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Permits, starts, and completions : structural relationships vs. real options Somerville, Tsur Feb 28, 2001

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     CUER Working Paper     C. Tsuriel Somerville Permits, Starts and Completions: Structural Relationships vs. Real Options December 2001 CUER Working Paper 01-03                                 CENTRE FOR URBAN ECONOMICS AND REAL ESTATE Faculty of Commerce & Business Administration, University of British Columbia 2053 Main Mall, Vancouver, B.C., Canada V6T 1Z2  T 604 822 8399, F 604 822 5350,   Permits, Starts, and Completions: Structural Relationships vs. Real OptionsC. Tsuriel Somerville§forthcoming in Real Estate Economics*The author wishes to thank Amir Hossein Sepasi for excellent research assistance.  Thecomments of  Joe Gyourko, Chris Mayer, Danny Quan, Stuart Rosenthal, and the unnamed referees,as well as participants at the AREUEA midyear meetings and UBC Urban Land Economicssummer symposium are greatly appreciated.   This work was supported by a UBC-HSS grant andthe Real Estate Foundation of British Columbia.    § Faculty of Commerce & Business Administration, University of British Columbia, 2053 Main Mall,Vancouver, BC V6T 1Z2 Canada, tsur.somerville@commerce.ubc.caAbstractReal estate development from raw land to completed structures is a multi-stage process.  Given thecurrent view of development as the exercise of a real option, the question arises whetherdevelopment should be modeled as a compound option.  This paper tests the validity of thecompound option characterization by determining whether builders start units for which they havepermits and then complete units started in a fashion consistent with the predictions of the realoptions model.  To do so, we first identify a reduced form relationship between permits and startsand then between starts and completions.  The parameters of this relationship indicate how wellpermits proxy for starts and starts for completions.  Then, we determine whether controlling forthis structural relationship, new information and uncertainty in returns affect permit exercise andcompletion rates as would be the case if these actions were the exercise of real options.  We findthat current and previous quarter permits forecast current single family starts, while multi-familystarts require more quarterly lags of permits.  More than one and two year’s worth of lagged startsnumbers are needed to estimate current quarter completions for single and multi-family buildingsrespectively.  The principal result is that once building permits have been obtained, thedevelopment process proceeds to completion.  While there is no evidence that completion is theexercise of an option embedded in a start, some aspects of starts are consistent with builderstreating them as an option for starts.  However, even if they do, it takes large changes in marketconditions to affect small changes in starts. 1IntroductionReal estate development is now modeled as the exercise of a real option.  The entire process ofbringing raw land into developed use or redeveloping existing sites is not a single step, but aseries of irreversible investments.  Rather than a single option, this suggests modelingdevelopment as a compound option.  While theoretically appealing this may not be realistic if thetotal cost of delay for some stages is higher than the benefit builders would get from doing so.  Inthis paper we test the empirical support for compound options by determining whether buildertiming of starts and completions is consistent with these activities as the exercise of distinct realoptions.  To do so we first identify the reduced form relationships between permits and starts andbetween starts and completions separately for single and multi-family construction.  This has theadded value of indicating how effective permits and starts are as proxies for starts andcompletions. The relationship between permits, starts, and completions is important for housing marketresearch, analysis, and forecasting.   Statistics on residential construction are subject to intensescrutiny because construction tends to lead both recessions and recoveries (Green 1997).  Buildingpermits and housing starts are used to gauge construction activity, yet they measure differentphenomenons.  Permits are the permission to build, while a start occurs with the beginning ofconstruction, typically defined as when a foundation or slab is laid.  The issuance of a permit is noguarantee that construction will occur.  Starting construction does not ensure that construction willbe completed in a timely manner.  If the exercise and completion decisions are sensitive to marketconditions, then the economic impact of building permits and housing starts will not be constantover the market cycle.  For researchers these differences raise the question whether using permits2to proxy starts or either in place of completions introduces bias or extra noise in housing supplystudies.1 The results of the analysis presented here indicate that single family permits for the current andprevious quarters do an excellent job of describing starts.  Within three months, 95 percent ofsingle family permits are exercised, although only 14 percent are exercised in the month of issue. In almost all cases, once a unit is started, it is completed.  For single family construction, 41percent of starts are completed within three months, and 99 percent within a year after that. Theexercise rate for multi-family permits is slower: 8 percent of permits are exercised in the month ofissue, after the same three months only 54 percent of permits have been exercised, and it takes 15months to reach an exercise rate of 94 percent.2  Construction time is substantially longer too: ittakes 26 months to achieve a completion rate of 95 percent. In this paper we study whether real estate development is best treated as a compound option.  Weassume that in total real estate development is the exercise of a real option, but investigate whetherit is appropriate to interpret the final two stages of the development process, starting a unit forwhich a permit has been obtained or pulled and completing a unit that has been started, as theexercise of separate real options.  We use two approaches for this test.  The first is based on thefundamental result of the real options model that, controlling for the discount rate, increases in thevolatility of returns slows option exercise.  Because of potential problems with both the empiricalapplication of this test and the quality of the measures for forward-looking uncertainty, we also usean indirect test.  In a real options model, new information affects exercise behavior because thebenefit of the option is the ability to delay until the flow of information reveals more about the3state of the world.  We identify whether builders respond to shocks that occur after permits arepulled or units started by changing the timing of starts or unit completion as would be the case ifthese actions are the exercise of  real options. Our results are mixed.  Uniformly, estimates of demand volatility have no effect on permit exerciseor completions.  In contrast, new information does affect the timing of starts, which is consistentwith permits as real options.  Even so, it takes large shocks to trigger small changes in starts.  Theinherent problems of using a backward measure of demand volatility to proxy for forward-lookinguncertainty in returns, we place less analytical weight on the former result.  There is no robustevidence from either approach that the completion of construction is the exercise of a real option. Given the strong evidence Holland, Ott, and Riddiough (2000) and Bulan, Mayer, and Somerville(2000) present that development is the exercise of a real option, our results indicate that the mostimportant exercise decision occurs by the time a permit is obtained.  The latter stages have optionproperties, but builder behavior indicates that the benefits to delay must be at best only slightlygreater than the total cost of doing so.  The remainder of the paper is structured as follows.  First, we outline the theoretical construct ofthe real options model and empirical specification used in this paper.  Second, we review theexisting literature on the relationship between permits, starts, and completions and the empiricalapplication of real options theory in real estate.  We then present the Canadian data and theempirical results, and finally conclude the paper with some thoughts on future research.Testing Permits and Starts as  Real Options4Over the last fifteen years there has been a tremendous volume of research on the application ofoption theory to investment in real assets under uncertainty.3  The basic real options model findsthat increases in uncertainty in the future returns on an asset increase the value of the option toinvest, delaying actual investment.   For the model to hold the investment must be able to bedelayed, at least partially irreversible, and uncertainty about asset values must be revealed overtime.  There are two approaches to determine the timing of individual investments, dynamicprogramming and contingent claims.  The former imposes fewer restrictions, as the latter relies oncomplete markets and a no-arbitrage condition to achieve a solution.  In both cases the solutiondepends on the uncertainty of future returns.  In the absence of complete markets the solutionrequires a project specific discount rate and either the expected asset appreciation or the dividend(convenience) yield.  With complete markets, the CAPM is used to replace the project specificreturns with the risk-free rate of return, market price of risk, market uncertainty, and the asset’sbeta.  There are a number of factors can weaken or even reverse the basic investment activity anduncertainty relationship that are particularly pertinent for development.  Bar-Ilan and Strangedemonstrate that in either the presence of long lags (1996) or if investment process ischaracterized as a series of multiple options (1998) that uncertainty can actually increaseinvestment activity.  Grenadier (1999) presents a Cournot-Nash equilibrium where the optionvalue falls with the number of competitors.  There are institutional factors specific to residential development that can limit the applicability ofthe real options model.  The terms of construction loans impose a fixed duration and completion5must occur without excessive delay.  While these are negotiable, in a repeat financing game thesignal and cost from violating terms may be high.  Building and development permits typicallyrequire that construction begin within a fixed interval following issuance and proceed at areasonable rate.  While permits have the potential to be renewed, there is no guarantee.  Theseconditions limit the ability to or the returns from delay.  Our data do not allow us to address all ofthese complications, which limits the efficiency of our tests.  However, we are able to observe ifbuilders respond to new information in starting and completing units, as required in the realoptions model.   To start construction a builder must first obtain a building permit.4  If all permits are immediatelyexercised by starting construction and all starts completed as expeditiously as possible, then thestart and completion decisions are not control variables, but technical steps in the housingproduction process.5  In contrast, if builders treat these stages as the exercise of real options, thendepending on the evolution of market shocks, a builder with a permit in hand will choose to delayor accelerate the start of construction, and a builder who has commenced construction willaccelerate or lengthen the construction process.  For both permits and starts there are arguments in favor of each framework.  Though the permititself is typically inexpensive, many impact fees are paid and property taxes can rise at the time apermit is drawn.  Liquidity constrained builders are likely to wait until they are ready tobuild to obtain permits.  With a fixed life and renewal uncertain, there can be a high cost toobtaining a permit too early.  Alternatively, if there are time or fixed costs in applying for a permitor uncertainties about how future development applications will be treated by the land use6regulatory process, then builders and developers have an incentive to bank permits and use them asmarket conditions dictate.  Completions should occur promptly because an uncompleted unit issusceptible to weather damage, vandalism, and theft.  Most builders are capital constrained, withtight cash flows, which limits their ability to hold unfinished units.  To minimize agency costs,most construction loan contracts demand timely completion of units.  On the other hand, completionclearly involves additional capital outlays and slowing construction or abandonment may well bethe optimal strategy if the change in return from completing rather than abandoning or delayingdoes not outweigh the marginal cost of the action.  We test whether or not builders treat permits or starts.  To do so,  we determine whethercontingent on the number of permits drawn (units started), starts (completions) fall with increaseduncertainty in future real estate returns or change with new information on market conditions.  Thepermit confers the right, but not the obligation to build so our prior is that builders do treat permitsas options.  For the decision to complete construction, our prior is that this is not a real optionbecause holding costs and the terms of construction loans severely limit the ability to delay.  Inboth cases, this ability is constrained, so any real options behavior should be modest at best.  Below we present the empirical specification.There is some vector X that contains the market information that causes a builder to obtain a permit(start construction).  In a starts (completions) regression, where current and lagged permits (starts)are on the right-hand side, the only component of X that matters for starts (completions) is theinformation orthogonal to the decision to pull a permit (start construction). Current and laggedpermits pmt to pmt-k (current and lagged starts st to st-k) must embody market information and past7st pm X rtct s X rtk t k t tj t j t tkkjj= å + + += +å + +--==b gs hd m ls k0022shocks.  Discrete time ensures that Xt will contain current period information that arrives afterpermits are pulled (units started).6  Thus, when X is included along with current and lagged permits(starts) it will describe new information that affects the exercise decision because other relevantinformation is embodied in current and lagged permits (starts).  As a more formal test we addmeasures of market volatility Ft2 and the risk free rate of interest r, generating the followingregression  specifications:(1)The explicit test for real options behavior is whether the coefficients on F2 is statistically differentfrom zero and negative.  Our implicit test depends on the signs and significance of  $ and : ,which indicate whether builders update their decisions given new information.   The Existing LiteratureThe Relationship of Permits, Starts and CompletionsThe nature of the U.S. time series for housing starts makes precise estimates of the relationshipbetween permits and starts hard to achieve.  In the United States, the starts series is derived fromsamples rather than complete count data.  The permit series is a complete count, but only forreporting jurisdictions, currently 8,500 for the monthly data and 19,000 for annual numbers. Goodman (1986) proposes using  information in the permits numbers to develop a more preciseestimate of actual starts than is possible with the starts survey alone.  One justification he uses forthis approach is a set of relationships he derives from Census Bureau data to indicate that within8six months, 99 percent of the permits pulled in a given month eventually become starts.7  Thispaper revisits these relationships using Canadian metropolitan area data.  These data haveadvantages over the U.S. series which we outline below in section IV.  Other contributions hereare that we estimate the structural relationships for permits, completions, and starts for both singleand for multi-family construction.Coulson (1999) applies an inventory framework to monthly time series of US national housing datato study the relationship between starts and completions.  He concludes that unfinished units, thosestarted but not completed, act as an inventory for housing production.  This determines starts: asunits are completed, they leave the inventory and new units are started to replace them.  This has avery appealing intuition, treating residential investment like other types of inventory investment. Despite its conceptual appeal, the empirical research on manufacturing inventories has struggled tofind empirical support for this approach.8  The analysis here differs from Coulson’s work in goals, data, and methodology.  First, this paperhas the added goal of determining whether the permit exercise and construction completiondecisions of builders are consistent with the real options model of real estate development. Second, we compare both permits with starts and starts with completions and extend the analysisto study both single and multi-family construction using metropolitan area panel data.  Oneadvantage of using data at the level of housing markets is that it avoids some of the aggregationproblems identified in Goodman (1998).  Finally, the characterization of construction in this paperis more consistent with the institutional framework of the development process.9It is hard to reconcile the inventory model with the standard terms of a construction loan.  Treatinghomes under construction as inventory means that there are always a certain number of unfinishedunits waiting for sufficient demand, or their explicit purchase by consumers, to justify theircompletion.  Yet, residential construction is a highly leveraged enterprise: builders obtain short-term construction loans for upwards of 75 percent of total project costs.  It is a standard provisionof these loans that the builder must complete construction expeditiously.  Leaving units unfinishedas part of an inventory works against the interests of lenders who experience higher default riskwith no additional upside gain from project delays.  While there are units for which construction ishalted, the existence of such units is not itself evidence of delay in option exercise.  Finally, it isnot clear why inventory behavior should occur at the construction stage.  Builders and developerswith sufficiently deep pockets or vendor financing can develop an inventory of raw land, serviced lots, or in the case of urban environments, built-up properties suitable for redevelopment ordevelopers may hold options on sites rather than purchasing them outright.9  Empirical Studies of Real Options in Real EstateThere is a well-developed theoretical literature on the application of real option models todifferent aspects of real estate development.  Early applications include Titman (1985) andWilliams (1991).  This framework has been applied toe city growth (Capozza and Helsley 1990),overbuilding in office markets (Grenadier 1995a), leases (Grenadier 1995b), and regulatorytakings (Riddiough 1997), among other papers. In contrast, the empirical literature is quitesparse.10  Using micro data on sales of undeveloped industrial land in Seattle, Quigg (1993) estimates the10development option to be worth 6 percent of site value.  She uses hedonic regressions to estimatetransaction values by parcel and backs out intrinsic values from rents.  The option value is thedifference between the two.  One problem with her methodology is that even a small predictionbias in her hedonic specification can generate large errors in her estimates of the option value.  Aswell, she only has a derived measure of volatility.  Holland, Ott, and Riddiough (2000) are the first authors using real estate data to find that aggregateinvestment, new construction, falls with higher levels of uncertainty in real estate prices or returns. They test all elements of the solution for real options under a complete markets assumption foreach of several classes of investment real estate.  Using two different measures of uncertainty, aforward-looking version derived from mortgage spreads, and the standard deviation of recentREIT returns.  They find that new construction activity falls with the volatility of expected realestate asset returns.  However, not all estimated coefficient signs and significance fit the CAPMframework, most likely because of  the absence for real estate of complete markets.  Bulan, Mayer, and Somerville (2000) present a micro-data analysis of the real options model. Looking at the timing of individual developments in a duration model of development, they tie theempirical analysis to the fundamental prediction of the model, that increased uncertainty delaysdevelopment, rather than stopping it completely.  They find robust support for the model, highervolatility in returns lowers the hazard rate and the effect is significant.  As noted above, theempirical analysis here differs from these papers because we focus only on whether it isappropriate to treat permits and starts as separate options, rather than testing if the developmentprocess in the aggregate reflects the exercise of a real option.  11Data DescriptionThis study uses an unbalanced panel of quarterly time series data for 15 Canadian censusmetropolitan areas (CMAs).11  CMAs in the data include all major Canadian metropolitan areas,but exclude several smaller CMAs with incomplete data, including St. Catharines-Niagara, SaintJohn, and St. John’s. Canadian data offer a number of advantages over similar series for U.S.metropolitan statistical areas (MSAs).  First, permits, starts, and completions series are availablefor CMAs for more than twenty years.  These quarterly series are formed from data reported by alljurisdictions in each CMA, though the monthly series use sampling for communities of less than10,000 population for two out of three months each quarter.  Third, these series are a census of allactivity in a jurisdiction, rather than a sample, as they are in the United States.  Finally, over thelast twenty years the geography of  CMAs  changed less dramatically than has that of MSAs. Table 1 presents the pooled means and standard deviations as well as the minimum and maximumCMA mean values.  Permits, starts, and completions vary with the large differences in city sizesand growth rates.  Overall, real house prices between the mid-1970's and mid-1990's have beenessentially flat.  The mean quarterly percentage increase in real house prices for single family unitswas -0.003 percent.12  This does vary widely by city:  ranging from a low of -0.49 percent inRegina to a high of 0.92 percent in Vancouver (all cities experienced nominal price increases).The house price series are created from median sales prices reported by the national realtor RoyalLePage for two storey mid-market single family units.  Their brokers provide quarterly mediansales prices for select cities by house type in major Canadian CMAs, creating a data set similar tothe NAR median house price series in the United States.  The alternative cross-CMA measure isthe Statistics Canada new housing price index.  Comparing both to a repeat sales house price12series for Vancouver demonstrates the superiority of the Royal Le Page data, principally becausethe Statistics Canada new house price series fails to adjust for changes in the location of newconstruction.13   Over the 1983-93 trough to peak for Vancouver prices, the real repeat sales indexof single family house prices increased by 114 percent.  This compares with 108 percent for theRoyal LePage series and a decrease of 4 percent for the Statistics Canada series.  The correlationswith the real repeat sales index are 0.95 and 0.16 respectively. The standard test for real options behavior is whether controlling for the discount rate, increases inuncertainty in asset returns lowers housing starts and completions.  The volatility of the percentagechange in house prices describes this uncertainty for geometric Brownian motion.  We also use thevolatility of the vacancy rate and the number of competed but unsold units to characterize theuncertainty facing builders because studies such as DiPasquale and Wheaton (1994) and Mayerand Somerville (2000) have shown that prices are not a complete sufficient statistic for demand.The commonly used measure of volatility, the standard deviation of recent returns, is problematicfor our data.  Papers using financial markets data such as Leahy and Whited (1996) and Holland,Ott, and Riddiough (2000) can use daily returns over the previous month or quarter to generate thistype of measure of uncertainty.  With quarterly data, a measure of forward-looking uncertainty inreturns of this type would have to be based on quarterly returns over the past eight or more years. To obviate this problem we use a Garch conditional variance estimate for the percentage change inreal house prices, vacancy rates, and the number of completed but unsold units.   This measure isgenerated as follows.  Let %)pit be the percentage change in real house prices for period t inCMA i.  In the first stage of the Garch we estimate an ARMA(1,1) model for %)pit:13% %, , ,D Dp pi t i i i t i i t it= + × + × +- -a a a e e0 1 1 2 1$ $, , ,s b b s b m mi t i i i t i i t it2 0 1 12 2 1= + × + × +- -(2)The vector of residuals  , from (2) is used to estimate the conditional variance itself.  Themaximum likelihood estimator of the conditional variance is a (1,1) process:(3)Garch offers a particular set of advantages for our data. First, the Garch is a reduced form of Loand Wang’s (1995) methodology for option pricing when asset returns have an auto-regressivecomponent, which Case and Shiller (1989) and Quigley and Redfearn (1999) show applies tohouse prices.  Second, uncertainty is a function of deviations from predicted values, whichcontrols for the serial correlation in real estate values.  Because this is not the standard deviationin future returns that is part of the explicit real options model, we cannot estimate modelparameters.  However, higher deviations from expected values, which yield higher Garchestimates of the conditional variance, are consistent with higher volatility in returns.  Theweakness of this approach is that our per CMA series size is too small for consistent estimation ofa Garch model that is asymptotically accurate.  With this in mind we find volatility measures varydramatically across cities.  For instance, mean house price volatility in Vancouver is 70 times thelevel in Saskatoon.  Our panel has up to 100 quarters of data for some CMAs, with no more than 15 cross-sectionalobservations.  This difference can result in estimation problems because of the time seriesproperties of the data.  In Table 2 we present the results of Im-Pesaran-Shin (1997) panel unit root14tests and the number of CMAs for which a series is I(1) and I(0) based on individual by CMAaugmented Dickey-Fuller tests.  We find that variables that can increase without bound, such asreal house and lumber prices and rents, are non-stationary.  We would expect the stock of housingalso to be non-stationary.  Since starts, permits, and completions describe changes in the stock,they should be I(0), which they are in these data.14  Intuitively permits, starts, and completionsshould move together, but as stationary series they cannot strictly be co-integrated.   The number ofcompleted but unsold units is stationary, but with a lower level of confidence, the same is true withthe vacancy rate.  The former should follow starts, while the latter seems unlikely to be a variablethat can increase without bound.  Our empirical analysis uses only stationary series, so for any I(1)series we use differences in the regressions.  Empirical ResultsStructural RelationshipsWe first identify the reduced for parameters for the structural relationship between permits andstarts and between completions and starts for both single-family and multi-family construction. These tests are presented for both monthly and quarterly series.  The monthly series allow a moreprecise identification of the relationship, are consistent with the data periodicity used byforecasters and market analysts, and generate results that allow a direct comparison with USparameters cited by Goodman (1986).  Results for quarterly series are useful because most MSA-level housing market research uses quarterly data.  As well, to test for behavior consistent with thereal options model we need to have series that are of the same quarterly periodicity as the othervariables in the data.15Table 3.1 summarizes the monthly starts-permits and completions-starts relationships for singleand multi-family units in an unweighted pooled sample of fifteen CMAs between 1972 and 1998. Table 3.2 does the same for quarterly data.  The structural relationships are identified with OLSregressions of starts on current and lagged permits and completions on current and lagged startswith monthly or seasonal dummies.  The actual regression results are presented in Tables A-1 andA-2 in the appendix.  There are very clear differences between single family and multi-family construction.  While 94percent of single family permits are exercised within 90 days of being obtained (pulled), thecorresponding figure for multi-family permits is only 55 percent.  For the latter, it takes more than10 months before 95 percent of permits obtained in a given month are exercised.  A number offactors may contribute to this lag.  Multifamily construction tends to be subject to far more rigorousland use regulation than is the case for single family units.  As a result, builders may choose to taketheir permits as soon as possible to protect against any changes in the regulatory regime. Financingmay also play a role in the longer lags.  For strata-title (condominium) multi-family construction inCanada, permits must be obtained before units can be pre-sold, and a certain  percentage of pre-sales are a condition for obtaining for financing.  Depending on the rate of pre-sales there could bea non-trivial lag between obtaining permits and commencing construction.  The quarterly data inTable 3.2 are consistent with these results.  For single family permits approximately 100 percentare exercised in the quarter of issue or with a one quarter lag.  Over the same period only 66percent of multi-family permits are exercised.Comparing the figures derived from Canadian metropolitan area data with those compiled for the16United States national series by Goodman (1986) reveals a number of differences.  Goodmancalculates that 56 percent of permits are started the same month of issue, and 80 percent with onemonth lag, and 94 percent with a three-month lag.  From Table 3.1, the exercise rate in Canadiancities for both single and multi-family development in the month of issue is substantially lowerthan the figures calculated by Goodman, 14 and 8 percent respectively.  For single family permits,the rate increases rapidly to 64 percent after a one month lag and essentially all permits are issuedafter a lag of three months.  For multi-family construction, the exercise rate increases over time,but at 63 percent after a three-month lag, remains much slower than Goodman’s figures.15  Whetherthis difference is an artifact of the data, because we examine Canadian metropolitan areas, orbecause they represent actual counts rather than sampling is hard to determine.  However, becausethey are based on complete counts rather than sampling, they should inspire more confidence thanthe figures reported by Goodman.Single family units are completed much more quickly than multi-family units.  Within 120 days ofstarting construction, 54 percent of single family units are completed, though it takes another 10months for completions to reach 90 percent of starts.  It takes one year before 50 percent of multi-family starts are completed, and another year on top of that to reach a 95 percent completion rate. The long construction periods are rather striking.  Part of the long lag for single family constructionmay be because of contract construction, where an owner of a site contracts with a firm to custom-build a unit if builders are better able to keep contractors to schedule than are individuals.  Formulti-family construction, large buildings take time.  The translation of starts into completions isnot sufficiently quick to inspire confidence in using quarterly starts data to describe the evolutionof the stock unless a large number of lagged values are included.  This is an issue for stock-flow17models where researchers have tended to let current period starts or permits determine theevolution of the stock with few if any lags.Testing for Real OptionsThis paper uses two approaches to test for real options behavior in the exercise of permits andcompletion of units.  The first is the inclusion of measures of return volatility, described by thevolatility of demand, and the risk-free rate to the regression specifications from Tables 3.1 and 3.2.  If builders treat these stages as the exercise of real options, than the coefficients on bothvariables should be negative in both the starts and completions regressions.  The second approachdetermines whether builder reaction to shocks reflects real options exercise.These specifications both suffer from potential simultaneous equations bias.  Market conditions aremeasured as the percentage change in real house prices and the number of completed butunoccupied units for single family activity, and the percentage change in real house prices, realrents, and the vacancy rate for rental units for multifamily units.  All these measures areendogenous to new construction activity.  We instrument for the market condition variables inevery regression specification.  Instruments include lagged values of percentage change inpopulation and provincial employment, mortgage rates, and lagged own values.  A comparison ofregressions with and without instrumental variables, indicates that the IV methodology has theexpected effect on coefficient values and increases standard errors. Starts as the Exercise of an Option Embedded in Permits.  Tables 4.1 and 4.2 present theanalysis for determinants of quarterly single family and multi-family starts respectively.  Both18tables included current and lagged permits issued and the number of lags of permits issued that areconsistent with the structural results summarized in Table 3.2.  For single family units, theregressions in Table 4.1 show that builders change their exercise rate of permits with newinformation on housing market conditions.  Uniformly, controlling for permits drawn to date, startsrise with increases in the quarterly percentage changes in real house prices.16  The effect isstatistically different from zero but quite small.  Applying a two percentage point increase in thequarterly percentage change in real house prices in regression (4), equal to an annual real increaseof 8.2 percent, raises starts by 27 units, or 3.1 percent of the mean.  These effects are quite small,the price increase is 1/3 of a standard deviation while the effect on starts is only 2 percent of thesame. Converting this to an elasticity for Vancouver yields a paltry 0.007.  In the presence of sticky prices, other variables must adjust to equilibrate the market.  Followinghousing supply side work we use the number of completed but unsold units as an alternativemeasure of demand.17   Increases in this measure lower the exercise rate on permits.  However,both the magnitude of this effect and the elasticity are also quite small: from regression (2), a onestandard deviation increase in the number of completed and unsold units lowers quarterly starts by37 units or 4.3 percent, an elasticity of only 0.038. Changes in lumber prices have a positive effect on permit exercise, the reverse of our expectationsthat higher input costs reduce starts.   One possible explanation is endogeneity: national lumberprices move with aggregate national construction and most CMAs move with the national cycle. We cannot easily correct for this endogeneity because we lack instruments for lumber prices thatare independent of those used for the measures of demand.  19The new information approach suggests that indeed builders treat permits as options.  However,when we explicitly test the relationship between permit exercise and volatility, we find thedemand uncertainty has no statistically meaningful effect on permit exercise.  Adding estimatedconditional variance measures to regressions (4)-(7) of Table 4.1, we find that while house pricevolatility affects the exercise of starts in the expected negative direction, the coefficient onvolatility in the number of completed but unsold units has the “wrong” sign.  In both cases theestimated coefficient is never statistically different from zero.18  The risk free rate of return is part of a formal test of the real options model when there arecomplete markets.  However, depending on assumptions about the relationship between the risk-free rate and other variables in the real options model, then increases in the risk-free rate canaccelerate or delay option exercise.  Uniformly the coefficient on the risk-free rate is notstatistically different from zero, though it tends to be negative.  One complication is thatconstruction loans tend to have adjustable rates, so higher real rates will also mean higher projectcosts, which would make builders less likely to begin construction.  This is not for option exercisereasons, but because construction costs, labor, materials, and financing costs, are now higher.  New information about market conditions also affects the decision to exercise multi-familypermits.  Contingent on  permits issued, Table 4.2 shows that the effects of changes in real rents(regression 1), vacancy rates (regressions 4-5), and changes in real estate (house) prices(regressions 2-5) all have the expected signs, but only the coefficient on prices is statisticallydifferent from zero.  This suggests that the future rent increases capitalized in prices are moreimportant than current rents for builders, possibly because most multi-family starts since the mid-201980's in Canada have been for condominiums rather than rental units.  As with single family starts, the effects are not large.  A 2 percentage point increase in thepercentage change in real house prices raises the number of multi-family starts by 69 units, or 11percent, equivalent to an elasticity of 0.096 for Vancouver.  These figures for multi-family startsare at least an order of magnitude higher than for single family starts.  One possible explanation isthat because for multi-family construction, incremental exploratory construction by building only afraction of the units within a project is not possible.  Consequently there is a greater gain to delay.Surprisingly, the coefficients on house price and vacancy rate volatility are positive, thoughalways far from being statistically different from zero.  As with single family starts, real interestrates have a negative but not statistically different from zero effect.There are a number of reasons that may explain the failure of the uncertainty measures in theseregressions.  First, permit expiry limits the scope of builders to delay at this stage of thedevelopment process and uncertainty works directly through the ability to delay.  Second, weinclude variables that describe market conditions, reflecting “new information” that should affectoption exercise decisions.  Consequently, there is less variance to be explained by uncertainty. Third, our measures of time varying variance of returns, number of unsold units, and the vacancyrate are not accurate measures of the relevant forward-looking uncertainty faced by developers andbuilders.  Fourth, the nature of residential development, which includes the multi-stagedevelopment process and the limits on builder “monopoly power” because of competition from theexisting stock and other new projects, may limit or reverse the standard effect of uncertainty.  Wedo not have sufficient data to include all parameters of the real options model, raising the21possibility of left out variable bias. Our conclusions from these results are that there is support for the argument that builders treatstarts as the exercise of a real option.  They change their permit exercise decisions in light of newinformation, a behavior consistent with permits as a real option.  In contrast, the estimatedcoefficients on the demand uncertainty variables lack statistical significance to support this claim.We believe that problems with these variables are the likely explanation for their performance. The reaction to new information approach is immune to this problem and inherently reflects theoption nature of the process, the ability to delay.  Even so, the coefficient values  on price changesand the number of completed but unsold units are sufficiently small that new information has anonly modest effect on the speed with which permits are exercised. Completions as the Exercise of an Option.  Regressions of current completions on current andlagged starts, new market information, and uncertainty measures find little support for the claimthat residential builders treat the completion of a unit already started as an option.  Contingent oncurrent and past starts, neither the measures of uncertainty nor new information have a statisticallydifferent from zero effect on completions.  The regressions follow the same form and structure asTables 4.1-4.2: Table 5.1 presents the estimates of single family completions and Table 5.2 doesthe same for multi-family completions.  Controlling for the number of current and lagged starts, the effects of shocks to price changes,shocks to the number of completed but unsold units, and the degree of price volatility on singlefamily completions are not statistically different from zero.  Comparing coefficient estimates, the22effects of  price changes on the completions in Table 5.1 are 12-21% of the size of those on startsin Table 4.1.  For house price volatility, the coefficient in Table 5.1 is less than 10 percent the sizein absolute value of the estimate in Table 4.1. As with the other variables, the sign on thecoefficient is wrong.  The results for multi-family completions are more intriguing.  Unlike the case for starts in Table4.2, house price changes in Table 5.2 have no discernable effect on the rate at which multi-familyunits are completed, controlling for two years worth of starts.  However, the rate of completiondoes fall with the vacancy rate, with estimated coefficient values in regressions five and six thatare twice those in Table 4.2.  In the former regression the coefficient is statistically different fromzero with 90 percent confidence, and close to that in the latter.  Still, the magnitude of the effect issmall.  A one standard deviation increase in the vacancy rate results in a drop in completions of 41units, or about 8 percent.  As an elasticity this is quite low, 0.092.  The sign on vacancy ratevolatility has the wrong sign, though the estimated coefficients for price volatility are both largerthan those for multi-family starts in Table 4.2 and of the correct sign. There are a number of reasons that may explain why multi-family completion rates display weakevidence of real options behavior while single family rates do not.  First, the longer constructionprocess may allow builders more latitude to delay within the framework of their loans than is thecase for single family construction.   Second, single family completions include custom-builthomes and speculative stars for which sales contracts have already been signed so that there is nooption.  While some multi-family units are pre-sold they are only a percentage of all units in aproject, and custom-built multi-family projects do not occur. 23Overall, the evidence is that once a unit has been started, builders finish construction. Completions occur independent of the evolution of housing market conditions.  Consequently,  theconstruction process does not have option properties.  These results also reject the thesis thatbuilders treat units under construction as an inventory for completed units, for if they were to doso, we would have to see evidence of counter-cyclical starts behavior.  ConclusionThis paper investigates two issues: where real options behavior occurs in the real estatedevelopment process and whether starts and permits are appropriate proxies for completions andstarts respectively.  We find that builders respond to new information in deciding whether or not toexercise permits, though it takes large changes in market conditions to generate small changes inpermit exercise rates.  While this behavior is consistent with the real option framework, we do notobtain the standard result, that uncertainty in returns itself is important.  There is scant evidence ofthis type of options behavior by builders in the timing of completions.  Overall, these resultssuggest that if developers and builders do treat development as a real option, the important stage isat or prior to the time of the decision to actually draw a building permit or obtain a developmentpermit.  Avenues of future research include a more developed analysis of the model, allowingfeedbacks among the three variables in a VAR type framework.  This would allow the estimationof current starts or completions while controlling any earlier decisions to exercise at a more rapidrate.  As a practical matter for evaluating housing market conditions and forecasting, the results of this24paper suggest that single family permits can proxy for starts.  It is important to create the proxyusing current and lagged values.  For multi-family activity the number of lags needed is greater andthe predictive accuracy lower.  While starts do turn into completions, the very long lags needed toreach a point where 95 percent of starts become completions allows too much possibility forimprecision in a prediction to offer more than a very general insight.  These results are importantfor metropolitan area analysis in the US, where reliable starts series are not available for mostMSAs.25BibliographyBar-Ilan, A. and W. Strange.  1996.  Investment Lags.  American Economic Review  86: 610-622.  _____________________.    1998.  A Model of Sequential Investment.  Journal of EconomicDynamics and Control  22: 437-63.Blinder, A. S. and L.J. Maccini. 1991. Taking Stock: A Critical Assessment of Recent Research onInventories.  Journal of Economic Perspectives  5(1). Brennan, M.J. and L. Trigeorgis, eds.  2000.  Project Flexibility, Agency, and Competition. Oxford, UK: Oxford University Press.  Bulan, L.T., Mayer, C. and C.T. Somerville.  2000.  Real Options and the Timing of NewInvestment: Evidence From Real Estate Development. UBC Centre for Real Estate and Urban LandEconomics Working Paper.  Capozza, D.R. and R.W. Helsley. 1990. The Stochastic City.  Journal of Urban Economics  28:187-203Capozza, D.R. and G.M. Schwann. 1989. The Asset Approach to Pricing Urban Land: EmpiricalEvidence. AREUEA Journal  17: 161-174.  Case, K.E. and R.J. Shiller. 1989.  The Efficiency of the Market for Single Family Homes.American Economic Review 79: 125-37.Coulson, N.E.  1999.  Housing Inventory and Completion.   Journal of Real Estate Finance andEconomics  18: 89-106.  Dale-Johnson. D. and S.W. Hamilton.  1998.  Housing market Conditions, Listing Choice, andMLS Market Share.  Real Estate Economics  26: 275-308.  DiPasquale, D. 1999.  Why We Don’t Know More About Housing Supply.  Journal of Real EstateFinance and Economics  18: 5-8.  DiPasquale, D. and W.C. Wheaton. 1994.  Housing Market Dynamics and the Future of HousingPrices.   Journal of Urban Economics  35: 1-28.  Dixit, A.K. and R.S. Pindyck.  1994.  Investment Under Uncertainty.  Princeton, NJ: PrincetonUniversity Press.Goodman, J.L.  1998.  Aggregation of Local Housing Markets.  Journal of Real Estate Financeand Economics  16: 43-54. ____________.  1986.  Reducing the Error in Monthly Housing Starts Estimates.  AREUEA26Journal  14: 557-566.  Green, R.K.  1997.  Follow the Leader: How Changes in Residential and Non-residentialInvestment Predict Changes in GDP.  Real Estate Economics  25: 253-270.  Grenadier, S.R. 1995a.  The Persistence of Real Estate Cycles.   Journal of Real Estate Financeand Economics  10: 95-120. ___________.  1995b. Valuing Lease Contracts: A Real-Options Approach.   Journal ofFinancial Economics 38: 297-331. ___________. 1996.  The Strategic Exercise of Options: Development Cascades andOverbuilding in Real Estate Markets.  Journal of Finance. 51: 1653-79. ___________.  1999.  Option Exercise Games: An Application to the Equilibrium Strategies ofFirms.  Stanford University Graduate School of Business unpublished mimeo.  Holland, A.S., Ott, S.H., and T.J. Riddiough.  2000.  The Role of Uncertainty in Investment: AExamination of Competing Investment Models Using Commercial Real Estate Data.  Real EstateEconomics  28: 33-64.  Im, K.S., Pesaran, M.H., and Y. Shin.  1997.  Testing for Unit Roots in Heterogeneous Panels. Cambridge University Working Paper.  Leahy, J.V. and T.M. Whited.  1996.  The Effect of Uncertainty on Investment: Some StylizedFacts.  Journal of Money, Credit, and Banking  28: 64-83.  Lo, A.W. and J. Wang.  1995.  Implementing Options Pricing Models When Asset Returns ArePredictable.  Journal of Finance 50: 87-129.  Mayer, C. and C. T. Somerville. 1996. Regional Housing Supply and Credit Constraints. NewEngland Economic Review  November/December: 39-51. _________________. 2000.  Residential Construction: Using the Urban Growth Model toEstimate Housing Supply.  Journal of Urban Economics 48: 85-109.  Quigley, J. and C. Redfearn.  1999.  Housing Market Efficiency and the Opportunities For ExcessReturns.  University of California, Berkeley mimeo.Pinches, G.E.  1998.  Real Options: Developments and Applications.  Quarterly Review ofEconomics and Finance  38: 533-35.Poterba, J.M.  1984.  Tax Subsidies to Owner Occupied Housing: An Asset Market Approach. Quarterly Journal of Economics  99: 729-52.  27___________.  1991.  House Price Dynamics: The Role of Tax Policy and Demography. Brookings Papers on Economic Activity   143-183.Quigg, L.  1993.  Empirical Testing of Real Option Pricing Models.  Journal of Finance   48:621-640.  Riddiough, T.J.  1997.  The Economic Consequences of Regulatory Taking Risk on Land Valueand Development Activity.  Journal of Urban Economics   41: 56-77.  Somerville, C.T.  1996.  The Contribution of Land and Structure to Builder Profits and HousePrices.  Journal of Housing Research  7: 127-141.Titman, S.  1985.  Urban Land Prices Under Uncertainty.  American Economic Review  65: 505-14.  Williams, J.T.  1991.  Real Estate Development as an Option.  Journal of Real Estate Financeand Economics   4: 191-208.   28Data AppendixThe permits, starts, and completions series are used to estimate the structural relationship betweenstarts and permits and then completions and starts.  We generate estimates of the coefficients inthese structural relationships from OLS regressions of seasonally adjusted starts on current andlagged permits and completions on current and lagged starts.  For monthly series these regressionsare presented for both single family and multi-family units.  Table A-1 shows the results usingmonthly series and Table A-2 for the quarterly series.  One complication is that data series valueschange with new CMA definitions, but historic values are not adjusted to reflect these changes. The Canadian census occurs quinquenially, but with the exception of Ottawa-Hull, most CMAshave only one change.  We construct adjusted series by altering values for years prior to  newCMA geographic definitions by the percentage change resulting from any additions or subtractionsin the year of the redefinition.  291.Metropolitan area studies of housing supply tend to use permits to measure new construction(Poterba 1991, Dreiman and Follain 1998, and Mayer and Somerville 1998), while nationalestimates use starts (Topel and Rosen 1988, DiPasquale and Wheaton 1994, Mayer andSomerville 2000). 2.We use data series on apartment construction, buildings with six or more units, for multi-family. Both rental and condominium (strata-title) properties are included in the multi-family series.Single family series are for single detached units.  Our breakdown excludes single family attached,row houses, and multi-family buildings with 3-5 units. 3.The theoretical foundations and applications of this model are covered in Dixit and Pindyck(1994), Pinches (1998), and Brennan and Trigeorgis (2000).  Holland, Ott, and Riddiough (2000)provide a clear summary of the issues in applying the model to real estate.  4.By pulling a permit, the builder is assured of the right to build without delay or additionalregulatory cost during the life of the permit (typically a year), even if there are changes in theregulatory environment or increases in impact fees.  In most jurisdictions permits are transferable,and, subject to review, they may also be extended.5.This discussion pre-supposes that all starts are speculative starts.  In the US approximately 40 ofstarts are speculative.  6.This is not a problem for completions because of long construction times.  7.Goodman uses 1984 Construction Reports C20 data but does not explain his methodology.8. Blinder and Maccini (1991) demonstrate that actual production is typically more volatile thansales in the manufacturing sector, implying that little smoothing occurs.  The same is true forhousing where starts are more volatile than sales. 9.Some large national US builders prefer to construct units only once they have a buyer.  Pre-salesare quite common for condominium developments in Asia and Canada and are frequently part of adeveloper’s marketing strategy.  10.Capozza and Schwann (1989) is the first empirical treatment, but they have severe dataproblems.  11.CMAs are analogous to US MSAs.  Data are from Royal Lepage,Statistics Canada, CMHC, and the Bank of Canada .  Panel is 1975:1-1996:4.  For permits, starts, and completions wehave both monthly and quarterly data for 1972 through 1998.  House prices start between 1975-1981.  We only have rent data for 12 of the 15 cities. Endnotes3012.Real series are developed using a smoothed inflation value, average of quarterly inflation overthe current and previous three quarters with declining weights of 4, 3, 2, and 1. 13.See Dale-Johnson and Hamilton (1998) for the Vancouver repeat sales index. 14.These series are not consistently stationary in tests using US data.  Mayer and Somerville forUS quarterly regional  (1998) and national (2000) series find them to be I(0).  Using monthlynational US series Coulson (1999) finds that starts and completions are I(1).  15.For purposes of comparison we also estimated a starts-permits relationship for total permits. As the weighted average of single and multi-family estimates, the Canadian data again reveal amuch slower initial exercise rate.  16.The Durbin-Watson statistics in Table 4.1 are rather high.  AR(1) regressions yield anestimated D of only -0.25 and the coefficient estimates are essentially unchanged.  Consequently,we choose to keep the current specification and avoid the problems associated with IV estimationwith a serially correlated error structure.17.This is related to the median time to sale variable that Poterba (1984), DiPasquale andWheaton (1994), and Mayer and Somerville (2000) find has significant effects on newconstruction in the aggregate U.S. data.  18.This result is robust across measures of demand volatility.  Using the standard deviation ofprice changes over the previous eight quarters to measure uncertainty yields a qualitatively similarresult to that presented in the tables using the Garch estimate of demand variance.  As well wetried interacting volatility and price change to test for asymmetric effects, but did not obtain robustresults.  


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