Modelling Revenue and Allocation Effects 

of the Use of Tax-exempt Bonds for 

Private Purposes 

by Harvey Galper and Eric Toder 

OTA Paper 44 December 1980 

This paper was delivered at a conference on Efficiency in the 

Municipal Bond Market sponsored by the Center for Capital Market 

Research College of Business Administration, University of 

Oregon, Portland, January 24-25, 1980. 

Office of Tax Analysis

U.S. Treasury Department, Room 4217 

Washington, D.C. 20220 

Issued: December 1980 
TABLE OF CONTENTS 

Page 

. I. INTRODUCTION .............................................. 1 

11. Fixed Allocation Revenue Estimates ........................ 6 

111. Modelling Allocation Effects of Tax-exempt Mortgage Bonds . 15 

4 
Modelling Revenue and Allocation Effects of the Use of 

Tax-exempt Bonds for Private Purposes 

by Harvey Galper and Eric Toder* 

I. INTRODUCTION 

The volume of tax-exempt bonds issued for private purposes --

factories, pollution control equipment owned by private firms, 

private hospitals and private housing, among other uses -- has 

increased dramatically in recent years, both in absolute terms and 

as a share of all tax-exempt borrowing. Although no data have been 

compiled showing a breakdown between uses of tax-exempt bonds for 

private and public purposes -- perhaps because no one definition of 

what constitutes a public use is universally accepted -- data 

compiled by the Public Securities Association (PSA) showing a 

breakdown of tax-exempt borrowing by type of activity provide a 

rough picture of the growth of private borrowing. The two PSA 

categories that comprise most private purpose borrowing are 

industrial aid (which includes pollution control bonds and all other 

industrial development bonds issued for corporations) and social 

welfare (which includes housing and hospital bonds). Borrowing for 

these two functins has increased from 9 percent of all new tax 

*U.S. Department of Treasury and Department of Energy, respectively. 
-- 

-2-

-exempt borrowing (excluding refunding) in 1970, to 20 percent in 

1972, 28 percent in 1976, 35 percent in 1977, and 41 percent in the 

first six months of 1979. The continuing expansion of the use of 

tax-exempt bonds to finance owner-occupied housing and the 

proliferation of proposals in Congress to allow tax-exempt financing 

of energy-related projects both suggest that tax-exempt financing of 

private investments could continue to grow rapidly. 

Allowing a particular type of private investment to be financed 

by tax-exempt borrowing has two effects: 

- A capital allocation effect, causing more capital to flow to 

the favored private activity and less to other private sector 

investments and to State and local public purpose investments. 

- A loss of revenue to the Federal Treasury, resulting in a 

larger budget deficit, increased tax rates, or reduced spending on 

other Federal programs. 

These two effects -- on capital allocation and Federal revenues 

have important implications for the productivity of the capital 

stock and the distribution of the tax burden among income c1a:;ses. 

This paper provides a general approach for estimating the 

revenue and capital allocation effects of the use of tax-exempt 

financing for private purposes. As an illustratiot?, we ~di.sc:i.l:~si.1) 

detail methods of estimating the revenue and capital allocation 

effects of allowing the use of tax-exempt bonds to finance owneroccupied housing. The same methods used to analyze housing bonds 

could, with minor modifications, be applied to any other proposql 

+hat expands or contracts the use of tax-exempt financinq for 

private purposes. 
-3-

. 

We present two models for estimating the revenue loss from a 

given volume of tax-exempt housing bonds -- one extremely simplified 

and the second more complex. Both models can be termed general 

equilibrium models because they explicitly account for all substitutions that occur as a result of tax-exempt financing. Thus, 

even the highly simplified model avoids the gross errors that would 

result from a failure to account for all financial transactions 

required to equilibrate sources and uses of funds. 

Section I1 outlines the method used to estimate the revenue loss 

in the simplest general equilibrium application -- the case where 

(1) the elasticity of demand for housing services is zero, and (2) 

the elasticity of demand for tax-exempt bonds is infinite. Under 

these admittedly unrealistic but highly simplifying assumptions, 

tax-exempt and taxable interest rates remain unchanged -1/ and there 

are no capital allocation effects. There is, however, a revenue 

loss to the Federal Treasury resulting from the substitution of 

tax-exempt for taxable sources of housing finance, offset in part by 

a reduction in mortgage interest deductions claimed by homeowners. 

For the remainder of this paper, we shall refer to these two 

assumptions -- zero elasticity of demand for housing services and 

infinite elasticity of demand for tax-exempt bonds -- as the fixed 

allocation assumptions. 

The fixed allocation assumptions used in Section I1 were used by 

both the Congressional Budget Office and by the Treasury Department 

in deriving revenue estimates presented to Congress in 1979.2/-

Kormendi and Nagle have claimed that these estimates are overstated 

because CBO (and Treasury) erroneously assume that new buyers of 
-- 

-4-

tax-exempt bonds are sellers of taxable debt.3/ - We show in Section

TI that the fixed allocation estimates computed by Treasury and CBO 

using a two asset model are not changed by taking account of the 

existence of other financial assets. 

However, the revenue estimates are affected when account is 

taken of likely changes in interest rates and the allocation of the 

stock of capital resulting from tax-exempt housing bonds. To 

estimate these effects, and to determine likely impacts on the 

capital stock, it is necessary to develop a more realistic general 

equilibrium model incorporating explicit assumptions of demand 

elasticities for capital used in the production of housing services, 

other private goods and services, and State and local public 

services. It is also necessary to specify the demand function for 

financial assets in order to calculate the rise in tax-exempt rates 

needed to induce savers to hold a stated additional volume of taxexempt bonds. Although the magnitudes of the relevant parameters 

are uncertain, simulating a simple general equilibrium model with r3 

range of plausible values can provide reasonable bounds on the 

likely effects. 

Such a model is developed in Section 111 ot this paper. The 

model has three physical capital assets -- owner-occupied housing, 

private plant and equipment, and State and local government capj t?l 

and two forms of financing -- tax-exempt bonds and taxable bonds. 

This model is simulated to show the likely effects on Treasury 

revenues and on the allocation of capital across sectors resulting 

from the use of tax-exempt housing bonds. 
-5-

The simulations in Section I11 show that the revenue loss 

estimate derived from the initial naive, fixed allocation model, is 

generally somewhat lower than the loss that would be estimated with 

a more realistic model. Ignoring capital allocation and interest 

effects of tax-exempt housing bonds ignores changes that both 

increase and decrease the revenue loss; the net effect, however, is 

an understatement of the loss. The principal change causing a 

larger revenue loss with a more realistic model is the substitution 

of housing capital for private plant and equipment due to the 

reduction in mortgage interest rates for those homeowners 

benefitting from tax-exempt mortgage financing. This change in 

capital allocation increases the revenue loss because owner-occupied 

housing, unlike private plant and equipment, generates no taxable 

income. 

On the other hand, changes in interest rates increase revenue to 

the Treasury. The tax-exempt rate must rise to induce savers in 

lower tax brackets to hold tax-exempt bonds; as lower bracket taxpayers switch away from taxable bonds the loss to the Treasury from 

substituting tax-exempt for taxable bonds declines. Changes in 

taxable interest rates affect revenue received from remaining 

taxable corporate and Federal debt and revenue lost from interest 

deductions on remaining taxable mortgages, and also affect the cost 

of Federal borrowing. The -

. net combined effect of all the offsetting 

changes from using a more realistic model, though increasing the 

revenue loss, is small compared to the revenue loss in the fixed 

allocation model. However, the more realistic model includes an 

expenditure effect because of the increase in interest on the 
Federal debt. As a consequence, the estimated increase in the total 

budget deficit, in this model, is, in some cases, substantially 

greater than that estimated from the fixed allocation model. 

Finally, the simulations in Section I11 show that the total 

long-run capital allocation effects are relatively small, compared 

to the volume of tax-exempt mortgage bonds issued. In most simulations, the estimated increase in housing capital is no greater 

than 30 percent of the volume of tax-exempt housing bonds. Whether 

increased housing displaces more or less private capital than State 

and local public capital depends on the responsiveness of demand for 

tax-exempt bonds to changes in relative interest rates. 

11. FIXED ALLOCATION REVENUE ESTIMATES 

Estimation of Revenue Loss in a Two-asset World 

In the two-asset model, the only financial assets are tax-exempt 

bonds and taxable bonds. Issues of tax-exeinpt housing bonds 

displace taxable debt used to finance housing. The Treasury no 

longer collects tax revenue on the displaced debt; however, it 

recovers some of the lost revenue because homeowners who finance 

their homes with the proceeds of: tax-exempt housing bonds rathcr 

than taxable bonds claim smaller mortgage interest deductions. 

Algebraically, the revenue loss to the Treasury, per dottar of t.;.i:<. 

exempt housing bonds outstanding, is equal to: 

rt tb* th 

where rt is the interest rate on taxable bonds, re is the 

interest rate on tax-exempt bonds, tb* is the marginal tax rate of 
-7-

savers switching from taxable to tax-exempt bonds and th is the 

average marginal tax rate of homeowners receiving tax-exempt 

mortgage financing (with a marginal rate of zero attributed to 

non-itemizers.) This simplified model assumes that all of the 

benefit of tax-exempt finance is passed through to homeowners.4/-

The marginal tax rate, tb*, of additional buyers of tax-exempt 

bonds will be determined by the relative supplies of taxable and 

tax-exempt bonds. With a graduated rate structure, tax-exemption is 

most valuable to the highest bracket saver. As the supply of 

tax-exempt bonds increases, the tax-exempt interest rate must rise 

relative to the taxable rate to attract additional savers from lower 

tax brackets. In equilibrium, for given supplies of taxable and 

tax-exempt bonds, both types of securities will be equally 

attractive to the marginal buyer, the lowest bracket saver who can 

be induced to hold tax-exempt bonds. The two securities yield the 

same after-tax interest when: 

Combining (1) and (2), we can express the Treasury revenue loss per 

dollar of tax-exempt housing bonds as 

(rt - 'e) 

Suppose that rt = 10 percent, re = 7 percent, and th = 0.30. 

Then, the revenue loss to the Treasury would equal $.021 per dollar 

of housing bonds outstanding, or $21 million for each $1 billion of 
tax-exempt housing bonds.5/- This revenue loss can be subdivided 

into two pieces -- a loss of $30 million per $1 billion from reduced 

taxation of interest income and a pickup of $9 million per $1 

billion because of lower mortgage interest deductions claimed by 

homeowners. 

Equivalence of Two-asset and Multi-asset Model 

Although the two-asset model cannot describe the entire chain of 

financial transactions that must occur when tax-exempt bonds replace 

taxable bonds, the existence of other assets does not affect the 

ultimate revenue loss to the Treasury in the fixed allocation case. 

This can be most clearly illustrated by considering a world with 

three financial assets -- one fully taxed, another partially taxed 

(for example, corporate shares), and a third tax-exempt. An 

addition to the stock of tax-exempt housing bonds causes a net 

increase in the stock of tax-exempt assets matched by an equal net 

reduction in the stock of taxable assets. As in the two-asset 

model, maximization by savers of after-tax returns still requires 

that the lowest bracket savers hold taxable assets, while the 

highest bracket savers hold tax-exempt assets. Taxpayers in middl? 

brackets will hold partially taxed assets; the return on these 

assets will be sufficient to provide a niche �or some middle-bracket 

savers who will earn after-tax returns higher than they would on 

either tax-exempt or fully taxed assets. The equilibrium before-tax 

return on these partially taxed assets, relative to other assets, 

will depend on their total supply and on the distribution of savers' 

marginal tax rates. 
-9-

When the supply of tax-exempt housing bonds increases, the 

additional tax-exempt bonds will be purchased by relatively highbracket savers among those initially holding partially taxed assets. 

These partially taxed assets will then be sold to savers in lower 

tax brackets initially holding fully taxed assets. 

The revenue loss to the Treasury under this set of transactions 

consists of two pieces. First, Treasury loses revenue because of 

the declink in holdiigs of partially taxed assets by high-bracket 

savers who purchase tax-exempt bonds. Second, there is a loss 

because low-bracket savers exchange fully taxed assets for partially 

taxed assets. It can be shown that the sum of these two losses, per 

dollar increase of tax-exempt debt, is exactly equal to the 

estimated loss using the two-asset model. 

Suppose, for example, that the tax-exempt interest rate is 7 

percent, the taxable interest rate is 10 percent, and the before-tax 

return on the partially taxed asset is 8.5 percent. Assume further 

that the partially taxed asset is taxed at half the rate of the 

fully taxed asset. In this example, there will be three rather than 

two marginal investors. A taxpayer with a marginal tax rate of 

26.09 percent will be indifferent between partially taxed and fully 

taxed assets (in both cases the after-tax return is 7.391 percent). 

A taxpayer with a tax rate of 35.29 percent will be indifferent 

between partially taxed and tax-exempt assets (in both cases the 

after-tax return is 7.00 percent). Taxpayers with marginal rates 

below 26 percent will prefer fully taxed assets; taxpayers with 

marginal rates above 35 percent will prefer tax-exempt assets, and 

taxpayers with marginal rates between 26 and 35 percent will 

maximize returns by holding partially taxed assets. 
-10-

Suppose the supply of tax-exempt assets increases by $1. The 

tax-exempt bond will be purchased by a saver with a marginal tax 

rate of 35.29 percent selling a half taxed asset yielding 8.5 

percent before tax. Thus, the reduced tax paid by this saver is 

.3529 times .0850 times .5, or $.015 per dollar. The half taxed 

asset will be purchased by a taxpayer with a marginal tax rate of 

26.09 percent, who will sell a fully taxed asset yielding 10 

percent. The reduced tax collected by the Treasury from this 

taxpayer equals the revenue foregone on the taxable asset, .2609 

times .1000, minus the revenue collected on the partially taxed 

asset, .2609 times .0850 times 0.5. This net change also equals a 

loss of $0.15 per dollar of asset switched. The lost revenue 

collected from both taxpayers is $0.03 per dollar, exactly the loss 

in revenue that results when a taxpayer in the 30 percent bracket 

switches from taxable to tax-exempt bonds. The existence of a third 

asset does not affect the revenue loss. 

More generally, suppose that r P is the before-tax return on 

partially taxed assets and lla'l is the fraction of income earned on 

this asset that is included in taxable income. For the taxpayer to 

be indifferent between fully taxed and partially taxed assets, the 

after-tax return on both must be the same. This condition holds 

when: 

rt (l-tl*) = r 

P (l-atl*) 
-11-

Rearranging the terms of (3), the marginal tax rate of the 

marginal holder of fully taxed assets can be expressed as: 

tl* = ( rt-r P )/(rt-arp) (4 1 

For the marginal holder of tax-exempt bonds, the after-tax 

return on partially taxed assets equals the tax-exempt interest 

rate.6/­

r P ( l-at2*) (5) 

Rearranging terms, the marginal tax rate of the marginal holder 

of tax-exempt assets is: 

t2*= (rp-re)/ar P 

The revenue loss, L, per dollar of substitution of tax-exempt 

for taxable bonds is equal to: 

L= tl* + t2* ar P 

The first term of (7) represents the loss from the change in the 

portfolio of low-bracket savers (from fully taxed to partially taxed 

assets), while the second term represents the loss from the change 

in the portfolio of high-bracket savers (from partially taxed to 

tax-exempt assets) . 
-12-

Substituting (4) and (6) into (7) and combining terms, we 

obtain: 

L=rt - re 

The revenue loss is exactly the same as the loss in the 

two-asset model from the substitution of tax-exempt for taxable debt 

in savers' portfolios. 

Comments on Kormendi-Nagle Analysis 

Kormendi-Nagle (hereafter KN) argue that the CBO/Treasury 

estimates are "flawed by the extreme upward bias that results from 

ignoring the existence of assets other than fully taxable and 

tax-exempt bonds."7/ - Their criticism focuses on the fact that

buyers of tax-exempt bonds would not generally be selling fully 

taxable securities to finance their purchases. Mostly, new buyers 

of tax-exempt bonds would be shifting out of equities (half taxed 

assets, in their example); small numbers would be shifting out of 

fully taxable bonds and tax shelters and durables (the latter two, 

untaxed in their example.) On the average, buyers of tax-exempt 

bonds are shifting out of half taxed assets. 

KN do not specify their assumptions of the effect of tax-exempt, 

housing bonds on the allocation of the real capital stock. However, 

there are two likely inferences that one can make. In either case, 

their model fails to provide a basis for the conclusion that the 

CBO/Treasury revenue estimates are understated. 

Because KN do not comment on the capital allocation effects, it 

nppears that they accept the assumptions of the fixed allocation 

model. In that model, tax-exempt housing bonds substitute for 
-- 

-- 

a 

-13-

taxable housing bonds as a source of housing finance and there are 

no other net changes in asset holdings, even though the distribution 

of asset holdings among savers changes across the entire spectrum of 

assets. If so, the discussion in the preceeding section of this 

paper indicates that KN err by looking at only part of the portfolio 

adjustment process. The revenue estimate is exactly the same when 

the existence of assets other than tax-exempt and taxable bonds if 

fully accounted for as when such assets are ignored. KN's error can 

be clearly seen when comparing their computation in Table I11 to the 

three-asset example shown above.8/- In our example, the revenue loss 

consists of two equal pieces the loss from the sale or partially 

taxed assets (equities) by savers buying tax-exempt bonds and the 

loss from the sale of taxable bonds by savers buying equities.9/- In 

their Table 111, KN compute a revenue loss of $15 million per $1 

billion, excluding the recapture from reduced mortgage interest 

deductions, by including only the loss from the sale of assets by 

savers buying tax-exempt bonds and ignoring the other, equally 

large, portion of the revenue loss. It is not surprising that their 

revenue estimate, before the mortgage interest offset, is almost 

exactly half of the Treasury estimate ($30 million per $1 billion) 

before the mortgage interest offset. 

Alternatively, one can suppose that KN believe that the shift 

from equity holdings to tax-exempt bonds by savers is the entire 

story the increase in the supply of tax-exempt bonds results 

mostly in a reduction in net equity holdings. For this to be true, 

there must also be a reduction in the stock of capital financed by 

equity. Therefore, the statement by KN that 82 percent of buyers of 
e 

-14-

tax-exempt housing bonds are selling equities could be interpreted 

to mean that 82 percent of housing financed by tax-exempt bonds 

substitutes for corporate capital financed by equities.lO/ -

The simulations in the next section show that this result is 

very unlikely. For any reasonable assumption about demand 

elasticities for capital in different sectors, most housing financed 

by tax-exempt bonds substitutes for housing financed by taxable 

bonds, not for other forms of capital. However, if this capital 

allocation were accepted as a basis for a revenue estimate, KN's 

computation of the revenue loss is even more grossly understated. 

If tax-exempt housing bonds are assumed to displace corporate 

capital, one must compute not only revenue losses resulting from the 

change in financing -- from partially taxed to tax-exempt financial 

assets -- but also the revenue loss from the change in the 

composition of the capital stock. 

A substantial revenue loss occurs when housing is substituted 

for corporate capital because the return to corporate capital is 

taxed, while the return to investment in owner-occupied housing is 

untaxed. The average marginal tax rate on corporate income is about 

44 percent (taking a weighted average of large corporations taxed at 

46 percent and small corporations taxed at lower rates), reduced to 

an effective rate of at least 30 percent by various preferences. 

Thus, it can be seen that the revenue loss from this shift in the 

allocation of capital is at least twice the revenue loss from the 

change in the form of financing (which assumed about a 15 perent 

effective tax rate), even without accounting for addition81 

individual taxes from dividends received from the return on 

corporate equity. 
-15-

.. 

The next section of this paper estimates revenue losses using a 

more detailed model that allows for likely effects of changes in 

capital allocation and interest rates. 

111. MODELLING ALLOCATION EFFECTS OF TAX-EXEMPT MORTGAGE BONDS 

Structure of Model 

Tax-exempt housing bonds have two initial price effects. They 

lower the cost of housing, thereby causing households to desire a 

larger stock of housing capital, and at the same time they raise the 

cost of all tax-exempt financing because higher tax-exempt interest 

rates are required to induce additional savers to hold tax-exempt 

bonds. These initial effects have repercussions on the entire 

structure of interest rates, holdings of financial claims, and the 

allocation of real capital. In this section, we outline a general 

equilibrium model of debt finance and apply that model to estimate 

the effects of policies that permit issuance of a specified volume 

of tax-exempt housing bonds on interest rates, Treasury revenue and 

the allocation of real capital assets. 

The model has three types of capital: owner-occupied housing, 

private business capital, and State and local government capital. 

In addition, the Federal debt absorbs a specified amount of private 

savings. All capital is debt financed. The interest on loans used 

to finance private plant and equipment and the Federal debt is 

taxable. State and local capital is financed by issuing tax-exempt 

bonds. In the base case, housing is financed by issuing taxable 

bonds. This world is compared to a world in which the political 

authorities allow a specified volume of tax-exempt housing bonds to 

be issued, with the remainder of the housing stock still financed by 

taxable bonds. 
-16-

All taxable bonds are viewed as perfect substitutes by buyers 

regardless of the activity financed, and tax-exempt bonds for 

housing and State and local capital are also assumed to be perfect 

substitutes. The total supply of debt capital (demand for bonds) in 

all uses is held constant. 

This model is designed only to estimate capital allocation 

effects. Therefore, total savings in the economy are held constant 

by assuming that private savings are inelastic with respect to the 

after-tax rate of return and that the government revenue loss from 

the tax-exempt housing bonds is financed by other tax increases or 

reductions in transfer payments. 

Equations (8)-(16) describe the model. 

8) K= Ke + Kt . . capital stock identity 

9) Ke = G + He . . market equilibrium for tax-exempt 

bonds 

10) Kt = F + P + Ht . . market equilibrium for taxable 

bonds 

11) In G = g1 + 

g21n(((l+re) (l+d,)/ (l+i))-l) . . . demand for state/local 

capital 

12) In F = P1 + 

p2 ln(((l+rt) (l+dp)/(l+i))-l) . demand for private plant 

and equipment 
-17-

13) H = Ht + he . . . housing stock identity 

14) In H = hl + h2 ln(((l+(l-th)rh) (l+dh)/(l+i)) -1) 

demand for housing capital 

15) (Ke/K) = R(re/rt);T) . . . demand for tax-exempt bonds 

16) rh = (reHe + rtHt)H . . definition of average interest rate 

on housing capital 

The variable definitions in Equations (8)-(16) are: K = total 

stock of capital Ke = total holdings of tax-exempt debt, Kt = total 

holdings of taxable debt, G = State and local government capital, He 

= housing capital financed by tax-exempt bonds, F = Federal 

government debt held by the public, P = private business capital, Ht 

= housing capital financed by taxable bonds, H = total housing 

capital, re = tax-exempt interest rate, rt = taxable interest rate, 

rh = average interest rate paid by homeowners, d = annual average

g 

depreciation rate of State/local capital, dP = average annual 

depreciation rate of private business capital, dh = average annual 

depreciation rate of private housing stock, i = rate of inflation, 

th average marginal tax rate of homeowners, T = structure of 

marginal tax rates on personal income, and gl, g2, pl, p2, hl, and 

h2, are constants. 

Given the constants, the depreciation rates (dgl dpf and dh), 

the rate of inflation (i), the total capital stock (K), the size of 

the Federal debt (F), and the volume of tax-exempt housing bonds 
(He), the nine equations in the model solve for the nine unknowns 

Kef Kt, G, P, Ht, H, re, rt, and rho 

Equations (8)-(10) and (13) are identities defining total 

capital market equilibrium, the uses of tax-exempt funds, the uses 

of taxable funds, and the composition of sources of housing finance. 

Equations (ll), (12), and (14) are demand equations for State and 

local capital, private business capital, and housing. These demand 

equations are all constant elasticity functions of the real user 

cost of capital. The user cost of business capital equipment 

depends on the real taxable interest rate (rt) and the rate of 

depreciation of private plant and equipment. The user cost of 

housing capital depends on the real taxable interest rate, net of 

mortgage interest deductions, and the depreciation rate of housing 

capital. 

Equation (15) expresses the demand for tax-exempt (and taxable) 

bonds as a function of their relative yields and the tax structure. 

As the interesst rate on tax-exempt bonds rises, relative to taxable 

rates, savers will be induced to hold more tax-exempt debt. The 

shape of this demand schedule for tax-exempt bonds depends on the 

savings-weighted distribution of marginal tax rates of potential 

bond holders. 

Equation (16) expresses the interest rate paid by homeowners as 

an average of tax-exempt and taxable rates, weighted by the shares 

of housing financed by tax-exemt and taxable debt. 

Parameters, Constants, and Exogenous Variables 

The initial values of different components of the capital stock 

rnay be measured by end of 1978 values reported by the Federal 

Reserve Board.ll/ - In the base case, they are: G = $291 billion, P 
-19-

= $1,194 billion, and H = $751 billion. All values refer to capital 

financed by debt. The size of the Federal debt (Treasury debt less 

Federal Reserve holdings) is $507 billion. 

All housing capital is financed by taxable bonds in the base 

case. The value of P, private business capital financed by debt, is 

equal to the sum of corporate bonds ($318 billion), mortgages for 

multi-family residences ($120 billion), commercial mortgages ($211 

billion), farm mortgages ($76 billion, bank loans not elsewhere 

classified ($279 billion), open market paper ($25 billion), and 

other ($162 billion). 

Initial period interest rates are re = 7 percent and rt = 10 

percent. The marginal tax rate of savers who are indifferent 

between tax-exempt and taxable debt is therefore equal to 30 

percent. The average marginal tax rate of homeowners is also 30 

percent. The depreciation rates for the three types of capital are: 

%= 0.04, dP = 0.095, and dh = 0.025.12/- The expected rate of 

inflation is assumed to be 7 percent per year. These values, 

combined with assumptions about the demand elasticities, g2, p2, and 

h2, allow computation of the other constants gl, pl, and hl by 

applying Equations (ll), (12), and (14). 

Method of Simulation 

Starting from the base case with all housing financed by taxable 

mortgages, one can allow the issuance of tax-exempt housing bonds 

and solve the model described by Equations (8)-(16) for the new 

equilibrium levels of tax-exempt and taxable interest rates and 

capital invested in the three sectors. To obtain a solution of the 

model, it is necessary either to assume an explicit interest 
-20-

elasticity in Equation (15), the demand for tax-exempt bonds, or to 

choose this elasticity implicitly by assuming an equilibrium value 

for re/rt, the ratio of tax-exempt to taxable interest rates at 

which savers are willing to hold the new and larger stock of taxexempt bonds. The relationship between the yield ratio and the 

supply of tax-exempt bonds has not been estimated econometrically 

for large changes in the stock of tax-exempt assets. Therefore, we 

have simulated the model using various values of re/rt, representing 

likely bounds on the yield ratio required to induce savers to absorb 

a large increase in the stock of tax-exempt housing bonds. 

For each assumed value of re/rt, we solve the model by a process 

of iteration. This is done by varying the value of re in search of 

an equilibrium. For each set of values of re and rt, the demand 

equations of the model will determine the dollar volume of each type 

of capital that investors wish to hold. The sum of these capital 

demands is then compared to the fixed capital supply. If there is 

excess demand for capital, re is increased in the next trial; if 

there is excess supply, re is decreased. Iteration of the model 

continues until we have found an re at which aggregate capital 

demand equals aggregate capital supply. 

Tax-exempt housing bonds increase the total value of housing 

desired by the public because they lower the average cost of housing 

capital. (This could happen either through increases in the number 

of people owning homes or increases in the average quantity of 

housing services per housing unit. We are assuming the physical 

supply of housing capital is perfectly elastic). With a fixed total 

capital supply, the increase in housing capital demanded creates an 
-- 

-- 

-21-

excess demand for capital. Interest rates must rise to choke off 

this increased demand and to equilibrate total demand and supply for 

capital. The increase in interest rates both taxable and 

tax-exempt dampens the initial increase in housing demand and 

decreases desired holdings of private business capital-and State and 

local capital. (We assume that Federal borrowing is unaffected by 

the interest rate increase.) 

The change in the ratio of the tax-exempt and taxable rates 

depends on the demand curve for tax-exempt bonds described in 

Equation (15). At one extreme, if the volume of savings by 

taxpayers in the 30 percent bracket is large enough to absorb the 

entire increased volume of tax-exempt debt, then there will be no 

change in the relative yields on taxable and tax-exempt bonds. 

Taxable and tax-exempt interest rates will rise in the same 

proportion to choke off excess demand for capital. At the other 

extreme, if the volume of savings by all taxable savers is 

insufficient to absorb the additional volume of tax-exempt debt, 

then tax-exempt savers will be holding tax-exempt bonds. In this 

equilibrium, the tax-exempt interest rate will equal the taxable 

interest rate. The tax-exempt rate will rise almost to the initial 

level of the taxable rate (10 percent), while the taxable rate will 

fall slightly. Both housing capital and private business capital 

will increase slightly; only State and local capital will decline. 

While the results of this extreme case may appear counterintuitive, it is clear that the taxable rate must decline if the 

demand curve for tax-exempt bonds drives the two rates to equality. 

If the taxable rate remained unchanged, total capital demanded would 
-- 

-- 

-22-

be less than capital supplied because the higher tax-exempt rate 

would reduce only State and local capital demanded but would have no 

effect on either housing or business capital. A lower taxable rate 

is needed to increase the use of capital in these two private 

sectors so as to balance total capital demand and supply. 

Generally, for reasonable assumptions about the equilibrium 

yield differential, the taxable interest rate will increase. This 

will be necessary because the increased housing caused by the shift 

from taxable to tax-exempt finance exceeds the reduction in State 

and local capital demanded as a result of the rise in the tax-exempt 

rate. The taxable rate will therefore have to rise, suppressing 

excess demand for capital by reducing housing and private business 

capital. 

Results of Simulations 

Tables 1-4 provide estimates of the effects of allowing the 

issuance of tax-exempt housing bonds equal to 30 percent of the base 

case stock of home mortgages ($225.3 billion). The relative effects 

on taxable and tax-exempt interest rates, capital employed in each 

of the three sectors owner-occupied housing, private business, 

and the State/local sector and Federal revenue depend on thP 

elasticities of demand for capital by State and locdl governments, 

private business firms, and homeowners, and the change in the yizld 

differential between tax-exempt and taxable bonds. In all cases, 

the total increase in the Federal budget deficit is greater than the 

revenue loss estimated in the fixed allocation model. The stock of 

housing increases and the stock of private business capital and 

State and local capiital both decline. Vowever, the relative 
-23-

decline in the two types of capital and relative changes in interest 

rates are both highly sensitive to the demand elasticities for the 

three types of capital and to the yield differential required to 

induce savers to hold the larger stock of tax-exempt bonds. 

Table 1 shows the long-run capital allocation effects of 

tax-exempt housing bonds when the elasticity of demand for State and 

local capital is -0.4, the elasticity of demand for private business 

capital is -0.65, and the elasticity of demand for housing capital 

is -0.8. These assumed elasticities are believed to be at the lower 

range of plausible values. (The rationale for the elasticity 

assumptions is discussed in the Appendix.) 

The first row of Table 1 shows the base case with no tax-exempt 

housing bonds allowed. The remaining rows show the effect of 

allowing $225 billion of tax-exempt housing bonds, 30 percent of the 

original stock of housing, under alternative assumptions about the 

effect of an increased supply of tax-exempt bonds on the yield 

differential between taxable and tax-exempt bonds. This yield 

differential is expressed in the table as the critical tax rate at 

which savers are indifferent between holding taxable and tax-exempt 

bonds. 

It is uncertain how much this critical tax rate would change 

with an increase of about $200 billion in tax-exempt bonds (some of 

the tax-exempt housing bonds would displace other tax-exempt bonds). 

Extrapolating findings by George Peterson that imply a 4-7 basis 

point increase in the tax-exempt rate .

per $1 billion of tax-exempt 

bonds would suggest that the yield differential could be totally 

eliminated.l3/ - In contrast, Kormendi and Nagle believe the effect 
- 24 -

Table 1 

Capital Allocation Effects of Tax-exempt Housing Bonds: 

Low Elasticity Assumptions 

Components of Capital Stock 

Allowed Tax-exempt : Critical : Interest Rates : (Changes from Base Case)

Housing Bonds : Tax Rate : re rt : G : P H 

( $ bill ions) (Percent) (.... Percent ..., (...... $ billions ......) 

0 30 7.00 10.00 291 1194 75 1 

(01 (0) (01 

225 30 7.43 10.61 279 1157 800 

(-12) (-37) (+49) 

225 24 7.92 10.42 268 1168 800 

(-23) (-26) (+49) 

225 20 8.24 10.30 262 1175 799 

(-29) (-1 9) (+48) 

225 16 8.56 10.19 256 1182 799 

(-35) (-12) (+47) 

Variable Definitions: 

re = tax-exempt interest rate 

r = taxable interest rate 

Gt = State and local capital 

P = private business capital 

H = owner-occupied housing 

Elasticity Assumptions: 

g2 = elasticity of demand for State and local capital = -0.4 

p2 = elasticity of demand for private business capital = -0.65 

h2 = elasticity of demand for housing capital = -0.8 
-25-

on the yield differential would be very small.l4/ - Hendershott has

suggested that a reduction of long-run yield differential from 30 

percent to 20 percent might be plausible given the current distribution of holdings of taxable bonds.l5/ -

It is difficult to forecast the effect on the yield differential 

because we have no experience of such a large increase in the volume 

of tax-exempt bonds ($225 billion of tax-exempt housing bonds would 

increase the total stock outstanding of all tax-exempts by more than 

75 percent!) Therefore, the tables all show results for a range of 

plausible effects. 

The second row of Table 1 shows the effect of tax-exempt housing 

bonds if there is no change in the yield differential, In this 

case, tax-exempt and taxable interest rates rise to 7.43 percent and 

10.51 percent, respectively. The total housing stock rises by $49 

billion, displacing $37 billion of private business capital and $12 

billion of State and local capital. 

The remaining rows of Table 1 show cases where the 

tax-exempt/taxable yield differential must rise to attract 

additional savings to tax-exempt bonds. The lower rows of the table 

show successively greater reductions in the yield differential. It 

can be seen that, as the yield differential is reduced, the amount 

of State and local capital displaced increases, while less private 

business capital is displaced. A smaller yield differential has a 

greater impact on State and local capital because the tax-exempt 

rate rises as the yield differential narrows, thereby reducing State 

and local borrowing. 
-26-

The net housing stock increase -- about 22 percent of the supply 

of tax-exempt housing bonds -- is almost completely unaffected by 

changes in the yield differential. The change in the stock of 

housing is composed of two separate pieces -- (1) an increase in 

housing on the part of homeowners eligible to receive tax-exempt 

financing, and (2) a reduction in housing on the part of homeowners 

not receiving the subsidized bonds and as a result bearing the costs 

of the increase in the taxable interest rate. A narrower yield 

di�ferential, therefore, has two offsetting effects. First, the 

increase in the tax-exempt interest rate reduces the value of the 

subsidy provided by tax-exempt bonds, thereby causing a smaller 

increase in housing consumption by subsidized home buyers. Second, 

at the same time, the reduction in the taxable rate lowers the cost 

of housing to unsuhsidized buyers, relative to its cost under a 

constant yield differential. These two effects -- the reduced 

subsidy to subsidized homeowners and the smaller additional interc>sl 

costs imposed on unsubsidized homeowners -- offset each other almost 

perfectly as the yield differential narrows. Total housing 

consumption, as a consequence, is almost completely unattected I))! 

changes in the yield differential. 

Table 2 shows the capital allocation effects of tax-exempt: 

housing bonds using upper bound estimates of capital demand 

elasticities. Compared to Table 1, the results in Table 2 show a 

greater increase in the housing stock (about 30 percent of the 

volume of tax-exempt housing bonds) and slightly smaller inct-easc?r; 

in interest rates. The composition of capital displaced by 

increased housing remains heavily dependent on the yield 
-27-

differential; for small changes in the yield differential most of 

the decline in non-housing capital is accounted for by private 

business sector, while for larger changes in the differential the 

decline in non-housing capital comes mostly from the State/local 

government sector. Again, the net increase in the housing stock is 

almost completely unaffected by the assumed equilibrium interest 

rate differential. 

Table 3 shows the effects of extreme variations in the 

elasticity of demand for State and local capital. All the rows in 

Table 3, except the base case, assume that a yield differential of 

20 percent is required to induce savers to hold the new stock of 

tax-exempt bonds. In the second row, the demand for State and local 

government capital is assumed to be almost completely unresponsive 

to the cost of capital (g2 = -O.l), in marked contrast to the 

responsiveness of private firms and households to changes in 

relative prices.l6/ - Most of the reduction in non-housing capital

($36 billion) comes from the private business sector; State and 

local government demand for capital falls by less than 20 percent of 

the increase in the housing stock ($8 billion). The third row 

duplicates the fourth row of Table 2, the high elasticity 

assumptions for all capital demands. The fourth row shows an 

extreme high value of -1.0 for the elasticity of State and local 

capital, equal to the responsiveness of private firms and households 

to changes in the cost of capital. Under this assumption, the 

changes in the State/local capital stock account for about 80 

percent of the reduction in non-housing capital. 
- 28 -

Table 2 

Capital Allocation Effects of Tax-exempt Housing Bonds: 

High Elasticity Assumptions 

Components of Capital Stock 

Allowed Tax-exempt : Critical : Interest Rates : (Changes from Base Case)

Housing Bonds : Tax Rate : r 

e rt : G : P H 

($ bill ions) (Percent) (.... Percent ....1 (...... $ billions ...... 

0 30 7.00 10.00 291 1194 75 1 

(01 (0) (0 1 

225 30 7.39 10.56 275 1142 819 

(-16) (-521 (+68 1 

225 24 7.89 10.38 259 1158 819 

(-32) (-36) (+68) 

225 20 8.21 10.26 249 1169 818 

(-421 (-251 (+67) 

225 16 8.53 10.15 241 1179 816 

(-501 (-15) (+65) 

Variable Definitions: 

re = tax-exempt interest rate 

r - taxable interest rate 

Gt State and local capital 

P = private business capital 

H = owner-occupied housing 

Elasticity Assumptions: 

g2 = elasticity of demand for State and local capital = -0.4 

p2 = elasticity of demand for private business capital = -0.55 

h2 = elasticity of demand for housing capital = -0.8 
- 29 -

Table 3 

Capital Allocation Effects of Tax-exempt Housing Bonds: 

Alternative Elasticities of Demand 

for State and Local Capital 

Demand Components of Capital Stock 

Allowed Tax-exempt : Elasticity : Interest Rates : (Changes from Base Case) 

Housing Bonds : of G : re r t* G : P H 

( $ bi 11ions (.... Percent ....> (...... $ billions ......) 

0 ... 7.00 10.00 291 1194 75 1 

(0) (0) (0 

225 -0.1 8.31 10.38 283 1158 795 

(-8 1 (-36 1 (+44 

225 -0.6 8.21 10.26 24 9 1169 818 

(-42 1 (-25) (+67 

225 -1 .o 8.15 10.19 227 1176 

(-64 (-18) (+82 

Variable Definitions: 

t 

re = tax-exempt interest rate 

r - taxable interest rate 

Gt State and local capital 

P = private business capital 

H = owner-occupied housing 

Elasticity Assumptions: 

p2 = elasticity of demand for private business capital = -1.0 

h2 = elasticity of demand for housing capital = -1.0 

Critical tax rate assumptions: 

t = (rt - re)/re = 30 percent in base case (first row), 20 percent when 

tax-exempt housing bonds = $225 billion. 

833 
-30-

Table 3 also shows that the increase in the housing stock, for 

any given housing demand elasticity, is sensitive to changes in the 

elasticity of demand for other types of capital. Reading down the 

table from row 2 to row 4, one finds that as the demand elasticity 

for government capital increases (in absolute terms), the 

equilibrium housing stock also increases. In a general equilibrium 

framework, the increase in the housing stock caused by tax-exempt 

housing bonds depends not only on the amount of increased housing 

desired by homeowners when housing costs fall, but also on the 

responsiveness of other capital users to increases in their costs of 

capital. When the State and local demand for capital is more 

responsive to increases in the tax-exempt interest rate, the 

increases in both taxable and tax-exempt interest rates required to 

achieve capital market equilibrium are smaller, and therefore the 

equilibrium housing stock is larger. 

Revenue Effects 

The changes in capital allocation and interest rates shown in 

Tables 1-3 can be used to compute changes in Federal revenues and 

expenditures from tax-exempt bonds. 

The three types of debt-financed capital in the model each 

generate different amounts of taxable income: 

- Business capital. Business capital generates taxable income 

in the form of interest earnings to suppliers of debt finance to the 

business sector. In a world of all debt finance with interest 

payments tax-deductible, there is no additional net tax at the 

ownership level. (If there were an equity-financed corporate sector 

in the model, there would be additional Federal revenue at the 
-31-

corporate level because payments to equity owners in the form of 

dividends cannot be deducted in computing corporate income tax 

liability). 

- Housing capital. Housing capital financed by taxable bonds 

generates no net taxable income. The taxable income of bondholders 

is exactly equal to the amount of deductions that may be claimed by 

homeowners. There may be some net revenue loss if homeowners are in 

a higher marginal tax bracket than bondholders. Housing capital 

financed by tax-exempt bonds generates negative taxable income. 

Bondholders pay no tax on their interest income, but homeowners may 

still claim mortgage interest deductions. 

- State and local capital. State and local capital generates no 

taxable income. Bondholders pay no tax on their interest earnings 

and State and local governments, as tax-exempt entities, cannot 

claim a deduction for interest paid. 

In addition, the existence of Federal debt requires Federal 

expenditures on interest payments. Some of this expenditure is 

returned to the Federal government as tax revenue collected on the 

interest earnings of holders of Federal debt. 

When tax-exempt housing bonds are allowed, there are three types 

of changes that affect the Federal budget, all shown below in 

Equation (17): 

- Changes in the amount of taxable debt outstanding. Federal 

revenue collected from savers falls when the amount of taxable debt 

is reduced. The annual revenue loss from this source is equal to 

the reduction in taxable debt times the initial period interest rate 

times the average marginal tax rate of savers switching from taxable 

to tax-exempt debt. (Line 1 of 'Equation (17)) 
-32-

- Changes in the stock of tax-exempt and taxable housing. 

Federal revenue collected from homeowners rises when homeowners 

switch from taxable to tax-exempt debt because these homeowners 

claim lower mortgage interest deductions per dollar of housing 

capital owned. Federal revenue collected from homeowners falls when 

capital invested in housing increases because of the mortgage 

interest deductions claimed on the additional housing. The total 

Federal revenue loss from changes in the composition and amount of 

homeownership is equal to the taxable mortgage interest rate times 

the net increase in the housing stock times the marginal tax rate of 

homeowners minus the interest rate differential times the volume of 

housing switching from taxable to tax-exempt finance times the 

marginal tax rate of homeowners. (Line 2 of Equation (17)). 

- Changes in taxable interest rates. Federal revenue from all 

remaining holders of taxable debt and Federal debt service costs are 

affected by changes in the taxable interest rate. Changes in the 

taxable interest rate also affect interest deductions claimed by 

homeowners whose homes continue to be financed by taxable bonds. 

The net revenue change from these sources is equal to the product of 

the average marginal tax rate paid by bondholders, the amount of 

taxable debt outstanding and the change in the taxable interest rate 

minus the product of the average marginal tax rate of homeowners, 

the amount of remaining housing financed by taxable bonds, and the 

change in the taxable interest rate. (Line 3 of Equation (17)) 

The change in Federal expenditure is equal to the stock of 

Federal debt (excluding Federal Reserve holdings) times the change 

the taxable interest rate. (Equation (18)). 
-33-

The revenue change can be expressed algebraically as: 

* 

R = rtotb ( P + Ht) (effect of change in amount of 

taxable debt) 

0 + th((rb - re 1

)H~- r: H) (effect of changes in financing 

and quantity of housing stock) 

1 1

+ rt(tb (P+F) - thHt) (effect of change in taxable 

interest rate) 

* 

In Equation (17), rt is the taxable rate, tb is the average 

marginal tax rate of savers switching from taxable to tax-exempt 

bonds, P is the change in private business capital, Htis the change 

in housing capital financed by taxable bonds, th is the average 

marginal tax rate of homeowners, re is the tax-exempt interest rate, 

He is the allowed volume of tax-exempt housing bonds, H is the 

total change in housing capital, rt is the change in the taxable 

interest rate, tb is the average tax rate paid by bondholders, and F 

is the stock of Federal debt (excluding Federal Reserve holdings). 

Superscripts 0 refer to base case values (without tax-exempt housing 

bonds); superscripts 1 refer to values when tax-exempt housing bonds 

. are permitted. 

Line 1 of Equation (17) is negative (a revenue loss) because 

both P and H are negative. The first expression in Line 2 is 

positive because rot is greater than ri; the second expression is 
-34-

negative because H is positive. The first expression in line 3 is 

positive if rt is positive (the usual case) and otherwise negative; 

the second expression is negative if rt is positive and otherwise 

pos i tive . The change in Federal expenditures is equal to: 

E= rtF 

Equation (18) is equal to the change in interest on the Federal 

debt. The total increase in the budget deficit is computed by 

adding the revenue loss and the expenditure increase. 

In the fixed allocation case, P=O, H=O, Ht = -H e’ re=O, and 

rt=O. Therefore, Equation (17) is reduced to: 

Equation (19) is the same expression for the fixed allocation 

revenue loss used in Section I1 of this paper. 

Table 4 shows the revenue loss from tax-exempt housing bonds 

under all the cases illustrted in Tables 1-3. In computing the 

* 

loss, t,b the marginal tax rate of savers switching from taxable t.0 

tax-exempt bonds is assumed to be half-way between the i~~ar(]in,?l bel': 

rate of the first new tax-exempt buyers (30 percent) and the 

marginal tax rate of the last new tax-exempt buyers (the critical 

tax rate in the final equilibrium). The average tax rate of 

1 bondholders tb, is assumed to be 55 percent of the critical rate in 

the final equilibrium.l7/ -
- 35 -

Table 4 

Federal Budget Effects from Tax-exempt 

Housing Bonds Under Alternative Elasticity Assumptions 

($ million per $ billion of Houaing Bonds) 

. Change in Deficit : Revenue loss Excluding 

: Critical : Revenue : Expenditure : Total : Effect of Changes in 

Elasticity :

. Tax Rate :. Loss : 

. Increase : Change : . Interest on Existing 

Debt 

Zero 30 21 .o 0.0 21.0 21.0 

Low .30 24.4 13.9 38.3 27.2 

.24 23.6 9.6 33.2 24.5 

.20 22.7 6.9 29.6 22.9 

.16 21.6 4.3 25.9 21.4 

High 30 26.8 12.7 39.5 29.1 

.24 25.2 8.5 25.9 

0 20 23.8 5.9 23.9 

.16 22.3 3.4 25.8 22.1 

Low g2 .20 24.7 8.7 33.3 '24.9 

High g2 .20 23.3 4.2 27.5 230 3 

Elasticity Assumptions: 

Zero: g2 = C.0, p2 = 0.0, h2 - 0.0 

LOW g2: g2 = -0.1, p2 = -1.0, h2 = -1.0 

High g2: g2 = -loo, p2 = -1.0, h2 = -1.0 

a 

g2 = elasticity of demand for State and local capital 

p2 = elasticity of demand for private business capital 

h2 = elasticity of demand for housing capital 
-36-

Column 5 shows the total budget effect of tax-exempt bonds. In 

the fixed allocation case, there is no expenditure effect because 

interest rates are unchanged. In all other cases, interest rates 

rise, reducing the Federal revenue loss (because increased revenue 

from bondholders exceeds increased interest deductions by remaining 

non-subsidized homeowners), but increasing interest on the Federal 

debt. In all cases shown, the net increase in the budget deficit 

exceeds the revenue loss in the fixed allocation case. Thus, it 

appears that failure to consider capital allocation and interest 

rate effects leads to an understatement of the cost to the Treasury 

of tax-exempt housing bonds. 

The last column of Table 4 shows the revenue loss ignoring the 

effects of changes in interest rates. The estimates in this column 

are computed from the first two terms in Equation (17); thus there 

is no change in interest payments on the Federal debt and no change 

in revenue from remaining holders of taxable debt and remaining 

suppliers of taxable mortgages.l8/ - The computed revenue losses, 

even ignoring the third term of Equation (17), still exceed the 

fixed allocation revenue loss in all cases. 

IV. Conclusions and Extensions 

This paper has examined alternative ways of modelling revenue 

and capital allocation effects of the use of tax-exempt bonds Eor 

private purposes. Using tax-exempt housing bonds as an example, we 

reviewed the basic revenue estimating method used by the Treasury 

Department and the Congressional Budget Office. We showed that the 

revenue loss derived from a multi-asset model would be exactly the 
-37-

same as the revenue loss computed from the type of simple, two-asset 

model used by Treasury and CBO. The discussion of the multi-asset 

model revealed where critics of the CBO/Treasury method erred. 

Section I11 of this paper illustrated how capital allocation and 

revenue effects could be estimated from a general equilibrium model 

of capital markets in a world of all-debt finance. Using reasonable 

bounds on capital demand elasticities and on the response of the 

tax-exempt/taxable bond yield differential to increases in the stock 

of tax-exempt bonds, we estimated that the total housing stock would 

increase by between 20 and 30 percent of the volume of tax-exempt 

housing bonds. In the context of a fixed kapital supply, it was 

shown that the composition of the decline in non-housing capital is 

very sensitive to the effect of tax-exempt housing bonds on the 

tax-exempt interest rate. For large increases in the tax-exempt 

interest rate, most of the displaced capital would be other 

tax-exempt investments (mainly State and local public sector 

capital, but also IDBs in a broader model). For small increases in 

the tax-exempt rate, most of the displaced capital would be private 

business capital. 

The estimated cost to the Federal government of tax-exempt 

housing bonds appears to be understated by estimating methods that 

ignore changes in the allocation of the real capital stock. This 

underestimation results principally from the fact that additional 

housing financed by tax-exempt bonds generates negative revenue to 

the Treasury, while displaced private business capital would 

generate positive revenue and displaced State and local capital 

generates no revenue. Thus, the Treasury/CBO estimates, which 
-38-

ignore these allocation effects, probably understate the revenue 

loss. The degree of understatement, however, is uncertain and may 

be small. 

The assumption that all capital is debt financed is an important 

simplification that may affect the revenue loss estimate. The next 

research step would be to broaden the model to take account of the 

share of capital financed by equity and of substitutions between 

debt and equity finance. A model that allows for equity finance 

would be considerably more complex than the all debt model because 

it would be necessary to consider choices by savers among assets 

with different risk and e,xpected returns and decisions by investors 

on the mix of debt and equity finance. The all debt model is 

simpler because savers are concerned only with maximizing after-tax 

returns and investors with minimizing interest costs, when choosirq 

between the two financial assets. Neither is balancing changes in 

expected after-tax returns against changes in perceived risk in 

choosing an optimum portfolio. 

Ignoring equity capital probably understates the revenue loss 

from tax-exempt housing bonds for two reasons. First, ret:urns to 

corporate equity are more heavily taxed than returns to corporate 

debt capital; thus, any losses from a declins in private bu?inesaq 

capital are underestimated by considering debt capital only. 

Second, allowing housing to be financed by tax-exempt bonds will 

increase the share of housing that is debt financed for subsi”tized 

homeowners. This substitution of debt �or equity will 3153 fricr~c~~?~ 

I-he loss to the Federal Treasury because, as noted above, ‘7ol~sing 

financed by tax-exempt bonds, unlike housing financed by equity ?r 

kaxable debt, generates negative taxable income. 
-39-

Finally, this paper has not examined two important effects of 

tax-exempt housing bonds -- the effect on economic efficiency and 

the effect on the after-tax distribution of income. Policies to 

divert capital from business plant and equipment to owner-occupied 

housing, by reinforcing the existing bias in the tax system, could 

very well lead to a less efficient allocation of scarce capital 

resources. Also, the use of tax-exempt bonds as a method of subsidy 

reduces the progressivity of the tax system. Although public 

concern and debate has focused on the potential revenue impacts of 

tax-exempt housing bonds, potential equity and efficiency losses may 

be a more serious problem. 
-40-

******* 

The authors would like to thank Larry Dildine for his assistance 

in developing the general equilibrium model used in this paper, 

Hudson Milner for helping with the Appendix, and Pat Hendershott, 

John Samuels, and Ben Cohen for useful discussions on the general 

topic of tax-exempt mortgage bonds. Also the work of Nancy Kawtoski 

and Amie Powell in preparing the manuscript is very much 

appreciated. 

FOOTNOTES 

-1/ Kormendi and Nagle have argued that even if as much as 42 

percent of the mortgage market were financed by tax-exempt

bonds, the effect on interest rates would be very small. See 

Roger C. Kormendi and Thomas T. Nagle, The Interest Rate and Tax 

Revenue Effects of Mortgage Revenue Bonds, paper produced for 

Public Securities Association, July 26, 1979. 

-2/ See Tax-exempt Bonds for Single Family Housing, a study prepared

by the Congressional Budget Office (Washington, D.C., U.S. 

Government-Printing Office, 1979). 

-3/ See Kormendi and Nagle, op. cit. 

-4/ Treasury and CRO revenue estimates presented to Congress take 

account of two minor complications not discussed in this paper.

First, States and localities have generally set aside about 15 

percent of the proceeds of tax-exempt housing bonds for reserve 

funds on which they are permitted, under current Treasury 
-- 

-41-

regulations, to earn arbitrage profits; only 85 percent of the 

proceeds of loans actually go to homeowners. Second, to date,

brokers and financial intermediaries have charged very high

fees, benefitting from the spread between tax-exempt and taxable 

rates and capturing some of the windfall that would otherwise go 

to homeowners receiving the favored loans. These unusually high

profits to intermediaries could, of course, be driven down by

competition as the supply of tax-exempt housing bonds grows and 

more institutions enter the market to offer the needed brokerage

services. 

Taking account of these two factors, one can derive the 

following expression for the revenue loss per dollar of 

tax-exempt housing bonds: 

where fh is the fraction of the proceeds ot tax-exempt housing

bonds used for mortgage loans, p is the excess profits of 

brokers, per dollar of outstanding issues, and t, is the 

marginal tax rate of brokers earning excess profits. Note that 

if th = tin, i.e., the marginal tax rate of brokers and 

homeowners is the same, the revenue loss expression simplifies

to: 

rttb 

In other words, the division of the benefit of tax-exempt

housing bonds between brokers and homeowners only affects the 

revenue loss if the two groups are in different marginal tax 

brackets. 

-5/ If, in addition, we assume that tm = th (homeowners are in the 

same marginal tax bracket as brokers earning excess profits �rom 

tax-exempt housing bonds) and th = '7.55, then the revenue loss 

is $22.35 million per $I billion. This is the figure used by

Treasury in deriving revenue costs. CHO us?d slightly ditferent 

assumptions for the offset, thereby computing an estimated 

revenue loss of $22.5 million per $1 billion. 

-51 These marginal conditions for holders of different assets are 

a1.50 derived and discussed in Harvey Salper and Dennis 

Zimrnerman, "Preferential Taxation and Portfolio Cl-~oice: Yoin('

Empirical Evidence," National Tax Journal, Vol. YXX, No. 4, 

December 1977. 

-7/ See Kormendi and Nagle, op. cit., p. 12. 

7/ Ibid., p. 16. 

rh/ These two pieces need not be equal. From Equations (4), (51, 

~nd(7), it can he seen that the two pieces arc! ~ ~ J L only I ~ I if 

thc yield on the partially taxed asset is halfway bc?twc(?rith(' 
-42-

yields on the fully taxed and tax-exempt assets. The total 

revenue loss is unaffected by the division between the two 

pieces. However, KN's analysis does imply that the yield on 

partially taxed assets is roughly halfway between the tax-exempt

yield and the taxable yield. 

-10/ Kormendi and Nagle, op, cit., p. 16. 

-11/ See Flow of Funds Accounts, Assets and Liabilities Outstanding, 

1968-78, (Division of Research and Statistics, Board of 

Governors -of the Federal Reserve System, Washington, D.C., 

September 1979). 

-12/ These depreciation rate assumptions are based on rough estimates 

computed using preliminary research findings in a paper by 

Wykoff and Hulten that provides estimates of depreciation rates 

for different asset classes. See Frank C. Wykoff and Charles R. 

Hulten, Tax and Economic Depreciation of Machinery and Equipment - A Theoretical and Empirical Appraisal, Phase I1 Report

Submitted to U.S. Treasury Department, July 26, 1979. Using the 

Wykoff-Hulten data, we compute estimated average annual 

depreciation rates of 2.5 percent for structures and 13 percent

for all business plant and equipment. The depreciation rate 

used for owner-occupied housing is the depreciation rate on all 

structures. The depreciation rate used for all private business 

capital is two-thirds of the combined estimated depreciation 

rate for plant and equipment, since about one-third of private

business capital is non-depreciable land and inventory. The 

depreciation rate used for State and local capital assumed that 

about 80 percent of State and local capital has the same 

depreciation pattern as structures, and the remaining 20 

percent has the same depreciation pattern as all private

business capital. This is based on the observation that a large

proportion of State and local capital appears to be in longlived structures (highways, schools, and other buildings), but 

some fraction of the public capital stock is composed of 

machinery and equipment. 

-13/ See George Peterson, Tax-exempt Financing of Housing Investment 

(Washington, D.C.: The Urban Institute, 1979). 

-14/ Kormendi and Nagle, op. cit., pp. 9-11. 

-15/ See Patric H. Hendershott, Mortgage Revenue Bonds: 

Tax-exemption With A Vengeance, in this volume. Hendershott 

uses a yield differential of 16 percent when the stock of 

tax-exempt housing bonds is $285 billion. An earlier version of 

the same paper estimated the yield differential would be 19 

percent with a stock of $249 billion. 

-16/ Hendershott assumes a demand elasticity of -0.1 for real State 

and local capital. See Hendershott, op. cit., Appendix. 
-43-

_.17/ This results from two empirical facts. First, the average

marginal tax rate paid by all bondholders, weighted by interest 

carnings, is almost the same as the critical marginal tax rate. 

Data on the Treasury model indicate that the average marginal 

tax rate on all interest earnings is 31 percent. This figure is 

estimated by increasing the interest earnings of all taxpayers 

on the file by 1 percent and computing the resulting increase in 

tax liability per dollar of additional taxable income. 

Second, about 40 percent of taxable interest is earned by nontaxpayers (tax-exempt organizations, foreign bondholders, and 

individuals who fail to report taxable income.) This estimate 

is derived from data in a recent IRS publication that reconciles 

taxable interest income with interest income as measured in the 

national income accounts. See Estimates of Income Unreported on 

Individual Income Tax Returns, Department of the Treasury,

Internal Revenue Service, Publication 1104, September 1979, 

pp. 69-74. 

This 40 percent figure would rise to about 45 percent when $225 

billion of tax-exempt housing bonds are allowed because 

virtually all the savers switching into tax-exempt bonds would 

he taxpayers; the non-taxpayers would continue to hold taxable 

bonds. 

-18/ In this case, the revenue loss is equal to: 
-44-

APPENDIX 

Demand Elasticity Assumptions 

The demand elasticity for capital in any sector of the economy 

(X) can be computed by the formula: 

Ekr = -(LxS + K x 

E 

X P

) (All 

where Ekr = elasticity of demand for capital in sector X with 

respect to the cost of capital, L, = labor's share in the production 

of output X, S = elasticity of substitution of capital for labor in 

the production of output X, Kx = capital's share in the production 

of output X, and E

XP = price elasticity of demand for final output 

x.19/ -

The demand elasticities used in the model are derived by 

applying Equation (Al) to assumed values of the demand elasticity 

for final goods and the elasticity of substitution of labor for 

capital in production. 

The demand elasticity for final output in all three sectors is 

assumed to be -1.0. This assumption is consistent with the results 

of many econometric studies of8the demand for housing; if the 

elasticity of demand for housing with respect to its relative price 

is -1.0, then the demand elasticity for all other private sector 

goods and services would also be -1.0. 

The elasticity of substitution of labor for capital in private 

sector industrial production has been estimated in many econometric 

studies; estimates have generally varied between around 0.5 for 
-45-

cross-section studies and 1.0 for time series studies.20/ - In

deriving the low elasticity assumptions used in Table 1, we use a 

value of 0.5 for the elasticity of substitution in the housing 

sector and private business sector; in deriving the high elasticity 

assumptions we assume the elasticity of substitution is 1.0. The 

elasticity of substitution in production of State/local services is 

assumed to be half the size of the elasticity of Substitution in t5e 

private sector (0.25 for the low elasticity case, 0.5 for the high 

elasticity case). This assumption is based on a belief that the 

public sector is generally somewhat less responsive to economic 

incentives than the private sector. 

The values used for capital's share of output are 0.7 in housing 

(a capital-intensive sector), 0.3 in the private business sector 

(based on an approximation of capital's share of income in the 

entire private economy), and 0.2 for the State and local public 

sector (a labor-intensive sector). 

Inserting these values into Equation (,\.I), we obtain the valiues 

of the elasticity of demand for capital jn the housing sector, %'.le 

private business sector, and the State and 1.0ca1 7iiblic sec-tor II:;~?~ 

in Tables 1 and 2. In Table 3, as noted in the text of t.he paper, 

we examine the effects of assuming extreme V~~IJPS(-0.1 (qn? -1 .Oj I.?{ 

the demand elasticity for State and local public Cr)pit.al. 
-46-

FOOTNOTES TO APPENDIX 

-20/ For a discussion of these studies, see Ernst R. Berndt, 

"Reconciling Alternative Estimates of the Elasticity of 

Substitution, The Review of Economics and Statistics, Vol. 

LVIII, No. 1, February 1976.