It has been argued that the design of housing policy in the western countries has shiftedfrom general subsidies stimulating new construction towards a policy more targeted at low-
� The research upon which this study is based is Wnanced by The Norwegian State Housing Bank. Per Medbyfrom NIBR gave valuable comments to an earlier version of this work. Comments from the editor and two re-viewers enabled me to improve strongly the quality of the article.
280 V. Nordvik / Journal of Housing Economics 15 (2006) 279–292
income households or households with special needs (Turner and Whitehead, 2002). Achange like this has also taken place in Norway. In Norway several diVerent targeted inter-ventions are included in the menu of housing policy. Among these, grants and loans forWrst-time buyers, and housing allowances can be classiWed as demand-side subsidies. Publichousing is classiWed as a supply side intervention. This study analyzes whether, and to whatextent, these selective programs have any impact on the housing stock. Furthermore it dis-cusses how the eVects of supply and demand-side policies diVer.
The main Wnding is that new public housing at initially low levels of the public stockadds to the housing stock. SpeciWcally, the construction of 100 new public units increasesthe total stock by 60 units. In addition, selective targeted loans toward the purchase ofowner-occupied housing yield an increase in the housing stock. The eVects of both theseprograms are decreasing in scale.
The question: What is the best housing policy? in the attempt to improve the situation ofthe not-so-well-oV, is posed by Apgar (1990). Although Apgar’s conclusion leans towardsupply side subsidies, he emphasizes that the answer depends on the situation in the localhousing market. This study can be read as part of an eVort to describe the situation in theNorwegian housing market. This is accomplished by analyzing the marginal eVects ofimportant selective interventions on the housing stock in 432 Norwegian municipalities in2001.
The analysis of the study is meant to contribute towards an answer to the question:What is the best housing policy? It does not provide a complete answer. A welfare analysisof diVerent housing policies would have to treat their eVects on aVordability, the size andquality of the housing stock and the distribution of the housing stock. We only analyze thepartial question of whether, and to what extent, diVerent programs aVect the total numberof housing units in a local housing market.
Subsidies and targeted interventions in local housing markets can improve the circum-stances of the households to whom they are allocated. However, such programs will alsoaVect the situation of others through the eVects upon market equilibrium. Hence, the basicapproach of the study is to analyze how the market equilibrium is aVected by the designand scale of the programs. Rothenberg et al. (1991) express related thoughts when theywrite (p. 48):
Housing market events and government policy initiatives which impact one submarketwill have their primary eVects in that submarket, with secondary eVects appearing inother submarkets to the extent those submarkets are linked in substitution possibilitieswith the original target submarket.
Substitution possibilities should here not be understood in a narrow sense. For marketsegments to be related the direct substitution between the markets need not be strong. Twomarket segments can be related because both segments are close substitutes to a third seg-ment, see Nordvik (2004).
Although the literature on the topics of this study is rather thin, there exist some rele-vant studies that are summarized in part 3. Furthermore, the existing literature on thistopic has given diverging empirical results and is US-centric. Consequently, an additionalstudy based on European data is a useful extension of the literature. This study adds to theexisting literature by testing the hypothesis that public housing interventions have adecreasing marginal impact on the housing stock by using a continuous piecewise linearspline.
V. Nordvik / Journal of Housing Economics 15 (2006) 279–292 281
Apart from the introductory remarks of Section 1, an informal theoretical backgroundis given in Section 2. Section 3 brieXy reviews the literature. The data used in the empiricalwork is described in Section 4. Formulation of an empirical model is treated in Section 5,while Section 6 contains the estimation results and their interpretations. Concludingremarks, included some speculations on how to extend the knowledge of the topic, is givenin Section 7.
2. Theoretical background
This is mainly an empirical study on how the housing stock is aVected by the presenceand scale of diVerent selective housing programs. A brief non-formal theoretical frame-work for the empirical analysis is given in this section. The basic approach relies on theassumption that housing markets clear, and that market clearing in the long- and short-rundiVers.
Consider a housing market with a Wxed number of housing units and a Wxed number ofpotential households.1 A (short-run) equilibrium in this market is an allocation of (poten-tial) households over the existing housing units. If the number of households is higher thanthe number of housing units, one can describe the equilibrium in terms of those who havetheir own housing unit and those who do not. Those who have their own housing unit willbe called insiders while those who do not, are called outsiders. The outsider who is closestto getting access to the housing stock is called the marginal consumer.
Under a system where prices move to clear the market, both prices and rents are also anatural part of a description of the equilibrium in a local housing market. It can be shownthat the short-run equilibrium price is slightly above the marginal consumer’s willingnessto pay for housing.
What happens if a selective type of demand-side intervention is introduced, or its scale isexpanded, in this market? The short-run consequences depend on how the demand-sidesubsidies are allocated. Two extremes can be considered:
(i) All demand-side subsidies are allocated to insiders in the market. This will not aVectthe equilibrium of the local housing market. The economic position of the insiderswill be improved.
(ii) All demand-side subsidies are allocated to outsiders. This will improve the competi-tive strength of the outsiders. In eVect they can outbid some of the initial insiders, andprices and/or rents will shift upwards. Hence a change in the distribution of consum-ers and an increase in prices are the eVects of the program.
Empirically, most demand-side programs will work as a combination of the twoextremes above. Note also that a ‘mere’ change in the distribution of the consumers intoinsiders and outsiders is not necessarily a socially ineYcient outcome. Quite to the con-trary, it can be an (or even the) intended eVect of a demand-side program. If, for example, ademand-side housing subsidy targets families with children, it may be eVective but will, atleast in the short-run, produce a tighter housing market and worse housing conditions for
1 Börsch-Supan and Axel (1986) deWnes a nucleus as a single person or a couple (with or without children) thatcan possibly form a household of its own. A nucleus will be the same as a potential household, and the latter termis used here.
282 V. Nordvik / Journal of Housing Economics 15 (2006) 279–292
others. It is important that policy makers are aware of this. Consequently, an importantpart of the construction of selective housing programs is the design of eligibility criteria.
Hence our understanding of the possible societal gains from housing policy programs isnot as restrictive as that of Sinai and Waldfogel (2005). In their view, a housing programshould either increase the number of housing units or increase the quality of the housingstock if it is to be regarded as successful. We also see intended eVects on housing distribu-tion as part of the possible return of a housing program. Of course, the dimensions empha-sized by Sinai and Waldfogel are very important. Their focus on equilibrium outcomesrather than initial allocations does take empirical research on selective programs in localhousing markets an important step forward.
Under a longer time horizon the assumption of a Wxed number of housing units is nolonger appropriate. Prices act as signals for new construction. If observed prices exceed thecost of expanding the housing stock, new construction is proWtable and the size of thehousing stock increases. A larger housing stock would in turn depress the equilibrium levelof house prices. If, on the other hand, prices are lower than the cost of expansion, not evenreplacement investments will be undertaken; consequently the size of the housing stock isgradually reduced and prices are increased. These structures yield the well-known meanreverting structure of house prices over time.
The quantitative long-run eVect of price increases depends on the elasticity of housingsupply. The more elastic the supply is the stronger is the eVect on the housing stock and theweaker is the long-run price eVect. In Poterba’s terms, a perfectly elastic supply corre-sponds to a horizontal long-run marginal cost of expansion of housing capital, while a per-fectly inelastic supply corresponds to a vertical curve. Empirical estimates of supplyelasticity vary quite a great deal, see Malpezzi and Maclennan (2001). Furthermore, there isno reason to believe that the elasticity of housing supply should not diVer among localhousing markets. However, most estimates indicate that the marginal cost curve is upwardsloping. Above it was argued that the magnitude of short-run eVects on prices depends cru-cially on how demand-side subsidies are allocated. As a consequence the long-run eVect onthe housing stock will also depend on the allocation policy.
In the short-run a selective housing policy on the supply side works quite diVerentlyfrom demand-side policies. Consider a supply side policy that consists of construction ofpublic housing units, or that provides incentives for private or other agents (either forproWt or non-proWt) to produce housing for targeted groups. The low-income housing taxcredit scheme in the US is an example of this latter type. For a description, see Cummingsand DiPasquale (1999). The initial eVect of such programs is an increase in the total hous-ing stock equal to the housing units built under the program.
The increased stock of targeted housing produced under a supply side program willprobably absorb part of the demand that otherwise would have been directed towards theordinary housing stock. A downward shift in the demand for ordinary housing shifts pricesdownwards. A suYcient condition for aggregate demand for ordinary housing to shiftdownwards is that some subsidized units are allocated to insiders in the local housing mar-ket. Reduced prices reduce the proWtability of new construction and consequently the levelof new construction. Note that downward adjustments of the housing stock may last a verylong time before a new long-run equilibrium is reached. Furthermore, the speed of adjust-ment in a growing market and in a steady-state (and also in a declining) market diVerstrongly. In a growing market, absorption of some demand for ordinary housing shifts newconstruction downwards and expansion of the housing stock is slower than it otherwise
V. Nordvik / Journal of Housing Economics 15 (2006) 279–292 283
would have been. In a steady-state market the equilibrium stock of ordinary housing islower than the initial stock. An absolute reduction of this kind must occur through depre-ciation, and this is a slow process.2
Hence, direct additions to the housing stock through supply side programs will probablyincrease the long-run equilibrium housing stock, but the increase will be lower in magnitudethan the program size. One can say that public housing partially crowds out ordinary hous-ing. The crowding out works through absorption of demand. As for demand-side subsidies,the eVects of supply side interventions also depend on allocation schemes. This is due to thefact that the extent of absorption crucially depends on how access to a program is allocated.
This far, only supply side policies that consist of new construction have been considered.Introduction, or expansion, of a public or targeted housing stock can of course also be doneby purchasing units in the existing stock. The long-run equilibrium eVect of such a purchasestrategy (and the path towards it) would be very similar to the eVect of demand-side policies.
When the eVects on prices and housing stock in a long-run equilibrium are discussed,the question of how the subsidies are allocated should be understood in a somewhat moredynamic way than when we discussed the short-run equilibrium. The interesting consider-ation in this context is whether they are allocated to households that in a long-run equilib-rium without any housing programs would have had a housing unit of their own. This isformally analyzed in Nordvik (1997). Instead of investigating whether subsidies are allo-cated to insiders or outsiders, one can interpret the eVect of demand-side subsidies byobserving whether they increase aggregate demand or not—and to what extent this occurs.For supply side interventions, such as the supply of public housing, the important questionis whether public housing crowds out demand that would otherwise have been directedtowards the ordinary housing stock (see Sinai and Waldfogel, 2005).
The eVect of targeted programs is strongest if they are allocated to households thatwould otherwise not be able to obtain a housing unit of their own. These households arethose most in need of assistance in the housing market. One can say that an eYcient hous-ing policy should be directed towards the neediest Wrst. If such concerns govern the alloca-tion of subsidies, a small-scale program would have a larger marginal impact on totaldemand, and consequently on the equilibrium housing stock, than a large-scale programwould have. This applies to both supply and demand-side programs.
Our description of the eVects of selective supply and demand-side interventions in alocal housing market, in the short- and in the long-run, is based on the housing marketmodel developed by Poterba (1984). Poterba treated housing capital as being homogenous.Our discussions are even more simpliWed as we treat housing units as homogeneous as well.This makes the arguments less complicated and more intuitive than if this assumption hadbeen replaced by a more realistic assumption of a heterogeneous housing stock.
From this rather general theoretical discussion some hypothesis can be extracted:
(i) Selective demand-side programs will increase the size of the housing stock. The mag-nitude of the increase will probably be lower than the number of consumers directlybeneWting from the program.
(ii) The eVect on the housing stock today of demand programs some years ago is stron-ger than the eVect of more recent programs.
2 This process can be speeded up by transformation of buildings from housing to other purposes.
284 V. Nordvik / Journal of Housing Economics 15 (2006) 279–292
(iii) New construction of public housing will increase the size of the housing stock. How-ever, the magnitude of the increase will be lower than the initial growth of the stockof public housing.
(iv) The eVect on the total housing stock today of new construction of public housingsome years ago is weaker than the eVect of more recent additions.
(v) Due to scale and allocation eVects, the marginal eVect of a selective program in alocal housing market is expected to be decreasing in the size of the program.
The empirical parts of the study consist of an attempt to test these hypotheses and toquantify the impact on the size of the housing stock. The existence and strength of priceeVects will be addressed at a later stage.
Qualitatively one would obtain the same type of results as those reported here if anequilibrium model of a heterogeneous local housing market had been employed. Oneexception is that such a model also would yield results on how the composition of thehousing stock may be aVected by the housing policy. A good example of a model thattreats the heterogeneity of the stock of housing units is given by Anas and Arnott (1991).This topic will not be further pursued here.
3. Previous research
The question of how the presence and scale of selective programs in local housingmarkets aVect equilibrium outcomes has not attracted much attention in empiricalhousing market analysis. The cross-section analysis undertaken in this study resemblesthe analyses of Malpezzi and Vandell (2002), Sinai and Waldfogel (2005), Nordvik(1997). Murray (1983, 1999) analyzes how new construction of subsidized targetedhousing units aVects the size of the non-subsidized housing stock within a time-seriesframework.
Malpezzi and Vandell (2002) estimate a model for the variation in housing units percapita among US states. The estimated eVects of the supply and demand-side programs arenot very conclusive. The most striking result is that the standard errors are so large that nointeresting economic hypothesis can be rejected. They suggest that the highly aggregateddeWnition of markets might be one explanation of their noisy estimates.
Sinai and Waldfogel (2005) on the other hand analyze quite similar data, but use Wnerdivisions into local housing markets. Furthermore, they try out two diVerent deWnitions oflocal housing markets. One of the sets they are using contains 22,872 census designatedplaces, while the other set contains 252 SMAs. Their main Wnding is that one extra subsi-dized unit adds 0.35–0.52 units to the total housing stock. The standard errors of the esti-mates are suYciently small for the analysts to reject both hypotheses of no crowding outand of complete crowding out. The contrast to Malpezzi and Vandell (2002) is striking. It isalso interesting to note that the estimated eVects diVer quite substantially with the deWni-tions of local housing markets.
Nordvik (1997) analyses the dependency between diVerent parts of the equilibriumhousing stock. SpeciWcally, the eVect of variations in the size of the public housing stock isaddressed. He also gives some coarse empirical estimates of the impact of public housingon the total housing stock. These estimates indicate that the marginal impact is decreasingin size of the public housing stock. Using the distribution of the public housing stock for1990, he Wnds that the marginal eVect is in the 0.35–0.50 range.
V. Nordvik / Journal of Housing Economics 15 (2006) 279–292 285
Even though both Murray (1983) and Murray (1999) are time-series analyses of thequestion of whether subsidized housing does crowd-out non-subsidized housing, they diVerboth in approach and results. The more recent of these two articles utilizes tools of cointe-gration and annual data over a 52 year long time span and estimates reduced form equa-tions. The main Wndings are that low-income housing does not seem to crowd-out ordinaryhousing. Moderate-income subsidized housing on the other hand ‘most likely adds little ornothing to the total housing stock’. In the terms of the discussion in part 2 of this paper, thisis consistent with a mechanism by which moderate-income housing is allocated to insidersin the market while low-income housing is allocated to outsiders.
Murray (1983) formulates a structural model for the supply and demand of housingstarts. This model is estimated on data ranging from 1961 to 77. He Wnds that convention-ally Wnanced moderate-income housing crowds out unsubsidized housing starts perfectly,even in the short-run. Governmentally Wnanced low-income housing starts are crowdingout unsubsidized starts by a factor of 0.27 in the short-run and 0.65 in the long-run.
In short one can conclude that the empirical studies referred to above indicate that pub-lic housing adds to the total housing stock, but far from a one-to-one level. Murray’s stud-ies indicate that housing targeted towards low-income households aVect the housing stockfar more than housing targeted towards medium-income households.
4. Formulating an empirical model
The main framework for our analyses is regression models where a set of variables isused to explain variations in the number of housing units per 1000 people more than 20years old in Norwegian municipalities. Our goal is, however, not to give a completedescription and analysis of the determinants of the size of the housing stock within a localhousing market. The purpose of the formulated models is to work as an environment fortests of the eVects of selective programs in local housing markets. To put it another way, alarge portion of the variables used in our models are working as controls. The set of con-trols are described in more detail in the next section. This research strategy is similar tothat of Sinai and Waldfogel (2005).
The choice of explanatory variables is guided by three types of considerations. (1) Avail-ability of data; (2) theoretical knowledge about which factors aVect equilibrium in localhousing markets; and (3) variables that are simultaneously determined together with thesize of the housing stock should not be included as independent variables in estimationswhen a simple one-equation strategy is chosen.
The eVect of the magnitude of housing programs on the long-run equilibrium housingstock crucially depends on how aggregate demand for housing units is aVected by theprograms. In order to identify eVects it is therefore important to delimit the local hous-ing markets in a suitable way. It is, for example, natural to speculate on whether thestriking diVerences between the estimation results of Sinai and Waldfogel (2005) andMalpezzi and Vandell (2002) have something to do with diVerences in the delimitation ofmarkets.
Our estimations use a cross-section of 432 Norwegian municipalities as observations.Most of the information is from 2001, but some historical information is also utilized. Apragmatic reason for this choice is that this type of data is easily accessible. One otherimportant reason for using municipalities as observations is that most subsidies in Norwayare allocated at a municipal level. We think that this yields an appropriate division of local
286 V. Nordvik / Journal of Housing Economics 15 (2006) 279–292
housing markets. However, it could be asked whether our deWnition is too disaggregatedbecause some local housing markets contain more than one municipality.
In the empirical model the share of the population in the municipality that commutes toanother municipality is included as an explanatory variable. This is meant to capture someof the interdependencies between municipal housing markets. For the same purpose adummy for municipalities which are a part of the Oslo-region is included.3 In the conclud-ing remarks some further comments on this topic are given.
One important aspect with the empirical model is that it should allow for scale varyingeVects of the programs. To allow for this a piecewise linear spline was chosen. The linearspline was chosen over, for example, a quadratic or a logarithmic speciWcation because it ismore Xexible and constrains the form of the marginal eVects less. It is also simpler. Thespline approach facilitates a direct test of whether the marginal eVects diVer at the diVerentsegments. A spline function consists of linear segments where the segments are delimited byknots. The splines used here are continuous with kinks at the knots (Greene, 2003, p. 120).As the purpose of the spline functions is to test for the existence of diVerences in the mar-ginal eVects of programs, predetermined knots are used in the formulation of the empiricalmodel.4 The models test for one single knot in each of the three programs analyzed. For thesize of the public housing stock in 2001 and for the number of grants, the median size ofthe programs are used as knots. For the number of loans to Wrst-time buyers, the upperquartile is used.
In Section 2 it was hypothesized that the eVect of recent additions to the public housingstock diVers from the eVect of additions made a longer time ago. This is expected becausecrowding out and adjustments towards a new long-run equilibrium housing stock involvea lengthy process. In the dataset there is information on year of construction, but only inquite course categories. This is utilized to check whether the coeYcients of recent additionsdiVer from coeYcient of the older stock. The public housing stock is split into pre-1990 anda post-1990 stock. For the 1990 public housing stock, the same spline is used as for the2001 stock. Public housing units constructed after 1990 are treated as additions to the pub-lic housing stock. The spline for the additions is constructed using information on the1990-stock. As explained below, the designation s1 measures additions up to the median ofthe 2001 public housing stock, and s2 measures additions in excess of the median.
The use of a cross-section to estimate how housing programs aVect the long-run equilib-rium housing stock is based on an assumption that variations around the long-run equilib-rium are random and unbiased. This is a quite strong assumption. Sinai and Waldfogel(2005) argue that a cross-sectional approach with a large number of observations will moreclearly capture equilibrium than a time-series analysis would. We also aim to capture long-run equilibrium eVects in our estimation results. However, we believe that the question ofwhether cross-section or time-series analysis is more appropriate should be addressedfurther.
3 Similar dummies were tested out for other metropolitan areas. It turned out that the coeYcients of thesedummies were both small in magnitude and insigniWcantly diVerent from zero. They were skipped in the reportedestimations.
4 An alternative procedure could have been to start out with an assumption that there exist knots at some un-known level of program size, and then use some semi-parametric smoothing procedure to determine the locationof the knots. Under such a procedure, the tests for diVerences in marginal eVects would be complex. This line ofresearch will not be pursued in this study.
V. Nordvik / Journal of Housing Economics 15 (2006) 279–292 287
We are not as convinced as Sinai and Waldfogel about the superiority of an unrestrictedcross-section sample for achieving this end.
The empirical models should be interpreted as a reduced form. What the models reallydo is compare the situation (i.e., the housing stock) in local housing markets where thescale of housing programs diVers. Hence, the estimated parameters are a mixture betweenthe structural parameters of the supply and demand-sides of the local housing markets.Nordvik (1997) shows that the parameters of reduced forms like those estimated here arecomposed of parameters of the supply and demand functions, and also of the (marginal)allocation schemes used.
5. Data
The empirical model described above is estimated on a dataset put together from diVer-ent sources. Information on size and composition of the housing stock and the populationin 2001 is taken from the census of that year. Income level, number of people working out-side the municipality, population change and density are taken from the data bank of Sta-tistics Norway.
The demand-side programs analyzed here are grants and two diVerent targeted loansfor the purchase of owner-occupied housing or co-ops. Both of these two types of loans areprimarily meant for Wrst-time buyers. One is allocated by the municipalities, while the lat-ter is funded directly by the State Housing Bank. Both the loans are Wnanced by the StateHousing Bank. Data on the use of these types of loans in Norwegian municipalities overthe period 1999–01 were provided by the State Housing Bank. These two types of loans aregiven to Wrst-time buyers and are in all respects similar. They have therefore been aggre-gated and are called loans to Wrst-time buyers. There are also some grants for purchase ofowner-occupied housing or co-ops. These grants are strongly targeted towards householdswith low present incomes and low expected future income. In practice most of these grantsare given to households whose main source of income is a disability pension. Data on themwere also provided by State Housing Bank.
Table 1 reports how some of the important variables used in the analysis are distributed.Means and percentiles are given.
The distributions of the variables will not be discussed here. The exact speciWcationof the variables has to a large degree been determined by availability of information.
288 V. Nordvik / Journal of Housing Economics 15 (2006) 279–292
While their content is quite intuitive, their scaling needs some explanation. Housingunits, both the total number and public units, are measured in number of units per 1000persons more than 20 years old. The grants are measured as the number of grants givento selected household for purchase of an owner-occupied unit over the period 1997–2001. This number has been normalized so that it expresses the number of such grantsper 1000 inhabitant 20 years old or more. Loans for Wrst-time buyers are measured inthe same way.
As previously described, in order to test for whether the marginal eVect on the housingstock of the three policy programs depends on levels, the regression model includes linearsplines; that is, continuous and piecewise linear eVects are estimated. The public housingstock is divided into two segments. The segments are termed s1 and s2, and the knot delim-iting this segment is equal to 21.6. When the public housing stock of 1990 is used in themodel the same knot is used. The eVect of the loans to Wrst-time buyers is also allowed todiVer at two segments, above and below a level of 5.6 loans per 1000 inhabitant, while theknot for the grants is 1.8.
6. Estimation results
Based on the issues and data described above, a linear regression model is formulatedand estimated. In the estimations we follow Sinai and Waldfogel (2005) and Malpezzi andVandell (2002) and weight each observation by the number of inhabitants in each of themunicipalities. The model is estimated using OLS.5 Two versions of this model are pre-sented in Table 2. Note that the estimated model included eight regional dummies notreported here.
The reduced form equations estimated here are mainly meant as an environment fortests of how the (equilibrium) housing stock is aVected by the size of housing programs onthe supply and demand-sides of local housing markets. Hence the interpretation of theresults will focus on the coeYcients of the explanatory variables describing the policyinstruments. One can, however, note that the signs of the other coeYcients conWrm withour a priori expectations. Model 1 will be the main source of these discussions. Model 2 isset up in order to test one speciWc hypothesis. This is the question of whether recent addi-tions to the stock of public housing aVect the housing stock stronger than earlier additions.
In order to illustrate and discuss the magnitude of the eVects we will use a hypotheticalmunicipality with one thousand inhabitants aged 20 years or more.
Variation in the size of the public housing sector below the knot of the spline (21 publicunits per 1000 inhabitants) increases the total housing stock. This increase is clearly signiW-cantly greater than zero. Note that the hypothesis of no crowding out at this level of publichousing stock (i.e., that the coeYcient equals unity) is rejected at a .05 level of signiWcance.
The coeYcient of ‘Public housing s2’ measures the marginal eVect of variations in thepublic housing stock above the median of the distribution of the public housing stock.From Table 2 one sees that the eVects here are far less than at the lower levels of the publichousing stock, and not signiWcantly greater than zero. At this level of the public housingstock, the hypothesis of no crowding out is Wrmly rejected.
5 Both Sinai and Waldfogel (2005) and Malpezzi and Vandell (2002) tried out an instrumental variable ap-proach, but found that this did not alter their results.
V. Nordvik / Journal of Housing Economics 15 (2006) 279–292 289
The coeYcient on the Wrst segment is 0.60, while the coeYcient on the second segment is0.08. An F-test shows that the diVerence is signiWcantly diVerent from zero at a .01 level.Hence the hypothesis that crowding out is increasing in the size of the public housing stockis Wrmly supported by our estimates.
In the hypothetical municipality with 1000 inhabitants, 100 new public dwellingsincrease the total housing stock by 60 units if one starts from a low level. If one starts froma level above the median public housing stock, the predicted increase of the total housingstock as a result of an increase in public housing of 100 units is only 8 units. This is notonly a statistically signiWcant diVerence, but also a substantial one.
Even though the marginal eVect of public housing units is signiWcantly greater thanzero, it is not very precisely estimated. A 95% conWdence interval for the eVect stretchesfrom 0.26 to 0.95. Hence the estimated model can not be used to make very concise predic-tions of what the eVect on the equilibrium housing stock of public housing programs willbe.
Model 2 tests the hypothesis that the impact of recent additions to the stock of pub-lic housing aVect the total housing stock more than previously accumulated publichousing. This is done by using information on the stock of public housing constructedin 1990 or earlier together with additions after that as explanatory variables. The testdoes not enable us to reject a hypothesis that the eVect of the older stock is weaker thanthe eVect of more recent additions. Quite to the contrary, recent increases of the publicstock seem to add less to the total housing stock. It is diYcult to explain these results;
Table 2The determinants of housing units per capita—estimation results
¤ SigniWcant diVerent from zero at a .10 level.¤¤ SigniWcant diVerent from zero at a .05 level.
Model 1 Model 2
CoeV SE CoeV SE
Const 28.85 166.01 42.08 165.8Inhabitants (100.000) 0.02¤¤ 0.005 0.02¤¤ 0.005Population growth 1.14¤¤ 0.36 1.23¤¤ 0.36Population reduction ¡0.74 0.49 ¡0.32 0.51Commuting ¡0.36¤¤ 0.08 ¡0.36¤¤ 0.08Capital area (dummy) ¡5.85¤ 3.05 ¡5.77¤ 3.04Population density 0.41¤¤ 0.04 0.38¤¤ 0.04Share over 70 years old 2.95¤¤ 0.46 2.93¤¤ 0.46Share 20–30 years old 1.91¤¤ 0.63 1.87¤¤ 0.62Log income 35.22¤¤ 13.19 34.41¤¤ 14.33Public housing s1 0.60¤¤ 0.17Public housing s2 0.08 0.06Public housing s1—1990 0.74¤¤ 0.18Public housing s2—1990 0.20¤ 0.10� Public housing 1990–01, s1 0.25 0.28� Public housing 1990–01, s2 ¡0.10 0.21Loans—Wrst time owners, s1 0.77¤ 0.47 0.79¤ 0.46Loans—Wrst time owners, s2 0.19 0.42 0.07 0.42Grants, s1 1.47 1.05 1.66 1.05Grants, s2 0.19 0.66 0.13 0.66R2-adj 0.9115 0.9128No observations 432 432
290 V. Nordvik / Journal of Housing Economics 15 (2006) 279–292
they may be a combined eVect of an inaccurate year constructed variable6 and noisyestimates.
The speciWcation of the eVects of loans for Wrst time owners has a structure that in manyways is similar to the eVects of public housing. Here a knot for the spline equal to the upperquartile was chosen. In municipalities where the use of these loans was below this knot acoeYcient signiWcantly larger than zero, though only at a .10 level, was found. Above thislevel the coeYcient turns out not to be signiWcantly diVerent from zero. However, thecoeYcients for the number of loans above and below the knot are not signiWcantly diVerentfrom each other. Hence the results indicate, but do not conWrm, a decreasing marginaleVect of the size of this particular demand-side program.
The estimated magnitude of the eVect of the loans for Wrst time owners is surprisinglystrong. Hundred selective loans for Wrst-time buyers are estimated to increase the housingstock by 77 housing units if the total size of the program is below the upper quartile of thedistribution of program size. This estimate is even noisier than the estimated coeYcientsfor public housing. A 95 percent conWdence interval stretches from ¡0.15 to 1.67.
Estimates such as the one for the eVect of selective targeted loans on the housingstock are, of course, useful as part of the discussion of how to design low-income hous-ing policy. Some caution, however, should be exercised in interpreting the results pre-sented here. Based on the theoretical discussion in part 2, one expects demand-sidesubsidies to work indirectly on the housing stock. Demand pressure should push pricesupwards and in turn stimulate new construction. In the empirical model information onquite recent loans are used to predict the housing stock. It might be the case that our esti-mates arise because of a positive correlation between recent and prior use of selectiveloans.
One special feature which this study focuses on is how the marginal eVects of housingprograms depend on their scale. The hypothesis is that the larger a program is, the less itmarginally impacts aggregate demand, and consequently the housing stock. This hypothe-sis is clearly supported by our empirical estimates. This result corresponds well to sometime-series results in both Murray (1983) and Murray (1999). An interpretation of theresults of this study is that the marginal eVect of targeted programs is largest when a pro-gram is allocated to those least capable of handling their housing situation satisfactorily ontheir own. As a program is extended, an increasing share of the newcomers in the programwould have been able to handle their housing situations in the absence of the program, andthe marginal eVect on the housing stock shrinks. This is exactly what Murray (1999) Wnds.When a public housing program is targeted towards low-income households the marginaleVects are very high, i.e., no crowding out occur. When a program is directed towardsmedium-income households the marginal eVects approaches zero—complete crowding outoccurs.
A related eVect is found in Sinai and Waldfogel (2005). They develop a measure ofexcess demand for subsidized housing and Wnd that the larger this excess demand is, thestronger is the marginal eVect on the total housing stock if the subsidized stock isincreased.
Finally we note that the estimated eVects of the grants for purchase of owner-occupiedhousing are quite high, but insigniWcantly diVerent from zero.
6 In the census, the tenants are asked to report when the housing units they occupy were set up.
V. Nordvik / Journal of Housing Economics 15 (2006) 279–292 291
7. Concluding remarks
Starting from an informal theoretical analysis, this study extracts Wve empirical hypoth-eses on the impacts that housing programs will have on the housing stock in a local hous-ing market. Three out of Wve did get empirical support in the models that were estimated.The hypothesis that recent additions to the stock of public housing have a stronger impacton the size of the total housing stock did not get support. Data did not allow testing of theWfth one, i.e., the hypothesis that the impact of demand-side subsidies some years ago isstronger than more recent subsidies.
Both selective demand-side subsidies and supply side interventions increase the size ofthe housing stock. Starting from a relatively low level, 100 new public housing unitsincrease the total housing stock by 60 units. Also starting from a low level, an increase inthe use of loans for owner-occupation of 100 loans appears to increase the housing stockby 77 new units. Both of these eVects are signiWcantly greater than zero. The estimatedeVects are quite high, especially the eVect of loans for Wrst time homeowners. It shouldtherefore be noted that the coeYcients are not very precisely estimated, yielding conWdenceintervals that are quite wide.
In the theoretical discussion it was argued that the marginal impact of both supplyand demand-side programs is decreasing in the scale of the program. The estimationresults conWrmed this hypothesis. Variations in the size of the public housing stockbelow the median increase the housing stock, while above the median no signiWcanteVect is found. If targeted units are Wrst allocated to households who are least able toobtain a housing unit on their own, this is the pattern that will emerge. Hence allocationdoes, not too surprisingly, matter for the equilibrium impact of housing programs. Oneimportant lesson for policy design to be learned from this is that even if a particular pro-gram works well in a market, this does not mean that it is necessarily a good idea toexpand its scale.
The estimated eVects of public housing, in housing markets with a public stock belowthe median, are somewhat higher than in most estimates in the previous literature on thistopic. This is probably due to the fact that we allow for scale varying eVects. We thusregard the empirical results as expanding the general knowledge of the working of selectiveinterventions and subsidies in local housing markets. As such, it can also be useful inchoice and design of a housing policy. However there are some important dimensions thatshould be taken account of in future work. Three topics, or dimensions, stand out as espe-cially important in this context.
First, while this study uses a spline approach to treat partial scale eVects and non-linear-ities, future work should develop tests for multidimensional scale eVects. An examplewould be looking at whether the marginal eVect of one particular program depends on thescale of other programs. The answer to this question is potentially very important for thedesign and scale of the total menu of housing policies at the local level.
Second, the division of a national housing market into a Wnite number of local housingmarkets is an analytical construct made out of convenience. In reality many markets inter-act with each other, and support allocated in one market can have impacts on other mar-kets as well. This can be captured by accounting for some kind of spatial autocorrelation.Alternatively one could aggregate municipalities up to labor market regions. The largediVerences in the estimated eVects in Malpezzi and Vandell (2002), who use a highly aggre-gated deWnition of the local markets, and Sinai and Waldfogel (2005), who use a more
292 V. Nordvik / Journal of Housing Economics 15 (2006) 279–292
disaggregated approach, can be interpreted as an indication that spatial aggregation andinterdependencies are an important part of the picture.
Finally future work should put more eVort into understanding the dynamic patterns ofintervention eVects. The theoretical analysis of part 2 of this study indicates that this is alsopotentially important. As suggested by Malpezzi and Vandell (2002), this can be incorpo-rated within an eVort to handle the possible presence of temporal disequilibrium in localhousing markets. A step on the path towards an empirically based understanding of thedynamics of the impact of selective policy measures in local housing markets would be toanalyze the interdependencies between prices, rents and housing policies empirically—per-haps in a manner that resembles the analysis of the housing stock of this study.
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