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with size measures and the quality of the house are found to be important ..... House-. Income. Dwelling. Size per. Costs per. Down ment. Rate for. Number.
Manfred M . Fischer and Elisabeth Aufhauser

Housing Choice in a Regulated Market: A Nested Multinomial Logit Analysis The paper integrates several important elements of the institutionalized and regulated nature of the housing market and analyzes the relationship between household type and housing choice in Vienna within a nested multinomial logit framework. In particular, the concept of household specific choice sets is used to account for institutional, informational and income-based constraints of the choice process. Government subsidies (such as housing and rent allowances, non-interest-bearingstate loans)are explicitly taken into account in the definition of variables. Housing choice is considered in three stages: the choice of a dwelling unit given dwelling type and residential zone, the choice of a dwelling type given residential zone, and the marginal choice of a residential zone. The coefficients are derived by means of a sequential ML-procedure. The empirical results clearly indicate that demographic variables have significant impacts on housing choice behavior. lncome as a single explanatory variable as well as its interacting with size measures and the quality of the house are found to be important criteria for dwelling unit choice, as housing cost variables for dwelling type choice behavior. The dwelling unit and dwelling type choice submodels fit reasonably well, whereas the residential zone model is less successful. 1. INTRODUCTION

Much of the empirical research on housing markets is based on Rosen’s (1974) hedonic theory and puts considerable emphasis on the estimation of hedonic price functions within Marshallian or Walrasian frameworks (Straszheim 1975; Mayo 1981). As Ellickson (1981), however, noted, the estimation of hedonic price functions provides limited information about consumer behavior. Growing dissatisfaction with this approach has stimulated the application of the discrete choice methodology to housing markets which is more in tune with the view that houses are indivisible commodities. The initial and seminal work The authors are es ecially grateful to the Institute of Urban Research in Vienna for providing generously the data f$e for the empirical analysis.

Manfred M . Fischer is associate professor and Elisabeth Aufhauser is a Ph.D. student in the department o f geography, University of Vienna. Geographical Analysis, Vol. 20, No. 1 (January 1988) @ 1988 Ohio State University Press Submitted and accepted 3/87.

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utilizing a nested multinomial logit model in a housing market context is Quigley’s (1976) study of short-term housing demand in Pittsburgh where the dwelling type choice is combined with locational choice. During the past decade a wide range of disaggregate models of housing choice hlave been developed (Lerman 1977; McFadden 1978; King 1980; Anas 1982; Iloehm 1982; Onaka and Clark 1983;van Lierop and Nijkamp 1984; van Lierop and Rima 1984; Clark and Onaka 1985; Quigley 1985; van Lierop 1986; BorschSupan and Pitkin 1987).In his study of Washington, Lerman (1977), for example, incorporates not only residential location and housing choice, but also a wider range of choice dimensions such as car ownership and travel mode to work within a joint-choice multinomial logit model. Anas (1982) attempts to model travel demand and residential location in the Chicago SMSA. Onaka and Clark (1983) and Clark and Onaka (1985)extend the housing choice models suggested by Quigley (1976) and McFadden (1978)by explicitly incorporating transaction costs of relocation and analyzing residential mobility and housing choice in St. Joseph County (South Bend, Indiana) within a nested multinomial logit framework. Similar in spirit is van Lierop’s work (van Lierop and Nijkamp 1984; van Lierop and Rima 1984; van Lierop 1986) in which the residential location and dwelling choice decisions are treated within a probit framework. Most of these and other studies, however, disregard the institutional structure of housing imarkets. Very few exceptions, such as the papers by King (1980),Weibull(1983), and Anas and Cho (1986), attempt to treat explicitly the institutionalized and regulated nature of the housing market. Clearly, the institutional structure of housing markets varies widely among countries. In the United States, for example, housing markets are essentially free of governmental control and interventions and, thus, can b e adequately analyzed by applying the economic theory of competitive markets. In Western Europe, however, housing markets are characterized by the coexistence of a freely competitive part of the market with a part that is subject to varying degrees and forms of governmental regulation. For this reason it is often noted that housing markets in a European context are not best conceived as being unitary, competitive, and equilibrium systems (see, e.g., MacLennan 1986). The general setting of this paper is the Vienna metropolitan housing market, a prototype of a highly regulated and institutionalized market. Rental housing is by far the dominant tenure category in this housing market (Aufhauser, Fischer, and Schonhofer 1986b). This paper attempts to integrate several important elements of the institutionalized nature of the housing market and to analyze the relationship between household type and housing choice within a nested multinomial discrete choice framework. The institutionalized nature of the housing market is considered in three ways. First, dwelling units are categorized on the basis of institutional settings. Second, household specific choice sets are defined in order to account for institutional, but also informational and income-based, constraints of the choice process. Third, government subsidies, such as housing and rent allowances and non-interest-bearing state loans (for covering the down payments a household has to provide in exchange for the right to move into a newly built dwelling) are explicitly taken into account, in both the choice and definition of dwelling unit and dwelling type specific variables (i.e., residual income, housing costs, and a dummy variable) as well as in the formation of household specific choice sets. The paper is organized as follows. Section 2 outlines the conceptual framework of the analysis and briefly introduces the basic structure of the nested multinomial logit model of housing choice. Section 3 describes the data and the

Manfred M . Fischer and Elisabeth Aufhauser / 49 categorization of households utilized to capture the influence of life-cycle factors on housing choice. Section 4 provides a brief exposition of the methodology used to estimate the nested logit choice model. The choice model is fitted on the basis of individual data for seven household types as well as for the total sample. In section 5 the results are presented. Finally, some general conclusions are drawn. 2. THE CONCEPTUAL FRAMEWORK AND THE NESTED CHOICE MODEL

Housing consumption decisions are discrete in nature. Choices are made among a set of discrete alternatives. Thus, an appropriate model for analyzing housing choice at the individual level is one of the family of discrete choice models (for a review see, e.g., McFadden 1981; Ben-Akiva and Lerman 1985; Fischer and Nijkamp 1985). The simplest and most convenient functional form for a discrete choice model is the multinomial logit form. The computational advantages of this model form, however, are paid for by a strong implication for the substitution pattern between choice alternatives, the so-calledIndependence of Irrelevant Alternatives (IIA) property, namely, that the relative probability of choice of any two alternatives depends on their attributes. In a choice context where some of the alternatives are similar the multinomial logit model may lead to counterfactual behavioral predictions. The housing market for any metropolitan area is in reality a complex of related submarkets for dwelling units with various degrees of substitutability. Dwelling units belonging to the same dwelling type are more similar than those belonging to different dwelling types. Moreover, within a given residential zone the dwelling types available are likely to be similar, at least with respect to locational characteristics, but not as similar as housing alternatives of a given dwelling type and residential zone (see Clark and Onaka 1985).An analysis of housing choice has to take these differing degrees of relatedness between dwelling units into account. Hierarchy is a way of organizing these differences. Figure 1 describes the structure of similarities between dwelling alternatives that are assumed to exist in the metropolitan housing market of Vienna. The elemental alternatives i are on the bottom of the hierarchy. The classes of the second level represent dwelling types and the classes of the third level residential zones. It is important to note that this hierarchy only represents an analytical device that reflects the relative degree of similarity among choice alternatives and does not imply that a household choosing a dwelling unit necessarily follows a path down the tree. There is strong empirical evidence that the Vienna housing market is stratified into seven dwelling types as assumed in Figure 1 where several dwelling unit specific characteristicsare valued similarly by households. These dwelling types are public housing ( d = l ) , private regulated rental old housing (d=2), private nonregulated rental old housing ( d=3) ,owner-occupied old housing (d=4), single family housing (d=5), rental/cooperative new (less than 10 years in age) housing (d=6), and owner-occupied new (less than 10 years in age) housing (d=7).Rental housing is by far the dominant tenure category. About two-thirds of the dwellings in Vienna belong to this category. About half of these dwellings are owned and managed by private landlords (type d=2) and about 40 per cent by the local authority of Vienna (type d = l ) . This high proportion of rental dwellings underlies rent control and strong security-of-tenurelegislation. In dwellings of type d=2, tenants have practically the same rights an owner would have. Not only the tenant himself but, with a few restrictions, also the children of the tenant

-

Private Non Regulated Rental Old Housing 4=3

OwnerOccupational Old Housing

Rentall Owner Cooperative OccupaNew tional Housing New Housing Public Private Housing Regulated Rental Old Housing

Private Non Regulated Rental Old Housing 4=3

Sinqle Rental/ OwnerFamily Cooperative OccupaHousing New tional Housing New Housing

Public Private Private Single Housing Regulated Non Family Rental Regulated Houslng Old Rental Housing Old Housing 471 d=2 4=3 d=I

DWELLING TYPE

FIG.1. Structure of Similaritiesbetween Dwelling Alternatives in the MetropolitanHousing Market of Vienna

Dwelling Unit jd,

/I\ /I\ /I\ /I\ /I\ /l\ /I\ /I\ /I\ /I\ /I\ /I\ /I\ /I\ /I\ /I\

UNIT

DWELLING

d=l =2 6 =l d=2 _ _ 4_ - - - - -d =-4 - -4 =- -4 =-7 - -d -- - - - -d =-5 -d-= 6- -4 =-7 - - - - - - - - - - - - - - - - - - - -

Public Private Housing Regulated Rental Old Housing

Manfred M . Fischer and Elisabeth Aufhauser / 51 enjoy the protection for the tenant in terms of the conditions necessary to terminate a contract. The dwelling can practically be inherited (seeFischer, Purschke, and Schubert 1985). This categorization of the dwellings also reflects both the differential and varied effect of housing subsidies provided by the federal and provincial governmental authorities, and captures the different nature of entry conditions to the submarkets and the aggregate nature of institutionalconstraintsupon individual choice. A household applying for a dwelling in public housing (d=l),has to enter the public queue. Only Austrian lower-income households have access. The government agency which performs the rationing of public housing follows a socioeconomic need-priority-based system in regulating the allocation of housing in this sector. In the new housing sector (d=5, d=6, and d=7, but also in new public housing) households gain access only if they are able to afford a certain amount of money (down payments) which covers a certain share of the construction costs. In order to obtain a dwelling in the privaterent-controlled old housing sector (d=2), one usually has to provide a certain amount of illegal key money (apart from costs for improvement activities carried out by the pretenant or landlord). In the free-rented private old housing sector (d=3) no key money is needed in general, but the rent levels are substantially higher than in the rentcontrolled sector (see Aufhauser, Fischer, and Schonhofer 1986b for more details). In the Vienna metropolitan housing market the spatial distribution of dwelling units exhibits strong spatial autocorrelation. To take this similarity into account the metropolitan area is divided into three major spatial submarkets: core area (z=l),suburbs (z=2), and outer regions (z=3).The first two residential zones are located in Vienna which is not only a municipality, but simultaneously an autonomous province (Land). The outer regions belong to the province of Lower Austria. Thus, this-even though rather crude-spatial disaggregation of the metropolitan area implicitly pays attention to the fact that different concrete forms of housing policy are specified and executed at the provincial level. The nested multinomial logit model, an empirical generalization of the multinomial logit model, has been developed to permit a more flexible pattern of substitution (McFadden 1978, 1981; Fischer and Nijkamp 1985; Clark and van Lierop 1986). The nested multinomial logit model based on the hierarchy of groupings of alternatives into subsets of similar choices depicted in Figure 1 is given by

where zeZ = (1,..., z’) denotes a residential zone, deD,, a dwelling type availableinzonez,andzJ,d, aspecificdwellingunitof typed inzonez. p h (z,d,i) is the probability of a household of type h choosing a dwelling unit i of type d in zone z ; ph ( i 1 z,d) is the conditional probability of choosing a dwelling unit i given its dwelling type d and zone z ; ph ( d l z ) is the conditional probability of choosing dwelling type d given its zone z ; and ph (z) is the marginal probability of selecting residential zone z. The conditional and marginal probabilities have the form of multinomial logit models:

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where the inclusive values Z and Z D, are defined by

~ i ( z , d= ) In

i*

C IZd exp ( v h ( z , d , j * ) )

(5)

t

and

and where z)h (z,d,j) is the systematic component of utility of zone z , dwelling type d and dwelling unit j [alternative (z,d,j)];uh (z,d) is thesystematic component of utility of zone z and dwelling type d [alternative ( z , d ) ] ;and uh ( z )is the systematic component of utility of zone z . The inclusive value coefficient A' ineasures the correlation among the random terms due to dwelling unit similarity within a dwelling type and zone, with A' = 0 denoting no correlation and ,k = 1indicating nearly identical unobserved attributes. Similarly, the inclusive value coefficient A is a measure of correlation among unobserved dwellingtype related attributes within a zone. The choice probability model (1)- (6) can be derived from utility maximization by defining the stochastic utility for a household of type h as

+

+

where the random utility terms ch(z,d,j),Eh(z,d,j) ~ h ( z , d and ) eh(z,d,j) ch(z,d) c h ( z ) are assumed to be independent and identically Gumbel-distributed (Ben-Akivaand Lerman 1985).A sufficient condition for theutility maximization interpretation is that all inclusivevalue coefficientslie in the unit interval (McFadden 1978, 1981).Thus, in the estimation of the nested multinomial logit model, if the estimated coefficients of the inclusive values are outside the unit interval, one can consider this as evidence of a specification error. Using a linear-in-the-parametersspecification of the systematic components of utility, equation (7) may be specified as follows:

+

where x, represents a vector of attributes specific to residential zones; x , d , a vector of attributes specific to residential zones and dwelling types; x z d i , avector of attributes specific to residential zones, dwelling types, and dwelling units; and

Manfred M . Fischer and Elisabeth Aufhauser / 53 a t, a td and a tdi,vectors of corresponding parameters for a household of type

h. The nested multinomial logit model defined by (1)- (6) connects the levels of the hierarchy outlined in Figure 1 with each other in the sense that the attributes of the lower branch alternatives influence the choice among any choice set of upper branches. For example, both the dwelling unit and the dwelling type specific attributes also influence-via the inclusive values-the residential zone choice. Thus, recursivity is an important feature of the nested choice approach. It is worth noting that this property is the major difference of a nested to a sequential choice model where the levels of the hierarchy are unrelated (BorschSupan and Pitkin 1987; see also Fischer and Maier 1986). 3. DATA AND HOUSEHOLD TYPES

The data used to estimate the nested logit model outlined in the preceding section are drawn from a home interview survey conducted in 1977 by the Austrian Institute for Empirical Social Research. The data were collected to analyze the housing costs and the economic situation of households in the Austrian urban agglomerations (Kaufmann, Knoth, and Hartmann 1979). The basic data file for the metropolitan area of Vienna consists of 2,218 households and dwellings they occupy. For the purpose of our analysis a mover household is defined as one which moved into the observed dwellingbetween the time period of 1968- 1977. After the elimination of stayer households, households moving into the compensatory housing sector, and cases with incomplete records, 1,181 (weighted) observations remained in the sample and were used to analyze the dwelling unit choice. The sample size was increased for the dwelling type and residential zone choice models, in using dwelling type-specific and zone-specific average values for the missing measurements. The hedonic theory of housing consumption implies that households differ in their marginal valuations of housing relevant attributes. Up to now, there are, however, only limited theoretical and empirical guidelines for identifying households with similar housing preferences (Onaka and Clark 1983). Here, and to some extent in accordance with previous studies, household categories are defined on the basis of life-cycle aspects. Criteria such as age of household head (