The Determinates of Holding Period Durations in the Attached Residential
Housing Market
Paper to be presented at the
Annual Meeting of the American Real Estate and Urban Economics Association
January, 2006
Boston, MA
Submitted by
Wayne R. Archer
Professor of Real Estate
Warrington College of Business
University of Florida
Gainesville, Florida 32611
wayne.archer@cba.ufl.edu
(352) 392-1330
David C. Ling
William D. Hussey Professor of Real Estate
Warrington College of Business
University of Florida
Gainesville, Florida 32611
david.ling@cba.ufl.edu
(352) 392-9307
Brent C. Smith
Virginia Commonwealth University
School of Business
Department of Finance Insurance and Real Estate
PO Box 844000
Richmond, VA 23284-4000
The Determinates of Holding Period Durations in the Attached Residential Housing Market
Objective
This study will conduct an empirical analysis of factors influencing the holding period
decisions of owners of attached residential housing units. It structures the analysis using a proportional
hazard model of ownership duration, discussed more fully below. A unique challenge with
individually owned multifamily residences (including townhouses, condominiums and cluster homes)
is that their market is driven by a combination of owner occupancy demand and rental investment
demand. Thus, “turnover” rates for individual multifamily residences are driven by a mixture of
household variables and characteristics and general investment considerations.
To estimate the hazard function, the study employs a unique and particularly rich dataset from
the city of Chicago Assessor’s Office over the 1992-2002 period. The transaction data set is combined
with information on neighborhood characteristics and the location of tax increment financing districts
(TIFs) to control for space-varying covariates of duration of ownership. The extensive nature of the
data supports multivariate analysis of intrametropolitan holding periods in a number of respects not
possible with previous studies. The continuous nature of the sales transaction data lends itself well to
the use of the Cox proportional hazard model for estimating variations in transaction frequency across
a single metropolitan area.
It is anticipated that the determinates of holding periods will differ between owner-occupants
and rental investors. Turnover for both types of owners will be influenced by local economic growth;
the inflation rate, interest rates; structural characteristics; and intraurban housing dynamics, including
neighborhood life cycles, reurbanization, road construction and other influences on neighborhood
emergence and decline. In addition, turnover for both types of owners may be influenced by local
government development policy. Especially for owner occupants, household demographics and local
employment conditions should strongly influence turnover rates. In addition, median housing cost,
median income, the percent of households in poverty, neighborhood racial composition should be
factors.
For investor owners, factors affecting investment return should dominate, including changing
vacancy rates, and factors influencing neighborhood appreciation. Especially for investors, the
decision to hold or sell should be based on incremental or marginal return criteria that compare the
benefits of retaining ownership to the benefits of an immediate sale (Bruggemen and Fisher, p. 388).
To fully analyze whether a property should be sold or retained requires investigation into 1) the
alternative investments, or homes, available and the benefits those alternatives provide, and 2) the
transaction costs and tax consequences of selling one property and acquiring another. It is this
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The Determinates of Holding Period Durations in the Attached Residential Housing Market
decision process that is impacted by factors that are both exogenous and endogenous to the
neighborhood and individual owner that will be analyzed in this research.
Introduction
Background: Analysis of Duration in Housing Markets and Real Estate Investment
Recent years have witnessed ongoing and sizable fluctuations in residential housing activity. In
many cases, market fluctuations are not well predicted, suggesting relatively high levels of variation in
liquidity and total risk in housing investment (Deng, Gabriel, Nothaft; 2003). Accordingly, investors,
regulators, and analysts have focused on improving our understanding of housing market dynamics,
including the rental housing market. Gabriel and Nothaft (2000) provide an assessment of rental
vacancy incidence and holding period duration and argue that these measures are essential to an
improved understanding of the rental price adjustment process in housing markets. However, little is
known about the determinants of multifamily holding period durations. Clearly, improved
understanding of this prominent and growing market would provide new insights regarding turnover,
building and unit occupancy, market activity and frequency of sale.
The limited literature on the duration of ownership in attached housing is due in large part, to a
lack of appropriate data. Early analyses rely on limited data resources and/or fail to specify duration of
residence in a proportional hazard framework [see, for example, Guasch and Marshall (1987),
Rosenthal (1988) and Gronberg and Reed (1992)]. Deng et al. and Gabriel and Nothaft (2000) use a
proportional hazard model to analyze rental vacancies. The BLS-CPI dataset they employ is available
across MSAs and is rich in both geographic and intertemporal detail. Semiparametric estimation of
such a model can provide significant insight with respect to both time-varying and time-invariant
determinants of ownership duration within a single metropolitan area.
Duration models have also been employed in the housing market to model time on market
(Belkin et al, 1976, Zuehlke, 1987, Haurin, 1988, and Kluger and Miller,1990), and vacancy rates.
Sternberg (1994) modeled the probability of exiting vacancy status employing a relatively restrictive
constant hazard rate framework. As suggested above, the focus of the Gabriel and Nothaft (2000)
analysis was the disaggregation and evaluation of the incidence and duration of residential vacancies,
particularly as regards estimation of equilibrium vacancy rates.
Fisher and Young (2004) examine ownership duration utilizing the commercial investment
property database maintained by the National Council of Real Estate Investment Fiduciaries
(NCREIF). Fisher and Young find that institutional investors have an average holding period of ten
years; however, their data set contains very limited information on property or location characteristics
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The Determinates of Holding Period Durations in the Attached Residential Housing Market
Finally, there is a stream of literature on optimal holding periods that focuses on the effects of
tax law changes, such as depreciation, amortization, or tax rates (especially capital gain rates). These
studies have typically been based on theoretical models or numerical simulation as opposed to any
empirical research. For example, Brueggeman, Fisher and Stern (1981) and Fisher and Stern (1982)
show how well such complexities as depreciation, recapture, tax rates, the alternative minimum tax,
discount rates, and inflation can be modeled to help investors determine optimal ex ante holding
periods. Gau and Wang (1994) develop and empirically test a holding period model recognizing not
only taxes, but also refinancing and investor-specific determinants. Based on a sample of over 1,000
real estate transactions with observed holding periods, the results of their tests support the conclusion
that investors’ consumption and investment preferences and prevailing market interest rates are more
important than tax issues in determining the holding periods of real estate investors.
The Model
The proportional hazard model originally introduced by Cox (1972) provides a particularly
useful approach to analyze the duration of residential ownership. Cox’s regression is a semiparametric
approach to survival analysis. The proportional hazard model is the most general of the regression
models because no assumptions concerning the nature or shape of the underlying survival distribution
are required. The model assumes that the underlying hazard rate (rather than survival time) is a
function of the independent variables (covariates). The method does not require that a probability
distribution be formally specified; however, unlike other nonparametric methods, Cox’s regression
does use regression paramaters in the same way as generalized linear models. The hazard function in
this model is defined as the product of a baseline hazard and a proportional factor. The hazard rate for
failure at time t is defined as,
h(t)=probability of failing between times t and t + t/((t)*(probability of failing after time t)) [1]
This hazard rate is modeled as a function of the baseline hazard (h0) at time t, and the effects of one or
more x variables as
h(t )  h0 (t ) exp( 1 x1   2 x2  ...   k xk )
[2]
or, equivalently,
ln[ h(t )]  [h0 (t )]  1 x1   2 x2  ...   k xk
[3]
where h0(t) is the baseline hazard function. “Baseline hazard” means the hazard for an observation with
all x variables equal to 0. In the case of this analysis the baseline hazard function describes the overall
shape of the hazard rate for residential ownership over time. Cox regression estimates this hazard
nonparametrically and obtains maximum-likelihood estimates of the parameters. The proportional
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The Determinates of Holding Period Durations in the Attached Residential Housing Market
hazard model evaluates the probability of ownership duration conditional on ownership of the unit to
that point in time. Therefore, the model not only evaluates the determinants of ownership termination
at the time of termination, but also analyzes owner behavior over the entire event history of ownership.
One condition of the Cox model is continuous observation of the events over the observation period.
This condition is typically not met by most economic data. Such data are most often gathered
periodically in discrete time intervals requiring augmentation of the model similar to that employed by
Deng et al. (2003). The sales observations utilized in this analysis include the day the sale occurred,
thus; the data accommodates the requirement for continuity.
One particular feature of the ownership duration data is the possibility of left censoring. Left
censoring occurs when the residential ownership starts prior to the starting point of the sample.
Concerns regarding left censoring of sample data have been well documented in the labor economics
literature. Here it is assumed that the mechanisms associated with the left censoring of the ownership
duration data are random and therefore will not bias our estimates.
The Data
The sample of multifamily parcels is derived from a database compiled by First American Real
Estate Information and Services of closed property sale transactions of single-unit sales of attached
residential dwellings.1 It is based on data from real estate transfer declarations filed with the Cook
County Assessor between January 1992 and June 2002. The dataset contains actual market transaction
and location information, occupancy status (rental versus owner occupied at time of assessment) as
well as minimal structural, and site variables. This rich data set provides a unique opportunity to
conduct a time-varying analysis of the factors determining the duration of ownership in multifamily
properties. The data set for the analysis includes approximately 30,000 observations after cleaning and
recoding. Cleaning of the data is necessary to remove those observations with missing variables and
transaction observations involving more than one property in a single transaction. The use of
multifamily property data is a viable alternative to studying the traditional detached single-family
market in Chicago because of the extensive number of residential units that are classified as
multifamily. This includes all attached residential units in the city from two-unit adjoining townhouses
through multistory apartments, comprising over 71 percent of the total residential housing stock in the
city of Chicago (US Census Bureau, 2000).
In addition, Census tract level economic indicators such as median housing cost, income,
percent of households in poverty, and racial composition represent some of the factors that are
1
Numerous transactions involving more that one residential unit were deleted from the dataset.
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The Determinates of Holding Period Durations in the Attached Residential Housing Market
hypothesized to influence turnover rate. The tract level data are obtained from the Census Bureau’s
Summary Tape File 3 for 1990 and 2000. In addition to reported values, tests will be conducted on
change variables derived from those two time periods. It is anticipated that tracts (our proxy for
neighborhoods) that are improving or deteriorating relative the city as a whole will exhibit significantly
different levels of market activity as exhibited by the duration of the ownership. Information on the
tax increment financing districts, the primary local economic development tool employed in the city of
Chicago over the last ten years, has been obtained directly from the Chicago Department of Planning
and Development, Illinois Department of the Treasury and includes data on individual TIF
characteristics such as year of origin, location, boundaries and investment to date. The data from the
various sources is combined through the use of spatial geocoding of the sales transactions and by
linking locational and area data to each observation.
Conclusion and Potential Impacts
The research proposed here is expected to produce important empirical evidence on the
determinates of holding periods in attached residential housing markets using one of the most detailed
datasets applied to this type of analysis. Further, knowledge will be enhanced on the factors that
influence duration at the intramarket level. This will be useful information for mortgage analysts as
well seeking to reduce or disperse default and prepayment risk in portfolios of loans. In the analysis
here we are decomposing the market for attached single family dwellings in Chicago into a pool of
segmented markets each with a unique set of spatial characteristics that proxy for factors that affect
stability in housing ownership. The breakthrough in this research is in this practitioner and analyst
presentation of a duration model for isolating localized market risk factors that should be considered
when seeking to diversify risk within across a single metropolitan real estate market.
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The Determinates of Holding Period Durations in the Attached Residential Housing Market
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