the dynamic effects of land title systems

Ž .Journal of Urban Economics 47, 370]389 2000doi:10.1006rjuec.1999.2145, available online at http:rrwww.idealibrary.com on

The Dynamic Effects of Land Title Systems1

Thomas J. Miceli

Department of Economics, Uni ersity of Connecticut, Storrs, Connecticut 06269

C. F. Sirmans

Department of Finance, Uni ersity of Connecticut, Storrs, Connecticut 06269

and

Geoffrey K. Turnbull2

Department of Economics, Louisiana State Uni ersity, Baton Rouge,Louisiana 70803-6306

E-mail: [email protected]

Received November 2, 1998; revised July 6, 1999

The question of title concerns which specific individual enjoys the property rightsto a particular parcel of land when there are competing claims. This paperexamines how the title system affects urban development in a market economy. Itconsiders two alternative title systems, recording and registration. Both hasten thedevelopment pace relative to the social planner benchmark, but the registrationsystem is generally closer than the recording system to the benchmark. The effectsof the two systems on the capital-land ratio depend on whether the demandedcapital-land density is rising or falling over time. Q 2000 Academic Press

Key Words: land registration; land title; property rights; urban development.

1. INTRODUCTION

One of the least controversial principles in the economics of landmarkets is the notion that the more clearly defined the property rights, the

w xgreater the land market efficiency 3, 9 . As important, but largely ne-glected in the economics literature, is the question concerning the rules orconventions establishing title to land, that is, the method used to establishwhich specific individual enjoys the property rights to a particular parcel of

1 We thank two referees and the Editor for their helpful comments and suggestions.2 To whom correspondence should be addressed.

3700094-1190r00 $35.00Copyright Q 2000 by Academic PressAll rights of reproduction in any form reserved.

LAND TITLE SYSTEMS 371

land when competing claims occur. Hardly an arcane institutional detail,the question of title assurance is fundamental to the market process, sinceit is a key element in the transfer of the defined bundles of ownershiprights among individuals.

Defects in land title can arise from two primary sources: errors oromissions in the public record, and differences in opinion by searchers

w xabout how to interpret the record. As a result of these problems, ‘‘ t hew xpossibility for error in establishing the chain of title for the requisite

Ž w x.period . . . is . . . very high’’ Bostick 5, p. 70 . One measure of themagnitude of the problem is the annual dollar amount of claims paid bytitle insurers in the U.S., which was $389 million in 1989.3 To put this inperspective, it represents 0.05% of the value of total residential real estate

w xtransactions in 1989, a relatively small but not inconsequential amount 1 .Moreover, these costs are widely felt, affecting everyone who buys or sellsland. During 1997, for example, the average title insurance premium in theU.S. per $100,000 worth of coverage was $465 for owners and $397 for

w xlenders 4 .This paper focuses on the question of how the methods or principles

that are used to establish title to land affect the timing and density ofurban development in a market economy. This question is important forevaluating proposals to reform existing systems as well as deciding whichsystem to establish in transitional economies. We examine two alternative

w xtitle systems: recording and registration 8, 10, 11 . The recording systempredominates in the U.S. while England has used the registration systemsince 1925. Nonetheless, both systems are relevant to the U.S. experience;variants of each have been and continue to be used in the U.S.4 Yet, eachof these methods of title assurance is built upon fundamentally differentpremises. Reduced to the simplest level, if, as a result of past errors oromissions in records, there are two individuals claiming a particular landparcel, then the registration system awards ownership to the currentpossessor while the recording system awards ownership to the individualwith the earlier claim. The recording and registration systems reflect thetrade-offs inherent in questions of title, given that no single title systemcan protect the property interests of both the current possessor and the

w xclaimant 2 .

3 Annual claims for the decade 1980]1989 ranged from $92.2 million in 1980 to $390.5w xmillion in 1988, for an average of $234.2 million. See 1 .

4 In the U.S. as many as 20 states have enacted some form of title registration legislation atw xone time or another 5, 12 , although many have repealed their registration statutes for lack

of use. Areas with the most extensive continuous experience with registration systems includeŽ .Hawaii, Massachusetts particularly counties surrounding Boston and the Eastern seaboard ,

Ž .Minnesota particularly counties around the Twin Cities and Duluth , and Cook County,Ž .Illinois until registration was repealed in 1992 .

MICELI, SIRMANS, AND TURNBULL372

w x w xMiceli and Sirmans 10 and Micel et al. 11 examine the implications ofthe two title systems for static efficiency and equity. Taking their results asthe point of departure, we extend the analysis of registration and recordingsystems to a dynamic context and ask how the different methods of titleassurance affect the intertemporal allocation of resources in urban landmarkets.

This analysis demonstrates that both title systems tend to increase thepace of land development relative to the normative benchmark, but thatthe registration system comes closer to the benchmark than does therecording system. The effects of each title system on capital intensity ofdevelopment, relative to both the normative benchmark and each other,depend upon how the demands for different land uses are changing overtime. Generally, sites where the demanded capital-land density is risingover time tend to be developed less densely while sites where the capital-land density is declining over time tend to be developed more densely thanthe social planner benchmark.

The discussion is organized as follows. Section 2 derives the landdevelopment conditions for our normative benchmark, establishing a pointof reference for comparing the relative performance of the alternative titlesystems. Section 3 examines how the recording system affects the landdevelopment pattern while Section 4 analyzes the effects of the registra-tion system. Section 5 provides a comparison of the effects of the alterna-tive title systems on the pace and density of urban development relative toeach other and to the normative benchmark. Section 6 presents theconclusions.

2. A NORMATIVE BENCHMARK

This section presents the model and establishes a normative benchmarkdevelopment strategy for subsequent comparisons. Our benchmark is thedevelopment strategy that would be undertaken by the social plannermaximizing the present value of net land rents without concern for thepattern of private ownership. This normative benchmark is analogous tothe neoclassical notion of economic efficiency in which resource ownershipis not a consideration.

We consider a unit of undeveloped land in an urban area land market.Ž .Once undertaken, development is irreversible. R k, t is the rent at time t

for the land developed with capital k, and is assumed to be differentiableto the second degree. Using subscripts to denote derivative, the rent

Ž . Ž .function is assumed to be increasing in t R ) 0 , with R 4 0, R 0, t )t k kŽ .0, and strictly concave in capital density R - 0 .k k

We let R 4 0, which allows for the economic factors that drive ak tvariety of development patterns observed in urban land markets, althoughwe assume that R does not change sign over time for a given plot ofk t


w xland. As in Turnbull 13 , the sign of R can vary for plots of land acrossk tdifferent locations even within the same urban land market. This formula-

Ž .tion nonetheless includes as a special case the popular variant R k, t sŽ . Ž . Ž .p t Q k , where building service per unit of land, Q k , is an increasing

function of capital density, and the rent per unit of building services at t isŽ . 5p t , with p ) 0. This is easily recognized as a special case of the R ) 0˙ k t

case in our model. On the other hand, the static model used in Miceliw xet al. 11 can be interpreted as a version of the special case R s 0 in thisk t

model.Ž .To complete the model, the agricultural rent at t is w t G 0, where w

w .exists ; t g 0, ` . The price of each unit of capital is normalized to unity.The rent trajectories are known with certainty. The only uncertainty in themodel is that which is introduced by the title system used to resolvepotential competing claims of ownership.

The relevant discount rate is r so that the present value of net returnsfrom the plot of land developed with capital k at time t is

t `yr t yr t yrtF k , t s w t e dt q R k , t e dt y ke . 1Ž . Ž . Ž . Ž .H H

0 t

˜� 4The social planner’s unique optimal development strategy k, t for this˜Ž .plot of land maximizes F k, t without addressing land ownership issues.

The efficient strategy satisfies the conditions6

`yr tF s R k , t y r e dt s 0 2Ž . Ž .Hk k

t

yrtF s w t y R k , t q rk e s 0, 3Ž . Ž . Ž .t

Ž .2where F - 0, F - 0, and J s F F y F ) 0 holds under ourtt k k tt k k kt

concavity and growth assumptions. These conditions establish our bench-Ž .mark for comparing the different title systems. Condition 2 requires that

the land be developed with the capital density maximizing the expectedpresent value of rents in the developed state net of the user cost of capital.

Ž .Condition 3 reduces to the efficient development timing condition, thatthe development be undertaken when the benefit of further postponementŽ .saving the user cost of resources to be used in developing the land, rk

Žequals the cost of postponement foregoing the incremental rent that canŽ . Ž ..be obtained by developing the land, R k, t y w t .

5 Ž . g tFor example, p t s p e is the certainty analog of the rent trajectory typically assumed0w xin land value models based on option pricing 6, 7 .

6 We restrict our attention to land parcels with interior solutions, t ) 0.


ŽWhile the issue of who owns the land and therefore is entitled to the.returns to the land is irrelevant when deriving our normative benchmark,

the issue of ownership affects the market determined development pat-tern. The title assurance system can and generally does affect the marketoutcomes. We examine the development patterns under the recording andregistration systems, respectively, in the next two sections.

3. LAND DEVELOPMENT UNDER THE RECORDING SYSTEM

The recording system of title assurance is essentially a library system.The deed recorder’s office keeps the written records of title, relevanttransfers, and exceptions. By referring to the written documentation,interested parties can reconstruct the chain of title over time. It isimportant to note, however, that the claim only establishes e¨idence oftitle; it does not assure that the possessor holds title to the land. If at sometime in the past, errors, omissions, or fraud occurred that escaped noticeuntil later in the chain, once verified, the legitimate prior claimant holdstitle to the property rather than the possessor.

The general setting is a dynamic version of that envisioned by Miceliw xet al. 11 . In this model the developer is the land possessor, the presump-

tive owner unless a legitimate prior ownership claim is forthcoming. Theexistence of such a claim and the point in time at which it might be

Ž .forthcoming if such a claim exists are not known with certainty. DenoteŽ .the probability that a claim has been made by t as u g t where u ) 0 is a

nonstochastic shift parameter introduced to capture changes in the proba-bility structure. The probability of no claim having been made by t is

Ž . Ž .1 y u g t . The probability of a claim being made at t is u g t G 0.˙Ž . Ž .Further, g 0 s 0 and lim u g t s ul, where 0 - l - 1. Increases in ut ª`

increase the probability of a claim being made at any t, decrease theprobability of a claim not having been made by t, and increase theprobability of a claim forthcoming through the indefinite future.7

If a legitimate claim is forthcoming at t in the recording system of titleassurance, then the claimant is awarded the title and is entitled to anyearnings from the land thereafter. If the possessor had invested in capital

Ž .improvements to the land, k prior to t, then the claimant and now ownerreimburses the possessor for the improvements that were made. Thus, inthe event that a claim is made after the land has been developed, the

7 Ž .The focus of our analysis is on developer response to given uncertain claimant actions.We do not present an explicit model of claimant behavior. The probability structure ofpotential claims can differ across the recording and registration title systems. In order toestablish a basis for comparing the two title systems, though, we assume identical probabilitydistributions for both. The effects of nonidentical probability distributions are easily seenfrom the comparative static results derived later in the paper.


possessor ends up paying only the user cost of capital over the interval thathe is in possession of the developed land.

The developer’s expected net return to the plot of land must take intoaccount the possibility of a claim arising in the future. It must also takeinto account that once one claim arises, he receives the appropriatecompensation for any capital improvements but loses the earnings fromthe land thereafter. The probability that the developer will garner the netrents during any t is simply the probability that no claim has been made by

w Ž .xthat time, or 1 y u g t . Thus, the expected return for each t before thew Ž .x Ž .intended development time t is 1 y u g t w t . The net rent at the

development time t is the rent less development cost so that the expectedw Ž . xw Ž .xreturn to the developer for this period is R k, t y k 1 y u g t . Simi-Ž .w Ž .xlarly, the expected net rent for t ) t is R k, t 1 y u g t . In the event

Ž .that a claim is made after development, with probability u g t for t, the˙developer no longer owns the land, but is reimbursed by the claimant forthe irreversible improvements made to the land, k. The expected reim-

Ž .bursement for t ) t is therefore u g t k.˙Discounting each term by eyr t and integrating over t yields the present

value of the expected return to the land from the possessor’s perspective:

t `yr t yr tF k , t s 1 y u g t w t e dt q 1 y u g t R k , t e dtŽ . Ž . Ž . Ž . Ž .H H

0 t

`yrt yr ty k 1 y u g t e q u g t ke dt.Ž . Ž .˙H

t

In order to simplify this expression, apply integration-by-parts to the lastterm,

` `yr t yr t yrtu g t ke dt s k u g t re dt y u g t e .Ž . Ž . Ž .˙H H

t t

Ž .Substituting this into F k, t and rearranging yields the developer’s objec-tive function as

tyr tF k , t s 1 y u g t w t e dtŽ . Ž . Ž .H

0

`yr tq 1 y u g t R k , t y rk e dt. 4Ž . Ž . Ž .H

t


� U U4The developer follows the unique development strategy k , t maxi-Ž .mizing 4 , which satisfies

`yr tF s 1 y u g t R k , t y r e dt s 0 5Ž . Ž . Ž .Hk k

t

yr tF s 1 y u g t w t y R k , t q rk e s 0, 6Ž . Ž . Ž . Ž .t

Ž .2 Ž .where F - 0, F - 0, and D s F F y F ) 0. Condition 5 re-tt k k tt k k kt

quires that when the land is developed, it is developed at the density kU

maximizing the expected present value of the rent net of the user cost ofŽ .capital. This condition is recognizable as the social planner’s condition 2

Ž .modified by the duration probability 1 y u g t at each future t, whichtakes into account the likelihood that the developer still has possession of

Ž .the property to enjoy the net returns at t. Condition 6 reduces to theŽ . Ž .social planner’s development timing condition, R k, t y w t s rk.

Because the sign of F turns out to be important in later analysis, it iskt

worthwhile to take a closer look at this term before proceeding further.Ž .From 4 ,

yrtF s y 1 y u g t R k , t y r e . 7Ž . Ž . Ž .kt k

Ž . Ž .To evaluate 7 , integrate 4 by parts, setting F s 0 to obtaink

yrt1 y u g t R k , t y r eŽ . Ž .k

`yr ts y 1 y u g t R k , t y u g t R k , t y r e dt 8� 4Ž . Ž . Ž . Ž . Ž .˙H k t k

t

Ž .so that substituting 7 for the left hand side yields

`yr tF s 1 y u g t R k , t y u g t R k , t y r e dt. 9� 4Ž . Ž . Ž . Ž . Ž .˙Hkt k t k

t

Notice that in the absence of any risk of a claim, u s 0 and F is entirelykt

determined by the sign of R , that is, whether the marginal rental returnk tto capital density per unit of land is rising, stable, or falling over time.When the demanded capital density is rising over time, R ) 0 so thatk tF ) 0 and capital density k and waiting time t are complementary inputskt

in the land development process. When the demanded density is fallingover time, R - 0 so that F - 0 and capital density k and waiting time tk t kt

are substitute inputs in the land development process. Finally, R s 0k timplies F s 0, in which case the waiting time and capital are unrelatedkt

Ž .inputs in the development process. The sign of R hence F generallyk t kt

w xvaries across locations within a single urban area 13 .


In the presence of a risk of a claim, u ) 0 so that the probability of aw xclaim being made during t, t q dt , u g G 0, modifies to some extent the˙

relationship between the sign of R and F via the second term withink t kt

the integral expression above. Nonetheless, as long as the sign of R doesk tw . Ž .not change over t , ` , it can be shown that the sign of the first term in 8

dominates:8

w x w xsgn F s sgn R . 10Ž .kt k t

Using these relationships, we have the following result.

PROPOSITION 1. Under the recording system of title assurance, an increaseŽ .in the probability of a legitimate claim du ) 0 speeds the pace of deëlop-

ment at all sites where the demanded density is increasing or decreasing oërtime. An increase in the probability of a claim increases the capital density perunit of land at locations where the demanded density is declining oër time,has no effect on the capital density at locations where the demanded density isconstant oër time, and decreases the capital density at locations where thedemanded density is rising oër time.

Proof. The general effect of the probability of a claim on the devel-Ž . Ž .oper’s optimal strategy can be found by differentiating 5 and 6 with

respect to u :

t Uru s F F rD 11Ž .ku kt

kUru s yF F rD. 12Ž .ku tt

The comparative static predictions hinge upon the sign of F . To evaluateku

Ž .this term, differentiate 5 :

`yr tF s y g t R k , t y r e dt.Ž . Ž .Hku k

t

Ž . Ž .Using this and 2 and 5 , we have F q u F s F . But F s 0 atk ku k k� U U4k , t so that

u F kU , t U s yF kU , t U , 13Ž . Ž . Ž .ku k

Ž U U . ` w Ž U . x yr tUwhere F k , t s H R k , t y r e dt.k t k

8 Ž . Ž . w Ž .xNotice from 3 and 7 that F s 1 y u g t F . It can be shown that F iskt kt kt

completely determined by the time path of R . Because F takes the same sign as F , thek t kt kt

result follows.


Ž .There are two cases. If R ) 0 then 5 implies that there exists an «k tŽ U .such that R k , t y r 4 0 for t 4 « , satisfyingk

«U yr t1 y u g t R k , t y r e dtŽ . Ž .H k

Ut

Ù yr tq 1 y u g t R k , t y r e dt s 0.Ž . Ž .H k

«

Apply the generalized mean value theorem to each integral: there existŽ U . Ž .a g t , « and b g « , ` such that

«U yr t1 y u g a R k , t y r e dtŽ . Ž .H k

Ut

Ù yr tq 1 y u g b R k , t y r e dt s 0.Ž . Ž .H k

«

Ž . w Ž .x wThe conditions 0 F u g t - 1 and g G 0 ensure 1 y u g a ) 1 y˙Ž .xu g b , so that R ) 0 and the previous equation together implyk t

« Ù Uyr t yr ty R k , t y r e dt - R k , t y r e dt ;Ž . Ž .H Hk k

Ut «

that is,

Ù U U yr tF k , t s R k , t y r e dt ) 0.Ž . Ž .Hk k

Ut

Ž U U .If R - 0 similar manipulations reveal F k , t - 0. Thusk t kw Ž U U .x w Ž U U .x Ž .sgn F k , t s sgn R k , t in general. Recalling 10 , this impliesk k tw Ž U U .x w Ž U U .x Ž .sgn F k , t s sgn F k , t , so that 13 revealsk kt

U U U Usgn F k , t s ysgn F k , t . 14Ž . Ž . Ž .ku kt

Ž . Ž . Ž .Evaluating the signs of 11 and 12 using F - 0, D ) 0, and 14 ,ttU Ut ru - 0 and k ru 4 0 as F 3 0 and the proposition follows.kt

Intuitively, the probability of a claim shortens the investor’s expectedtime horizon for garnering any gains from developing the property, whichgives the investor an incentive to develop the land earlier. The capitaldensity results follow the relationship between waiting time and density inthe profit function. When substitutes, the earlier development time iscoupled with a decrease in capital density; when complements, the earlierdevelopment time is coupled with an increase in capital density.


Ž . Ž .The comparative statics 11 and 12 lead to the principal normativeresult for recording systems.

PROPOSITION 2. The recording system of title assurance replicates thesocial planner benchmark if and only if the demanded density of capitalimpro¨ements per unit of land is constant o¨er time.

Proof. Sufficiency is easily verified by observing that the social planner’sŽ . Ž . Ž .optimal conditions 2 and 3 and the private developer’s conditions 5

Ž . Ž . Ž . Ž .and 6 simplify to R k s r and R k y w t s rk for R s 0: Thek k tdeveloper’s optimal strategy satisfies the conditions for the unique socialplanner solution. Necessity is established in the proof of Proposition 1

Ž .where it was shown that R / 0 and condition 5 together implyk tŽ U U .F k , t / 0: the developer’s optimal strategy does not replicate thek

social planner benchmark when R / 0.k t

How relevant is the case in which the developer’s strategy does replicatethe normative benchmark? The existing literature suggests that the neces-sary and sufficient condition in Proposition 2, R s 0, is not likely to hold.k t

w xFor example, Turnbull 13 shows that, in the context of a growingmonocentric urban residential land market, R s 0 can hold for landk t

Ž .situated at at most one distance from the city center in the urban area.Thus, the practical import of Proposition 2 is that the recording systemdoes not meet our normative standard in general.

4. LAND DEVELOPMENT UNDER THEREGISTRATION SYSTEM

In the registration system, individuals register their property with theregistrar or designated government office, at which time the owner isissued a certificate establishing the title to the land and extinguishing priorclaims. Thus, the salient feature of the registration system is that thedeveloper retains ownership of the land and its improvements regardless oflegitimate prior claims. The claimant, however, is compensated for his lossof the land ownership. We consider several compensation methods inorder to separate the development incentive effects of land registrationfrom the incentive effects of the method used to compensate claimants. Inall cases considered in this section, though, the developer is responsible forcompensating the claimant.

There are any number of feasible schemes for compensating legitimateclaimants. We formally consider two methods that represent polar cases,then offer a general result pertaining to any compensation method thatgeneralizes either or both methods considered here. The first methodcompensates the claimant with the expected present value of residualincome, both in the pre-development agricultural state and in the devel-


oped state, under the developer’s chosen strategy. The second methodcompensates the claimant with the expected present value of agriculturalreturns to the plot of land without taking into account the anticipatedreturns to the land in the developed state.

A. Compensation Based on Returns in Both Pre- andPost-De elopment States

Consider the first case, where the developer is responsible for theclaimant’s damages based on the anticipated residual income to the land

Ž .developed according to the developer’s strategy. Denote H k, t ; t as theexpected present value of returns to land following the development

� 4strategy k, t , evaluated at time t. Thus, given that the probability of aŽ .claim forthcoming at time t is u g t , the expected damages to be paid at t˙

Ž . Ž .equal u g t H k, t ; t . Prior to the development time, the expected return˙to the developer is the present value of net returns from the pre-develop-ment state plus net returns from the post-development state, less theexpected present value of damages paid to potential claimant, or

t `r Ž tys. r Ž tys.H k , t ; t s w s e ds q R k , s y rk e dsŽ . Ž . Ž .H H

t t

`r Ž tys.y u g s H k , t ; s e ds ; t F t . 15Ž . Ž . Ž .˙H

t

After development has taken place, the developer’s expected return isequal to the net value of expected returns in the developed state less theexpected present value of damages paid to claimant,

`r Ž tys.H k , t ; t s R k , s y rk e dsŽ . Ž .H

t

`r Ž tys.y u g s H k , t ; s e ds ; t G t . 16Ž . Ž . Ž .˙H

t

Ž . Ž .The Appendix shows that 15 and 16 yield the developer’s objectiveŽ .function H k, t ; 0 as

t `yr tyu g Ž t . yr tyu g Ž t .H k , t s w t e dt q R k , t y rk e dt . 17Ž . Ž . Ž . Ž .H H

0 t

� UU UU4 Ž .The developer’s choice k , t maximizing 17 satisfies the conditions

`yr tyu g Ž t .H s R k , t y r e dt s 0 18Ž . Ž .Hk k

t

yrtyu g Žt .H s w t y R k , t q rk e s 0, 19Ž . Ž . Ž .t


Ž .2where H - 0, H - 0, and D s H H y H ) 0 under our as-k k tt k k tt t ksumptions.

The timing condition H s 0 implies the same condition seen earlier int

Ž . Ž .both the benchmark outcome and the recording system: R k, t y w t srk. On the other hand, the condition H s 0 requires that the capitalkdensity be set to maximize the present value of per unit rents over the usercost of capital, but further discounted by the probability of a claim beingmade against the land. The latter effect takes into account that higher netincome from greater capital density also increases the present value ofdevelopment, hence the potential penalty in the event of a claim.

The relationship between timing and density in the objective functionŽ .again plays an important role in what follows. Differentiating either 18 or

Ž .19 ,

yrtyg Žt .H s y R k , t y r e . 20Ž . Ž .t k k

Ž .Integrate 18 by parts to obtain

yrtyg Žt .H s R k , t y r e r r q u g tŽ . Ž .˙k

`yr tyg Ž t .q R k , t r r q u g t e dt s 0.Ž . Ž .Ž .˙H k t

t

Ž .Substituting 20 into the first term leaves

`yr tyg Ž t .H s r q u g t R k , t r r q u g t e dt. 21Ž . Ž . Ž . Ž .Ž .˙ ˙Hkt k t

t

Ž .g t G 0 implies that the sign of H follows the sign of R . The market˙ kt k tconditions, in terms of increasing or decreasing demanded density overtime, determine the effects of a potential claim on the developmentpattern. Interestingly, the probability of a claim qualitatively alters thedevelopment pattern as it does in the recording system.

PROPOSITION 3. Under the registration system of title assurance in whichthe possessor is responsible for compensating the claimant for expected landincome in both the pre- and post-de elopment states, an increase in the

Ž .probability of a legitimate claim du ) 0 speeds the pace of deëlopment atall sites where the demanded density is increasing or decreasing oër time. Anincrease in the probability of a claim increases the capital density per unit ofland at locations where the demanded density is declining oër time, has noeffect on the capital density at locations where the demanded density isconstant oër time, and decreases the capital density at locations where thedemanded density is rising oër time.


Ž . Ž .Proof. Differentiate 18 and 19 with respect to u to find the compar-ative statics,

t UUru s H H rD 22Ž .ku kt

kUUru s yH H rD , 23Ž .ku tt

which hinge upon the sign of H :ku

`yr tyu g Ž t .H s y g t R k , t y r e dt. 24Ž . Ž . Ž .Hku k

t

Ž .There are two cases. If R ) 0 then by 18 there exists an « such thatk tŽ UU .R k , t y r 4 0 for t 4 « , satisfyingk

« ÙU UUyr tyu g Ž t . yr tyu g Ž t .y R k , t y r e dt s R k , t y r e dt .Ž . Ž .H Hk k

UUt «

25Ž .

Ž .Further, by the generalized mean value theorem, there exist a g t , «Ž .and b g « , ` , satisfying

«UU yr tyu g Ž t .g a R k , t y r e dtŽ . Ž .H k

UUt

«UU yr tyu g Ž t .s g t R k , t y r e dt 26Ž . Ž . Ž .H k

UUt

ÙU yr tyu g Ž t .g b R k , t y r e dtŽ . Ž .H k

«

ÙU yr tyu g Ž t .s g t R k , t y r e dt. 27Ž . Ž . Ž .H k

«

Ž . Ž . Ž .Recall that a - b means that g a - g b , so 25 implies

«UU yr tyu g Ž t .yg a R k , t y r e dtŽ . Ž .H k

UUt

ÙU yr tyu g Ž t .- g b R k , t y r e dt.Ž . Ž .H k

«

Ž . Ž . ŽSubstituting 26 and 27 in the above and simplifying, we get recall thatŽ . Ž . .26 is negative and 27 positive for R ) 0k t

ÙU yr tyu g Ž t .g t R k , t y r e dt ) 0. 28Ž . Ž . Ž .H k

UUt

Ž .Therefore, by 24 , R ) 0 implies H - 0.k t ku


If R - 0 then repeating the derivations leaves H ) 0. Thus, ink t ku

w x w x Ž .general, sgn H s ysgn R and 21 therefore impliesku k t

UU UU UU UUsgn H k , t s ysgn H k , t . 29Ž . Ž . Ž .ku kt

Ž . Ž . Ž . UUThe signs of 22 and 23 follow from H - 0, D ) 0, and 29 : t ruttUU- 0 and k ru 4 0 as H 3 0, which is the proposition.kt

The efficiency result for this registration system resembles that for therecording system considered in the previous section. The proof of thefollowing parallels that of Proposition 2.

PROPOSITION 4. The registration system of title assurance in which thepossessor is responsible for compensating the claimant for land income in boththe pre- and post-de elopment states replicates the social planner benchmark ifand only if the demanded density of capital improëments per unit of land isconstant oër time.

Our earlier comments concerning the generality of the R s 0 case alsok tpertain here. Thus, in general, this registration system does not in generalmeet the normative benchmark.

B. Compensation Based on Returns in Pre-Deëlopment State

We now consider the second case, in which the claimant’s compensationŽ .is calculated as the present value of agricultural rents. Let V t s

` Ž . r Ž tys. � 4H w s e ds. The return to the developer for strategy k, t is the sumtof the pre-development and post-development residual income flows lessthe expected compensation to potential claimants,

t `yr t yr tH k , t s w t e dt q R k , t y rk e dtŽ . Ž . Ž .H H

0 t

`yr ty u g t V t e dt , 30Ž . Ž . Ž .˙H

0

Ž . Ž .where the expected compensation to potential claimants at t is u g t V t .˙� UU UU4The optimal strategy k , t satisfies H s H s 0, which are identicalk t

Ž . Ž .with the social planner’s optimal development conditions 2 and 3 . Theresults follow immediately:

PROPOSITION 5. Under the registration system of title assurance in whichthe possessor is responsible for compensating the claimant for the residualincome to land in the pre-de elopment state, the probability of a legitimateclaim has no effect on the pace or density of deëlopment. This registrationsystem replicates the social planner benchmark.


The intuition underlying this proposition is straightforward. The presentvalue of returns to land held perpetually in the pre-development state isunaffected by the developer’s timing and density decisions. When theclaimant’s compensation equals this amount, the expected compensationpayment represents a lump-sum cost facing the developer. In this case,changes in the probability of a legitimate claim can affect only thislump-sum cost and therefore do not affect investment decisions.

The compensation methods actually used in registration systems in theU.S. are essentially hybrids of the two extreme cases considered here. Inthe context of our model, any legitimate claimant can assert ownership for

Žsome period when the land was in the pre-development state i.e., at some.time prior to t s 0 . Even if the land court specifies the compensation as

Žbased strictly upon a measure of value in ‘‘current use’’ that is, the use inwhich the land was dedicated at which time the legitimate claim was

.usurped , the market value in the pre-development state nonethelessreflects the anticipated future urban use. In practice, it is difficult toascertain how much of this anticipated value in urban use will be allowedby the land court when establishing the compensation that is to be paid tothe claimant. Thus, in order to consider these intermediate cases, supposethat the compensation rule applied in the registration system is a weightedaverage of the two rules examined above. Let the compensation due the

Ž . Ž . Ž .claiming arising at t be the convex combination g V t q 1 y g H k, t ; t ,Ž .where g is the compensation parameter 0 F g F 1 reflecting the com-

pensation policy used in a particular registration title system. It followsthat Propositions 3 and 4 extend to all such compensation schemes forwhich 0 F g - 1. In general, the greater the extent to which the compen-sation rules rely on anticipated earnings as developed property, the closerthe claimant compensation method comes to case one in our analysis, andthe greater the distortionary effect of the registration system on thedevelopment pace and pattern.

5. COMPARING THE RECORDING ANDREGISTRATION SYSTEMS

The preceding section concludes that the registration system falls shortof the normative benchmark except under very restrictive conditionsŽ .Proposition 4 . The registration and recording systems both speed devel-opment relative to the social planner’s efficient pace, and both alter thecapital density. But the question remains: which of these two systemscomes closer to replicating our normative benchmark?

To answer this question, consider Figs. 1 and 2, pertaining to theincreasing and decreasing demanded density cases, respectively. The locusof points in k y t space satisfying the timing condition F s 0 is identicalt

with the H s 0 locus, as depicted in each figure. In order to compare thet


FIG. 1. Comparing the recording and registration title systems when demanded density isincreasing over time.

relative locations of the F s 0 and H s 0 loci in the diagrams, note thatk kŽ . yu g Ž t .1 y u g t - e for all t. Further, the difference between these two

`w Ž .xw Ž . x yr tterms is increasing in t. This means that H 1 y u g t R k, t y r e dtt` yu g Ž t .w Ž . x yr tc H e R k, t y r e dt as R b 0; that is, F c H as R b 0.t k t k k k t

Ž .Thus, the F s 0 locus must lie to the left right of the H s 0 locus fork klocations in the land market where the demanded density is increasingŽ .decreasing over time.

U UU U UU Ž U UU .It is clear that t - t in both diagrams and k - k k ) kŽ .when the demanded density is increasing decreasing over time. Put

simply, developers are more sensitive to the possibility of an adverse claimin the recording system than in the registration system.

Pulling together the various possibilities, we summarize the comparisonof the registration and recording title systems in the next result.


FIG. 2. Comparing the recording and registration title systems when demanded density isdecreasing over time.

PROPOSITION 6. The recording system speeds deëlopment more than theregistration system does when the demanded density is increasing or decreasing

Ž .oër time. The recording system results in less greater capital density than theregistration system at locations where the demanded density is increasingŽ .decreasing oër time.

In their case study of the American experiences with registration landw xtitle systems, Shick and Plotkin 12 hypothesize that one benefit of

registration is that it speeds development relative to the recording system.In terms of the effect on development speed, Proposition 6 demonstratesjust the opposite; there is an incentive to develop land sooner under therecording system than under a registration system. Further, the supposi-tion that faster development is necessarily better is questionable, too.Nonetheless, one implication of Proposition 6 is that, regardless of therelative effects on timing or density, the registration system of titleassurance is generally closer than the recording system to the normativebenchmark.


6. CONCLUSION

The system or set of rules used to settle questions of land title affectsthe pace, pattern, and efficiency of the land development process. Wefound that the potential for legitimate adverse claims tends to hastendevelopment in the recording system. The effect on development densityŽ .that is, the use to which land is ultimately put varies systematically acrosslocations in an urban land market. In contrast, the effects of claim risk ondevelopment timing and density in the registration system are in the samedirection as, but are weaker than, the effects in the recording system.

The normative conclusions presented in this paper are stronger thanw xfound thus far in the literature. The static analysis in Miceli et al. 11

requires that the individual possessing the land have greater valuation ofthe land in order for the registration system to clearly dominate therecording system. In contrast, here we find that even without the idiosyn-cratic valuation the registration system is generally closer to the socialplanner benchmark than the recording system when both timing andcapital density are endogenous. The difference between the two titleassurance systems arises in the dynamic setting because of the interplaybetween the time spent waiting to develop and capital improvements in theland profit function. The fact that each title system assigns the landownership to different parties leads to different time paths of penalties inthe event of adverse claims. In the recording system, the risk of losing theearnings from developed property functions like a uncertain cutoff date onthe returns to investment; it prods the land possessor to develop the landsooner than he would in the absence of such risk. In the registrationsystem, the risk of compensating a claim functions like an uncertain tax onthe investment returns, reducing but not eliminating post-claim returns tothe developer. As a consequence, the possibility of an adverse claim has astronger effect on the developer’s timing decision in the recording systemthan in the registration system. Because it is the developer’s response toownership risk that drives a wedge between the market outcome and thenormative benchmark, the registration system of title assurance dominatesthe recording system.

These conclusions do not necessarily imply that the U.S. should uni-formly convert to a registration system, given the high transaction costs ofdoing so. They do, however, suggest that registration may be the preferredchoice for developing countries that are in transition to market economiesand private property systems.

APPENDIXŽ .To derive the objective function 17 for the registration title system

case, we begin with the expected present values over the pre- and post-de-


velopment intervals:

t `r Ž tys. r Ž tys.H k , t ; t s w s e ds q R k , s y rk e dsŽ . Ž . Ž .H H

t t

`r Ž tys. w xy u g s H k , t ; s e ds ; t g 0, t A1Ž . Ž . Ž .˙H

t

`r Ž tys.H k , t ; t s R k , s y rk e dsŽ . Ž .H

t

`r Ž tys. w xy u g s H k , t ; s e ds ; t g t , ` . A2Ž . Ž . Ž .˙H

t

Ž .Differentiate A2 with respect to t to obtain the equation describing theevolution of the present value of expected returns to the land afterdevelopment,

H k , t ; t s y R k , t y rk y u g t H k , t ; tŽ . Ž . Ž . Ž .˙t

`r Ž tys.y r R k , s y rk y u g s H k , t ; s e ds.Ž . Ž . Ž .˙H

t

Ž .Substitute A2 for the integral term and simplify,

H k , t ; t y r q u g t H k , t ; t s y R k , t y rk .Ž . Ž . Ž . Ž .˙t

Change the time index to s, multiply both sides of the above equation byeyr syu g Ž s., and integrate from t forward to get

`yr syu g Ž s.H k , t ; s y r q u g s H k , t ; s e ds� 4Ž . Ž . Ž .˙H t

t

`yr syu g Ž s.s y R k , s y rk e ds,Ž .H

t

which yields

`yr tyu g Ž t . yr syu g Ž s.H k , t ; t e s R k , s y rk e ds.Ž . Ž .H

t

Evaluate at t :

`r Žtyt .qu g Žt .yu g Ž t .H k , t ; t s R k , t y rk e dt. A3Ž . Ž . Ž .H

t

Ž . w xDifferentiate A1 to get the asset valuation equation for t g 0, t ,

H k , t ; t y r q u g t H k , t ; t s yw t .Ž . Ž . Ž . Ž .˙t


Ž .Solving this differential equation in t and using A3 to definitize theconstant at t yields

tyr Žtyt .yu g Žt .qu g Ž t . r Ž tys.qu g Ž t .yu g Ž s.H k , t ; t s H k , t ; t e q w s e dsŽ . Ž . Ž .H

t

so that, using t for the time index,

tyrtyu g Žt . yr tyu g Ž t .H k , t ; 0 s H k , t ; t e q w t e dt. A4Ž . Ž . Ž . Ž .H

0

Ž . Ž .Substituting A3 into the first right hand side term in A4 leaves theŽ .objective function 17 in the paper:

t `yr tyu g Ž t . yr tyu g Ž t .H k , t ; 0 s w t e dt q R k , t y rk e dt.Ž . Ž . Ž .H H

0 t

A5Ž .

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the dynamic effects of land title systems

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