Technical Paper Series

Macroeconomic Analysis and Tax Analysis Divisions

Congressional Budget Office

Washington, D.C.

TAXING GOVERNMENT

IN A NATIONAL RETAIL SALES TAX

William G. Gale

Evan F. Koenig

Diane Lim Rogers

John Sabelhaus

October 1998

1999-5

Technical papers in this series are preliminary and are circulated to stimulate discussion and critical

comment. The analysis and conclusions expressed in these papers are those of the authors and do

not necessarily represent the position of the Congressional Budget Office. References in

publications should be cleared with the authors. Papers in this series can be obtained by sending an

email to techpapers@cbo.gov.
1. See H.R. 2001, "The National Retail Sales ax Act of 1997."

2. As discussed further below, these are "tax-inclusive" rates. In the AFT proposal, for example, the sales tax would be 23 percent of the total

cost -- that is, of the price of the good plus the tax. This corresponds to the sales tax representing a 30 percent mark-up over the price of

the good.

3. Selected recent analyses of the national retailsales tax include Bartlett (1995), Burton and Mastromarco (1997), the Congressional Budget

Office (1997a, b), Due and Mikesell (1994), Feenberg, Mitrusi, and Poterba (1997), Gale (1998b), Metcalf (1998), Mikesell (1997), and

Murray (1997).

2

In recent months, proposals to replace all or most of the existing federal tax system with a national

retail sales tax have received increased attention. The most prominent proposals include those by Reps.

Dan Schaefer, R-Colo., and Billy Tauzin, R-La., and by a group called Americans for Fair Taxation

(AFT). Schaefer-Tauzin (S-T) would replace existing personal and corporate income taxes, the estate

tax, and some excise taxes with what they term a 15 percent sales tax.1

 AFT would replace taxes on

personal and corporate income, estates, and payrolls with what they term a 23 percent sales tax.2

These proposals raise a number of interesting issues.3

One of the more controversial and interesting features of these proposals is that all

consumption and investment purchases made by federal, state, and local governments would be subject

to the sales tax. These provisions increase the statutory sales tax base by more than 40 percent. The

proposals would also tax all private consumption of goods and services sold by the government to

households. 

In this report, we examine the treatment of government in a national retail sales tax, with

emphasis on three issues: What are the alternatives for taxing federal, state, and local governments

under a national retail sales tax? How does taxing government affect the sales tax rate required to
3

maintain the real value of government programs? What are the implications of these results for

existing sales tax proposals?

We find that taxing federal, state, and local government purchases in a national retail sales

tax would provide consistency in comparisons of the sales tax with other taxes, such as the income

tax or the flat tax. It may also help establish neutrality between public and private provision of goods

or services in a sales tax.

However, we also find that taxing government purchases does not affect the tax rate needed

in a sales tax to maintain the real value of government spending. This result may be surprising. How

can it be that increasing the tax base by 40 percent by taxing government does not reduce the

required tax rate?

Before providing a more detailed summary of this finding, we note two items. First, consider

the current income tax. If the government decided not to tax its interest payments on government

bonds, it could issue the bonds at a lower interest rate. Government expenditures would fall because

gross Treasury interest rates would fall, even though the after-tax return would not. Government

revenues would fall by the same amount because no one would pay taxes on interest on government

bonds. Thus, no other tax rates would be affected. This provides an example of how choosing to tax

or not to tax government can leave all other tax rates unaffected. 
4

Second, we emphasize that there can be a difference between a "revenue-neutral" tax reform

-- that is, one that raises the same amount of nominal tax revenue as the current system -- and a tax

reform that maintains the real value of government spending -- that is, one that allows government

to pay its current real obligations without increasing seignorage or bond sales to the public. Because

sales taxes drive a wedge between producer prices and consumer prices, whereas the flat tax (Hall

and Rabushka 1995) and income tax do not, maintaining the real value of government spending in

the sales tax can involve a different level of nominal spending (and hence a different nominal

revenue target) than in either the flat tax or income tax.

Now consider the case in which the producer price level stays the same when the sales tax

replaces the income tax. This implies that consumer prices (prices including the sales tax) would

have to rise by the amount of the sales tax. Under these circumstances, if the federal government

taxed its own purchases and wanted to maintain the same real programs, it would have to allow its

nominal spending and its nominal revenue target to rise by the exact amount of the tax payments it

made to itself. Thus, the tax on government would have no impact on the tax rate needed to maintain

current government programs.

For state and local governments, the issue is similar. If they are forced to pay federal sales

taxes on their purchases, then either (a) the federal government will reimburse them for the added

payments, which raises the federal spending level and revenue target by the exact amount of the taxes

paid, (b) state and local governments will have to raise their own taxes to cover the payment, or (c)

state and local government spending will have to be reduced. Thus, if the real value of government
5

spending is to be maintained, taxing government in a retail sales tax will not influence the required

tax rate.

These results have important implications for analysis of current sales tax proposals. Both the

AFT and the S-T proposals aim to raise the same nominal revenue as the existing system, and both

proposals would tax government purchases as well. Therefore, to the extent that producer prices

remain constant (i.e, to the extent that consumer prices rise) after conversion to a NRST, the AFT and

S-T proposals would require cuts in the size of government, or increased deficits, or higher tax rates.

All of the discussion above assumes that producer prices will stay constant. What if producer

prices fall after switching from the current system to a NRST? In that case, the existing level of

government spending plus the sales taxes on that spending could be financed with the current

nominal government revenue, but the sales tax base -- the producer price of goods and services times

the quantity consumed -- would shrink relative to the base envisioned by the AFT and S-T proposals.

Thus, in this case as well, the AFT and S-T proposals, at the tax rates they report, would not generate

enough revenues to maintain the real size of government programs.

Therefore, regardless of how switching to a sales tax would affect the producer price level, we

find that if tax reform options are compared holding constant the real value of government programs

and without increasing seignorage or bond sales, then taxing or not taxing government does not affect

the required sales tax rate. In addition, current sales tax proposals require either significant cuts in
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government spending, increases in the deficit (reductions in the surplus), or significantly higher tax

rates than currently advertised. 

For example, our calculations indicate that, under conservative assumptions, the AFT proposal

would reduce the real value of federal, state, and local government spending on purchases of goods

and services and transfer payments by about 17 percent, or more than $400 billion annually, if the

deficit (surplus) were held constant in real terms. For the S-T proposal, the analogous shortfalls are

11 percent, and $270 billion. Alternatively, to maintain the current real value of government programs

in the AFT or S-T proposals would require increases in the sales tax rate above the rates proposed.

For example, for the AFT proposal, the required increases would be 10 to 12 percentage points,

measured on a tax-inclusive basis, or 19 to 24 percentage points, measured on a tax-exclusive basis.

Thus, comparing the existing sales tax proposals to the current system is misleading, since

the sales tax proposals involve substantial cuts in government or increases in deficits at the tax rates

proposed, or require significantly higher tax rates. Debating the size of government is a completely

legitimate issue, but it is different from, and should not be confused with, debates about the structure

of taxes. Comparisons of the reform proposals and the existing system can only be done clearly when

each proposal maintains the same real size of government, without increasing reliance on real nontax

revenue sources like bond sales or seignorage. 

We also note that the issues examined in this report are not fundamentally about taxing income

versus consumption, but are rather concerned with the equivalent treatment of government under
4. The Joint Committee on Taxation (1996) contains an extended discussion of issues involved in the taxation of government under

fundamental tax reform options.

5. Formally, the proposals claim they would tax government consumption and investment, not "purchases." However, government consumption,

as listed in the national income and product accounts and in the proposals' tax bases, includes depreciation of government capital. This

depreciation is an imputed measure, and does not correspond to either a cash flow or a market transaction. Moreover, if the gross investment

purchase is taxed, the depreciation should not also be subject to taxation. For all these reasons, it is both likely and appropriate that a sales tax

7

direct and indirect taxes. Direct taxes are imposed on individuals or corporations as in the income

tax and the proposed flat tax. Indirect taxes are imposed on transactions, as in retail sales taxes and

value-added taxes (Stiglitz 988).

The remainder of the report develops these findings in more detail. Section I discusses

alternative approaches to taxing governments in a retail sales tax. Section II provides a series of

simple models that demonstrate that taxing government does not affect the required tax rate as long

as real government spending on programs is held constant. Section III applies these results to recent

proposals. Section IV develops corresponding formula for the required tax rate in the income tax and

the proposed flat tax. Section V offers concluding remarks.

I. Alternative Approaches to Taxing Government4

In general, the appropriate treatment of government in a NRST depends on what is intended,

conceptually, to be the tax base. If the goal is to include all value added with respect to final goods

and services, then value added by government should be included in the tax base.

The AFT and S-T proposals would tax all federal, state, and local government purchases of

goods and services, including the wages and nonpension fringe benefits of government workers, new

government investments, and inputs of goods and services.5 However, government purchases of
not subject depreciation to tax.

8

property and services for purposes of resale or production would be exempt. For example, the

Government Printing Office's purchase of paper for printing for books that were sold to the public

would be exempt (Burton and Mastromarco 1996). The proposals would also tax all household

purchases of government-provided goods and services.

It may seem strange to tax government in a national retail sales tax. At the very least, the

significance of a government taxing itself requires some explanation. Moreover, only 8 of the 45

states with state-level retail sales taxes apply the tax generally to state and local government

purchases (Due and Mikesell 1994). It would be interesting to examine why so few states choose to

tax their own purchases.

The taxation of government is further complicated by the fact that governments consume,

produce, and redistribute resources. Indeed, in some contexts, it is difficult to determine whether the

government is a producer or a consumer (see Joint Committee on Taxation 1996). Thus, taxing

government in the retail sales tax poses some difficult questions.

However, complete exemption of government from taxation in the sales tax would not be

consistent either with the existing system or with the proposed flat tax. The income tax base includes

the wages of government workers and the profits that businesses earn on sales of goods or services

to the government. Under the flat tax, wages of government workers would be taxed under the

individual tax, and revenues from business sales to government would be taxed under the business tax.
6. It may seem that taxing government wages on a prepayment basis and also taxing government sales of goods and services to households

could lead to double taxation on the value added to government goods and services sold to households (Joint Committee on Taxation,

1996). This treatment, however, is roughly the same as in the current system and in the flat tax. Under both systems, government workers

pay taxes on their wages and government-provided goods are purchased with after-tax wages. Under the proposed sales tax, government

would pay taxes on its workers' wages, and households would use pretax wages to purchase goods and pay sales taxes.

9

This does not provide an exact correspondence between the flat tax and income tax with respect to

taxing government because the business tax base varies between the income tax and the flat tax. But

it does show a rough correspondence between the treatment of government in the two systems.

In the NRST, one approach would tax all government provision of goods and services to the

household sector. Government sales of goods and services to households are a component of private

consumption expenditure and are thus appropriately taxed under an NRST. However, many

government-provided goods or services are not obtained via market transactions. Moreover, for

many or most of these items, it would be difficult to establish a market price, on which to base a

sales tax, and/or would be difficult to determine who the consumer of the good or service is, and thus

who should pay the tax. Thus, it is not practical simply to tax all government-provided goods and

services at the point of consumption.

An alternative is to tax government on a prepayment basis, as the proposals would. This

involves placing a tax, paid by government, on all government purchases, which would allow taxation

of the government sector even in the absence of market transactions for government-provided goods

and services. The prepayment approach also helps remove any tax advantage the government might

have over the private sector in producing goods and services if government were completely exempt

from taxes in a NRST. In short, the prepayment approach makes the sales tax more consistent with

the flat tax and the current system than total exemption of government would.6
10

The taxation of transfers raises a variety of issues. Cash transfers represent neither production

nor consumption and so should not be subject to the NRST. Instead, the value of cash transfers

would be taxed if and when the household spends the funds on consumption. The current system

taxes some cash transfers, such as social security, unemployment insurance, and government interest

payments. Cash transfers would not be subject to the flat tax.

In-kind transfers represent final consumption, but are often provided in the absence of a

market transaction. Moreover, in-kind transfers are not taxed under the income tax, nor would they

be under the flat tax. For both reasons, the appropriate treatment would be to exempt in-kind

transfers from a sales tax. Of course, the resources that governments used to produce in-kind

transfers would be taxed under the prepayment approach noted above, just as they would be in the

flat tax or the current system.

II. Effects on the Required Tax Rate

The required tax rate in a national retail sales tax depends on numerous factors, including:

the taxes to be replaced; the statutory sales tax base, net of any demogrants, exclusions, deductions,

or credits; the rate of evasion; the effect of economic growth on the tax base; and any transition relief

provided. For purposes of making our calculations comparable to those done by others, we assume

the sales taxes replace existing taxes as specified in the AFT and S-T proposals; the statutory sales tax
7. This includes the assumptions that personal consumption expenditures as measured in the National Income and Product Accounts, with

some adjustments to housing consumption, represents fully taxable transactions, and that depreciation of government capital is taxed (see

footnote 5).

8. Excellent discussions of the monetary policy response and the incidence of income and sales taxes may be found in Bull and Lindsey

(1996), Hall (1996), and Slemrod and Bakija (1996).For evidence on the actual price level effects of replacing income taxes with

consumption taxes, see Buiter and Miller (1981), Poterba, Rotemberg, and Summers (1989), and Tait (1991).

11

base is as specified in those proposals;7

 and the evasion rate in a sales tax is zero. Likewise, we

ignore possible effects of economic growth on the tax base, and assume there is no transition relief.

Our analysis focuses on the effects of two other issues on the required tax rate in a NRST:

how the producer price level changes after the switch to an NRST; and how government is treated

-- including the taxation of government spending and maintenance of nominal or real government

program spending.

How the producer price level responds can be interpreted as an issue of the Federal Reserve's

response to tax policy, and/or the incidence of removing an income tax and adding a sales tax. For our

purposes, it does not matter whether either interpretation or some other interpretation is used. The

analysis only requires information on how the producer price level changes, not why.8

 The consumer

price level is just the producer price plus the amount of any sales tax. Thus, if an item costs $100 and

there is a $30 tax payment, the producer price is $100 and the consumer price is $130. 

The standard approach for controlling for the size of government is to focus on

"revenue-neutral" tax changes. This approach holds the size of government constant as long as there

are no price level changes or changes in the point of taxation. However, the sales tax would tax at

the point of consumption, whereas the flat tax and the income tax place taxes on wages and business
9. Holding just the deficit constant is not a sufficient way to compare tax systems, because one system can have lower revenues and lower

spending, but the same deficit, as another.

12

profits. Thus, in comparing the sales tax to the other tax systems, it is necessary to hold constant the

real deficit and real government spending on programs, not including the sales tax payments on

government purchases, rather than total revenues.9

A. Tax-Inclusive and Tax-Exclusive Tax Rates

Suppose a good costs $100 and there is a $30 sales tax placed on the item. Most people

would probably consider that to be a 30 percent sales tax, since the tax is 30 percent of the selling

price, or producer price. This is known as the tax-exclusive tax rate and is calculated as T/P, where

T is the total tax payment and P is the producer price. This rate is termed "exclusive" because the

denominator excludes the tax.

There is an alternative approach, however. The alternative would divide the $30 tax payment

by the total cost of the good to the consumer ($100+$30) and report a 23 percent rate. This is known

as the tax-inclusive tax rate, because the tax payment is included in the denominator in determining

the rate. This rate is calculated as T/(P+T).

Sales taxes are typically quoted in terms of tax-exclusive rates. Income tax rates, however,

are typically quoted as tax-inclusive rates. For example, a household that earns $130 and pays $30

in taxes would normally think of itself as facing about a 23 percent (30/130) income tax rate.
13

Although there is no single correct method of reporting the rate, it is crucial to understand

which type of tax rate is being quoted, for at least two reasons. First, comparing a proposed sales tax

with existing sales taxes is easier to do if one uses the tax-exclusive rate in the proposed sales tax.

Comparisons with current income taxes or the flat tax are clearer using the tax-inclusive approach.

Second, the tax-inclusive rate is always lower than the tax-exclusive rate. If the tax-exclusive

rate is given by t, the tax-inclusive rate is simply t/(1+t). The difference between these measurements

grows dramatically as the rate rises. At a rate of 1 percent the difference is negligible, but a 50 percent

tax-exclusive rate corresponds to a 33 percent tax-inclusive rate. The 15 percent rate in S-T and the

23 percent rate in AFT are tax-inclusive. The equivalent tax-exclusive rates are about 17.5 percent and

30 percent, respectively. In the analysis below, we report tax-exclusive rates, except where noted.

B. Modeling the Effects of Taxing Government

In the pre-sales-tax economy, let

C = consumption expenditures,

G = government expenditures on goods and services (including

wages and investments)

T = government transfers to households,

α = the proportion of such transfers that are untaxed in the pre-sales-tax economy (0< <1), α

D = a cash-flow measure of the budget deficit (D<0 represents a surplus), and 

R = government revenues.
10. For example, a household that currently receives $100 in transfers and pays 20 percent in income taxes has a net-of-tax transfer of $80.

Suppose that, in the switch to a sales tax with a 20 percent tax-inclusive rate, the producer price level remained constant and consumer

prices rose. The household could then make the same net-of-tax purchases as before with a gross-of-tax nominal transfer of $100. That

is, the nominal transfer does not have to change to retain its value, if the producer price does not change and the transfer is currently taxed

at the same rate as it would be under the sales tax. If the nominal transfer were adjusted in accordance with consumer prices, the nominal

transfer would rise and the household would receive a windfall gain.

14

All values except are in nominal dollars, and G and T include the tax payments that α

government workers and transfer recipients, respectively, make under the existing income tax. Note

that C, G, and T represent expenditures rather than quantities of consumption.

One might expect that, to hold the size of government constant, all transfer payments would

have to be adjusted in accord with any changes in the consumer price level. However, some transfer

payments are currently subject to income taxation, which alters the adjustment needed to maintain

real purchasing power. For example, suppose that all transfer payments are currently taxed under the

income tax at the same (tax-inclusive) tax rate as would be imposed under the sales tax. In this case,

removing the income tax and adjusting the nominal value of such transfers in accordance with

changes in the consumer price level would generate windfall gains for recipients of such transfers.

In contrast, removing the income tax and adjusting the nominal value of the transfer in accordance

with changes in the producer price level would maintain the real purchasing power of the transfer.10

Thus, to hold the real purchasing power of transfers constant, transfers that are currently untaxed

need to be adjusted in accord with the consumer price level. Transfers that are currently taxed at the

same (tax-inclusive) rate that a national sales tax would have can be adjusted in accord with the

producer price level and still retain their real after-tax value under a sales tax.
11. Note that this implies that transfers that are currently taxed, but at a lower rate than would apply in a sales tax, need to be adjusted by an

amount between the changes in the consumer and producer price level changes. Transfers that are currently taxed at a higher rate than

a sales tax would generate need to be adjusted by less than the change in the producer price level to retain their purchasing power.

12. It is also worth noting that, in the current system, transfers such as social security benefits are indexed explicitly for inflation, and other

benefits, such as Medicare and Medicaid, may be thought of as implicitly indexed. Transfer payments such as net interest are not indexed.

Our calculations do not depend, however, on what proportion of transfers are indexed.

15

If all transfers were currently taxed in the income tax at either a zero rate or the rate that

would prevail in a sales tax, could be thought of simply as the proportion of transfers that are α

untaxed. In the more general case, where transfers are currently taxed at a variety of rates in the

income tax, the notion of the proportion of transfers that is untaxed is given by 1-ty 

I

/ts

I

, where ty

I

 is

the average tax-inclusive income tax rate on all transfers currently received, including those taxed

at zero rates, and ts

I

 is the tax-inclusive sales tax rate.11, 12

The deficit is the difference between total government outlays and revenues, so revenue is

given by:

(1) R = G + T - D.

The major sales tax proposals include provisions for "demogrants." These are payments to

each household equal to an exempt amount of consumption times the sales tax rate. Typically, the

exempt amount is set to compensate households for consumption expenditures up to the poverty line.

We define 

 X = the aggregate exempt amount of consumption expenditures (holding producer prices

constant) in the demogrant in the sales tax (X=0 in the pre-sales-tax economy).

In each of the cases examined below, we follow a similar procedure. First, we develop an

equation for tax revenues by multiplying the sales tax rate by the statutory tax base. Second, we

develop a government budget constraint that adjusts government spending on goods and services, the
13. Untaxed transfers rise to (1+t1) T from T. Taxed transfers remain constant at (1- )T. The sum of these two items is (1+ αα α α

t1)T.

16

deficit, and a proportion of transfers for changes in prices. Then we combine the two equations α

to solve for the required tax rate. In case j, j=1 to 4, tj indicates the sales tax rate (on a tax-exclusive

basis), and Rj indicates the nominal revenue requirement. 

(i) Nominal wages and producer prices are constant

When nominal wages and producer prices are constant after a switch to a sales tax, the

consumer price level will rise by the full amount of the sales tax; that is, consumer prices, including

the sales tax, will rise by t percent, where t is the tax-exclusive sales tax rate.

(a) Government spending is tax-exempt

If government spending on goods and services is tax-exempt, the statutory tax base is private

consumption, so the tax revenue equation is 

R1 = t1 C.

Note that t1 is a tax-exclusive rate, so that aggregate consumption expenditure, not including sales

tax payments, is the same as in the pre-sales-tax economy.

The real value of current government spending on goods and services can be maintained with

nominal government spending of G since nominal producer prices are constant and government

spending is not in the tax base. Nominal government spending on transfers rises to (1+ t1 α )T from

T.13 The government provides demogrants that compensate households in aggregate for taxes on

consumption of X. The budgetary cost is t1X. To hold the real deficit constant, the nominal deficit is
14. If the consumer price level rises, the real value of outstanding government debt falls. Allowing the real public debt to be restored to its

pre-sales-tax value would involve running large nominal budget deficits. In principle, this can be thought of as a broader view of what

constitutes "holding real government policy constant." However, in practice, current budgetary rules would forbid enacting a tax policy

that would generate sustained deficits.

17

allowed to rise to (1+t1)D since the consumer price level rose.14 This generates a government budget

constraint of

R1 = G+(1+ t1)T+t1X-(1+t1 α )D.

Combining the tax revenue equation and the budget constraint yields

(2) t1 = R/(C-X- T+D). α

Before discussing this finding, we consider the case where government is taxed.

(c) Government spending is taxed

Adding government spending on goods and services to the tax base, but adjusting the nominal

revenue target to hold real government spending on goods and services constant introduces two

changes, which offset each other exactly. First, the statutory tax base is now given by the sum of

private consumption and government spending on goods and services, so the tax revenue equation is

R2 = t2(C+G).

Second, since government spending is now taxed, to maintain real government spending α

on goods and services, nominal spending must rise by the same percentage as the consumer price

level; that is, it must rise from G to (1+t2)G. All other spending is as in the previous case. The new

government budget constraint is given by

R2 = (1+t2)G + (1+ t2)T + t2X - (1+t2 α )D.

Equating the two formulas for R2 yields

(3) t2 = R/(C-X- T+D). α
18

Several aspects of (3) merit comment. First, t2 = t1; that is, taxing government does not affect

the required sales tax rate if government spending on items other than the sales tax is maintained in

real terms. Second, relative to the first example, the statutory tax base is larger by an amount G,

which raises tax revenues by t2G. However, again relative to the first example, nominal government

spending is higher by an amount t2G, exactly offsetting the impact of a higher tax base on tax rates.

Thus, in comparing an income tax or a flat tax to a sales tax, holding the real value of government

spending constant does not necessarily imply holding nominal revenues constant.

Third, although the statutory tax base includes government spending (G), the effective tax

base not only omits G, but also subtracts from consumption the exempt amount of consumption in

the demogrant and the currently untaxed portion of transfers. G is omitted because to hold real

government spending constant requires an increase in nominal spending that offsets the tax revenues

collected on government spending. Consumption that is financed with demogrants is not part of the

effective tax base because financing the demogrants requires higher tax revenues. Consumption that

is financed with untaxed transfers is not part of the effective tax base because, to retain their real

purchasing power, such transfers must be adjusted the same way as the consumer price level

changes. The effective tax base also includes the pre-sales-tax deficit. The larger the deficit, the

larger the effective tax base and hence the lower the required rate. Smaller deficits (or larger

surpluses) require higher sales tax replacement rates.

Finally, it may be helpful to consider a special case where all transfers are untaxed ( =1), and α

there is no deficit. In that case, the required tax rate is just R/(C-X-T). Thus, even when government
15. Nominal transfers in the pre-sales-tax economy may be divided into untaxed ( T) and taxed ((1- )T) components. To hold these α α

transfers constant in real terms, taxed transfers should change in accordance with the producer price level, and thus should fall to

(1- )T/(1+t3 α α ), while untaxed transfers change in accordance with the consumer price level, and thus remain at T. The sum of these

two components is (1+ t3)T/(1+t3 α ).

19

is included in the statutory tax base, the effective base is only the portion of consumption that is not

financed by untaxed government transfers or demogrants, as long as the size of government is

maintained.

(ii) Nominal wages and producer prices decline

If nominal wages and producer prices decline by the full amount of the removed income tax,

the consumer price level (including the sales tax) would remain constant after switching to a sales tax.

(a) Government spending is tax-exempt 

If government spending is tax-exempt, the tax base is given by private consumption

expenditures. Although the quantity of consumption remains the same after tax reform (by

assumption, since the size of the economy stays the same), private consumption expenditures, not

including the sales tax, would fall by the same proportion as producer prices. Thus, the tax revenue

equation is

R3 = t3C/(1+t3).

To hold real government spending on goods and services constant, nominal government

spending falls by a factor 1/(1+t3) since nominal wages and producer prices decline and government

is not in the tax base. Nominal transfers fall from T to (1+ t3)T/(1+t3).15 α Nominal deficits remain

constant since the consumer price level is constant. Nominal demogrant amounts are given by

X/(1+t3). This generates a government budget constraint of 
20

R3 = G/(1+t3) + t3X/(1+t3) + (1+ t3)T/(1+t3 α ) - D.

Combining the tax revenue equation and the budget constraint yields

(4) t3 = R/(C-X- T+D). α

As before, the effective tax base is consumption less untaxed transfers and demogrants, plus

the deficit.

(d) Government spending is taxed

As before, there are two changes. First, the statutory tax base is expanded to include

government spending on goods and services as well as private consumption, but since wages and

producer prices have fallen, each component is deflated by the factor (1+t4). Thus, the tax revenue

equation is 

R4 = t4(C+G)/(1+t4).

Second, to maintain real government spending on goods and services, nominal government

spending, including the sales tax payments on government spending, is held constant. Transfers, the

demogrant, and the deficit are the same as in the previous example. Thus, the government budget

constraint is given by 

R4 = G + t4X/(1+t4) + (1+ t4)T/(1+t4 α ) - D.

Equating the tax revenue equation and the budget constraint yields:

(5) t4 = R/(C-X- T+D). α

Two aspects of (5) merit comment. First, (4) and (5) show, as before, that the required sales

tax replacement rate does not depend on the inclusion of government in the tax base, as long as the

real size of government is maintained. Second, comparing t3 and t4 to t1 and t2 shows that, in the
21

specification above, the required tax rate also does not depend on whether the producer price level

stays constant or falls.

The latter result depends crucially on the assumption that transfer payments would change

in the same way whether the producer price level falls or is constant. This may not be the most

realistic assumption. After all, if producer prices fall, it may prove difficult for political reasons to

make downward nominal adjustments to taxed transfers such as social security benefits and net

interest payments. Note that if the downward nominal adjustments are not made, the required sales

tax rate rises. Thus, our assumption that the adjustment is made may understate the true replacement

sales tax rate when producer prices fall, but generates the correct formula assuming that the real size

of government is held constant.

III. Application to Sales Tax Proposals

The results above indicate that the formula for computing sales tax replacement rates is given

by 

(5) t4 = R/(C-X- T+D). α

It is worth emphasizing the tax rate in (5) is tax-exclusive. The equivalent tax-inclusive tax rate

would be

(5') t4

I

 = R/{(C-X- T+D)+R}= t4/(1+t4 α ).
22

A. Replacement Rates in the AFT and S-T Proposals

In contrast to the equations above, replacement rates in the S-T and AFT proposals are

calculated, on a tax-exclusive basis, as

(6) s = R/(C-X+G),

and on a tax-inclusive basis as

(6') s I = R/(C-X+G+R) = s/(1+s).

It is straightforward to show that these require reductions in real government spending. Let

the statutory tax base include private consumption and government spending on goods and services,

so that the tax revenue equation is given by 

(7) R* = t* (C+G).

Now, let the government budget constraint be given by

(8) R* = G + T + t*X - D.

Note that G, total nominal government spending on goods and services, includes any sales tax

payments on those purchases.

Solving (7) and (8) for t*

 yields

(9) t* = R/(C-X+G),

the formula used by AFT and S-T to calculate replacement tax rates, and reported in (6).

Now consider the interpretation of these equations. First, suppose that wages and producer

prices stay constant after switching to a sales tax. This implies that consumer prices will rise by the

amount of the sales tax. In that case, the revenue equation (7) is specified appropriately, but (8) does

not hold the real size of government constant. Note that, in (8), total nominal government spending
23

(including the sales tax it pays to itself) on goods and services, transfers and the deficit are held

constant even though the consumer price level has risen and government spending on goods and

services is included in the tax base. Net of sales taxes, this requires real declines in government

spending, transfers, and deficits.

Alternatively, assume that wages and producer prices decline after tax reform. Then (8) is

specified appropriately, but (7) is not. In particular, C and G in (7) should be deflated by 1+t*. Thus,

in either case, the tax rate derived in (6) and (9) would not generate enough revenue to sustain real

government spending, and the specification used by AFT and S-T implies reductions in real

government spending or in the deficit.

Holding the deficit constant, the implied decline in real government spending under existing

sales tax proposals is given by 

(10) G+T - [G/(1+t) + T/(1+t) + (1- )T] = {t/(1+t)} (G + T), αα α

where t is the tax-exclusive sales tax rate. The intuition for this is easiest to see in the case where the

consumer price level rises after the switch to the sales tax and the producer price level remains

constant. In the pre-sales tax-economy, nominal government spending on goods, services, and

transfers is G+T. Under the AFT and S-T plans, nominal government spending on goods and services,

including sales tax payments, and untaxed transfers is fixed; therefore, real outlays on these items fall

by the factor 1/(1+t). Nominal taxed transfers are also fixed, but they retain their original value, since
16. The last statement is approximate, since income tax rates vary across households.

17. Recent government data modify these revenue figures, but the net revenue target is roughly the same. For example, updated NIPA figures

indicate that the taxes AFT would replace raised $1,344 billion in revenues in 1995. In our calculations below, we retain the AFT revenue

target for purposes of comparability.

24

the producer price level is constant and the income tax on such transfers is removed.16 Of course,

if the real deficit were to rise by the amount in (10), the real value of government spending could

remain constant.

Thus, there is a fundamental inconsistency in comparing the AFT and S-T plans to other tax

reform plans or to the existing system. To calculate how high the sales tax rates would need to be,

and to estimate the implied reduction in government under the existing AFT and S-T proposals,

requires estimates for each parameter in the equations above.

B. Parameter Estimates

We develop parameter estimates under two sets of assumptions. The first holds constant the

real value of federal, state, and local government. The second only holds the federal government

constant.

Tax revenues for the taxes to be replaced by the S-T and AFT proposals are shown in table

1. Thus, R is $803 billion for the S-T plan and $1,362 billion for the AFT plan.17

18. To simplify calculations, we use the same tax base for the AFT and the S-T proposals. In practice, the proposed bases differ somewhat

in their treatment of state and local taxes, housing, and tax-exempt organizations, and their calculation of the demogrant. Because the

differences between the proposals largely offset each other in terms of their effects on the size of the tax base, incorporating the differences

would have only small effects on our results.

26

The proposed tax base for the AFT plan is shown in table 2 and summarized below. We

specify the various parameters as follows: 

Private consumption tax base $4,620.0

Less state taxes -238.3

C: Equals net private consumption 4,381.7

X: The demogrant 1,137.1

G: State and local spending 841.7

Federal spending 516.5

Total government purchases 1,358.2

Note that C-X+G add up to $4,602.8, the "AFT tax base" in table 2. Federal, state, and local

spending equals $1,358 billion, raising the tax base by over 40 percent, from $3,244.6 billion to

$4,602.8 billion.18

28

We adjust this tax base, however, because measured government consumption includes the

imputed depreciation on government capital, which should not be taxed under a sales tax. As shown

in the table, depreciation equaled $122.4 billion in 1995; the remaining tax base is $4,480.4 billion.

Government consumption net of depreciation (G*) was $1,235.8 billion for all levels of government,

$448.3 billion for the federal government and $787.5 billion for state and local governments and is

used in the calculations below.

To estimate T, we note that federal transfers to individuals totaled $709.4 billion in 1995 and

state and local transfers totaled $280.6 billion, for total transfers to persons of $990 billion. The

federal government made net interest payments of $224.8 billion, while state and local governments

made net interest payments of -$59.6 billion (that is, they received net interest). Thus, total net

interest payments were $165.2 billion, total transfers were $1,152.7 billion, and total federal transfers

were $934.2 billion (NIPA, Tables 3.1, 3.2, and 3.3). 

Estimating precisely is difficult and we attempt only to provide a rough calculation. The α

following transfers can be subject to federal income taxation: net interest payments ($181.7 billion),

50 percent to 85 percent of social security benefits ($163.8 billion to $278.5 billion), unemployment

insurance ($21.7 billion), federal employee retirement ($67.3 billion), and state and local employee

retirement ($66.3 billion) (NIPA table 3.12). If only 50 percent of social security benefits are subject

to taxation, these transfers total $501 billion in 1995 or 43.5 percent of total transfers, suggesting α

= 0.565. If 85 percent of social security benefits are taxed, taxed benefits equal $616 billion in 1995,

suggesting that = 0.466. α

30

These figures should be raised, however, for two reasons. First, not all taxable transfers are

actually taxed (because of the zero tax rate bracket in the income tax). For example, only about 15

percent of social security benefits are taxed, because benefits are only taxable if other income

exceeds certain thresholds. About two-thirds of net interest payments are taxed, reducing taxable net

interest by $60 billion (Congressional Budget Office (1997b, p. 16).) Thus, only $327 billion, or 28

percent, of transfers would be taxable, suggesting that = 0.72. Likewise, preliminary calculations α

using the Joint Committee on Taxation individual tax model suggest that over three quarters of

transfers are not taxed.

Second, some -- presumably large -- proportion of taxed transfers face the 15 percent rate in

the existing system, which is below the rate that would apply in a national retail sales tax.

Preliminary calculations from the JCT model indicate an average tax rate of roughly 21 percent on

the small minority of transfers that are actually taxed. This is below what would be required in the

AFT proposal, which should raise further. α

Thus, setting = 0.75 may still understate the true value. To provide some sensitivity α

analysis below, we use = 0.50 and = 0.75. Higher values of would generate higher sales αα α

tax replacement rates than reported below.
31

To estimate D, we note that the federal budget deficit measured on a current basis was $174.4

billion in 1995. To this figure, we add federal gross investment ($66.1 billion) and subtract

depreciation of federal capital ($68.2 billion), for a federal cash flow deficit of $172.3 billion. The

corresponding state and local figures are a current surplus of $103.1 billion, gross investment of

$147.4 billion, and depreciation of $54.2 billion, for a cash flow surplus of $9.9 billion. The overall

government cash flow deficit was therefore $162.4 billion (NIPA tables 3.1, 3.2, 3.3, and 3.7).

To hold only federal government constant, we use estimates of G (or G*, as noted), T, and

D based on federal statistics only. State and local spending on goods and services is placed in C --

that is, it is treated just like private consumption. This raises C to $5,169.2 billion. In this case, state

and local transfers are not protected against price changes. For convenience, all of the parameter

values for the two cases are summarized in table 3.

C. Results

Table 4 reports estimates of the implied decline in the real value of government spending

under existing sales tax proposals, holding the real deficit constant. The AFT proposal (using G in

the statutory base) would require a tax-inclusive rate of 22.8 percent using equation (6'), or a

tax-exclusive rate of 29.6 percent using equation (6). Removing government depreciation from the

tax base raises the rates slightly. In either case, however, the proposal would not raise sufficient

revenues to finance existing levels of government. 

33

If = 0.75, (10) implies that the real value of annual federal, state, and local government α

spending on goods and services (G*) and on transfers to persons would fall under the AFT proposal

by about 20 percent, or $483 billion annually. The decline in real federal spending would be about

19 percent, or $264 billion, and the decline in real state and local spending would be about 22

percent, or $219 billion. If = 0.50, these figures are somewhat smaller, as shown in table 4, but α

would still total over $400 billion annually for all levels of government, a 17 percent decline.

Alternatively, the figures above represent the increase in the real deficit that would occur if the real

value of government programs were held constant under the AFT or S-T proposals.

Table 5 uses (5') and (5) to show the tax rate needed to maintain the size of government

programs. If = 0.75, holding federal, state, and local government constant, the AFT proposal α

would require a 34.9 percent tax rate on a tax-inclusive basis or a 53.6 percent rate on a tax-exclusive

basis. Even if is as low as 0.50, the analogous figures are 32.5 percent and 48.1 percent, α

respectively. Thus, maintaining the size of federal, state, and local government would require

tax-inclusive tax rates that are between 10 and 12 percentage points higher than claimed by AFT,

and tax-exclusive tax rates that are between 19 and 24 percentage points higher than the

tax-exclusive rate implied by AFT's claims.

35

If only the size of the federal government is maintained, the required tax-inclusive rates

would be between 26 and 28 percent, and the required tax-exclusive tax rates would be between 36

and 39 percent. Thus, even in this case, which would reduce real state and local spending by over

$200 billion, the AFT proposal significantly understates the required tax rate.

The S-T proposal faces similar problems. It would require a tax-inclusive rate of 14.9 percent

using equation (6'), or a tax-exclusive rate of 17.5 percent using equation (6) and using G in the base.

Using G*, the rates are slightly higher. But at either set of rates, the proposal would not raise

sufficient revenues to finance existing levels of government.

If = 0.75, (10) implies that the real value of annual federal, state, and local government α

spending on goods and services and on transfers to persons would fall under the S-T proposal by

over 13 percent, or $315 billion annually, if the real deficit were held constant. The decline in real

federal spending would be about $172 billion, and the decline in real state and local spending would

be about $143 billion. If = 0.50, these figures are somewhat lower, but still equal about $272 α

billion, or 11 percent of government spending on goods, services and transfers.

If = 0.75, table 5 shows that the S-T proposal would require a 24.0 percent tax-inclusive α

rate or a 31.6 percent tax-exclusive rate, to hold federal, state, and local government constant. Ifα

= 0.50, the S-T proposal would require a 22.1 percent tax-inclusive rate or a 28.4 percent

tax-exclusive rate. Thus, maintaining the size of the government would require tax-inclusive tax rates
19. We use R = $941 billion and C-X = $2,073 billion (from Feenberg, Mitrusi and Poterba 1997), = 0.5 (by assumption), T = α $889

billion (NIPA, tables 3.2 and 3.3), and D = $214 billion (NIPA, table 3.1, 3.7).

36

that are between 7 and 9 percentage points higher than claimed by S-T, and tax-exclusive tax rates

that are between 11 and 14 percentage points higher than implied by S-T's claims.

If only the size of the federal government is maintained, the required tax-inclusive rates

would be between 17 and 19 percent, and the required tax-exclusive tax rates would be between 21

and 23 percent.

Our analysis also applies to the results of Feenberg, Mitrusi, and Poterba (1997). Using 1991

data, they calculate that -- to replace revenues from taxes on personal and corporate income, estates,

and payrolls -- a sales tax with a poverty-level demogrant would require a 45.4 percent tax-exclusive

tax rate. They calculate the replacement sales tax rate as R/(C-X).

Their discussion (pages 56 and 57) makes clear that they are aware of the problems with

placing government in the base and the change in valuation of transfers. Notably, their estimates do

not assume that government purchases are in the effective tax base, which explains why their rate

estimate is so much higher than the analogous AFT estimate of 29.6 percent. However, their estimate

does not account for untaxed transfers or the deficit. Using 1991 data for these items and equation

(5) indicates a tax-exclusive tax rate of 51.1 percent.19 This adjustment is relatively minor, compared

to the tax-exclusive tax rate adjustments required of the AFT and S-T proposals, because Feenberg,

Mitrusi, and Poterba (1997) do not place government spending in the sales tax base.
20. For a comparison of income and consumption tax bases without these simplifying assumptions, see Congressional Budget Office (1997b).

37

IV. Comparisons With Income Tax and Flat Tax

The sales tax replacement rates computed above are derived from data on aggregate tax

revenues and aggregate spending by households and governments. Under an income tax or a flat tax,

the starting point to compute rates is aggregate income earned in the private and government sectors.

In this section, we use the national income accounting relationships between aggregate spending and

aggregate income to show how the replacement sales tax rates compare to the required rates under

an income or flat tax. To focus on the main issues, we set transfers and deficits to zero, so that the

government spending equation is R=G, and we compare taxes with flat rates and no demogrants,

exemptions, or deductions.20 Under these assumptions, the equations above imply that the

tax-exclusive sales tax rate would be 

ts

E

 = R/C,

and the tax-inclusive rate is

ts

I

 = R/(C+R).

For an income tax, let

R = ty

I

 *(W+K)

be the revenue equation, where ty

I

 is the tax-inclusive income tax rate, W is wages, and K is not

capital income. W and K are measured inclusive of the tax payments that households and businesses

have to pay on those incomes. Solving for ty

I

 yields

ty

I

 = G/(W+K) = R/(W+K).
38

Note that the standard aggregate income identity requires that the sum of incomes paid to factors of

production (W+K) equals spending across sectors

W + K = C + (H - ) + G, ∆

where H=gross investment and = depreciation. Then the tax-inclusive income tax rate is ∆

ty

 I = R/(C+H- +G)= R/(C+H- +R), ∆ ∆

since G=R, and the tax-exclusive rate is

ty

E

 = R/(C+H- ). ∆

For the proposed flat tax, all wage income is taxed at the personal level. Gross capital income

is taxed at the business level, and gross investment (not depreciation) is subtracted from total sales

when computing taxable cash flow. Thus, if there are no personal exemptions, the flat tax base is 

W + (K + - H) = C + R. ∆

Note that while it is well-known that the Hall-Rabushka flat tax is a consumption tax, the tax base,

in this formulation, is C+R, not C. This occurs because the flat tax rate -- which is derived here by

starting with the income tax base and making adjustments -- typically inherits the standard income

tax practice of having rates quoted in tax-inclusive terms. The flat tax revenue equation is 

R= tf

I

 (W+K+ -H), where tf

I

 is the tax-inclusive flat tax rate. Solving for tf

I ∆ yields

tf

I

 = R/(W+K+ -H) = R/(C+R). ∆

The tax exclusive rate would be

tf

E

 = R/C.

These comparisons show that, setting the sales tax demogrant and the flat tax exemption equal

to zero, and controlling for the taxes to be replaced and other assumptions like the rate of evasion, the
39

flat tax and sales tax replacement rates are the same, as they ought to be since both tax consumption

in the aggregate. In addition, although both the proposed flat tax and the income tax clearly tax

government, the correct formulas for the tax-exclusive tax rate contain neither R nor G in the

denominator. The correct formula for the tax-inclusive tax rate includes only R or G in the

denominator, not both. This corresponds to the specifications in equations (5) and (5') for the sales

tax. In contrast, equations (6) and (6') show that the AFT and S-T proposals have essentially

double-counted, by including both G and R in the denominator of the tax-inclusive tax rate, and by

including G in the denominator of the tax-exclusive rate.

V. Conclusion

Taxing government in a national retail sales tax would provide consistency with the way

other plans treat government and would eliminate a potential tax advantage for government

production over private production. However, it would not reduce the required tax rate. Analysis of

structural tax reform is subject to two key constraints -- the need to hold the real deficit constant as

well as the need to hold real government programs constant. Holding government constant involves

adjusting government spending to reflect changes in the consumer price level and changes in the

after-tax purchasing power of government transfers. Given these constraints, the sales tax may

require different nominal revenue targets than the flat tax or income tax. This result is not an issue

of consumption versus income taxation, but rather one of taxing via direct or indirect methods. The

same issue would arise in a value added tax, for example.
40

These findings imply that current sales tax proposals contain significant, unstated, reductions

in the real value of government spending, or increases in the real deficit. To avoid these shortfalls,

the retail sales tax would require a significantly higher tax rate than is reported in the proposals

themselves.

We note, also, that the replacement rates reported in this paper adjust the S-T and AFT

proposals only to maintain the real value of government spending. The net effect of making other

plausible adjustments--for example, to allow for nonzero evasion rates, to provide for transition

relief, to account for economic growth, and to account for states changing their income taxes to sales

taxes, etc. -- could raise the required replacement tax rate in a national retail sales tax to significantly

higher levels than those reported here (see Gale 1998b).
41

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