spatial lock-in: do falling house prices constrain residential mobility?

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Ž . Journal of Urban Economics 49, 567586 2001 doi:10.1006juec.2000.2205, available online at http:www.idealibrary.com on Spatial Lock-in: Do Falling House Prices Constrain Residential Mobility? 1 Sewin Chan Rutgers University, Department of Economics, 75 Hamilton Street, New Brunswick, New Jersey 08901-1248 E-mail: sewin@rci.rutgers.edu Received August 6, 1999; revised October 16, 2000; published online March 21, 2001 Falling house prices have caused numerous homeowners to suffer capital losses. Those with little home equity may be prevented from moving because of imperfections in housing finance markets: the proceeds from the sale of their home may be insufficient to repay their mortgage and provide a down payment on a new home. A data set of mortgages is used to examine the magnitude of these constraints. Estimates show that average mobility would have been 24% higher after 3 years had house prices not declined, and after 4 years, it would have been 33% higher. Among those with high initial loan-to-value ratios, the differences are even greater. 2001 Academic Press Key Words: lock-in, house price decline, mobility, down payment, mortgage, liquidity constraint. I. INTRODUCTION The last recession brought with it a sharp fall in house prices in many parts of the United States, and homeowners were taken by surprise as they saw the primary component of their wealth diminish and their hopes to move thwarted. As widely reported by the media, owners who suffered severe house price declines often had mortgage balances that were higher than the value of their home. 2 Once a household has a mortgage balance greater than approximately Ž . 90% of their total assets predominantly the house value , it becomes spatially locked. The household is unable to repay the mortgage and make a down 1 I thank Andrew Caplin, Michael Cragg, Charles Freeman, and Joseph Tracy for their guidance and encouragement and Gary Engelhardt, Jan Brueckner, and two anonymous referees for helpful comments. The generosity of Chemical Bank in providing data and assistance is gratefully acknowledged. 2 For example, The New York Times writes, ‘‘For many who bought starter houses in the middle 80s, the fall in prices has forced the postponement of purchase and relocation decisions that are essential to long-term family well-being. Unable to recover all their equity if they sell, these Ž . families are unable to buy and ‘move up’ ’’ September 19, 1993 . 567 0094-119001 $35.00 Copyright 2001 by Academic Press All rights of reproduction in any form reserved.

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Page 1: Spatial Lock-in: Do Falling House Prices Constrain Residential Mobility?

Ž .Journal of Urban Economics 49, 567�586 2001

doi:10.1006�juec.2000.2205, available online at http:��www.idealibrary.com on

Spatial Lock-in: Do Falling House Prices ConstrainResidential Mobility?1

Sewin Chan

Rutgers University, Department of Economics, 75 Hamilton Street, New Brunswick,New Jersey 08901-1248

E-mail: [email protected]

Received August 6, 1999; revised October 16, 2000; published online March 21, 2001

Falling house prices have caused numerous homeowners to suffer capital losses.Those with little home equity may be prevented from moving because of imperfectionsin housing finance markets: the proceeds from the sale of their home may be insufficientto repay their mortgage and provide a down payment on a new home. A data set ofmortgages is used to examine the magnitude of these constraints. Estimates show thataverage mobility would have been 24% higher after 3 years had house prices notdeclined, and after 4 years, it would have been 33% higher. Among those with highinitial loan-to-value ratios, the differences are even greater. � 2001 Academic Press

Key Words: lock-in, house price decline, mobility, down payment, mortgage, liquidityconstraint.

I. INTRODUCTION

The last recession brought with it a sharp fall in house prices in many partsof the United States, and homeowners were taken by surprise as they saw theprimary component of their wealth diminish and their hopes to move thwarted.As widely reported by the media, owners who suffered severe house pricedeclines often had mortgage balances that were higher than the value of theirhome.2 Once a household has a mortgage balance greater than approximately

Ž .90% of their total assets predominantly the house value , it becomes spatiallylocked. The household is unable to repay the mortgage and make a down

1I thank Andrew Caplin, Michael Cragg, Charles Freeman, and Joseph Tracy for their guidanceand encouragement and Gary Engelhardt, Jan Brueckner, and two anonymous referees for helpfulcomments. The generosity of Chemical Bank in providing data and assistance is gratefullyacknowledged.

2 For example, The New York Times writes, ‘‘For many who bought starter houses in the middle80s, the fall in prices has forced the postponement of purchase and relocation decisions that areessential to long-term family well-being. Unable to recover all their equity if they sell, these

Ž .families are unable to buy and ‘move up’ ’’ September 19, 1993 .

567

0094-1190�01 $35.00Copyright � 2001 by Academic Press

All rights of reproduction in any form reserved.

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SEWIN CHAN568

payment on a new home since banks generally do not issue mortgages withloan-to-value ratios greater than 95%, and the transactions costs associated withselling and buying a new home typically exceed 5% of the house value.3

This paper uses a set of mortgages to examine the degree to which thesecapital losses constrain homeowners from moving. The data are of remarkablyhigh quality since they are based on mortgage application information verifiedby underwriters and on institutional mortgage servicing records. Thus, there isarguably little measurement error in spell length or explanatory variables.

The extent of spatial lock-in is measured by first estimating a hazard modelof housing spell durations in which the key explanatory variable is thehousehold’s contemporaneous loan-to-value ratio. The estimates present strongevidence that lock-in exists. The estimated model is then used to conduct asimulation in which households with cumulative house price declines over thesample period are instead given a zero house price change. Simulated hazardrates are calculated based on this new set of house price movements using theestimated model and contrasted with those based on actual house pricemovements. According to the simulation results, the number of households thatmoved would have been 5 percentage points or 24% higher after 3 years hadhouse prices not declined. After 4 years, the average mobility rate would havebeen 9 percentage points or 33% higher. Among homeowners with high initial

Ž .loan-to-value ratios LTVs , the increases are even larger.Since over two-thirds of households are homeowners, the majority financing

with a mortgage, the resulting decline in mobility can have significantlydamaging economic effects.4 Studies have shown that mobility plays a predom-

� �inant role in macroeconomic adjustment; for example, Blanchard and Katz 3demonstrate that the principal regional adjustment mechanism in the UnitedStates is labor mobility rather than job creation or job migration. When regionalimbalance exists, workers move to jobs rather than vice versa.5 Therefore, thehousing market and the nature of housing finance could be hindering the spatial

3 � �According to DiPasquale and Wheaton 14 , realtor fees for selling a home range from 3 to 6%of the sale price and closing costs on a new home range from 1 to 3% of the purchase price. Inaddition, bridge financing, which allows the buyer to purchase a new home while the old one isbeing sold, costs almost 1% of the house value for every month of dual ownership.

4According to the 1990 U.S. Census, 69% of households are homeowners and 67% ofhomeowners have an outstanding mortgage. Among homeowners who moved into their homeswithin the previous 5 years, 84% have a mortgage.

5 � � � � � � � �See similar findings by Da Vanzo 12 , Topel 27 , Barro and Sala-i-Martin 1 , Bartik 2 , and� �Borjas et al. 4 .

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allocation of labor as households are locked out of alternative markets withbetter income prospects.6

The situation is exacerbated by the fact that negative labor market shocks arecorrelated with nominal house price depreciation.7 In a local market, thedemand for housing depends on the level of amenities and the income of theresidents, while the supply of housing is inelastic in the short run. A decline inlocal wages lowers the demand for housing and leads to a fall in house values.Thus, a great degree of risk is introduced into the homeowner’s portfolio asthere is a positive covariance between its two most important assets: humancapital and housing capital. Eventually, out-migration of workers should miti-gate the decline in wages, but in the short run, lock-in occurs precisely whenhouseholds would most want to move. An inefficiency arises because thehousehold would have higher earnings potential elsewhere. If they couldborrow against the value of this human capital, they could use the proceeds tofinance the shortfall in home equity and would thus be able to move. However,there are well-known problems with borrowing against human capital.

In terms of the mortgage contract, the lender is no worse off than holding theexisting high LTV mortgage if it allowed the borrower to take out a newmortgage on a new home at a similar or slightly lower LTV. Given a desire tomove, the spatially locked borrower would clearly benefit from such an option.However, this mechanism for mitigating lock-in is not available in the currentmarket.8

Looking from a slightly different perspective, one of the primary reasons forthese lock-in constraints is the dominance of housing in the household’s assetportfolio: the median household has the vast majority of nonpension assets inresidential housing.9 If households did not have such a huge proportion of theirportfolio tied to their homes, then a real estate downturn would be less likely tolead to spatial lock-in because the household would have other assets to coverthe losses. However, housing is as much an item in the consumption bundle asit is an investment vehicle, and allocating fewer assets to housing would imply

6 The constraints to mobility discussed here are somewhat different in nature from those ofŽ � �.job-lock due to employer provided health care benefits see Madrian 21 or defined benefit

pension plans. Spatial lock-in refers only to residential mobility; the worker is constrained in choiceof dwelling but may be free to switch jobs without penalty. However, as far as spatial adjustment ofthe labor market is concerned, the two mechanisms have essentially the same effects: workers arediscouraged from looking for jobs in other regions because moving away from their presentresidence would involve significant losses.

7 � � � � � �See Bartik 2 , Blanchard and Katz 3 , and Caplin et al. 8 for empirical estimates.8A mechanism that would allow spatially locked borrowers to move within the institutional

limitations set by their current mortgage would be difficult to implement. A major problem is thatwith widespread securitization of mortgages, there are usually more concerned parties than just amortgagor and a mortgagee. Coordination between all the various players would be needed to makeany changes to the original contract.

9 Ž .According to the 1995 Survey of Consumer Finances average includes nonhomeowners .

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reduced housing consumption, which households are evidently unwilling to� �accept given their revealed preference. Brueckner 7 demonstrates how housing

consumption motives can lead to tremendous distortions in the chosen assetportfolio.

This paper clearly illustrates the severity of spatial lock-in constraints. Theremainder of this paper is organized as follows. Section II reviews relatedliterature and describes the various options available to spatially locked house-holds who want to move. The data used in the analysis are presented in SectionIII, the econometric strategy in Section IV, and the results of the empiricalanalysis in Section V. Conclusions are given in Section VI.

II. SPATIALLY LOCKED HOUSEHOLDS

Once prices begin to fall, some households will become spatially locked,whether they had anticipated the decline or not.10 Not only are they unable tofinance a down payment on a new home from the sale proceeds of their currenthome, they will also need additional funds to repay the existing mortgage.11

In order to qualify for a mortgage on another home, a borrower will typicallyhave to make a down payment of at least 5�10%, and any borrower with lessthan 20% down payment has to pay for additional private mortgage insurancewhich essentially raises the interest rate for as long as the loan is above 80%LTV. In addition to this pure down payment constraint, borrowers also face anincome constraint in loan qualification. As a rule of thumb, mortgage bankswill not lend more than three times a borrower’s income, so if the householdhas also suffered an income shock, an even higher down payment would beneeded to bring the loan-to-income ratio down to the lender’s maximum. Sincehouseholds who do not move are not subject to the same requirements and areallowed to remain in a home with low or negative equity, mobility can beseverely hindered by a fall in house prices.

� �Stein 26 constructed a theoretical model that illustrates how the effects ofdown payment constraints on repeat buyers can reduce mobility. When pricesfall, households who must rely on the sale of their current home for the downpayment on a new home may be prevented from moving. Constrained house-holds may ‘‘fish’’ for a buyer: list the house for sale at a price above market inthe hope that a buyer will be found. The substantial impact of liquidityconstraints in housing markets is also highlighted by Ortalo-Magne and Rady´

10 � �The survey by Case and Shiller 10 provides some evidence that the fall in house prices mayhave been largely unanticipated. They find that households appear to be backward looking in theirhouse price forecasts and that homeowners in areas that had experienced price gains in the late1980s thought that prices would continue to rise even though the trend had already flattened oreven declined.

11 It is nominal house value declines that give rise to spatial lock-in since the mortgage isdenominated in nominal dollars. If house values fell in real but not nominal terms, lock-in wouldnot occur as the house would still be worth more than the balance on the mortgage.

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� �22 . Their dynamic model shows how fluctuations in housing prices can beexplained by down payment requirements and the need for households to makeseveral adjustments to their housing consumption over the life-cycle.

There has been little direct empirical evidence on the extent of lock-in effects� �at the household level. Genesove and Mayer 17 use a sample of condomini-

ums listed for sale in Boston to show that high LTV properties take muchlonger to sell and that if a sale occurs, the transaction price is significantly

� �higher than for properties with low LTVs. Engelhardt 16 uses the NationalŽ .Longitudinal Survey of Youth NLSY and finds that intrametropolitan mobility

is strongly affected by collateral constraints while the results for intermetropoli-tan mobility is mixed. In addition, several empirical studies suggest thatmortgage qualification requirements are likely to constrain household behavior.

� �Engelhardt 15 shows that households significantly increase consumption� �following the purchase of a new home, Linneman and Wachter 20 find

evidence that income and wealth constraints affect the homeownership deci-� �sion, and Zorn 28 finds that almost two-thirds of households are constrained

into purchasing less owner-occupied housing than they would like. Caplin et al.� �9 observe that many households living in areas that suffered house pricedeclines do not refinance their fixed rate mortgages even though they havelarge financial incentives to do so, suggesting that homeowners who want tomove may be similarly constrained.

Reduced mobility in areas of falling house prices may also arise from lossaversion whereby individuals tend to be reluctant to sell at a loss because of aperceived entitlement to a former price, leading to seemingly irrational behav-

12 � �ior. Genesove and Mayer 18 find direct evidence of loss aversion using datafrom the Boston condominium market. They show that owners subject tonominal losses set higher asking prices, attain higher selling prices, and havelower hazard rates of sale than other sellers.

ŽThere are very few options available for a negative equity or close to.negative equity household if they want to move. Defaulting on a mortgage

would adversely affect the household’s credit history and increase the costs offuture borrowing. The constrained household could rent out the negative equityhome and either buy a new home using any remaining assets or move intorental property, but this decision is fraught with complications. First, the costsof renting out the existing property as an absentee landlord are substantial.13

Second, if the household does decide to rent out the existing property and buy a

12 � �Kahneman et al. 19 , among others, provide experimental evidence on the loss aversionphenomenon.

13 Finding a suitable tenant involves search costs, and rental income after taxes may not besufficient to cover mortgage payments. A management agent may be needed and maintenance costswill be higher than under owner occupation as the tenant does not have an incentive to keep theproperty in good condition. It can also be extremely difficult to evict a tenant in some areas, even ifrent payments are delinquent.

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new home, it would have to find sufficient additional assets to cover a newdown payment and it would have to take on yet more real estate debt. Third, ifthe household decides to rent a new home, they may not be able to find adesirable rental unit in a desirable location: rental properties are often differentin both physical and neighborhood attributes from owner-occupied ones andthere are many types of owner-occupied homes that have no rental substitute.

Thus, a spatially locked household is not left with many options except toremain in the negative equity home, with the hope that prices eventuallyappreciate. We now turn to the data used to examine empirically the extent ofthis spatial lock-in.

III. THE DATA

The Chemical Bank Mortgage Sample

The data are a sample of residential single-family 30-year mortgages origi-nated in New York, New Jersey, and Connecticut between November 1989 andJanuary 1994 by Chemical Bank, one of the largest commercial banks in theregion during this time period. The sample is representative of borrowers that

Žmeet the underwriting standards of Fannie Mae the Federal National Mortgage.Association : they have no bankruptcies, no serious delinquencies in the past 2

years, and few new credit inquiries in the past year and are current on allaccounts. These types of borrowers account for 90% of the total market.14 Theyare less likely to be constrained than those with poor credit, and so there will bea bias against finding evidence of spatial lock-in.

The data contain all the information found on a mortgage application formafter verification by underwriters. Both refinances and purchases of new homesare represented. Loan performance is tracked by recording all payments,prepayments, defaults, and delinquencies. Prepayments can arise due to refi-nancing of the mortgage or sale of the property; the data do not allowdifferentiation between the two. This poses a problem for using mortgageduration as a proxy for housing duration, especially when interest rates arefalling, as they do toward the end of the sample period. There are likely to bean unacceptable number of type II errors: households that are classed as movingbut have merely refinanced their mortgage. For this reason, fixed rate mort-

Ž .gages FRMs are removed from the sample. This sample restriction means thatthe lock-in results that follow are conditional on the choice of an adjustable rate

Ž .mortgage ARM and may not generalize to FRM borrowers who tend to beŽless mobile, as shown in ARM�FRM choice models see Brueckner and Follain

� �.5 .

14 Ž .That is, 90% of the total securitized conventional i.e., nongovernment mortgage market bydollar value, according to Moody’s Investor Service.

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Among the remaining ARMs there is very little refinancing since themortgage contract includes an option to convert to a fixed rate loan at the

Žmarket rate a relatively small conversion fee is charged compared with the.substantial cost of refinancing the mortgage . From a subsample of 140

terminated ARMs from New York City that were matched with records ofŽ .deeds and uniform commercial codes title to cooperative apartments filed at

the New York City Department of Finance, there were only 3 in whichownership of the property did not change.15 Thus, we can conclude that forARMs, mortgage duration is a good proxy for housing duration with respect tothese type II errors.

Unfortunately, there is no easy way of checking the extent of type I errors inthe sample: households who move without terminating the mortgage. Insofar asthese households are likely to be renting out their house to others while livingelsewhere, an extremely small 3% of households in the 1990 ConsumerExpenditure Survey report any sort of rental income, and these will includeowners of vacation homes, multifamily residences, and others who boughtproperties purely for investment purposes.

The resulting sample consists of 5,778 observations, with 5,094 nonmoversand 684 movers as of January 1994, the last date that behavior is observed.Approximately 2% of the loans defaulted and these are treated as censoredobservations; excluding them from the sample or including them as moversgives similar results. Table 1 shows summary statistics measured at the time ofmortgage origination based on move status at the end of the sample period. Onaverage, movers have higher original loan amounts, higher initial propertyvalues, and higher assets.16 Their demographic composition is also different:they are more likely to be married and less likely to be a female-headedhousehold or prior owners.17 Movers are less likely to have paid mortgagepoints, consistent with there being little incentive to pay points up front inexchange for a lower interest rate if the mortgage is not going to be held verylong.18

Figure 1 shows the distribution of loans by initial LTV. The large number ofŽ .loans at 80% is explained by the fact that private mortgage insurance PMI has

to be paid at initial LTVs of greater than 80%. The PMI is charged as apercentage of the entire loan balance, not just the marginal amount above 80%LTV, and so those who would have otherwise chosen an LTV slightly above80% have a strong financial incentive to accumulate a larger down payment in

15 This search was conducted using a database of public records owned by Public DataCorporation.

16 The differences discussed here are all statistically significant at 5%.17 ŽA female-headed household in this sample is one in which the sole borrower is female whether

.she is single or not , or both the primary and secondary borrowers are female.18 Mortgage points are simply a percentage of the loan amount that can be paid up front to the

lender in exchange for a reduction in the interest rate.

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TABLE 1aSummary Statistics by Mover Status

Wholesample Nonmovers Movers

% moved 14.1Variables measured at the time of mortgage origination

Ž .Median loan amount $ * 140,000 136,000 170,000Ž .Median property value $ * 203,007 197,012 250,000

Ž .Mean LTV % 68.8 68.9 68.3% with LTV � 80% 13.3 13.4 12.9% paid mortgage points* 22.0 22.4 19.5

Ž .Median liquid assets $ * 11,200 10,600 13,700Ž .Median monthly income $ 7,670 7,532 8,466

Ž .Mean age years 39.2 39.3 39.0Mean years of schooling 16.7 16.7 16.8% married* 56.2 55.4 60.5% with children 29.4 29.0 32.2% female head of household* 22.9 24.3 14.0% prior owner 53.5 54.1 49.7

b,Cumulative change in house prices *Ž .Median % 0.13 0.10 0.15

Ž .Standard deviation % 4.30 4.15 5.13

Number of observations 5,778 4,965 813

aDemographic variables refer to the borrower. Income and assets are for the borrower andŽ .coborrower if any combined.

bCumulative change from the beginning to the end of the sample period or until the householdmoved.

*Movers and nonmovers are statistically different at the 5% level of significance based ondifferences in the means.

FIG. 1. Distribution of loan-to-value ratio in the sample.

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TABLE 2aSummary Statistics by Initial Loan-to-Value Ratio

Wholesample LTV�80% LTV�80%

% moved 14.1 14.2 13.5Variables measured at the time of mortgage origination

Ž .Median loan amount $ 140,000 144,000 139,825Ž .Median property value $ * 203,007 210,002 165,000

Ž .Mean LTV % * 68.8 65.9 88.1% with LTV � 80% 13.3% paid mortgage points* 22.0 21.7 23.9

Ž .Median liquid assets $ * 11,200 11,300 10,900Ž .Median monthly income $ * 7,670 7,895 6,667

Ž .Mean age years * 39.2 39.8 35.4Mean years of schooling 16.7 16.8 16.6% married 56.2 56.4 54.3% with children 29.4 29.7 27.3% female head of household 22.9 23.2 20.6% prior owner* 53.5 55.7 38.5

b,Cumulative change in house prices *Ž .Median % 0.13 0.14 0.10

Ž .Standard deviation % 4.30 4.12 5.33

Number of observations 5,778 5,012 766

aDemographic variables refer to the borrower. Income and assets are for the borrower andŽ .coborrower if any combined.

bCumulative change from the beginning to the end of the sample period or until the householdmoved.

*Households with LTV � 80% and those with LTV � 80% are statistically different at the 5%level of significance based on differences in the means.

order to reduce the ratio to 80%. Only those without the necessary up-frontcash will pay the PMI. Thus, there is a priori a reason to believe that thosewho have initial LTVs above 80% are more likely to be constrained than thoseat or below 80%. Table 2 gives summary statistics by initial LTV status.Differences between high and low LTV households are evident: higher initialLTV households have lower initial property values, less income, and fewerother assets and are generally younger with less prior ownership experience.

House Price Performance and Contemporaneous LTV

To assess with absolute precision the effects of property market declines onmobility, the market value of every home would have to be known in everyperiod. Unfortunately and not unsurprisingly, such data are unavailable. Instead,county level weighted repeat sales house price indices constructed using the

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� � 19methodology of Shiller 24 are used as a proxy. As always, measurementerror plagues the linkage of macro data to a micro sample: the house priceseries will not be representative of all houses within a county partly because ofintracounty variation and idiosyncrasies that may be based on the size, quality,or exact location of a particular dwelling.

The last rows of Tables 1 and 2 provide some summary statistics on thecumulative change in house prices experienced by sample households duringthe sample period. The median change in the sample was 0.13%, although thismasks a good deal of variation. Almost one-quarter of the sample householdsexperienced a cumulative house price decline.

Table 3 shows a comparison of counties in the sample that were above andbelow the median in cumulative house price changes over the sample period,using information from the 1990 U.S. Census.20 The self-reported house values,household income, and demographic characteristics of homeowners with mort-gages are not significantly different between the two groups. Thus, there doesnot appear to be an obvious pattern of sorting by households into counties thatexperience major house price declines and those that do not.

IV. ECONOMETRIC STRATEGY

The goal is to derive unbiased estimates of spatial lock-in by examining thebehavior of households living in areas with different house price dynamics. Amodel of housing spell duration is estimated using the standard proportionalhazard framework. In this parameterization, the estimated hazard is proportionalto a baseline hazard function that is solely a function of time,

� �h � g t exp � LTV � � HP � � LTV � � �X � u , 1Ž . Ž .i t 1 i t�1 2 i t�1 3 i0 i t i t

where i refers to each household and the hazard rate h is the probability ofi t

moving after t periods conditional on not having moved before t periods. TheŽ .� ’s and � are the parameters to be estimated, g t is the baseline hazard, and

u is the error term.21i t

19County level indices for New York, New Jersey, and Connecticut were obtained from CaseShiller Weiss, Inc. These included most counties represented in the Chemical Bank sample. Theexceptions were Manhattan and Queens, for which a similarly constructed index for the New YorkCity primary metropolitan statistical area compiled by Freddie Mac was used.

20 By using each of the sample counties as the unit of observation, the median cumulative changeŽ .in house prices was a decline of 6% over the sample period November 1989�January 1994 . This

differs from the cumulative change in the sample of households because not all the householdswere observed for the whole period and also because the households were not evenly distributedamong the counties.

21 The methodology used here is in the spirit of mortgage prepayment models. For example, see� �Deng et al. 13 .

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TABLE 3

Summary Statistics for the Sample Counties by Cumulative House Price Change Over theaŽ .Sample Period November 1989�January 1994

Counties above the median Counties below the medianb bchange in house price change in house price

Cumulative change in house prices*Ž .Median % �1.9 �11.8

Ž .Standard deviation % 2.1 3.8

Among homeowners with mortgages% moved in last 5 years 42 39

Ž .Median property value $ 150,000�175,000 150,000�175,000Ž .Median annual household income $ 58,200 55,300

Ž .Mean age years 40.5 42.2% married 39 37% with children 14 14Average education level Some college Some college

aData source: U.S. Bureau of the Census 1990 and Case Shiller Weiss, Inc.b The median cumulative house price change for the sample counties over the sample period was

�6%.*The two groups are statistically different at the 5% level of significance based on differences in

the means.

The explanatory variables include the lagged contemporaneous LTVŽ .LTV , which is constructed using the outstanding loan balance in eachi t�1

month and the appropriate county level house price index. A household with acontemporaneous LTV of over approximately 95% will be unable to repay their

Žmortgage from the sale proceeds of the house since transactions costs are at.least 5% , and a household with an LTV of over 90% will be unable toi t�1

repay their mortgage and make a minimal down payment on a new home. Thecoefficient � can be used to test if there is a lock-in effect due to down1

Ž .payment constraints: � is negative if lock-in exists. A 1-month lag t � 1 is1

used for all time-varying contemporaneous variables since it would take at leastthis long for homeowners to implement a decision to move; a two-period lag isalso tested.

HP is the cumulative growth in the county’s house prices from the timei t�1

the mortgage is originated to the previous period. This variable serves twopurposes. First, local house price changes are to some extent capturing localeconomic conditions, in particular good labor market opportunities which mayinduce those living in these areas to stay rather than move and vice versa.Second, even in the presence of the contemporaneous LTV, the cumulativeeffect of house prices HP may still affect unconstrained households whoi t�1

exhibit loss aversion and are unwilling to realize a capital loss. Consideringthese together, we would expect a negative coefficient on positive house price

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changes, while the coefficient on negative house price changes is ambiguousdepending on the extent of loss aversion versus the incentive to move awayfrom depressed local areas.

ŽLTV is a high initial LTV indicator equal to one if initial LTV is strictlyi0.greater than 80% that captures any unobservable characteristics that may

determine mobility behavior and are correlated with initial LTV. As discussedin the previous section, there is reason to believe that those who have initialLTVs above 80% are more likely to be constrained than those at or below80%.

X is a vector of covariates that may explain other systematic differences ini t

mobility behavior, such as age, children, and prior homeownership. Mortgagepoints are included as they have been shown to be an indicator of ex antemobility expectations in nonfalling interest rate environments.22 Banks typi-cally allow borrowers to reduce the interest rate on a mortgage by paying apercentage of the loan amount up front. The value of the rate discount clearlydepends on how long the mortgage is held and therefore the points decision canbe used as a revealed preference sorting device to determine whether house-holds have a high ex ante probability of moving soon. Ex post, any points paidare a sunk cost, so the mortgage points indicator of expected mobility can beinterpreted as another household characteristic included in the X vector thati t

denotes an otherwise unobservable propensity to move.Also included are variables that relate to the propensity of moving even if

negative equity is encountered, such as income and the presence of other assets.Ideally, we would like a measure of contemporaneous ‘‘extended LTV’’ where

loan balance � other assetsextended LTV � .

house value

Thus, the variable of interest is other assets as a proportion of the house valueand we would expect a negative coefficient in our estimations. Unfortunately, acontemporaneous measure of other assets is not at hand; we can only proxywith the level of assets reported to and verified by underwriters at the time themortgage was booked. While these asset levels can be adjusted for subsequentasset returns, errors will still arise since households have little incentive toreport more assets than is sufficient to comfortably qualify them for themortgage, and in any case, their asset positions can change over time. Similarly,errors arise from using initial reported income adjusted for wage inflation as aproxy for contemporaneous income.

22 � � � �See Chan 11 and Brueckner 6 for detailed explanations. This interest rate�mortgage pointtrade-off and its relation to expected holding length is documented in both trade and consumerpublications.

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Mortgage interest rates were historically low and falling during some of thesample period and may have given an added incentive for households to movesince they could take out a new mortgage at a low rate. Thus, we include thedifference between the household’s actual interest rate and the contemporane-ous market interest rate for conventional fixed rate mortgages to capture thisincentive, again, with a 1-month lag.

V EMPIRICAL RESULTS

Figure 2 presents the monthly housing duration data as an empirical hazard:the probability of moving in each month conditional on not having movedbefore that month. Graphed along with the empirical hazard is the estimatedbaseline hazard, which is fitted using a series of smoothed splines that are onlydependent on time. Following the proportional hazard framework, other subse-quent explanatory variables can be interpreted as deviations from this baseline.The baseline is of the form

t � � t � �g t � exp � � � t 1 � � � � � � t � , 2Ž . Ž . Ž . Ž .1 1 2 2ž / ž /ž /

Ž . Ž .where � � � t and � � � t are the two splines. The smoothing factors1 1 2 2

between the splines are based on the cumulative standard normal distributionfunction � and were best fitted with � � 28 and � 3 in all the specifica-

FIG. 2. The empirical and estimated baseline hazards.

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SEWIN CHAN580

tions discussed below.23 Column 1 of Table 4 presents the estimates of thisbaseline without other covariates.

Column 2 of Table 4 presents the baseline hazard together with a series ofindicator variables representing the contemporaneous LTV. A negative coeffi-cient implies that the hazard of moving is lower as the covariate goes from zeroto one. The estimates show that having a contemporaneous LTV higher than50% has a significantly negative impact on mobility, and the effect becomesmore severe as LTV rises. This finding clearly supports the lock-in hypothesis.The coefficients imply that an increase in contemporaneous LTV from 85�90%to over 95% would result in a hazard rate that is just 30% of the original, while

23 Parameterizing the baseline hazard using standard distributions such as the exponential orWeibull yielded a poorer fit but gave similar qualitative results for the subsequent explanatoryvariables.

TABLE 4aHazard Model of Housing Spell Duration

1 2 3 4 5 6

Log likelihood �4137 �4085 �4030 �4028 �4028 �3979Ž .Baseline hazard g t

� �7.218 �6.633 �6.792 �6.771 �6.777 �6.9601Ž . Ž . Ž . Ž . Ž . Ž .0.163 0.193 0.216 0.216 0.216 0.548

� 0.155 0.160 0.169 0.169 0.169 0.1751Ž . Ž . Ž . Ž . Ž . Ž .0.012 0.012 0.012 0.012 0.012 0.013

� �1.431 �1.301 �0.584 �0.588 �0.586 �0.4782Ž . Ž . Ž . Ž . Ž . Ž .0.703 0.707 0.737 0.737 0.737 0.748

� 0.071 0.075 0.078 0.078 0.078 0.0822Ž . Ž . Ž . Ž . Ž . Ž .0.019 0.020 0.020 0.020 0.020 0.021

Ž .Contemporaneous LTV LTVt�1

40�50% �0.272 �0.272 �0.270 �0.272 �0.194Ž . Ž . Ž . Ž . Ž .0.177 0.178 0.177 0.177 0.179

50�60% �0.373* �0.319* �0.325* �0.326* �0.294Ž . Ž . Ž . Ž . Ž .0.158 0.157 0.157 0.157 0.161

60�70% �0.641* �0.626* �0.632* �0.632* �0.599*Ž . Ž . Ž . Ž . Ž .0.154 0.154 0.154 0.154 0.158

70�80% �0.681* �0.659* �0.671* �0.670* �0.618*Ž . Ž . Ž . Ž . Ž .0.133 0.134 0.134 0.134 0.140

80�85% �1.327* �1.107* �1.291* �1.297* �1.283*Ž . Ž . Ž . Ž . Ž .0.198 0.205 0.227 0.227 0.235

85�90% �1.112* �0.917* �1.317* �1.323* �1.317*Ž . Ž . Ž . Ž . Ž .0.186 0.189 0.279 0.279 0.285

90�95% �1.252* �0.941* �1.406* �1.417* �1.379*Ž . Ž . Ž . Ž . Ž .0.260 0.275 0.354 0.354 0.367

� 95% �2.336* �1.566* �2.189* �2.193* �2.308*Ž . Ž . Ž . Ž . Ž .0.467 0.484 0.570 0.570 0.580

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TABLE 4Continued

1 2 3 4 5 6

Ž .Cumulative house price growth HPt�1

� �12% �1.446* �1.218* �1.219* �0.903*Ž . Ž . Ž . Ž .0.370 0.382 0.382 0.395

�12 to �6% �1.018* �0.864* �0.865* �0.571*Ž . Ž . Ž . Ž .0.218 0.230 0.230 0.244

�6 to �4% �0.622* �0.568* �0.583* �0.380Ž . Ž . Ž . Ž .0.230 0.231 0.231 0.252

�2 to �4% �0.295 �0.266 �0.272 �0.146Ž . Ž . Ž . Ž .0.213 0.213 0.213 0.221

0�2% 0.117 0.098 0.095 0.130Ž . Ž . Ž . Ž .0.124 0.124 0.124 0.128

2�4% �0.145 �0.174 �0.182 �0.009Ž . Ž . Ž . Ž .0.203 0.204 0.204 0.210

4�6% �0.867* �0.907* �0.906* �0.651*Ž . Ž . Ž . Ž .0.278 0.281 0.281 0.291

� 6% �1.160* �1.215* �1.235* �1.021*Ž . Ž . Ž . Ž .0.203 0.203 0.205 0.219

Ž .Original LTV � 80% LTV 0.467 0.470 0.5820Ž . Ž . Ž .0.434 0.434 0.435

Assets�house value 0.011 �0.001Ž . Ž .0.027 0.028

Ž .Monthly income $000 0.004*Ž .0.002

Paid mortgage points �0.524*Ž .0.097

Actual mortgage interest rate � market rate 0.104Ž .0.086

bTime dummies and demographic variables No No No No Yes

Note. Sample contains 5,778 households and 134,745 household-months. Standard errors are inparentheses.

a Ž . � �Estimated equation is h � g t exp � LTV � � HP � � LTV � � �X � u ,i t 1 i t�1 2 i t�1 1 i0 i t i tŽ . �Ž .� ŽŽ . .� Ž .� ŽŽwhere the baseline g t � exp � � � 1 � � 1 � � � � � � � 1 � � 1 �1 1 2 2

. ..��� � .b Demographic variables are dummies for marital status, having children, female head of

household, younger than age 35, older than age 55, high school graduate, some college, collegegraduate, and prior homeownership.

*Statistically significant at 5%.

an increase from 70 to 80% to over 95% would result in a hazard rate that is20% of the original.

Column 3 of Table 4 adds another series of indicators representing thecumulative growth in house prices lagged one period. The estimates show thatthere is a negative effect of positive house price changes: cumulative house

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SEWIN CHAN582

price increases of 4% or more are associated with reduced mobility. Thepositive house price changes are likely to be capturing good local economicconditions which induce less movement out of the area.24 However, if localeconomic conditions were the whole story, we should also see increasedmobility during periods of falling house prices. In fact, the estimated effect ofnegative cumulative house price changes of greater than 4% are significantlyassociated with less mobility, and the effect rises with the magnitude of thehouse price decline. This lends support to the possibility of loss aversiondiscussed in the previous section. In any case, support for the lock-in hypothe-sis remains as the addition of these house price change variables does notsignificantly alter the estimates on contemporaneous LTV.

Column 4 of Table 4 adds a dummy variable for a high initial loan-to-valueratio, intended to capture any systematic differences between households who

Ž .were and were not able to obtain the more favorable 80% or less LTVmortgage. The coefficient is insignificant and has the wrong sign. Usingdifferent initial LTV thresholds or the addition of a series of indicator variablesrepresenting initial LTVs between 80 and 85% and 85 and 90% and greaterthan 90% does not change this result.

In column 5, we try to take into account the fact that a household withsufficient other assets will be able to overcome any negative equity effects andbe able to move. The coefficient on assets�house value is intended to capturethe ‘‘extended LTV’’ idea presented in the previous section: extended LTV �LTV � assets�house value.

If it is extended LTV that matters for spatial lock-in, we would expect apositive coefficient on assets�house value; however, we find a small and

Žinsignificant result that actually reverses sign in the next specification column.6 . This is possibly due to mismeasurement since the asset variable is based on

reports at the time of mortgage origination. Alternative adjustments for assetreturns do not change this result.25 The result is also possibly attributable to the

� �rigidity of mental accounts, of the sort described by Shefrin and Thaler 23 .Under this premise, funds are not fungible between different mental accountsand individuals will not use other assets to cover their housing market losses.

In column 6, other explanatory variables are added including a set of timedummies and demographic variables. The time dummies are insignificant andtheir inclusion or exclusion does not affect the results. Being married signifi-cantly increases the likelihood of moving, and the effect of having children isalso positive, though insignificant. Female heads of household have signifi-cantly reduced mobility. The age and education level of the household head do

24 The addition of calendar time indicators did not change the result in column 3, and the timeindicators themselves were not significant.

25 This included extrapolating initial wealth by using inflation, stock market returns, and a varietyof interest rates.

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SPATIAL LOCK-IN 583

FIG. 3. Mobility rates based on actual and simulated nonnegative house prices.

not significantly affect mobility.26 Prior home ownership also has no effect.Higher-income households are significantly more mobile, perhaps reflecting thefact that they are more able to overcome any negative equity constraints.

As expected, the coefficient on mortgage points is negative and significant: ifa household paid points to reduce the interest rate, they are less likely to move.The actual interest rate on the mortgage minus the contemporaneous mortgage

Ž .rate the Freddie Mac rate for fixed rate mortgages lagged one period ispositive but insignificant.

Our variable of interest, the contemporaneous LTV, remains negative andsignificant for LTVs above 60%. Moreover, the coefficients are very stable tothe inclusion of other explanatory variables. The coefficients in column 6 implythat an increase of contemporaneous LTV from 85 to 90% to over 95% wouldresult in a hazard rate that is just 37% of the original, while an increase from70 to 80% to over 95% would result in a hazard rate that is 19% of theoriginal. A lag of 2 months on the contemporaneous variables or no lag at alldid not yield noticeably different results.

Figures 3 and 4 show the results of a simulation that isolates the effect oflock-in that arises from house price declines. Households in the sample thatexperienced a cumulative decline over the sample period have their cumulativehouse price growth set to zero, with the corresponding change in their contem-poraneous LTVs. A new set of hazard rates are calculated using the estimates incolumn 6 of Table 4 and these simulated hazards are contrasted with those

26 The education categories included here are indicators for high school graduate, some college,and college graduate, while the age categories are indicators for younger than age 35 and older thanage 55. A richer set of education and age specifications did not yield significant results.

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SEWIN CHAN584

FIG. 4. Mobility rates based on actual and simulated nonnegative house prices for householdswith initial LTVs greater than 80%.

calculated from the actual house price movements. Figures 3 and 4 show thecumulative unconditional moving probabilities generated by the hypotheticalhazards and those based on actual house price movements. After 3 years, theaverage mobility rate among the entire sample would have been 5 percentagepoints or 24% higher had house prices not declined. After 4 years, the averagemobility rate would have been 9 percentage points or 33% higher. Among thesubset of households with initial LTVs greater than 80%, the increase is evenlarger, at 6 percentage points or 39% after 3 years and 10 percentage points or50% after 4 years, as shown in Fig. 4.

VI. CONCLUSIONS

The empirical findings provide clear evidence that there are severe con-straints to mobility as a result of negative housing market shocks. The averagemobility rate among the sample would have been one-third higher after 4 yearsif house values had not declined. The constraints arise from households notbeing able to repay their existing mortgage and maintain sufficient funds for anew down payment when the value of their home substantially falls. House-holds with high initial loan-to-value ratios are particularly affected. There isalso evidence of loss aversion among households that experience falling houseprices. Although this is not an economic constraint strictly speaking, it doescontribute to the lower mobility rates.

An explicit welfare loss calculation is beyond the scope of this paper, butpossible consequences can be noted. The loss of labor mobility will havedamaging impacts for the smooth function of the economy as people move in

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SPATIAL LOCK-IN 585

response to labor market incentives and mobility arbitrages wage and unem-ployment differentials across regions. There will also be a welfare loss frommisallocating housing and local public goods.

The constraints stem from both the nature of housing finance and the massiveconcentration of housing in the household’s asset portfolio that is a conse-quence of housing being both a consumption good and an investment vehicle.For those who are already spatially locked, the options are few except to waitfor future appreciation. However, in the longer run, there are possibilities forthe design of new contracts that mitigate these mobility constraints by introduc-

� �ing some form of risk sharing. Caplin et al. 8 propose a system of housingpartnerships whereby a household and financial institution take joint ownershipof the property; upon sale, both partners receive pro rata shares of the proceeds.The major benefit of such a proposal is that it reduces the amount of debt thathouseholds require to enjoy the benefits of homeownership and thus lowers theconcentration of real estate in their portfolios. Another approach that allowsindividuals to diversify their portfolios is the price index futures of Shiller and

� �Weiss 25 in which the homeowner takes out a futures contract on a houseprice index and would be compensated if the index fell below a predeterminedminimum. Given the importance of mobility to the macroeconomy and thewelfare of consumers, there is a need for more research in this area to writemore efficient contracts, prevent spatial lock-in constraints, and facilitate theoperation of mobility.

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