tenant turnover, rental contracts, and self-selection

Journal of Housing Economics 8, 301–311 (1999)

Article ID jhec.1999.0253, available online at http://www.idealibrary.com on

Tenant Turnover, Rental Contracts, and Self-Selection

Thomas J. Miceli

Department of Economics, University of Connecticut, Storrs, Connecticut 06269E-mail: [email protected]

and

C. F. Sirmans

Department of Finance and Real Estate Center, School of Business Administration,University of Connecticut, Storrs, Connecticut 06269

Received April 15, 1999

I. INTRODUCTION

Whenever a tenant vacates a rental unit, the landlord incurs the costs ofreplacement, including search costs and the costs of reconditioning the unit.Landlords therefore have an interest in minimizing turnover. One way that theycan do this is by attracting tenants with an inherently low propensity to move.The problem is that such a propensity is unobservable, so landlords have todevise ways to attract and reward long-term tenants by means of self-selection.In this paper, we examine two contractual methods for accomplishing this objec-tive—namely, long-term leases and declining rent contracts (otherwise knownas length-of-residency discounts).1

In our model, we distinguish long-term leases from short-term, or period-by-period, leases by assuming that the former obligate the tenant to pay rent overthe full term of the lease even if he or she leaves early.2 In return, the landlordoffers the tenant a lower per-period rent compared to a short-term lease. In atwo-period model in which the long-term lease lasts for both periods, this schemeresembles a two-part price in which the tenant obtains a lower per-period priceby, in effect, promising to pay an “exit fee” (the second period rent) if he or sheleaves after the first period. (In the absence of the exit fee, all tenants would

1 The problem facing landlords is identical to that facing a firm that incurs training costs when ithas to hire new workers. The classic analysis of how firms minimize turnover costs by means ofself-selection is by Salop and Salop (1976).

2 Leases of this sort are common in the commercial real estate market (Geltner, 1990; Benjaminet al., 1990, 1992) but are not frequently seen in the residential market.

301

1051-1377/99 $30.00Copyright q 1999 by Academic Press

All rights of reproduction in any form reserved.

302 MICELI AND SIRMANS

obviously prefer the long term lease because of the lower rent.) Self-selectionoccurs under this structure because low-mobility tenants place more weight onthe rent discount and less on the exit fee than high-mobility tenants.

A similar logic underlies the declining rent contract.3 Specifically, self-selectioncan be induced by this contract if the rent starts above, and then falls below, therent in a flat rent contract. The declining rent structure therefore in effect requiresthat tenants pay an “entry fee” in period one in order to obtain the discountedrent in period two. (As above, if the first period premium were not required, alltenants would opt for the declining structure.) Slow movers prefer the decliningrent contract because they place more weight on the future discount and less onthe entry fee than fast movers.

The purpose of this paper is both to illustrate the use of self-selection devicesby landlords to limit turnover costs and to explain some commonly observedfeatures of rental contracts. The analysis is organized as follows. Section II setsup the model, Section III examines the long-term lease, and Section IV examinesthe declining rent contract. Finally, Section V concludes.

II. GENERAL SETTING

Knowledge of a tenant’s probability of moving is valuable to landlords becauseit is costly to fill a vacant unit. Suppose, in particular, that if a tenant vacates aunit at the end of a period, the landlord must incur a cost of c at the start of thenext period to fill the unit. For simplicity, we assume that by spending c, thelandlord fills the unit with certainty. Thus, there are never any unfilled vacanciesin the building.4 Let R be the periodic rent for a unit, which we assume is paidat the beginning of the period. Thus, the landlord receives R at the start of thefirst period and R-pc at the start of all subsequent periods, where pc is theexpected cost of filling the unit if the tenant from the previous period had vacated.5

Over an infinite horizon, the present value of the landlord’s net revenue per unit(ignoring opportunity costs) is

PV 5 R 1 o`

t 5 1(R 2 pc)/(1 1 r)t 5 R 1 (R 2 pc)/r. (1)

Because this expression is decreasing in p, the landlord prefers tenants with lowprobabilities of moving.

3 The literature on length-of-residency discounts in real estate (both theoretical and empirical)includes Goodman and Kawai (1985), Guasch and Marshall (1987), Miron (1990), and Hubert (1995).

4 This follows the specification of Goodman and Kawai (1985).5 This assumes that R $ c, so that it is profitable to fill the vacancy (see the further discussion

below). The qualitative nature of the results would not change if spending c filled the unit withprobability less than one.

TENANT SELF-SELECTION 303

Suppose there are two types of tenants: slow movers and fast movers. Slowmovers have a probability ps of moving at the end of any period, and fast movershave a probability pf of moving, where pf . ps . 0. Let a be the fraction ofslow movers in the population of tenants, and 1 2 a the fraction of fast movers.Tenants know their own types, but landlords only know the proportion of eachtype and their probabilities of moving. Finally, let b be the per-period benefit oftenancy for a tenant, and let x be the tenant’s next best return if he or she vacates.These variables can represent either profits for commercial tenants or the dollarvalue of consumption benefits of housing for residential tenants. In either case,we assume that the variables are the same for both slow and fast movers andare common knowledge.

The problem for landlords is to attract slow movers in such a way as tominimize turnover costs. We examine two ways in which landlords can do this,both using self-selection. The first is by offering a long-term lease as opposedto period-by-period lease, and the second is by offering a declining rent contractto long term tenants. To keep the analysis as simple as possible, we consider atwo-period model. In that case, (1) reduces to

PV 5 R 1 (R 2 pc)/(1 1 r). (2)

We begin by considering long-term (two-period) leases as self-selection devices.

III. LONG-TERM VERSUS SHORT-TERM LEASES

Suppose that landlords can offer either two-period leases or one-period leases.The two-period lease requires tenants to pay the rent in both periods even if theyvacate in the second period, whereas the one-period lease allows tenants to payon a period-by-period basis (with an option to renew at the same rent for thesecond period). This form of long-term lease therefore protects the landlord fromturnover costs imposed by tenants.6 It thus differs from the long term contractsstudied by Hubert (1995), which provide tenants with protection against eviction.7

Let R2 and R1 be the per period rents under the two- and one-period leases,respectively.8 We are interested in deriving a separating equilibrium that has thefollowing characteristics: (1) slow movers self-select the two-period lease andfast movers self-select the one-period lease; (2) the two types of leases yield

6 We ignore risk-sharing considerations in the design of rental contracts. Optimal risk sharing mayaccount for the absence of long-term contracts in the residential market since under these contracts,tenants bear all of the risk arising from their random mobility.

7 In Hubert’s model, tenants potentially incur costs of movement if evicted, whereas landlordsincur no turnover costs.

8 We assume that under the two-period lease, neither the landlord nor the tenant is able to renegotiatethe second period rent for strategic purposes.


equal profits for landlords so that both are offered in equilibrium; and (3) landlordsearn zero profits. We first derive the conditions for tenant self-selection, givenarbitrary values for R1 and R2.

Consider first the net benefit of the one-period lease for a tenant whoseprobability of moving is pi , i 5 s,f. This is given by

NB1(R1, pi) 5 b 2 R1 1 [pi x 1 (1 2 pi)(b 2 R1)]/(1 1 r). (3)

In contrast, the tenant’s net benefit under the two-period lease is

NB2(R1, pi) 5 b 2 R2 1 [pi x 1 (1 2 pi)b 2 R2]/(1 1 r). (4)

The only difference between (3) and (4) is that, under the two-period lease, thetenant must pay R2 whether or not he or she moves.

To obtain a separating equilibrium of the type described above, we need thefollowing two conditions to hold:

NB1(R1, pf) $ NB2(R2, pf) (5.1)

NB1(R1, ps) # NB2(R2, ps). (5.2)

By (5.1), the fact mover prefers the short-term lease, and by (5.2), the slowmover prefers the long-term lease. Substituting into these conditions from (3)and (4) yields

R1 # R2[(2 1 r)/(2 1 r 2 pf)] (6)

for the fast mover and

R1 $ R2[(2 1 r)/(2 1 r 2 ps)] (7)

for the slow mover. The fact that pf . ps implies that

(2 1 r)/(2 1 r 2 pf) . (2 1 r)/(2 1 r 2 ps). (8)

Thus, a separating equilibrium exists if R1 and R2 satisfy

(2 1 r)/(2 1 r 2 pf) $ R1/R2 $ (2 1 r)/(2 1 r 2 ps) . 1. (9)

Note that the last inequality implies that, in a separating equilibrium, it must betrue that R1 . R2. Intuitively, per-period rent must be higher for one-period leasesthan for two-period leases. Otherwise both types of tenants will prefer the one-period lease, given that the latter includes both the right to renew and the right


FIG. 1. Self-selection with long-term leases.

to vacate without incurring further rental obligations. This result is consistentwith the empirical evidence on the relationship between rent and lease term incommercial leases.9

Figure 1 graphs conditions (6) and (7) written as equalities. Together, theydefine the shaded area, which shows the pairs of R1 and R2 that satisfy self-selection for both tenants (i.e., the pairs that satisfy (9)). The fact that pf . p s

ensures that this area is a nonempty set.A separating equilibrium also requires that landlords earn sufficient revenue

to cover their opportunity costs under both leases and that the leases be equallyprofitable, so that both are offered. From (2), the present value of net revenuefor a landlord offering a one-period lease, assuming that it is chosen by fastmovers, is given by

PV1 5 R1 1 [(1 2 pf)R1 1 pf(R1-c)]/(1 1 r)

5 R1 1 (R1 2 p f c)/(1 1 r). (10)

If we define the present value of opportunity costs of landlords to be p0, thengiven free entry of landlords, PV1 5 p0 in equilibrium. In addition, recall fromabove that R1 $ c is necessary in order for landlords to find it profitable to fillany vacancies in the second period. We assume that these two conditions are

9 Specifically, Benjamin et al. (1990) found a negative and significant relationship between rentand lease term in retail leases, and Benjamin et al. (1992) found a similar result for office leases.


consistent with one another. Specifically, we rule out a situation where PV 5p0 implies R1 , c.

Under a two-period lease, recall that the landlord receives the rent R2 fromthe first-period tenant in both periods, regardless of whether or not he or shevacates in period two. This yields a present value of revenue equal to R2 1 R2/(1 1 r). In addition, if the first-period tenant vacates, the landlord also has theoption to find a new tenant by spending c. Since the second period is the finalone (by assumption), the landlord can only offer the new tenant a one-periodlease at rent R1, yielding net revenue of R1 2 c $ 0. The resulting present valueof expected revenue from a two-period lease, assuming that it is selected by aslow mover, is given by

PV2 5 R2 1 [R2 1 ps(R1 2 c)]/(1 1 r). (11)

As above, we require that PV2 $ p0.Setting PV1 equal to PV2 and rearranging yields the condition for equal profit-

ability from the two leases:

R1 5 [(2 1 r)/(2 1 r 2 ps)]R2 1 ( pf 2 ps) c/(2 1 r 2 ps). (12)

Note that this equation describes a positively sloped straight line in (R1, R2) spacewith slope (2 1 r)/(2 1 r 2 ps) . 1 and intercept ( pf 2 ps)c/(2 1 r 2 ps) .0. The line is therefore parallel to the slow mover self-selection line as definedby (7) and, given the positive intercept, it intersects the self-selection set at pointA as shown in Fig. 1. As a result, any point on this equal-profit locus at or abovepoint A satisfies the self-selection conditions for both types of tenants.

To determine which point is the equilibrium, we first calculate the coordinatesof point A by writing (6) as an equality and solving it simultaneously with (12).This yields

RA1 5 c, (13)

RA2 5 (2 1 r 2 pf)c/(2 1 r) , RA

1 (14)

Given (13), the constraint R1 $ c is clearly satisfied for any R1 at or above A.Further, since we assumed that PVi $ p0 is consistent with R1 $ c, the landlord’szero profit constraint must be satisfied over this range as well. It follows that anequilibrium satisfying self-selection exists. If we assume that PV1 5 p0 occursexactly at R1 5 c, then free entry will drive the equilibrium to point A, yieldingthe rents in (13) and (14). At this point, the self-selection condition is bindingfor fast movers; that is, they are just indifferent between the two types of leases(condition (5.1) holds with equality). In contrast, slow movers are strictly betteroff with the long-term lease (condition (5.2) holds with a strict inequality). Slow


movers, being the “scarce resource,” therefore receive a surplus (Salop and Salop,1976). It is possible, however, that the equilibrium will be at a point above Aon the equal profit locus (e.g., if PVi , p0 at A). In that case, the equilibriumoccurs where PVi 5 p0, and since neither self-selection constraint will be binding,both types of tenants will receive a surplus.

IV. DECLINING RENT FOR LONG-TERM TENANTS

We next consider the use of a declining rent contract (or rent discount) forlong-term tenants as a self-selection device. Although previous authors havedescribed the possible screening function of declining rent contracts,10 they havegenerally argued that landlords lower rent for “preferred” tenants after observing(or updating) their type. The current model differs in that we derive an equilibriumin which preferred (low-mobility) tenants reveal their types up front by theirselection of the declining rent contract.11

For purposes of the analysis, we define R to be the rent charged in each periodunder a “flat” rent contract. Thus, under a declining rent contract, let the firstperiod rent be R 1 R1 and let the second period rent be R 2 R2. Although wedo not constrain R1 and R2 up front, note that a declining rent contract requiresthat they both be nonnegative. Our conjecture is that such a structure will yielda separating equilibrium wherein slow movers choose the declining rent contractand fast movers choose the flat rent contract.

Proceeding as above, note that tenants of type i (i 5 s, f) receive net benefitsequal to

NBF(R, pi) 5 b 2 R 1 [pi x 1 (1 2 pi)(b 2 R)]/(1 1 r), (15)

under the flat rent contract and net benefits of

NBD(R1, R2, pi) 5 b 2 (R 1 R1) 1 [pi x 1 (1 2 pi)(b 2 R 1 R2)]/(1 1 r)

(16)

under the declining rent contract. The self-selection conditions in this case, giventhe conjectured equilibrium, are

NBF(R, pf) $ NBD(R1, R2, pf) (17.1)

NBF(R, ps) # NBD(R1, R2, ps) (17.2)

10 See the references in footnote 3 above.11 It should be noted that Hubert (1995) considers both the initial selection of contracts by tenants of

different types and the adjustment of contract terms as the landlord learns more about the tenant’s type.


Using (15) and (16), these become

R1 $ [(1 2 pf)/(1 1 r)]R2 (18)

R1 # [(1 2 ps)/(1 1 r)]R2. (19)

These conditions, along with the fact that pf . ps, imply that a separatingequilibrium exists if

[(1 2 ps)/(1 1 r)]R2 $ R1/R2 $ [(1 2 pf)/(1 1 r)]R2. (20)

Figure 2 graphs conditions (17.1) and (17.2) written as equalities. The shadedarea shows combinations of R1 and R2 where these conditions are satisfied.

As in the previous section, the condition for landlords to be willing to offerboth types of contracts is found by equating the profits from them, assumingself-selection. Under the flat rent contract, the present value of net revenue isgiven by

PVF 5 R 1 (R 2 pfc)/(1 1 r), (21)

whereas under the declining rent contract, the net revenue is given by

PVD 5 R 1 R1 1 [ps(R 2 c) 1 (1 2 ps)(R 2 R2)]/(1 1 r)

5 R 1 R1 1 [R 2 psc 2 (1 2 ps)R2]/(1 1 r). (22)

FIG. 2. Self-selection with declining rent contracts.


Note that the declining rent contract assumes that if the first period tenant vacatesthe unit, the landlord can only offer a flat rent contract to a new tenant. In both(21) and (22), we assume, as above, that PVj $ p0 for j 5 F, D (i.e., bothcontracts at least cover the landlord’s opportunity costs) and R $ c, so that it isprofitable to refill vacancies at the flat rate under either contract in period two.

The equal profitability condition is found by equating (21) and (22) to yield

R1 5 [(1 2 ps)/(1 1 r)]R2 2 ( pf 2 ps)c/(1 1 r). (23)

This equation defines a straight line with slope (1 2 ps)/(1 1 r) . 0, and intercept-( pf 2 ps)c/(1 1 r) , 0. As Fig. 2 shows, this line is parallel to the fast mover’sself-selection constraint and cuts the self-selection set at point A. Thus, as in theprevious section, any (R1, R2) pair that lies on the equal profit locus at or abovepoint A induces self-selection by both types of tenants.

The coordinates of point A are found by solving (18) (written as an equality)and (23) simultaneously:

RA1 5 (1 2 pf)c/(1 1 r), (24)

RA2 5 c. (25)

We also need to solve for the flat rent, R. Note that this rent corresponds to therent under the short-term lease in the previous section R1, given that PVl andPVF are identical. Thus, for sake of comparison, we initially assume that thesetwo rents are the same in equilibrium and that point A is the equilibrium pointin Fig. 1. Thus, let R 5 c. It follows from (24) and (25) that under the decliningrent contract, the rent schedule (R 1 R1, R 2 R2) is given by

(c 1 (1 2 pf)c/(1 1 r), 0). (26)

Note that in this equilibrium, if the tenant stays for the second period, he payszero rent. That is, the rent discount is exactly equal to the base rent, which equalsthe cost of filling a vacant unit. Obviously, this is an extreme case. More generallywe would expect that R . c, in which case the long-term tenant will pay apositive but reduced second period rent. As in the previous section, the specificpoint depends on the landlord’s opportunity cost.

V. CONCLUSION

Minimization of turnover costs is an important objective for landlords in boththe residential and commercial real estate market. One problem landlords face,however, is that a tenant’s mobility is unobservable at the time the parties enter


into a rental relationship. In this paper, we examined how landlords can usecontractual mechanisms as self-selection devices to attract low mobility tenantsand thereby reduce turnover costs. Although there is an extensive literature onthe use of contracts to induce self-selection in various market settings, there hasbeen relatively little application of these methods to the rental housing market.12

The analysis focused on two types of contracts, both observed in the real estatemarket—namely, long-term leases and declining-rent contracts. Under a long-term lease (which is primarily seen in the market for commercial real estate),tenants commit to remain in the unit (or at least agree to pay rent) for a setnumber of months or years. We showed that if the long-term lease offers asuitable rent discount over the short-term (period-by-period) lease, then low-mobility tenants will prefer the long-term lease and high-mobility tenants willopt for the short-term lease. This sort of self-selection is possible because thelow-mobility tenants place a relatively higher value on the rent discount, whereashigh-mobility tenants place a relatively higher value on the option to vacate atwill without incurring further rental obligations.

While long-term contracts are frequently used with commercial tenants, theyare rare in the residential market. What is more common in residential real estateis rent discounts for long-term tenants. We showed that if these discounts arepaired with an initial rent premium as part of a “declining rent contract,” thenlow-mobility tenants will self-select the declining contract and high-mobilitytenants will opt for the flat rent. Although rental discounts have been associatedby previous authors with landlords’ efforts to reduce turnover costs, they havenot been modeled as self-selection devices. Rather, landlords were seen as offeringlower rents to tenants as an inducement to stay. The analysis here demonstratesthat a promised discount in the future can allow landlords to attract low-mobilitytenants in the first place. In the competition for a favorable tenant population,this can be a valuable tool.

REFERENCES

Benjamin, J., Boyle, G., and Sirmans, C. F. (1990). “Retail Leasing: The Determinants of ShoppingCenter Rents,” AREUEA J. 18, 302–312.

Benjamin, J., Shilling, J., and Sirmans, C. F. (1992). “Security Deposits, Adverse Selection andOffice Leases,” J. Amer. Real Estate Urban Econ. Assoc. 20, 259–272.

Geltner, D. (1990) “Return Risk and Cash Flow Risk with Long-Term Riskless Leases in CommercialReal Estate,” AREUEA J. 18, 377–402.

Goodman, A. and Kawai, M. (1985) “Length-of-Residence Discounts and Rental Housing Demand:Theory and Evidence,” Land Econ. 61, 93–105.

Guasch, J. L. and Marshall, R. (1987) “A Theoretical and Empirical Analysis of the Length ofResidency Discount in the Rental Housing Market,” J. Urban Econ. 22, 291–311.

12 Exceptions include Miceli (1989) and Hubert (1995).


Hubert, F. (1995) “Contracting with Costly Tenants,” Regional Sci. Urban Econ. 25, 631–654.

Miceli, T. (1989) “Housing Rental Contracts and Adverse Selection with an Application to the Rent-Own Decision,” AREUEA J. 17, 403–421.

Miron, J. R. (1990) “Security of Tenure, Costly Tenants and Rent Regulation,” Urban Stud. 27,167–183.

Salop, J. and Salop, S. (1976) “Self-Selection and Turnover in the Labor Market,” Q. J. Econ.90, 619–627.

tenant turnover, rental contracts, and self-selection

Documents