# A Conditional Analysis of Movers' Housing Responses

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James N. Morgan (1989) ,"A Conditional Analysis of Movers' Housing Responses", in NA - Advances in Consumer Research Volume 16, eds. Thomas K. Srull, Provo, UT : Association for Consumer Research, Pages: 93-104.

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http://acrwebsite.org/volumes/6888/volumes/v16/NA-16

Panel data allow us to answer such questions in a dynamic model with fewer assumptions, and also to test for lags. Lags in response are likely to be larger for changes in housing than for changes in food consumption, and lags in the effect of income changes are likely to be slower than lags in response to changes in family size. Cross-section data reveal mostly long-term effects, since most people in any income group have been there for a while.

Housing can be adapted to changes in need for space or in ability to pay only sporadically, and mostly by a costly process of moving. A full behavioral model would first account for the decision to move, combining a variety of factors including moves forced by job changes, fire, loss of tenancy, or induced by changes in income or family size. And one might want to examine the lags, to see whether adjustments to changes in family size (which might sometimes be endogenous or jointly determined) come faster than adjustments to changes in income or wealth.

We prefer to ask a hopefully easier question-given a decision to move, for whom does prior change in income or needs for space have the most effect? There are dangers in such an approach. Younger, more affluent people, or those with more education, might move more frequently, with less incentives from changes in income or family size, so it would look like such changes had less effect on the increase in their housing costs. A full simulation of the effects of economic or demographic changes would have to include both the effects on the probabilities of moving, and on the extent of change in housing costs for the movers, dealing, in other words, with possible selection bias.

One might also want to assess the lags -- how long it takes before changes in the environment or the family have their effects. However, lags should mostly affect whether the family moves, though once a family moves, the more distant the prior changes in income or family size, the more likely the family has already adjusted to them by moving earlier, or by habituation.

SEARCHING FOR STRUCTURE

At any rate, it seems useful to present some results of a search for population groups which differ as to the effects of the five-year prior income trend on movers' change in house values. We take the change in housing from a year ago, before the move took place, minimizing the inflation effects, and do not deflate the income change variables since it is interpersonal differences we seek, rather than an unbiased estimate of the marginal propensity to spend income increases on housing.

Some people rent, and some neither own nor rent. We make a rough conversion by multiplying the annual rent, or rent-equivalent estimated by respondents who neither own nor rent, by 10. This minimizes the problem except for those who switch into or out of owning, since that switch commonly goes along with substantial changes in real housing costs (abundant evidence exists that people are willing to pay more to own a house than they would pay to rent the same house). Hence, we take account of changes to and from ownership coincident with the move .

Indeed. as we shall soon see, we have a mixture of effects from the past and from initial situations, with the effects of other changes taking place at the same time as the move. Once again, we are attempting to deal with a part of a larger problem which includes a set of joint decisions about changes in family, residence, and jobs.

We use a pre-programmed, reproducible, computer program called SEARCH, and within that a means option, a regression search option which seeks to separate groups with widely different simple regressions of five-year income path on change in number of rooms or in house value, and a new "slopes only" option which recenters all groups and isolates those with different effects of income trend on housing upgrading. (Housing costs and hence consumption are a reasonably linear function of house value.) The groups which result from the regression option maximize the variance accounted for by both the mean change in rooms or house value and the effects of income change on that change. Of course, a difference in the mean of Y will do much more to reduce unexplained variance than a difference in the regression slope on income change. Since the slopes option is so new, we present some results for both it and the regression option for comparison.

The data are from the Panel Study of Income Dynamics, using the 1984 multi-year family tape. We combine all cases who moved in any of the five years 1978-1983, shifting the explanatory variables so they are relative to the year of the move. But in any year, some families have a new head, because a former wife divorced or became widowed, or because a child left home to form a new household. Hence we force the search process first to split off families with the same head or a wife who became head, and then to split off the pure same-head families. Later we select only moves where the family has had the same head for the prior five years, only 2887 out of the 8120 moves over the five years. The dependent variable is the difference in house value or rooms (value divided by the mean of the two to avoid scale-effects). One predictor, later a covariate, is the five year trend in family money income divided by the five year mean, i.e. the slope of the trend in income relative to its level. We looked at the change in house value (divided by the sum) using both the past trend in income and the coincident change in income (difference over sum) as explanatory variables.

VARIABLES AND METHODS

To justify the use of a difference divided by the sum (or mean) notice the nice symmetry it produces for changes in both directions (Table 1). So averaging two people one of whose house value doubled and one of whose house fell to half, would give an average of 0 rather than +25%.

We look first at change in number of rooms, which avoids problems of measurement as between owners and renters, and problems of differential inflation of house values and rents. And since prior income changes are not expected to be so dominant, we do not use the covariance search but a simple search with prior income change as one of the explanatory variables.

We introduce the following categorical "predictors" in all the analyses, allowing the SEARCH routine to divide the sample at any point down the rank order that would do the most good. (Numerical variables were put into categories, losing almost none of their potential power.):

Temporally prior variables:

Trend in family income over the five years prior to the move, divided by the five-year average income. Trend is the regression on time, simple to compute because time has values -2,-1, 0, l and 2.

Alternatively, the time-trend in family income relative to needs over the five years prior to the move. This is a better measure of increasing level of ability to pay for housing, and minimizes the distortions from the few families that changed composition in the five years before the year of the move .

Actual minus required rooms just before the move, a measure of pressure for more space. ("Required" specifies that two different gender children can share bedrooms until they are 10 years old, and same-gender children until they are 18.)

Change in required number of rooms in five years ending after move, as a measure of longer-term pressure building up.

Change in actual number of rooms in five years ending before move, as a measure of prior housing adjustments. (Perhaps we should have replaced these last two with the change in actual-required rooms.)

Change in whether a wife in the unit, a proxy for marriage or divorce, and for family cohesion and interest in the home We use five groups: got married, stayed married, stayed single man, stayed single woman, got divorced.

Timeless background variables:

Head's education, a proxy for income stability and a longer time horizon

Race, a proxy for income insecurity, restricted choices, etc.

Region, a proxy both for availability and cost of housing, and for differential rates of increase in housing prices.

Size of largest city in the area, a proxy for job opportunities, cost of housing, differential inflation, and number of available alternatives?

Age, as a proxy for likely length of residence and job tenure and probably having made the necessary adjustments, or else for the fact that older people face declining space needs, but better financial ability to avoid reducing space.

Decile of family income/needs the year before the move as an indicator of affluence and ability to satisfy changing housing needs, or to use more of any income increase to upgrade housing.

Changes During the Year of the Move:

Change in home ownership, because our conversion of rent and rent-equivalents to house values is imperfect. and because owners spend more on housing than renters. We use four groups: became an owner, stayed an owner, stayed a non-owner, ceased owning.

Change in family composition, a complex classification ranging from no change in family members to new families created by splitoffs or marriages of women.

Number who moved into the household during the year

Number who moved out of the household during the year

Change in income in the year after the move, a proxy for moving in anticipation of the increase, or moving to a better job.

ANALYSIS OF CHANGE IN NUMBER OF ROOMS

Figure 1 shows the results for change in number of rooms for the 8120 family-moves between 1978 and 1983. OveralL there was an average decrease in 0.18 room, because most of the families with new heads are splitoffs, with an average decrease of 1.92 rooms leaving the rest with an average increase of 0.14 rooms. That remaining group is then divided into families with the same head and those where a prior wife became head, by divorce or death of the husband. After forcing those first two splits, the program itself decides on the rest in such a way as to maximize the explained variance. The group of changed heads is divided into single women who got married (with an increase in rooms of .38) and the splitoffs who formed new households, with an average decrease of 2.69 rooms.

Turning to the families-with no change in head, the dominant factor accounting for change in rooms was the initial surplus or shortage of rooms relative to an estimate of "required rooms" based on the assumption that children could share bedrooms till age 18 if they were of the same gender, and until they were 12 if they were of different genders.

The only other factors important enough to cause a split in any of the groups were ownership or becoming an owner. One might argue that this is simply a problem in converting rents to house values, except that as we shall see, similar results appear in the covariance search, and a constant shift in the dependent variable should not affect a regression coefficient. We interpret it to mean an interaction whereby a combination of income increase and a decision to become an owner have a synergistic effect, but dominated by the decision to become an owner.

What did not matter is more impressive and unsettling, particularly the absence of effects of income level or change, or age. Life course theory might well argue for early increases, even in anticipation of later needs, and decreases late in life to avoid the burden of maintenance. Consumer economics would assume that income changes lead to upgrading, including more rooms as well as more dollars per room.

What we appear to have is family changes and prior failures to adjust to them as indicated by initial shortages or surpluses of rooms, plus a decision to become or remain an owner, dominating changes in number of rooms. The 12 splits form 13 final groups which account for 3290 of the overall variance in the change in number of rooms. An examination of the remaining potential within the final groups for accounting for residual variance with prior income trends shows only one group where it could have accounted for as much as half of 1% of the original variance, and for that group the initial surplus/shortage of rooms could account for twice as much. Indeed for only two groups could prior income trend account for mole of the remainder than more detail on initial surplus/shortage of rooms: One is a small group of 162 who became homeowners at the time of the move, and who had no big shortage or surplus of rooms before the move, but a prior decrease in number of rooms. Hence, upgrading takes place in response to an income increase mostly when it also involves becoming an owner. The other group is 226 owners. Both groups had large average increases in number of rooms.

Economic effects are clearly present, but just as clearly dominated by other considerations in most moves. A realtor looking for customers would do well to focus less on people being promoted than those getting married, divorced, having children, losing children, or on children leaving home.

ANALYSIS OF CHANGE IN VALUE ECONOMIC UPGRADING

But perhaps the upgrading is largely in the value per room, so we turn to an analysis of the change in house value. We divide the change by the mean of the before and after values, to put it in symmetric relative terms and to avoid scale effects and resulting spurious correlations. (We are interested in behavioral responses, not persistent interpersonal differences.)

We did this analysis in two ways, once treating the relative change in house value as a simple dependent variable with the prior relative income trend as one of the explanatory characteristics, and again in a covariance search, looking for groups where two simple regressions of change in house value on prior trend in income accounted for the most variance. Actually the regression or covariance search is dominated by differences in the mean of the dependent variable (change in house value), so 12 splits, forming 13 final groups accounted for the same total amount of variance, even though one analysis took account of income change in every group, while the other never took account of it since it was never powerful enough to split any group. In both cases the divisions after the initial two forced ones to isolate families with the same head, were mostly not on initial shortage or surplus of rooms, but becoming an owner or a renter, or having changes in family size or marital status. Since, however, the regression slopes, which are a kind of income elasticity of demand for housing, are more interesting than the fraction of the variance explained, Figure 2 presents the covariance search analysis, with each box showing the mean relative change in house value, the regression slope of value change on income change (income elasticity) and the size of the correlation coefficient.

Think then of that simple regression, which for all 8120 movers reveals that a mean relative change in house value of .061 results from a constant term change of .026 plus an income change effect of .478 times an average relative income trend of .075. The correlation of .14 means that the income trend accounted for only 2% of the variance.

Can we then find a division of the sample where two different regressions will account for more of the overall variance than the one simple regression on the whole sample? We hardly need a Chow test, since anything worth looking at with so many cases will surely be significant, even if we reduce the degrees of freedom to account for the sample design effects (clustering).

CHANGE IN NUMBER OF ROOMS, FOR 8120 WHO MOVED BETWEEN 1978 AND 1983

Since the explanation of variance in Figure 2 is dominated by means (level of dependent variable) rather than slopes (size of income-change effect), we look first at the mean changes which vary from a 46% increase for same-heads who became home-owners, and 69% for a few with a prior shortage of rooms and additions to the family (presumably children being born, since change in marital status did not do it). Of course new heads mostly reduced their house value, particularly women who were married or widowed (.248), except of course for women who got married to a non-sample person (+.360). And same-head families with two or more members disappearing at the time of the move, reduced their housing (-.-266). This is partly men leaving a wife and children, but partly children or relatives leaving home or dying.

Turning to the income effects, we notice First two negative ones, wives who became heads and moved (widowed or divorced), where housing may have been part of a divorce settlement, or an estate; and heads s,ho did not change tenure status but moved away from two or more others in the family, presumably mostly by divorcing. If we want to focus on income effects, we should look at the groups at the lower left with same head, no change in tenure status, no change in family size, where the income elasticity is far higher for owners who bought again than for renters who rented again. This cannot be polluted by problems of converting rents to house value equivalents, nor by differential inflation of rents and house values. It presumably means that housing is important to owners, and income changes allow them to upgrade it. However, the group with the highest income elasticity, and the strongest correlation, was the group with a concomitant increase in family size and a prior shortage of rooms to boot, but it is a small group. And the group with a shift to renting had a strong income effect, accentuated if we separate them according to prior surplus or shortage of rooms.

Once again, the families where there is a new head, whether a former wife whose husband died or left, or a single woman who married, or a splitoff starting out, decreased their consumption of housing, while families that moved but kept the same head increased their house values by 16%, more than the general rate of inflation of house values. One might have thought, since owners usually are willing to spend more on housing than renters, that people who moved to become owners would also increase their housing consumption more, and they did, except where there was a substantial decrease in family size. Those who became owners had the large increases, particularly if they were well educated and presumably had stable incomes. (Neither past income trend nor initial income/needs level appeared to matter directly, though they could have precipitated the switch to ownership). It is important to keep in mind that many moves are driven by job changes or neighborhood considerations, and there are substantial differences in house prices and rents in different areas, sometimes reflecting recent growth, as in California and New England, and sometimes reflecting differences in the level of public services, and what fraction of that cost is covered by property taxes. On the other hand, a group who went from owning to renting did have a decrease in housing. What else mattered? 1 he initial surplus or shortage of rooms, and the concurrent changes in family composition.

FOCUSING ON MOVERS WITH THE SAME FAMILY HEAD FOR FIVE YEARS

Of the 8120 moves during the five year period, 16% involved a change in the head at the time of the move (including a wife who became a head). Many "moves" are kids leaving home. Remember, that when a divorce occurs there may be two moves, and there is usually at least one. And since we are interested in the five year prior trend in income, we need to focus on families with the same head during that period. Some 61% of moves are by households without the same head for the five years prior to and during the move. So for the rest of the analysis, we restrict ourselves to moves where the family head was unchanged during the move and the prior period of estimating income trend. If we take the remaining 4887 cases of moves, we can force the first split to separate out the cases where there is a change in the wife (man got divorced, or married, or widowed or some combination of those). (Group 3 in Figure-3). The average change in housing is downward, but with a substantial effect of prior income change in the expected direction, implying that there were larger reductions in housing when the prior income trend had been worse.

Many of the splits set aside groups where things other than the past income trend are affecting the housing change: ownership, a (probably expected) income fall after the move, a retirement transition for those 55-64 years old, or ability to upgrade as indicated by immediately prior income/needs. But income "elasticities" never get very large. We move on quickly because the main purpose of Figure 3 was to compare it with the next Figure 4 which focuses on differences in income effects.

THE NEW SLOPES-ONLY OPTION, SEARCHING FOR MOVERS WITH DIFFERENT EFFECTS OF PRIOR INCOME ON UPGRADING

The new option in the SEARCH program eliminates the domination of the splitting by changes in the mean house value, by recentering each subgroup around its own mean changes in house value and income. Figure 4 deals again only with the 9887 moves where the head had not changed for five yea-s, applies the identical predictors and strategy, but uses the new slopes-only option:

After the forced splitting of those with a change in wife, the automatic search for groups with different income effects first set aside Group 4, those around retirement age, where the prior income trend is largely meaningless as an indicator of future ability to afford housing, and where the correlation is substantially negative. Next we segregate the top 8 deciles of the income/needs distribution (Group7) with a smaller effect of prior income trend, implying that level of affluence affects the relative upgrading of housing when income changes! The lower two deciles were affected by non-linearity in the effect of prior income trend, and by income change after the move, expectation of which apparently enhanced the effect of prior income changes. Among the rest, those with other changes in the family during the move (Group 9) are set aside, with a negative effect of prior income trend. Perhaps children whose earnings had been rising split when the family moved, reducing both the family income and the need for space.

The remaining splits continue to illustrate beautifully the way in which one can sort out some reasonably normal unconstrained groups whose response to prior income trends might be considered a good estimate of the income elasticity of the demand for housing.

Continuing with the "mainstream" group 8, we set aside:

those with a prior shortage of rooms (Group 10)

those whose income fell after the move (presumably expected) (Group 12)

those in the depressed north central part of the country (Group 14)

those in deciles 3-4 of income/needs, presumably unable to respond to income trends fully because of lack of borrowing power (Group 18)

Each time we eliminate one of these special groups, the estimated effect of income trend on housing upgrading becomes larger, and the correlation higher. The final division, however, identifies those who became home owners where a synergistic effect led to very large upgrading and a very large estimated effect of prior income trends. What, then, is the effect of income trends on housing upgrading? Only a simulation model which specified which subgroups received the income increases could provide a reasonable estimate. If one wanted the base, unconstrained unstimulated (by becoming an owner) estimate, it would the 1.52 of group 23.

Remember that the "income elasticity" we measure is the effect of the prior five year annual trend in dollar family income relative to the five year mean, on the change in house value or rent relative to the mean of the two values, a kind of arc elasticity not dominated by extreme cases, and symmetrical in treating increases and decreases. Without using such a measure, the average of the effects of increases and decreases would be biased upwards by using the (larger) base for decreases.

The overall picture is one of a genuine effect of income trend on housing upgrading among movers not constrained by other things, or not propelled into moving by other events. But if we look at the total "housing market" we find that an economic model predicting the demand for housing on the basis of prior family income trends, would be predicting only a small fraction of the buyers. A simulation model which incorporated changes in family composition, retirements, accumulated shortages of rooms, and areas of temporary income changes or rapidly changing housing prices (as in the metropolitan areas), would do better, since these other events do not randomize out across time or space.

Full modeling would of course also have to deal with the decision to move in the first place, but it is likely that that decision is even more dominated by considerations other than prior income trends, things like marriage, divorce, arrival or departure of children or other relatives.

To what extent are the things other than income trends that affect upgrading of housing randomly distributed noise that averages out, or at least have random changes over time in their effects on the aggregate demand? There are some large demographic changes related to the baby boom and bust that should affect aggregate trends, and there are effects of good or bad times on the speed with which children leave home to set up their own households. And national monetary policy can certainly change the apparent price of houses by altering interest rates.

Finally, even though housing changes for many are dominated by many things other than prior trends in family income, could we believe that the clear effects we observe in the unconstrained cases also apply to others, being simply masked by other things, so that trends in family income would have those same effects on all movers, whatever else mattered? It seems doubtful in the case of the main exceptions -- those with changes in the husband or wife, when there is someone leaving home or a divorce.

ANALYSIS OF EFFECTS OF PRIOR CHANGE IN INCOME/NEEDS

Figure 5 and 6 repeat the analysis except that the covariate is not the prior trend in family income, but the prior trend in family income/needs, a better measure of ability to pay, but less directly providing estimates of pure income elasticities of demand. The results are similar. And the differences between the regression option and the slopes-only focus on different income effects are similar. We make just a few comments on Figure 6: Movers in the west had upgrading more strongly related to changes in ability to pay, presumably reflecting the skyrocketing housing prices.(Group 4). And a small group in the west around retirement age decreased their housing, inversely in proportion to prior changes in ability to afford it. (Group 16). Other age groups in the West responded more to prior changes if their income want up after the move -presumably because they knew it would.

In the rest of the country, responsiveness to prior changes in ability to pay (income/needs) was greater among the more affluent (Group 7) and the least affluent (Group 8) particularly outside the metro areas for the least affluent (Group 15) and among those 25-34 years old among the most affluent (Group 24). The effects of prior changes in ability to pay among the middle-income group were hidden or distorted if there were changes in the family composition (other than head or wife, presumably children arriving or leaving home), or if they went from owning to renting, perhaps reflecting difficulties in estimating house values for renters. We probably should have raised the lower limit on number of cases for any group to be split off, since regression slopes in particular can become quite unstable for small groups, such as Group 23 and Group 20.

DISCUSSION

Since our analysis is conditional on a prior decision to move which we have not analyzed, the main power of economic factors might appear in that decision. Prior analyses by Jack Goodman and Sandra Newman show that initial economic disequilibrium is important. (Their disequilibrium relates actual to "expected" house value.)

But there remain wide differences in the impact of prior income change, or prior change in income/needs, on the change in house value produced by the move. Income seems to have the most effect when it combined with other incentives like the need for space or the desire to own one's own house, but free of distortions or other pressures like family changes or initial shortages so we can measure it.

Given the wide differences in estimated income elasticities among different groups, attempts to use multiple regression to estimate a single such elasticity would appear unwise. Only if the different groups had different average changes in house value, but similar regression slopes, would such pooling be appropriate. Economic theory lives, and there are people at the margin with freedom to make choices, who respond as the theory predicts. But testing economic theories with survey data requires searching out the subgroups where it applies, and realizing that the strength of the response may differ widely. The aggregate response of income changes to housing demand is thus complex result of differential income changes among different groups with different responses. Microanalytic modelling is essential, and data analysis searching for different subgroup responses also appears essential.

A final warning: Regression slopes are notoriously unstable, and the weights used to keep the PSID representative introduce heterogeneity into already high-variance data. Rerunning the SEARCH slopes-only program on unweighted data gives sometimes dramatically different subgroups and different estimated income-trend effects within the same subgroups. We are still working on this. In the meantime, large minimum group sizes may be suggested, as well as care about outlyers.

APPENDIX: OTHER RELATED RESEARCH AND WRITING

Several summaries of research on housing (supply, demands, and markets) have been done:

Lawrence B Smith, Kenneth T. Rosen, and George Fallis, "Recent Developments in Economic Models of Housing Markets", Journal of Economic Literature, 26:29-64 (March, 1988)

Frank de Leeuw, "The Demand for Housing: A Review of Cross Section Evidence",Review of Economics and Statistics, 53:1-10 (Feb, 1971)

Stephen K Mayo "Theory and Estimation in the Economics of Housing Demand", Journal of Urban Economics, 10:95-116 (July, 1981)

John M. Quigley, "What have we Learned About Urban Housing Markets?", in Peter Mieszkowski and Mahlon Straszheim, eds.,Current Issues in Urban Economics, Baltimore, The Johns Hopkins Press, 1979.

(The next two point out difficulties with hedonic price models)

Michael P. Murray, "Mythical Demands and Mythical Supplies for Proper Estimation of Rosen's Hedonic Price Model", Journal of Urban Economics, 14:326-3371 (Nov, 1983)

James--N Brown and Harvey S. Rosen, "On the Estimation of Structural Hedonic Price Models", Econometrica, 50:765-768 (MaY, 1982)

But in all this, little attention has been paid lo the potential for differential income elasticities of demand for housing, nor to the size or variability of lags in adjustments to income (surely longer than adjustment to changes in family size>). But lots of attention has been paid to the investment aspects, which may alter the consumption decisions, particularly when combined with shifts into or out of ownership. Should demand for housing be imbedded in a full portfolio choice model? Starts appear in:

J. Vernon Henderson, Economic Theory and the Cities, Orlando Fla, Academic Press, 1985

Jerome Rothenberg, "Housing Investment, Housing Consumption and Tenure Choice", in The Urban Economy and Housing, Ronald E. Grieson. ed., Lexington MA, Heath, Lexington Books, 1983.

Finally, one study using panel data:

Sandra J. Newman and Greg J. Duncan, "Residential Problems, Dissatisfaction, and Mobility", in Five Thousand American Families: Patterns of Economic Progress, Vol VI, Greg Duncan and James Morgan, eds., Ann Arbor, Michigan, Institute for Social Research 1978.

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