Chapter 1

Real estate, Stock flow models

1.1 Introduction

Real estate, Stock flow models chapter focuses on price movements according to change onstock in housing market. It also briefly analysis lack of models and its biases.

1.2 Model

The paper House Price Dynamics: The Role of Tax Policy and Demography focuses on pricemovements in U.S. between early 70s and late 80s. Author tries to base reasons of pricefluctuations on two factors which are changes in tax code and demography of households inUS.

Figures belong to housing market indicates how it is important for overall economy. In1990s households (abbreviated as HH from now on) net worth is $17.1 trillion where $4.6trillion in gross values of it belongs to owner occupied homes. The fact that corporate equityowned by HH, which is around $2.4 trillion, is far less than owned house.

Three different data has been used for regressions. A data from Census Bureau Datahas been used for aggregated information according to Census Regional criteria. 1 Moredisaggregated data is available from the National Association of Realtors (NAR) and reportsquarterly median house prices for 115 Standard Metropolitan Statistical Areas (SMSA).While Census Bureau constant quality prices index for valuing only structure, NAR medianhouse prices captures combines cost of land and structure. Third and last data set belongsto Urban Land Institute (ULI) which provides semi decadal data based on survey of landcost and available since 1975. The survey asks experts to price a standard improved 10.000sq. foot in 30 different cities.

In order to explain house price movements, we need to indicate that Housing marketconsist of two sub-markets: Stock for existing house and flow of new construction. Priceof house determined by existing stock house whereas level of new investment is determinedby flow of new constructions. Thus, any shock to those sub-markets will effect house price.Equilibrium of owner occupied house market requires house owner should get some return

1See Appendix 1

1

2 CHAPTER 1. REAL ESTATE, STOCK FLOW MODELS

from investing to houses as they could get some return when they invest on any other asset.Furthermore, this requires equation 1 which is user cost equation.

‘where RH denotes the marginal value of the rental services per period on owner-occupiedhomes, PH the price of existing houses, θ the investor’s marginal tax rate, i the nominalinterest rate, τp the property tax rate as a share of house value, δ the depreciation rateon housing capital, α the risk premium required on assets with the risk characteristics ofhousing, m the maintenance cost per unit value, and πe the investor’s expected rate ofnominal house price appreciation.’ 2

The fact that the issue with this equation is that it assumes all house has same quality,location and other characteristic. Nevertheless it help us determine what investor will doafter looking at cost of investing via this equation. Housing stock is determined at beginningof every period by past investment and housing stock then determines RH. In the equation1, everything except e are endogenous. So, expected housing inflation shapes rational expec-tations on housing investors. Then, it becomes a connection between housing price todayand housing investment in future. This relation is demonstrated on equation 2.

Under the assumption of expectation which is formed with future prediction, πet =

(PH,t+1PHt)/PHt, equation 1 and 2 becomes pair and initial house price should be deter-mined in order to solve forward. In this framework, real price can increase by supply shockwhich can cause an increase on price of current or future construction cost or by current andanticipated demand shocks which can cause an increase on value of rental services of owneroccupied house stock. On the other hand we can shape framework with extrapolative ex-pectations rather than rational. This allow systematic overbuilding of houses in the housingmarket and also allow to predict what excess return will be on houses. House price move-ment during 70s and 80s showed that investor in housing have extrapolative expectationstherefore there are not rational on investment decision making process.

There are three popular way of explanation of price raise on 70s. First one is shock toconstruction cost which caused systematic change. Afterwards, it resulted with an increasein housing price relative to GNP deflator. Second one is favorable and unexpected demandshock. As it is demonstrated on equation 1, U.S. tax code allows households to deductnominal interest rate from taxable income. If nominal interest rates increase 1 by 1 accordingto inflation rates, then [(1-θ)i-πe] which is after tax of borrowing declines as inflation rateincreases. The tax reform during 80s reduced marginal tax rates, and this increased marginal

2taken from Poterba, J.M., Weil, D.N., and Shiller, R. (1991). House Price Dynamics: The Role of TaxPolicy and Demography.

1.2. MODEL 3

cost of housing and it stressed the price of homes, especially hold by higher income ofhouse owners. Third one is based on demography. The forecast is that people between25-35 years old will demand a house more than other part of community due to fact thatmarriage, becoming independent etc. So, Mankiw and Weil(1989) argue that entry of largecohort into 24-35 age period should be forecasted earlier than they start demanding newhouses. However, they found that price increase in during 70s mainly caused by baby-boomgeneration. They fall into 24-35 age bracket during 70s and high demand increased houseprices. In addition to that, next generation was not populated as much as baby-boomgeneration and this could be one of the reasons of price fall during 90s.

In order to estimate price change on relative appreciation of different sized houses, re-gression has run based on hedonic approach. Big-size houses that can be bought by highincome household and small size houses can be bought by low income households are definedas a trade-up houses and starter houses respectively by author. Findings shows that broadpatter of price change on different sized houses has a same patter with a change on realuser cost as it can be seen on table 2. But, hedonic approach has a shortcomings. A betterhousing index should include analyzing repeat sales of houses. Because repeat sales method

4 CHAPTER 1. REAL ESTATE, STOCK FLOW MODELS

has advantage of capability of controlling for the heterogeneity in housing characteristic andthe less data requirement in the estimation. For that, Karl E. Case and Robert J. Schillerdiscuss about repeat sales in their article, The Efficiency of the Market for Single-FamilyHome, which is published on The American Economic Review on March, 1989. Their papertries to find an answer to efficiency in housing market for years from 1970 to 1986 for fourdifferent cities; Atlanta, Chicago, Dallas and Oakland/San Francisco. They use repeat saledata on individual homes which havent have apparent characteristic change. On their paper,they modified a model based on Martin J. Bailey, Richard Muth and Hugh Nourse (InitialsBMN) and called it as Weighted Repeated Sales. It is three-step weighted procedure. Forfirst step, BMN model followed, which produces estimation and standard errors for housingprice index by using ordinary least square regression method on change in log price of eachhouse. In second step, squared residuals from first regression has regressed again on a con-stant and the time distance between sales. Constant term is estimate of variance of noisein price and slope term is estimate of variance of individual housing value through time.In the last step, they first divide each observation in the regression in step-one by squareroot of fitted value in second step regression, then they run regression again. They foundout that citywide real hosing prices in given certain year tends to anticipate a change onsame direction for the following year. Also, forecasted change in real interest rates does notseem to be incorporated in prices. Additionally, taxes and rental rates reveal that city wiseafter-tax return excess are predictable.

However, Man Cho also indicates that there is various potential biases on repeat saleswhich comes from the structural changes between sales or by some time-varying structuralqualifications. There are 5 different type of bias in repeat sales indices: renovation bias whereis caused by structural changes between two sales; hedonic bias which is a bias comes fromvalues of some structural and locational characters changes over time; trading- frequency

1.2. MODEL 5

bias where trading frequency causes some bias on measured rate of appreciation; sample-selection bias where occurs when there is a bias on estimates of the changes in the value ofthe stock of housing and aggregation bias where time interval causes bias. In order to solvethese issues, 3 different methods are suggested: Hedonic Repeat Sales Model which modelsthe effects of the age of structure, a vector of time dummies in the hedonic model, and aset of time dummies in the Repeat Sales Model on the covariance between repeat sales andhedonic residuals; Intercept Repeat Sales Model which adds a fixed effect item to RepeatSales Model and estimate mean and variance of fixed and temporal items of repeat salesby using maximum likelihood method , and Distance Weighted Repeat Sales Model thatdecompose the price appreciation as per-period expected return, jurisdiction-specific return,and random changes private property to a house, then assumed distributional characteristicsof error terms designate covariance between housing returns of those two jurisdictions.

It is also important to analyze price change in city level over time according to changein demography, construction cost, incomes and tax rates. Equation 3, reduced form crosssection model gives us the relation in empirically.

’where pit is the logarithm of the real median house price in city i at period t, cit denotesthe logarithm of real construction costs, dit is the logarithm of a demand measure based onpopulation structure, yit is the logarithm of real per capita income, uit is an indicator ofreal user costs of home-ownership, and vit are residuals.’ 3 The demand pattern is result ofholding a house, household formation decisions and decision about how much to purchasebased on holding conditions. All of those are effected by price level. Migration decisions arealso affected by price level. Thus, in order to prevent endogeneity , dit is calculated by usingnational index of aged specified housing demand. Another variable is a measure of user costof housing in different cities. Including nominal interest rates and expected inflation, mostof components of user cost doesnt change among cities. However, federal marginal tax ratesvary among cities where households can deduct mortgage interest and property taxes.

What about the question of forecast of price movements. Recent studies convey thatprices can be anticipated. Equation 4 demonstrates this arguments empirically.

where rt in a return on 90-day Treasury Bills and dependent variable is excess on housinginvestment.

3taken from Poterba, J.M., Weil, D.N., and Shiller, R. (1991). House Price Dynamics: The Role of TaxPolicy and Demography.

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1.3 Conclusion

As a conclusion, demographical changes might be a possible explanation for price declineduring 80s. There is a strong relation between level of real house price and housing demandrelated with age profile of population for United States. Caution is needed in extrapolatinghistorical trend of hosing prices and demography far into future. Because, even if thereis relation, on SMSAs level demography-house price link doesnt always hold. Investors inowner occupied house market does not have a rational expectations but extrapolating forestimating future capital gains on housing. This could be a reason of price movement during80s due to fact that investors hadnt realized yet that user cost is higher than 70s. Sameintuition can be make price decline late 80s. Investors had extrapolated price deductionsstarter mid-80s and shaped their decisions according to recent price decline.

References

Poterba, J.M., Weil, D.N., and Shiller, R. (1991). House Price Dynamics: The Role of TaxPolicy and Demography. Brookings Papers on Economic Activity, Vol. 1991, No. 2, pp.143-203.Case, K.E. and Shiller, R.J. (1989). The Efficiency of the Market for Single-Family Homes.The American Economic Review, Vol. 79, No. 1, pp. 125-137.Cho, M. (1996). House Price Dynamics: A Survey of Theoretical and Empirical Issues.Journal of Housing Research, Volume 7, Issue 2, pp. 145-172.

1.3. CONCLUSION 7

Appendix 1