contracting with costly tenants

ELSEVIER Regional Science and Urban Economics 25 (1995) 631-654 ECONOMICS

Contracting with costly tenants

F r a n z H u b e r t

Freie Universitdt Berlin, lnstitut fiir Wirtschaftspolitik U. Wirtschaftsgeschichte, Boltzmannstr. 20, D-14195 Berlin, Germany

Received May 1993; final version received January 1995

Abstract

This paper analyses rental contracts in the housing market assuming asymmetric information about tenant-related 'service cost' and imperfect mobility. On the positive side, it explains why long-standing tenants tend to enjoy lower ren t s - the so-called 'tenure discount'. On the normative side, it shows that the market equilibrium is not efficient, because contracts protecting the tenant against arbitrary eviction suffer from adverse selection. Tenure security laws, therefore, have the potential to improve welfare.

Keywords: Rental contracts; Tenure security; Adverse selection

JEL classification: D82; R21; K12

1. Introduction

The relationship between a landlord and a tenant often stretches over many months or years. It may be governed by a series of short- term contracts or by a long-term contract stipulating conditions for the termination of the lease, rules for rent reviews, etc. This paper analyses rental contracts in the housing marke t assuming asymmetric information about tenant-re la ted 'service cost ' and imperfect mobility. Post-contractual selection, taking place after landlords obtained information on their tenants through experience, is the basis for pre-contractual selection, in which different contracts are used as a screening device. Within this f ramework (i) we explain the empirical feature that long-standing tenants tend to enjoy

0166-0462/95/$09.50 (~) 1995 Elsevier Science B.V. All rights reserved S S D I 0 1 6 6 - 0 4 6 2 ( 9 5 ) 0 2 1 0 2 - 7

632 F. Hubert / Regional Science and Urban Economics 2.5 (1995) 631-654

lower rents than new tenants, the so-called ' tenure discount', and (ii) we show that tenure security laws could improve efficiency.

It has repeatedly been observed that long-standing tenants pay less than those who entered their contract more recently (B6rsch-Supan, 1986; Behring, 1988). In this paper, the tenure discount is explained as an attempt to reduce the turnover of 'low-cost' tenants and to increase the turnover of 'high-cost ' tenants. The basic idea is as follows. In order to keep the cost of maintenance and administration low, a landlord expects his tenant to minimize wear and tear, avoid trouble with neighbours, etc. Many aspects of the tenant 's conduct, however, are not contractable - being unobservable by a third party acting as an arbitrator, or too vague to be explicitly stipulated. It is, therefore, the landlord who bears the tenant-related service costs (Miron, 1990). Tenants differ with respect to their expected service costs, but a landlord will not be able to observe the difference when filling a vacancy. Experience gained during the course of tenure, however, will improve his assessment of his tenant's character. The scope to react then is determined by the nature of the contract chosen in the first place. In the case of a long-term contract with tenure security, the landlord has to put up with a high service cost until the tenant leaves voluntarily. Being non- contractable the service cost will not amount to a clear-cut breach of contract. If the contract entails an option to be termined at will, he will evict high-cost tenants, and if the relationship is based on a sequence of short- term contracts, he will raise the rent of 'bad ' tenants upon renewal. Since higher rents increase the probability of a move, the landlord has an incentive to keep rents down for tenants with a record of low service cost. However , whether or not 'good' tenants enjoy a ' tenure discount' in equilibrium depends on parameters as mobility cost and the expected service cost of unknown tenants and experienced tenants.

The hypothesis that landlords grant a ' tenure discount' in order to prevent good tenants from moving is common in the literature (Schlicht, 1983; Goodman and Kawai, 1985; Guasch and Marshall, 1987; Miron, 1990). The formal models, however, are not explicitly built upon differences in the quality of tenants, but on unspecified ' turnover cost' borne by the landlord. Given these, a tenure discount may arise if the tenant's willingness to pay decreases over time (Schlicht, 1983), or if the landlord's assessment of the tenants ' preferences improves (Guasch and Marshall, 1987). One difficulty with this approach is that a difference in the quality of tenants does not imply that the turnover cost is positive, on average. As the move of a good tenant increases the service cost, so would the move of a bad tenant decrease it. This paper explicitly analyses selection at the post-contractual stage by taking these effects into account. But it is assumed that turnover cost, in the narrow sense of moving cost, is borne by the tenant. In

F. Hubert / Regional Science and Urban Economics 25 (1995) 631-654 633

equilibrium, low rents and a low turnover of good tenants, as well as high rents accompanied by a high turnover of bad tenants, contribute to the tenure discount.

In many countries tenure laws for residential leases protect the tenant against eviction, provided the landlord has no 'just cause' for doing so (e.g. breach of contract, rent arrears). Historically, tenure security laws were often introduced to enforce rent controls and to slow down the rate of conversion to other, less regulated, forms of tenure. More recently, however , protection against arbitrary eviction has become the prime object ive in some cases. Notably in Germany , the tenure security act of 1971 (Wohnraumkiindigungsschutzgesetz) brought to an end a period of complete deregulat ion by introducing mandatory protection against eviction. While the initial rent of a new lease is freely negotiable, later rent reviews are tied to the rent level of recent lettings of comparable dwellings (Vergleichs- mietenregelung) . Similarly, in France, the 'M6haignerie Act ' of 1986 deregulated rents for new leases while requiring a minimum term of four years, during which rent increases were tied to the index of construction cost. The regulation of rent updating is clearly necessary to prevent the loophole of ' economic e v i c t i o n ' - a n arbitrary increase of rent intended to force the tenant to give notice on his own.

Eekof f (1987), Hirsch (1988), Engels et al. (1984), Homburg (1993) and, with qualifications, Miron (1990) suggest that these regulations will lead to a welfare loss if the cost of providing tenure security is higher than the tenant ' s valuation of i t - a n d are not necessary otherwise. B6rsch-Supan (1986) shows that long-term contracts providing tenants with tenure security and ex ante specified rent may be superior to a sequence of short- term contracts if tenants are risk-averse and prone to the exploitation of immobili ty. Nevertheless, his justification of the regulations appears to be p remature because he does not explain why the bet ter contracts are not voluntarily chosen in an unregulated market . This paper provides such an explanation based on asymmetric information and adverse selection. As in B6rsch-Supan (1986) we assume that forced moving involves cost. Tenants, therefore , value pre-determined rents and protection against eviction. However , if a tenant knows himself to be a low-cost type, we would expect a lower probabil i ty of being evicted, if this option is not precluded in advance. Under a sequence of short- term contracts he would expect a lower rent in the future. Hence , if tenants know their type beforehand they will differ with respect to their preference for tenure security and stable rents. This, in turn, enables uninformed landlords to use the option to give notice at w i l l - or, alternatively, the right to set future rents at w i l l - as a screening device at the pre-contractual stage. Since short- term or terminable contracts tend to attract low-cost tenants, while long-term contracts with tenure

634 F. Hubert / Regional Science and Urban Economics 25 (1995) 631-654

security suffer from adverse selection, the supply of the latter will be inefficiently low. Tenure security laws, therefore, have the potential to improve welfare.

Finally, the paper is related to research stressing the importance of incentives. Hom burg (1993) claims that contracts with protection against eviction are likely to be inefficient because they fail to provide the tenant with p roper incentives to keep service cost low. Kanemoto (1990) argues that an efficient contract will allow the party in charge of maintenance and upgrading to reap the benefits of the investment: either the tenant is in charge and enjoys tenure security or the landlord carries the duty and is able to evict the tenant. In these papers 'service cost ' , respectively investment levels, is endogenously determined in response to the incentives set by the contract. It is, however, assumed that all tenants react in exactly the same way to an incentive scheme. In this case, landlords would not bother to find and to keep 'good ' tenants. These issues, which are the theme of this paper , arise only if different tenants respond differently to an incentive scheme.

The next section introduces the basic assumptions of the model. In Section 3 the focus is on selection at the pre-contractual stage. In order to simplify the analysis we consider only long-term contracts for which post- contractual selection is particularly simple: either evict or keep the tenant. In Section 4 we bypass the issue of pre-contractual selection to analyse post-contractual selection in a sequence of short- term contracts, in more detail. The final section summarizes the main results and explores further welfare implications of mandatory tenure security. To ease the exposition, most of the proofs have been relegated to the appendix. A second appendix contains the more tedious calculations. It is available on request.

2. Basic assumptions

Consider a competi t ive marke t for rental housing services. In each of infinitely many periods a cohort of new tenants or 'youngsters ' enters the market . It exits after two periods of consumption. The size of the cohorts is constant. Hence , at any time there are as many 'youngsters ' as 'oldsters ' in the market . Landlords live infinitely long. When entering the market , youngsters mix with moving oldsters to compete for rental contracts. 1 These could be short- term contracts that set a rent only for the first period, leaving everything else open to negotiation at the beginning of the second period, or

The interpretation in terms of overlapping generations is not to be taken too literally. An alternative would be to introduce exogenous moves as in Greenwald (1986). It must only be ensured, that evicted tenants can "hide' in the market.


long-term contracts that fix the rent for both periods. In the latter case, contract termination might be excluded (non-terminable contracts) or be allowed for ( terminable contracts).

A s s u m p t i o n 1 (Preferences). The utility functions of landlords and tenants depend only on rent and are additive in time. Landlords are risk-neutral. Tenants are not risk-loving. The common discount factor is 6 E (0, 1). The tenants ' utility in each period is denoted U : ~---~ ~ with U ' < 0, U" ~< 0.

Tenants differ in two aspects: (i) their 'quality ' , e.g. the propensity to cause service cost, and (ii) their 'mobil i ty ' , e.g. the cost (or gains) that accrue to the tenant if the contract is dissolved after the first period.

A s s u m p t i o n 2 (Quality). Tenants differ in the probabili ty 4~ ~ q~ = [0, 1] to cause c units of service cost during a given period. ~b is distributed with the cumulat ive probabili ty H.

The average cost-probabili ty of all tenants is p --- .[, ~/, dH. Later , we will consider subsets of all tenants, e.g. those who select a particular contract or have a particular record of service cost. The average cost-probabili ty of these subgroups will be denoted by adding subscripts.

An important feature of housing tenure is t h a t - i n the absence of contractual stipulations - landlords enjoy some latitude regarding the rent of sitting tenants. Not all tenants will move when their present rent increases slightly beyond the level that is charged for vacancies. Mobility-cost may result f rom psychological a t tachment to a fiat and neighbourhood, as well as f rom sunk investments in complementary consumption goods, expenses for moving and renovation, etc. On the other hand, some tenants will move even if the present rent is lower than the equilibrium rent for vacancies. Moving benefits may be due to a bet ter wage offer elsewhere, formation or splitting up of a household, etc.

A s s u m p t i o n 3 (Immobil i ty) . If the contract is terminated at the end of the f i rs t period, a tenant of type 0 experiences an additive utility loss 0 E O = [_0, 0]. 0 is stochastically independent of ~b and distributed with twice differentiable cumulative probabili ty F and finite density f.

Note , that _0 < 0 indicates a gain from moving. Later on, some additional technical restrictions on the distribution F will be required to hold. Now, we turn to the information structure and the timing of events (see Fig. 1 for an illustration).


Tenants know d~ and F landlords know H and F

I

Landlords Tenants offer select contracts contracts

I I

1. negotiation

Either Tenants learn continuation mobility cost 0 (possibly landlords with new observe service terms) or cost and termination calculate p~, p~, of contract Time

I I I D

1. period 2. negotiation 2. period

Fig. 1. Timing of events.

Assumption 4 (Hidden information), Tenants know their 'quality ' ~h and the distribution of mobility cost F(O) at the outset. Landlords know only the distributions H(d~) and F(O).

Central to the analysis is the assumption of asymmetric information on the tenants ' character. The assumption that information on mobility cost is initially the same on both sides of the market is adopted for analytical convenience. It appears adequate if mobility cost develops during the course of consumption. If, on the contrary, mobility is considered as a mat ter of personal character, each tenant would know his 0 before entering the rental contract. This would complicate the analysis slightly without changing the main results.

The first negotiation consists of two steps: (i) landlords offer c o n t r a c t s - being well aware that different contracts will attract different types of tenants, and (ii) tenants choose the contract that provides them with the highest expected utility. Since the landlord (i.e. the principal) takes the initiative, the model belongs to the 'screening approach ' . The alternative 'signaling approach ' would see the tenants (i.e. the agents) 'signal' their type by announcing their offers first. There is, however, no first-mover advantage at this stage because negotiations take place in a perfectly competit ive f ramework. The asymmetry of information on the expected service cost of a tenant provides the basis for pre-contractual selection. Post-contractual selection is shaped by the way landlords learn about their tenants.

Assumption 5 ( Imperfect learning). Each landlord observes the occurrence of service cost for his own tenant. Hc does not obtain information on the mobility 0.

By observing the occurrence of service cost in the first period, a landlord obtains an improved assessment of the tenant 's character. Those with a bad record, 'bad tenants ' for short, have a higher probabili ty of causing service


cost in the future than tenants with a good record (Pb ~>Pg). Hence, when negotiating for contract renewal, the landlord will take a tougher stand towards the former. The particular form of these negotiations depends on the contract chosen in the first place and will be discussed later.

A s s u m p t i o n 6 (No public record). The landlord cannot obtain information on previous tenures of an applicant.

Informat ion accumulated within a contract is not reveled to the market . Hence , a tenant who moves is cleared of his r e p u t a t i o n - whether good or bad. This is an important difference to otherwise similar models of the labour market , where employers face the problem of assessing the productivity of prospective workers. Freeman (1977) assumes that competing employers have the same information on productivity as the current employer . Even if such information is private in the first place, employers could make inferences from previous job assignments (Waidman, 1984) or quit decision (Greenwald, 1986). Failure to obtain good job assignments within the original firm or repeated quitting are taken as evidence of poor per formance . In the housing market it is, however, much more difficult to draw useful conclusions from information on previous tenures. First, there exists nothing comparable to the internal market of big firms. Second, most contract terminations result from a change of family composit ion, income or job. Hence, quitting as such does not provide much information on the l and lord- tenan t relationship. Third, information given by the present landlord cannot be trusted. Since a good recommendat ion may ease a separat ion, the present landlord is bet ter off when lying about a bad tenant. In contrast to the labour market , there is no "reputation' to curb this incentive for opportunistic behaviour in the (private) rented housing market . For these and other reasons landlords often do not bother to obtain information on previous tenures, even though they are concerned about selecting 'good ' tenants.

Contract ing is analysed as a multi-stage, non-cooperat ive game within the f ramework of an overlapping-generations model with free entry. Therefore the set of equilibrium contracts has to be (i) a subgame-perfect Nash equilibrium of the contracting game sketched in Fig. 1 and (ii) for each contract expected cost must equal expected revenue. The zero-profit constraint merely substitutes the explicit modeling of the overall supply of housing. Subgame-perfectness rules out contracts using empty promises or empty threats concerning the final negotiation on contract renewal (post- contractual selection). It also implies that landlords take into account the impact that their offers have on the tenants ' choice of contracts (pre- contractual selection). Finally, the Nash equilibrium requires that, given the existing offers - and the induced self-selection - there must not exist another


contract that earns strictly positive profits. As usual, the equilibrium is to be found by backward induction. The analysis is restraint to stationary equilibria.

3. Tenure security in long-term contracts

In this section I consider two types of long-term contracts. Both contracts stipulate constant rents (rt, r n) for the time of duration, protecting thereby the tenant against ex post exploitation of his immobility. In the first one, indexed with t (terminable), the landlord retains the right to give notice at will at the end of the first period. The second one, indexed with n (non-terminable), protects the tenant against being evicted. For expositional convenience it will be ruled out that tenants give notice to q u i t - a restriction that will be dropped in the next section. Formally, this requires _0 i>0 and trivially implies that the average tenant has a preference for staying E0 =- fo 0 dF > 0.

The initial negotiation (see Fig. 1) consists of two steps. First, landlords set rents r~, r . E R for both contracts. Since no tenant would strictly prefer the terminable contract if not for being cheaper, we can restrict the set of rents to R = {(r~, rn) E R 2 I rt ~< rn}" Second, tenants choose among the offers. It will be seen below that this choice can be described by a variable a(r t, r . ) E ~, with the property that, given (r,, r , ) all youngsters of type 4' < a strictly prefer the terminable contract. H(a) is the market share of terminable contracts. The cost probability of youngsters choosing the terminable contract is pt(a) = E(4' 1 4' <~ a) = fo 4' dH/H(a) . For later use, note that limao 0 p t ( a ) = p t ( 0 ) = 0 and that

p = H ( a ) p t ( a ) + ( 1 - H ( a ) ) p n ( a ) , V a E q b , (1)

where p , denotes the cost-probability of tenants choosing the non-terminable contract. During the first period of consumption, landlords observe the occurrence of service cost. Hence, each landlord knows whether his tenant has a good or a bad record (indexed g and b, respectively) when he decides whether or not to keep the tenant for the second period.

3.1. Giving notice to quit

Having observed the occurrence of service cost in period one, the landlord calculates the conditional cost probability for tenants with a good (respectively, bad) record (pg, Pb)" From Bayes' rule for the calculation of


conditional expectat ions it follows that Pb > P g - Since the probabili ty of service cost is a fixed character of the tenant, it must be true that 2

Pt =P tPb + (1 --Pt)Pg • (2)

If a contract is terminated, both parties will turn to the marke t where evicted oldsters mix with youngsters. The expected profit with an old tenant staying for a second period before exiting the market , 7r i, is

Tr ~ = (r t -- pi c) + 67r t , i E {g, b } , (3)

where ~-t, the expected profit with a new terminable contract, can be written as

"77" t = [(r t --pt c) + (1 -pt)Yg(rt--pgC) + P t T b ( r t - - p b c)

+ 6(1 - p , ) ( 1 - ~,g)(r, - p g C ) + @ t ( 1 - 7b)(r, - p . c ) ] / [ ( 1 - , ~ ) Z ] ,

(a)

with

Z-= 1 + (1 - p t ) y g +P,Yb + 6 ( 1 -- pt)(1 --yg) + 6pt(1 - - % ) .

Let 7g, Yb E [0, 1] denote the probabili ty of evicting a tenant with a good (respectively bad) record. The landlord chooses 7g, 7b in order to maximize the expected profit.

P r o g r a m 1. Decision to evict

max ~r 2 = ~ . 7r t + (1 - y)~.i i E {g, b} z,,

Note that yg and Yb in the expression for 7r t refer to the simultaneous decisions of other landlords and are, therefore, no instruments of the program.

P r o p o s i t i o n 1. In equ i l i b r ium, a tenant is evic ted i f and on ly i f he has go t a bad record y ~ = l , y ~ = O.

The terminable contract can be interpreted as an implicit agreement that makes the eviction conditional on the occurrence of service cost in the first period. This is possible because it is in the landlord's best interest to follow the agreement even though the exact type of his tenant is not revealed to him and the service cost of an unknown new tenant depends on the behavior of the other landlords.

Note that p, is also the fraction of tenants with a bad record after period one.

640 F. Hubert / Regional Science and Urban Economics 2,5 (1995) 631-6,54

3.2. The tenant 's choice o f contracts

Given the prospect of becoming evicted, the expected utilities for the contracts are (1 + 6)U(r: , ) and (1 + 6 ) U ( q ) - achE& respectively. Setting both equal defines a marginal tenant, a E 4 :

0 ~ a Eo ,1~. (5)

Any tenant with O ~< a weakly prefers the terminable contract.

3.3. The landlords' contractual offers

As usual in selection models, the Nash equilibrium for the contractual offers is characterized by two conditions: first, profits must be zero for every contract; second, given the existing offers, there must not exist another contract that earns strictly positive profits. For the non-terminable contract, rent revenue and expected service cost are the same for both periods, hence the zero-profit condition simply requires:

0 = r,, - pn(a)c . (6)

The corresponding expression for the terminable contract is obtained by evaluating (4) at 7" and using (2):

(1 +p~) + ~(1 -p~) O = r : - p t ( a ) c ' 3 7 ( a , 6 ) , ~l(a, 6 ) - ( l + p , ) + ~ ( 1 - p , ) " (7)

Note that ~(a, 6) > 1 since Pb >Pt and 6 E (0, 1), and that l i m ~ 1 ~ = 1. This reveals the first externality in the market operating via post-contractual selection. A landlord who evicts a bad tenant reduces his cost at the cost of other landlords offering vacancies. Clearly, in a stationary equilibrium, this externality nets out when aggregated. Hence, if we abstract from discounting, the rent for the terminable contract must be equal to the expected service cost of youngsters choosing this contract. To enjoy the low cost of tenants with a good reputat ion, landlords have to bear the higher cost of an unknown tenant in the first period. This ' front-end loading' of the cost profile requires a rent that is higher than the expected cost when discounting is taken into account.

A landlord will not be able to attract any tenant if he charges a rent higher than that of his competitors. Lowering r t will certainly decrease profits since it attracts tenants who are 'worse ' than those who have already chosen the terminable contract. Lowering the rent of the non-terminable contract , however, attracts tenants with a lower average service cost, which might offset the reduction of revenue. Hence, a zero-profit offer (r* n, r*),

F. Hubert / Regional Science and Urban Economics 2.5 (1995) 631-654 641

compatible with the self-selection constraint, is a Nash equilibrium if no non-terminable contract charging a lower rent is profitable:

n ~ n (r , , r*) ~> ~r (r . , r*) , VF. < r * . (8)

3.4. Equi l ibr ium

Since 78, %* have been incorporated already when deriving (5) and (7), the Nash equilibrium of the contracting game is given by a*, r,,* r,,* which simultaneously fulfil expressions (5), (6), (7) and (8).

As usual in screening models, for particular parameters a Nash equilibrium may fail to exist. In response to the possible non-existence of a Nash equilibrium, alternative equilibrium notions have been proposed. Referring to Wilson (1977), a zero-profit offer is called a 'Wilson equilibrium' if no other contract exists that would yield a positive profit even after all contracts that make losses as a result of the entry have been withdrawn. According to Riley (1979) a 'reaction equilibrium' is a set of zero-profit contracts for which no defecting contract with positive profits exists that in itself cannot be made unprofitable through a reacting contract. Unfortunately, the two concepts appear to lead to different equilibrium outcomes (Riley, 1979). 3 Furthermore, both equilibrium concepts make demanding assumptions on the agents' awareness of the reactions of competitors. This might be appropriate for markets in which a small number of sophisticated suppliers operate, e.g. the insurance market. It is less appealing when applied to the rental housing market with its large number of small suppliers. We, therefore, restrict our attention to parameters for which a Nash equilibrium exists.

Proposi t ion 2. A situation in which only non- terminable contracts are traded, a = O, cannot be a Nash equil ibrium.

Even if both contracts are being traded in equilibrium ( O < a * < l ) , the separation of tenants is incomplete. All tenants whose cost probability d~ is below the threshold value a* are 'pooled' at the terminable contract; all others choose the non-terminable contract. Partial pooling is possible because the screening device is discrete, the protection against eviction is either being granted or denied, and only the rent can be varied in a continuous manner. Therefore, the fine tuning between two parameters of the contract (wage and education; insurance premium and coverage, etc.), which usually erodes any pooling constellation in sorting models, is not

Since Wilson developed his notion for a finite set of agents, while Riley considered a continuum, a direct comparison is difficult.


possible in the present context. 4 Partial pooling is even necessary for the credibility of the sanction. If self-selection were perfect - as it would be if there were only two types of tenants in the market - the landlord would be unable to make any additional inferences from the observation of service cost. Hence , there would be no incentive to evict tenants for bad performance , which, in turn, makes the threat of doing so incredible.

3.5. Comparative statics

Assuming that an equilibrium exists, we can derive the comparat ive statics of the pre-contractual selection from Eqs. (5), (6) and (7), bearing in mind condition (8). r t* and r n* are strictly increasing in p, and p , , which, in turn, are strictly increasing in a*. Hence, it is sufficient to consider a*, which determines the market share of terminable contracts.

Proposition 3. The market share of terminable contracts H(a*) decreases (i) as mobility cost increases Oa*/OEO < 0 , and (ii) as the precision of learning (the value of experience) increases Oa*/Opb <0. (iii) Terminable contracts become more competitive if service cost increases Oa* / Oc > 0. (iv) The impact of discounting is ambiguous, Oa* / 06 ~ O.

These results are in line with intuition. Higher mobility cost, EO, makes the tenants less inclined to forgo tenure security in order to obtain a lower rent. This result suggests that a lower mobility cost might be one of the reasons why long-term contracts providing tenure security play only a minor role in the Uni ted States, while in Europe they apparently had been well estab- lished even before tenure laws made them obligatory. 5 As the difference between Pb and pg increases, with Pt being kept constant, the private gains f rom evicting tenants with a bad record become bigger. Since evicted tenants turn to other landlords, total cost is not reduced. Instead, cost for unknown applicants in the first period increases and cost for good tenants in the second period decreases. The cost profile becomes more ' f ront-end loaded ' , which makes terminable contracts less competit ive. A general increase in service cost c makes terminable contracts more attractive for landlords due to their lower probabili ty of such a cost. The impact of an

If stripped of its particular time structure, the model is one of screening, as in Rothschild and Stiglitz's (1976) treatment of the insurance market. They consider two classes of customers and a continuum of contracts. Here, in contrast, the customers are represented by a continuum, but there are only a discrete number of contracts. In this respect, the model is similar to the original selection model of Akerlof (1970), who considers a continuum in the quality of cars and the decision to buy or not to buy, using a simple sale contract.

5 On the differences of mobility, see Schneider et al. (1985); on early forms of tenure, see International Labour Office (1924).


increase in the discount factor 6 (or a decrease in the discount rate) is ambiguous. Tenants will be deterred from terminable contracts because they are more concerned about the expected utility loss of forced moving. Landlords will be attracted because they have less worry about the front-end loading of service cost.

3.6. Efficiency

Homst r6m and Myerson (1983) suggest the distinction of ex ante and interim efficiency depending on the time of the assessment. Ex ante efficiency refers to the time when even the better informed side is ignorant - in our case, before tenants learn ~b. Interim efficiency is evaluated when the

asymmetry of information has d e v e l o p e d - t e n a n t s know their type but landlords are not informed. The efficiency of the equilibrium is assessed by comparison with the case of tenure security regulations that make terminable contracts infeasible (formally the latter corresponds to a = 0; n = pnc = pc).

Proposition 4. (i) I f both contracts are traded in equilibrium (a* < 1) tenure security laws improve interim efficiency according to the compensation criterion and ex ante efficiency according to the Pareto criterion; (ii) i f only terminable contracts are traded ( a * = l ) interim efficiency is improved according to the Pareto criterion.

The possible inefficiency of markets plagued by asymmetric information has been well known since Spence (1974). Here , terminable contracts decrease welfare in two ways: (i) the time profile of service cost becomes front-end loaded because high-cost tenants move more often, and (ii) forced moving implies mobility cost. Foregoing protection against eviction serves as a signal for being a good tenant. The private costs of signaling are the expected utility loss in the case of contract termination, and compensation for the front-end loading of the cost profile. Private gains result from a redistribution of rent payments among tenants, and are, therefore, matched by a social cost of the same magnitude.

4. Short-term contracts

In the preceding section the set of feasible contracts has been restricted to long-term contracts with fixed rents for both periods. This leaves the landlord little choice but to evict tenants with a bad r e c o r d - if the option was not precluded in advance. Now we consider a sequence of short-term


contracts. Since any single contract fixes the rent for only one period, the landlord can adjust the rent according to previous experience. In order not to clutter up the analysis of post-contractual selection, we skip the issue of pre-contractual selection. Short-term contracts are of particular interest since they trivially fulfil the requirement of incentive compatibility. Nothing is promised for the second period, hence no promises can be broken. They entail the option of contract termination through 'economic eviction'; that is, a rent high enough to induce even the most immobile tenant to give notice. Moreover , short-term contracts are less costly to write and enforce. Lower transaction cost will give them a specific advantage when competing against long-term contracts.

Since attention is restricted to those who choose short-term contracts in equilibrium, the game (see Fig. l) starts with the landlords setting the first period rent, r , , and proceeds to the second negotiation when landlords and tenants have to agree on a second term or to separate. Tenants know their mobility cost, 0, at this stage. Landlords only know the distribution of this characteristic, F. Based on the experience gained in the first period, they set two rents r i, i E {b, g}, depending on whether the record is good or bad. The tenants respond by accepting the offer or by giving notice to quit. In the latter case, they turn to the market and rent for rj.

This sequence gives the landlord a first-mover advantage in the negotiation for contract renewal that enables him to exploit the tenant 's immobility. He is, however, prevented from reaping all the gains from trade by his imperfect knowledge of the mobility cost. Most of the following results do not depend on this particular distribution of bargaining power. If the tenant were to enjoy the strategic advantage of a take-it-or-leave-it offer, the landlord would be left just indifferent between renting at ri, i ~ {b, g} and renting at r, to an unknown tenant. Second-period rents, as well as rates of turnover , would be l o w e r - b u t otherwise the results would be similar.

In this section we assume that some tenants do benefit from moving, (0 < 0). To ensure that the problem of post-contractual selection is well behaved, it is assumed that (1 - F(O)), i.e. the probability that mobility cost is above a given value, is log concave. 6

~This requires that In[1-F(AO, + ( 1 - A ) 0 2 ) ] > A I n [ 1 F ( 0 ~ ) ] + ( 1 - A ) l n [ l - F ( 0 2 ) ], VOt~E O, A ~ [0, 1]. The class of log-concave distributions includes (in some cases with restrictions on the parameters) the multivariate beta, Dirichlet, exponential , gamma, Laplac, normal , uniform, Weibull, and Wishart . See Caplin and Nalebuff (1991) and the references cited there. Since 0 E [_0, 0] is the loss from moving, we can define y -- -O as the gains from moving, with distribution G(T) ~ 1 - F(O ). In other words, we assume that the distribution of moving gains is log concave.


4.1. T h e dec i s ion to m o v e

The tenant 's decision to accept the rent offered or to move can be described by the marginal tenants in terms of mobility cost, O~E[_O,O], i ~ {b,g}:

o , O ~ ( r , , r ~ ) = U ( r , ) - U ( r i ) ,

-~,

iff U ( r , ) - U(r i ) <0_ ,

i f f U ( r l ) - U(r , ) E [_0,0],

iff U ( r ~ ) - U ( r , ) > 0 .

(9)

The fraction of tenants who move is F(Oi) , i E {b, g}. We define r and ~ as rents for which all tenants move (respectively stay) by F ( O i ( r z , r ) ) ~ O (F(O'(r I , 7)) =- 1).

4.2. S e c o n d - p e r i o d rents

On contract renewal, landlords propose the second-period rents that maximize their expected profits, 7r 2. Obviously, ri < r can never be optimal and profits are invariant for r~ > ?. Hence, we can restrict the instrument to [r, 31.

P r o g r a m 2. Second-period rents

71- 2 max = F(O')rc ~ + (1 - F(Oi))~r ' , r I

subject t o r i E [ r , - r ] , i ~ { b , g } ,

where ~. i= (r i - P i " c ) + 6rr ' is expected profit, conditional on the record i ~ {b, g} and ~v ~ is the expected profit with a short- term contract chosen by an unknown type of tenant. To ease notation, we denoted partial derivatives of 7r with subscripts and define F/=-d/dr~ F(Oi(r l , ri) ) = - f . U ( r ~ ) > 0 and Fi i =- d2 / dr ~ F(O i (r l , r i ) ) = f " U '2 - f " U' . The following lemma is crucial for the characterization of post-contractual selection and the comparat ive statics.

L e m m a I. I f 7r~ = 0 at ri, then ¢ri 2 = - 2 F i + F~i(Tr S - 7r i) < - F i , i E {g, b}.

L e m m a 1 is an implication of the log-concavity of 1 - F (and non-convexity of U). While stronger than necessary to ensure that Program 2 is well behaved, it is crucial for the comparat ive statics. In this sense, the


r e q u i r e m e n t of the log-concavi ty of 1 - F is tight. Since L e m m a 1 rules out any local min ima , the solut ion to P rog ram 2, deno ted r*, is given as

f r , iff 1 + (~r~- 1r~)~ ~< O, a t r , r i* = r i , i f f l - F ( 0 ~ ) + ( T r S - 7Ti)F/ = 0 , a t r ~ E ( r , ~ ) , (10)

1 ~ , iff(Tr ~ - 7r ~ )F , />0 , a t 3 .

4.3. Contractual offers

A s in the prev ious sect ion, profits are zero in equi l ibr ium and there mus t not exist a n o t h e r sho r t - t e rm cont rac t earn ing posi t ive profits. T h e zero- prof i t condi t ion (11) can be ob ta ined f rom (4) with obvious subst i tut ions:

7r ~ = (r I - p c ) + (1 - p ) F ( O g ) ( r i - pgC) + pF(Ob)(rl -- pb c)

+ a(1 -- p ) (1 -- F(O g))(rg - pgC) + 6p(1 - F(O b))(r b - pb c)

= 0 . (11)

A cont rac t (r~, r g, r ~ ) fulfilling (10) and (11) const i tu tes a Nash equi l ibr ium if no cont rac t charging a lower initial rent is profi table:

s . . >- ~ ~ * , * (12) 7r ( r , , r g , r ~ ) ~ T r (r, rg, r~) V F < r , .

Such a cont rac t c rea tes lower r evenue but it also induces m o r e tenants to quit thei r cur ren t contracts . Express ion (12) rules out that there are enough addi t ional move r s with a very low cost probabi l i ty to offset the fall in r evenue by a decrease of expec ted cost.

4.4. Equi l ibr ium

T h e next p ropos i t ion and its corol lary charac ter ize the equi l ibr ium.

Proposi t ion 5. In equil ibrium, landlords charge bad tenants strictly higher rents than (i) good tenants (rg < r~) and (ii) u n k n o w n tenants (r~ < r~).

Corollary 1. The mos t mobile (i f not all) bad tenants move - some o f them do so in spite o f positive mov ing cost: 1 >~F(0 b) > F ( 0 g) />0 . Good tenants have a strictly lower turnover than bad t e n a n t s : F(0 b) > F(O g) >10.

Pos t -con t rac tua l select ion is charac te r ized by the t r ade-of f that a landlord faces at the beginning of the second per iod. On one hand , he would like to exploi t the t enan t ' s immobi l i ty at that s t a g e - s u g g e s t i n g a ' m a r k up ' on initial rent . In the case of a bad record , this inclination is even fos te red by the wish to get rid of high-cost tenants . On the o the r hand , in the case of a good record , he wants to keep the t enan t - suggest ing a rent discount . If all


the bargaining power rests with the landlord, the result of this trade-off be tween exploiting the switching cost of sitting tenants, and preventing low-cost tenants from moving, remains open. If the tenant should have the first-mover advantage in the negotiation for renewal, a tenant with a good reputat ion would always demand a tenure discount.

Table 1 displays the different types of equilibria. 7 An equilibrium of type 1 resembles very much the marke t for long-term terminable contracts. All tenants with a bad record would be 'economically ' evicted by a sufficiently high rent F(O b) = 1, all good tenants would be prevented from moving by a low rent F(O g) = 0. Given the assumption that some tenants prefer to move

* < r ~ , to achieve this. In a type 4 _0 < 0 , a tenure discount is required, rg equilibrium only the most mobile tenants of both groups move (0 < F(O g) < F ( 0 b ) < l ) and mix with new entrants after the first period. The other equilibria are mixed cases.

4.5. Comparative statics

Table 2 summarizes the result of the comparat ive statics for the equilib- r ium of type 4. Given the empirical evidence supporting a tenure discount

* ~ r * for average long-standing tenants, we consider the case r 1 g. Owing to the higher turnover of bad tenants, the expected cost in the first

per iod of a contract is higher than in the second. At the same time, compet i t ion among landlords is strong at this stage. In the second period, when costs are already lower, the landlord is able to exploit the immobili ty of his old tenants. Therefore , the landlord faces a deficit in the first period of a contract and enjoys surplus in the second. The zero-profit condition requires that the interest on this ' investment ' is covered by the rent payments . As the discount factor 8 increases - the discount rate decreases -

* induces a downward shift of rg compet i t ion forces rents down. The fall in r I

T a b l e 1

T y p e s o f e q u i l i b r i u m

T y p e 1 T y p e 2

0 = F(Og) < F(O b) = 1 O< F(Og) < F(O b) = 1 O ~ --( 'B "s ~"B 'g)Fg -- 1 O = 1 - F(O*) + ('n "s - ~rg)Fg 0 ~< 7r ~ -- "n" 0 ~< "n "~ - "n "b

T y p e 3 T y p e 4

O = F(Og) < F(O t') < l O < F(Og) < F(O") < I 0 <~ - ( ~ - ~g)Fg - 1 0 = 1 - F(O g) + ('rr ~ - "rrg)Fg O = l - F ( o b ) + ( ' r r ~ - T r b ) F b 0 1 F(Ob)+(cr~--~b)Fb

7 It c a n be s h o w n b y n u m e r i c a l e x a m p l e s t h a t all t hese equ i l i b r i a d o , in fac t , exist .

648 F. H u b e r t / R e g i o n a l S c i e n c e a n d U r b a n E c o n o m i c s 2 5 ( 1 9 9 5 ) 6 3 1 - 6 5 4

Table 2 Compara t ive statics: Equil ibrium type 4

r,* r*~ r h* F(O ~) F(O b)

6 - - - + +

E O - " " + ~' + ' - . . . . p ~ + _ ~ + _ ,, + , , d

c + + + '? ? ? '?

b r g ---~ El .

' p--+ 1. " p -~" O.

and r~,, which is, however, not strong enough to prevent the turnover from rising. To determine the impact of mobility, the expected mobility cost E0 is considered as a parameter , shifting the distribution F in the sense of first-order stochastic dominance, (FEo < 0 ) . As moving cost increases, tenants would become more prone to ex-post exploitation. Rents for oldsters increase, while turnover rates decrease. At the same time, the tenure discount gets smaller.

The impact of an improved assessment of the tenants at the post- contractual stage (pg, Pb moving away from p) depends on whether the landlords learn 'more ' about good tenants or bad tenants. From (2) it follows that for a given p , p g and Pb are related according to

P (1-pb) . P g - 1 - p

If the cost probabili ty of youngsters p is high, then not observing cost during the first period is 'good news' , from which a very low pg can be inferred, while 'bad news' is hardly news at all. In this case, a small increase in p , must be accompanied by a large drop of pg, to keep p constant. If p is low, pg is insensitive to a change of Pb" Some results can only be obtained for the limiting cases p - ~ 1, when landlords learn only about the low cost of good tenants, and p - + O, when landlords learn about the high cost of bad tenants. In the latter case, a marginal increase of Pb raises r~, so much that the turnover of bad tenants rises. The resulting increase of the expected

* which puts the first-period cost of unknown tenants leads to a rise of r~, landlords in a stronger position vis-fi-vis old tenants with a good record.

* is weak in relation to the increase of r i, so Nevertheless , the change of rg that the turnover of good tenants declines. As p approaches one, an increase of Pu results in a much reduced cost probabili ty of tenants with a good record. Landlords lower rg, reducing the turnover of good tenants. The withdrawal of low-cost tenants from the pool of movers requires an increase of r~, making the overall impact on the turnover of bad tenants ambiguous.


An increase of c means that all tenants are becoming more costly to serve. It has to be compensa ted by a general increase in rent. Since the cost increase is in proport ion to the cost probability, the absolute difference be tween good and bad tenants grows. It could therefore be expected that the incentives to keep good tenants and to deter bad tenants becomes stronger. For the type 4 equilibrium, however, no clear cut results could be derived.

4.6. Efficiency

Efficiency requires that tenants move if and only if they benefit f rom moving. With short- term contracts the time profiles of expected rents are upward-sloping for bad tenants and (possibly) downwards-sloping for good tenants. As with terminable long-term contracts, the turnover of tenants with a bad record is, therefore, inefficiently high. The turnover of good tenants, however, might be too low. If their rent is lower than the initial rent of a new contract (the case of a tenure discount) some tenants will forgo the gains from a move in order to cash in on their good reputation. Since it will be difficult to prevent landlords f rom offering good tenants favourable rents, the scope to improve efficiency through regulation is more limited in this case.

5. Concluding remarks

This paper is based on the assumptions that tenants differ with respect to non-contractable service cost and that landlords learn about these differences through experience. The analysis of the preceding sections addressed two related questions: (i) How do landlords respond to information which they gain during tenure, given the contract they agreed upon in the first place? (ii) What types of contracts will be chosen in equilibrium?

In Section 4 the focus was on post-contractual selection. It was shown that within a sequence of short- term contracts the landlord would charge tenants with a bad record a higher rent upon renewal than tenants with a good record. Correspondingly, the rate of turnover of bad tenants would be higher than that of good tenants. In an extreme case, all tenants with a bad record would be economically evicted by a very high rent, and the turnover of good tenants would be inhibited by a large enough tenure discount. Compara t ive statics suggest that a tenure discount is more likely in equilibrium if mobility cost is low and if a good (or a bad) record of service cost leads to a substantial revision of expected service cost.

In Section 3 the focus was on pre-contractual selection. To ease the exposit ion we restricted the class of feasible contracts to long-term contracts


with and without tenure security and ruled out that tenants want to move. Post-contractual selection is absent in a non-terminable contract and takes the simple form of evicting all tenants with a bad record in a terminable contract. Since the probability of eviction is smaller for low-cost tenants, terminable contracts are able to 'skim the cream' if tenants are better informed about their type ex ante. Contracts providing tenure security, in turn, suffer from adverse selection. The equilibrium will always entail some trading of terminable contracts. Their market share increases as mobility cost decreases or as non-contractable service cost increases.

Terminable contracts enable low-cost tenants to differentiate themselves from the high-cost tenants. Compared with a situation with equal treatment, the rent of the former is reduced at the cost of the latter. This redistribution among tenants is achieved at some c o s t - t h e moving cost in the case of eviction. But eviction serves no social a im- se rv i ce cost is fixed and the evicted tenant will rent from another landlord anyway. Hence, tenure security laws that force all parties to enter non-terminable contracts increase welfare.

Tenure security regulations can be found in Japan and in most European c o u n t r i e s - e . g . Germany, France, the Netherlands, Italy and (until recently) in Great Britain. As for the United States and Canada, tenure laws are not uniform. Most jurisdictions, however, follow a free market approach towards contracting in the rental housing market. On its normative side, the paper has, so far, emphasized the potential of tenure security laws to enhance welfare. It should be stressed that this result applies only to regulations that are not combined with measures to depress rents. The German Tenure Security Act of 1971 or the French 'Mrhaignerie Act ' of 1986 can be regarded as examples of this kind. Furthermore, the unambigu- ous impact of tenure security laws on welfare depends on the fact that, given Assumptions 1 and 2, society can provide tenure security at zero cost. This feature is easily lost if we draw a more realistic picture of contracting problems.

(1) If the tenant has some discretion over the probability or the size of the service cost, the landlord's threat to give notice creates incentives to keep this cost low. 8 Protection against eviction would entail costs in the form of a higher incidence of nuisance, negligence, etc. which have to be traded off against the welfare gains of reduced contract disruptions and stable rents.

(2) The right to give notice prevents the landlord against becoming stuck with a 'bad ' tenant. If landlords are risk averse, security of tenure can no longer be provided without a premium for this risk.

8 See Stiglitz and Weiss (1983) for a general discussion of the incentive effects of contract termination and Homburg (1993) for an application to the housing market.


(3) It has been assumed that the expected service cost of a tenant is independent from the landlord. In reality, landlords differ in their valuation of the service cost. An old lady subletting parts of her house may consider lady visitors after ten o'clock unacceptable, whereas a manager of a commercial building company would probably not mind. To reduce the service cost, the more difficult tenants should be matched with the less sensitive landlords. The abolition of terminable (or short-term) contracts through tenure security laws would result in an increase in the mismatch cost.

While each of these modifications makes the protection against eviction costly, none of them restores necessarily the efficiency of an unregulated market . Owing to adverse selection, the private cost of providing tenure security still surmounts the true social cost. Hence, in equilibrium the provision of tenure security would still be to low at the margin. Making protect ion against eviction mandatory for all leases, however, would have an ambiguous impact on welfare. Such a measure may force tenants to pay a premium for the insurance, which surmounts their valuation of it.

It is interesting to note that the aforementioned regulations in Germany and France account for the different cost of providing tenure security. In France the minimum term during which eviction is not possible is four years when the landlord is an ordinary person, but six years for commercial landlords. In Germany, protection against eviction is not granted if the dwelling is furnished or if the landlord shares a small house with his tenants. Presumably private landlords, and in particular those sharing the house with the tenant, are more risk averse and more sensitive to the service cost than commercial landlords.

Like many other interventions in the market, tenure security laws need complementary measures that might cause additional problems. The most prominent is the need to regulate the updating of rent in on-going contracts in order to prevent tenure security from being loopholed by economic eviction. In France rent reviews have been indexed on construction cost - a proxy for the cost of living index which cannot be used for legal reasons. In Germany a rent increase is linked to the rent of other 'comparable ' dwellings. At least in principle, rents of old contracts can be adjusted to the overall conditions of the housing market. Recently, indexation on the rate of inflation has been introduced as an alternative option. Fixing the rent in real terms isolates the contract against the development of the market for the duration of the term. The schemes have different implications for the allocation of housing as well as the equilibrium price distribution if the housing market is subject to real shocks (Hubert , 1990). The optimal indexation has to strike a balance between the insurance provided by fixed real rents and the efficiency of allocation provided by adjustable rents.

However , real-world housing policy is often more concerned with (re)distribution rather than efficiency. Presumably, politicians will find it more

652 F. Hubert / Regional Science and Urban Economics 2.5 (199.5) 631-654

difficult to resist pressure to 'keep rents down' if some form of 'rent control ' is already in place. The recent experience in Germany provides a good example. When growing disposable income and a wave of immigration pushed up rents in the late 1980s, politicians gradually toughened restrictions on rent increases.

Within a couple of years, minor legal modifications regarding the determination and applicability of 'comparable rents' have profoundly changed the operation of the market (Hubert, 1993). What was meant to be a complementary measure to provide a secure tenure has mutated into a system of thinly disguised rent controls. Nowadays, in most big cities tenure security appears 'necessary' to support legally depressed rents - as it used to be in traditional 'rent controls'.

Acknowledgements

Helpful comments by Elmar Wolfstetter, Horst Tomann, Choon Poh Tan, the referees and the editor are gratefully acknowledged.

Appendix: Selected proofs

P r o o f o f Proposit ion i. Define X so that ~.t =- X[(1 - 6 )Z] i. X < Z(r, - pgc) ~ t _ rrg = (1 - 6 )7r t - (r, - pgC) < 0, which implies y g = 0. From X > Z(r t - p b c) it follows that y ~ = 1. Whatever the other landlords do, the best response is to evict a tenant if and only if he has got a bad record. Being a dominant strategy it establishes a unique Nash equilibrium in the final subgame.

P r o o f o f Proposit ion 2. For a = 0, (6) and (7) require r t = 0, r,, = pc > 0 for which (5) implies a > 0 - a contradiction.

P r o o f o f Proposit ion 4. Since landlord's profits are zero in both cases, we are only concerned with the impact on the tenants' welfare. Under regulation the expected utility is (1 + 6 ) U ( p c ) for every tenant. In market equilibrium expected utility before learning, 05, is given as H(a*)[(1 + 8 )U( t* ) - 6EO] + (1 - H(a*))(1 + 6 ) U ( n * ) . Substitution with the help of the zero profit condition and division by (1 + 6) yields

(s) H ' U ( p t c ' ~ ) + ( 1 - H ) ' U ( p n c ) - H ( 1 + 6 ) E 0 <

H" U(p tc ) + (l - H ) " U(pnc ) <~ U ( p c ) . (13)

F. Hubert / Regional Science and Urban Economics 25 (1995) 631-6.54 653

The last inequali ty follows f rom (1) and the non-convexi ty of U. The first par t o f (i) is obta ined by interpret ing H as a probabi l i ty when calculating the expected utility; the second by taking it as a weight when aggregating. Claim (ii) follows obviously f rom setting a* = 1.

Proof o f Lemma 1. Note , that the log-concavity of 1 - F implies

d 2 - f ' ( 1 - g ) - f 2 d0 2 In(1 - F ) : (1 - g ) 2 < 0 ,

1 - F - f - f ' - - f - - < O .

Since ¢r~ = 0 implies - ( 1 - F ) / F i = (Tr" -7 r i ) , the claim is equivalent to (recall U ' < 0, U" < 0)

1 - F - F , - < 0 ,

1 - F f ' U ' - ( f " U ' 2 - f ' U '') < 0

- f " U' '

- U ' - f - f ' - - f - - - - ~ - r ( 1 - F ) < 0 .

- ) by log-concavity

Proof o f Proposition 5. If r,* ~ (_r, i ) , then 027r2/ariOpi =picF, > 0 implies r* s i d i/dpi > 0 . Note that rr - T r = ( ! - 6 ) 7 r ~ - ( r - p , c ) is increasing in p~. If

the border condi t ion holds for r b =_r, it will also hold for rg = r ; if the border condi t ion holds for r =3, then it holds for r b =3. Hence , we have to rule out that r*g =~ or r b* =r_ to prove (i).

A s s u m e r*=~,g then (10) requires r - p g c ~ O , (9) implies r*;<r*g=~, hence r ~ - p g c < O . All tenants would move , but a landlord would make losses even if he catches a good tenant , which contradicts (11). Assume

* _ _ * 1 > * But rt, = r , then (10) requires r-pbc>~O; from (9) it follows that r~ r b. then a landlord would make profits on all groups in the first per iod, again contradic t ing (11). The final step of the previous a rgument also proves (ii).

R e f e r e n c e s

Akerlof, G.A., 1970, The market for 'lemons': Quality uncertainty and the market mechanism, Quarterly Journal of Economics 84, 488-500.

Behring, K., 1988, Mieth6he: Bonus fiir Sel3haftigkeit, IFO-Schnelldienst I1, 7-13. B6rsch-Supan, A., 1986, On the West German tenants' protection legislation, Journal of

Institutional and Theoretical Economics 142, no. 2, 380-404,


Caplin, A. and B. Nalebuff, 1991, Aggregation and imperfect competition: On the existence of equilibrium, Econometrica 59, no. 1, 25-59.

Eekhoff, J., 1987, Wohnungs-und Bodenmarkt (J.C.B. Mohr (Paul Siebeck), Tiibingen). Engels, W., W. Stiitzel, Wolfgang, C.C. von Weizs/icker et al., 1984, Mehr Market in der

Wohnungswirtschaft, Frankfurter Institut f/Jr Wirtschaftsforschung. Freeman, S., 1977, Wage trends as performance displays productive potential: A model and

application to academic early retirement, The Bell Journal of Economics, no. 2, 419-443. Goodman, A.C. and M. Kawai, 1985, Length-of-residence discounts and rental housing

demand: Theory and evidence, Land Economics 61, no. 2, 93-105. Greenwald, B.C., 1986, Adverse selection in the labour market, Review of Economic Studies

53, 325-347. Guasch, J.L. and R.C. Marshall, 1987, A theoretical and empirical analysis of the length of

residency discount in the rental housing market, Journal of Urban Economics 22, 291-311. Hirsch, W.Z., 1988, Law and economics, An introductory analysis (Academic Press, Inc.,

Boston, San Diego, New York, Berkeley). Holmstr6m, B. and R. Myerson, 1983, Efficient and durable decision rules with incomplete

information, Econometrica 51, 1799-1819. Homburg, S., 1993, An analysis of the German tenant protection law, Journal of Institutional

and Theoretical Economics 149, no. 2, 464-474. Hubert, F., 1990, Long term rental contracts, Freie Universit~t Berlin, Economics Department. Hubert, F., 1993, German's housing policy at the crossroads, Working paper, Freie Universit/it

Berlin, Economics Department. International Labour Office, 1924, European housing problems since the war, Studies and

Reports. Series G, No. 1, Geneva. Kanemoto, Y., 1990, Contract types in the property market, Regional Science and Urban

Economics 20, 5-22. Miron, J.R., 1990, Security of tenure, costly tenants and rent regulation, Urban Studies 27, no.

2, 167-184. Riley, J.G., 1979, Informational equilibrium, Econometrica 47, no. 2, 331-359. Rothschild, M. and J. Stiglitz, 1976, Equilibrium in competitive insurance markets: An essay on

the economics of imperfect information, Quarterly Journal of Economics 90, 629-649. Schlicht, E., 1983, The tenant's decreasing willingness to pay and the rent abatement

phenomenon, Journal of Institutional and Theoretical .Economics 139, 155-159. Schneider, W., K. Stahl and R.J. Struyk, Residential mobility in the United States and the

Federal Republic of Germany, in: K. Stahl and RJ . Struyk, eds., U.S. and West German housing markets (Springer, Berlin) 23-54.

Spence, M., 1974, Competitive and optimal responses to signals: An analysis of efficiency and distribution, Journal of Economic Theory 7, 296-322.

Stiglitz, J.E. and A. Weiss, 1983, Incentive effects of terminations: Applications to the credit and labor markets, the American Economic Review 73, no. 5, 912-927.

Waldman, M., 1984, Job assignments, signalling, and efficiency, The Rand Journal of Economics 15, no. 2, 255-267.

Wilson, C., 1977, A model of insurance markets with incomplete information, Journal of Economic Theory 16, 167-207.

contracting with costly tenants

Documents