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Article Excerpt
Introduction
In their celebrated article, Klein and Kosobud (1961, 178) had pioneered the use of both "fundamental parameters" and "simple ratios" in economic theory. Housing economists had been following the FHA techniques by focusing on such parameters and ratios in their housing demand models for a long time. We find that both these studies emphasized caution in the use of ratios. In the former, the authors stated that "... stability or plainly systematic variation in ratios must be found in order to enhance their usefulness." In the latter, the guide warned that while participation rates based on labor force or employment data "... are both useful in estimating and projecting population they have some shortcomings ... primarily from the unavailability and limitations of pertinent locality data and from the adjustments that may be required to reflect the level and trends of unemployment" (FHA 1970, 33).
As an example of the use of ratios, the FHA guide, most likely, has outdone any other framework in optimizing the number of ratios to be used in a housing analysis. Besides the participation rates, it prescribed the use of household sizes, institutional populations, demolition rates, and the rate of construction for the single and multi-family units. The guide requires inputs for at least two census years, a current period, and a forecast period, and it uses long-term natural growth rates for population, households, labor force, employment, and construction permits. These rates are kept at a high level, perhaps with an eye for simulating "golden" growth scenarios where a combination of variables would move simultaneously in the same trend and cycle. At a local level, it is apparent that market analysts would be time-constrained to perform "stability" and "variations" studies for these parameters. Hence they would be prevailed upon to accept these studies on faith as uncontroversial stable ratios and parameters. A better way for practitioners in the field to overcome such problems would be to use a less time-consuming method that could enhance their model's estimation and predictive performance. This paper provides one such method, namely, the simulation of stable parameters and normed variables within the FHA model for family and elderly market analysis.
The Models
The FHA guide subdivides housing markets into family, elderly, and military, in terms of their relative price, rent, size and other measurements. Both the family and the elderly markets have a rental component. Traditionally, the family market has rentals for both, the family and the independent living adult population between the ages of 45 to 62. The elderly rental component, which we presume to target (persons 62 years of age and over) are mostly housed in either independent living, Retirement Service Centers (RSCs), Assisted Living (ALF), Board and Care (BC), Nursing Homes (NH), and Alzheimer's (ALZ) facilities. The population housed in RSCs is characterized by an "at risk" criterion, i.e., persons 62 and over who can perform less than three activities of daily living (ADLs) or instrumental activities of daily living (IADLs) with difficulty. The population housed in the ALFs, BCs, NHs, and ALZs are primarily 62 years of age and over who have varying levels of care dependency, who can perform three or more ADLs or IADLs with difficulty. (1)
A major premise that we investigate is that while the FHA technique had a long gestation period, it has not evolved statistically. For instance, the family market is based on the premise that either rising labor force or an increase in population translates quantitatively into household growth, which in turn is a measure of demand for the new housing units. The quantity is then put into an income growth stream to estimate the effective demand. (2) For the elderly, we may rely on the living arrangements of the one-person households for the demand estimates, and use a survival methodology to age that population. We will look at some of the controversy in the aging cohort process below, particularly relating to Mankiw and Weil's (1989) work. A novel aspect of this paper is that it perturbs the assumptions of natural, psychological, or institutional drivers in order to assess market conditions. For the family market, we will conduct such an estimation in terms of the quantitative level. In this case the income level's influence is evaluated usually in a subsequent process of the analysis. We will also suggest a new approach to distribute family demand by rents and bedroom types in Appendix 1. For the elderly market, we will qualitatively estimate the age-income-qualified population that is integral to the processes of estimating the needs. Also, we offer new ways on how to combine ADL and IADL factors with the help of the new technology of belief functions in Appendix 2. The rest of this paper is divided into two major parts, addressing the family and the elderly markets, respectively.
I. Family Market
The first step in characterizing the FHA model is to postulate that the market demand and supply of housing units are quantity vectors that depend on some predetermined variables. The FHA handbook states that housing is "... a commodity in the physical sense; it is identified with and measured in terms of the dwelling units or housing units" (FHA 1970, 9). While the handbook failed to identify the structure of the housing market in the economic sense (monopolistic and/or oligopolistic competition), it allowed lots of theoretical and practical leeway for analysts to implement a study. For instance, besides the physical differentiation, it includes some differentiating characteristics and excludes others. The excluded characteristics are "service" and "rights" while housing type, quality, location, and sub-market determination such as tenure, price, rent, size, and other variables are taken into account. Since price is treated as an exogenously determined variable, it appears that the housing market is characterized by price-taking and product differentiation. In such a market we expect to find concessions, service packages, and other non-price variables dominating price competition.
A second step in determining the FHA model is to incorporate some market clearing operations. Assuming that the market is competitive, and that it is not in equilibrium, it is sufficient to show that there is an equilibrium price, [P.sub.e], such that if [P.sub.i] is any other price, then, excess demand, z(p) [right arrow] as [P.sub.i] [right arrow] [P.sub.e]. The market mechanism or an auctioneer yields that outcome, raising the price if z(p) > 0, lowering or not raising the price if z(p) < 0, and would never make price negative, or vary it when z(p) = (Arrow and Hahn 1971). If one does not view the market as a competitive one, then similar adjustments can be envisioned. For instance, in the non-price area the vacancy rate, excess construction, concessions and other variables would be foremost in play. Equilibrium can then be restored with entry and exit operations. (3) A variation of the model may be obtained by arguing that if normal vacancy is a constant and supply is fixed for simplification, then the market vacancy rate and the rents are inversely related. This is more of an empirical than a theoretical proposition. Following Smith (1974, 479) let the vacancy level, be VL = (S)upply - (D)emand. Dividing through by (S)upply, and making (D)emand a function of (R)ents, then the changes in rents will be inversely related to the vacancy rates, that is, VL/S = [1 - (D= f(R))]/S.
The next step in the family model requires more complex dynamic analysis. For instance, if the price in the housing market is sticky, then a disequilibrium price can persist for a long period of time. Also, during fixed price episodes, the vacancy level may not equal the natural vacancy rate. Smith (1972, 228) reasoned that disequilibrium is more likely in the rental than the owner market. In the rental market, price reduction in vacant units is difficult to maintain and not passed on to other occupied rental units. Therefore, rents will be sticky downwards because the necessity to lower rents across the board in a price reduction attempt may adversely affect revenues. Another instance of complex dynamics occurs under the market conditions of excess supply or demand. If demand exceeds supply, then the buyers will go unsatisfied, and if supply exceeds demand, suppliers will go unsatisfied. Thus, it will be reasonable to argue that if the observed quantity is either D for demand or S for supply, it follows that the observed quantity will be Q = min(D,S) according to Fair and Jaffee (1972, 501). The analysis can be extended to the normal behavior in the mortgage market if we replace price by the mortgage rate. Then, we will not only be concerned with observing the traditional flexible adjustment to equilibrium in the market, but we should also take into account the state of the credit market equilibrium or disequilibrium. Sometimes excess credit will have an effect only in the subsequent period when the rate of interest adjusts, but will have no effect in the current period. On the other hand, tight credit will have an immediate effect (Ricks 1972, 226).
Another complex dynamic situation would be to evaluate the optimal stock for the owner or the renter. It is worth explaining the term optimal because some analysts perceive the housing market as having multiple equlibria. For example, it might appear that a market with a normal vacancy rate of 5 percent is in an equilibrium state, and the one with a vacancy rate of nearly 10 percent is in a disequilibrium state. This would imply that a market with a vacancy rate in the interval of 5 to 9.99 percent is in equilibrium. Under these circumstances, the housing market will have multiple equilibria. The FHA technique seeks an optimal equilibrium from a generalized welfare function point of view. Such an optimal point of view is obtained if we start from the FHA model that states that the "... aggregate of the individual scales of preference links dwelling units, types, quality, and location in an area." This statement however, disregards Arrow's impossibility theorem, which states that one cannot have such an aggregation without a dictator solving conflict situations. But modern investigators also take a pragmatic route around the impossibility theorem. Following Anas and Arnott (1991), let the consumer be endowed with an intertemporal utility function, U = [beta]U(*). Let k = 1, ....., K be housing types of sub markets or bundles of housing. Let [S.sup.t.sub.k] be apartments in k, and assume that the consumer can choose and rent one apartment per year, given that all apartments are in the choice set. Furthermore, let the consumer have a contemporaneous budget where each year's income is spent on that year's consumption, and let the constraints include: 1) a budgetary allowance; 2) credit availability; 3) FHA's participation in the supply of adequate and affordable housing; 4) fiscal policy incentives (taxes in particular) and 5) market conditions, such as changes in rents that are inverse to demand. Then, the problem at hand is to find the optimal stock of rental housing and the optimal path of consumption of renters by solving this discrete maximization problem for the given constraints. A simple example of how these problems can be solved for the above assumptions can be illustrated by using the Cobb-Douglas utility function, [U.sub.a] = [x.sup.0.25.sub.1] [x.sup.0.5.sub.2] for one state of the economy, and [U.sub.a] = [x.sup.0.25.sub.1] [x.sup.0.25.sub.2] for another state of the economy. The first and second periods of endowment can be e = ([e.sup.a1], [e.sup.a2]). Other considerations may include market tightness or softness, rational expectations that assume a probability distribution over the possible states of the economy, an intertemporal dependent utility function, and the inclusion of price and concession signals that the players may observe. We now focus on the specific cases in which the FHA model can include several of those phenomena through a simulation of changes in its parameters and variables.
Table 1 displays some typical assumptions we make in estimating quantitative demand for the owners and the renters. (4) Here we are using only uniform and normal distributions to perturb the stable parameters. The uniform distribution is a natural choice for those variables that have boundary values. For example, it takes two to three months to build a single-family home, and in the case of demolition, we typically do not know the actual number of units that are demolished but estimate it to be in the 0.002 to 0.005 interval of the inventory. The normal or t-distribution would be a natural choice for those estimated parameters and the variables that are associated with standard errors, such as the numerous census variables. In estimating the participation rate, for instance, we use the ratio of the census employment or labor force to the census population. (5) The first column of Table 1 presents the typical assumptions of the FHA technique under the headings of participation rates, driver, household size, non-household population, population, permits, and vacancies. The second column of Table 1 shows how we can specify a statistical distribution, which can be either normal or uniform, to the assumption or parameter described in column one. The number of replications is indicated by the variable "z." For instance, the first entry in the table indicates that the 1990 participation rate (PR1990) is defined as a two-parameter family distribution with a mean value equal to the 1990 census ratio of the driver to the population of the housing market area and a standard error of 0.2. The single family construction period (SFCONSTPERIOD) is defined as a uniform distribution that takes on a time period between two to three months. In general the variables are self-explanatory but where necessary the cues are noted in the footnote following the table.
In the statistical parlance we are engaged in an experiment. We draw equilikely values for our parameters and variables through the use of a normal or a uniform distribution for the experiment on theoretical grounds. The experimenter can follow other procedures such as historical data, "bootstrap" methods that select historical data at random, or the development of an approximate distribution from data at hand. But the FHA technique suggests looking at the "... trend in labor force and nonagricultural employment" (FHA 1970, 265) as it relates to local job situations. This can be achieved either through "extrapolation," "ratio," "school enrollment" or "housing units" methods. In Table 1, the years 1990 and 2000 PR ratios are set by the Census for those years. However, the current and forecast PR ratios are extrapolated from the Census trends. The contribution we make to this method is that the ratios are perturbed before extrapolation via the normal distribution.
After specifying the distribution, we also need to be aware of the distribution of the resulting parameter estimates for the purpose of setting up confidence intervals. The experiment involves filling 18 boxes with a random transaction before a point estimate of demand...
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