speculating on home improvements

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Journal of Financial Economics

Journal of Financial Economics 111 (2014) 609–624

0304-40http://d

☆ HarNationaHannoMonetaFinance

n CorrE-m

journal homepage: www.elsevier.com/locate/jfec

Speculating on home improvements$

Hyun-Soo Choi a,n, Harrison Hong b,d,e, Jose Scheinkman b,d,c

a Lee Kong Chian School of Business, Singapore Management University, 178899, Singaporeb Department of Economics, Princeton University, NJ 08540, USAc Department of Economics, Columbia University, NY 10027, USAd The National Bureau of Economic Research, MA 02138, USAe China Academy of Financial Research, Shanghai, China

a r t i c l e i n f o

Article history:Received 9 August 2011Received in revised form4 June 2013Accepted 3 July 2013Available online 4 December 2013

JEL classification:G11R21

Keywords:SpeculationHome improvementsReal estateRemodeling

5X/$ - see front matter & 2013 Elsevier B.V.x.doi.org/10.1016/j.jfineco.2013.11.011

rison Hong and Jose Scheinkman acknowl Science Foundation Grants. We also thanLustig, Brian Melzer, and students at the Gry and Financial Studies (CEMFI), Shanghai Asummer schools and anonymous referee foesponding author.ail address: hschoi@smu.edu.sg (H.S. Choi).

a b s t r a c t

We develop a speculation-based theory of home improvements. Housing services areproduced from a mix of land and structures. Homeowners optimistic about future pricesfor these services speculate by making improvements, which we model as themincreasing their structures holding fixed their land. The recoup value (the differencebetween the resale value of improvements and construction costs) is simultaneouslyincreasing in home price appreciation and falls with construction cost growth. Thisprediction stands in contrast to a consumption-cum-financial constraints motive in whichrising home prices loosen financial constraints and lead to lower recoup values. Weprovide evidence consistent with a speculative motive using data on the costs and recoupvalues of remodeling projects across US cities.

1. Introduction

We seek to develop a theory of home improvements—alittle-studied but important economic activity. While thesignificance of new home constructions for economicgrowth during the housing bubble years of 2003–2007 iswell documented, the contributions of home remodelingexpenditures, though less heralded, are no less impressive.The Joint Center for Housing Studies (2009) of HarvardUniversity reports that home improvement expenditureson, for instance, a new bathroom or a new deck jumpedfrom around 1% of gross domestic product (GDP) ($229

ledge support fromk Antonio Bernardo,erzensee, Center fordvanced Institute ofr helpful comments.

billion) in 2003 to 2% of GDP ($326 billion) in 2007.1

Spending on remodeling projects then dropped precipi-tously after 2007 with falling home prices, thereby exacer-bating the Great Recession of 2008. These figures suggestthat home remodeling is an important industry for the USeconomy and that the pro-cyclicality of these expenditurescontributes to business cycle fluctuations.

A consumption-cum-financial constraints motive is anatural way to rationalize remodeling activity. Risinghome values loosen financial constraints as banks aremore apt to lend to homeowners who might want toindulge in home improvements as a form of pleasure.Remodeling as consumption is consistent with the pre-vailing professional view that such activities are typicallynot profitable as the value-added of the improvements is

1 These figures include professional remodeling projects and do-it-yourself (DIY) jobs. The purchase of raw materials from companies suchas Home Depot for DIY jobs are accounted for in these GDP figures butnot the opportunity costs of DIY labor.

H.S. Choi et al. / Journal of Financial Economics 111 (2014) 609–624610

often less than the construction cost. For instance, home-owners who install pink tile in their bathrooms to satisfytheir idiosyncratic tastes decrease the recoup value oftheir improvements. An eminently reasonable additionalassumption of moving costs would reinforce the consump-tion motive as remodeling becomes a substitute for mov-ing to a newer or nicer place.

However, a number of other stylized patterns regardingremodeling suggests that speculation in addition to con-sumption could be an important economic force behindhome improvements. First, significant anecdotal evidenceexists that homeowners think of improvements as aninvestment in the same way they think about the purchaseof a home. For instance, “fix it and flip it” is a phrase oftenassociated with real estate investing in which it is thoughtthat the completion of a few choice remodeling projectsadds significant value to the price of a home.2 Thushomeowners undertake major renovation projects withthe mistaken belief that improving the place will result inbig profits. Instead, they often end up not realizing thesegains. Second, home improvements are more likely to beundertaken by sellers or households planning to move (seeJoint Center for Housing Studies, 2009) and remodelingactivity picks up when moving costs are low as opposed tobeing high in the time series.

And, third, rapid price appreciation during the recenthousing bubble years and the potential for quick capitalgains no doubt reinforced the “fix it and flip it” mentality.The forces driving home improvements during the pre-vious housing boom decade could not be more differentthan the ones driving home improvements after thecollapse of home prices: “Back then, people wanted torenovate their places so that they could trade up to biggerhomes, or because their home equity was soaring and theywanted to reinvest some of the spoils. Now, the opposite ishappening: Many people who bought during the boomyears are accepting the reality that they won't soon beswapping up for a sybaritic spread. Their mortgages mayremain above water, but after years of falling home prices,their equity is so low that the transaction costs of buying anew house would leave little for a down payment” (TheWall Street Journal, 2010).

As such, we pursue in this paper a speculation-basedtheory of home improvements. We develop a model with apure speculative motive for home improvements and thenexpand it to also account for a consumption-cum-financialconstraints motive to highlight a key testable predictionthat differs across these two motives. Our model has thefollowing features. A unit of housing services is given by aCobb-Douglas production function of land and structureswith constant returns to scale. We fix the supply of landbut assume that there is an upward-sloping supply curvefor structures. Homeowners have an option to buildadditional structures.

Housing unit prices are determined by the beliefs ofthe homeowners regarding the level of future prices.Homeowners have an equal chance of becoming optimistic

2 The results of a Google search for “fix it and flip it” and manyhousing sites discuss this phenomenon.

or pessimistic. In other words, homeowners are hit by asentiment shock. When homeowners receive the positiveshock, they undertake home remodeling. When theyreceive a negative shock, they do not.

We derive three key results. The first result is that alarger growth in home prices is correlated with homeimprovement activity. To the extent home prices arecorrelated with optimism among homeowners, this natu-rally increases the optimal amount of structures in a givenplot of land. This effect is partially moderated by anincrease in the cost of structures. Our model generatesthe exaggerated pro-cyclical pattern in remodeling expen-ditures with home prices. The reason is that homeimprovement is a homogeneous function of degree largerthan one in the beliefs of the optimistic homeowners. Weperform a simple calibration that shows that the kind ofmistakes we attribute to homeowners can explain in partthe high level of improvements relative to GDP duringthe main bubble years of 2003–2007 in contrast to therelatively low levels over the previous decade (1993–2003), when prices grew just as much in total but over alonger period of time.

The second result is that there is on average excessiveinvestment in improvements by optimistic homeowners,which can be measured by either the recoup value, definedas the difference between resale value of improvementsand construct costs, or the recoup ratio, which is the resalevalue over the construction costs. We show that theexpected recoup ratio is less than one on average andthe expected recoup ratio is lower the higher the level ofhome improvements. This result is consistent with theview among professionals that such activities are onaverage not profitable. The prevailing view is that this isbecause home improvements are consumption. But thissecond result suggests that it might also be driven byspeculative forces.

The third result is that the realized recoup ratio ispositively correlated with realized home price apprecia-tion, controlling for construction cost growth. Even thoughhomeowners are too optimistic about future home pricesand do too much remodeling, this speculation can beprofitable when realized home prices meet or exceedthese expectations. But their optimism leads to losseswhen construction cost growth is high, controlling forhome price appreciation. Hence, the recoup ratio increaseswith home price growth, controlling for construction costgrowth, and decreases with construction cost growth,controlling for home price appreciation.

The third result is particularly interesting because itcuts against the consumption-cum-financial-constraintsmotive. To see why, we extend our pure speculation modelto allow for a consumption-cum-financial-constraintsmotive. A bank with rational beliefs (which we assumeto be perfect foresight on the path of home prices) lends tohomeowners who are financially constrained. The keyassumption is that financial constraints are always bindingfor homeowners. As such, homeowners’ recoup values aretoo high because they would like to indulge in more pinktile but cannot. But higher home prices, which banks canrationally anticipate, loosen financial constraints and allowhomeowners to borrow and, hence, consume more pink

H.S. Choi et al. / Journal of Financial Economics 111 (2014) 609–624 611

tile, which leads to lower recoup values. Under a consu-mption-cum-financial-constraints motive, we show thatrecoup values and home price appreciation are negativelycorrelated.

We conduct a test of this prediction using data onconstruction costs and resale value of home improvementprojects across the US. The data come from RealtorMagazine, which collects surveys of construction costand resale value for a basket of home remodeling pro-jects. We use cross-sectional variation to test the thirdhypothesis by regressing recoup values in different citieson realized home price appreciation and constructioncost growth. The main idea of our exercise is that there iscross-city variation in home price growth and we use thisvariation to test our third prediction. During the housingboom years of 2003–2009, significant home improve-ments were made. We expect to find higher recoupvalues over this period in cities where home pricesperformed relatively well, controlling for constructioncost growth, than in cities where home prices performedrelatively poorly.

In the cross section, we find that cities with more homeprice appreciation did have higher recoup ratios duringthe housing boom period, 2003–2009. Moreover, we findthat those with higher construction cost growth havewitnessed a fall in recoup ratio. These relations arestatistically and economically significant. We conduct aseries of robustness checks to verify that these relationsare robust. The negative relation between the recoup ratioand cost growth is consistent with our model becauseexcessive speculation drives up the cost of constructionand lowers the recoup ratio. But this result can also beconsistent with a consumption motive because moreremodeling for pleasure delivers lower recoup values andat the same time also drives up high construction costs.The home price comparative static pins down the spec-ulation motive and rules out the consumption-cum-financial-constraints one.

Our paper is related to work on home improvements,including Montgomery (1992), Helms (2003) andGyourko and Saiz (2004). Importantly, Gyourko and Saiz(2004) find that home improvements cease when thevalue of the home is low relative to construction costs,suggesting a rational investment motive consistent withour premise. Our paper is also related to a recent interest-ing paper by Glaeser, Gyourko, and Saiz (2008), who arguethat home prices went up more in low supply elasticitystates (such as New York and California, where land islimited and zoning and development rules are stricter)because supply could not quickly adjust to the rising homeprices. We can use their work to motivate a further test ofour model, which is to see if the effect of the change inhome prices on the change in recoup value is greater inlow as opposed to high elasticity cities. After all, we knowfrom their work that much of the speculation in thepurchase of homes occurs in low elasticity areas. It standsto reason that if our regression specification is picking upspeculative remodeling effects, then the change in homeprices ought to have more of an effect on change in recoupvalues in low elasticity areas. We confirm this prediction inthe data.

Our theory and empirical analysis contributes to theburgeoning literature of household finance [see Campbell,2006; Barber and Odean, 2011 for surveys]. Much of thisliterature has focused on the financial decisions of house-holds such as stock market participation or financialproducts such as types of mortgages that are used andwhether the appropriate decisions are made. A consensusexists poor and uneducated households do not makeappropriate decisions. But this literature has entirelyignored home improvement decisions and whether theright level of remodeling is undertaken. These economicdecisions account for an enormous industry that extendsto even wealthy households, with consequences for themacroeconomy. Our paper suggests that there are exces-sive expenditures on home remodeling.

Our paper also adds to the burgeoning literature on theeffect of asset prices or bubbles on real investments. Thisliterature examines whether capital investments by firmsare influenced by stock price bubbles, with the dot-combubble being the primary object of focus (see, e.g., Polkand Sapienza, 2008; Gilchrist, Himmelberg and Huberman,2005; Farhi and Panageas, 2004).

We present our model and derive the key comparativestatics results in Section 2. We expand our model for aconsumption-cum-financial-constraints motive in Section 3.We discuss the empirical work regarding home improve-ment projects in Section 4. We conclude in Section 5.

2. Model

We begin our analysis by presenting a simple model ofhome improvements.

2.1. Set-up

Our model has three dates t ¼ 0;1;2. The interest rate isset to zero. A housing unit or service Ht is derived fromtwo inputs: land Lt and structure (i.e. construction) St. Inparticular, we assume that the units of housing Ht is givenby a Cobb-Douglas production function with constantreturns to scale:

Ht ¼ Lαt S1�αt ; ð1Þ

where α is the share of land in housing.Let

Po1 4Pp

1 40: ð2ÞAt time 1, with probability 1/2, homeowners becomeoptimistic and believe that P2, the price of a housing unitat t¼2, which includes both rents and capital gainsassociated with one unit of housing, has the distribution

P2 �Uniform½P1o�K; P1

oþK�: ð3ÞThat is,

E1½P2jOptimism� ¼ Po1 : ð4Þ

With probability 1/2, they become pessimistic and believethat P2 is distributed as

P2 �Uniform½P1p�K; P1

pþK�: ð5Þ

That is,

E1½P2jPessimism� ¼ Pp1 : ð6Þ

We assume that agents are risk-neutral so that the price P1of housing at time 1 is equal to either Po

1 or Pp1 with equal

probability. At t¼0, the price of housing units equals thesehomeowners' expectations on P1 given by

E0 P1½ � ¼ 12Po1þ

12Pp1 ¼ P0 : ð7Þ

Homeowners are endowed with H0 housing units at t¼0and so have identical wealth of P0H0.

This set-up is a simple way to capture the followingscenario. The economy is in steady-state at t¼0 and theprice of a housing unit at t¼0 is given by P0. At t¼1, thereis a shock to agents’ expectations regarding the price ofhousing unit at t¼2. At t¼1, homeowners have an optionto add structures depending on their expectations tomaximize the expected home value (i.e., choosing S on afixed land size L0). More formally, they maximize expectedprofits depending on the draw to their expectations

MaxSfPi1L

1�α�ωðS�S0Þg ð8Þsubject to the constraint that

SZS0; ð9Þand where iAfo; pg. The constraint is an irreversibilityconstraint that says that homeowners cannot decreasetheir structures. The homeowners who resell their housingunits at t¼2 then expect a payoff of Pi

1Lα0S

1�α and theircost is ωðS�S0Þ.

To close the model, we assume that there is an upward-sloping supply curve for structures given by

ω¼ SS0

� �β

: ð10Þ

β measures the elasticity of the supply curve.

2.2. Equilibrium at t¼1

The key outcome of interest is how home improve-ments depend on the shock to the expectations of thehomeowners at t¼1. Proposition 1 characterizes the equi-librium at t¼1.

Proposition 1. If P1 ¼ Pp1 , then S¼ S0. If P1 ¼ Po

1 , then home-owners' optimal choice of structures at t¼1 is simply

S¼ ½ð1�αÞPo1L

β0�1=ðαþβÞ: ð11Þ

If homeowners are pessimistic at t¼1, they stay withtheir old structure S0. If homeowners are optimistic at t¼1,they naturally add structures S�S040.

Proposition 2. When there is home price appreciation,Po1 4P0 , the equilibrium level of structure at t¼1, S is greater

than S0, the equilibrium level of structure at t¼0. And theequilibrium cost of structure at t¼1 is greater than theequilibrium cost of structure at t¼0.

It is easy to see that the higher their expectation Po1 is

relative to P0, the more structures they add.

2.3. Comparative statics

In this subsection, we use the equilibrium results fromSection 2.2 to derive some comparative statics.

2.3.1. Improvements are a homogenous function of degreebigger than one of home price appreciation

The first result concerns the relation between thegrowth of structures that result from home improvementand home price appreciation. The price in period 1, P1; iseither P

014P0 or P

p1oP0; and if P14P0; S4S0 in equili-

brium. Proposition 3 relates the growth of structures thatresult from home improvement S=S0 to home price appre-ciation P1=P0.

Proposition 3. Home improvement is a homogeneous func-tion of degree 1=ðαþβÞ in home price increase, that is

¼ Po1

!1=ðαþβÞ

: ð12Þ

The result follows from the expression for the S thatsolves the homeowners' problem. The sensitivity of homeimprovement to price appreciation depends on the shareof land in the value of houses (α) and the slope of thesupply curve in structures (β). If, for instance, α¼ 1=2 andβ¼ 1=4 (i.e., land is half of the value of homes), then thedegree of homogeneity is 4/3.

The first implication of the proposition is that anincrease in home prices leads to a higher optimal amountof structures in a given plot of land. This is consistent withthe pro-cyclical pattern in remodeling expenditures withhome prices. The second implication of the proposition isthe homogeneity of degree 1=ðαþβÞ. If α is not near oneand β is not large, then we can have the case where1=ðαþβÞ41.

Using this observation, a simple calibration then showsthat the economic forces we highlight here can explain inpart the high level of improvements relative to GDP duringthe recent housing bubble (2003–2007) in contrast tothe relatively low levels over the previous decade (1993–2003). The cumulative house price increases between theten-year period of 1993–2003 is roughly equal to that ofthe five-year period of 2003–2007 (both are around 100%).This means that the home price appreciation per yearduring the five-year period is roughly double that of theper year appreciation in the earlier decade. Remodelingalso nearly doubled during the five-year period of 2003–2007 (rising from 1% of GDP to 2% to GDP).

Our model can rationalize this fact. A large price changein a given year engenders a bigger response in remodelinginvestments than do a series of small increases across manyyears when 1=ðαþβÞ is large. For instance, say αþβ¼ 0:5,then the homogeneity is of degree 2. Then, if the annual pricechange in the 1993–2003 period is 1.1, this means remodel-ing of S=S0 of 1.21. But if the annual price change in the2003–2007 period is 1.2, this leads to a 1.4 in remodeling.Depending on the degree of homogeneity, one can getsignificant differences in remodeling with home price appre-ciation. This calibration is necessarily rough and should

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Optimism bias

Fig. 1. Optimism bias and expected recoup ratio. The figure plotsexpected recoup ratio and optimism bias. Optimism bias is defined asPo1=P0�1, where P

o1 is the expected home price by optimistic home-

owners. For the calibration, following parameters are used: α¼ 0:25 andβ¼ 0:25.

be taken with a grain of salt as many other factors alsochanged during this period.

2.3.2. Excessive remodelingMoreover, when investors are optimistic, they on aver-

age lose from these improvements. One way to measurethis is to look at the recoup ratio, defined as the ratioof resale value or value-added to construction costs ofimprovements. The recoup ratio depends on the realiza-tion of the price P2 at t¼2 and the cost of the improve-ments S�S0 that are incurred at t¼1.

Importantly, we can calculate the value-added of addi-tional structure, which is given by

P2Lα0S

1�α�P2Lα0S

1�α0 ¼ P2L

1�α0

� �1�α

" #: ð13Þ

The cost of additional structure is given by

ω S�S0ð Þ ¼ SS0

� �β

S�S0ð Þ ¼ S0SS0

� �β SS0

�1� �

: ð14Þ

Using these two quantities, we can calculate in closedform the recoup ratio, which is simply the ratio of value-added of additional structures to the cost of additionalstructures:

R¼ P2Lα0S

1�α�P2Lα0S

1�α0

ωðS�S0Þ¼

P2Lα0S

1�α0

� �1�α�1

� �

S0 SS0

� �βSS0�1

� �

¼ 11�α

� �1�α�1

� �βSS0�1

� � : ð15Þ

The expected recoup ratio is given by

11�α

� �1�α�1

� �βSS0�1

� � : ð16Þ

Proposition 4. Expected recoup ratio is less than or equal toone and the greater the structure growth, the lower therecoup ratio.

Let S=S0 be X. Then

11�α

� �1�α�1

� �βSS0�1

� � ¼ 11�α

X1�α�1XβðX�1Þ : ð17Þ

Applying L'Hopital's Rule allows us to show that theexpected recoup ratio is one when X-1, i.e., when thereis no home improvement. We also can show that

∂∂X

11�α

X1�α�1XβðX�1Þ

" #o0: ð18Þ

That is, the more home improvements there are, the lowerthe recoup ratio on average. Because investors are opti-mistic at t¼1, there is too much remodeling in equilibriumand the degree to which the expected recoup ratio isbelow one is an ex ante measure of this.

In Fig. 1, we consider a simple calibration of how theexpected recoup value varies with the optimism bias ofhomeowners. The optimism bias, defined as ðPo

1=P0Þ�1,lies in the interior of �0;2½ in the calibration. The share ofland in housing services α is set at 0.25, and the slope ofthe supply curve for construction β is set at 0.25. Thesetwo parameters are set to give a degree of homogeneity tothe growth of structures or improvements equal to two. Inthis example, an optimism bias of 50% leads to an expectedrecoup value of 0.729. In the data below, the expectedrecoup value is 0.78. So our model can easily match thelow expected recoup value and the high growth rate ofstructures during the sample period.

2.3.3. Price appreciation, construction costs and recoupvalue

The third result we derive, which is testable and that isthe focus of our empirical work below, is that the recoupratio is positively related to realized price P2 and nega-tively related with Po

1 (optimist's expectation) and S�S0(additional remodeling due to optimistic view).

As such we can formally state Proposition 5, which isthe focus of our empirical work. This discussion assumesthat, in period 1, investors are optimists and there is actualremodeling.

Proposition 5. The recoup ratio is positively correlated withhome price appreciation P2�P1 and negatively correlatedwith construction cost ω.

A related quantity to the recoup ratio is the recoupvalue

P2Lα0S

1�α�P2Lα0S

1�α0 �ωðS�S0Þ: ð19Þ

The recoup value also increases with P2�P1. In addi-tion, when recoup ratios are below one, a decrease inrecoup ratios implies a decrease in recoup values. Thus,because recoup ratios are negatively correlated with con-struction costs ω and typically below unity, recoup valuesare also negatively correlated with construction costs ω.

The speculation on home improvements can pay off forhomeowners depending on howmuch appreciation occursbetween periods 1 and 2. This depends on the draw of theuniform distribution for P2. When there are positive drawsin P2, the speculation pays off, as Proposition 5 shows. Thisis a natural outcome of speculation assuming no financingconstraints whatsoever.

2.4. Overconfidence on construction costs instead ofoptimistic beliefs about home prices

In our current set-up, we assume that home improversare optimistic enough about the path of home prices to getexcessive home remodeling. Alternatively, we can modelhomeowners as being overconfident about their ability toinstall structures.3 They think they can do the improve-ments at the time-0 cost (wS;0) when it fact the time-1 cost(wS;1) prevails. This is a way of modeling that, with highercost growth, improvers are overconfident about the cost atwhich they can install new structures. Either modelingchoice (mistaken beliefs on path of home prices or over-confidence on cost of remodeling) yields similar econom-ics, which is an excessive amount of structures that getbuilt. We provide details of this alternative model in theAppendix. We also generalize the set-up to allow forflexible land prices in addition to flexible structure pricesand show that we get similar results.

3. Adding a consumption-cum-financial-constraintsmotive

In this section, we extend our pure speculation modelto allow for a consumption-cum-financial-constraintsmotive. That is, homeowners also derive utility fromhousing units as opposed to purely benefiting from profit.They are financially constrained and have to borrow fromcompetitive banks to finance their investments. Other-wise, the model set-up is the same as before.

To model the consumption motive, we assume thathomeowner utility is quasi-linear in housing units, h and c,where c is some other consumption basket:

uðc;hÞ ¼ uðLαS1�αÞþc: ð20Þ

At t¼0, homeowners start with housing unit Lα0S1�α0 .

They have to borrow an amount λP0Lα0S

1�α0 to finance their

purchase, where λ represents their loan-to-equity value.The loan is obtained from competitive banks that we

assume have perfect foresight about P2 at t¼1: Pb1 ¼ P2.

At t¼1, homeowners maximize expected home valueby adding more structure on a fixed land size. They chooseS to maximize

U ¼ uðLα0S1�αÞþPi1L

1�α�Pi1L

1�α0 �ωðS�S0Þ; ð21Þ

3 Plentiful evidence on retail trading behavior indicates that thetypical retail investor trades on noise and loses money to trading cost as aresult of this noise trading [see, e.g., Barber and Odean, 2001; Odean,1999]. The poor performance of small business owners is shown byMoskowitz and Vissing-Jorgensen (2002), who suggest that either over-confidence or tax evasion is a plausible explanation.

subject to a irreversibility constraint SZS0 and a creditconstraint:

wðS�S0ÞrPb1L

1�α�λP0Lα0S

1�α0 ; ð22Þ

and where iAfo; pg .The objective function includes both consumption

utility and profits from these investments. The creditconstraint means that the cost of remodeling cannotexceed banks’ expected value of remodeled house sub-tracting pre-existing debt.

Suppose the credit constraint binds. Because the bankhas perfect foresight, i.e., Pb

1 ¼ P2, we can write the creditconstraint as

wðS�S0Þ ¼ P2Lα0S

1�α�λP0Lα0S

1�α0 : ð23Þ

The recoup value is given by R¼ P2Lα0S

1�α�P2L

1�α0 �ωðS�S0Þ. We can rewrite the recoup value by

substituting in the credit constraint:

R¼ λP0Lα0S

1�α0 �P2L

1�α0 : ð24Þ

The recoup value decreases in P2. Because the creditconstraint binds, this means the higher is P2, the bank'sperfect foresight expectation, the more it is willing to lendfor the homeowner to do home improvements, the morethe homeowner can scale improvements and, hence, thelower is the recoup value. This result concerns the recoupvalue as opposed to the recoup ratio. However, a decline inthe recoup value implies a decline in the recoup ratio,provided the recoup ratio is not too much below one.

The recoup value is negatively associated with con-struction cost. For each P2, S in equilibrium is determinedby Eq. (23). Let

FðP2; SÞ ¼wðS�S0Þ�P2Lα0S

1�αþλP0Lα0S

1�α0 : ð25Þ

Because ð∂F=∂P2Þo0 and ð∂F=∂SÞ40, we get

∂S∂P2

¼ � ∂F∂P2

∂F∂S

40:�

ð26Þ

The equilibrium structure increases with P2, and construc-tion cost, ω¼ ðS=S0Þβ , also increases with the P2.

4. Empirical work

Our empirical analysis centers on testing our theory'sprediction regarding the change in the recoup value ofremodeling projects being positively correlated with thepercentage change in home prices and negatively corre-lated with construction cost growth. We test this predic-tion using data across US cities and regressing thepercentage change in recoup value of projects in each cityon the percentage change in construction cost of theseprojects and the percentage change in home prices.

4.1. Data

Our data on home improvement projects come fromthe Cost vs. Value Report provided by Realtor Magazine,which is the official monthly magazine of the NationalAssociation of Realtors. It provides information regardingcosts and resale value (value added to home) for a rangeof major home improvement projects across many cities

starting in 1998 and ending in 2009. (The magazine didnot conduct a survey in 2006 and, hence, data are missingfor this year.) The projects and cities are listed in theAppendix. The projects covered are ranging from atticbedroom remodel to deck addition. For some of theprojects, starting in 2002, the magazine separated theprojects into a mid-scale and an up-scale version thatdiffer in terms of square footage and use of high-endfinishes. The core projects covered have increased slightlyfrom 12 in 1998 to 14 in 2009. So the set of projects hasremained relatively stable over time. These projects repre-sent major remodeling as opposed to small ones such asreplacing a door, which would more appropriately belabeled as maintenance. The magazine started the citiessurveyed from 60 cities in 1998 and increased the coverageto 80 cities in 2009. The list of cities includes the 35 metromarkets listed as the top remodeling markets by the JointCenter for Housing Studies.

For each remodeling project in each city, the databasereports for each year its cost, resale value, and recoupvalue, which is simply the resale value divided by the cost.The cost and resale figures in the annual reports arecompiled separately. The cost figures come from Home-Tech Information Systems, a remodeling estimating soft-ware company in Bethesda, Maryland. HomeTech collectscurrent cost information quarterly from thousands ofcontractors nationwide. The project costs are based onestimates for hypothetical projects made by the firm basedon their information of the real costs of projects under-taken. The figures include markup and are adjusted toaccount for pricing variations in different parts of thecountry. The construction cost figures include labor, mate-rial, subtrades, and contractor overhead and profit. Thecost data in the early years of the sample were split amongvarious firms but, for most of the samples since, it hasbeen completed by HomeTech Information Systems.4

HomeTech is a leading provider of construction costestimates for various projects across the country.

It is interesting to consider what is driving differencesin home improvement costs across different cities. Wegathered anecdotal evidence on this issue by readingmaterial provided by HomeTech on its website and varioussources on the Internet regarding home remodeling.Wages in different cities account for only a fraction ofthe differences in costs. Variations also exist in lumber andmaterials prices in different cities depending on factorssuch as the number of lumber suppliers in that cityaccording to HomeTech. Moreover, a bigger source of costinflation that is often reported for the high-end improve-ment projects that are at the center for our data set is thatthere is a trade-off in terms of the speed of constructionand cost. For instance, consider the cost of an Italianmarble bathroom. The biggest cost is procuring the Italianmarble, and, depending on search time, the cost differ-ences can be substantial. In cities in which people are in a

4 For 1998, cost estimates for projects were from three publishersof construction cost estimating guides and software: Craftsman Books,Carlsbad, California; HomeTech Information Systems, Bethesda,Maryland; and R.S. Means, Kingston, Massachusetts. For 1999, R.S. Meanswas the only source for the cost estimates.

rush to build, busy contractors are less picky about howmuch such quality items cost. Instead of searching for anextra month to find the same quality at a lower price, thecontractor uses the most expensive one. This is the big costdifference across cities and over time between buildingduring the bubble years versus the nonbubble years.5 Soone should think of variations in remodeling costs fromthis database across cities as driven by these local supplyfactors in addition to any wage differences. We look at thisissue of wages in residential construction more closely andrelate it to our model in Section 4.4.

Resale values (or value-added) of these home improve-ments are based on the professional judgment of membersof the National Association of Realtors. To obtain thesejudgments, the magazine sent out surveys containingcustomized cost-to-construct data for each city, as wellas information on median house prices, via e-mail toappraisers, sales agents, and brokers. The magazine givesinstructions in the survey for the respondents not to makejudgments about the motivation of the homeowner inthe decision either to undertake the remodeling project orto sell the house. The real estate professionals thenresponded with dollar figures for each remodeling projectthat represent the value the completed project would addto the selling price of the house under current marketconditions. The surveys are obtained from hundreds of realestate professionals and aggregated to provide the resalevalues in the magazine.

We construct for each city by year a COST variable,which is simply the equal-weighted average of the costs ofthe projects in that city. We construct a similar variableRESALE, which is the average of the resale values for theprojects in that city. We divided RESALE by COST to obtainRECOUP, which corresponds to recoup value in our theo-retical analysis and is our main dependent variable ofinterest. Our home price index for each city obtained fromthe Federal Housing Finance Agency is HPI. Data for HPI isdefined at the level of the Metropolitan Statistical Area(MSA). So we use as the home price for each city the priceof the MSA that it belongs to.

Our analysis largely focuses on the three variables ofRECOUP, HPI, and COST. Our theory can be completelysummarized by these variables. To test our theory, we donot need to look at any other variables. But for complete-ness of analysis, we include demographic variables in ourrobustness checks. They should have no material impacton the relations we are predicting. As such, we do not havemany comments regarding the demographic variables. Therelations of these demographic variables to our variablesof interest in all likelihood is determined by complicatedequilibrium effects.

The demographic variables are as follows. INC isincome per capita in the city. POP is population in thecity. We do not have data for INC and POP for 2009 yet andso in our analyses involving these variables we can lookat changes in INC and POP only up to 2008. These two

5 See, for instance, coverage on this issue at http://moneywatch.bnet.com/saving-money/article/five-home-renovations-that-pay-off/353008/.See also the description in http://www.remodeling.hw.net/remodeling/cost-vs-value-report-2006.aspx.

variables are from the Bureau of Economic Analysis.UNEMP is the unemployment rate in a city, which isprovided by the Bureau of Labor Statistics.

Table 1 provides the summary statistics for our mainvariables of interest. In Panel A, we report the time seriesaverage (across years) of the cross sectional (across citiesfor each year) means and standard deviations for thefollowing variables. The mean COST of a typical projectin a typical city is $39,189 with a standard deviation of$4,193. As these numbers attest, the projects are majorremodeling undertakings and most of them have roughlythe same average value. The mean RESALE is $29,428 witha standard deviation of $7,959. The recoup value is 0.78with a standard deviation of 0.18. The recoup value is onaverage less than one, and there is a reasonable differencein recoup values across cities. The mean HPI is 162 with astandard deviation of 26. The per capita income (INC) is$35,437 with a standard deviation of $6,319. The popula-tion of a typical city in our sample is around 1.2 millionpeople with a standard deviation of around 1.5 millionpeople. The unemployment rate (UNEMP) is around 6%with a standard deviation of 2%.

Panel B provides the time series average of the cross-sectional correlations of these variables of interest. The keythings to observe from this panel are the following. COSTand RESALE are positively correlated with a correlationcoefficient of 0.61, and COST and RECOUP are also posi-tively correlated with a coefficient of 0.23. In other words,cities with higher COST also have higher RESALE andRECOUP values. This positive correlation is in levels andcaptures potentially many unobservables. Hence, COST andRECOUP need not be mechanically hardwired to be nega-tively correlated because RESALE also adjusts. Our theory

Table 1Summary statistics.

Panel A reports the time series average of cross-sectional means and standaraverage of correlation matrix for the variables of interest. COST and RESALE areRECOUP is the recoup ratio by year and city defined as RESALE/COST. HPI is the hthe level of Metropolitan Statistical Area (MSA). The HPI of MSA is used when thsize by year and city. INC and POP for 2009 are excluded due to the data availabiby year and city from Bureau of Labor Statistics.

Panel A: Means and standard deviations

Variable Mean Standard deviation

COST 39,189.3 4,193.0RESALE 29,428.2 7,958.7RECOUP 0.78 0.18HPI 162 26.6INC 35,436.9 6,319.4POP 1,181,105 1,506,280UNEMP 0.06 0.02

Panel B: Correlation matrix

Variable COST RESALE RECOUP

COST 1RESALE 0.61 1RECOUP 0.23 0.88 1HPI 0.29 0.50 0.45INC 0.40 0.52 0.40POP 0.33 0.29 0.18UNEMP 0.28 �0.01 �0.13

does not have much to say about levels because it is gearedto understanding the implications of how a change inhome prices stimulates home improvements. When welook at changes in these variables, the comment regardingthe hard-wiring of COST and RECOUP in levels applies tochanges; that is, the correlation of changes in these twoquantities need not be hard-wired to have a particularsign. Moreover, the correlation of HPI with COST, RESALE,and RECOUP are all positive. Hence, cities with higherhome prices captured by HPI also have higher COST,RESALE, and RECOUP values.

4.2. Baseline results

Our theory is concerned with the relation betweenchanges in RECOUP associated with a change in homeprices HPI and changes in COST. To this extent, ourempirical design is centered around looking at how COSTand RECOUP values and HPI changed during the bubbleperiod of 2003–2009. Fig. 2 plots the time series for theaverage RECOUP, HPI, and COST across cities in each year.COST has gone up substantially from a low of around$20,000 in 1998 to around $60,000 in 2009. These arenominal levels and reflect the inflation in wages, materialcosts, and potentially other types of zoning and regulatorycosts. RECOUP starts at 0.8 in 1998 and rose to a high of 0.9in 2005 and then decreases with the collapse of housingprices starting in 2007 and into 2009. HPI starts at 118 in1998 and rose to a high of 210 in 2007 and falls to 185 in2009. The year 2003 or 2004 is generally viewed as thebeginning of the housing bubble period. Any stronginference here is impossible given the limited time series.

d deviations for the variables of interest. Panel B reports the time seriesthe equal-weighted measures across different projects by year and city.ouse price index by the Federal Housing Finance Agency. HPI is defined ate city belongs to the MSA. INC is income per capita, and POP is populationlity from Bureau of Economic Analysis. UNEMP is the unemployment rate

HPI INC POP UNEMP

10.41 10.24 0.11 1�0.11 �0.24 0.20 1

RECOUP

1998 2000 2002 2004 2006 2008Year

120140160180200220

1998 2000 2002 2004 2006 2008Year

20,000

30,000

40,000

50,000

60,000

1998 2000 2002 2004 2006 2008Year

Fig. 2. Average RECOUP, HPI, and COST. The figure plots RECOUP, HPI, and COST averaged across cities for various years. RESALE and COST are the equal-weighted measures across different projects by year and city, and RECOUP is the recoup ratio by year and city defined as RESALE/COST. See Table 1 forvariable definitions.

We try to test our prediction by looking at the correlationof changes in recoup values with changes in HPI and changesin construction costs across cities. Our first set of results,reported in Table 2, concerns the relations between changesin recoup value, %ΔRECOUP, and changes in %ΔHPI andchanges in cost %ΔCOST. We focus our analysis here on thechanges in these variables during the period of 2003–2009.This is our baseline sample period. We consider robustnesschecks below for subperiods.

Panel A of Table 2 reports the summary statistics forchanges in our variables of interest over this period.Construction cost grew by about 57% with a standard devia-tion of 7%. Recoup values fell on average by 14.6% with astandard deviation of 21.2%. Home prices rose on average byabout 20.8% with a standard deviation of 15.9%. Income andpopulation also expanded and so did unemployment becausewe have 2009 in our sample. The income and populationnumbers are calculated from 2003 to 2008 because we donot yet have data for 2009 for these two variables.

Panel B reports the correlation of these variables overthis period. The key take-aways are the following. Thepercentage changes in COST and RECOUP are negativelycorrelated across cities. Higher HPI is correlated withhigher RECOUP. These correlations are consistent withour theory. Home improvers gain from their improve-ments when home prices are higher and lose whenconstruction costs growth are higher. But only the correla-tion of RECOUP and HPI is distinct to a speculative motive,whereas the negative correlation of RECOUP with COSTmight also be consumption-driven.

Panel C reports the results for our main regression ofinterest: the percentage change in recoup value on per-centage change in HPI. In Column 1, we report the simple

univariate regression with only the percentage change inHPI on the right-hand side. The regression has 35 cities asobservations. The coefficient of interest is 0.320 with a t-statistic of 2.0. A standard deviation of %ΔHPI is 0.16. So a1 standard deviation increase in %ΔHPI is associated withan increase in %ΔRECOUP of 0.05 (0.32n0.16¼0.05) whichis about 24% of a standard deviation of %ΔRECOUP. Theeconomic significance is clearly very sizable.

The corresponding plot of this regression is shown inFig. 3 with the fitted line of this regression plotted againstthe scattered observations. It clearly shows a prominentpositive sloping relation between these two variables ofinterest that does not seem to be driven by outliers.

In Column 2, we add %ΔCOST and a host of demographicvariables. The coefficient in front of%ΔCOST is �1.174 with at-statistic of 2.38. Importantly, the coefficient now in front ofprice change increases to 0.563 with a t-statistic now of5.034. This specification represents the strongest evidence ofour model in which both of our variables of interest areeconomic and statistically significant as predicted. Of thecontrol variables, only the percentage change in incomecomes in with a statistically significant effect but, interest-ingly, it attracts a counterintuitive negative sign. Our modelis silent on what to expect from this change in incomevariable, and this variable probably is better interpretedin a consumption-based model. It appears this percentagechange in per capita income variable is correlated with thepercentage change in home prices variable, and its additionto the regression specification boosts the explanatory powerof home price changes. The main take-away for us is that ourtwo variables of interest, cost growth and home price changeattract the predicted coefficients even with the inclusion of anumber of demographic variables.

Table 2%ΔRECOUP on %ΔHPI and %ΔCOST.

Panel A reports the mean and standard deviation of percentage change (%Δ) in variables from 2003 to 2009. Panel B reports the correlation matrix of %Δin variables from 2003 to 2009. Panel C reports regressions of %ΔRECOUP on %ΔHPI from 2003 to 2009. In Column 1, univariate regression of %ΔRECOUPon %ΔHPI is reported. Column 2 reports the regression of %ΔRECOUP on %ΔHPI with %ΔCOST and %Δ of demographic control variables. The table reportspoint estimates with t-statistics in parentheses. Standard errors are clustered by the US Census division. nnn, nn, and n denote 1%, 5%, and 10% statisticalsignificance, respectively. See Table 1 for variable definitions.

Panel A: Means and standard deviations

Variable Mean Standard deviation

%ΔCOST 0.572 0.071%ΔRECOUP �0.146 0.212%ΔHPI 0.208 0.159%ΔINC 0.245 0.078%ΔPOP 0.034 0.077%ΔUNEMP 0.424 0.285

Panel B: Correlations

Variable %ΔCOST %ΔRECOUP %ΔHPI %ΔINC %ΔPOP %ΔUNEMP

%ΔCOST 1%ΔRECOUP �0.47 1%ΔHPI �0.04 0.24 1%ΔINC 0.26 �0.18 0.51 1%ΔPOP �0.31 0.10 0.06 �0.42 1%ΔUNEMP 0.34 �0.20 �0.29 �0.24 �0.16 1

Panel C: %ΔRECOUP on %ΔHPI and %ΔCOST

Variable %ΔRECOUP

(1) (2)

%ΔHPI 0.320n 0.563nnn

(2.038) (5.034)%ΔCOST �1.174n

(�2.328)%ΔINC �1.109nn

(�2.549)%ΔPOP �0.635

(�1.298)%ΔUNEMP �0.0572

(�0.899)Constant �0.212nnn 0.726nn

(�3.646) (2.597)

Number of observations 35 35R2 0.058 0.354

In Table 3, we consider a number of robustness exer-cises. In Panel A, the results are broken down by midrangeand upscale projects. The results are similar across thesetwo types of projects. In Panel B, we briefly summarize ouranalysis by presenting the results project by project. Thecoefficients for all the projects have the right signs.

In Panel C, we focus on the periods 2001–2007 and 1998–2009. We consider whether the collapse of home pricesduring the years of 2008 and 2009 are driving all our results.Even if this was the case, it would not necessarily beinconsistent with our model. It turns out, however, that theresults are largely similar. Another reason we consider thisrobustness check is the timing of the survey results. Ifhomeowners’ beliefs as proxied by the surveys of realtorson resale values are forward-looking while the surveys ofcontractors are backward-looking or stale, then this mightexplain why resale did not keep up with construction costgrowth during the crash of home prices from 2007 to 2009.

This issue of timing is less critical when we consider longhorizon periods. Even if the construction cost estimates arestale, they eventually catch up to the resale values overlonger periods. In Panel D, we cluster the standard errors byregion instead of by divisions. The results are similar.

4.3. Results by housing supply elasticity

Having established our baseline regression specifica-tion and result, we turn to testing an auxiliary implicationof our model. Namely, the effect of home prices on recoupvalues ought to be stronger in cities with a low as opposedto a high housing supply elasticity index of Saiz (2010). Inother words, if we re-run our preferred regression speci-fication separately for low versus high housing supplyelasticity areas, we expect a larger economic effect for thelow supply elasticity areas.

−0.60

−0.40

−0.20

%ΔRECOUP

−0.20 0.00 0.20 0.40 0.60%ΔHPI

Fig. 3. %ΔHPI and %ΔRECOUP. The figure plots %ΔRECOUP and %ΔHPIacross cities. %ΔRECOUP is the percentage change in RECOUP from 2003to 2009. %ΔHPI is the percentage change in HPI from 2003 to 2009.See Table 1 for variable definitions.

The reason we expect this is that Glaeser, Gyourko, andSaiz (2008) show that low supply elasticity states (such asNew York and California, where land is limited and zoningand development rules are stricter) in which supply couldnot quickly adjust to the rising home prices are moreprone to bubbles than high elasticity areas where supplycan adjust quickly. One can think of low elasticity areas ascities with limited supply and limited supply is a strongdeterminant of speculative behavior (Hong, Scheinkman,and Xiong, 2006). When there is too much supply, it isdifficult perhaps for households to believe that prices canrise enough to justify their speculative behavior. One onlyneeds to recall the dot-com bubble in which the vastmajority of the speculative trading during the 1996–2000period was concentrated in a small group of Internetstocks (Ofek and Richardson, 2003).

As for how the cost growth should affect recoup valuesin these two subsamples, we do not have a clear predic-tion. The reason is that only the home price growth parthas an unambiguous prediction in our model comparedwith the consumption-cum-financial-constraints story.Cost growth could influence recoup values negatively forboth consumption and speculation reasons. So the sign weexpect to see for cost growth depends on how importantremodeling is for consumption reasons across these areas,which would potentially depend on other unobservablefactors.

In Table 4, Panel A, we report the housing supplyelasticity index for the cities in our sample along with%ΔCOST and %ΔHPI in each city. We sort the cities bysupply elasticity from low to high. The low elasticity ordifficult-to-build places are Miami, Florida; and LosAngeles, San Francisco, and San Diego, California. The highelasticity or easy-to-build places are Columbus, Ohio; SanAntonio, Texas; Kansas City, Missouri; and Indianapolis,Indiana. The index goes from a low of 0.6 for Miami to ahigh of 4 for Indianapolis. In Panel B, we calculate thecorrelation with supply elasticity with %ΔCOST and%ΔHPI. As we would expect, low elasticity places haveexperienced higher cost growth and higher home priceappreciation.

In Panel C, we divide up our sample into two groups,low versus high elasticity cities, and we report the sum-mary statistics for our key variables of interest. The split isdown the middle: 17 cities in the low and 17 cities in thehigh elasticity group. The low elasticity areas have experi-enced a bigger decline in recoup values, much higherhome price appreciation, and somewhat higher costgrowth than the high elasticity areas.

In Panel D, we run our baseline regression specificationof change in recoup values on change in home prices andcost growth separately for low versus high elasticity areas.The first column reports the results for the low elasticitycities. The coefficient in front of %ΔHPI is 0.841 with at-statistic of 5.9. The coefficient in front of %ΔCOST is �1.4with a t-statistic of 1.5. The second column reports theresults for the high elasticity cities. The coefficient in frontof %ΔHPI is 0.410 with a t-statistic of 1.05, and thecoefficient in front of %ΔCOST is �1.6 with a t-statisticof 2.75. The economic effect of home price changes onrecoup values is much greater for low than high elasticitycities, consistent with our model. The economic effect forcost growth is only slightly larger for high elasticity citiesthan low elasticity cities. The unambiguous difference forthe home price change coefficients across these twosubgroups compared with the ambiguous difference forcost growth coefficients is very much in line with ourtheory.

4.4. Additional robustness checks and alternativeinterpretations

In this subsection, we discuss a number of robustnesschecks we have done but do not report for brevity. First,we have chosen to focus on recoup values in Table 2,which is the most natural quantity that encompassesmistakes in the resale value or in construction costs. Wecould have also focused on resale values and redoneTable 2 with resale values and obtained similar results.In other words, our results are robust to the choice ofrecoup or resale values, very much in line with theeconomics of our model and the alternative set-updiscussion.

Second, several caveats are warranted for the data. Themethodology used to compiled this database was changedslightly in 2007, when the magazine gave clearer guide-lines on the projects. It argues that this led to moreaccurate construction costs estimates. The Home ValuationCode of Conduct (HVCC) took effect on May 1, 2009. Thepurpose is to try to bring more fairness into appraisals byhaving the appraiser of a home be randomly chosen from apool. To the extent that the respondents of the resalesurveys are influenced by observed appraisals, this couldhave had an effect on their responses. We dealt with thisissue using various beginning and end dates for theregression sample and found roughly similar results. Therecoup value results are robust to these perturbations.Some of these results are presented in Table 3.

We gather residential construction wage data for coun-ties from the Bureau of Labor Statistics and find that wagesin this industry are correlated with the costs of theimprovements in the city and that changes in these costs

Table 3Robustness.

Certain projects are broken down by midrange and upscale level. Panel A reports regressions of%ΔRECOUP on%ΔHPI and %ΔCOST within midrange andupscale projects. The dependent variable is %ΔRECOUP, the percentage changes from 2003 to 2009 in RECOUP which is an equal-weighted measure acrossdifferent midrange projects by year and city. In Columns 1 and 2, %ΔRECOUP is regressed on %ΔHPI and %ΔCOST with %Δ of demographic variablescontrolled. Column 1 reports the regression of midrange projects, and Column 2 reports the regression of upscale projects. COST is an equal-weightedmeasure across different midrange projects by year and city. Panel B reports the regression of %ΔRECOUP on %ΔHPI and %ΔCOST for individual projectswith %Δ of demographic variables controlled. The dependent variable is %ΔRECOUP, the percentage change from 2003 to 2009 in RECOUP of the project byyear and city. %ΔCOST is the percentage change from 2003 to 2009 in COST of the project by year and city. Only the coefficient and t-statistics for %ΔHPIand %ΔCOST are reported for brevity. M and U represent midrange and upscale project, respectively. Panel C reports the regressions of %ΔRECOUP on%ΔHPI and %ΔCOST for different time horizons, from 2001 to 2007 and from 1998 to 2009. Panel D reports the regression in Table 3 with standard errorclustered by the US region. The table reports point estimates with t-statistics in parentheses. Other than Panel D, standard errors are clustered by the USCensus division. nnn, nn, and n denote 1%, 5%, and 10% statistical significance, respectively. See Table 1 for variable definitions.

Panel A: By projects’ quality level

Midrange projects Upscale projectsVariable %ΔRECOUP %ΔRECOUP

(1) (2)

%ΔHPI 0.599nnn 0.521n

(6.955) (2.023)%ΔCOST �1.201nn �1.753nn

(�2.741) (�2.481)%ΔUNEMP �0.00539 �0.0497

(�0.0748) (�0.423)%ΔINC �1.122nn �0.967

(�2.676) (�1.618)%ΔPOP �0.551 �0.456

(�1.336) (�0.744)Constant 0.696nn 0.547nn

(3.491) (3.075)

Panel B: By individual project

Project %ΔHPI %ΔHPI t-statistic %ΔCOST %ΔCOST t-statistic

Basement remodel (M) 0.409n (2.250) �1.100nn (�2.683)Bathroom addition (M) 0.347nn (2.870) �0.603nn (�3.236)Bathroom addition (U) 0.418 (1.810) �0.733nn (�2.776)Bathroom remodel (M) 0.606nn (2.602) �1.313n (�2.157)Bathroom remodel (U) 0.322 (1.682) �0.706 (�1.821)Family room addition (M) 0.652nnn (6.365) �0.852 (�1.630)Major kitchen remodel (M) 0.891nnn (4.915) �2.120nn (�2.581)Major kitchen remodel (U) 1.235 (1.442) 0.349 (0.218)Master suite addition (M) 0.762nnn (4.661) �0.836nn (�2.456)Master suite addition (U) 0.555nn (2.925) �1.851nn (�3.268)Window replacement (M) 0.327 (0.724) �1.508n (�2.355)Window replacement (U) 0.233 (0.893) �1.534 (�1.807)

Panel C: By different sample periods

From 2001 to 2007 From 1998 to 2009Variable %ΔRECOUP %ΔRECOUP

(1) (2)

%ΔHPI 0.118 0.162(1.362) (1.339)

%ΔCOST 0.257 �0.444nn

(0.491) (�3.112)Constant �0.324 0.602n

(�0.643) (1.884)Number of observations 50 52R2 0.050 0.099

Panel D: Clustering standard errors by US region

Variable %ΔRECOUP

(1) (2)

%ΔHPI 0.320 0.563nn

(2.205) (3.365)

Table 3 (continued )

%ΔCOST �1.174nn

(�5.538)%ΔUNEMP �1.109

(�1.975)%ΔINC �0.635

(�0.942)%ΔPOP �0.0572

(�0.741)Constant �0.212nnn 0.726nn

(�6.827) (3.316)Number of observations 35 35R2 0.058 0.354

and changes in these wages over time are also correlated.This provides a check as to the accuracy of the cost data,though other factors such as zoning or regulatory rulesand the other local supply factors that vary across citiescould also impact substantially improvement costs.

However, our cost data are better than wage growth totest our theory for a few reasons. Wage growth in theresidential construction sector is correlated with wagegrowth in the city. Hence, wage growth also behaves likean income effect in the city, and a consumption theorypredicts that cities with higher wage or income growthshould have higher recoup values because householdswant more amenities. We find that this type of an effectis not very significant, however, in the data. Hence, ourchange in cost variable is robust to the addition of a wagegrowth variable and suggests that the part of the costvariable that is picking up supply factors such as lumber orthe cost of Italian marble seems to be, consistent with ourpriors and discussion above, the dominant variation influ-encing our regressions.

4.5. Potential extensions and comments

Our model is very stylized and there are potentiallyinteresting extensions to it that could generate more testableimplications of interest to the household finance literature.The first is modeling moving and moving costs. In our purespeculation model, moving costs do not matter becausehouseholds want to take remodeling investments regardlessof whether they plan to move or not. The relevant margin inthe speculation decision is the opportunity cost of what elsethe household would do with its time or money. In the dot-com period, it would have been in our model to trade dot-com stocks instead of doing remodeling.

This observation gives an interesting prediction thatcould be testable, which is to see if households substituteday-trading for home improvements. For instance, of thehouseholds that engaged in speculative home improve-ments during the housing bubble, what fraction were alsoday traders during the Internet bubble period? This wouldrequire both remodeling activity data at the householdlevel and trading data for the household's portfolio. Thisseems a tall order, but these variables could be attainableat the city or zip code level.

Anecdotal evidence suggests that people do remodelingbefore moving, which is a sign that the remodeling is forresale value as opposed to consumption. However,

introducing moving and moving costs would be interest-ing in our consumption-cum-financial-constraints model.Here, households do face a trade-off in terms of remodel-ing their home or buying a new place. Buying a new placein our model means that the household could have theflexibility of optimizing over both land L and structures Sas opposed to remodeling, which is simply to optimizeover S holding fixed their endowed L. We would see in thisscenario remodeling be less correlated with moving. Inother words, if we had remodeling data, we could try todiscriminate between the speculative and consumptionhypotheses by seeing if remodeling and moving arepositively correlated as in the speculative scenario ornegatively correlated as in the consumption scenario.

We have described the speculative remodeling impulse asbeing tied to owners being overly optimistic about the recoupvalues of their investments. Another way this speculativemotive is manifested is in the belief among homeowners thatremodels cut down the time their home stays on the marketwhen they sell. They believe that cutting down time on themarket is valuable because they will get much higher prices asa result. A belief among homeowners and real estate agents,true or not, is that the longer a house sits on the market, thelower the price it will receive because buyers will becomesuspicious that there is something wrong with the house. Wecan then think of overoptimism about remodeling as ownersoverestimating the degree to which improvements reduce thetime their homes sit on the market.

5. Conclusion

Home improvements are an important economic activ-ity. Such activity accounts from around 1% to 2% of GDPeach year, and this is not even accounting for the oppor-tunity cost of time of many homeowners who tend toundertake these efforts by themselves. This tremendouslyimportant economic activity has been, with a few excep-tions, largely neglected by researchers. We believe thatthis topic deserves the same amount of attention thateconomists have given to consumption and investmentdecisions in financial markets. We develop a theory ofhome improvements in which optimistic homeownersspeculate on future home prices by engaging in remodel-ing. This theory yields a number of results includingconvexity of improvement expenditures to home pricechanges, overinvestment in home remodeling, and highergrowth in recoup values in areas with higher home price

Table 4%ΔRECOUP on %ΔHPI by housing supply elasticity.

Panel A reports the housing supply elasticity from Saiz (2010), %ΔCOST, and %ΔHPI from 2003 to 2009 across different cities. Panel B reports thecorrelation matrix between supply elasticity, %ΔCOST, and %ΔHPI with heteroskedasticity-consistent t-statistics in parentheses. Panel C reports thesummary statistics by supply elasticity. Panel D reports regressions of %ΔRECOUP on %ΔHPI, %ΔCOST by supply elasticity from 2003 to 2009. Column 1reports the regression results using the cities with low supply elasticity, and Column 2 reports the regression results using cities with high supply elasticity.The table reports point estimates with t-statistics in parentheses. Standard errors are clustered by the US Census division. nnn, nn, and n denotes 1%, 5%, and10% statistical significance, respectively. See Table 1 for variable definitions.

Panel A: Housing supply elasticity, %ΔCOST, and %ΔHPI

City Supply elasticity %ΔCOST %ΔHPI

Miami, FL 0.60 0.57 0.24Los Angeles, CA 0.63 0.65 0.32San Francisco, CA 0.66 0.59 0.21San Diego, CA 0.67 0.60 0.08Salt Lake City, UT 0.75 0.51 0.40New York, NY 0.76 0.74 0.34Chicago, IL 0.81 0.67 0.18New Orleans, LA 0.81 0.60 0.32Virginia Beach, VA 0.82 0.56 0.64Boston, MA 0.86 0.65 0.09Seattle, WA 0.88 0.54 0.40Tampa, FL 1.00 0.62 0.22Cleveland, OH 1.02 0.50 0.00Milwaukee, WI 1.03 0.57 0.22Portland, OR 1.07 0.57 0.42Orlando, FL 1.12 0.57 0.28Pittsburgh, PA 1.20 0.53 0.20Detroit, MI 1.24 0.61 �0.25Minneapolis, MN 1.45 0.65 0.08Denver, CO 1.53 0.52 0.07Phoenix, AZ 1.61 0.47 0.23Providence, RI 1.61 0.62 0.16Washington, DC 1.61 0.62 0.36Philadelphia, PA 1.65 0.58 0.40Buffalo, NY 1.83 0.56 0.24Dallas, TX 2.18 0.46 0.16Houston, TX 2.30 0.47 0.28St. Louis, MO 2.36 0.54 0.20Cincinnati, OH 2.46 0.50 0.09Atlanta, GA 2.55 0.48 0.09Columbus, OH 2.71 0.51 0.08San Antonio, TX 2.98 0.50 0.34Kansas City, MO 3.19 0.69 0.11Indianapolis, IN 4.00 0.53 0.07

Panel B: Correlation matrix

Variable Supply elasticity %ΔCOST %ΔHPI

Supply elasticity 1 �0.377 (�1.97) �0.27 (�2.11)%ΔCOST 1 0.02 (0.16)%ΔHPI 1

Panel C: Summary statistics by housing supply elasticity

Low supply elasticity High supply elasticity

Variable Number of observations Mean Standard deviation Number of observations Mean Standard deviation

%ΔRECOUP 17 �0.179 0.218 17 �0.121 0.211%ΔHPI 17 0.267 0.150 17 0.160 0.151%ΔCOST 17 0.590 0.062 17 0.547 0.069%ΔINC 17 0.278 0.074 17 0.213 0.073%ΔPOP 17 0.016 0.089 17 0.052 0.062%ΔUNEMP 17 0.418 0.270 17 0.401 0.291

Panel D: %ΔRECOUP on %ΔHPI and %ΔCOST by housing supply elasticity

Low supply elasticity High supply elasticityVariable %ΔRECOUP %ΔRECOUP

(1) (2)

%ΔHPI 0.841nnn 0.410(5.892) (1.055)

Table 4 (continued )

%ΔCOST �1.419 �1.626nn

(�1.542) (�2.750)%ΔINC �1.214 �0.873

(�1.450) (�1.057)%ΔPOP �0.769 �1.376

(�1.031) (�0.751)%ΔUNEMP �0.0832 �0.228

(�0.651) (�0.737)Constant 0.817n 1.052nn

(2.028) (2.456)

appreciation controlling for construction cost growth. Wetest this last prediction using data on home improvementcosts and resale values across US cities. This prediction alsocuts against a consumption-cum-financial-constraintsmotive in which higher home prices should be correlatedwith lower recoup values. Consistent with our theory, wefind that cities with higher home price appreciationexperiences higher recoup value growth during the recenthousing bubble period of 2003–2009.

Appendix A. Proofs of propositions

Proof of Proposition 1. Homeowners choose S (SZS0) tomaximize

1�α�ωðS�S0Þ: ð27ÞIf P1¼Po

1 , homeowners solve

0¼ 1�αð ÞPo1L

�α� SS0

� �β

ð28Þ

to get

S¼ ð1�αÞPo1L

h i1=ðαþβÞ40: ð29Þ

If P1¼Pp1 , homeowners do not change their structure

because they cannot decrease the structure. Thus,S¼ S0. □

Proof of Proposition 2. S0 is the optimal level of structurewhen the price of housing units is P0 . Homeowners solve

ð1�αÞP0Lα0S

�α0 ¼ω¼ 1: ð30Þ

We normalize the cost of structure with the cost at t¼0.From Eqs. (29) and (30), we get

S¼ Po1

!1=ðαþ β Þ

S0: ð31Þ

When Po1 4P0 , S is greater than S0. The equilibrium cost of

structure, ω¼ ðS=S0Þβ , is greater than one, which is theequilibrium cost of structure at t¼0. □

Proof of Proposition 3. From Eq. (31), we get

¼ Po1

!1=ðαþ β Þ

: □ ð32Þ

Proof of Proposition 4. Let X ¼ S=S0. Then

11�α

� �1�α�1

� �βSS0�1

� � ¼ 11�α

X1�α�1XβðX�1Þ : ð33Þ

Because XZ1

∂∂X

X1�α�1XβðX�1Þ r0; ð34Þ

where the equality holds with X¼1. Note that

limx-1

11�α

X1�α�1XβðX�1Þ

" #¼ lim

X�α

ð1þβÞXβ�βXβ�1

" #¼ 1 ð35Þ

by l'Hospital's Rule. Thus, expected recoup ratio is lessthan one and the greater the structure growth (X ¼ S=S0),the lower the expected recoup ratio. □

Proof of Proposition 5. Recoup ratio is

P2Lα0S

1�α�P2Lα0S

1�α0

ωðS�S0Þ¼ 1

1�α

� �1�α�1

� �βSS0�1

� � : ð36Þ

Recoup ratio is positively correlated with home priceappreciation, P2�P1 ¼ P2�Po

1 . From Eq. (34)

∂∂X

X1�α�1XβðX�1Þ o0; ð37Þ

with X41. Conditional on there being remodeling at t¼1(X41), recoup ratio is negatively correlated with X andω¼ Xβ . □

Appendix B. Supplementary data

Supplementary data associated with this article can befound in the online version at http://dx.doi.org/10.1016/j.jfineco.2013.11.011.

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