have traded down more in the 1980s than in the 1970s, so real average house prices should have increased less in the 1980s than in the 1970s. 85+

18 514 Dowell Myers and John R. Pitkin Figure 4. Cohort Trajectories of Mean House Value Deflated by Peek-Wilcox Adjusted Freddie Mac Index Value per Householder (Thousand $) Age of Householder (Years) In sum, the recently developed Agency Index appears most congruent with the cohort record of housing consumption by householders in the marker cohorts during the 1980s. 12 Using this index as a deflator, real housing consumption of householders in late middle age increased by only 2.2 percent, less than half the increase estimated with the earlier Freddie Mac Index and one-sixth that estimated by the Peek-Wilcox Adjusted Freddie Mac Index. If the inferences we have suggested from the invariant consumption indicators for the same cohort populations are correct, then even the Agency Index is on the low side. By contrast, the use of the GNP-Res or the Adjusted Freddie Mac Index as a deflator is sharply incongruent with the record of the corresponding invariant indicators. 85+ Directions for Further Research Census data have the virtue of complete coverage of the universe of owner-occupied homes. This coverage is nationwide and extends down to small geographic areas. 12 House value changes during the 1980s were also estimated with census data for both 1980 and 1990, using a larger, 1-in-100 sample and defining a broader cohort aged in 1980 and in Very similar results were obtained, indicating that the consumption trends estimated here are not an artifact of using the fall 1989 AHS (as adjusted) or of small sample sizes.

19 Evaluation of Price Indices by a Cohort Method Figure 5. Cohort Trajectories of Mean House Value Deflated by Freddie Mac Fannie Mae Agency Index 120 Value per Householder (Thousand $) Age of Householder (Years) However, the major constraint to using census data in price index research is the 10-year interval between observations, which restricts census data solely for use as a valuable cross-check on cumulated short-term data series. AHS data offer similar coverage, but with much smaller sample sizes. However, their advantage is that the biennial frequency of data collection permits periodic estimation of value trends during the decade of the 1990s. The mode of analysis demonstrated in this article can be improved by further research. Foremost, research is needed to learn whether the accuracy of homeowners selfestimates of house values has shifted over time. The Goodman and Ittner (1993) study with AHS data from the mid-1980s deserves to be replicated with data from the mid- 1970s. Resolving the lingering questions about self-estimated house values is essential to instill greater confidence in the cohort criterion for evaluating price deflators. An additional set of problems for analysis concerns the role of net changes in cohort populations average housing consumption as they age. Can an exact age be defined in the housing life cycle at which average quality level is neither increasing nor decreasing but holds constant over a decade? Has this point of stability remained constant between 85+

20 516 Dowell Myers and John R. Pitkin decades, or is it shifting? Answers to these questions will help to identify more precisely the cohorts most useful for evaluating the accuracy of deflated price trends. Further questions concern the relationship between home sales and house value. How does the turnover in each cohort differentially affect the cohort s mean house value? Is there systematic attrition of higher or lower valued homes at any age of householder? Still another set of questions pertains to the effects of mortality in reshaping the composition of cohorts in the denominator of per capita housing consumption. What more can be learned about the differential effects of mortality by tenure status and by quality level? How might those differentials have shifted over time? Firm answers to the foregoing research questions are likely to be obtained more easily than answers for some of the thornier problems in the literature on housing price indices. The most difficult problem is the challenge of overcoming selection bias in repeat-sales data. In a recent 10-year period, we have found that 62 percent of existing owner-occupied homes failed to turn over even once. Other problems include correcting for the potential bias in refinancing appraisals and controlling for quality changes due to depreciation and remodeling. Development of a more reliable cohort criterion with census data will not eliminate the need to solve these other problems in the price index field, but it may help by providing a measurement device useful for evaluating, validating, or even benchmarking price indices constructed from less complete samples over shorter time intervals. Conclusions The preceding analysis has relied on continuities in average housing consumption of cohort populations as a gauge for evaluating the accuracy of different price deflators over 10-year intervals. We began with the finding that our previous cohort studies of housing capital value seemed to produce unusually large increases in value that continued from middle age into the elderly years. Either the force of upward cohort momentum is even stronger than is plausible, or several of the alternative deflators available to us must be called into question. Given the novelty of this approach, our precise conclusions must be tentative. It appears that the GNP-Res deflator is much too low, as most observers would have expected. We find also that the Adjusted Freddie Mac Index is low by about 8 percent, a finding that would not be expected, while the Unadjusted Freddie Mac Index looks far more accurate. Under our criterion, the best index is the newest, the Agency Index of combined Freddie Mac and Fannie Mae data. The relative accuracy of the Freddie Mac and Agency Indices may be explained by a fortuitous but not implausible net canceling out of depreciation and remodeling. This analysis has demonstrated how the cohort membership of householders can be used as a marker to enable longitudinal analysis of large segments of the housing stock. Cohort populations were used to define quasi-panels of homeowners whose housing can be compared between successive censuses. Repeated observations of cohort members housing values provide some of the virtues of repeat-transaction indices (but without the selection biases). Not only is housing quality fairly stable for cohorts passing through late

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