THE INEFFICIENCY OF TRANSFERS IN KIND: THE CASE OF HOUSING ASSISTANCE

THE INEFFICIENCY OF TRANSFERS IN KIND: THE CASE OF HOUSING ASSISTANCE

HENRY J. AARON and GEORGE M. VON FURSTENBERG’ Washington, D.C. and Indiana University

Economists have long argued that recipients are better off with cash grants than with tied subsidies imposing the same cost on the government.’ While this is undoubtedly coirect, recent studies have emphasized that donors may have the opposite preference.2 In fact, if redistribution is a public good for transferors and not merely the result of coercion or “taking,” the preferences of donors help determine both the extent and the form of redistribution. Hence, once interdependence of preferences is introduced and donors, though altruistic, are not indifferent t o the recipients’ spending pattern, Pareto-optimal redistribution can take forms other than cash.

The argument for the superiority of cash transfers over commodity transfer is thus not logically compelling. Nevertheless, it would be empirically persuasive, if the difference between the cost of commodity subsidies and of cash transfers that accomplish the same increase in utility for the recipients were very large. Before one can gauge what weight would have to be accorded t o differential external benefits3 or to the preferences of donors t o tip the choice to commodity subsidies, it is necessary to quantify the welfare loss that tying imposes on the recipients. This paper attempts t o quantify this loss for housing.

I. SIMULATIONS OF INEFFICIENCY AND THE CHOICE OF UTILITY FUNCTIONS

The components involved in the quantitative estimates are set forth in Figure 1. A household operating along a budget line AB maximizes utility at point E, purchasing OD units of housing and ED units of all other goods. Assume now that the government subsidizes housing and permits the household t o buy as much housing as it wishes. The new effective budget line is AC; the household maximizes at G ; the subsidy cost t o the

*The authors are indebted to the Editor whose repeated comments greatly improved both exposition and content.

1. Cash will be strictly preferred by the recipient in all but the trivial case of zero elasticity of supply or demand for the subsidized commodity.

2. See especially [4] [ 111 and [ 131. James Buchanan 13, p. 1881 fmds the use of consumer sovereignty to derive allocative norms inconsistent with the choice of social welfare functions to express distributional objectives.

3. With regard to physical externalities it has long been argued that bad housing creates external costs. See Daniel Wlner 121, po&m]. Alvin Schon 118. pp.7-331, and Jerome Rothenberg [ 17, p. 581 for summaries of this literature. No author has succeeded in estimating the cost of such externalities in money terms, and Alice Rivlin [ 161 explains why the prospects of doing so are poor.

184

AARON AND VON FURSTENBERG: HOUSING SUBSIDIES 185

Fieure 1

government is GP, measured in other goods. Had the government given the household the smaller amount MP in cash and allowed it to buy goods freely at market prices, the household could have achieved the same level of welfare as it receives under the housing subsidy. The government wasted GM in redistributing income through housing subsidies so that the housing subsidy is ( 1 00 GMIGP) percent less efficient than cash transfers in raising the welfare of the recipient household.

If the government requires the household to purchase a particular quantity of housing at the subsidized price, the efficiency of the subsidy may be affected. There is some point, such as Q, on line AC at which an offer of a particular quantity of housing at a subsidized price is as efficient as an equal-cost, untied cash transfer in raising household utility. An all-or- nothing offer of the quantities of housing shown at R or S has zero efficiency in raising household welfare.

A utility function must be chosen before the inefficiency of subsidies tied to the consumption of housing services can be quantified. For our purposes, only those functions will be suitable which imply realistic income and price elasticities of demand. Estimates of both vary, though the range of uncertainty has recently been reduced.

The size of the income elasticities reported in the literature depends on how the theoretical concept of permanent income has been approximated by different researchers and on what allowance has been made for differences in credit terms both over time and across income classes. Furthermore, the demand for housing services need not be influenced by the same factors as the investment demand for the asset from which they flow, and housing services may not be proportional to house values. Perhaps more importantly, the tastes and hence the preference maps of consumers in both the owner and renter classes change systematically

186 WESTERN ECONOMIC JOURNAL

with the level of income. At low levels of normal income, only those families with unusually high demand prefer to buy, while at high levels almost everyone owns, and only families with unusually low demand are left in the class of renters. This composition effect depresses the Engel curve for renters at the upper end, while it raises the curve for owners at low income levels, compared to the position each curve would have if the tastes of the representative consumer could be held constant. As a result, the slopes of both schedules are reduced, and the income elasticities estimated for owners and renters separately may be biased ciown- wards. Alan Winger (22, pp. 230-3 1 ] has demonstrated that the income elasticities depend also on supply factors, especially the composition of the sample between new and used home buyers.

In spite of the need for difficult adjustments, Frank de Leeuw [ 5 , pp. 7-10] concluded that the normal income elasticity appears to range from 0.8 to 1 .O for renters and from 0.7 to 1.5 for owners. For the latter, Rich- ard Muth also estimated an elasticity of around 1 .4 Thus, it seems safe to conclude that the income elasticity is close to unitary, though possibly a little higher for owners than for renters.

There is far less agreement on the size of price elasticities, partly b e cause both the homeowner and the renter component of the consumer price index are unreliable. In pricing "representative" accommodations, no attempt is made to hold the physical characteristics of the unit approxi- mately constant, and researchers are frequently forced to construct their own price index series. There is also a question of whether financing charges, interest, utility costs, and the cost of household furnishings should be included on a par with construction costs, since adjustment speeds and expectations horizons differ. De Leeuw suggests compensated price elasticities for renter households of between -0.7 and -1.5 after adjusting lower estimates for appreciable bias [ 5 , p. 91. Tong Hun Lee [9, p. 881 reports price elasticities of the stock demand of owners ranging from -1 to -2, with the preferred estimates centered around -1.4. Again the price elasticity appears to be not far different from unity, with a value of -1.5 representing the upper limit.

Since these estimates are less well assured than the findings on income elasticities, we present a set of alternatives by choosing constant elasticity of substitution (CES) utility functions, which always imply unitary income elasticities but allow variation in the price elasticities of demand.'

4. [lo, pp. 29-96]. Lec (71 (81 disagrees with Muth and suggests elasticities below one. 5. The general constant elasticity of substitution utility function is U=[DH'+ (1 - D)C']-'",

where D and ( I - D) are distribution parameters and r is a substitution parameter. The elasticity of substitution. s, is l i e d tor by the identity s - I / ( I +r). A value of D was then chosen such that the household initially spent 25 percent of income on housing. For instance, if s = 0.5 or I = I , the marginal rate of substitution in the absence of subsidies is -DW2/(1 - 0) G2 - -pH/pG = - I . Setting C qua1 to 3H yields 0.10 for D.

AARON AND VON FURSTENBERG: HOUSING SUBSIDIES I87

Choosing functions with elasticities of substitution of 2, 1.5, 1 (the Cobb Douglas case), 0.75, and 0.5, the implied income-compensated price elasticities of demand for small subsidy percentages are -1.48, -1.12, -0.75, -0.57, and -0.38,6 respectively, with the corresponding Marshallian meas- ures being higher by 0.25 in absolute value.

II. THE QUANTITATIVE ESTIMATES

The utility functions have two arguments. In the implicit form, U = f f G , H ) , H is housing and G is a composite of all other goods, defined so that the price of each good is $1. A household maximizes U subject to a budget constraint, Y, on the assumption that a certain fraction of total outlays, a, is initially spent on housing and f I - a ) on all other goods. Next, the government pays a subsidy that cuts the price of housing to tenants by b cents per unit, and the household maximizes U subject to Y achieving a level of utility U'= f f H ' , G' l at a cost to the government of bH' dollars per unit. Finally, holding utility at U', the price of housing is restored to its unsubsidized level to yield the level of expenditures Y", necessary to achieve U' (at point V in Figure 1). The amount f Y " - Yl= A T is the unrestricted cash transfer that would raise utility by the same amount as the commodity subsidy costing bH'. The relative inefficiency of the latter is equal to the cost difference, bH' - A T, divided by bH'.

To derive explicit solutions, both the housing subsidy to tenants and the fraction of total outlays that the household would voluntarily spend on housing at market prices are varied. The prices charged by suppliers are fixed, and the government is assumed to be as efficient in producing or procuring goods and services as the private sector. The efficiency of commodity subsidies then depends only on three parameters: the elasticity of substitution, the subsidy fraction, and the ratio of housing to total expenditures. The first two of these parameters proved to be im- portant, the third unimportant.

Table I (a) shows the degree of inefficiency of commodity subsidies for the five elasticities of substitution and for subsidies of 10 to 80 percent. In each case, households are assumed to allocate 25 percent of their budget to housing when it is not subsidized. The table confirms that

6. If the elasticity of substitution, s, is defmed to be positive, and the change in the price of housing, - d p H , is given by the subsidy fraction b , while pG remains fixed at unity. then s = (GdH - HdG)/bHG = -E - dG/bG, where E is the uncompensated relative price elasticity of demand for housing and dG = G'- G. The incombcompensated price elasticity, E*, is then found by using the Slutsky equation Eo = u + E , where u is the initial budget share of housing equal to 25%. With an income of 100, G is initially 75 and dG turns out to be 0.97 if b is 10% and s is 0.5. Hence EoS 0.25 - 0.63 = -0.38, if the arc ebticity'is approximated by using relations prevailing in the absence of the small subsidy. The results are, of course, invariant to scale because the indifference curvvcd are homothetic.


housing subsidies by themselves are not the most efficient means of raising standards of living for the poor, unless external benefits from improved housing are present or taxpayers want the poor to be better housed rather than better clothed, entertained, or fed, and some weight is accorded to the preferences of donors.

Table l(b) shows the size of the unrestricted income transfer that would raise utility by the Same amount as the indicated commodity subsidy. Unless the housing subsidy rate is very large and households are permitted to consume as much housing as they want, housing subsidies cannot raise real income by large amounts. However, the gain in income is larger than standard deflation procedures indicate. For instance, if the base period quantity weight of housing is 25 percent, a 50 percent price reduction produces a real income gain of only 0.125/0.875, or 14.3 percent, compared to 16.4 percent shown for the lowest elasticity of substitution in Table 1 (b).' Moreover, families living in federally-assisted housing often benefit from other subsidies as well. As part of a package

Table 1 Elasticity of Substitution 10% 20% 30% 40% 50% 60% 70% 809i

Sue of Commodity Subsidy, b

(a) The Inefficiency Percentage of Housing Subsidies, 100 (1 - A T/bH ')* 2 .o 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 1.5 5.7 11.8 18.1 24.8 32.0 39.8 48.4 58.2 1 .o 3.9 8.2 13.0 18.3 24.3 31.4 39.8 50.5 0.75 2.9 6.3 10.1 14.4 19.5 25.6 33.2 43.3 0.5 2 .o 4.3 7.0 10.1 13.9 18.6 24.3 33.2

(b) The Income Effect of Housing Subsidies, 100 (ATIOA) 2 .o 2.8 6.2 10.7 16.7 25.0 37.5 58.3 100.0 1.5 2.7 6.0 10.0 15.1 21.8 31.2 45.5 71.4 1 .o 2.7 5.7 9.3 13.6 18.9 25.7 35.1 49.5 0.75 2.6 5.6 9.0 12.9 17.6 23.4 30.8 41.3 0.5 2.6 5.5 8.7 12.3 16.4 21.3 27.1 34.6

*The derivation of the results can be illustrated for s = I , b =50%. and the utility function U = M25G.75. With Y at 100. H is initially 25 and G is 75 yielding a utility index of 56.99. With the 50% subsidy, P becomes 0.5 while Pc remains 1. Using the marginal rate of substitution and the budget constramt, H'=50, G'= G = 75. and U's67.77, the cost of the tied subsidy is 25. Restor- ing the marginal rate of substitution to -1, substituting V; and solving for the sum of the resulting new values of H and G. Y' is found to be29.73 + 89.19, or 118.92. Hence, the equivalent income gain is 18.9% and the inefficiency percentage is (1 - 18.92/25), or 24.3%.

H

7. To the extent standard deflation techniques understate the real income gains, time series estimates of the income elasticity will be biased upward. This bias works in a direction opposite from that of the composition effect between owners and renters discussed in the previous section. The application to the price index problem was suggested by Nicholas Noe of Indiana University.

AARON AND VON FURSTENBERG: HOUSING SUBSIDIES I89

of commodity subsidies, housing subsidies would be more efficient than is shown in Table 1, and the equivalent income gain would be corre- spondingly larger.

111. RELATION TO EXISTING FEDERAL HOUSING PROGRAMS

The estimates just derived can be used to gauge the probable size of consumption inefficiencies connected with major federal housing programs if physical and preference externalities are absent. Under the low- rent public housing program, tenants pay about half of full economic rents for new units. Tenants paid 18 percent of their income in rent, while unassisted households with incomes of $4,000 per year, which is somewhat about the average income of public housing tenants, spent 26 percent of income on rent.' If public housing tenants are buying as much housing as they wish, the implied elasticity of substitution of housing for other goods is well under 0.50.9 In that case, the inefficiency of housing subsidies is about 10 percent. Alternatively, the elasticity of substitution may be higher and public housing tenants may be out of equilibrium, consuming less housing than they would like." If the elasticity of substitution is 1 , and the price reduction is 50 percent, the inefficiency is only 3.4 percent because the quantity of housing services provided is then constrained to be quite close to what would have been chosen had the subsidies been given in cash. In either case, rather small external benefits or concessions to possible preferences of donors for housing over other consumption by the poor are necessary to justify the commodity subsidies provided in public housing.

While public housing units form the overwhelming majority of federally assisted units now in existence, the relative importance of other programs will grow in the future."The rental and home ownership subsidies enacted

8. See 120, p. 1571. No attempt is made to estimate the actual distribution of benefits under each of these programs by groups of owners or tenants. For such estimates see [ 1 I I 2 1 161 [ 121 and

9. Still lower values of the elasticity of substitution, which would be implied if tenants were consuming more housing than they would like at the subsidized price, are implausible.

10. Even if the government charges rents equal to only 50 percent of its costs, the price reduction for tenants win be smaller if the govanmmt has been inefficient in acquiring the housing units or in providing houring services, as studies by Edgar Olsm [ 141 and Eugene Smolensky [ 191 aug- ga t . In such cases, the relevant price reduction to tenants would be smaller than 50 percent since part of the subsidy would merely offset the government's ineffiiency. If the relevant price reduction were, say, 30 percent, and the household is in equilibrium with an elasticity of substitution of unity, the consumption ineffKiency would be 13 percent as shown in Table 1 (a), on the assump tion that 25 percent of income is spent on housing. If the share of housing in the con sum^'^ budget is only 20 percent but the income elasticity remains unity, the ineffwiency percentage rises to 14 percent.

11. At the end of fiscal year 1970. annual contributions contracts covered an estimated 850.000 low rent public housing units, including leased units. The number of completed units under other major programs were: 23.233 under Section 235; 16.000 under Section 236; 131,014 under the Section 221 (d) (3) below-market interest rate program; and 31,078 under the rent supplement p r e gram. The last two programs are in the process of being replaced by Section 236 and thus are not mentioned in the text.

1141.


in 1968 provide assistance that varies according to housing costs and income of the occupant of federally-assisted units. Renters must pay at least 25 percent of income in rent, while owners pay no less than 20 percent of income for mortgage payments, taxes, and insurance before receiving assistance. Over some range, these charges are independent of the quantity of housing, so that the marginal subsidy percentage could rise to 100 percent. However, the federal subsidy may not exceed the difference between the full economic housing cost and the cost that would have resulted had 100 percent mortgage financing at 1 percent interest been available.

The median subsidy under both of the interest-reduction programs through the end of 1969 amounted to almost 40 percent of total housing costs.'* The inefficiency, assuming beneficiaries buy the amount of housing demanded if both the marginal and average subsidy rates were 40 percent, is 18 percent for an elasticity of substitution of 1. While space limitations are less stringent under the interest reduction programs, limits on the mortgage amount per unit accomplish much the same purpose and thereby keep inefficiency below this range. A newer system of assistance, Section 243, enacted as part of the Emergency Home Financing Act of 1970, will provide rather small benefits to large numbers of middle-income home owners. The maximum subsidy under this program probably runs around 15 percent (less if mortgage interest rates fall), which suggests that inefficiencies will be at most 5 percent.

In sum, if all housing programs operated with maximum consumption inefficiency, the same increase in the welfare of recipients could be pur- chased for about 10 to 15 percent less, depending on program mix. In fact, because of quantity constraints, the inefficiencies may be lower even if no external benefits are attached specifically to the increased consumption of better housing. If there are large inefficiencies in federally assisted housing, they will have to be found empirically, on the cost side, to the extent the administration of particular programs involves detailed federal regulations of the conditions of supply.

12. Or between 50 and 60 percent of the mortgage payment if market rates are 7.5 percent. In the ownership program the subsidy also applies to investment in home equities, and enabling low-income families to own homes may itself inclease the consumption of housing services. Also, there may be an additional inefficiency due to the 20 01 25 percent tax on increased income.

AARON AND VON FURSTENBERG: HOUSING SUBSIDIES 191

REFERENCES 1. H. J. Aaron, Decent Homes and Federal Policies, Brookings Institution, forthcoming. 2. R. L. Bish, “Public Housing: The Magnitude and Direction of Direct Benefits and Effects on

Houaing Competition,” JOW. Reg. Sci., Dec. 1969, 9, 425-38. 3. J. M. Buchanan, “What Kind of Redistribution Do We Want?” Economiar, May 1968, 35,

185-90. 4. G. G. Daly and J. F. Giertz. “Efficient and Inefficient Transfers,”paper presented at the meet-

5 . F. de Leeuw, ‘The Demand for Housing: A Review of Cross Section Evidence,” Rev. Econ.

6. J. S . De Salvo, “An Economic Analysis of New York City’s Mitchell-Lama Housing Program,”

7. T. H. Lee, “Housing and Permanent Income: Tests Based on a Three-Year Reinterview Survey,”

8. -, “More on the Stock Demand Elasticities of Non-Farm Housing,” Rev, Econ. Stat.,

9. -,”The Stock Demand Elasticities of Non-FarmHousing,” Rev. Econ. Stat., Feb. 1964,

10. R. F. Muth, ‘The Demand for Non-Farm Housing,” in m e Demand for Durable Goods. ed.,

11. E. 0. Olsen, “A Normative Theory of Transfers,” Ifiblic Choice, Spring 1969, 6, 39-58. 12. -, ‘Some Theorems in the Theory of Efficient Transfers.” Jour. Pol. Econ., Jan. 1971.

13. ___, ‘Transfers in Cash or in Kind,” Am. Econ. Rev., March 1971, 61, 220-24. 14. -, “A Welfare Economic Evaluation of Public Housing,” unpublished doctoral d i m -

15. M. V. Pauly, “ E f f ~ c n c y in the Provision of Consumption Subsidies,” Kyklos, 1970, Fasc. 1,

16. A. Rivlin, Systematic ninking and Social Action, Brookings Institution, forthcoming. 17. J. Rothenberg. Economic Evalucrtion of Urban Renewal. Washington 1967. 18. A. Schon, Slums and Social Insecurity, U.S. Department of Health, Mucation, and Welfare,

1963. 19. E. Smolensky, “Public Housing or Income Suppkments-The Economics of Housing for the

Poor,” lour. Am. Instit. Plan, March 1968.34.94-101. 20. G. M. von Furstenberg and H. Moskof, “Federally Asaisted Rental Housing Programs,” in Re

port of the President’s Committee on Urban Housing, Technicul Studies, Vol. 1, Housing Needs and Federal Housinghgmms. Washington 1968.

21. D. W h e r et al., n t e Housing Environment and Family Life: A Longftudinal Study of the Effects o f Housing on Morbidity and Mental Health. Baltimore 1962.

22. A. R. Winger, “Housing and Income.” Western Econ. lour.. June 1968, 6, 226-32.

ing of the American Academy of Arts and Sciences, Boston 1969.

Stat., Feb. 1971, 53, 1-10.

paper presented at the Winter meeting of the Econometric Society, 1970.

Rev. Econ. Stat., Nov. 1968,50. 480-90.

Nov. 1967,49,64042.

46, 82-89.

A. C. Harberger, Chicago 1960.

79. 166-76.

tation. Rice University 1968.

23, 33-58.

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THE INEFFICIENCY OF TRANSFERS IN KIND: THE CASE OF HOUSING ASSISTANCE