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Forecasting housing starts
International Journal of Forecasting 4 (1988) 125-134 North-Holland
125
FORECASTING HOUSING STARTS Anil K. PURI and Johannes VAN LIEROP Calqornia State University, Fullerton, CA 92634, USA
Abstract:
This paper develops a multi-equation econometric model of the U.S. housing sector and compares its forecasting performance to that of a time-series (ARIMA) model. The essential issue explored is whether a faithful modeling of relationships suggested by economic theory constitutes a real advantage in forecasting. The econometric model has a stock-flow structure with cost and credit availability variables emphasized in the housing supply equation. We conclude that unaided one-period ahead econometric forecasts are superior to the time-sereies forecasts. But, due to bias in the former, prediction by the ARIMA model turns out to be better for longer period forecasts. This disadvantage in the econometric model can be overcome by judgmental adjustments while the same is not necessarily true for the ARIMA model.
Keywords: Housing starts, Econometric forecasting, ARIMA models, Comparative
forecasts.
1. Introduction During the seventies residential construction constituted approximately five percent of the Gross National Product of the United States. In addition to being a major component of total GNP, the housing sector is one of the most volatile. The typical housing cycle peaks are 60 percent or more above troughs and the amplitude of the housing cycle seems to be increasing. Because of this, the forecasting of housing starts is both challenging and important to economic forecasters. This study presents the results of performance comparisons between the econometric (structural) modeling approach and the time series (nonstructural) analysis approach to the forecasting of housing starts. Comparative studies of this kind so far have been carried out in an environment of extremes: the econometric models tested have been large-scale macroeconomic models involving fifty to several hundred equations, whereas the time series models were either univariate ARIMA or autoregressive models. Examples of such studies are Cooper (1972), Nelson (1972) and Christ (1975). A useful review of these studies is contained in Granger and Newbold (1977). It is by now well known that in many cases these econcmetric models unaided by judgment of experienced forecasters predict poorly compared to time series models. It is interesting to note that of the macroeconometric models published in the seventies, the most successful in terms of unaided forecasting accuracy was that of Fair (1974). The Fair model differs from others in two important ways: the model is small (14 stochastic equations) and more than average attention is paid to the autocorrelative structure of model residuals. Thissuggests that time series methods may be outperforming large-scale macro-econometric models with hundreds of equations with usually little attention given to autocorrelated residuals. But this may not generally be the case where econometric models 4re small and careful attention is paid to the autocorrelation structure of residuals. 0169-2070/88/$3.50
@ 1988, Elsevier Science Publishers B.V. (North-Holland)
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A. K. Puri and J. Van Lierop / Forecasting housing starts
The first section of this paper presents an econometric model of housing construction consisting of eight equations. In spite of the relatively small number of equations involved, the specification of the model carefully incorporates all the basic features of currently used housing forecast models. We pay attention to the structure of residuals at the estimation stage. The second section presents an ARIMA model of housing starts. We generate two types of forecasts, up to four periods ahead, for the econometric and the time-series models. The comparison of forecasts highlights the strengths and weaknesses of each model and suggests the judicious use of each of the models.
2. An econometric model of housing starts One of the many decisions to be made at the outset of the construction of a housing model is the choice of a measure of output. We have selected the number of dwelling units started as our measure rather than the aggregate value of construction. The chosen variable is most widely used and discussed by economic forecasters and, consequently, seems the most useful choice for an exercise in comparative forecasting. The second decision required is the level of aggregation in the model. On theoretical grounds, it is desirable to separate markets for rental and owner-occupied housing. Time series on housing starts, however, are not separated by tenure mode. Some authors use structural type as a proxy for tenure where single-family units are assumed to be produced for owner occupation and multiple family structures for the rental market [Jaffee and Rosen (1979)]. This seems to be a poor proxy at best. In 1980, for example, over 31 percent of renter-occupied units were single-family dwellings. ’ Our choice has been to aggregate housing starts, rather than estimate separate equations for various structural types. Simple tests do not indicate any serious biases resulting from this choice. One of the features that distinguishes housing markets from most other commodity markets is the extreme durability of the product. Consequently, the proportion of existing dwellings to newly constructed dwellings is always very high. In such markets the interaction between supply and demtid is best described in a stock-flow model. At anv ooint in time there exists a certain housing stock and a demand function for occupying dwelling units. House price levels adjust to establish momentary (stock) equilibrium between the two. Housing producers respond to this price level by moving up or down a supply curve for the produ.ction of new housing. Flow equilibrium then means that housing producers are on their supply curve, given the momentary equilibrium price that yields stock equilibrium. The cumulative effect of such production changes the existing stock to produce a different stock equilibrium, and so on. Fig. 1 presents a flow diagram to make these relationships more specific. The diagram presents a demand-supply model but it is more complex than a simple model due to interaction between stock and flow variables and their relationship to financial markets. The econometric specification leads to a recursive model which can be estimated equation by equation. We describe below first the stock equilibrium and then flow equilibrium and present the estimated equations.
’ U.S. Bureau of the Census, 1980 Census of Population and Housing: Provisional Estimates of SocLr. Economic, and Housing Characteristics (U.S. Government Printing Office, 1982). Jaffee and Rosen (1979) really don’t make use of these data in their model. However, Rosen (1979) explores this issue intensively. Hendershott (1980) uses an adjusted homeownership rate which is somewhat different from the headship rate. Yet he takes the number of households to be predetermined.
A. K. Puri and J. Van Lierop / Forecasting homing starts
)
127
MORTGAGE coMuITMENTs (+I
R0W OF
DEPOSITS
VABIOUSINTEREST RATES f-1 I
(+I
(+I
( M"i%iiGE
t-1
> H%t:G /1\
t-1
w CURRENT?iOUSING
1 (+I PUDIJC COMPLETION Fig. 1.
2. I. Stock equilibrium The stock equilibrium is represented primarily by the house price equation. The real or deflated price level (HPRICE/CPI) in time period t is determined by the existing stock of units, the demographic demand for housing and mortgage rate. The equation in terms of levels of variables exhibited high autocorrelation. The demographic demand is derived from the total population, its age distribution and its propensity to group itself in household units. It has been suggested that the number of households be used to represent demographic influences on the housing market [Jaffee and Rosen (1979), in fact, use thiq measure]. The problem with this suggestion is that by definition the number of household units is equal to the number of occupied units. In our model if housing stock increases, it decreases housing prices which in turn will increase the number of household units and restore equilibrium in the housing market. Clearly then the number of households is an endogenous variable which, together with housing price (HPRICE), is endogenously determined. There are, of course, other factors affecting household formation. [See, e.g., Masnick (1983).] Our purpose in the construction of a demographic variable is to develop an exogenous variable. We pick the approximate midpoint of our sample period, 1970, as base, and create an index which measures demographic influences. Headship rates are defined as the ratio of the number of household heads in an age group to the population in that age group. Then we create our demographic variable called Weighted Population ( WPOP) by weighting population in four age groups by the headship rates for 1970. Specifically we used the following equation: house
WPOP = (0.046 POT24 + 0.467 P25T34 + 0.537 P35T64 + 0.619 P65UP) * POP, where POT24, P25T34, P35T64, P65UP represent population
share by age group O-24, 25-34,
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35-64 and 65 and up, respectively, POP represents total U.S. population in thousands and the coefficients are the 1970 headship rates. Our index WPOP does not completely capture all relevant demographic factors since headship rates do appear to follow an exogenous trend. 2 Still, we believe that it is preferable to the number of households which is strongly endogenous to housing market conditions. The ratio STOCK/ WPOP measures the relative scarcity of housing. The level of housing stock appears in the equation since long term growth in the housing stock will increase the demand for residential land which will increase land prices and in turn house prices. ’ The error term is modeled as a first-order autoregressive process. The estimated equation in generalized difference form is as follows:
HPRICE/CPI=108.8+0.657HPRICE(-l)/CPI(-1) (6.95)
-0.152~-6 [RM* STOCK-0.657~~(-~)*STOCK(-l)] (1.98) +0.313 E-4[
STOCK-O.657 * STOCK(- l)]
(7.84) -(;.~;~[sT0cK/wp0p-o.657 a STOCK(-~)/wPoP(-l)].
(1)
.
The numbers in brackets are absolute t-values ( R2 = 0.975, Sample: 4 1966 : 43-1980 : 42, Method of estimation: Maximum Likelihood). The next equation describes the housing stock variable (STOCK) utilized in eq. (1). It is calculated as the sum of the housing surviving from the previous period and the previous period completions of private dwelling units ( COMPS), mobil house shipments (MOBIL) and public dwelling units (PUBLIC).To calculate the surviving stock of housing units, we estimated quarterly removal rates of 0.001971 for the sixties and 0.000825 from 1970 on. The removal rates are estimated by simulating equation (2) for the 1960-70 and 1970-80 periods, respectively, and choosing those removal rates that generate the observed housing stock counts in the 1970 and 1980 census.
STOCK= (0.999175 -0.001146 *D6O)STOCK(- l)+ COMPS(- l)+ MOBIL(- 1) +PUBLIC(-l), where 060 is a dummy variable which takes the value 1 between 1960 and 1970 and zero thereafter. The equation for private dwelling units completed is estimated as a distributed lag model. Discussions with industry analysts and the Construction Report of the Census Bureau suggest that ’ See William C. Apgar, ‘Housing in the 1980s: A Review of Alternative Forecasts’, MIT-Harvard Joint Center for Urban Studies, Working Ppper No. 283-2, revised July 1983, p. 8. At the time of the writing of this paper, we were not aware of any satisfactory economic formulation of the headship formulation function. To the extent that headship rates are variable, the present study is limited. 3 For data sources, see appendix. Hendershott (1980) used a measure of user cost in this equation which he has estimated himself. 4 Sample sizes for certain estimated equations sometimes are different because the needed data series did not go back far enough.
AK. Puri and .I. Van Lierop / Forecasting housing starts
most units are completed equation:
within two to three quarters
129
after being started. Hence the following
COMPS=0.267STARTS+(;3f!;STARTS( -1) +0.2OOSTARTS(-2)+0.1OOSTARTS(-3). (3.64) . (2.27) (1.33)
(3) This series is non-existent estimation: Ordinary Least Mobile home shipments the cycle of housing starts,
prior to 1968:Ql ( R2 = 0.70, Sample 1968:Ql-198O:Q2, Method of Squares). play a minor role in our model. Since the cycle in these closely parallels we estimated the following equation based on that correlation:
M0~1~=2.17+0.922MoBrL(-l)+o.i31[s~~~T~-0.922 STARTS((18.8) (9.69)
(4)
( R2= 0.906, Sample: 1966:Q3-198O:Q2, Method of estimation: Maximum Likelihood.) Public dwelling units completed (PUBLIC)is exogenous to our model. 2.2. Flowequilibrium The specification of the supply function for newly built housing is based on the following three arguments. First, there is widespread agreement that an important, if not the most important, determinant of the housing cycle is the volatile nature of the supply of mortgage credit. Second, in most of the literature on mortgage markets, it is commonly assumed that mortgage lenders use ‘non-price’ rationing, i.e., conditions of the contract other than the effective rate [see, for instance, Jaffee (1972), for a different view see Meltzer (1974)]. Third, the supply function slopes upward with respect to price. Because of the first two reasons, we include both cost and availability of credit variables. For a proxy of mortgage credit availability we follow Jaffee and Rosen’s (1979) general approach. As part of the policy to moderate the housing cycle a number of federal agencies have been set up for the express purpose of increasing the availability of mortgage credit, notably: the Federal Home Loan Bank (FHLB), the Federal Home Loan Mortgage Corporation (FHLMC), the Federal National Mortgage Association (FNMA) and the Government National Mortgage Association (GNMA). The flow of advances to lending institutions by FHLBB and mortgage commitments by the other three agencies is one of the credit availability variables (FACOM).The other is the flow of deposits into the financial institutions that supply the majority of mortgage credit, i.e., Savings ad Loan associations (S&Ls) and Mutual Savings Banks (MSBs). This produces the following equation:
A STARTS=773.9A( HPRICE/CPI)-0.934E-3 A( RM*STOCK) (4.40) (2.45) +0.204 A( FLDEP/HPRICE) (0.78) +0.657 A( FACOM/HPRICE)-49.9 aQl+ (4.96) (1.86)
104.5 A Q2 +73.5 A Q3 (8.07) (10.4)
( R2= 0.896, Sample: 1966:Q3-198O:Q2, Method of estimation:
Maximum Likelihood.)
(5)
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The symbol A is the first difference operator. The first difference specification was chosen since the residuals of the original, undifferenced specification exhibited a random walk pattern. Other variables are FLDEP, flow of deposits into S&Ls and MSBs (millions of dollars); Ql, Q2, Q3, seasonal (dummy) variables for the first, second and third quarters respectively; FACOM, flow of loan commitments and advances by the above federal agencies (millions of dollars). (For fuller description see appendix) The mortgage rate variable (RM) is scaled by the housing stock and FACOM is divided by the houseprice index (HPRICE) as an appropriate deflator to measure its impact on housing starts. (FACOM/ HPRICE measures commitments to finance in ‘real’ housing units.) All coefficients have the correct sign but the credit availability variables are not very significant, casting doubt on the credit rationing hypothesis. Because of the widespread belief that these variables do matter however, we consider the prior probability of positive coefficients on these variables quite high and leave them in the model. For the mortgage rate equation, we view the mortgage interest determination as a partial adjustment process A RM=k
[RM*-RM(-I)],
where RM * is the equilibrium mortgage rate. The one period change in the mortgage rate is only a fraction k of the gap between equilibrium and previous period’s mortgage rate value. The equilibrium value RM * is expected to depend on various interest rates, credit availability and demand for mortgage credit. Only the interest rate variables proved significant resulting in the following equation: 5 A
RM= -0.?309+0.079RTB (6.78)
+;.;6$35(-1) .
+0.271SRATE-;.;;;RM(-I), (4.78) .
(6)
where RTB = rate on 3-month T-bills, R35 = rate on 3-5 year T-bills, SR4 TE = effective interest rate paid on deposits by FSLIC insured savings and loan associations ( R2 = 0.801, Sample: 1966:Q3-198O:Q2, Method of estimation: Ordinary Least Squares). The savings and loan deposit interest rate is a cost variable representing the average interest rate on deposits. Jaffee and Rosen (1979) interpret the significance of this variable as indicating cost markup price-setting behavior by thrift institutions in setting mortgage rates. This has important implications for the effect of regulation Q-ceilings on mortgage rates. Pyle (1982) criticizes this specification on the grounds that marginal rather than average cost of funds should be considered and, additionally, that thrift institutions are price takers rather than price setters in mortgage markets. He attributes the significance of the coefficient to spurious correlation. The continued significance of the variable beyond the Jaffee- Rosen sample period (1965 : Q3- 1978 : Q2), however, makes the spurious correlation argument not very credible. Finally, the deposit flow into the thrift institutions (FLDEP) depends on the amount of new personal savings generated, the interest paid on deposits by these institutions in the previous period and the interest rate differential between this rate and the rate on alternative financial instruments. The T-bill rate (RTB) is taken as a proxy for the latter. The variables are scaled by lagged deposits, DEP( - 1) and personal savings, SA V, for a better fit. 5 The equation reported here indicates that, for our data set at least, variables other than those reported added little to the explanatory power.
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The following equation explains the deposit-flow scheme and completes the model:
FLDEP= -932.3+~08~5s~v+(y;~E-2[~R4~~(-1)*~~~(-1)] .
.
-2.94(RTB-SRATE) SAV. (7.87)
(7)
(R2 = 0.702, Sample: 1966:Q3-198O:Q2, Method of estimation: Ordinary Least Squares.) Note that, by definition, DEP = DEP(- 1) + FLDEP.AlsoSA V = personal saving at seasonally adjusted annual rate ($ millions) and DEP = total deposits in S&Ls and MSBs ($ millionsj. The negative coefficient of the interest differential reveals the regulation Q interference in the credit markets, making thrift institutions less competitive than others in obtaining funds in periods of relatively high interest rates.
3.Evaluation of forecasting performance To evaluate the comparative forecasting performance of the model described above, we developed two time series models for housing starts. The first is a univariate ARIMA model and the second a bivariate leading indicator model with a time series on private dwelling units authorized as a leading indicator series. Due to the short lag between the indicator and the housing starts series [over 90% of authorized housing units are started in the same quarter) and the difficulty in forecasting the indicator series, the ARIMA model performed the better of the two. The indicator model was therefore dropped from the analysis. After applying standard Box-Jenkins identification procedures, the following ARIMA model was estimated: (1 - B)(l -
B4)STARTS,=(1 +0.127 B)(l -0.929 B4) u,, (1.02)
(12.55)
(8)
where B is the backward lag operator. TO evaluate the forecasting performance, both models were simulated for the 10 quarters immediately following the sample period, i.e., 198O:Q3-1982:Q4. This period covers the mini-recovery that started in 1980 followed by the decline to the lowest level in 25 years in the second quarter of 1982, and the start of the subsequent recovery. This period, therefore, is a particularly trying one for forecasting. The majority of comparative forecasting performance studies have calculated econometric forecasts using actual values of exogenous variables. [An exception is Hirsch et al. (1974).] In these cases an econometric model is primarily intended as a testing ground for competing economic theories or evaluation of policy alternatives. The model simulations then establish the degree of confidence in the model. In those cases where the model is intended as a forecasting tool, the use of actual future values may bias the comparison in favor of the econometric models since exogenous variables can rarely be predicted with certainty. We performed simulations using actual values of exogenous variables and also simulated the model using forecasted values of exogenous variables. To do this, we estimated ARIMA models for each of the exogenous variables CPI,WPOP, PUBLIC,FACOM, RTB,R35,SRATE,SAK and generated forecast for one, two, three and four periods ahead. Since the ARIMA forecasts for these variables are probably not the best ones available, this procedure may bias comparisons against the econometric model. Table 1 presents the root mean square error (RMSE) of the three simulations.
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A. K. Puri and J. Van Lierop / Forecasting housing starts
Table 1 Root Mean Squared Error: Period 198O:Q3-1982:Q4. a Periods ahead
RMSE EAVEX
EPVEX
ARIMA
1
55.6 (0.515) 100.3 (0.652) 119.4 (0.783) 133.7 (0.897)
55.0 (0.642) 97.0 (0.708) 130.6 (0.628) 156.8 (0.559)
65.6 (0.076) 76.6 (0.001) 99.5 (0.047) 100.3 (0.142)
2 3 4
a The numbers in brackets represent the fraction of error due to bias.
Cohunn one refers to the econometric model with actual exogenous variables (EAVEX), column two to the econometric forecast with predicted exogenous variables (EPVEX), and column three to the ARIMA forecasts. It should be noted that while ten one-period ahead forecasts were generated, for the two, three, and four-period ahead forecast only nine, eight and seven forecasts respectively were calculated. The table shows that the econometric forecasts outperform the ARIMA model for one period ahead forecasts. For two, theree and four period ahead forecasts the ARIMA model works better, although neither model produces acceptable unaided three and four period ahead forecasts. Comparison of columns one and two reveals that for one and two periods ahead, there is no significant difference between EAVEX and EPVEX, i.e., between using actual values and ARIMA forecasts of exogenous variables. This may seem somewhat surprising but is actually a quite common result, see, for instance, Evans et al. (1972). A noteworthy difference between ARIMA and econometric forecasts is the proportion of the error that is due to bias. The ARIMA forecasts are virtually unbiased and the fraction of error due to bias is very low. This fraction is very large for the econometric model. In plotting exercises, we noticed that the econometric model actually tracked the fluctuations over the simulation period quite well but at too low a level. (It may be due to the downward bias in our WPOP variable.) For the purpose of using the model as a forecasting tool this difference is quite important. It is undoubtedly true that by applying the kind of judgmental adjustments described by Young (1982) the bias in the econometric models forecast can be greatly reduced, and result in very acceptable forecasts. No such improvement would be expected if the economic forecaster were to take the ARIMA forecasts as his starting point.
4. Summary and conclusions In this paper we presented an econometric model of the housing market. The durable nature of the product gives rise to the stock-flow structure of the model. Key variables in the housing supply equation are cost and availability of credit variables. The main point of the exercise described here is to add to the body of evidence that exists regarding the econometrician’s versus the time-series analyst’s approach to economic forecasting. The issue is whether the method of faithfully trying to model the relationships suggested by economic theory constitutes a real advantage for forecasting purposes.
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We believe that the research presented adds to this body of evidence in two specific ways: First, the present study is microeconomic in nature whereas the existing literature is largely macro oriented; second, we have chosen to investigate a time series the volatility of which is several times greater than the typical series that existing research has reference to. Our conclusion is that the unaided econometric forecast outperforms the ARIMA model for one period ahead forecasts and that these forecasts are quite acceptable given the volatile nature of the housing start series. The ARIMA mode! performs better than unaided econometric forecasts for multi-period ahead forecasts. The reason for this is the bias in the econometric forecasts. At the same time it is clear that this bias can be greatly reduced in actual forecasting situations by judgmental adjustment based on the monitoring of previous forecast errors. This evidence strongly suggests the utility of the econometrician’s use of economic theory for forecasting purposes.
Appendix SAV
RTB R35 RM CPI DEP SLDEP, MUDEP FHLA HPRICE COMPS STARTS MOBIL NCFHLMC, NCGNMA, NCFNMA POP SRA TE FACOM PQT24 P25T34 P35T64 P65UP
= Personal Savings at seasonally adjusted annual rates from the Survey of Current Business, various issues. All the following interest rate series are from the Federal Reserve Bulletin. = T-bill Rate (3 month bonds), Federal Reserve Bulletin. = Rate on 3-5 year treasury bond rate, Federal Reserve Bulletin. = Effective mortgage rate on conventional mortgages (includes initiation costs, points) FHLBB series, Federal Home Loan Bank Board. = Consumer Price Index, Federal Reserve Bulletin. = SLDEP + MUDEP = Total deposits in S&L and Mutual Savings Banks respectively, end of period in millions, from the Federal Reserve Bulletin. = FHLBB advances outstanding at the end of period in millions, FHLBB Journal = Price Index of new one family houses sold (1977 = loci, index based on type of homes in 1977) from the Bureau of the Census = Private dwelling units completed from Bureau of the Census = Private dwelling units started from the Bureau of the Census = Mobile Home Shipments from the Bureau of the Census = New commitments to purchase mortgages by FHLMC, FNMA and GNMA respectively from the Federal Reserve Bulletin = Total population (including armed forces overseas) Current Population Reports - Population Estimates and Projections, Series P-25 = Effective interest/divided rate paid by insured FSLIC Savings and Loan all districts from FHLBB Journal Associations = (FHLA - FHLA( - 1)) + FHLMC + NCGNMA + NGFNMA = Population shares by age group, O-24, 25-34, 35-64, 65 and up, respectively from Population Characteristics, Bureau ofthe Census.
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References Apgar, William C., 1983, Housing in the 1980s: A review of alternative
forecasts, Working paper no. W83-2, July (MIT-Harvard Joint Center for Urban Studies, Cambridge. MA). Christ, CF., 1975, Judging the performance of econometric models of the U.S. economy, International Economic Review 16, 54-74. Cooper, R.L., 1972, The predictive performance of quarterly econometric modzis of the United States, in: B.G. Hi&man, ed. Econometric Models of Cyclical Behavior, (Columbia University Press, New York). Evans, M.K., Y. Haitovsky and G.J. Treyz, 1977, An analysis of the forecasting properties of U.S. econometric models, in: B.G. Hickman, ed., Econometric models of cyclical behavior (Columbia University Press, New York). Fair, R.C., 1974, An evaluation of a short-run forecasting model, International Economic Review 15, 285-303. Granger, C.W. and P. Newbold, 1977, Forecasting economic time series (Academic Press, New York). Hendershott, Patric H., 1980, real users costs and the demand for single-family housing, Brookings Papers on Economic Activity 2, 401-452. ‘affee, D.M., 1972, An econometric model of the mortgage market, in: E.G. GrahIich and D.M. Jaffee, eds., Savings deposits, mortgages, and housing: Studies for the federal reserve-MIT-Penn economic model, Lexington. Jaffee, D. and K. Rosen, 1979, Mortgage credit availability and residential construction, Brookings Papers on Economic Activity, 333-376. Masnick, George S., 1983, The demographic factor in household formation, Working paper no. W83-3, June (MIT-Harvard Joint Center for Urban Studies, Cambridge, MA). Melzer, A., 1974, Credit availability and economic decisions: Some evidence from the mortgage and housing markets, Journal of Finance, 763-777. Nelson, C.R., 1972, The prediction performance of the F.R.B.-M.I.T.-PENN model of the U.S. economy, American Economic Review 62,902-917. Pyle, David H., 1982, Deposit costs and mortgage rates, Housing Finance Review 1, 43-48. Rosen, Harvey S., 1979, Housing decisions and the U.S. income tax: An econometric analysis, Journal of Public Economics 11. Young. R.M., 1982, Forecasting with an econometric model, Journal of Forecasting 1, 189-203.
Biography:
Anil K. PURI is an associate professor of Economics at California State University, Fullerton. He received his Ph.D. from the University of Minnesota. His research interests include applied econometrics and public finance. Johannes VAN LIEROP, after the work on this paper, has joined the Southern California Gas Company. He received his Ph.D. in Economics from the University of Toronto. His research has concentrated on housing and financial markets.
125
FORECASTING HOUSING STARTS Anil K. PURI and Johannes VAN LIEROP Calqornia State University, Fullerton, CA 92634, USA
Abstract:
This paper develops a multi-equation econometric model of the U.S. housing sector and compares its forecasting performance to that of a time-series (ARIMA) model. The essential issue explored is whether a faithful modeling of relationships suggested by economic theory constitutes a real advantage in forecasting. The econometric model has a stock-flow structure with cost and credit availability variables emphasized in the housing supply equation. We conclude that unaided one-period ahead econometric forecasts are superior to the time-sereies forecasts. But, due to bias in the former, prediction by the ARIMA model turns out to be better for longer period forecasts. This disadvantage in the econometric model can be overcome by judgmental adjustments while the same is not necessarily true for the ARIMA model.
Keywords: Housing starts, Econometric forecasting, ARIMA models, Comparative
forecasts.
1. Introduction During the seventies residential construction constituted approximately five percent of the Gross National Product of the United States. In addition to being a major component of total GNP, the housing sector is one of the most volatile. The typical housing cycle peaks are 60 percent or more above troughs and the amplitude of the housing cycle seems to be increasing. Because of this, the forecasting of housing starts is both challenging and important to economic forecasters. This study presents the results of performance comparisons between the econometric (structural) modeling approach and the time series (nonstructural) analysis approach to the forecasting of housing starts. Comparative studies of this kind so far have been carried out in an environment of extremes: the econometric models tested have been large-scale macroeconomic models involving fifty to several hundred equations, whereas the time series models were either univariate ARIMA or autoregressive models. Examples of such studies are Cooper (1972), Nelson (1972) and Christ (1975). A useful review of these studies is contained in Granger and Newbold (1977). It is by now well known that in many cases these econcmetric models unaided by judgment of experienced forecasters predict poorly compared to time series models. It is interesting to note that of the macroeconometric models published in the seventies, the most successful in terms of unaided forecasting accuracy was that of Fair (1974). The Fair model differs from others in two important ways: the model is small (14 stochastic equations) and more than average attention is paid to the autocorrelative structure of model residuals. Thissuggests that time series methods may be outperforming large-scale macro-econometric models with hundreds of equations with usually little attention given to autocorrelated residuals. But this may not generally be the case where econometric models 4re small and careful attention is paid to the autocorrelation structure of residuals. 0169-2070/88/$3.50
@ 1988, Elsevier Science Publishers B.V. (North-Holland)
126
A. K. Puri and J. Van Lierop / Forecasting housing starts
The first section of this paper presents an econometric model of housing construction consisting of eight equations. In spite of the relatively small number of equations involved, the specification of the model carefully incorporates all the basic features of currently used housing forecast models. We pay attention to the structure of residuals at the estimation stage. The second section presents an ARIMA model of housing starts. We generate two types of forecasts, up to four periods ahead, for the econometric and the time-series models. The comparison of forecasts highlights the strengths and weaknesses of each model and suggests the judicious use of each of the models.
2. An econometric model of housing starts One of the many decisions to be made at the outset of the construction of a housing model is the choice of a measure of output. We have selected the number of dwelling units started as our measure rather than the aggregate value of construction. The chosen variable is most widely used and discussed by economic forecasters and, consequently, seems the most useful choice for an exercise in comparative forecasting. The second decision required is the level of aggregation in the model. On theoretical grounds, it is desirable to separate markets for rental and owner-occupied housing. Time series on housing starts, however, are not separated by tenure mode. Some authors use structural type as a proxy for tenure where single-family units are assumed to be produced for owner occupation and multiple family structures for the rental market [Jaffee and Rosen (1979)]. This seems to be a poor proxy at best. In 1980, for example, over 31 percent of renter-occupied units were single-family dwellings. ’ Our choice has been to aggregate housing starts, rather than estimate separate equations for various structural types. Simple tests do not indicate any serious biases resulting from this choice. One of the features that distinguishes housing markets from most other commodity markets is the extreme durability of the product. Consequently, the proportion of existing dwellings to newly constructed dwellings is always very high. In such markets the interaction between supply and demtid is best described in a stock-flow model. At anv ooint in time there exists a certain housing stock and a demand function for occupying dwelling units. House price levels adjust to establish momentary (stock) equilibrium between the two. Housing producers respond to this price level by moving up or down a supply curve for the produ.ction of new housing. Flow equilibrium then means that housing producers are on their supply curve, given the momentary equilibrium price that yields stock equilibrium. The cumulative effect of such production changes the existing stock to produce a different stock equilibrium, and so on. Fig. 1 presents a flow diagram to make these relationships more specific. The diagram presents a demand-supply model but it is more complex than a simple model due to interaction between stock and flow variables and their relationship to financial markets. The econometric specification leads to a recursive model which can be estimated equation by equation. We describe below first the stock equilibrium and then flow equilibrium and present the estimated equations.
’ U.S. Bureau of the Census, 1980 Census of Population and Housing: Provisional Estimates of SocLr. Economic, and Housing Characteristics (U.S. Government Printing Office, 1982). Jaffee and Rosen (1979) really don’t make use of these data in their model. However, Rosen (1979) explores this issue intensively. Hendershott (1980) uses an adjusted homeownership rate which is somewhat different from the headship rate. Yet he takes the number of households to be predetermined.
A. K. Puri and J. Van Lierop / Forecasting homing starts
)
127
MORTGAGE coMuITMENTs (+I
R0W OF
DEPOSITS
VABIOUSINTEREST RATES f-1 I
(+I
(+I
( M"i%iiGE
t-1
> H%t:G /1\
t-1
w CURRENT?iOUSING
1 (+I PUDIJC COMPLETION Fig. 1.
2. I. Stock equilibrium The stock equilibrium is represented primarily by the house price equation. The real or deflated price level (HPRICE/CPI) in time period t is determined by the existing stock of units, the demographic demand for housing and mortgage rate. The equation in terms of levels of variables exhibited high autocorrelation. The demographic demand is derived from the total population, its age distribution and its propensity to group itself in household units. It has been suggested that the number of households be used to represent demographic influences on the housing market [Jaffee and Rosen (1979), in fact, use thiq measure]. The problem with this suggestion is that by definition the number of household units is equal to the number of occupied units. In our model if housing stock increases, it decreases housing prices which in turn will increase the number of household units and restore equilibrium in the housing market. Clearly then the number of households is an endogenous variable which, together with housing price (HPRICE), is endogenously determined. There are, of course, other factors affecting household formation. [See, e.g., Masnick (1983).] Our purpose in the construction of a demographic variable is to develop an exogenous variable. We pick the approximate midpoint of our sample period, 1970, as base, and create an index which measures demographic influences. Headship rates are defined as the ratio of the number of household heads in an age group to the population in that age group. Then we create our demographic variable called Weighted Population ( WPOP) by weighting population in four age groups by the headship rates for 1970. Specifically we used the following equation: house
WPOP = (0.046 POT24 + 0.467 P25T34 + 0.537 P35T64 + 0.619 P65UP) * POP, where POT24, P25T34, P35T64, P65UP represent population
share by age group O-24, 25-34,
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35-64 and 65 and up, respectively, POP represents total U.S. population in thousands and the coefficients are the 1970 headship rates. Our index WPOP does not completely capture all relevant demographic factors since headship rates do appear to follow an exogenous trend. 2 Still, we believe that it is preferable to the number of households which is strongly endogenous to housing market conditions. The ratio STOCK/ WPOP measures the relative scarcity of housing. The level of housing stock appears in the equation since long term growth in the housing stock will increase the demand for residential land which will increase land prices and in turn house prices. ’ The error term is modeled as a first-order autoregressive process. The estimated equation in generalized difference form is as follows:
HPRICE/CPI=108.8+0.657HPRICE(-l)/CPI(-1) (6.95)
-0.152~-6 [RM* STOCK-0.657~~(-~)*STOCK(-l)] (1.98) +0.313 E-4[
STOCK-O.657 * STOCK(- l)]
(7.84) -(;.~;~[sT0cK/wp0p-o.657 a STOCK(-~)/wPoP(-l)].
(1)
.
The numbers in brackets are absolute t-values ( R2 = 0.975, Sample: 4 1966 : 43-1980 : 42, Method of estimation: Maximum Likelihood). The next equation describes the housing stock variable (STOCK) utilized in eq. (1). It is calculated as the sum of the housing surviving from the previous period and the previous period completions of private dwelling units ( COMPS), mobil house shipments (MOBIL) and public dwelling units (PUBLIC).To calculate the surviving stock of housing units, we estimated quarterly removal rates of 0.001971 for the sixties and 0.000825 from 1970 on. The removal rates are estimated by simulating equation (2) for the 1960-70 and 1970-80 periods, respectively, and choosing those removal rates that generate the observed housing stock counts in the 1970 and 1980 census.
STOCK= (0.999175 -0.001146 *D6O)STOCK(- l)+ COMPS(- l)+ MOBIL(- 1) +PUBLIC(-l), where 060 is a dummy variable which takes the value 1 between 1960 and 1970 and zero thereafter. The equation for private dwelling units completed is estimated as a distributed lag model. Discussions with industry analysts and the Construction Report of the Census Bureau suggest that ’ See William C. Apgar, ‘Housing in the 1980s: A Review of Alternative Forecasts’, MIT-Harvard Joint Center for Urban Studies, Working Ppper No. 283-2, revised July 1983, p. 8. At the time of the writing of this paper, we were not aware of any satisfactory economic formulation of the headship formulation function. To the extent that headship rates are variable, the present study is limited. 3 For data sources, see appendix. Hendershott (1980) used a measure of user cost in this equation which he has estimated himself. 4 Sample sizes for certain estimated equations sometimes are different because the needed data series did not go back far enough.
AK. Puri and .I. Van Lierop / Forecasting housing starts
most units are completed equation:
within two to three quarters
129
after being started. Hence the following
COMPS=0.267STARTS+(;3f!;STARTS( -1) +0.2OOSTARTS(-2)+0.1OOSTARTS(-3). (3.64) . (2.27) (1.33)
(3) This series is non-existent estimation: Ordinary Least Mobile home shipments the cycle of housing starts,
prior to 1968:Ql ( R2 = 0.70, Sample 1968:Ql-198O:Q2, Method of Squares). play a minor role in our model. Since the cycle in these closely parallels we estimated the following equation based on that correlation:
M0~1~=2.17+0.922MoBrL(-l)+o.i31[s~~~T~-0.922 STARTS((18.8) (9.69)
(4)
( R2= 0.906, Sample: 1966:Q3-198O:Q2, Method of estimation: Maximum Likelihood.) Public dwelling units completed (PUBLIC)is exogenous to our model. 2.2. Flowequilibrium The specification of the supply function for newly built housing is based on the following three arguments. First, there is widespread agreement that an important, if not the most important, determinant of the housing cycle is the volatile nature of the supply of mortgage credit. Second, in most of the literature on mortgage markets, it is commonly assumed that mortgage lenders use ‘non-price’ rationing, i.e., conditions of the contract other than the effective rate [see, for instance, Jaffee (1972), for a different view see Meltzer (1974)]. Third, the supply function slopes upward with respect to price. Because of the first two reasons, we include both cost and availability of credit variables. For a proxy of mortgage credit availability we follow Jaffee and Rosen’s (1979) general approach. As part of the policy to moderate the housing cycle a number of federal agencies have been set up for the express purpose of increasing the availability of mortgage credit, notably: the Federal Home Loan Bank (FHLB), the Federal Home Loan Mortgage Corporation (FHLMC), the Federal National Mortgage Association (FNMA) and the Government National Mortgage Association (GNMA). The flow of advances to lending institutions by FHLBB and mortgage commitments by the other three agencies is one of the credit availability variables (FACOM).The other is the flow of deposits into the financial institutions that supply the majority of mortgage credit, i.e., Savings ad Loan associations (S&Ls) and Mutual Savings Banks (MSBs). This produces the following equation:
A STARTS=773.9A( HPRICE/CPI)-0.934E-3 A( RM*STOCK) (4.40) (2.45) +0.204 A( FLDEP/HPRICE) (0.78) +0.657 A( FACOM/HPRICE)-49.9 aQl+ (4.96) (1.86)
104.5 A Q2 +73.5 A Q3 (8.07) (10.4)
( R2= 0.896, Sample: 1966:Q3-198O:Q2, Method of estimation:
Maximum Likelihood.)
(5)
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The symbol A is the first difference operator. The first difference specification was chosen since the residuals of the original, undifferenced specification exhibited a random walk pattern. Other variables are FLDEP, flow of deposits into S&Ls and MSBs (millions of dollars); Ql, Q2, Q3, seasonal (dummy) variables for the first, second and third quarters respectively; FACOM, flow of loan commitments and advances by the above federal agencies (millions of dollars). (For fuller description see appendix) The mortgage rate variable (RM) is scaled by the housing stock and FACOM is divided by the houseprice index (HPRICE) as an appropriate deflator to measure its impact on housing starts. (FACOM/ HPRICE measures commitments to finance in ‘real’ housing units.) All coefficients have the correct sign but the credit availability variables are not very significant, casting doubt on the credit rationing hypothesis. Because of the widespread belief that these variables do matter however, we consider the prior probability of positive coefficients on these variables quite high and leave them in the model. For the mortgage rate equation, we view the mortgage interest determination as a partial adjustment process A RM=k
[RM*-RM(-I)],
where RM * is the equilibrium mortgage rate. The one period change in the mortgage rate is only a fraction k of the gap between equilibrium and previous period’s mortgage rate value. The equilibrium value RM * is expected to depend on various interest rates, credit availability and demand for mortgage credit. Only the interest rate variables proved significant resulting in the following equation: 5 A
RM= -0.?309+0.079RTB (6.78)
+;.;6$35(-1) .
+0.271SRATE-;.;;;RM(-I), (4.78) .
(6)
where RTB = rate on 3-month T-bills, R35 = rate on 3-5 year T-bills, SR4 TE = effective interest rate paid on deposits by FSLIC insured savings and loan associations ( R2 = 0.801, Sample: 1966:Q3-198O:Q2, Method of estimation: Ordinary Least Squares). The savings and loan deposit interest rate is a cost variable representing the average interest rate on deposits. Jaffee and Rosen (1979) interpret the significance of this variable as indicating cost markup price-setting behavior by thrift institutions in setting mortgage rates. This has important implications for the effect of regulation Q-ceilings on mortgage rates. Pyle (1982) criticizes this specification on the grounds that marginal rather than average cost of funds should be considered and, additionally, that thrift institutions are price takers rather than price setters in mortgage markets. He attributes the significance of the coefficient to spurious correlation. The continued significance of the variable beyond the Jaffee- Rosen sample period (1965 : Q3- 1978 : Q2), however, makes the spurious correlation argument not very credible. Finally, the deposit flow into the thrift institutions (FLDEP) depends on the amount of new personal savings generated, the interest paid on deposits by these institutions in the previous period and the interest rate differential between this rate and the rate on alternative financial instruments. The T-bill rate (RTB) is taken as a proxy for the latter. The variables are scaled by lagged deposits, DEP( - 1) and personal savings, SA V, for a better fit. 5 The equation reported here indicates that, for our data set at least, variables other than those reported added little to the explanatory power.
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The following equation explains the deposit-flow scheme and completes the model:
FLDEP= -932.3+~08~5s~v+(y;~E-2[~R4~~(-1)*~~~(-1)] .
.
-2.94(RTB-SRATE) SAV. (7.87)
(7)
(R2 = 0.702, Sample: 1966:Q3-198O:Q2, Method of estimation: Ordinary Least Squares.) Note that, by definition, DEP = DEP(- 1) + FLDEP.AlsoSA V = personal saving at seasonally adjusted annual rate ($ millions) and DEP = total deposits in S&Ls and MSBs ($ millionsj. The negative coefficient of the interest differential reveals the regulation Q interference in the credit markets, making thrift institutions less competitive than others in obtaining funds in periods of relatively high interest rates.
3.Evaluation of forecasting performance To evaluate the comparative forecasting performance of the model described above, we developed two time series models for housing starts. The first is a univariate ARIMA model and the second a bivariate leading indicator model with a time series on private dwelling units authorized as a leading indicator series. Due to the short lag between the indicator and the housing starts series [over 90% of authorized housing units are started in the same quarter) and the difficulty in forecasting the indicator series, the ARIMA model performed the better of the two. The indicator model was therefore dropped from the analysis. After applying standard Box-Jenkins identification procedures, the following ARIMA model was estimated: (1 - B)(l -
B4)STARTS,=(1 +0.127 B)(l -0.929 B4) u,, (1.02)
(12.55)
(8)
where B is the backward lag operator. TO evaluate the forecasting performance, both models were simulated for the 10 quarters immediately following the sample period, i.e., 198O:Q3-1982:Q4. This period covers the mini-recovery that started in 1980 followed by the decline to the lowest level in 25 years in the second quarter of 1982, and the start of the subsequent recovery. This period, therefore, is a particularly trying one for forecasting. The majority of comparative forecasting performance studies have calculated econometric forecasts using actual values of exogenous variables. [An exception is Hirsch et al. (1974).] In these cases an econometric model is primarily intended as a testing ground for competing economic theories or evaluation of policy alternatives. The model simulations then establish the degree of confidence in the model. In those cases where the model is intended as a forecasting tool, the use of actual future values may bias the comparison in favor of the econometric models since exogenous variables can rarely be predicted with certainty. We performed simulations using actual values of exogenous variables and also simulated the model using forecasted values of exogenous variables. To do this, we estimated ARIMA models for each of the exogenous variables CPI,WPOP, PUBLIC,FACOM, RTB,R35,SRATE,SAK and generated forecast for one, two, three and four periods ahead. Since the ARIMA forecasts for these variables are probably not the best ones available, this procedure may bias comparisons against the econometric model. Table 1 presents the root mean square error (RMSE) of the three simulations.
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A. K. Puri and J. Van Lierop / Forecasting housing starts
Table 1 Root Mean Squared Error: Period 198O:Q3-1982:Q4. a Periods ahead
RMSE EAVEX
EPVEX
ARIMA
1
55.6 (0.515) 100.3 (0.652) 119.4 (0.783) 133.7 (0.897)
55.0 (0.642) 97.0 (0.708) 130.6 (0.628) 156.8 (0.559)
65.6 (0.076) 76.6 (0.001) 99.5 (0.047) 100.3 (0.142)
2 3 4
a The numbers in brackets represent the fraction of error due to bias.
Cohunn one refers to the econometric model with actual exogenous variables (EAVEX), column two to the econometric forecast with predicted exogenous variables (EPVEX), and column three to the ARIMA forecasts. It should be noted that while ten one-period ahead forecasts were generated, for the two, three, and four-period ahead forecast only nine, eight and seven forecasts respectively were calculated. The table shows that the econometric forecasts outperform the ARIMA model for one period ahead forecasts. For two, theree and four period ahead forecasts the ARIMA model works better, although neither model produces acceptable unaided three and four period ahead forecasts. Comparison of columns one and two reveals that for one and two periods ahead, there is no significant difference between EAVEX and EPVEX, i.e., between using actual values and ARIMA forecasts of exogenous variables. This may seem somewhat surprising but is actually a quite common result, see, for instance, Evans et al. (1972). A noteworthy difference between ARIMA and econometric forecasts is the proportion of the error that is due to bias. The ARIMA forecasts are virtually unbiased and the fraction of error due to bias is very low. This fraction is very large for the econometric model. In plotting exercises, we noticed that the econometric model actually tracked the fluctuations over the simulation period quite well but at too low a level. (It may be due to the downward bias in our WPOP variable.) For the purpose of using the model as a forecasting tool this difference is quite important. It is undoubtedly true that by applying the kind of judgmental adjustments described by Young (1982) the bias in the econometric models forecast can be greatly reduced, and result in very acceptable forecasts. No such improvement would be expected if the economic forecaster were to take the ARIMA forecasts as his starting point.
4. Summary and conclusions In this paper we presented an econometric model of the housing market. The durable nature of the product gives rise to the stock-flow structure of the model. Key variables in the housing supply equation are cost and availability of credit variables. The main point of the exercise described here is to add to the body of evidence that exists regarding the econometrician’s versus the time-series analyst’s approach to economic forecasting. The issue is whether the method of faithfully trying to model the relationships suggested by economic theory constitutes a real advantage for forecasting purposes.
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We believe that the research presented adds to this body of evidence in two specific ways: First, the present study is microeconomic in nature whereas the existing literature is largely macro oriented; second, we have chosen to investigate a time series the volatility of which is several times greater than the typical series that existing research has reference to. Our conclusion is that the unaided econometric forecast outperforms the ARIMA model for one period ahead forecasts and that these forecasts are quite acceptable given the volatile nature of the housing start series. The ARIMA mode! performs better than unaided econometric forecasts for multi-period ahead forecasts. The reason for this is the bias in the econometric forecasts. At the same time it is clear that this bias can be greatly reduced in actual forecasting situations by judgmental adjustment based on the monitoring of previous forecast errors. This evidence strongly suggests the utility of the econometrician’s use of economic theory for forecasting purposes.
Appendix SAV
RTB R35 RM CPI DEP SLDEP, MUDEP FHLA HPRICE COMPS STARTS MOBIL NCFHLMC, NCGNMA, NCFNMA POP SRA TE FACOM PQT24 P25T34 P35T64 P65UP
= Personal Savings at seasonally adjusted annual rates from the Survey of Current Business, various issues. All the following interest rate series are from the Federal Reserve Bulletin. = T-bill Rate (3 month bonds), Federal Reserve Bulletin. = Rate on 3-5 year treasury bond rate, Federal Reserve Bulletin. = Effective mortgage rate on conventional mortgages (includes initiation costs, points) FHLBB series, Federal Home Loan Bank Board. = Consumer Price Index, Federal Reserve Bulletin. = SLDEP + MUDEP = Total deposits in S&L and Mutual Savings Banks respectively, end of period in millions, from the Federal Reserve Bulletin. = FHLBB advances outstanding at the end of period in millions, FHLBB Journal = Price Index of new one family houses sold (1977 = loci, index based on type of homes in 1977) from the Bureau of the Census = Private dwelling units completed from Bureau of the Census = Private dwelling units started from the Bureau of the Census = Mobile Home Shipments from the Bureau of the Census = New commitments to purchase mortgages by FHLMC, FNMA and GNMA respectively from the Federal Reserve Bulletin = Total population (including armed forces overseas) Current Population Reports - Population Estimates and Projections, Series P-25 = Effective interest/divided rate paid by insured FSLIC Savings and Loan all districts from FHLBB Journal Associations = (FHLA - FHLA( - 1)) + FHLMC + NCGNMA + NGFNMA = Population shares by age group, O-24, 25-34, 35-64, 65 and up, respectively from Population Characteristics, Bureau ofthe Census.
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References Apgar, William C., 1983, Housing in the 1980s: A review of alternative
forecasts, Working paper no. W83-2, July (MIT-Harvard Joint Center for Urban Studies, Cambridge. MA). Christ, CF., 1975, Judging the performance of econometric models of the U.S. economy, International Economic Review 16, 54-74. Cooper, R.L., 1972, The predictive performance of quarterly econometric modzis of the United States, in: B.G. Hi&man, ed. Econometric Models of Cyclical Behavior, (Columbia University Press, New York). Evans, M.K., Y. Haitovsky and G.J. Treyz, 1977, An analysis of the forecasting properties of U.S. econometric models, in: B.G. Hickman, ed., Econometric models of cyclical behavior (Columbia University Press, New York). Fair, R.C., 1974, An evaluation of a short-run forecasting model, International Economic Review 15, 285-303. Granger, C.W. and P. Newbold, 1977, Forecasting economic time series (Academic Press, New York). Hendershott, Patric H., 1980, real users costs and the demand for single-family housing, Brookings Papers on Economic Activity 2, 401-452. ‘affee, D.M., 1972, An econometric model of the mortgage market, in: E.G. GrahIich and D.M. Jaffee, eds., Savings deposits, mortgages, and housing: Studies for the federal reserve-MIT-Penn economic model, Lexington. Jaffee, D. and K. Rosen, 1979, Mortgage credit availability and residential construction, Brookings Papers on Economic Activity, 333-376. Masnick, George S., 1983, The demographic factor in household formation, Working paper no. W83-3, June (MIT-Harvard Joint Center for Urban Studies, Cambridge, MA). Melzer, A., 1974, Credit availability and economic decisions: Some evidence from the mortgage and housing markets, Journal of Finance, 763-777. Nelson, C.R., 1972, The prediction performance of the F.R.B.-M.I.T.-PENN model of the U.S. economy, American Economic Review 62,902-917. Pyle, David H., 1982, Deposit costs and mortgage rates, Housing Finance Review 1, 43-48. Rosen, Harvey S., 1979, Housing decisions and the U.S. income tax: An econometric analysis, Journal of Public Economics 11. Young. R.M., 1982, Forecasting with an econometric model, Journal of Forecasting 1, 189-203.
Biography:
Anil K. PURI is an associate professor of Economics at California State University, Fullerton. He received his Ph.D. from the University of Minnesota. His research interests include applied econometrics and public finance. Johannes VAN LIEROP, after the work on this paper, has joined the Southern California Gas Company. He received his Ph.D. in Economics from the University of Toronto. His research has concentrated on housing and financial markets.