vacant land paper

8/3/2019 Vacant Land Paper

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An Empirical Test of Property Valuation in a

Real Option-Pricing Framework

Kevin Gillen*

March 22, 2002

AbstractThis paper empirically tests the predictions of property valuation in a real optionsframework. While there is an abundance of empirical research using the Black-Scholesmodel of asset pricing to examine traditional financial assets such as stocks and bonds,very little investigation has been done with real estate. Moreover, the majority of thiswork has been theoretical. This theoretical translation of Black-Scholes to real estateviews the possession of a plot of vacant land as equivalent to holding a call option todevelop a tangible property. The exercise price is the cost of construction and the asset

price is the sale value of the final developed property. The profit-payoff is the differencebetween the two. This paper tests whether an increase in the uncertainty of future realestate asset prices induces an increase in both the level and volatility of land prices, as themodel predicts it should. An increase in uncertainty over future asset prices enters in theform of a policy change that substantially relaxes zoning restrictions on developable landin Philadelphia. I find that the increase in uncertainty increases both the level andvolatility of land values, and this result is robust with respect to a number of parameters.

Special Thanks to Paul Amos, Prof. Michael Brandt, Dr. Gerald Carlino, Dr. Brad Case, Prof. JoeGyourko, Prof. Chris Mayer, Prof. Todd Sinai, Prof. Susan Wachter, and Aaron Cohen for theirsupport and input. All mistakes, of course, are solely due to the author.

*PhD Student, Real Estate Dept., The Wharton School, U. of Pennsylvania, Philadelphia PA,19104.; (215) 898-4818; [email protected]
mailto:[email protected]:[email protected]


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legacy of William Penn, a bronze likeness of whom stands atop this tower2. It was William Penn whofounded the colony of Pennsylvania and the city of Philadelphia, and who also designed downtownPhiladelphias critically-acclaimed efficient grid layout of streets. In fact, it is City Hall that sits at thegeographic center of downtown Philadelphia at the intersection of Market and Broad streets, from wherethe statue of William Penn holds eternal vigilance over his City of Brotherly Love. The building is alsonotable for the fact that, with 14.4 acres of floor space, it has continuously held the record for the largestmunicipal building in the world for the past 101 years (2).

However, in the mid-1980s this height restriction was de facto eliminated when the construction of thebuilding known as Liberty One commenced via the backing of the Rouse Company (3). Standing at 945

feet (61 stories), Liberty One persists today as the tallest building in Philadelphia (4). The construction ofsix other buildings that exceed the height of City Halls tower commenced soon thereafter (5).

Table 1. Philadelphias Top Ten Tallest Buildings

Rank Name Usage Height No. Stories Year Completed

1 Liberty One Office 945 ft. 61 1987

2 Liberty Two Office 848 ft. 52 1989

3 Mellon Bank Center Office 793 ft. 53 1990

4 Verizon Tower Office 739 ft. 55 1991

5 Blue Cross-Blue Shield Tower Office 700 ft. 50 1990

6 Commerce Square II Office 572 ft. 41 1992

7 Commerce Square I Office 572 ft. 41 1987

8 Philadelphia City Hall Municipal Ofc. 548 ft. 37 + Statue 1901

9 1818 Market Street Office 500 ft. 40 197410 Loews Philadelphia Hotel Hotel 492 ft. 38 1932

Source: www.skyscrapers.com

2At 37 feet in length, the statue of William Penn is the largest single piece of sculpture on any building in the world. Source: AccessPhiladelphia, pp. 63.


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This paper will test the predictions of real estate valuation in the options-pricing framework by examiningthe changes in land values and returns that followed the removal of this height restriction. Specifically, itwill test whether the relaxation of a (presumably binding) zoning law induced a one-time, but permanent,increase in both the value and volatility of land in the geographic market to which this zoning restrictionapplied, as theory predicts it should. The outline of the paper is as follows: Section I of the paper willoutline the basic real options model framework for real estate. Section II demonstrates the comparativestatics of how the relaxation of zoning laws increases uncertainty over future property values3, anddiscusses the economic implications of this increase in uncertainty. Section III will give a simplenumerical example of the comparative statics, and Section IV tells the institutional story of how the heightrestriction came to be removed. Section V discusses the empirical strategy and the data, and Section VIpresents the estimation results of a hedonic valuation model of vacant land in Philadelphia. Section VIIwill present the hypothesis tests of the model and also give some checks of the models robustness. SectionVIII will summarize the conclusions and give suggestions for further research.

I. Real Estate in a Real Options FrameworkThe groundbreaking theoretical work in this area is due to Titman (1985) and Williams (1991). Titman(1985) adapts to real estate the methods that were originally innovated by Black and Scholes (1973) andMerton (1973). His approach most resembles the binomial option pricing models of Cox, Ross andRubinstein (1979) in a discrete-time setting. Williams (1991) provides a more sophisticated treatment than

Titman (1985) by generalizing the simple discrete-time binomial model to a continuous-time setting.However, the predictions of Williams model are not substantively different than Titmans version. For thepurposes of this paper however, it is not necessary to go beyond the framework provided by Titman (1985).

There has been a relative paucity of empirical work that tests the implication of option-based valuationmodels for real assets, however. Two of the most notable contributions have been by Quigg (1993) andBulan et al (2001). Quigg (1993) estimated the implicit option value of waiting to develop land using adataset of land sales in Seattle. She finds that the mean option premium in this market is 6% of thetheoretical land value. An increase in uncertainty over what will eventually be developed should alsoincrease this option premium of waiting. Similarly, Bulan at al (2001) examine condominiumdevelopments in Vancouver and find that an increase in risk, and thus uncertainty, leads developers todelay new real estate investments. Both results are consistent with the models application to real estatevaluation.

The basic intuition of the model is that the possession of a parcel of vacant land is the same as holding acall option to purchase any one of a number of different buildings that may be developed on it for anexercise price equal to the respective construction costs. The payoff, or profit, to the developer is thesimple difference between the sale price of the developed parcel minus the construction costs. The primarydifference between real estate and more traditional financial assets in a real options framework is that thedeveloper must decide not only when to exercise his option to develop, but also what (or how much) todevelop. Relaxing or even eliminating the zoning restrictions that apply to what may be developed on agiven parcel increases the variety of future properties that may be developed, thus increasing uncertaintyover the type and size of structure that will eventually be built. The powerful advantage of this approachover more traditional real estate valuation techniques such as appraisal or discounted-cash-flow lies in thefact that it is a function of readily observable variables and is independent of investors preferences.

Developed properties in this model will be characterized solely by their size, or square footage, q. I willmake the simplifying assumption that the qualitative type of building (e.g. office, retail, industrial,residential) that may be developed is already exogenously determined by the prevailing zoning.Consequently the endogenous choice variable faced by the developer is only quantitative, and notqualitative, in nature. While perhaps unrealistic, this does not affect the models predictions.

The exercise price of development is characterized by the cost of construction C, which is specified to beboth increasing and convex in the amount of square footage developed q:

3For semantic purposes, I will use land to always refer to an undeveloped or vacant plot, whereas property will always refer to adeveloped parcel that possesses a building atop it.


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0dq

Cd

0dq

dC

2

2

>

>

The justification for the second assumption is that labor costs tend to increase as the number of floors in abuilding increases (i.e. unions are more often than not involved in large-scale developments), and alsobecause larger, taller buildings must have deeper foundations and stronger load-bearing frames.

For a given date of development and cost of construction, the developer will maximize his profit bychoosing the optimal building size q* that satisfies:

(1)}q1:)q(Cq{pmaxarg)(pMax*q oq

o =

Where po is the prevailing market price per square foot of a developed property, and is the maximumpermissible building size allowed by the prevailing zoning regime.

The optimal q* is found by differentiating (1) with respect to q. The profit-maximizing building size willsatisfy:

(2)pdq

dCo=

Translated, the developer will continue to build until the value of the last square foot developed is justequal to its sale price. This of course is just the real estate version of the standard equilibrium conditionfound in traditional microeconomics. It should also be noted that because the developer can change q* in

response to changes in p0, that ( p0) is both an increasing and convex function of p0.

Uncertainty enters the model in the form of random realizations of the future sale price of the property in

the subsequent time period, denoted by

~. Because of this convexity property, it follows from Jensens

inequality that:1p

(3)))p~(E())p~((E 11 >

As the variance of the distribution of 1p~

increases, so too does uncertainty and thus the value of vacant

land.

Now, consider the simplest two-period case. The developer can develop today (date 0) or in the next

period at date 1. He will only develop land if it is profitable to do so:(p)>0. I will assume that onlyfuture values of p are uncertain, and not construction costs4. Furthermore, the date 1 price of developedproperty can only take on two values, pu and pd, where pu>pd. Consequently, the profit realized can only

take on two future values ( pu) and ( pd). The rent for a square foot of developed property, Rt, isassumed as exogenous. Finally, it is assumed that there exists a risk-free asset with return Rfand that thereare no taxes, carrying costs, transaction costs or short-selling restrictions. Under this framework, the parcelof vacant land can be considered as a contingent claim security whose date 1 value is completelydetermined by the date 1 value of the exogenously priced asset, p1.

Since there are three existing assets (land, building, and the risk-free investment), then the returns on vacantland can be exactly duplicated by a linear combination of the returns of the other two assets. To solve this,we first determine the state prices (i.e. the cost at date 0 of receiving $1 in one of the two states of nature

4This is not so unrealistic since construction costs tend to be a much more persistent and slow-moving (and thus more predictable)variable than property values, over relatively short horizons.


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and $0 in the other), and then sum the products of these state prices and the land values across the twostates of nature. Let su and sd denote the two state prices for the up- and down-states of nature,respectively. Then, they must satisfy the following two equations:

(5)ssR1

1

(4))s(sRpspsp

du

f

dutdduuo

+=+

+++=

Equation (4) expresses the date 0 price of developed property as a function of its date 1 cash flow.Likewise, equation (5) defines the price of a discount bond as a function of its date 1 cash flows.Rearranging these equations allows us to solve for the state prices in the up- and down-states of nature:

(7)pp

p-)R)/(1Rp((s

(6)pp

)R)/(1Rp((ps

du

ofthd

du

ftdou

++=

++=

Finally, if no opportunities for riskless arbitrage exist, then the price of vacant land at date 0 must be:

(8))s(p)s(pV dduu +=

If the land were to sell at any amount less than this, investors could earn riskless arbitrage profits bypurchasing the vacant land, short-selling the developed property, and investing the net proceeds in the risk-free asset. If the land were to sell at a price higher than the profit that could be realized by developingtoday, the developer will choose to have the parcel lie undeveloped. Otherwise, he will build at date 0 theoptimally-sized building that satisfies equation (2).

II. The Comparative Statics of Land Valuation Under Uncertainty

Uncertainty is defined as the difference between the future sale value of developed property in the up- anddown-states: (pu-pd). It is clear from equation (1) that if the building size q is constrained by some

maximum allowable value , then so is the future realization of 1p~

. Larger buildings are more expensive

than smaller ones. If the constraint is binding, then we have effectively censored the right tail of the

distribution of 1p~

. In the binomial case, this amounts to limiting the difference between pu and pd.

Conversely, if is increased or even eliminated altogether, then we have effectively increased thedifference between pu and pd by allowing pu to take on a higher value. It is readily believable that thiseffect will be real since developers face a very strong economic incentive to build at the highest density (orheight) allowable in a downtown CBD5. This is because land is the relatively scarcer and thus moreexpensive input to development. Consequently, developers will substitute kapital for land in thedevelopment process, which results in higher-density development in CBDs, and lower-densitydevelopment at the urban fringe.

Now suppose the governing municipality eliminates , thus causing the maximum attainable pu to increaseby x dollars. The reader can easily verify that if pd decreases by x(su/sd) dollars, then the state prices willremain unchanged, but we have increased the value of (pu-pd). Now, the new value of vacant land is:

(9)))s/sx(s-(px)s(pV dduduu ++=

Differentiating (9) with respect to x gives:

5Central Business Districts


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(10)))s/sx(s-(px)s(pdx

dVdduduu ++=

It then follows from the convexity of( p) that:

(11)))s/sx(s-(px)s(p dduduu >+

And thus:

(12)0dx

dV >

Hence the value of vacant land is increasing in uncertainty. It also follows that the future volatility ofvacant land values has also increased because (pu-pd) has increased.

The empirical implications of this are straightforward. An increase in uncertainty caused by theelimination of height restrictions should induce a one-time, but permanent, increase in both the value andvolatility of vacant land in the geographic jurisdiction to which the policy change applies. This alsoincreases the opportunity cost of developing land at the current time since it is now more likely that what isthe optimally-sized building today will be suboptimal in the future. This increase in the option value of

waiting implies that more vacant land parcels will lie vacant longer, but what is built will be built at higherdensities. Indeed, this assertion is consistent with what we observe in Philadelphia following theelimination of the height restriction. The city has had a long-standing problem with abandoned, vacantproperties and parcels, but Center City did see a building boom in office towers during this same period.

Williams (1991) summarizes the implications of relaxed zoning on land values nicely (6):

Of these comparative statics [of the valuation of real estate in an options-based framework], onlythe parts played by the optimal and maximum densities are novel to the literature on optionpricing...When zoning restrictions are binding, the maximum density is optimal...The option todevelop is more valuable with a flexible than fixed density. Given a flexible density [relaxedheight restriction], the owner then optimally defers development until he realizes a higher ratio ofrents relative to construction costs. This raises the optimal ratio [of rents to construction costs]and the optimal density [height] of development, and thereby the relative value of the undeveloped

property.

III. A Simple Numerical ExampleConsider a developer who owns a 10,000 square foot lot in Center City, Philadelphia that is zoned for aClass A office building. He may build either 50,000 or 100,000 square feet of space, after which he willsell at the prevailing market price. The developer must make two choices: to build either today or nextyear, and to build either 50,000 or 100,000 square feet of space. Uncertainty enters the model in the formof a currently unknown up-market or down-market state that will be realized next year. The decision rulethat the developer follows is that he will wait to develop if the value of the vacant parcel exceeds the profitthat would be realized from developing today. Otherwise he will build today.

Suppose the current market price of a Class A office tower is $125/SqFt, with an annual rental rate of$25/SqFt. The per unit construction costs of the 50,000 and 100,000 square foot buildings are $100 and

$115, respectively. The up-market price per square foot is $150 and the down-market price is $100.Finally, set the risk-free rate at 2%.

If the developer builds today, he will build the 50,000 square foot building since its profit is greater than ifhe built 100,000 square feet ($1.25m v. $1m). If he waits and the up-market scenario is realized, then it ismore profitable to develop the larger 100,000 square foot building ($3.5m v. $2.5m). Likewise, if thedown-market scenario is realized then he will develop the smaller 50,000 square foot property and justbreak even since developing the larger property would be done at a loss ($0 v. -$1.5m).

Computing the state prices according to (6) and (7) yields values of $.05 and $.93 for the up- and down-market scenarios, respectively. Substituting all of the above into (8) yields a current equilibrium value of$171,569 for the vacant plot, or $17.16/SqFt. A value of anything less than this amount would allow


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investors to earn risk-free arbitrage profits by purchasing the land and hedging the risk by short-selling thebuilding. This would earn a return equal to the risk-free rate, but would require no initial investment.Finally, since the value of the plot is less than the profit that would be realized if it were developedimmediately then the developer is likely to exercise his option to develop in the current period.

Now suppose that uncertainty increases in the form of an increased differential between the up- and down-market prices. It is easily verifiable that if this price differential is greater than $524, then the value ofvacant land will exceed $127.45/SqFt and it becomes unprofitable to build today. Hence the increase inuncertainty has also increased the value of the parcel to the point where the developer will rationally electto defer development to a future period.

IV. The Institutional StoryFor the purposes of empirically testing the models predictions, it is necessary to specify an actual date thatdesignates the policy shift. This is complicated by the fact that the removal of the height restriction wasanything but an exogenous policy shock. Indeed, a long public debate surrounded it. Moreover, it wouldbe difficult to utilize an event-study type of methodology to answer this question since real estate is notblessed with the type of high-frequency transactions data common to so many other financial assets whichallows the researcher to approximate continuous-time representations of valuation. So, it is necessary tobriefly review the institutional background of how the height restriction in Philadelphia came to be

eliminated, and how a particular date can be justified.

Cohen (2000) gives a detailed review of the public debate that surrounded the construction of Liberty One(7). Perhaps surprisingly, this restriction was not statutory nor was it enforceable under any existing laws.Rather, it was part of a long-standing public consensus by the Citys establishment to limit any futurebuilding heights to be no greater than the William Penn statue atop City Hall. Philadelphias famous cityplanner, Ed Bacon, was once famously quoted as saying that Philadelphia has a gentlemans agreement tobuild no taller than the William Penn statue. Whether or not you intend to build taller than William Pennwill tell us whether or not you are indeed a gentleman. (8).

Of course there were other, more formal ways to enforce this restriction. In particular, a line item in thePhiladelphia Redevelopment Authoritys (RDA) charter (implemented by Bacon and his pro-heightrestriction colleagues) limited the acquisition of land parcels to projects that conformed to the height

restriction. Large structures require relatively large plots of land, which are historically uncommon inPhiladelphia due to its tradition of preservation. Consequently, any attempt to assemble parcels into alarger plot essentially required the assistance and approval of the Redevelopment Authority, which had thestatutory power to condemn land. If the developers proposed project was not consistent with the RDAssupport of the height restriction, then it was unlikely to gain approval.

Developer Willard Rouse was the first to successfully challenge this restriction. On April 5th, 1984, hegave a presentation at the Free Library on his proposal to build Liberty One; the first public record of hisintention to develop above the height restriction. A vigorous public debate ensued during the course of thenext year. The primary argument used by the pro-development advocates was that the height restrictionkept needed capital out of Philadelphia due its relative physical underdevelopment. Since Philadelphia hasto compete with other cities for businesses, jobs and residents, they argued, then the citys lack of asufficient building stock to accommodate the desired level of firms and their employees prevented

Philadelphia from competing effectively. Consequently, the height restriction also acted as a self-imposedrestriction on the citys collective economic welfare. The debate culminated on May 17th 1985 when theCity Council formally voted on statutorily implementing a de jure height restriction. The vote failed by ahuge margin, with only two dissenters. Finally, on June 27th 1985 the Rouse company, with the Citysassistance, purchased the parcels on which Liberty One would be built and shortly thereafter commencedconstruction. Construction of the property was completed in 1987.

For the purposes of this paper, I will initially take the date of June 27th 1985 as the date on which therestriction was lifted and future uncertainty thus increased. My argument for this is that everything prior tothis was mere talk. It was only after this date that actual money was committed to the project and itsdevelopment was underway. Later, I will present a robustness check that the choice of this date wasappropriate.


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dtransacteparcelequarter thandyearwhatdenotingablesdummy variofA vectorYear_Qtr

inliesparceltract theCensuswhatdenotingablesdummy variofA vectorTract

saleblanketaofpartwasparceltheifdenotingabledummy variABlanket

iaPhiladelphofCitytheisparceltheofpurchasertheifdenotingabledummy variACity

FDRatioofsquareTheFDRatioDepthtoFrontofratioTheFDRatio

r)rectangula-non(i.e.shapedyirregularlisparceltheifdenotingabledummy variAIrreg

depthsparcel'theoflognaturalTheDepth

frontagesparcel'theoflognaturalTheFront

Dist_CBDofsquaretheoflognaturalTheDist_CBD

CBDthetodistancesparcel'theoflognaturalTheDist_CBD

SqftofsquaretheoflognaturalTheSqFt

footagesquaretotalsparcel'theoflognaturalTheSqft

tat timepricesalesparcel'iththeoflognaturalTheP

:Where

(13))Year_Qtr,Tract,Blanket,City

,FDRatio,FDRatio,Irreg,Depth,Front,Dist_CBD,Dist_CBD,SqFt,Sqft(fP

it

it

it

it

it

2

it

ititit

it

it

it

it

2

it

it

it

2

it

it

it

itititit

2

ititititit

2

itit

2

ititit

=

=

=

=

==

=

=

=

=

=

=

=

=

=

The Dist_CBD variables measure the parcels proximity to downtown, since traditional urban economictheory says that a given parcels value is monotonically decreasing with distance to the CBD. The mostfrequent purchaser of vacant lots (approx. 15% of all transactions) during this time period is the City of

Philadelphia. Hence it is plausible that the City has sufficient market power to affect prices, so the Citydummy variable attempts to proxy for this. Also, approximately 18% of all purchases in the data wereBlanket sales, which are defined as the sale of two or more parcels from the same seller to the same buyerat the same time for one, comprehensive blanket price. Since the square footage of each parcel is known,I compute the price per square foot of the total sale and apply this to the total square footage of eachindividual parcel to recover the parcels implied sale price. Most of these blanket sales are contiguouslyadjacent parcels purchased by a developer who is assembling the parcels for a future development that willspan the assembled lots total area. The Blanket dummy variable will test whether the purchaser isreceiving what amounts to the equivalent of a volume discount on the purchase of real estate, or converselywhether he/she is paying a premium to assemble adjoining parcels. The vector of Tract dummy variablesproxies for the bundle of locational attributes of the neighborhood which each parcel is located in. Finally,the vector of Year_Qtr dummy variables measure the change in average land values over time aftercontrolling for everything else. The estimation results are presented in table three in the Appendix.

VI. Discussion of Regression ResultsThe R2 of the regression is a respectable 57%. Thorsnes (2000) reports an R2 of 67% for his hedonicestimation, but his sample is restricted to residentially-zoned lots only so there is less variation in hissample to explain. The only hedonic variable that is not significant at the 5% level is Depth. Moreover,the results are consistent with urban economic theorys predictions. The value of land is increasing andconcave in its total square footage (SqFt>0, SqFt20, FDRatio2


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counterintuitive, but an examination of these parcels revealed them to typically be located at theintersection of more than two streets, which defined their non-rectangular shape9. Moreover, these parcelswere commonly zoned as commercial-retail. If you believe that retail sales are increasing in the amountof foot and vehicular traffic surrounding the stores location, then it seems likely that a parcel that lies atthe intersection of three streets could be more valuable than a parcel that lies at the intersection of only twostreets since the former would naturally have more traffic than the latter. Hence its value could presumablybe higher.

The City of Philadelphia appears to obtain an average discount of 15% on purchases that it makes (City=-0.15). Besides the fact that the City could plausibly have some price-setting power, the negative sign ofthis coefficient could also reflect the fact that many City purchases are of abandoned properties in marginalneighborhoods that are slated for demolition. So, the negative value of this coefficient could just simplyreflect the fact that City purchases are disproportionately located in relatively low-valued areas. Finally,blanket purchases receive an average discount of approximately 24% (Blanket=-0.24). This could be theresult of two possible factors at work. First, the purchaser could be receiving the equivalent of a volumediscount on land: the more square footage that is purchased, the cheaper the unit price the seller is willingto give. Secondly, many sellers are looking to unload unprofitable, problematic parcels whose tax billexceeds its value. They will often persuade the purchaser, as part of the overall deal, to take these parcelsalong with the relatively more valuable parcels that purchaser is actually interested in. The addition ofthese zero-value (or even negative-value) parcels to the overall blanket sale drags down the average unit

price of land in the transaction.

Finally, the vector of time coefficients is used to construct a hedonic index for vacant land in Philadelphia,which is graphed in Figure 2. The index is re-scaled so that the first quarter of 1980 takes a value of 100,and the vector of time coefficients is applied to recover the implied index. The vertical yellow linedelineates the pre- and post-policy shift periods:

Figu re 2. Hedoni c Index of Phi ladel phia Vacant Land: 1980-1996

70

90

110

130

150

170

190

1980

1980

1981

1982

1983

1983

1984

1985

1986

1986

1987

1988

1989

1989

1990

1991

1992

1992

1993

1994

1995

1995

1996

The terminal value of the index in the fourth quarter of 1996 is 158. This implies that a vacant parcelpurchased in Philadelphia for $100 in 1980 would be worth, on average, $158 by the end of 1996. Thereturn of 58% on this property is quite low considering that the risk-free 1-year U.S. Treasury bill earned

9Although most of Philadelphias street configuration is characterized by a traditional grid pattern, there are several major arteriesthat cut against it, like Passyunk, Ridge and Germantown avenues.


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352% over this same period! (9). Philadelphia weathered some very difficult times in the early 1990s whenit was hit by the double-whammy of a national recession and a fiscal crisis of its own making. Both thebull market in real estate of the late 1980s and the bear market of the early 1990s are observable in theindexs path during these periods.

From the graph, it appears visually evident that both the level and volatility of the index increased post-1985. The average return increased from 1.76% to 2.51% from the pre-1985Q2 period to the post-1985Q2period, while the standard deviation of returns likewise increased by 4% during the same time.

What is perhaps disconcerting is that the volatility of the index post-1985 appears implausibly high. Forexample, from the first quarter to the third quarter of 1992 the index increased in value from 97.7 to 159.1;a percentage increase of 63% in just six months! Further investigation into this revealed that there is somesample selection bias in the timing of sales. The Citys purchases of vacant lots are not uniformlydistributed across time. Philadelphias government will often purchase dozens of lots in one period, andvery few the next. And, most of these purchases are part of neighborhood revitalization initiatives inrelatively low-priced areas of the City that are for less than $1 per square foot. So when such transactionsoccur, it skews that periods distribution of land prices in a negative direction. The flip side of this story isthat purchases of parcels in Center City tend to be relatively rare in the sample, but they occur at very highprices of several hundreds of dollars per square foot. So when such transactions occur in a given year andquarter, they tend to skew that periods distribution of average prices in a positive direction. The sum of

these two effects is that one period of many (low-priced) purchases by the City subsequently followed by aperiod which sees several (very high-priced) purchases in Center City biases the change in the estimatedindex upwards. Additional volatility is thus induced into the index by this sample selection bias.

It is difficult to directly correct for this problem since it would require making assumptions about theunderlying and unobserved stochastic evolution of all land values over time, when in fact we are limited toonly observing those prices for parcels which happen to transact. But in Section VII I break the dataset intoCenter City and non-Center City subsamples, and perform some re-estimations which yield some insightsinto this result.

VII. Hypothesis Tests and Robustness Checks

Hypothesis Test I: A permanent upward shift in land values following the policy changeTo test this, I estimate the following regression:

abledummy varipolicy-postwith thetrendtimetheofninteractioTheg1985Q2_FlaTrend_Time

1985Q2)-(post22tif1ofvalueatakingabledummy variAg1985Q2_Fla

68to1fromvalueatakingvariabletrendtimeATrend_Time

tat timeindexhedonictheoflognaturalTheI

:Where

1,...,68t

(14))g1985Q2_FlaTrend_Time(g1985Q2_FlaTrend_TimeI

tt

t

t

t

tt3t2t10t

=

>=

=

=

=

+++=

This regression essentially fits a time trend to the index that also allows for a discrete jump following theremoval of the height restriction. The null hypothesis is that the policy change did not cause an additionalincrease in the value of the index:

0:oH 2 =

The results are presented in table 4.


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The results are very robust to the idea that the market considered mid-1985 to be the point when theremoval of the height restriction took place. If (14) is estimated with any dummy variable prior to 1985Q2,then the coefficient is not statistically significant at the 5% level (any column below the yellow line denotesinsignificance). One interpretation of this could be that the market considered the period prior to thecommencement of construction to be just talk. That is, no money had yet been committed to the projectprior to 1985Q2, so the market remained skeptical that the policy shift would ever actually be realized.

But the re-estimation of (14) with a dummy variable denoting a time period that is subsequent to 1985Q2 isincreasing in both magnitude and significance. This would be troubling were it not for the fact that theinteraction of the dummy variable with the time trend also becomes negative and grows in both magnitudeand significance as well. Naturally, the interaction term is capturing the negative slope of the index duringthe period of the property markets crash in the early 1990s. As a consequence, the dummy coefficientmust become larger in order to offset this effect and accurately capitalize the one-time, but nonethelesspermanent increase in land values following the policy shift. Hence I conclude that the theorys predictionsare robust with respect to the date of the policy shift that is designated.

Robustness Check II: The increase in land values is confined to the CBD marketTraditional urban economic theory adamantly asserts that high-density developments should occur only in amarkets CBD, where land is the scarcer and thus relatively higher-priced input to property development.There is no economic rationale for building at higher densities outside the downtown area. Consequently,

the increase in land values should be confined to Center City only. To test this, I break the dataset intoseparate Center City and non-Center City subsamples and re-estimate (14). I define Center City as thegeographic area from South St. to Spring Garden, and the Schuylkill to Delaware Rivers. The regressionresults are presented in tables 5 and 6 in the Appendix, and Figure 4 plots the two indices against eachother.

Before examining the two hedonic indices, it is worth discussing the regression results. Outside of CenterCity, the value of a land parcel is still increasing and concave in total square footage (SqFt>0, SqFt20, SqFt2>0). Moreover, these two coefficients are notsignificant for Center City, but removal of one of them will cause the other to be significant in any re-estimation. Distance to the CBD remains decreasing and convex for both subsamples, which implies thatthe benefits of agglomeration are highly localized even within such small geographic area like censustracts. Outside of Center City both depth and the ratio of frontage-to-depth is positive and significant

(Depth>0, FDRatio>0), suggesting that depth is valued over frontage, ceteris parebus. Since most of thismarket is residential (as opposed to commercial) properties, this could be interpreted as a preference forprivacy and quiet since distance to the noise and congestion of the street is increasing in a lots depth.

Finally, it is interesting to compare the values of the coefficients denoting land purchases by the City ofPhiladelphia. While the city of Philadelphia appears to receive a discount on land purchases outside ofCenter City (City=-0.21), the city pays a positive and significant premium on purchases in Center City(City=0.29). The former result is easily explained by the fact that most of the citys land purchases areprimarily for the demolition/revitalization of problematic properties in low-priced neighborhoods. But the(more interesting!) latter result could be explained by both the citys presumed desire to promote high-profile developments in its downtown area as well as an indicator of the high cost of development inPhiladelphia. Most major downtown development deals require the host citys assistance and approval.Where costs are so high as to effectively proscribe profitable development, the city may be willing to

subsidize the project by facilitating the assembly of smaller parcels into a single large one by applying itspowers of condemnation and directly purchasing the land for re-sale to the developer. Of course, it is alsopossible that the City could be convinced to subsidize a high-profile development even though such adevelopment would be profitable in the absence of public subsidy. But such a conclusion would require anexamination of the relative inelasticities of the Citys demand curve and developers supply curve, whichare unobservable. A review of the data suggests that the former explanation appears to be the case in mostof the transactions..

To test the hypothesis that the increase in land values accrues only to parcels in the downtown market, I re-estimate (14) using the two geographic subsamples separately. The results are presented in table 7.


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Table 7. Regression Results from Robustness Check II

Non-Center City Center City

VariableParameter

Estimate

Standard

Error

t-

ScorePr>|t|

Parameter

Estimate

Standard

Error

t-

ScorePr>|t|

Intercept 4.531 0.07088 63.93


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for removing the height restriction. This is an interesting and important question, but for the purposes ofthis paper I would argue that it does not matter. It may be unclear whether or not the policy change causedthe building boom or whether the economic forces caused by inter-city competition for businesses and jobsforced the policy change. But what is clear is that the building boom most certainly could not haveoccurred in the absence of the policy shift.

Hypothesis Test III: A permanent increase in the volatility of land values following the policy shiftRelaxing the zoning laws that apply to a particular land parcel increases the uncertainty of what size andtype of building will eventually be developed on that parcel. This is exactly analogous to increasing thevariance of future returns on the underlying asset in the Black-Scholes framework (1973). In this particularexample, we are interested in testing whether the policy change also induced further volatility of thehedonic index around its long-run mean. To test this, first note that the regression specification in (14) isessentially fitting a long-run trend line with a discrete jump to the hedonic index. Hence the residuals fromthe regression may proxy for the volatility of the index around its mean. So I proceed in the manner ofSchwert (1990) and Walsh (1998) by using the squared residuals from (14) in a specification that regressesthe squared residuals on an intercept and a dummy variable denoting the post-policy shift period:

1985Q2)-(post22tif1ofvalueatakingabledummy variAg1985Q2_Fla

tat timeindexhedonicthefromresidualsquaredtheoflognaturalTheR

:Where

1,...,68t

(15)g1985Q2_FlaR

t

t

t10t

>=

=

=

+=

The null hypothesis is that the policy change did not cause an additional increase in the volatility of theindex:

0:oH 1 =

The results are presented in table 9.

Table 9. Regression Results from Hypothesis Test III: R2=0.063

Variable Parameter Estimate Standard Error t-Score Pr>|t|

Intercept -6.08622 0.49482 -12.3 |t|

Parameter

Estimate

Standard

Error

t-

ScorePr>|t|

Intercept -5.35189 0.504 -10.6


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Table 3. Regression Results from Hedonic Estimation Using the Full Sample, R2=0.5743

Variable Parameter Estimate Standard Error t-Score Pr>|t|

Intercept 3.07284 0.59667 5.15


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Figure 4. Center City v. Non-Center City Hedonic Indices

0

50

100

150

200

250

300

1

980

1

980

1

981

1

981

1

982

1

982

1

983

1

983

1

984

1

984

1

985

1

985

1

986

1

986

1

987

1

987

1

988

1

988

1

989

1

989

1

990

1

990

1

991

1

991

1

992

1

992

1

993

1

993

NonCC Index

Ctr. City Index


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Endnotes

1) Access Press,Access Philadelphia (HarperCollins Publishers), 1998, pp. 63-64.

2) Access Press,Access Philadelphia (HarperCollins Publishers), 1998, pp. 63-64.

3) Access Press,Access Philadelphia (HarperCollins Publishers), 1998, pp. 84.


5) www.skyscrapers.com

6) Williams, Joseph T., Real Estate Development as an Option, Journal of Real Estate Finance andEconomics 4, 1991 pp. 196-198.

7) Cohen, Aaron Zal, A Tombstone for the Philadelphia Gentleman, 2001, forthcoming.


9) Center for Research on Security Prices, University of Chicago.
http://www.skyscrapers.com/http://www.skyscrapers.com/


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REFERENCES

Access Press,Access Philadelphia (HarperCollins Publishers), 1998, pp. 63-64.

Black, Fischer and Myron Scholes, The Pricing of Options and Corporate Liabilities, Journal of PoliticalEconomy, May/June 1973, 81, pp. 637-659.

Breusch T., and A. Pagan, A Simple Test for Heteroscedasticity and Random Coefficient Variation,Econometrica, 1979, 47, pp. 1287-1294.

Bulan, Laarni, Mayer, Christopher, and Tsur Somerville, Irreversible Investment, Real Options andCompetition: Evidence of Real Estate Development, Working Paper, September 2001.

Cox, John C., Ross, Stephen A., and Mark Rubinstein, Option Pricing: A Simplified Approach, Journalof Financial Economics, September 1979, 7, pp. 229-263.

Cohen, Aaron Zal, A Tombstone for the Philadelphia Gentleman, 2001, forthcoming.

Merton, Robert C., Theory of Rational Option Pricing, Bell Journal of Economics, Spring 1973, 4, pp.141-183.

McMillen, D.P. and J. F. McDonald, A Simultaneous Equations Model of Zoning and Land Values,Regional Studies and Urban Economics, 1991, 21, pp.55-72.

McMillen, D.P. and J. F. McDonald, Urban Land Value Functions with Endogenous Zoning, Journal ofUrban Economics, 1991, 29, pp.14-27.

Pogodzinski, J.M. and T. R. Sass, The Theory and Estimation of Endogenous Zoning, Regional Scienceand Urban Economics, 1994, 24, pp.601-630.

Quigg, Laura, Empirical Testing of Real Option-Pricing Models, The Journal of Finance, June 1993, 48,2, pp. 621-640.

Schwert, William G., Why Does Stock Market Volatility Change Over Time?, The Journal of Finance,December 1989, 44, 5, pp. 1,115-1,147.

Thorsnes, Paul, Internalizing Neighborhood Externalities: The Effect of Subdivision Size and Zoning onResidential Lot Prices, Journal of Urban Economics, 2000, 48, pp. 397-418.

Titman, Sheridan, Urban Land Prices Under Uncertainty, American Economic Review, 75, pp. 505-514.

Walsh, David M., Evidence of Price Change Volatility Induced by the Number and Proportion of Ordersof a Given Size, Australian Journal of Management, June 1998, pp. 39-55.

Williams, Joseph T., Real Estate Development as an Option, Journal of Real Estate Finance andEconomics 4, 1991, pp. 191-208.

White, H., A Heteroscedasticity Cosistent Covariance Matrix Estimator and a Direct Test ofHeteroscedasticity, Econometrica, 1980, 48, pp. 817-818.

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