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Bubble, Bubble, Toil and Trouble: An econometric analysis of the determinants of housing prices By REBECCA M. STORK A Thesis Submitted to the Division of Social Sciences New College of Florida in partial fulfillment of the requirements for the degree Bachelor of the Arts Under the Sponsorship of Dr. Richard Coe Sarasota, Florida April, 2010
2 Abstract In this thesis the housing demand function is upda ted to include a better representation of the investment component of home-ownership and the availability of credit. By modeling the investment component of housing with a av ailable substitute investments, similarly to the current model for the consumption component of housing, a more complete demand function was created that fully incorporated after-tax gains of homeownership into the demand function. Using an Autoregressive Distributed Lag (ADL) (2,1) model, the additions to the theoretical framework of housing demand were examined, in three time tiers. Despite high-levels of multicollinearity, the investment proxy of AAA rated bonds was found to be highly significant and negativ ely correlated to housi ng prices across all tiers indicating that the rate of return on other investments does affect housing prices. The credit availability proxy of LTV ratios were found to be fairly significant with a positive sign, leading the researcher to believe that as credit became more readily available housing prices increased. Dr. Richard Coe Division of Economics
3 Dedication: I dedicate this thesis and all th at it means to Nicholas Shelton and the other bright and talented friends who were taken far too soon. Nicky, I hope I made you and EPAT proud. Acknowledgements I would like to thank my parents for th eir unending support an d my brother for introducing me to this wonderful institution. Without one person I would have been lost this year and there are not enough words to thank you for all you have done. Prachi Murarka deserves much more than I can write here, for six years of support and proofreading. I hope she never forgets my gratitude and love. I would also like to thank all my committee members without whom none of this would have been within my capabilities; Dr. Rich ard Coe, Dr. Tarron Khemraj, and Dr. Joseph Mink.
4 Table of Contents Abstract . . . i Acknowledgments . . ii Table of Contents . . iii Chapter 1 Introduction ..... 4 Chapter 2: Housing Dynamics a Theoretical Overview . .. 6 2.1 Determinants of Housing 2.2 Changes in the Determinants of Housing 2.3 Synopsis of Theoretical Framework Chapter 3: Literature Review .. ... 18 3.1 Empirical Evidence of the Demand for Housing 3.3 Recent Theoretical Innovations 3.4 Analyzing Rapid Price In creases During the Bubble 3.5 Analyzing Rapid Price Increases After the Bubble 3.6 Lessons Learned Chapter 4: Econometric Model . . . 43 4.1 Data 4.2 Methodology 4.3 Notes on the Model 4.4 Results 4.5 Analysis Chapter 5: Conclusions . ... 59 Bibliography . .. 63 Appendix A: Model with Tax Rate 66 Appendix B: Full Model estimates .... . 69 Appendix C: Data on CD-ROM in excel format .... 73
5 Chapter 1: Introduction In the first part of the new century, housing prices began a rapid increase that culminated with a global financial crisis. While the hous ing bubble was partially credited with the financial collapse, the underl ying drivers of explosive pri ces were hotly debated. Some pointed to decreased credit st andards and the increase of ad justable rate mortgages. Others claimed the bubble was fueled by histor ically low interest rates, which decreased mortgage payments. This thesis examines th e major drivers of housing prices in a multitiered model in order to determine what precip itated the housing bubble. It first creates a new theoretical approach to housing dema nd, and then an econometric model is constructed to estimate the long run effects of several determinates of housing demand on housing prices. Building off past literature, a new m odel for housing demand is created that incorporates two new drivers. The investment nature of housing is fully modeled with an accompanying substitute variable. Additiona lly, decreases in credit standards are represented to accurately illustrate how the incr eased availability of credit affects housing markets. Using this new framework, the housing prices change s during the bubble are compared to changes prior to the price explosions. By using a multi-tiered model, one is able to isolate the poten tial drivers of housing pr ices during the bubble. Chapter 1 presents a brief overview of the theoretical unde rpinnings of housing
6 demand and also offers historical backgr ound to changes in determinates during the bubble period. I create new model for housing demand that more accurately accounts for investment component of housing. Chapter 2 outlines previous literature of housing demand focusing on empirical estimations of determinants, recent innovations in housing demand theory, and finally literature addr essing the bubble period in question. Chapter 3 creates an econometric model of housing pri ces and offers analysis of the resulting estimations. Chapter 4 details the main conclusions and future research.
7 Chapter 2: Housing Dynami cs: A Theoretical Overview The demand for housing is elaborate, compli cated further by both the consumption and investment potential for owner-occupied hous ing. The supply of housing in the United States is unique to most other developed ec onomies as it has a rela tively elastic supply curve. Therefore this thesis will focus on the demand for housing, assuming that supply will increase or decreas e to meet demand. For many Americans purchasing a home is the fulfillment of the American Dream, but the decision is complex and highly nuanced. A potential homeowner considers a wide array of factors. Personal pref erence is large factor; a pool for the kids, a good school system, friendly neighborhoods, or even the kitchens potential for entertaining guests. These pref erences cannot be quantified, bu t other quantitative factors affect the decision to purchase a home. A t ypical potential homeow ner may consider his ability to make a down payment or the size of the monthly mortgage payments. Another consideration is the expected future price of the home, as many homeowners use the sale of the primary home later in life as the largest contribution to their retirement. Determinants of Housing Consumption factors include the annual and in itial cost of purchasing a home, the price and availability of substitutes for owner-o ccupied housing, and permanent income and transitory income. The decision to purchase a home is greatly affected by the investment potential of the home, because in additi on to owner-occupied housing serving as a
8 consumption good, selling a home can yield capit al gains. Investment factors include expectation of increased home values and th e availability of more attractive substitute investment vehicles. All of these factors are used in the ag gregate to develop large macroeconomic models that predict demand for housing. Since the 1960s the accepted housing demand models have evolved to from a focus on pred icting residential investment to the owneroccupied models that are used today. Most of the current literature measures changes in demand by using a housing price index for repeat sales.. This evolution has encompassed not only the changes in the way owner-occupied housing is taxed and financed, but also the rising instances of investi ng in residential properties. At its very basic level housing demand can be defined as D ( X1, P U R ) S1 (1.1) Where Demand for housing is a f unction of exogenous variables X1 (such as personal preferences, demographics, and income), the r eal price level of housi ng P, the annual user cost of owning the home, and the alternative cost of renting housing R. S is the supply of homes, assuming equilibrium conditions dema nd and supply are equal. Within each of these variables one can see a myriad of f actors that influence their movements and by definition the demand for housing. 1 DiPasquale 3
9 The exogenous variable X1 includes the real factors of the whole macro economy as well as other unquantifiable preferences and demographic information. In most housing demand models X1 represents the income effect on demand, but it is not limited to income. Some economists have used demogr aphic data to illustrate how some classes, income levels, races, or age groups are more likely or less likely to demand owneroccupied housing.2 While demographics are worthy subjects to examine especially when considering different elasticities for demand, this thesis is con cerned not with how individual groups act, but rather how the aggr egate of all said fact ors can facilitate a housing price explosion. For that reason th e model set forth here will limit the X1 variables to the real macro ec onomic factors including several different types of income. The real price level of hous ing is perhaps the most st raightforward of all the variables affecting demand. According to basi c economic theory, if housing is a strictly non-inferior consumer good, as price increases quantity demanded should decrease. While in current literature future expected pr ices are component of user cost (U), the expectation of future price increases has a pos itive effect on demand w ithin the user cost variable. That is to say, in certain instances increasing prices of ho mes may in fact spur demand rather than decrease demand, but one mu st be able separate housing into both a consumer good as well as an investment good to monitor these ch anges. Therefore housing cannot be classified as a strictly non-inferior good. 2 Dusansky
10 User cost has evolved greatly as part of the housing demand function. Originally set forth in the 1980s, Kearl3 created a housing demand func tion that incorporated not only basic after-tax user cost, but also included a factor of the expected ra te of return. DiPasquale defines user cost as U ( i tp)(1 ty) E ( p p ) (1.2) Where i is the interest rate, tp is the property tax rate paid on the home, ty is the marginal tax rate facing the home owner, and E( p/p) is the expected fu ture gains on housing. This function is crucial to understanding cha nges within housing demand dynamics. Both mortgage interest payments and property taxes are deductible on federal tax returns; therefore the marginal tax rate has effect s on the end user cost. Additionally, the E( p/p) was incorporated to illustrate that owning a home not only has defined costs, but also unrealized returns. As the expected future pr ices increase, the annua l user cost decreases. The user cost variable also inherently contains maintenan ce costs and upfront costs such as closing costs and mortgage fees. Expa nding upon current litera ture this thesis examines how these expected future values f actor into investment decisions, specifically the expected future returns on alternative or substitute investment vehicles. Therefore I deviate from past literature and separate out expected future returns from user cost in order to create a substitute for other inve stments, similarly to how user costs are substitutes for renting. Finally, the ready availab ility of substitutes for owner-occupied housing can impact the decision to buy a home or rent. If we assume that housing is a consumption 3 Kearl
11 good, then renting a home and living in a home that one owns are nearly perfect substitutes. Therefore, if the rental s ubstitute annual cost decreases, the demand for housing should decrease. When considering expe cted future prices, this effect may be offset by the investment potential of owni ng a home. While preferences between owning and renting exist, this thesis assumes that any differing preferences have been accounted for in the exogenous variable X1 where demographics and preferences reside. The Bureau of Labor Statistics computes a rent index as a portion of the consumer price index, which is illustrative of the comparable cost of renting to owning. These determinants paint a fairly concise picture of housing demand, but while the model does account for a portion of the cost of financing within user cost it only accounts for interest rate payments. The larges t barrier to purchasi ng a home is usually the size of the down payment, which most ofte n is used to show good faith and offer the lender security. There is extensive literature th at predicts falling [housing] prices make foreclosures more likely by fostering negative equity.4 The securing of a down payment offers the lender a decreased likelihood of foreclosure if housing prices fall, as the borrower already has substantial equity w ithin the home. While foreclosure rates surrounding the sharp decline in housing prices is not within the scope of this thesis, it is important to note that by decreasing the require ment of down payments the initial cost of owning a home also decreases. The size of a downpayment is a large barrier to purchasing a home and can be considered an initial cost to owning a home. Moreover, as 4 Foote, et al.
12 the size of the downpayment increases the pr incipal and mortgage payment decreases, thereby decreasing the annual user cost. In lending terms, the down payment can be defined within the loan-to-value ratio (LTV). The LTV ratio is fairly self-explanat ory, it measures the amount of the loan to the value of the asset. Fo r example if a home has a value of $100,000, and the borrower places a $20,000 downpayment the LTV ratio is 80. Additionally the LTV ratio with respect to housing can be accurately examined in two separate ratios. The first measure of LTV ratio only incorporates the LTV ratios of newly originated mortgages, offering insight into the lending practices in a curre nt time period. Alternatively, the collective LTV (CLTV) ratio also incorporates s econd cashing out mortgages and additional loans used to pay the downpayment, and ma king it crucially relevant to the overall stability of the housing market. A low CLTV indicates greater home equity, while the previous example mortgage may have a LTV ratio of 80, if a second loan is used to finance the whole $20,000 downpayment the CLTV ratio would be 100. With a fairly high CLTV ratio, the probability of forecl osure during sharp housing price declines increases. Overall LTV ratios are fairly decen t indicator of credit standards, when LTV ratios are relatively high, one may assume that credit standards have been lessened. The traditional housing demand models lack a good representation of the investment component of housing. While r ecent models have captured the future expectation of price increases, they have failed to express them in relative terms to other investments. One may assume that just as the cost of rental substitutes affect the demand
13 for consumption of housing; concurrently the ra te of return of investment substitutes will affect the demand for investment component of housing. When considering how best to model other rates of return, one must take in to account not only real rates of return but also after-tax rates of return. Housing is uniquely positioned in after-tax rates of returns, because of the exemption of capital gains on th e sale of a primary residence. Currently, married couples face no tax on the first $500,000 of gains from the sale of a primary residence held for more than one year. While other investments such as stocks and bonds are subject to capital gains, the interest or gains on these investments are taxed at the capital gains rate. This thesis puts forth th e model for investment potential of homes: HomeGains [ E ( Pt H P1 H) [ E ( Pt H P1 H) Exemp ]( tCapGain)] (1.3) And the investment substitutes are defined as: OtherInvestmentGains E ( Pt i P1 i)(1 tCapGain) (1.4) Where E ( Pt i P1i) is the expected return of other investment vehicles and E ( Pt h P1h)is the expected return on housing, tCapGain is the capital gains tax rate, and Exemp is the value of the exemption from capital gains on the sale of primar y homes. Adding these variables into the housing demand model mo re accurately expresses the investment potential of homes relative to other substitutes. Previously the consumption factor is weighted by rental substitute s against user cost, concurren tly investment potential of owning a home is removed from user cost and we ighted against substitute rate of returns. The revised model finds that the de mand for housing is a function of X1, P, U, R, I, F, and C. By setting demand equal to housing su pply the new model can be constructed as:
14 S 1Income 2Hou sin g Pr ices 3UserCost 4Re ntal 5InvestmentSubstitutes ... 6ExpectedHou sin g Re turns 7CreditAvailability Changes in the Determinants of Housing In early by 2006, housing prices in the Un ited States accelerated quickly over the previous 5 years, with nationa l levels increasing by about 50 percent and some pockets of hot activity doubling.5 While sharp rises in housing pri ces gave way to higher expected future returns on housing, driving demand forw ard as the investment potential increased, some scholars began to anticipate a hous ing bubble. In 2003 two of the preeminent housing model scholars, Shiller and Case wr ote, a tendency to view housing as a investment is a defining char acteristic of a housing bubble.6 Although drastic rises in housing prices may signal a potential bubble, it is equally important to note that the real factors that drive housing mark ets can accelerate equally duri ng a rise in housing prices not precluding a true bubble. The remainder of this chapter examines the changes that took place during the 2001-2007 housing price in creases within the framework of the housing demand model. From 1997 through 2003 the US government changed the tax code in ways that may have significantly impacted several de terminants of housing demand. The Taxpayer Relief Act of 1997 (TRA97) drastically altered the invest ment potential of homeownership. Prior to TRA97, gains of more than $125,000 ($250,000 for married couples) from the sale of a home would be taxed as a capital gain if the homeowner was 5 Hwang Smith et al 6 Case and Shiller (2003)
15 under the age of 55 or did not re invest the gains in another ho me of equal or greater value within a year.7 The new exemption allowed for any gain up to $250,000 ($500,000 for married couples) to be excluded from capital gains tax if the home had been the main residence for two years in the past five. A dditionally, the top rate of capital gains was lowered from 28 percent to 20 percent8 with TRA97. The results of new exemptions of home sales show that the home sale rate increased after 1997 for homeowners with capital gains between $0 and $500,000 suggesting th at TRA97 reversed the lock-in effect of capital gains taxes for these homeowners.9 It is estimated that TRA97 changes in exemptions and capital gains rate affected semiannual sales rates of homes from 13-22 percent.10 In effect TRA97 increased mobility in the housing market, but unfortunately due to data issues there is no empirical ev idence on the change in housing prices due to TRA97. In 2001 President Bush enacted The Economic Growth and Tax Relief Reconciliation Act (EGTRRA), which lowered tax rates for low and high income households as well as married couples. In 2003 The Jobs and Growth Tax Relief Reconciliation Act (JGTRRA) immediately enac ted the reductions passed in EGTRRA as well as introduced another cut to top capital gains tax rate; cutting it to 15 percent, but also included dividend income. The marginal in come tax rate for the highest tax bracket was lowered from roughly 40 percent in 2001 to 35 percent by 2003; while lowest bracket moved from 15 percent to 10 per cent. Both tax reforms aimed at quickly 7 TRA 97 Section 312 8 Bautz 9 Shan 17 10 Shan 57
16 increasing take home incomes, with hope s of jumpstarting a lagging economy. The decreases in marginal tax rates from all three tax reforms have dual effects when looking at the demand for housing. Margin al tax rates are function of user cost, implying that as marginal tax rates fall the mortgage interest rate and property tax deductions also decreases. This movement alone would predict a decrease in housing demand. Secondarily, the decrease in marginal tax rates as well as capital gains tax rates can be predicted to increase the aggregate after tax income, but these gains in income would be offset by the recessionary period. Su ch an increase in income would positively affect the demand for housing. Additionally, the decrease in capital gains would also affect the investment potential variable, by increasing the attractiven ess of both after tax investment opportunities, but with the benefit differing only by the expected rate of return of the investments. The changes in the tax code may have a sea-saw effect, both increasing and decreasing real demand. Aside from changes in taxation, during the time period in question investment substitutes became more volatile as well as le ss attractive. In early 2001 on the heels of the dot-com bubble, the United States had begun to enter into a recession, which was exacerbated by the attacks in September of that same year. Even before the attacks, the stock market had begun to exhibit decreased ra tes of returns. Additionally, the volatility of the markets clouded real estimates of fu ture rates of return, making housing a more attractive investment as futu re price expectations on housi ng are generally regarded as positive. Furthermore, in an effort to stimulate a lagging economy, interest rates were
17 lowered several times. At the end of 2000 the Federal Funds rate was roughly 6.5 percent, but by the beginning of 2002 it was 1.75 percent. The interest rates continued to drop until mid 2004 at which point they began to rise again but never reaching their 2000 levels. With low interest rates, rates of re turn on newly issued bonds, new certificates of deposit, and traditional savings accounts shrunk. As the rate of return of substitute investments decreased, housing demand s hould increase according to the model. Interest rates are also found as a function of user cost. As interest rates fall, user cost decreases, but due to the mortgage inte rest deduction the decrea se is equal to the change in interest rate times (1-ty). As mentioned before marginal tax rates were lowered during this time frame, therefore there is movement in both directions. Without knowing the elasticity of demand due to user cost or investment substitutes, it would be mere conjecture to say that one or the other wa s a larger factor in increasing housing demand. Regardless, the lowering of interest rates pr edicts an increase in demand within both user cost and substitute investments. Finally, many scholars have named the sub-prime lending market as the major culprit in the rapid increase of prices. Duri ng this time period, credit standards took on a creative method to determine qualified borrowers. Adjustable rate mortgages were introduced, allowing potential hom eowners to pay a lower teaser rate for the first two years of the mortgage, after wh ich it adjusted to a higher rate Borrowers were required to pay lower down payments or allowed to use piggy-back loans to finance required down payments increasing the overall CLTV. Historically low interest rates offered incentives
18 for refinancing of older mortgages, while so me homeowners removed equity from their home using second mortgages. All the while new mortgages were being purchased by investment banks to be pooled together in order to form complex securities. These securities were then sold in a corporate bond structure. The invest ment banks increased the demand for consumer loans, allowing banks and licensed mortgage brokers to turn over mortgages much more rapidly with litt le financial risk, thereby increasing their incentive to make mortgages to subprime borrowers. The increased availability of credit for subprime borrowers as well as prime borrowers decreased the barriers to entry into the owner-occupied housing market. One hypothesizes that decreased cr edit standards evident by th e LTV ratios increased the demand for housing, further driving up home values. Synopsis of Theoretical Framework Current housing demand models have accounted for the substitution effect that rental equivalents have on housing prices. Future e xpectations of housing price increase have been incorporated into the mode l as part of user cost, but th is overlooks the substitutes for the investment component of housing. This thes is moves expected future returns out of the user cost function in order to correctly measure the effect while also incorporating a variable to account for the substitution effect of other investments.
19 Chapter 3: Literature Review Empirical Evidence of the Demand for Housing In a sweeping overview of the dynamics of the housing market, DiPasquale and Wheaton outline the basic movers and drivers while providing empirical estimates for the determinants of housing demand and supply. Building upon decades of literature, the authors construct a detailed model to offer forecasts for futures housing prices. The basic dynamics of the housing market are assumed; such that demand is determined by X1 the set of exogenous demographic variables such as macro indicators and likelihood of ownership, P the price of hous ing units, U user costs, and R, the price rent ratio: D ( X1, P U R ) S Supply (S) is defined as S C ( X2P ) S where C is new construction determined by X2 factor costs, and P is the price of housing units, and S is the level of depreciation of the current hous ing stock. User cost is further defined as U ( i tp)(1 ty) E ( P / P ) where ( i tp)(1 ty) is the after tax cost of debt and property taxes, where tp is the property tax rate and ty is the marginal income tax rate and expected future prices are defined by P [ P P ] where P* is the equilibrium price of a housing unit and P is the actual price and is the rate at which actual the price will converge to the equi librium price.
20 This addition to expected future prices lite rature takes into account that if future prices are serially co rrelated in regards to backward-l ooking expectations, then, current prices will be positively related to recent past prices, providing a further reason for serial price correlation.11 The overall model assumes th at rational exp ectations and equilibrium conditions will create adjustment s in both the supply and demand until prices and supply fall into equilibrium. The data used is found from the housi ng price index Federal Home Loan Bank Board, which includes existing units, and the Commerce Departments price index for newly constructed single-family homes and Freddie Macs series for existing houses. Rental data is derived from the Bureau of Labour Statistics. The exogenous determinants include personal consumption, a standard measure of permanent income, and two calculated demographic variables. One of the demographics calculate s the percentage of people who are likely to own, while the ot her considers household formation by age and marital status. In order to estimate the demand for housing two equations are combined: Pt* (1/ 4)[ St/ Ht 1Rt 2OWNt 3Waget 5Ut] PtPt* (1 ) Pt 1 Where P*is the market clearing price, P is the pr ice in time period t, R is the rental index, OWN is the age-expected ho meownership rate, WAGE is the permanent income per household and U is the user cost, and is the (annual) percentage rate at which actual prices converge to this equilibrium price. 11 DiPasquale 7
21 The elasticities for the determinants of demand are estimated for two separate data sets; one for actual households and the age-expected househ olds. The authors conclude that the estimates for age-expected households are much higher, but th e price elasticity of demand consistently is in the -0.009 to -0.19 range, more inelastic than that obtained by other studies by Kearl and Rosen. Furthermor e the elasticity of U is only around -0.004 or less than one thirtieth of that for P,12 supporting the notion that price levels effect demand much more than rents, user costs, a nd interest rates all of which have a much lower elasticity of demand. While the authors propose that price expe ctations are not as important in the demand for housing as price, it is also important to note that this is obscured by the fact that there are no separa te estimates for the elasticity of future expectations as it is incor porated in user cost. Case and Shiller created one of the mo st well known housing price indexes, and one that is used by most of the literature he re reviewed. By creating a dataset of repeat sale records of houses, the index monitors th e changes in housing prices more accurately than other indexes. Their 1990 article Forecasting Housing Prices and Excess Returns also estimated the coefficients of key co mponents of the housing demand function against changes in housing prices. The variables included were previous period change in housing prices, rent to price ra tio, mortgage payment to income ratio, construction cost to price ratio, unemployment rate, change in in come, change in construction cost, change in age of population, and changes in the marginal tax rate. 12 DiPasquale 18
22 The results find a high degree of serial corr elation, specifically that the change in prices from the previous time period accounted for about a third of the same change in the next period. Several of the variables were found not to be significant such as change in construction costs, unemployment rate, a nd change in the age of the population, and therefore were dropped in subsequent m odels. There were some problems with multicollinearity between rent to price ratio and mortgage payment to income ratio, where in the full model rent was taking a negative sign. When the authors ran two models separating the two ratios, the rent coeffici ent assumed a positive sign as theory would dictate. Additionally, changes in marginal tax rate were also negative and mildly significant in all the models, because the author s posit, the impact of marginal tax rates on after tax cost of housing seems to be offset by other provisions.13 While the authors make several claims of the significance of certain components, the R2 are relatively low averaging around 0.333, which tends to call into question the g oodness of fit of the overall model. Using house price series fr om seven different sources, Peek and Wilcox estimate the effects of key housing variables to comp are the differences between housing series. They find the Freddie Mac adjusted series which accounts for ex isting and new home sales but is limited by the Freddie Mac mortga ge ceiling that does not account for higher end homes. The independent variables are unem ployment, the after-tax rate of mortgage interest, income, the ratio of heads of house in their 20s to thos e aged 30-54, and the 13 Case and Shiller 1990 27
23 price of construction materials. All of the series had an R2 of 0.83 or higher, with the Freddie Mac adjusted having one of the hi ghest with 0.911 indicating the model was a good fit. All but two of the series ha d negative coefficients for the after-tax mortgage rate, but the authors suggest that from the Freddi e Mac Adjusted series that a one percent increase in interest rates decreased hous ing prices by 1.75 percent. Furthermore the income variable is signifi cant across all the se ries with an impact on housing prices ranging from 0.1 percent to 1.0 percent. Overall unemployment was only found to be significant in two of the series and took opposite signs in each. As expected the cost of construction variable was positive across all the series, and interestingly in the Freddie Mac Adjusted series was estimated to be 0.422 where cost of materials is about half the total cost of construction. In an article that explores internat ional housing price dynamics, Peter Englund uses fifteen Organization for Economic Co-operation and Development (OECD) countries including the U.S. to determine th e similarities between housing prices. Using an autoregressive (AR) model, changes in housing prices are found to be auto correlated, with a one-period lag having positive coefficients ranging from 0.23 to 0.74 at a 99 percent significance le vel. When using an AR(2) mode l, lagging the changes in housing prices for two periods, the fi rst order coefficient is positive and the second negative, which is consistent with finding of Case and Shiller who find positive autocorrelation in the first lags and negative autocorrelation as lags increase. Furthermore, housing price
24 changes from the previous time period along with lagged GDP growth rates and real interest rates are regressed for changes in housing prices. Englund finds that a one percentage point increase in GDP growth in the past time period increases current housing price changes by 0.77 percent. The interest rate coefficient was found to be significant in all the countries at a least a 10 percent level and was negative in all countries except Italy. Though the authors main undertaking was to examine the interdependence of housing markets in the inte rnational arena, thei r results show clear estimates on the effect of autocorrelati on in housing prices. The findings are firmly supported by previous literature. The empirical estimates for factors affecting housing prices and demand are relatively consistent in the sign of the coefficients, with a few exceptions such as unemployment. Overall it is clear that housi ng prices are positively autocorrelated in recent periods, and negative in subsequent peri ods. The income effect is largely thought to be significant as well as positive, although there exis t different methods about which income indicator should be used. The rent to price ratio is largely thought to be somewhat significant, but also suffers from some sta tistical problems when incorporated with a greater number of variables. Marginal tax rates are inco rporated into the models differently sometimes as a single independent va riable and more often incorporated into a user cost variable, therefore it is difficult to measure the true e ffect on housing prices. The studies briefly listed above are not unifo rm in regressors, which may account for the large variance in numeric coefficient estimates. The differences can also be attributed to the distinctive housing price series that ar e used for the dependent variable, although
25 Peek and Wilcox construct estimates for a number of series. These articles illustrate decades of housing dynamic evolution, but mo st of the authors admit that they do not paint a complete picture. This thesis hypothe sizes the investment factor of housing is misrepresented in current models, which recent literature explored theoretically and to a lesser extent empirically. Recent theoretical innovations in Housing Demand Dynamics While housing demand literature has often in corporated future expected prices and current prices, it often assumes that increases in current prices decrease demand while increases in future expected prices increase demand. Dusanksy et al asserts that this method obscures the process by which expectations are formed14 by limiting the effect of current prices on future expectations. Th erefore a two-period mode l of consumption of goods and housing services is constructed. In the first period the consumer works, earns an income, chooses an optimal amount of housing services (assuming the consumer does not rent, but has owner-occupied housing) a nd consumes a bundle of goods. In the second period it is assumed the consumer retires and consumes only rental housing services and a bundle of consumption goods. The utility function is defined as U U ( x1, h1, x2, h2 r) where x is the bundle of consumption goods in th e specified time period and h is the housing services consumed in each time period. The budget constraints in time period one is determined by income or wealth Y and is expressed as pi 1xi 1 p 1h1 i 1 n Y, where p is the price of consumption goods and 14 Dusansky 291
26 housing services. Under this assumption, the housing services in the first time period are both consumption goods in the current time an d an investment for time period two. In time period two, income is determined by a fi xed income S (i.e. social security, pension plans, and retirement savings) and the valu e of housing from time period one at the current price (p 2h1 ). The budget constraint is given as pi2xi2 pr2h2r i 1n S p2h1 where p again represents the prices of c onsumption goods and rental housing. Therefore the consumer must choose housing services in time period one not only to maximize utility in that time period, but also to maximize the ability to consume in time period two. Then using data from the 1990 Survey of Population Housing a new data set is constructed approximating for about 5 percent of housing units in the US. Other data is collected from Public Use Microdata Areas (PUMA) for hot spot s in the state of Florida with the supposition if capital gains e ffects were to be observed they would be observed in hot areas. Some demographics such as age, sex, race, income, married, immigrant status, dividend income, and educatio n are used in the model for the choice of tenure as well as demand, meaning the aut hors are examining the demand for and the choice to consume owner-occupied housing. Permanent income and the price of a standardized unit of housing are es timated using hedonic regressions.15 Dividend income 15 Permanent income: Yp() Yp 1 v Xp'p Dpp Where Yp = observed income of household Xp = the personal characteristics D is a vector of PUMA dummies = the Box-Cox nonlinear transformation parameter.
27 is defined as annual interest, dividend, or rental income of mo re than $400. Rental housing prices are also included. All demographic variables are significant except for education for the choice to own a home. In the regression for housing demand, sex and household size are not significant. Unlike tenure choice, education is significant as well as positive in the demand for housing. As previous theory dict ates permanent, transitory, and dividend income are positive and significant at a 0.05 level or better. The coefficient for dividend income is much larger in magnitude than th e other two forms of in come, perhaps because individuals with significant di vidend income tend to have higher incomes in general. Importantly, the price of owner-occupied housing is both positive and significant, which is contrary to demand theory for non-inferior goods. As housing is both an investment a nd consumption good, the demand for housing should be impacted by increase s in prices negatively in regards to consumption and positively in regards to investment. Therefor e the authors suggest a sufficiently strong capital gains effect can cause the own-dema nd for owner-occupied housing to be upward sloping, even though housing is a non-inferior good.16 Moreover, since the coefficient for the price of housing is positive they hypothe size that the investment potential of home dominates its role as consumption good. 16 Dusansky 297
28 In an attempt to determine the impacts of tax benefits for homeowners, Swank et al construct an extensive theore tical model of housing demand and supply and then use data to construct an empirical model. The aut hors distinguish between two types of owneroccupied housing starter homes or flats a nd larger dwellings or houses as well as between two types of house hunters starters consuming flats and movers consuming houses. The two types of hunters face th e decision to either move up the housing ladder or stay in their current consumption pattern. This multi-tier model makes several other assumptions or omissions; it ignores property and capital gains taxes, as well as taxation of imputed rent (the em pirical data includes some co untries that tax imputed rent unlike the U.S.), as well as the cost of main tenance and depreciation. With that said, the distinctions between house hunters and types of owner-occu pied housing are extremely useful in studying movements up the housing ladder. The model separately and simply defines the supply of houses and flats in accordance with the notion that house holds are consistently m oving up the housing ladder or remaining in their current housing situation. As movers upgrade to houses, flats become available to starters. Therefore the supply of flats is determined both by new construction, as well as the demand for houses. Concurren tly, new construction and the current housing stock determine the supply of houses. As in most housing literature, the level of new construction is dependent on the price of flats and houses respectively. The starters demand functi on is defined by income Ys and the difference between the real rent of the current home and the real cost of owning a fl at, in which the down
29 payments, mortgage payments, and expected fu ture returns are included in the price of owning the flat. The movers demand function is decomposed into two scenarios both dependent on permanent income Ym and the user cost of moving into a house, determined by the downpayment, transaction costs, and the expected future returns. They construct two scenarios, the first is where the home owner has cashed out al l capital gains on the current flat to retain a maximum loan-to-value (LTV) ratio or (1), where is the minimum downpayment ratio. The homeowne r is still constrained by a borrowing capacity of (1)(Ph-Pf) where Ph is the price of the house and Pf is the price received for the flat. This first scenario represents favorable tax treatment of mortgage deductibility, because in this environment effective yield of other financial assets would be greater than the effective interest rate with the mortga ge deductibility. Under this assumption the homeowner would cash out gains in order to invest in other assets, by maintaining the highest LTV ratio the owner frees capital to be invested. The second scenario is where the homeowner uses the full surplus on the flat as the downpayment on the new home, under the assumption that the mortgage deductibili ty from taxation is either absent or not large enough incentive to promote the cashing out of capital gains. The model ultimately utilizes the first scenario in order to fully investigate the impact of mortgage deductibility. By combining the equations for the demand of starters and movers and the supply for flats and houses and solving for prices Ph and Ph, the model analyzes the movement of prices due to changes in income, taxability and credit rationing for both types of house hunters. Using the theoretical model, it becomes evident that a rise in income for starters
30 increases both the price of flats and houses As demand for flats increase, the price increases, and thereby increases the capital gains for movers and c onsequently increasing the demand for houses therefore the price of houses. Conversely, if only the income of movers increases, houses increase in price and flats decrease as movers demand more houses increasing the supply of flats as they move. Therefore, the gap between house and flat prices depends on the sum of actua l and discounted expected future incomes of movers, with the effective interest rate faced by movers serving as the one-period discount rate.17 Under the assumption that movers te nd to have higher income, it can be verified that real income in creases for higher incomes can increase the ability of starters to purchase flats due to decreased flat prices. Turning to fiscal accommodations for mo rtgage interest deductions, the model incorporates marginal income tax deductibility of interest payments in the user cost section of demand. Theoretically, if the tax deductibility is increased for starters the prices of both flats and houses increase, with the price of flats increasing at a greater rate, unless the price-elasticity for the c onstruction of new flats is zero.18 Moreover, the tax deductibility for movers drives up the prices of houses, ther eby creating more incentives for new housing construction. The new cons truction enables more movers to move, thereby opening more flats for starters to pur chase. As movers vacate flats, the stock of flats will increase and drive down the price of flats. Consequently, Swank postulates, limiting the deductibility of mortgage interest paid by higher income groups (e.g. to the effective rate of tax relief faced by starters) would be detr imental for all income groups 17 Swank et al 8 18 Swank et al 9
31 seeking to move up the housing ladder.19 Although, when interest rates are extremely low and movers are facing higher than e xpected growth rates of income, the fundamental solution is violated20 and prices can explode an d may have destabilizing effects on the housing market. Finally, the theoretical model explores the m ovement of prices due to changes in the maximum debt-service ratio. As starters are income constrained, the assumption is that the mortgage payment cannot exceed some pr oportion of their inco me, a debt service ratio. If this ratio decreases due to lessen ing of credit standards, it would increase the price of flats.21 As previously discussed, this w ould increase the movers income and thereby the price of houses. Furthermore, high LTV for move rs can increase prices while also increasing instability, esp ecially in environments such as the first scenario, where tax benefits encourage the arbitrage be tween mortgage borrowing and financial investment.22 The movement of prices and stabil ity due to the lessening of credit standards is more fully examined in the empirical evidence. Moving past the theoretical c onstruction, the authors create an empirical regression of quarterly data, elasticities of new housing supply for price, wage, and capital costs, and producer confidence are estimated. Denmark, France, Germany, the Netherlands, the UK, and the US are all examined. The price elas ticities vary drasti cally across all the countries, but Denmark, the Netherlands, a nd the UK had the smallest as well as the 19 Swank et al 10 20 Swank et al 8 21 (1 ) ilPf* q Ys 10 22 16
32 highest housing price volatility defined by the variation coefficient over the time period. Germany had the lowest LTV ratio as well as the lowest price vol atility. Overall the authors attribute volatility in housing prices to inelastic supply for new construction, preferential tax treatment and high LTV ratios. Analyzing Rapid Price increases during the Bubble In the midst of the peak of housing prices economists were scrambling to explain the rapid run up in prices. In 2005 Robert Sh iller warned of the impending bubble and the catastrophic effects of its burst. While so me believed that housing prices had been discounted prior to the bubble and were just ad justing to real values others claimed that prices had deviated far from the fundamenta l values dictated by long established housing price indices. The research done during this period illustrates a deviance from traditional models of housing price dynamics, which in ma ny ways failed to correctly estimate the run up in prices. The investment component of housing came under new scrutiny as increases in prices made the capital gains from housing more attractive. Traditional models that measure the lik elihood of a bubble in the housing market rely heavily on comparing housing price indexes to other rental indexes to determine if housing prices are above fundamentals. In Bubble, Bubble, Wheres the Housing Bubble? Smith et al claim this method is flawed, as it does not measure true fundamentals of the housing market. In opposition to Shiller and Case who assert that, A tendency to view housing as an investment is a defini ng characteristic of a housing bubble,23 Smith et al 23 Case and Shiller (2003)
33 believe that valuing housing as an invest ment is a more accurate way to measure fundamentals. Therefore they utilize a model that expresses the net present value of a home in terms similar to bonds and stocks. The net present value (NPV) is calculate d by discounting the cash flow from the home, or the rental value consumed by the owner. The equation ta kes into account both the initial costs and future costs as well as a required rate of return. The NPV is defined as NPV X0 X1(1 R )1 X2(1 R )2 ... Xn(1 R )n From time period 1 through time period n where X0 is the downpayment, transactions co sts, and other out-of-pocket initial expenses and assumes a negative sign. Xt is the cash flow, rental value, less mortgage payments (interest payments deducted at the ma rginal tax rate), insurance, property taxes, and maintenance cost. And R is the individual s required rate of retu rn based on the rate of return for other investments. If the NP V is positive, the authors hypothesize the home is worth the cost, and, conversel y, if it is negative renting is a better choice. By solving for the price of the home that would make NP V zero, one can find the reservation price of the home, or the fundamental value. This rese rvation price is then used to determine if homes sold during the time peri od were bought at a premium. While much of housing market dynamics are dictated by indices, the authors believe that actual rent and home values are a much better indicator in measuring bubbles, because indices consider homes to be homogenous in both their amenities and locations and often overlook depreciation or remodeling value. Therefore the authors construct a data set of ten metro areas. Instead of using rent ratios or price indices, they
34 attempted to match home sales with equal rent al units to find more accurate price-to-rent ratios. In order to find the best equal subst itutes between rental and owner-occupied, they limit the differences between the two units ma tched to number of bathrooms, number of bedrooms, square feet, and distance from each other. The data was gathered in fall of 2005 looking at records from May-September with roughly 100 matches for each of the 10 metro areas including Atlanta, Dallas, Los A ngeles, Chicago, Indianapolis and several California counties. Further assumptions were made about mo rtgage standards including a 20 percent downpayment, a thirty-year fixed rate of 5.7 percent, closing costs of 0.5 percent of the price of the house, and annual maintenance cost of one percent. Marginal tax rates are fixed at 28 percent, a capital ga in tax rate of 15 percent fo r gains over $500,000, and state and local property taxes are used for each specific metro area. Two different holding periods are examined; a ten-year period and infinite period, assuming the house is never resold. Of all metro area matches used in pred icting ten-year horizons only San Mateo was found to have a premium on fundamental va lues of 42 percent. The remaining nine areas had estimated discounts ranging from 4 pe rcent to 68 percent. In an infinite horizon San Mateo and Orange County had a premium of 54 percent and 2 pe rcent respectively. The remaining areas still had discounts rang ing from 11 percent to 65 percent, under the assumption that housing prices increase 3 percent each year.24 The authors conclude that 24 Smith et al 26
35 the fundamental values of the homes explain the price increases, and find that almost all of the areas studied were not experiencing a housing bubble. In order to measure fundamental values correctly for future time periods where the growth rates for rents and housing pri ces are uncertain, the premiums are again estimated for several different rates with rent s increasing from 0 per cent, 3 percent or 6 percent and housing prices incr easing 2 percent 3 pe rcent or 4 percent. As annual rents increase, the discounts also increase especially as housing prices incr ease. At 4 percent annual rent growth and 6 per cent housing growth all areas are in discounts, even at 3 percent rental growth and 3 percent housing growth a ll but San Mateo county are discounted. Although at zero annua l home sale price growth, all but four of the metro areas have high premiums, but as soon as any annual home price growth is assumed discounts are realized across re ntal increases, except in San Mateo and Orange counties. When mortgages rates are incorporated, discoun ts begin to shrink some shifting into high premiums as the annual mortgage rate incr eases, as corollary di scounts increase as the mortgage rate decreases. According to this model only one metro ar ea exhibits signs of bubble behavior, because the estimated fundamental value is higher than the sale price. Post Bubble Analysis After the housing bubble had burst and prices declined rapidly, ma ny economists sought ways to explain the run-up of prices, which had previously been thought to be based on fundamentals. While Case implicated that irra tional expectations of future-housing prices was at the heart of the bubble, many placed the blame on subprime lending.
36 Coleman et al (2008) use data from twen ty metro areas to test the notion that subprime lending facilitated the price explos ion during 1998-2006. Util izing two separate time periods to investigate the credit regi me change that took place in 2003 when government-sponsored enterprises (GSE) Fre ddie Mac and Fannie Mae decreased their purchasing of conventional confor ming mortgages and MBS securities25 allowing many new less regulated brokers to enter the market. Additionally, Coleman asserts that the GSEs began to loosen credit standards as the Office of Federal Housing Enterprise Oversight (OFHEO) required in November 2004 that they increase their lending to facilitate affordable housing initiatives. By splitting the observed peri od into two separate models, the model attempts to see if the credit regime shift affected prices. The basic structural demand and supply functions discusse d earlier in other literature are used for housing demand and supply, with an equilibrium condition QDt = QSt imposed. Loan data were gathered from HMDA and First American Loan Performance to obtain owner-occupant a nd non-owner occupant loans as well as information about home purchase loans by type including alt-A, BC (subprime), and jumbo loans, as well as non-owne r occupant (investor) loans.26 LTV ratios for newly issued home loans are found in the Federal Housing Finance Board s Monthly Interest Rate Survey (MIRS); but since this set does not distinguish how many high LTV loans were issued, Loan Performance data is used to estimate the proportion of newly issued loans with LTVs above 90 percent in order to get a clearer pict ure of how many loans 25 Coleman et al 284 26 Coleman et al 272
37 were high risk. Additionally LTV ratios repo rted in both data sets do not take into account piggy-back loan s used to finance downpayments, therefore another LP data set, which includes combined loan-to-valu e ratios, was used. During the time period CLTVs increased from 77 percent in 1998 to 80 percent in 2006, in line with the earlier assertion by Swanks that in environments of tax favorable treatment of mortgage deductibility, homeowners will cash out capit al gains through second mortgages. For housing prices, the Case-Shiller housing price index was used for all twenty metro areas allowing for the separation into three distinct tiers based on value of the homes. For the supply side of the housing market the au thors use Wharton Residential Land Use Regulation Index, which produces a basic sn apshot of residentia l housing supply side limitations for over 2600 localit ies and all the major metro areas in the study. The demographic and macroeconomic variables ar e derived from both the Bureau of Labor Statistics and the Bureau of Economic Analysis. During regime one, 1998-2003, all the macroeconomic fundamentals were significant and assumed signs dictated by housing market theory; per capita income was positive and unemployment was negative. Furthermore it had the least auto-correlation. The subprime loan coefficients were positive and marginally significant on contemporaneous housing prices with 0.17 percent magnitude, meaning a 1 percent increase in subprime loan density increased quarterly HPI (Housing Price Index) returns by 0.17 percent. CLTV were also found to be significant, but nega tively correlated to housing prices but at only a 0.03 percent level. Interestingly, investor loans had a positive effect on housing prices in three, six, and ni ne-month lags; but changed signs after twelve
38 months. The authors posit that this effect may be due to intended flipping of homes after one year, because investor loans were us ed to purchase homes that were sold after a year. Therefore increases in non-owner occupied loans would drive up demand and thereby prices for a year, but after a year the house would be placed back on the market and increase the supply, ther eby decreasing the price. In regime two 2003-2006, the macroeconom ic fundamentals all lose their significance, which could be indicative of a bubble, as there were other factors driving housing price returns. Both jumbo loans and su bprime loans also lose significance during regime two, but alt-A and investor loans in crease in significance in the contemporaneous period. Similarly to regime one, investor loans maintain a positive impact on housing prices for a time, but the sign become negativ e after nine months. Furthermore the yield curve (the ratio of 10-year to 2-year treasury bi lls yield to maturity) is highly significant implying a flattening of the yield curve af ter the Fed began raising rates in 2004 had a strong accelerating effect on housing prices.27 This effect should dictate a decrease in demand for loans seeking low rates, but the authors suggest that many borrowers rushed to exit in order to lock in lower interest ra tes before they continue to increase. Regime two also had the highest estimated value of which may indicate the highest degree of momentum in housing returns due to auto correlation from previous periods. In the multi-tier model that differentiates the model based on values of homes, the subprimes effect was the strongest and pos itive in the high-end home tier with a 10 27 Coleman et al 286
39 percent increase in subprime density lead[i ng] to a 2.4 percent increase in quarterly returns after a year.28 Subprime density was not significant at the lower tiers. In the aggregate the authors suggest the percent of originated loans that were subprime had virtually no statistical significance on future home prices.29 Rather, the primary driver of housing prices from any initial time period up un til nine to twelve months tended to be investment loans, but decreased pric es after nine or twelve months. Overall Coleman et al believe their findings to support th e hypothesis that subprime was not the cause of the housing price e xplosion, rather that the shift away from GSEs dominant role as a mortgage le nder during the second regime. As GSEs decreased certain types of lending, other broke rs and private issuers entered the market supplanting conventional and perhaps safer loans. Therefore, they posit that the growth of subprime lending was a joint byproduct of a political shift in the GSE management, which coincided with high housing prices. In a related but separate ar ticle Foote et al examine s ubprimes role in foreclosure rates and not so much in driving of hous ing prices. While foreclosure rates and the financial crisis that followed are outside of th e scope of this thesis, standard models of housing finance predict that fa lling prices make foreclosur es more likely by fostering negative equity.30 Therefore, the resulting rise in foreclosures offer a respectable explanation for rapid decrease in housing prices, which may have created a bigger 28 Coleman et al 287 29 Coleman etl al 283 30 Foote et al 293
40 bubble burst than fundamentals would dictate, because as rates of foreclosure increase due to subprime lending, housing prices ar e likely to fall due to excess supply. Unlike Coleman, the data utilized are area specific to Boston and southern New England. While the only one of the metro ar eas is used, the Warren Groups Registry of Deeds data is particularly helpful as it tr acks real estate transactions by individual property. This method allows the construction of a complete owners hip experience. Since the Warren Group dataset lacks interest rates, First American Loan Performances is used to define interest rates as well as loca te where the mortgages ended up securitized. Subprime loans are defined not by credit scores or interest rates, but by the Housing and Urban Developments list of predominantl y subprime lenders and match mortgages issued to create the subprime loan data set. More specifically the th eory that adjustable rate mortgages (ARMs) caused high levels of fo reclosure due to reset ting rates is tested. Firstly, default rates are not found to be significantly correlated with ARMs across the years examined. Of the subprime ARMs issued in 2001 only 22.3 percent were still active three months after interest rates reset with about 66 percent refinanced and 34 percent were in default, concurrently of the loans issued in 2002 and 2003 roughly 74 percent had refinanced three months after the reset. In fact, default rates increase rapidly up until the first twelve months, but then fall dr astically. This is contrary to the theory that resetting interest rates caused high level of defaults, as one would expect to see spikes after twenty-four months or when the new interest rates come into effect.
41 Furthermore, the later years of subprime ARMs had higher default rates, most likely due to lack of time to build equity in the home before prices began to decrease. Many point to the lessening of underwriti ng standards as another factor in foreclosure and further claim that borrowers who should not have qualified for loans were offered subprime lending. FICO scores, LTV ratios, Debt-to-In come (DTI) ratios, and documentation status (the amount of paperwork recorded) are often used as characteristics in determining the qualific ation of borrowers. One would expect as unqualified borrowers entered into new loans th at average FICO scores would decrease, but from 1999 to 2006 average FICO score for subprime lending was increasing. This fact alone would make the subprime pool more stable, but looking at DTI and LTV one can see how the subprime market changed from low FICO scores. The CLTV ratios increase across all vintages as credit scores range from 580-700 to almost 95 percent in 2005-2006 for scores over 660. Similarly docum entation status falls starting at 620 and rising again at 740. The aut hors posit that potentially prime borrowers moved into subprime in order to finance higher prices Furthermore about 10 percent of subprime loans in the LP data set met criteria to appl y for lower interest rates from prime lending. The authors suggest that poten tially prime borrowers used sub-prime to finance larger homes that were either refinanced or sold before rates reset. Lessons Learned The body of literature on housing demand is varied in both its assumptions and methodology. The empirical estimates for de terminants of demand mostly focus on
42 changes in housing prices. These estimates of fer insight into what moves housing prices. By far the most significant determinate is previous housing prices; increases in the previous period are estimated to account for at least one third of current housing prices. The autocorrelation is important when bubbles start to form, as significant increases in housing prices in one period can account for a portion of increases in the next. Therefore sizable increases in housing prices can spur future increases, and if the negative effects of longer lags begin to decr ease a bubble could form. New literature has given rise to previously unstudied effects on housing. Swank et al create a theoretical model that predicts th at preferential tax tr eatment of mortgage interest in an environment of low interest rates can cause housing price explosions as house hunters face borrowing rates that are lowe r than their income growth rate. While the model is not actually empirically test ed, some conclusions are drawn from price volatility in countries with differing policie s. Conversely, Dusa nksy clearly outlines a simplified theoretical model for capital ga ins effects on housing choice and tests the model using data. They find that housing prices have a positive impact on housing demanded, and that strong capital gains eff ect or an investment effect can offset decreases in demand dictated by traditional consumption theory. Consequently, if the investment potential of a hom e is greater than other investment opportunities, more housing services can be demanded. Considering the formation of a housing bubbl e, the assumption is that a housing bubble exists when housing prices are drasti cally above fundamental values, usually
43 determined by rental indexes. Smith et al be lieved that housing prices were not above the fundamental values, and that prices were adju sting to equilibrium after being depressed. These assumptions are somewhat faulty, especia lly in light of the national standards they applied to their model. Du ring the bubble period, credit standards were lessened significantly. Coleman etl al fi nd that the percentage of s ubprime loans did not have an impact on housing prices, but rather non-owner occupied loans tended to increases prices. Furthermore, Coleman finds that the tr aditional determinants of housing became insignificant during the bubble period, pointi ng to that some other force was driving prices. In the next chapter, the model for housing prices is presented in which this assumption by Coleman et al comes into play.
44 Chapter 4: Econometric Model Data The data used to estimate determinants of housing prices comes mainly from government reports and datasets. Although the series fo r housing prices came from the National Association of Realtors, the data is for the national median average sale price of existing single-family homes. Both data sets for personal income and dividend income were accessed on the Federal Reserve Bank of St Louiss data portal Federal Reserve Economic Data (FRED), but were compiled by the U.S. Department of Commerce. Thirty-year mortgages rates were also accessed via FRED, but were complied by the Board of Governors of the Federal Reserve System. Loan to Value ratios were accessed at Federal Housing Finance Agencys website as part of their M onthly Interest Rate Survey (MIRS). Lastly the rental index wa s accessed at the Bureau Labor Statistics website as one part of the Consumer Price Inde x. All of the data was placed in quarterly series, for data that could not be collected as quarterly data the average of the three months in any given quarter was used. Below are the graphi cal representation of housing prices, LTV ratios, and AAA bond yield.
45 Graph A QuickTime and a decompressor are needed to see this picture. Graph B QuickTime and a decompressor are needed to see this picture.
46 Graph C QuickTime and a decompressor are needed to see this picture. Methodology First and foremost in order to estimate a time series regression all the variables must be made into stationary series. Since most of the data acquired was trending upwards, the first difference of each sets previous values we re used to create sta tionary series. These new series were run through an Augmented Dick ey-Fuller test in or der to see if a unit root existed. All of the series were found to not have a unit r oot with at least at the 90 percent confidence level. Only two could only be confirmed at the 90 percent confidence level; AAA bond yield and LTV. Furthermore only one, Rent index, was at the 95 percent confidence level, with the rest show ing no unit root at a 99 percent confidence
47 level. Since the data sets were not found to ha ve a unit root one can assert that they all were stationary. Model Now that a function from chapter two has b een created it becomes necessary to assign variables to represent them. X represents the exogenous f actors such as preferences demographics and income, therefore personal income was used in the regression. User costs are defined by both mortga ge interest rates and marginal tax rates, therefore the thirty-year mortgage rate is used. The rent al index is utilized for R, and Moodys AAA bond yield is used as a proxy for rates of retu rn on other investments. Finally the LTV represents credit standards. A simple Ordinary Least Squares re gression would be written as such: P 0 1Income 2MortgageRate 3Re ntalIndex 4AAABond 5LTV (3.1) When this simple regression was run through eViews, it was clear th at it suffered from auto correlation, evidenced by a low Durbin-Watson statistic. Furthermore, previous literature has established that housing prices suffer from pos itive autocorrelation in short lags. In order to remove the auto correlation dynamics are cr eated to account for inertia. Three types of inertia are widely accepted as the culprits for auto correlation; Psychological, Technological, and Institutional. By including lags on the regressors and regressant, one can account for changes over the time periods. In order to best illustrate
48 the lags; an Autoregressive Distributed Lagged (ADL) model was created. The ADL model lags both the dependent variable ( p ) and the independe nt variables ( q ). Therefore the model is defined as ADL ( p,q ). For housing demand an ADL(2,1) was found to be to suitable. The new model is as such: Pt 0 1Pt 1 2Pt 2 1Income 2MortgageRate 3Re ntalIndex 4AAABond 5LTV 6Incomet 17MortgageRatet 18Re ntalIndext 19AAABondt 110LTVt 1(3.5) This model fully incorporates all the necessary lags to remove the serial correlation. The long run multiplier of any of the independent variables can be estimated by their coefficients and the coefficients of lagged housing prices or from the following equation i j1 (12) (3.6) Where i is the coefficient of some variable in time t and j is the coefficients in time period t-1 Notes on the Model A correlation coefficient matrix is deve loped to see how each variable affected others. This is extremely important to determin e if there is multicollinearity, or that one or more of the variables is correlated to th e other. The matrix is in the table below. Table A HP2 PI MORTG2 RENT2 AAABOND2 LTV2 HP2 1.000 -0.097 0.126 -0.033 0.001 0.189 PI -0.097 1.000 -0.271 -0.173 -0.350 -0.054 MORTG2 0.126 -0.271 1.000 0.135 0.920 0.498 RENT2 -0.033 -0.173 0.135 1.000 0.138 0.021 AAABOND2 0.001 -0.350 0.920 0.138 1.000 0.448 LTV2 0.189 -0.054 0.498 0.021 0.448 1.000
49 As one can see Mortgage rates and AAA bond yield are highly correlated; where one variable makes up 92 percent of the changes in the other. This would produce problems of multicollinearity, which can decrease the significance level of the individual variable in the regression. This issue will be discussed in the following section. While the ideal user cost variable woul d be a function of maintenance costs, property taxes less the tax deductibility, and mortgage payments less tax deductibility; national data for property taxes and mainte nance costs could not be compiled. Which should leave the after tax cost of borrowing within this model as im(1 ty) where im is the mortgage rate and ty the marginal tax rate. When this function was created in Eviews and used for the user cost portion of housing prices, it was found to be insignificant. Therefore, the mortgage rate was used separa tely from tax rates. The tax rate was only found to be significant in the period befo re the bubble, alth ough it increased the significance of the rental inde x in the full model. The full output from the separated tax model can be found in Appendix A. The model was deemed inferior to the one chosen and discussed below as the significance of the variables decreased. Furthermore, a wide variety of different in dicators were originally used in a broad model. Different types of inco me, housing prices, and exogen ous variables were used, but were found to be insignificant. Moreover, th e bubble period could not be run separately because of the number of observations. The model was culled down several times. The raw output from these models can be found in Appendix B.
50 Results The model was run for three overlapping time pe riods to test both the robustness of the results as well as monitor changes that occurred during the specified Bubble period. The first model incorporated data from a ll time periods from the last quarter of 1990 through the last quarter of 2007. The second mo del was designated as prior to the bubble and incorporated the time series from 1990 through the last quarter of 2001. The final model examines the Bubble pe riod and runs from the first quarter of 2002 through the last quarter of 2007. The resu lts are reported in Tables AC, with significance levels indicated by asterisks, where three repres ents significance at a 99 percent confidence level, two represents significance at a 95 pe rcent confidence level, and one represents significance at a 90 percent confidence level.
51 Table A Table B Table C Table D Full Model 1990-2007 Variable Coefficient Std. Error Housing Prices(-1)*** 1.015 0.111 Housing Prices(-2)*** -0.355 0.122 Personal Income*** -436.956 105.097 30-year Mortgage Rate*** 6181.000 1514.574 Rental Index -510.905 477.541 AAA bond yield*** -8213.716 2111.673 LTV** 514.864 249.763 Personal Income(-1) 24.596 107.027 30-year Mortgage Rate(-1)*** -5630.140 1907.526 Rental Index (-1) 460.573 503.402 AAA bond yield(-1)* 4903.643 1842.245 LTV(-1) 276.648 258.491 R-squared 0.74469 Adjusted R-squared 0.689981 Prob(F-statistic) 0.000000 Prior to Bubble 1990-2001 Variable Coefficient Std. Error Housing Prices(-1)*** 1.019 0.125 Housing Prices(-2)** -0.320 0.141 Personal Income*** -407.569 93.234 30-year Mortgage Rate*** 7300.940 2027.464 Rental Index -92.964 629.646 AAA bond yield** -7235.155 2865.150 LTV*** 548.230 181.558 Personal Income(-1) 129.441 119.474 30-year Mortgage Rate(-1)*** -7691.990 2670.985 Rental Index (-1) 386.800 592.078 AAA bond yield(-1)* 5275.041 2644.818 LTV(-1) 374.974 338.300 R-squared 0.779021 Adjusted R-squared 0.696153 Prob(F-statistic) 0.000000 During Bubble 2002-2007 Variable Coefficient Std. Error Housing Prices(-1)*** 0.876 0.228 Housing Prices(-2) -0.255 0.187 Personal Income -572.862 349.181 30-year Mortgage Rate 5311.594 3455.366 Rental Index -1114.525 1459.404 AAA bond yield*** -11826.280 3647.870 LTV 864.515 1141.430 Personal Income(-1) 4.242 369.262 30-year Mortgage Rate(-1)* -7953.100 3863.735 Rental Index (-1) 1694.476 1324.331 AAA bond yield(-1) 8646.632 4933.578 LTV(-1)* 1791.952 937.547 R-squared 0.85626 Adjusted R-squared 0.699453 Prob(F-statistic) 0.00421 Long-run Multiplier 1/0. 340 1/0.300 1/0.379 Variable Full Model Prior to Bubble During Bubble Personal Income -120.823 -926.064 -915.783 30-year Mortgage Rate 1617.503 -1302.055 -4254.242 Rental Index -147. 790 978.367 934.032 AAA Bond yield -9719.44 3 -6526.469 -5120.94 LTV 2324.135 3073.936 4278.338
52 Table D shows the calculations for the long run multipliers of each variable in each period. These values were calculated by using equation 3.6 and the coefficients from each period. The combined coefficients fr om the current time period and the lagged period are multiplied by the values in the ta ble in the long run multiplier row. In the full model, the estimates for th e lagged changes in housing prices are consistent with literature and are highly significant. The first lag is positively correlated with current housing prices where the second is negative just as Case and Shiller find. All the concurrent variables are significant to at least a 95 percent confidence level except for the rental index. Personal income takes a nega tive sign, which is contrary to what theory would dictate. AAA bond yield in the current period is also negativ ely correlated with housing prices, which is congruent with the assu mption that as the rates of return on other investment increase that housing prices w ill decrease. Furthermore, LTV ratios are positive, which supports the notion that as one of the initial cost of owning a home (a downpayment) decreases that housing prices wo uld increase. In the second lag of the independent variables in the fi rst model only two are significant. Only mortgage rates are highly significant at a 99 percent confidence le vel, and this lagged value takes a positive sign. In the period leading up th e bubble the coefficients are similarly significant and all the signs are the same as in the full m odel. The only differences in significance arise in housing prices from two periods previ ous and AAA bond yield decreasing to a 95
53 percent confidence level. The R2 values increase in this pe riod, although the adjusted R2 is only about .007 higher, which is be due to the decreased degrees of freedom as there are only 45 observations compared to 69 in the full model. The Bubble period changes dras tically, only four of the variables are significant and only housing prices in the previous pe riod and AAA bond yield are highly significant at a 99 percent confidence level. The lags of both 30-year conventiona l mortgage rate and the LTV ratio are significant, but only at a 90 percent confidence level. Both of these slightly significant variables take the signs di ctated by theory. All things held constant an increase mortgage rates in the previous pe riod drive down housing prices, and an increase in LTV ratios increase housing prices. The housing prices from the previous time period are highly significant and are smaller than the other two pe riods, as is the second time period, which is not significant. The long run multiplier table shows the calcul ated effect of each variable in terms of the autoregressive housing price lags. Persona l income in all three periods is negative, which contradicts housing price theory. The 30year mortgage rate multiplier is positive in the full model, but negative in the other two. As interest rates increase the user cost of owning a home increases, therefore one would e xpect to see a negative correlation. While the bubble periods long run multiplier for mortga ge rates is negative, the significance is called into question as only the lagged pe riod was significant and even then barely. Furthermore the rental index between the pe riod prior to the bubble and the bubble period is very similar in magnitude, the coefficients in all three models were not found to be
54 significant. Interestingly AAA bond yield is negative acro ss all three pe riods with decreasing magnitude in the tiered periods a nd is significant across all models and lags except for the lag in the bubble period. The LTV ratio is positive acro ss all the periods, as expected and previously explained. These l ong run multipliers are difficult to utilize as they incorporate some coefficients that are not found to be significant, but this problem will be discussed later. Taking into consideration that multicollinearity exists between 30-year mortgage rates and AAA bond yield, one would expect that the coefficients would be less significant. In the full and pr ior to the bubble model both of the coefficients are highly significant in the concurrent time period; with mortgage rates remaining highly significant in the second period and AAA bond yield falling to 90 percent confidence level. In the bubble period c oncurrent mortgage rates are not significant, but the lagged coefficient is slightly significant. AAA bond yields are highly significant in the concurrent time period and not significant duri ng the lagged period. While there is some concern about losing significance due to the multicollinearity on the whole the coefficients will not change drastically, and since most of the variables are highly significant in spite of the multicollinearity handicap the model is not rejected as insignificant. As Blanchard wrote, Multicollinearity is Gods will.31 As the coefficients remain significant and the coefficients do not suffer from change, this thesis will allow Gods will to remain within the model. 31 Blanchard 1967
55 Analysis The entire period and prior to the bubble pe riod are extremely similar in both their significance and values of coefficients. This can be attributed to the fact that over half the observations in the full model are from the peri od prior to the bubble. Additionally, in the period prior to the bubble housing prices had relatively steady growth rate therefore should exhibit traditional values associated with housing demand. The autoregressive tendency of housing pr ices is crucial to understanding housing price dynamics. Tradit ional approaches to housing dema nd predict that housing prices will have a negative effect on housing dema nd, assuming a typical non-inferior good dynamic. Prices from the previous time pe riods are important indicators of current housing prices, but previous liter ature has found that short term lags of housing prices are positively correlated with future housing pr ices while longer lags are negatively correlated. The first lags positive correlati on can be attributed to inertia while the subsequent negative correlations of lagged prices conform to the notion that asset returns generally revert to a mean. The Bubble period is interesting because almo st all of the determinants lose their significance. Coleman et al have similar fi ndings in their bubble pe riod where all their macroeconomic indicators, which were sign ificant in the period before the bubble become insignificant. The loss of significance can be attributed to the fact that traditional drivers of housing prices were not driving th e rapid increases. Th e first lag of housing prices is highly significant driving housing prices forwar d. During the bubble years the
56 autoregressive tendency of housi ng prices can have explosive e ffects, as each subsequent time period has increases in prices, which cont inue to drive future prices. Concurrently, the negative effects of two la gs in housing prices decrea ses during the bub ble and loses significance; perhaps pointing the fact that negative price effects that help stabilize housing prices were decreased during the bubble. The past increases of housing prices during the bubble can be seen as expectations of furthe r housing price increases. As future expectations increased the investme nt potential of the owning a home increased, and people purchased housing for fear of being priced out of the market. Furthermore, AAA bond yield is extrem ely significant and negative supporting one of this thesis hypotheses that as the rate of return of other investments affects the demand for housing. During the bubble, as rates of returns of other investments fell, the expectation of future gains in housing was relatively high. Theref ore the investment component of housing was positively driving housing demand. Obviously traditional determinants of housing prices were not driv ing prices during th is bubble period, but from this model one can only assume that i nvestment potential of the home overrode all other determinants. The long run multipliers between the mode ls help show the robustness of the overall model. Personal income is negative in all three models and highly significant in the first two tiers. A negative correlation to housing prices for personal income is highly inconsistent with housing dynamic literature, but the negative correlation persisted even when several different income measures were used. Furthermore the period before the
57 bubble and during the bubble have extremely sim ilar values leading one to believe that the results are robust. The negative of eff ect of income on housing prices could be attributed to speculative housing purchases, where overall income decreased to pay for the home and demand increased. Although, this correlation cannot be proved. The conventional mortgage rate multiplie r took a positive sign in the full model but was negative in the other two. One w ould expect mortgage rate increases to negatively effect housing demand, as it does in two of the models. The rental index, while insignificant in all periods, also shows a sign shift, negative to positive, from the full model to the two separate ones. This shif t from the full model sign to the other two models may be due to the lagged value of both variables in the full model having a smaller magnitude, which in the other two models creates the sign shift. Both the AAA bond yield and LTV ratios are co nsistent across all the time tiers. AAA bond yield is significant in all periods and is nega tively correlated to housing prices. The negative correlation supports the assumption that as rates of return on other investments increase housing demand decrease s, something previously unexplored in complete housing models. Moreover LTV ratios are positively correlated to prices, which is particularly important to the effects of credit standards. As the size of the downpayment decreases (and LTV increases) housing prices would be predicted to increase. As these two variables have consis tent measures in the long-run multipliers are fairly significant in each coefficient in th e model these results are fairly robust.
58 The lingering question is What caused the housing bubble? From these results the most significant factors that drove housing prices in the bubble period are previous housing prices and AAA bond yiel d. As previous period housi ng prices increased, current prices continued to increase, and the regulating second lag, which brings housing prices back to a general mean, failed to be signi ficant and decreased in magnitude. This is consistent with the notion that the investment potential of a home began to outweigh the consumption component. As Dusansky hypothesized, the housing demand curve may have become upward sloping.
59 Chapter 5: Conclusions The housing price explosion at the beginning of this century was the impetus for an entire global recession. While housing prices are not th e sole culprit in the collapse, the rapid decreases in value over the la st three years has left ma ny Americans in underwater mortgages. Jamie Dimon, the head of J.P. Morgan Chase, summed up the major flaw in the financial collapse surrounding the housing ma rket in his testimony to Congress when he said they did not consider that housi ng prices would fall. The assumption by many Americans that housing prices continue to rise prompting many to purchase homes as an investment vehicle drove the bubble forward. In Chapter Two, I undertook a new theoretical model for housing demand that fully realizes the investment potential of owning a home. While pr evious literature has incorporated the expected futu re returns of housing, it has ne ver offset this with gains on other investments. In the new model the i nvestment component of housing is treated similarly to the consumption component, with both factors having a substitute variable included. By approaching housing demand this way, a more complete picture is painted with regards to changes in capital gains tax rates and exemptions. While the theoretical model could not be run exactly as it was formulated, Chapter Four offers insights into the drivers of housing prices, with special attention paid to the housing bubble of 2002-2007. The main new contribution to literature was the
60 addition of other investments, which were modeled using AAA bond yields. This variable was found to be significant in all of the periods, and negatively correlated to housing prices confirming the assumption that rises in other rates of return will decrease housing demanded. Consistent with literature I f ound that many of the normal drivers of housing prices were not significant during the bubble, but rather pr evious housing prices, loan-tovalue ratios, and the investment side of hous ing was the major force in escalating housing prices. As Robert Shiller wrote, a tendency to view housing as a inve stment is a defining characteristic of a housing bubble.32 The findings from the simple regression support his assertion that the bubble was caused by the investment side of housing. If more data was made available such as collective loan to value ratios, a more precise regression could be created. Further research around the bubble should incorporate the collateralizati on of mortgages that were used by financial intermediaries to package and sell securiti es. While the tax incentives of owner-occupied housing are detailed in the theoretical model, time and data constraints made an empirical study of them an impossibility. It would also be benefi cial to construct a re gion specific dataset, which stratifies housing values to observe ch anges price increases between tiers. All of these suggestions would offer more insights into the bubble period, while the new model presented here has only begun to scratch the surface of bubble-centered problems. After the rapid decrease in prices a nd record level foreclosure rates many Americans are pushing for policy changes in the housing market as a means to prevent 32 Case and Shiller (2003)
61 further bubbles. According to this model, the greatest tool the govern ment has in slowing down a housing bubble would be incr easing interest rates. An in crease in interest rates would work two ways, by increasing the us er cost and decrea sing the investment incentives of home ownership. While this so lution seems simple, interest rates are so closely tied to the national economy that a move in interest rates based solely around speculation of a housing bubble would not be we ll received. Increases in interest rates would signal an overheating economy and sl ow down investment. Perhaps a more effective and housing specifi c solution would be regula ting lending standards more closely. Loan-to-value ratios increased ove r five percent during the bubble, and were found to be positively and significantly corre lated to housing prices. If new regulation were to set a minimum-lending standard of LTV ratios, the initial cost of investing in a home would increase, further increased hom e equity has a stabilizing effect on housing markets especially in times of price decrea ses. Overall deregulation during the 1990s and 2000s was rampant in all sectors of the economy and the housing market was not immune. Policy changes need to focus on the drivers of housing pri ces as well as the lending practices that minimize risk to the issuer. In conclusion, housing market dynamics have evolved greatly over the last several decades transforming into a study of home ownership rather than residential investment. In this thesis I have undertaken creating an addition to current models, which through empirical evidence has b een found to be a noteworthy driver of housing prices, even during the bubble when many of the othe r drivers lost relevance. As the housing
62 market begins to stabilize th is groundwork should be able to aid in the understanding of how such rapid increases housing prices came to pass.
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66 Appendix A Tax Rates included in Model Full Model Dependent Variable: HP2 Method: Least Squares Date: 03/24/10 Time: 20:13 Sample (adjusted): 1990Q4 2007Q4 Included observations: 69 after adjustments Variable CoefficientStd. Error t-Statistic Prob. C 2316.9931199.8421.9310820.0586 HP2(-1) 0.9588640.1196548.013640 HP2(-2) -0.319080.112411-2.8385250.0063 PI -411.7986117.4371-3.5065460.0009 MORTG2 6785.5821703.2843.9838220.0002 RENT2 -835.8506481.3852-1.7363450.0881 AAABOND2 -8470.4092169.195-3.9048630.0003 LTV2 632.6376275.90642.2929430.0257 HIGHTAXR -44.2951428.55004-1.5514920.1265 PI(-1) 15.23396124.36660.1224920.903 MORTG2(-1) -6093.0991693.459-3.598020.0007 RENT2(-1) 155.507483.81740.3214170.7491 AAABOND2(-1) 4746.122151.2042.2062620.0316 LTV2(-1) 405.8453279.93841.4497660.1528 R-squared 0.755395 Mean dependent var298.0725 Adjusted R-squared0.69758 S.D. dependent var 1105.685 S.E. of regression 608.0467 Akaike info criterion 15.8374 Sum squared resid 20334644 Schwarz criterion 16.2907 Log likelihood -532.3904 Hannan-Quinn criter.16.01724 F-statistic 13.06559 Durbin-Watson stat 2.339383 Prob(F-statistic) 0
67 Prior to Bubble Dependent Variable: HP2 Method: Least Squares Date: 03/24/10 Time: 20:13 Sample (adjusted): 1990Q4 2001Q4 Included observations: 45 after adjustments Variable CoefficientStd. Errort-Statistic Prob. C 2583.7171216.8962.1232030.0418 HP2(-1) 0.9276670.1518226.1102190 HP2(-2) -0.2435380.144456-1.6859020.1019 PI -365.3032112.8464-3.2371710.0029 MORTG2 8337.3872205.373.7804930.0007 RENT2 -654.6933543.5344-1.2045110.2375 AAABOND2 -7918.7112674.433-2.9608930.0058 LTV2 689.2175284.40312.4233830.0214 HIGHTAXR -57.0039927.22054-2.0941540.0445 PI(-1) 117.2013129.92640.9020590.374 MORTG2(-1) -8360.0082482.558-3.3674980.002 RENT2(-1) -105.8756522.25-0.202730.8407 AAABOND2(-1) 5439.104 2712.0352.0055430.0537 LTV2(-1) 506.4822278.7551.8169440.0789 R-squared 0.806408 Mean dependent var277.0444 Adjusted R-squared0.725224 S.D. dependent var 984.9589 S.E. of regression 516.3067 Akaike info criterion 15.58083 Sum squared resid 8263750 Schwarz criterion 16.1429 Log likelihood -336.5686 Hannan-Quinn criter.15.79036 F-statistic 9.933096 Durbin-Watson stat 2.003681 Prob(F-statistic) 0
68 During Bubble Dependent Variable: HP2 Method: Least Squares Date: 03/24/10 Time: 20:14 Sample: 2002Q1 2007Q4 Included observations: 24 Variable CoefficientStd. Error t-Statistic Prob. C -13280.719612.959-1.3815430.1972 HP2(-1) 0.971950.2307314.2124820.0018 HP2(-2) -0.2813660.196974-1.4284410.1836 PI -352.243434.5381-0.8106150.4365 MORTG2 1418.3524612.1770.3075230.7648 RENT2 -684.12771180.813-0.579370.5752 AAABOND2 -9766.1444607.386-2.1196710.0601 LTV2 795.3459951.68050.8357280.4228 HIGHTAXR 362.4155250.91541.4443730.1792 PI(-1) 361.6839444.49930.8136880.4348 MORTG2(-1) -7034.3453212.69-2.189550.0534 RENT2(-1) 1948.3821324.1381.4714340.1719 AAABOND2(-1) 11222.58 4926.9162.277810.046 LTV2(-1) 821.43791232.5210.666470.5202 R-squared 0.881071 Mean dependent var337.5 Adjusted R-squared 0.726464 S.D. dependent var 1325.161 S.E. of regression 693.0683 Akaike info criterion 16.21133 Sum squared resid 4803437 Schwarz criterion 16.89853 Log likelihood -180.536 Hannan-Quinn criter.16.39365 F-statistic 5.698761 Durbin-Watson stat 2.509759 Prob(F-statistic) 0.004636
69 Appendix B Model with extraneous variables included: PI: Personal Income DI: Dividend Income Pop2: Population Unem: Unemployment Rate Savings: Savings Dow2: Dow Jones HighTax: Tax rate Capgain: Capital Gain Rate Mortg2: 30-year rate Rent2: Rental index AAABond: Bond yield LTV2: LTV ratio Full Model Method: Least Squares Date: 03/24/10 Time: 20:09 Sample (adjusted): 1990Q4 2008Q4 Included observations: 73 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 3515.611465.3412.3991750.0205 HP2(-1) 0.8318550.1223986.7963020 HP2(-2) -0.3416450.133509-2.5589720.0138 PI -305.7198158.2314-1.9321060.0594 DI -4.3227843.04458-1.4198290.1623 POP2 8.0716847.2654041.1109750.2722 UNEM 475.61571123.4110.4233670.674 SAVINGS 2.176793. 2219530.6756120.5026 DOW2 0.3668660.7911090.4637370.645 HIGHTAX -40.5997174.59699-0.5442540.5888 CAPGAIN -42.1074227.29269-1.542810.1296 MORTG2 6934.2411643.6544.2187950.0001 RENT2 -588.3153485.0087-1.2129990.2312 AAABOND2 -8639.0592085.485-4.1424710.0001 LTV2 405.2634293.2951.3817610.1736 PI(-1) 67.30925158.74050.4240210.6735 MORTG2(-1) -4050.3411915.023-2.1150350.0398 RENT2(-1) 328.0451536.35650.6116180.5437 AAABOND2(-1) 3230.561 2305.1511.4014530.1676 LTV2(-1) 405.0105277.98831.4569340.1518 DI(-1) -0.6242621.963977-0.3178560.752 POP2(-1) -12.027927.204192-1.6695720.1017 UNEM(-1) 100.59731097.950.0916230.9274 SAVINGS(-1) -4.918167 3.600503-1.3659670.1785 DOW2(-1) -0.2164640.846546-0.2557020.7993 HIGHTAXR(-1) -117.403351.86401-2.2636760.0283 R-squared 0.822326 Mean dependent var348.3973 Adjusted R-squared 0.727818 S.D. dependent var 1114.737 S.E. of regression 581.57 Akaike info criterion 15.84136 Sum squared resid 15896512 Schwarz criterion 16.65714 Log likelihood -552.2095 Hannan-Quinn criter.16.16646 F-statistic 8.701159 Durbin-Watson stat 2.479625 Prob(F-statistic) 0
70 Prior to Bubble Method: Least Squares Date: 03/24/10 Time: 20:08 Sample (adjusted): 1990Q4 2001Q4 Included observations: 45 after adjustments Variable CoefficientStd. Errort-Statistic Prob. C 4581.913314.3021.3824660.1829 HP2(-1) 0.7302580.2612052.7957310.0115 HP2(-2) -0.1910250.299049-0.6387750.5306 PI -121.3266248.3426-0.4885450.6308 DI -0.3944556.139026-0.0642540.9494 POP2 -11.0785619.66433-0.5633840.5798 UNEM 193.34461801.4520.1073270.9157 SAVINGS -2.0540747. 231329-0.2840520.7794 DOW2 0.5250361.6093750.3262360.7478 HIGHTAX 31.748593.408490.3398890.7377 CAPGAIN -57.5914261.27492-0.9398860.3591 MORTG2 7834.8343897.2532.0103480.0588 RENT2 -643.3064778.6316-0.8262010.4189 AAABOND2 -6998.7064304.031-1.6260820.1204 LTV2 456.8723486.42250.939250.3594 PI(-1) 396.9997278.70451.4244470.1705 MORTG2(-1) -7133.4434589.855-1.5541760.1366 RENT2(-1) -287.4404803.0943-0.3579160.7244 AAABOND2(-1) 5449.355 4586.2421.1881960.2494 LTV2(-1) 333.429446.99730.7459310.4648 DI(-1) -5.3785734.877668-1.1026940.2839 POP2(-1) -1.2885219.94277-0.0646110.9492 UNEM(-1) -379.88121728.72-0.2197470.8284 SAVINGS(-1) 3.290058 6.7092120.4903790.6295 DOW2(-1) 0.4427471.4287520.3098830.76 HIGHTAX(-1) -7.52822893.17316-0.0807980.9364 R-squared 0.828777 Mean dependent var277.0444 Adjusted R-squared0.603484 S.D. dependent var 984.9589 S.E. of regression 620.224 Akaike info criterion 15.99137 Sum squared resid 7308878 Schwarz criterion 17.03522 Log likelihood -333.8058 Hannan-Quinn criter.16.38051 F-statistic 3.678659 Durbin-Watson stat 1.906188 Prob(F-statistic) 0.002539
71 Further Culled Down Full Model Dependent Variable: HP2 Method: Least Squares Date: 03/24/10 Time: 20:09 Sample (adjusted): 1990Q4 2008Q4 Included observations: 73 after adjustments Variable CoefficientStd. Error t-Statistic Prob. C 672.7622912.15540.7375520.4641 HP2(-1) 0.9430790.1150528.1970090 HP2(-2) -0.2714090.112556-2.4113370.0195 PI -193.4623153.1722-1.2630380.2122 DI -3.6136511.618656-2.2325010.0299 DOW2 0.6046840.7601210.795510.4299 HIGHTAX 10.6972871.370210.1498840.8814 CAPGAIN -9.51656319.3978-0.49060.6258 MORTG2 7117.161641.9294.3346340.0001 RENT2 -594.2483.45-1.2290830.2246 AAABOND2 -8636.5672128.886-4.0568480.0002 LTV2 510.8864272.98741.8714650.0669 PI(-1) 161.2076154.12961.0459230.3004 MORTG2(-1) -6245.2181682.88-3.711030.0005 RENT2(-1) 398.1638540.06760.7372480.4643 AAABOND2(-1) 5521.1022151.6212.566020.0132 LTV2(-1) 393.8235276.71921.4231880.1607 DI(-1) -3.6087111.616274-2.2327350.0299 UNEM(-1) 1.322644138.15130.0095740.9924 DOW2(-1) 0.2272240.7854950.2892750.7735 HIGHTAX(-1) -79.8481968.15462-1.1715740.2467 R-squared 0.78971 Mean dependent var348.3973 Adjusted R-squared 0.708829 S.D. dependent var 1114.737 S.E. of regression 601.5153 Akaike info criterion 15.87291 Sum squared resid 18814676 Schwarz criterion 16.53181 Log likelihood -558.3611 Hannan-Quinn criter.16.13549 F-statistic 9.763853 Durbin-Watson stat 2.390837 Prob(F-statistic) 0
72 Prior to Bubble Dependent Variable: HP2 Method: Least Squares Date: 03/24/10 Time: 20:09 Sample (adjusted): 1990Q4 2001Q4 Included observations: 45 after adjustments Variable CoefficientStd. Errort-Statistic Prob. C 1805.1712136.2370.8450240.4064 HP2(-1) 0.9062880.1896084.7797930.0001 HP2(-2) -0.2888640.171491-1.6844230.1051 PI -160.623200.067-0.8028460.4299 DI -3.5150912.718542-1.2930060.2083 DOW2 1.1292851.3544880.8337360.4127 HIGHTAX 8.59927182.692350.1039910.918 CAPGAIN -27.981433.61491-0.832410.4134 MORTG2 8480.7992679.9293.1645610.0042 RENT2 -499.6556664.3461-0.7521010.4593 AAABOND2 -8558.1483198.416-2.6757460.0132 LTV2 576.5128363.22911.5871880.1256 PI(-1) 354.9364207.91381.7071320.1007 MORTG2(-1) -8421.9293347.118-2.5161730.019 RENT2(-1) 112.8932673.97520.1675040.8684 AAABOND2(-1) 7462.2563781.2871.973470.0601 LTV2(-1) 372.986339.55451.0984570.2829 DI(-1) -4.3778053.150178-1.3897010.1774 UNEM(-1) -126.6191246.8212-0.5129990.6126 DOW2(-1) 1.0589231.2294830.8612760.3976 HIGHTAX(-1) -15.7616982.67548-0.1906450.8504 R-squared 0.807857 Mean dependent var277.0444 Adjusted R-squared0.647738 S.D. dependent var 984.9589 S.E. of regression 584.5893 Akaike info criterion 15.88442 Sum squared resid 8201870 Schwarz criterion 16.72753 Log likelihood -336.3995 Hannan-Quinn criter.16.19872 F-statistic 5.045356 Durbin-Watson stat 2.033612 Prob(F-statistic) 0.00013
73 Appendix C