The duration of homelessness: evidence from a national survey

JOURNAL OF

Journal of Housing Economics 12 (2003) 273–290

HOUSING ECONOMICS www.elsevier.com/locate/jhe

The duration of homelessness: evidence from a national surveyq Sam Allgooda,* and Ronald S. Warren Jr.b a

Department of Economics, University of Nebraska, Lincoln, NE, USA Department of Economics, University of Georgia, Athens, GA, USA

b

Received 27 August 2002

Abstract This paper provides evidence on the determinants of the duration of homelessness. We use newly available data from a large-scale, comprehensive microeconomic survey to estimate a parametric survival model of the length of a spell of homelessness. We find that homeless spells are longer for persons with certain demographic characteristics (such as older men) and behavioral histories (for example, previous incarceration and a history of drug and alcohol abuse). Our results suggest that current eligibility criteria for receiving housing assistance, which give preference to drug-free, single women with young children, are unlikely to reduce homelessness substantially and in a cost-effective manner. Ó 2003 Elsevier Inc. All rights reserved.

1. Introduction In the aftermath of the 1981–1982 recession, the problem of homelessness gained prominence as a pressing social issue in the United States for the first time since the Great Depression. Policymakers responded to public concerns and special-interest lobbying by enacting in 1987 the Stewart B. McKinney Homeless Assistance Act, which established the Interagency Council on the Homeless. With federal, state, and private-sector funding, data were collected and research conducted to assess q We thank Dirk Early, Jonah Gelbach, Ed Olsen, Art Snow, and an anonymous referee for helpful comments on an earlier version of this paper. * Corresponding author. Fax: 1-402-472-9700. E-mail address: [email protected] (S. Allgood).

1051-1377/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.jhe.2003.09.001

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the magnitude of the homeless problem and describe the affected population (Jencks, 1994; OÕFlaherty, 1996; Rossi, 1989). Although estimates of the prevalence of homelessness varied widely, a tenuous consensus emerged that approximately 550,000 persons were homeless on a given day, while a much larger number (approaching seven million individuals) experienced one or more episodes of homelessness over a fiveyear period (Link et al. (1994)). Despite the unparalleled prosperity of the past decade, homelessness persists as a vexing social problem, and continues to draw attention from policy analysts and politicians. Recent research by OÕFlaherty (1995, 1996) identifies a shortage of low-cost housing as the primary cause of the persistence of homelessness. Along these same lines, Quigley et al. (2001) find that a modest increase in vacancy rates combined with a decrease in the rent-to-income ratio would substantially decrease the level of homelessness. Similarly, Early and Olsen (2002) argue that targeting housing assistance at the poorest households would eliminate almost all homelessness among households that apply for such assistance.1 In contrast, Burt et al. (1999) contend that homeless persons tend to have noneconomic ‘‘vulnerabilities’’ or risk factors, such as mental-health problems and substance-abuse histories, that increase their probability of becoming homeless. Early (2002) also finds evidence that various behavioral characteristics, such as drug and alcohol abuse, contribute to the likelihood of homelessness. Other research that is concerned with identifying individual risk factors for becoming homeless includes Wasson and Hill (1998) and Early (1999). The level of homelessness is a function of both the rate at which people enter homelessness and the rate at which they exit homelessness. Previous research has focused on the determinants of becoming homeless and, as a consequence, little attention has been given to the equally important and potentially distinct influences on the probability of remaining homeless. Knowledge of the factors determining the duration of homelessness would allow agencies providing housing assistance for homeless persons to target those social, behavioral, and demographic groups that are at greatest risk for lengthy spells. Accordingly, we analyze the role of individual demographic characteristics and behavioral histories in affecting the length of a spell of homelessness. Unfortunately, previous studies of the duration of homelessness are geographically very restrictive, or analyze only specific subgroups such as the sheltered homeless (Allgood et al. (1997); Culhane and Kuhn (1998); Shinn et al. (1998)) or the street population (Hall and Freeman (1989)). To remedy these shortcomings, we use newly available data from the National Survey of Homelessness Assistance Providers and Clients (NSHAPC). These data are national in scope, and contain extremely detailed information on the socioeconomic, demographic, and behavioral characteristics of almost three thousand individuals whose most recent episode of homelessness occurred either in a shelter or on the street and was either ongoing 1 Other studies that focus on housing-market problems as the principal cause of homelessness are Early and Olsen (1998) and Grimes and Chressanthis (1997). Honig and Filer (1993) find that the variation across metropolitan areas in the rate of homelessness can be attributed to a combination of housingmarket, labor-market, and social-policy characteristics.

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or complete at the time of the survey. Our study is the first, then, to analyze the determinants of the length of a homeless spell using a large-scale, comprehensive, microeconomic data set. We use these data to estimate a parametric, Weibull survival model of the length of homeless spells. We find that the length of a homeless spell increases with age and is longer for males, never-married persons, and those who have been incarcerated in the past. Compared with their suburban counterparts, the rural homeless have shorter spells. Homeless spells are longer, on average, for those with a history of both drug and alcohol abuse, but their length is unaffected by the presence of only an alcohol problem or only a history of drug abuse. Our results also reveal that a history of mental-health problems or having received government benefits in the past decreases the average length of a homeless spell. Finally, among the self-reported primary reasons for being homeless, having recently lost a job increases the duration of homelessness, while having been asked to leave the last residence or having the last residence condemned, destroyed, or sold decreases the length of a homeless spell relative to having had financial problems. We also examine whether the effects on the duration of homelessness of race, gender, and histories of mental-health, drug, and/or alcohol problems vary with age. Our estimates imply that a spell of homelessness lengthens with age both for whites and for males, relative to their respective nonwhite and female counterparts. Similarly, for those homeless who abused only alcohol or both alcohol and drugs, spell length increases with age compared to nonabusers. Somewhat surprisingly, the length of a spell of homelessness declines with age for those with a history of mental-health problems. These results reveal that the length of a spell of homelessness is greater for persons with certain demographic characteristics (for example, older men) and behavioral histories (such as previous incarceration and substance abuse). However, current housing programs give eligibility preference to single women with young children who are not abusing drugs or alcohol. As a consequence, existing policies may not be able to reduce homelessness substantially and in a cost-effective manner. Section 2 presents a theoretical model of homelessness, sets out a flexible, parametric model of the duration of homelessness, and describes the data. Section 3 reports the empirical results. Section 4 contains a summary of our findings, and discusses several issues that suggest possibilities for future research.

2. The model and data 2.1. Theory We assume that each individual receives utility from consuming housing h, leisure l, and other goods g, where h indexes a continuum of housing services. The utility function U ðh; l; gÞ is assumed to be twice continuously differentiable and strictly quasi-concave. Each period, everyone is endowed with M units of nonlabor income, as well as T units of time which is allocated among leisure, work, and the search s for

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permanent housing. The ‘‘full-income’’ representation of the individualÕs budget constraint is wðl þ sÞ þ g þ ph ¼ wT þ M; where w is the wage rate, p is the per-unit price of housing services, and the per-unit price of g is normalized to unity. Every period, individuals sample randomly from a known distribution of housing services described by the conditional probability density function f ðhjX Þ, where X is a set of individual characteristics (such as age, race, and marital status) that determine the moments of the distribution. Each individual locates permanent housing with probability pðX ; sÞ per period. A reservation (or minimum) level of housing services hr is chosen to equate the expected benefit of continued search—in the form of greater housing services—with the marginal cost of additional search. The individual is homeless if h < hr , where h is a (random) draw from the distribution of housing services f ðhjX Þ; for convenience, we set h ¼ 0 when the individual is homeless. Individuals choose goods g, leisure l, housing-search time s, and the reservation level of housing services hr to maximize utility subject to the budget constraint. Because an individualÕs housing status (homeless or housed) is the outcome of a random process, it is convenient to write the optimization problem in state-dependent form. Superscripts on the state-dependent choice variables (goods g and leisure l) denote values of these variables that are specific to the indicated state (homeless, 0 and housed, 1). The state-independent choice variables, search time s and the reservation level of housing services hr , do not have superscripts since they are chosen at the beginning of every period regardless of the outcome (homeless or housed) of the search process. The individualÕs choice problem is: max

l0 ;l1 ;g0 ;g1

Z hr

0

U ð0; l0 ; g0 Þ df ðhjX Þ þ

Z 1

hr

U ðh; l1 ; g1 Þ df ðhjX Þ

s:t: wðl0 þ sÞ þ g0 ¼ wT þ M or

wðl1 þ sÞ þ g1 þ ph ¼ wT þ M:

The solution functions for the state-dependent choice variables are as follows. When the individual is homeless (that is, when h ¼ 0 < hr ) the optimization problem is maxU ð0; l; gÞ l;g

s:t: wl þ g ¼ wT þ M
ws: The state-dependent demand functions for leisure and goods when the individual is homeless are, respectively, l0 ðw; 0; wT þ M
ws; X Þ; g0 ðw; 0; wT þ M
ws; X Þ; where wT þ M
ws is full-income minus the opportunity cost of time spent searching for housing. When the individual consumes housing (that is, when 0 < hr < h) the optimization problem is

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max U ðh; l; gÞ l;g

s:t: wl þ g ¼ wT þ M
ws
ph: The state-dependent demand functions for leisure and goods when the individual is housed are, respectively, l1 ðw; h; wT þ M
ws
ph; X Þ; g1 ðw; h; wT þ M
ws
ph; X Þ; where wT þ M
ws
ph is full-income minus the sum of the opportunity cost of search and the expenditure for housing. The relevant optimization problem for the choices of housing-search time s and the reservation level of housing services hr is R hr U ½0; l0 ðw; h; wT þ M
wsÞ; g0 ðÞ df ðhjX ; sÞ max 0 s;hr R1 þ U ½h; l1 ðw; h; wT þ M
ws
phÞ; g1 ðÞ df ðhjX ; sÞ hr s:t: wðl þ sÞ þ g þ ph ¼ wT þ M: The solution functions for s and hr are, respectively, sðw; wT þ M; X Þ hr ðw; wT þ M; X Þ: The duration of a spell of homelessness is expected to be negatively related to housing-search time and positively related to the reservation level of housing services. As in the theory of job search, however, the implications of changes in the wage rate or in nonlabor income for mean spell length are qualitatively ambiguous without imposing additional (and arbitrary) restrictions on the model [see Devine and Kiefer (1991, p. 2003)]. The purpose of the theoretical model, then, is simply to provide motivation for the specification of the econometric model and a framework for interpreting the empirical results, rather than to establish a set of refutable predictions. 2.2. Empirical hazard The transition from a theoretical model of housing search to an empirical model of the duration of homelessness requires the derivation of an expression for the survival function or, alternatively, the hazard function. To accomplish this task, we first derive the log-likelihood function for a parametric survival (or hazard) function to describe the duration of homelessness observed in our data. In particular, we specify a Weibull model that incorporates the presence of right-censored (incomplete) spells of homelessness. We then discuss the data used to estimate the model. Let C represent the length of a completed spell of homelessness. C can be characterized alternatively (but equivalently) by any one of three related probability functions: the probability density function f ðtÞ ¼ probðC ¼ tÞ, which gives the probability that the length of a spell of homelessness equals t; the survival function

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SðtÞ ¼ probðC P tÞ, which determines the probability that a homeless spell is at least of length t; and the hazard function, H ðtÞ ¼ f ðtÞ=SðtÞ, which gives the rate at which a spell of homelessness is completed at time t, given that the spell has lasted until t. Although a number of statistical distributions can be specified to represent these probability functions, we choose the commonly adopted Weibull distribution. The hazard function for the Weibull distribution is H ðtÞ ¼ kP ðktÞ

P
1

;

where P is the ‘‘shape’’ parameter and k is the ‘‘scale’’ parameter. When P ¼ 1, the Weibull hazard function reduces to the special case of an exponential hazard, which exhibits a constant ‘‘escape’’ or exit rate k. The Weibull hazard generalizes the exponential model by allowing for positive (P > 1) or negative (P < 1) dependence of the escape rate on time. With the addition of a set of time-invariant explanatory variables X , the hazard function associated with the Weibull distribution becomes H ðt; X Þ ¼ kðX ; bÞP ½kðX ; bÞtP
1 ; where k ¼ expð
X bÞ, and b is a vector of coefficients to be estimated. The time spent homeless is most naturally expressed in terms of the survival function, which is given by Sðt; X Þ ¼ expf
½kðX ; bÞtP g: Because our data consist of observations on individuals with complete and incomplete spells of homelessness at the time of the survey interview, some observations on spell length are right-censored. Following Greene (2000, pp. 943–944), let r ¼ 1=P and define a dummy variable d ¼ 1 if the homeless spell is complete at the interview date and d ¼ 0 if the spell is ongoing (or censored). We introduce a change of variable such that v ¼ P loge ðktÞ ¼ 1=rðloge t
X bÞ; where the probability density function for v is f ðvÞ ¼ ð1=rÞ expðv
ev Þ; and the survival function is SðvÞ ¼ expð
ev Þ: The log-likelihood function is X loge L ¼ ½ d loge f ðvÞ þ ð1
dÞ loge SðvÞ or loge L ¼

X bdðv
loge rÞ
ev c;

which can be maximized to obtain solution values for P ¼ 1=r and b. The conditional mean length of a spell of homelessness is EðtjX Þ ¼ expðX bÞC½ð1=P Þ þ 1, where C is the gamma density function.

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2.3. Data We use data from the public-use client files of the National Survey of Homelessness Assistance Providers and Clients (NSHAPC). These data were collected by the US Census Bureau under the direction of the Interagency Council on Homelessness, and electronic files were created by the Urban Institute. The Census Bureau interviewed the clients of various service providers over a 4-week period in late October and early November of 1996. Sampling took place from 66 geographical areas: (1) the 28 largest MSAs; (2) 24 randomly selected small and medium-sized MSAs; and (3) 24 randomly selected groups of rural counties or parts of counties. The result is a data set with 4207 observations on more than 3000 survey items. Of the 4207 individuals interviewed, 545 were classified as never having been homeless, 2974 were currently homeless, and 688 were classified as formerly homeless. After eliminating clients who were never homeless and deleting observations with missing data, we were left with a sample of 2920 persons comprised of 402 formerly homeless and 2518 currently homeless individuals. The people in this sample were interviewed at a variety of types of service providers. For example, 41% were interviewed at emergency or transitional shelters, and 38% were interviewed at soup kitchens, food pantries, or mobile food programs. Moreover, 63% reported that, during their most recent spell of homelessness, they stayed in a shelter, 20% stayed in a hotel, motel, apartment, or dormitory room, and 13% slept outside, in a vehicle, or in an abandoned building. Our data include information on a wide variety of behavioral, socioeconomic, and demographic characteristics. Table 1 provides a list of variablesÕ names, definitions, and descriptive statistics. Individuals who were homeless at the time of the interview were asked how long their current spell has lasted. The formerly homeless were asked about the length of their most recent spell. While some clients responded in days (Nd ¼ 141) or weeks (Nw ¼ 209), most responded in months (Nm ¼ 1264) or years (Ny ¼ 1306). We converted these spell-length responses to days by multiplying weeks by 7, months by 30, and years by 364. The resulting distribution of spell lengths is highly skewed; the mean duration of a homeless spell is about 761 days, although the median spell duration is only 270 days. The timing of the variables listed in Table 1 requires some explanation. The data give the respondentÕs age at the time of the interview, but this is not the relevant age for the formerly homeless. We know, however, how long it has been since such individuals were homeless. Therefore, the variable AGE is calculated by subtracting the time since the spell of homelessness ended (if more than a year ago) from the respondentÕs age at the time of the interview. The variables representing marital status, education, and criminal history are also measured at the time of the interview. However, formerly homeless persons may have changed marital status or schooling attainment during their most recent homeless spell, or they may have had their first incidence of incarceration after their last spell of homelessness. The variable measuring years of schooling is probably accurate, however, because only five clients were below age 17 during their most recent homeless spell. Marital status and criminal history are more likely to have changed, though, so we must interpret the estimates

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Table 1 Descriptive statistics and definitions of variables Variable

Mean

SD

Definition

DURATION

760.89

1248.52

Length of current or most recent spell of homelessness, in days Age in years 1 if gender is male; 0 otherwise 1 if race/ethnicity is white; 0 otherwise 1 if marital status is married; 0 otherwise 1 if marital status is never married; 0 otherwise 1 if marital status is divorced; 0 otherwise 1 if marital status is widowed; 0 otherwise 1 if ever had a mental-health problem; 0 otherwise 1 if ever had a drug problem but not an alcohol problem; 0 otherwise 1 if ever had an alcohol problem but not a drug problem; 0 otherwise 1 if never had an alcohol or drug problem; otherwise 1 if ever had both an alcohol and a drug problem; 0 otherwise 1 if a veteran of military service; 0 otherwise 1 if ever received any government benefits; otherwise 1 if ever incarcerated; 0 otherwise 1 if ever abused or neglected before age 18; 0 otherwise Years of schooling completed 1 if location is central city; 0 otherwise 1 if location is rural; 0 otherwise 1 if location is suburban/urban fringe; 0 otherwise 1 if left last residence because of financial problems; 0 otherwise 1 if asked to leave last residence; 0 otherwise 1 if left last residence because lost job; 0 otherwise 1 if left last residence because of physical abuse; 0 otherwise 1 if left last residence because doing drugs; otherwise 1 if left town, forced to relocate, looking for work, needed change of scenery or climate; 0 otherwise 1 if building was condemned, destroyed, or sold, lease expired, problems with condition or location; 0 otherwise 1 if problematic relationship with partner/relative or death or illness in family; 0 otherwise 1 if left last residence because of medical problems; 0 otherwise 1 if left last residence because of some other reason; 0 otherwise

AGE MALE WHITE MARRIED NEVERMAR DIVORCED WIDOWED MENTAL DRUG

38.462 0.660 0.406 0.077 0.481 0.405 0.037 0.559 0.132

10.899 0.474 0.491 0.267 0.500 0.491 0.188 0.497 0.338

ALCOHOL

0.161

0.367

SOBER DRUG + ALC

0.233 0.474

0.423 0.499

VETERAN BENEFITS EXCON ABUSED

0.226 0.838 0.541 0.266

0.418 0.368 0.498 0.442

EDUC URBAN RURAL SUBURBAN FINLPROB

11.824 0.765 0.097 0.138 0.209

1.975 0.424 0.296 0.345 0.407

ASKTOLV LOSTJOB PHYSABUSE

0.202 0.127 0.046

0.401 0.333 0.209

SUBABUSE TRANSIENT

0.078 0.078

0.269 0.268

NOHOUSE

0.070

0.254

FAMPROB

0.054

0.226

MEDPROB

0.047

0.212

OTHERRSN

0.089

0.285

N

2920

Sample size

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of the coefficients on these variables with special care. Although it is possible that a client may have developed a mental-health condition or a substance-abuse problem since his or her last homeless spell, these traits are typically thought of as lifelong afflictions. It seems less likely, then, that individuals would have acquired one of these problems after their last homeless spell. It is possible, however, that some individuals first received government benefits at the completion of their most recent homeless spell, so we must also interpret cautiously the coefficient estimate on the government-benefits variable. Finally, we do not include current labor-market status or income among the covariates in our empirical model because they are likely to have changed frequently. 3. Empirical results Table 2 contains the maximum-likelihood (ML) estimates of the parameters of the survival function for the observed spells of homelessness, using the Weibull specification. Absolute values of the asymptotic t-ratios are in parentheses under the associated parameter estimates. Since the coefficients are expressed in terms of the survival function, a positive estimated coefficient indicates that an increase in the value of the associated variable increases the conditional mean length of a homeless spell, ceteris paribus. The signs of the estimated coefficients reveal the qualitative relationship between the explanatory variables and homeless-spell length, but their magnitudes do not translate directly into estimated marginal effects. To calculate these marginal effects, we first construct a baseline hazard (or escape rate from homelessness) by setting all of the dichotomous explanatory variables equal to zero, setting AGE equal to 38 (approximately the sample mean), specifying years of schooling completed to be ten, and initially setting the length of a spell of homelessness at the median value of 270 days.2 Next, we calculate the value of the hazard rate when the dummy variable has a value of one, and subtract it from the value of the baseline hazard. The marginal effects are the estimated responses of the hazard or escape rate, so changes in the escape rate will be opposite in sign to the coefficients in the survival function.3 The number in braces under the t-statistic is the percentage change in the escape rate from the baseline hazard associated with either a one-unit change in a dummy explanatory variable, a one-year increase in years of schooling completed, or a 10-year increase in age. For example, males are 27.76% less likely than females to exit homelessness given the baseline characteristics specified in Footnote 2. 2 The baseline hazard refers, then, to a 38-year-old white, married female with 10 years of schooling and no history of mental-health, drug, or alcohol problems, who has never previously received government benefits nor served in the military, was not abused or neglected as a child, has never been incarcerated, is located in the suburbs, and has been homeless for 270 days primarily because of financial problems. 3 The marginal effects are expressed in terms of the escape rate for two reasons. First, while it is most common to estimate the parameters of the survival function, it is also most common to express the probabilities in terms of the hazard. Second, the daily survival rate is almost unity, and the resulting percentage change in the survival rate is almost zero.

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Table 2 Determinants of homeless duration Variable CONSTANT AGE

MALE

WHITE

NEVERMAR

DIVORCED

WIDOWED

MENTAL

DRUG

ALCOHOL

DRUG + ALC

VETERAN

BENEFITS

EXCON

ABUSED

EDUC

URBAN

9.1763 (9.94) 0.0280 (3.16) {)14.81} 0.5685 (2.59) {)27.76} )0.1236 (0.65) {7.32} 0.7001 (2.04) {)32.99} 0.4097 (1.19) {)20.89} )0.3998 (0.82) {25.69} )0.4911 (2.41) {32.43} 0.4331 (1.42) {)21.94} 0.1411 (0.50) {)7.75} 0.5994 (2.42) {)29.02} 0.1755 (0.72) {)9.55} )1.9470 (4.81) {204.48} 0.4043 (2.00) {)20.64} 0.1697 (0.81) {)9.25} 0.0002 (0.00) {)0.01} 0.3004 (1.17) {)15.78}

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Table 2 (continued) Variable RURAL

ASKTOLV

LOSTJOB

PHYSABUSE

SUBABUSE

TRANSIENT

NOHOUSE

FAMPROB

MEDPROB

OTHERRSN

r N

)0.7317 (2.17) {51.96} )0.5581 (2.05) {37.60} 0.6977 (1.85) {)32.90} 0.2705 (0.44) {)14.33} 0.3906 (0.93) {)20.02} )0.1542 (0.40) {9.22} )0.6445 (1.91) {44.57} 0.0267 (0.07) {)1.52} )0.3024 (0.71) {18.88} )0.6869 (2.08) {48.12} 1.7470 (17.59) 2920

For each set of results reported in Tables 2 and 3, we note that the estimate of r ¼ 1=P is significantly greater than one so that P is less than one. Thus, we reject the null hypothesis that the exponential distribution characterizes the conditional hazard function in favor of the more general Weibull distribution. Moreover, since P < 1 the estimated hazard is monotonically decreasing in time, implying that the exit rate from homelessness declines with the length of a spell; that is, there is evidence of negative (positive) escape-rate (duration) dependence. 3.1. Base model We first discuss the coefficient estimates reported in Table 2. The empirical results indicate that a variety of demographic, social, and behavioral traits affect the length

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Table 3 Age, race, gender, and substance abuse as determinants of homeless duration Variablea

I

II

III

AGE

0.0202 (1.39) {)10.90} 0.5450 (2.46) {)26.77} )0.1232 (0.64) {7.30} 0.4931 (0.73) {)24.56} 0.3680 (0.34) {)18.97} )1.9374 (2.00) {202.67} )1.0437 (1.27) {81.60} )0.0251 (1.54) {72.34} 0.0014 (0.05) {)3.00} 0.0503 (2.28) {)66.47} 0.0432 (2.11) {)60.91}

)0.0204 (1.28) {12.38} )0.9414 (1.42) {71.23} )2.0910 (3.17) {230.21} )0.4551 (2.23) {29.69} 0.4582 (1.50) {)23.03} 0.0480 (0.17) {)2.70} 0.6334 (2.53) {)30.36}

0.0506 (3.18) {)66.69} 0.0411 (2.47) {)59.04}

)0.0151 (0.79) {8.99} )0.5021 (0.73) {33.25} )2.1320 (3.12) {238.32} 0.6704 (0.96) {)31.83} 0.3473 (0.32) {)18.01} )1.1151 (1.10) {89.17} )0.8857 (1.04) {65.92} )0.0288 (1.70) {86.79} 0.0028 (0.11) {)5.95} 0.0288 (1.24) {)46.51} 0.0400 (1.89) {)58.08} 0.0519 (3.13) {)67.59} 0.0288 (1.66) {)46.54}

1.7504 (17.49) 2920

1.7493 (17.40) 2920

MALE

WHITE

MENTAL

DRUG

ALCOHOL

DRUG + ALC

AGE  MENT

AGE  DRUG

AGE  ALC

AGE  (DRUG + ALC)

AGE  WHITE

AGE  MALE

1.7494 (17.48) 2920

r N a

The estimated model also contains the control variables found in Table 2.

of a spell of homelessness. The duration of homelessness increases with age; a 48-year-oldÕs escape rate is about 15% lower than that of a 38-year-old, other things equal. This finding is commonplace (see Allgood et al. (1997) and Culhane and Kuhn (1998)), and may reflect both the rising costs of housing search as people get older

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and the age-cohort effects discussed by Piliavin et al. (1993). We find that older individuals are less likely to exit homelessness, and males are homeless for a longer period of time, on average, than observationally equivalent females. However, an individualÕs race does not affect the length of a homeless spell, ceteris paribus. Marital status, the presence or absence of a history of substance abuse, and the primary reason for homelessness are all defined in the data by multiple categories, so each is specified in the model by a set of dummy variables. The size and statistical significance of a coefficient for a given dummy variable within such a set will depend, of course, on which category is omitted. Moreover, the statistical significance of a single variable does not tell us if the entire set of dummy variables is a statistically significant predictor of the survival rate. To answer this latter question, we conduct tests of the joint significance of the dummy variables for marital status, substance-abuse history, and reasons for homelessness by calculating the appropriate v2 -statistics. Three dummy variables are used to describe an individualÕs marital status (MARRIED is the omitted category). The coefficients on DIVORCED and WIDOWED are not significantly different than zero, but homeless persons who have never been married have longer spells than do those who are married. The average escape rate from homelessness for a never-married individual is only two-thirds that of someone who is married, other things equal. Overall, marital status is a statistically significant predictor of the length of a homeless spell (v2 ¼ 9:72; p ¼ 0:02). Individuals with a history of mental-health problems have shorter spells of homelessness; their average escape rate is about 32% higher than those without a history of mental-health problems. This surprising result may stem from a greater familiarity with or access to the social safety net. Neither drug nor alcohol abuse in oneÕs past, by itself, affects homeless duration. However, a history of abusing both drugs and alcohol increases the length of a spell of homelessness. Individuals with a background of both drug and alcohol problems had an escape rate from homelessness that is 29% lower than those with no history of substance abuse. The coefficients on the three dummy variables indicating the presence or absence of a substance-abuse problem are jointly significantly different from zero (v2 ¼ 6:82; p ¼ 0:08). It is interesting to note that having had a mental-health problem shortens homeless spells, but a history of both alcohol and drug abuse lengthens such spells. One possible explanation for this finding is that many service providers will not assist an individual in finding permanent housing who is obviously intoxicated (Allgood et al., 1997). Although military veterans are over-represented in the homeless population (Burt et al., 1999)), the results in Table 2 suggest that observationally identical veterans and nonveterans who are homeless have the same expected duration of homelessness. Ex-convicts, however, have an escape rate that is 20% lower on average than individuals who have never been incarcerated, ceteris paribus. This last result is consistent with the finding of Allgood et al. (1997) that persons recently released from jail typically have longer stays at a homeless shelter. Not surprisingly, past receipt of government benefits shortens homeless spells; the escape rate of those who have received such benefits is over 200% larger than those who have not. Piliavin et al. (1993) find that a common denominator among the homeless is placement in foster care as a child. It is somewhat surprising, therefore, that spells

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of homelessness are not longer on average for those who were neglected or abused as a child. Although childhood neglect or abuse may increase the probability of becoming homeless, it does not independently affect the likelihood of exiting homelessness. In addition, since the average age of the individuals in the sample is 38, this finding may reflect an attenuated effect of childhood experiences on housing outcomes as an adult. Poor households in the US are distributed somewhat evenly between cities (43%, suburbs, (34%), and rural areas (23%) (Burt et al., 1999), whereas the homeless are heavily concentrated in cities (77%). However, while city dwellers and those residing in the suburbs do not have significantly different mean spell lengths, those living in rural areas have an average escape rate that is 50% higher than their suburban homeless counterparts. Survey respondents were asked to delineate one ‘‘primary reason’’ for having been (or currently being) homeless. The estimated coefficients on the dummy variables representing these reasons for homelessness are jointly different from zero (v2 ¼ 21:42; p value ¼ 0.01) so, collectively, the primary reasons people reported for being homeless help explain the length of a spell. The omitted reason for homelessness is having had financial problems, so the qualitative effects discussed below are interpreted relative to this category. Individuals who said they were homeless primarily because they lost a job had relatively longer spells, on average. In contrast, those whose primary reason for being homeless was either (1) they were asked to leave their last residence (ASKTOLV), or (2) their residence was condemned or destroyed or problems arose with its condition (NOHOUSE), or (3) some other, unspecified reason (OTHERRSN) experienced shorter mean spells of homelessness. Interestingly, persons who stated they were homeless primarily because of physical abuse (PHYSABUSE) or family-relationship problems (FAMPROB) did not have significantly longer homeless spells. Individuals whose primary reason for homelessness was reported as substance abuse (SUBABUSE) or medical problems (MEDPROB) experienced neither longer nor shorter spells. Finally, the length of a homeless spell for transients (TRANSIENT) was not significantly different from that of the omitted group. 3.2. Interactions with age As we suggested earlier, the effects on homeless duration of histories of substanceabuse and mental-health problems may vary with age. Column I of Table 3 shows the results of interacting AGE with DRUG, ALCOHOL, DRUG + ALC, and MENTAL. The coefficients on AGE in these regressions now measure the effect of a change in age on mean spell length for a person with a history of neither a substance-abuse problem nor a mental-health problem. The coefficients on the interactions between AGE and ALCOHOL (AGE  ALC) and AGE and DRUG + ALC [AGE  (DRUG + ALC)] are both positive and significantly different from zero. Evaluated at the sample-mean age (38.462 years), the effect of a history of alcohol abuse on homeless duration is now negative. However, the relationship between past drug and alcohol abuse and spell length remains positive. There is no evidence that

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0.0007

Escape Rate

0.0006

Alcohol Abusers (ALCOHOL = 1)

0.0005 0.0004 0.0003 Nonabusers (SOBER = 1)

0.0002 0.0001 0 0

10

20

30

40

50

60

70

Age in Years

Fig. 1. Estimated escape rates from homelessness: age and alcohol abuse.

the relationship between past drug abuse alone and the length of a homeless spell is age-dependent, since the coefficient on the interaction of AGE and DRUG (AGE  DRUG) is statistically insignificant. The mediating effect of age on the relationship between substance abuse and the duration of homelessness is best understood by examining Fig. 1.4 The escape rate does not vary dramatically with age for homeless persons who have neither a drug-abuse nor an alcohol-abuse history. For those with a background of alcohol abuse, however, the initial escape rate is much higher but declines more rapidly with age. We conclude from these results that as a person with a history of either just an alcohol problem or both a drug and an alcohol problem ages, mean duration of a homeless spell lengthens. Similarly, having a history of mental problems reduces the length of a spell of homelessness, as in Table 2, and the size of the reduction decreases with age. Stereotypically, old white men are portrayed as the face of the long-term homeless. Column II displays estimates of a model specification in which AGE is interacted with the race and gender dummy variables, and the interactions of AGE with the substance-abuse and mental-health-problem variables are dropped. These results confirm that the likelihood of remaining homeless increases with age for whites and for males relative to their respective nonwhite and female counterparts. Interestingly, the independent effect of a history of abusing only alcohol is now statistically insignificant. These findings persist when the variables interacting AGE with MENTAL, DRUG, and ALCOHOL (previously deleted) are once again included in the model, as the estimates presented in column III reveal.

4 The baseline hazard illustrated in Fig. 1 is calculated by setting years of schooling equal to 10 and all dummy variables equal to zero. Age varies from 18 to 60.

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Table 4 Incidence of substance abuse among males by age and race Age <32

ALCOHOL DRUG DRUG + ALC SOBER N % population

Age 32–38

White males

Others

White males

Others

0.1465 0.1338 0.4650 0.2548 314

0.0815 0.1498 0.4119 0.3568 454

0.0789 0.1184 0.6404 0.1623 228

0.1174 0.1722 0.5245 0.1859 511

26

25

Age 39–45 ALCOHOL DRUG DRUG + ALC SOBER N % population

White males 0.1511 0.0971 0.5576 0.1942 278 24

Age >45 Others 0.1517 0.1303 0.5640 0.1540 422

White males 0.3836 0.0849 0.2685 0.2630 365 24

Others 0.1782 0.1351 0.4224 0.2644 348

We infer from these results that there are interactions among age, race, gender, and substance abuse that are not completely controlled for in the models we have estimated. A model-free perspective on this issue can be obtained from Table 4, which reports the relative frequency of types of substance abuse by age between white males and all other race and gender groups. White males under the age of 32 are almost twice as likely as all others to abuse only alcohol (15% versus 8%). This pattern reverses for those between the ages of 32 and 38; white males in that age group are actually less likely to abuse only alcohol. Yet among homeless persons over the age of 45, 38% of white males abuse only alcohol versus just 18% of the remaining groups. 4. Concluding remarks The problem of homelessness in the US persists, despite a decade of unprecedented economic growth and overall prosperity. As a consequence, homelessness continues to attract the attention of researchers and policymakers, and various policies have been proposed or enacted to reduce its prevalence. Most research studies and policy proposals have focused on identifying the factors which determine an individualÕs risk of becoming homeless. Equally important, however, is understanding the demographic, social, and behavioral traits that affect the length of a spell of homelessness or, alternatively, the exit rate from homelessness into permanent housing. This paper has provided evidence on the determinants of the duration of homelessness, using data from the National Survey of Homeless Assistance Providers and Clients. Our study differs from the existing literature in several ways. First, we analyze a cross-section of individual clients of providers of assistance to homeless persons. Thus, our data include both those who, when interviewed, were formerly

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homeless (with completed spells) and others who were homeless at the time of survey (whose spells were ongoing). Previous studies examined the duration of homelessness using either administrative data on individuals with completed spells or survey data on persons whose homeless spells were ongoing. Second, these data were collected by a survey that is nationwide in scope, providing a sample that is more representative geographically than the data used in prior research, which were limited to one or two urban areas. Finally, previous studies of the length of homeless spells were confined either to residents of a shelter or to the street homeless. In contrast, we analyze a set of observations comprised of homeless individuals from both shelters and the street. OÕFlaherty (1995, 1996), Quigley et al. (2001), and Early and Olsen (2001) suggest that homelessness can be reduced substantially by simple adjustments (for example, tighter income targeting) to current housing-market policies. However, our research reveals that homeless spells are longer for people with particular demographic characteristics (like older men) and behavioral histories (such as prior incarceration and a history of substance abuse). On the other hand, eligibility criteria for participation in subsidized or public housing programs give preference to single, drug-free woman with young children. As a consequence, existing housing policies cannot address the homeless problem in a cost-effective manner because they do not target the groups most vulnerable to lengthy spells of homelessness. There are several limitations of our paper that should be noted. First, the sample we analyze is not entirely random, since the survey was administered to clients of homeless-assistance providers who may be not fully representative of the homeless population. For example, the homeless who do not seek assistance from socialservice providers may be more likely to have longer spells of homelessness and a greater incidence of substance-abuse and mental-health problems. If this is the case, our findings understate the effects of such problems on the duration of homelessness. Second, although we control for an extensive set of observable demographic, socioeconomic, and behavioral variables to explain differences across individuals in homeless-spell lengths, there undoubtedly remains some unobservable heterogeneity for which we do not account. Third, our measure of the duration of homelessness pertains to the length of the most recent (or current) spell only. Consequently, we cannot analyze with these data the duration of homeless careers (Piliavan et al. (1993)) among those with multiple spells. Nevertheless, the data and econometric methods we use reveal the importance of targeting individuals with specific characteristics for the design of policies that seek to address persistent homelessness.

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