40 Operating Costs in Public Housing Table 8. EXPLANATION OF TOTAL COSTS: The introduction of the square of the number of units as an additional variable gave results which indicated that it was serving essentially as a proxy variable for New York City. New York's public housing stock (federal programs only) at the end of the 1960's included about 70,000 units, more than double the number in the next largest authority (Chicago) and about six times as many as the average for the 23 cities. The square-of-units variable, together with the units variable, indicated the opposite of a U-shaped cost curve; namely, diseconomies of scale out to about 55,000 units, and economies of scale beyond that point. Its introduction was clearly reducing the residuals for New York and only slightly modifying results for other cities. Although by statistical tests the results were significant, it was felt that they were not a reliable guide to scale effects, and the square-of-units variable was dropped. Tenant Characteristics. The number of minors per unit has the expected positive association with costs. Its coefficients of 5.28 and 5.56 indicate that an additional minor in a unit raises its oper ating costs per unit per month by more than $5. A large part of this rise seems to be due to the fact that more minors per unit are associated with more rooms per unit in public housing; as noted The Cost of Public Housing Operation 41 earlier, the correlation between minors per unit and rooms per unit made it impossible to estimate the separate effects of additional rooms versus other ways in which minors raise costs. The number of persons per unit and the proportion of elderly units are also correlated with the number of minors per unit sufficiently so that it was not possible to estimate separate effects. The minors per unit variable, in other words, is a single measure reflecting a variety of cost influences having to do with age composition and size of units. On the average, minors per unit have changed very little during the sample period and thus have had a negligible effect on overall costs. Apparently the effect of more public housing for the elderly, which reduces minors per unit. has been roughly balanced by an increase in family size among units with minors. For individual cities and projects, of course, changes in numbers of minors per unit probably have had dramatic cost effects. The proportion of units with no wage earners present. Nonug, is estimated to have a small effect on costs. The coefficients of .30 and .26 indicate that a one percentage point increase in this pro portion (from 30 percent to 31 percent, for example) raises costs per unit per month by 26 to 30 cents. For the 23 cities as a whole, this proportion has been growing by about one percentage point per year, and has thus made a small contribution to the overail cost rise. The effect of Nonrg on tosta probably represents the greater proportion of persons in this group than among public housing tenants as a whole who require special services or who cause special maintenance problems. For two other tenant characteristica — the proportion receiving relief. Reif and the nonwhite proportion. Nonwh- there did not appear to be significant cost-raising efferta of this kind. A comparison of regression results with each of these three variables appears in Table 2 These results cast toubt in the relevance of Relf and Yongh to explaining costs. The coefferents of Relf and Vanych are much smaller than the Nonre efficient, and they are not statistically 42 Operating Costs in Public Housing Table 9. EXPLANATION OF TOTAL COSTS: ALTERNATIVE TENANT CHARACTERISTICS significant. The Relf coefficient, furthermore, has an unexpected negative sign. Nonwh is fairly closely correlated with Min (the simple correlation coefficient is +.69) and so in the regression including Nonwh and Min the latter variable also drops to insignificance. Regressions including both Nonwg and one of the other tenant characteristics suffer from most of these same statistical difficulties. SOME CHECKS ON THE POOLED REGRESSION RESULTS Confidence in the validity of the regression results above is strengthened by (1) examining regression results for the main components of costs, and (2) examining separately regression results across the 23 cities and regression results over the four years for each city. The first check permits judgment as to whether particular explanatory variables significantly affect the cost components to which they are most relevant for example, whether utility prices affect utility costs. The second check establishes whether there is a problem of separating short-run forces, expected to be especially important in year-to-year differences, The Cost of Public Housing Operation from long-run forces, which can be assumed to carry greater weight in cross-city differences. 43 In addition to these checks, regression results are presented excluding New York City from the sample, since New York public housing represents an extreme observation for many of the variables in the study. The components of total operating costs. Four major components of cost- administrative costs, utilities costs, routine maintenance costs, and extraordinary maintenance costs1 account for about 80 percent of total operating costs. In general, these cost components ought to be related to the variables which explain total costs. Indeed, as a matter of arithmetic, regressions of all cost components on all of the explanatory variables in the main regressions above would give coefficients which add up to the coefficients in the total cost regressions. The value of examining the cost components is to determine whether particular components are related to the particular variables that seem most likely to affect them. Among variables which contribute to explaining total costs, the general price or wage variables ought to affect all of the components. Utility prices ought to have an important effect on utility costs. Age ought to have an important effect on maintenance costs. Tenant characteristics ought to affect especially management and maintenance costs. It is not clear which components ought to be affected by the number of units. Results of regressions for the cost components appear in Table 10. All of the variables are tested for all of the components, with the exception of utility prices, which appear only in the utility cost regression. Reading across the coefficients of Ptot, it is evident that the only unexpected one is the small negative coefficient for extraordinary maintenance, and that the significant ones are positive 1. The separation of routine maintenance costs from extraordinary maintenance costs in public housing cost accounting is based on their frequency. Regularly recurring costs, such as painting or replacing light bulbs, are routine; infrequent costs, such as replacing boilers, are extraordinary. 42 Operating Costs in Public Housing Table 9. EXPLANATION OF TOTAL COSTS: ALTERNATIVE TENANT CHARACTERISTICS significant. The Relf coefficient, furthermore, has an unexpected negative sign. Nonwh is fairly closely correlated with Min (the simple correlation coefficient is +.69) and so in the regression including Nonwh and Min the latter variable also drops to insignificance. Regressions including both Nonwg and one of the other tenant characteristics suffer from most of these same statistical difficulties. SOME CHECKS ON THE POOLED REGRESSION RESULTS Confidence in the validity of the regression results above is strengthened by (1) examining regression results for the main components of costs, and (2) examining separately regression results across the 23 cities and regression results over the four years for each city. The first check permits judgment as to whether particular explanatory variables significantly affect the cost components to which they are most relevant - for example, whether utility prices affect utility costs. The second check establishes whether there is a problem of separating short-run forces, expected to be especially important in year-to-year differences, |