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w o r k i n g
p

9 7 1 2

Simulating U.S. Tax Reform
by David Altig, Alan J. Auerbach,
Laurence J. Kotlikoff, Kent A. Smetters,
and Jan Walliser

FEDERAL RESERVE BANK

OF CLEVELAND

Simulating U.S. Tax Reform

David Altig
Federal Reserve Bank of Cleveland
daltig@clev.frb.org

Alan J. Auerbach
University of California, Berkeley and NBER
auerbach@econ.berkeley.edu

Laurence J. Kotlikoff
Boston University and NBER
kotlikof@bu.edu

Kent A. Smetters
Congressional Budget Office
kents@cbo.gov
and

Jan Walliser
Congressional Budget Office
janw@cbo.gov

September 1997
The views expressed here are those of the authors and do not necessarily reflect those of the
Congressional Budget Office or the Federal Reserve Bank of Cleveland.

Abstract
This paper uses a new large-scale dynamic simulation model to compare the equity, efficiency,
and macroeconomic effects of five alternatives to the current U.S. federal income tax. These
reforms are a proportional income tax, a proportional consumption tax, a flat tax, a flat tax with
transition relief, and a progressive variant of the flat tax called the “X tax.”
The model incorporates intragenerational heterogeneity and kinked budget constraints. It
predicts major macroeconomic gains (including an 11 percent increase in long-run output) from
replacing the federal tax system with a proportional consumption tax. Future middle- and
upper-income classes gain from this policy, but initial older generations are hurt by the policy’s
implicit capital levy. Poor members of current and future generations also lose.
The flat tax, which adds a standard deduction to the consumption tax, makes all members of
future generations better off, but at a cost of halving the economy's long-run output gain and
harming initial older generations. Insulating these older generations through transition relief
further reduces the long-run gains from tax reform. Switching to a proportional income tax
without deductions and exemptions hurts current and future low lifetime earners, but helps
everyone else. It also raises long-run output by over 5 percent. The X tax makes everyone better
off in the long run and also raises long-run output by 7.5 percent. But it harms initial older
generations who bear its implicit wealth tax.

JEL: H20, C68

I. Introduction
Tax reform has been and remains a hot issue, and for good reason. The U.S. tax structure
is a hybrid of income- and consumption-tax provisions that is complex, distortionary, and replete
with tax preferences. The 1997 tax bill introduced further complexity. In so doing, it provided
further impetus for fundamental tax reform.1
As defined here, “Fundamental tax reform” means simplifying and integrating the tax
code. Simplification, in turn, means eliminating most deductions and tax preferences in both the
corporate and personal tax codes. Integration means applying common marginal rates to all
sources of capital income, independent of the point of collection. Fundamental reform also limits
opportunities for tax arbitrage.
Several current tax reform proposals certainly deserve to be called “fundamental.” They
include Hall and Rabushka's (1983, 1995) flat tax, the retail sales tax, and Bradford's (1986) X
tax. The flat tax and the retail sales tax are two alternative ways of taxing consumption. The X
tax also taxes consumption, but places high-wage earners in higher tax brackets than low-wage
earners. Another fundamental reform option is moving to a broad-based, low-rate income tax.

Auerbach and Slemrod (1997) argue that the problems of the 1981 tax reform prompted passage of the
Tax Reform Act of 1986.

This paper uses a computable general equilibrium simulation model to compare the
equity, efficiency, and macroeconomic effects of fundamental tax reform. The model is a
substantially enhanced version of the Auerbach-Kotlikoff (1987) dynamic life-cycle simulation
model.2 The new model follows the lead of Fullerton and Rogers (1993) by incorporating intraas well as intergenerational inequality. Specifically, the model posits 12 different groups within
each cohort, each with its own earnings ability (its own endowment of human capital).
Our new model approximates U.S. fiscal institutions much more closely than its
predecessor. It includes an array of tax-base reductions, a progressive Social Security system,
and a Medicare system. Incorporating tax-base reductions lets us analyze base broadening -- a
key feature of current reform proposals.

It also lets us use actual tax schedules in our

calibration.3 Leaving out these reductions would mean unrealistically low tax rates since the
current income tax base covers only 57 percent of national income.4 The improved modeling of
Social Security and Medicare also matters greatly. Both of these programs materially alter the
intergenerational and intragenerational distributions of welfare.
Like Auerbach and Kotlikoff (1987), but unlike Fullerton and Rogers (1993) who assume
myopic expectations, we compute the economy’s perfect foresight transition path. Given the
2

A similar model, used to consider only steady states, is presented in Altig and Carlstrom (1996).

The Fullerton-Rogers Model, in contrast, assumes that all agents face the same marginal tax rate
independent of income.
4

See CBO (1997).

magnitude of factor-price and tax-rate changes along our simulated transition paths, permitting
agents to think rationally about the future is of great importance. This and other advantages vis a
vis the Fullerton-Rogers model must be set against some disadvantages. Our model has a simpler
production and preference structure than the Fullerton-Rogers model, which features multiple
consumption and capital goods and industry-specific capital income taxation. The removal of
inter-sectoral tax distortions can lead to non trivial changes in relative prices that differentially
affect cohorts and earnings-groups within cohorts due to differences in their preference
structures. This aspect of tax reform also entails efficiency gains, which are omitted in our
analysis.
The model is used to examine five tax reforms. These reforms span the major proposals
now under discussion. Each of the reforms replaces the federal personal and corporate income
taxes, and each is simulated assuming the same growth-adjusted level of government spending
and government debt.5 The reforms are a) a “clean” income tax, b) a “clean” consumption tax, c)
a Hall-Rabushka flat tax, d) a Hall-Rabushka flat tax with transition relief, and e) a Bradford X
tax.
The clean income tax eliminates all personal exemptions and deductions and taxes labor
and capital income at a single proportional rate. The clean consumption tax differs from the
clean income tax except by permitting 100 percent expensing of new investment. This tax is
implemented as a wage tax at the household level and a cash-flow tax on businesses. The flat tax
differs from the clean consumption tax by including a standard deduction against wage income

To be precise, in each tax-reform simulation the levels of government purchases and outstanding debt are
held constant through time when measured in effective units of labor.

and by not taxing the implicit income from housing and consumer durables. The flat tax cum
transition relief permits continued depreciation of old capital (capital in existence as of the
reform). Finally, the X tax combines a progressive wage tax with a business cash-flow tax where
the business cash-flow tax rate equals the highest tax rate applied to wage income.
Each of the reforms broadens the tax base by eliminating tax preferences under the
current federal tax system. This permits a reduction in marginal tax rates on saving and labor
supply. So too does the implicit tax on existing wealth that arises in four of the five proposals.
The tax on existing wealth results from the favorable expensing afforded new capital. This tax
preference for new capital reduces the value of existing capital relative to that of new capital.
The expensing of new capital also effectively eliminates the taxation of capital income at the
margin. The different income and substitution effects arising from these alternative tax reforms
are the key to understanding the paper's results which are summarized as follows:
The clean income tax raises the long-run level of output by over 5 percent. It also
generates sizable increases in the capital stock and the supply of labor. However, the reform hurts
poor cohort members who face low federal income taxation in the current tax system due to its
deductions and exemptions.
The clean consumption tax raises long-run output by almost 11 percent. The income
effect associated with this tax reform reduces the welfare of the initial middle aged and elderly,
but their losses mean more national saving, investment, and utility for most future generations.
However, eliminating the progressivity of the existing tax structure lowers the welfare of the
poorest members of society in the long run by roughly 4 percent.

The flat tax's standard deduction alleviates some of the distributional concerns raised by
the clean income and clean consumption taxes. But this deduction increases the tax rate needed
to satisfy the government's intertemporal budget constraint. Consequently, the long-run output
gain is only 6 percent. Although the flat tax's standard deduction insulates the poor from welfare
losses, it hurts some middle-income groups alive in the early phase of the transition. Its capital
levy also hurts initial high-income elderly cohorts. Those welfare losses must be set against the
welfare gains enjoyed by all groups in the long run.
Adding transition relief to the flat tax limits the welfare losses of initial capital owners.
But this modification of the flat tax reduces aggregate income gains further, with long-run output
now rising by only 3.6 percent. Furthermore, because replacement tax rates must increase to
compensate for the lost revenue associated with transition relief, all but the richest and poorest
lifetime-income groups suffer welfare losses in the long run.
The X tax, which raises long-term output by 7.5 percent, provides no transition relief
from its expensing provisions. It also hits the rich with higher marginal tax rates than the poor.
It is not surprising, then, that the X tax helps those who are poor in the long run by more than it
helps those who are rich. Still, under the X tax there are no long-run losers; even the rich are
better off. The welfare gains for those alive in the long run range from 2 to 3 percent.
Fundamental reform of the US tax system can offer significant economic gains.
However, those gains come at the sacrifice of certain groups. Transition relief and adjustments
that prevent adverse distributional effects therefore mitigate the effects of tax reform on the
economy. That result stems from a model that captures many but not all inefficiencies of the

current tax system. Future research will show whether the addition of intra-sectoral distortions
and compliance costs would alter that finding.

II. The Model
This section provides a general description of the new model and its method of solution.

Demographic Structure
The model's cohorts are distinguished by their dates of birth and their lifetime laborproductivity endowments. Each cohort includes 12 lifetime-earnings groups. Each of these 12
groups has its own initial endowment of human capital and its own pattern of growth in this
endowment over its lifetime. The lifetime-earnings groups also differ with respect to their
bequest preferences. All agents live for 55 periods with certainty (corresponding to adult ages 20
through 75), and each j-type generation is 1+n times larger than its predecessor. At model age
21, each j-type cohort gives birth to a cohort of the same type. Population growth is exogenous,
and each cohort is (1+n)20 larger than its parent cohort.

Preferences and Household Budget Constraints
Each j-type agent who begins her economic life at date t chooses perfect-foresight
consumption paths (c), leisure paths (l), and intergenerational transfers (b) to maximize a
time-separable utility function of the form

1
γ
1
j
1
s,t+s21 ρ
1

U
(1)

j
t

1
s21
j
[ ∑75s=21 β  cs,t+s21
+ αl
1
1
γ
1
1
ρ

1
1
ρ




54
j
j γ
+ β µ b75,t+54
].
1

In (1) á is the utility weight on leisure, ã is the intertemporal elasticity of substitution in the
leisure/consumption composite, and ñ is the intratemporal elasticity of substitution between
consumption and leisure. The parameter ìj is a j-type specific utility weight placed on bequests
left to each child when the agent dies. The term â = 1/(1+ä) where ä is the rate of time
preference, assumed to be the same for all agents.
Letting as,tj be capital holdings for type j agents, of age s, at time t, maximization of (1) is
subject to a sequence of budget constraints given by

K
j
= (1+ r t ) ( a s,tj + g s,t ) + ws,tj ( E s,tj l s,tj ) - cs,tj - ∑ k=1
a s+1,t+1
T k ( B s,tj,k ) Nbs,tj .
j

(2)
l s,tj ≤ E s,tj

where rt is the pretax return to savings, gs,tj are gifts received from parents, Es,tj is the time
endowment, bs,tj denotes bequests made to each of the N = (1+n)20 children, and the functions
Tk(⋅) with tax base Bs,tj,k as an argument determine net tax payments from income sources
k=1,...,K. All taxes are collected at the household level, and the tax system includes both a
personal income tax and a business profits tax.
An individual's earnings ability is an exogenous function of her age, her type, and the
level of labor-augmenting technical progress, which grows at a constant rate ë. We concentrate
7

all skill differences by age and type in an efficiency parameter åsj. Thus, the wage rate for an
agent of type j and age s is ws,tj = åsj wt, where wt is the growth-adjusted real wage at time t. åsj
increases with age to reflect not only the accumulation of human capital, but also technical
progress. To permit balanced growth for our specifications of preferences given the restriction
on leisure shown in equation (2), we assume that technical progress also causes the time
endowment of each successive generation to grow at rate ë.6 Thus, if Es,tj is the endowment of
type j at age s and time t, then Es,tj = (1+ë) Es,t-1j, for all s, t, and j. Notice that the endowment Es,t
j

depends only on an agent's year of birth. Because E grows at rate ë from one cohort to the next,

there will be no underlying trend in wt.
Transfers are received by children, with interest, at the beginning of the period after they
are made by their parents. We restrict all parental transfers to bequests, so that bs,tj = 0, for s ≠ 75,
and gs,tj = 0, for s ≠ 56. In the steady state, therefore, gj = bj, for all j (where we have dropped the
age subscripts for convenience).

The Government
At each time t, the government collects tax revenues and issues debt (Dt+1) which it uses
to finance government purchases of goods and services (Gt) and interest payments on the
inherited stock of debt (Dt). Letting öj be the fraction of j-type agents in each generation, the
government's budget constraint evolves according to

See Auerbach, et al. (1989) for a more complete discussion of this strategy for dealing with balanced

growth.

t
(s21)
12
75
K
∑ k=1
Dt+1 + (1+ n ) ∑ j=1 φ ∑ s=21 (1+ n )
T k ( B s,tj,k ) = G t + (1+ r t ) Dt .
j

(3)

Government expenditures are assumed to be unproductive and generate no utility to
households. The values of Gt and Dt are held fixed per effective worker throughout the transition
path. Any reduction in government outlays resulting from a change in the government's real
interest payments is passed on to households in the form of a lower tax rate.
The model also has a social security system which incorporates Old-Age and Survivors
Insurance (OASI), Disability Insurance (DI), and Medicare's Hospital Insurance (HI). Old-age
benefits are calculated according to the progressive statutory bend-point formula while disability
and Medicare benefits are provided as lump-sum transfers. The OASI payroll tax is set at 9.7
percent and applied to wage income up to a limit of $62,700. HI and DI tax rates are set at 2.9
percent and 1.9 percent respectively. Like the OASI tax, DI contributions apply only to wages
below $62,700. The HI tax, in contrast, is not subject to an earnings ceiling.
Benefits are scaled to reflect spousal and survivor benefits using distributional
information provided in the 1997 OASDI Trustees Report. We set the perceived marginal link
between the OASI contributions and the OASI benefits at 25 percent. The perceived effective
OASI tax rate is, thus, 7.3 percent—75 percent of 9.7 percent.7 Lump-sum HI and DI benefits
are provided on an equal basis to agents above and below age 65, respectively.

See chapter 10 of Auerbach and Kotlikoff (1987) for a more detailed discussion.

Firms and Technology
Aggregate capital (K) and labor (L) are obtained from individual asset and labor supplies
as

t
(s21)
K t = (1+ n ) ∑12j=1 φ ∑75
a s,tj Dt ,
s=21 (1+ n )
j

(4)

and
t
(s21)
ε sj ( E s,tj l s,tj ).
Lt = (1+ n ) ∑12j=1 φ ∑75
s=21 (1+ n )
j

(5)

Output (net of depreciation) is produced by identical competitive firms using a
neoclassical, constant-returns-to-scale production technology.

The aggregate production

technology is the standard Cobb-Douglas form
Y t = AKθt L1t θ ,

(6)

where Yt is aggregate output (national income) and è is capital's share in production.
Some of our experiments assume costly adjustment of the capital stock. These costs are a
simple quadratic function of investment:

(7)

C( I t ) = [1 + 0.5 b( I t / K t )] I t

The competitive pre-tax, pre-expensing rate of return to capital at time t is given by the marginal
product of capital (defined in terms of the capital-labor ratio, ê)

r t = θAκ θt 1 .

(8)

In general, tax systems treat new and existing capital differently. Under the consumption
tax, new capital is permitted immediate expensing, while existing capital receives no such
deduction. Even under the existing income tax, the combined effect of accelerated depreciation
and the lack of inflation-indexing makes the depreciation allowances per unit of existing capital
lower than those given new capital. We model provisions that treat new and existing capital
differently using the mechanism of fractional expensing of new capital, at rate z. That is, we set z
to account for the extent to which new capital faces a lower effective tax rate than does existing
capital (with z=1 under the consumption tax). If ôtK is the time-t marginal tax rate on capital
income (net of expensing) then, given (7), arbitrage between new and existing capital implies
that the latter has a unit value of

q t = (1z t τ tK ) + (1τ tK ) b( I t / K t ),

(9)

assuming that adjustment costs are expensed. Equation (9) equals Tobin's q.
The arbitrage condition arising from profit-maximization implies that the post-tax return
is:

r~t =
(10)

)

+ 0.5 b ( I t / K t ) (1τ tK ) + q t+1 q t
.
qt
2

III. Calibration
Much of our model's parameterization is relatively standard. Exceptions include
earnings-ability profiles and the fiscal structure. We turn first to these elements and then discuss
more familiar preference and technology parameters.

Table 1 summarizes our selected

parameters.

Earnings-Ability Profiles
The growth-adjusted earnings ability profiles in equation (5) are of the form

ε sj = ea0 + a1 s + a2 s
j

(11)

j 2

+ a 3j s3

Values of the a coefficients for j-type groups 1 through 12—in ascending order of lifetime
income—are based on regressions fitted to the University of Michigan's Panel Study of Income
Dynamics, using a strategy similar to that in Fullerton and Rogers (1993). The procedure
involves (i) regressing the log of hourly wages on fixed-effect dummies, cubics in age, and
interactions between age, age-squared, and a set of demographic variables; (ii) using the
estimated coefficients from step (i) to generate predicted lifetime wage profiles; (iii) sorting the
data according to the present-value of implied lifetime income and dividing the sorted data into
the 12 classes according to lifetime-wage income; and (iv) estimating the coefficients of (11)
from the simulated data profiles of each of the 12 groups.
In sorting the data for steps (iii) and (iv), the population was divided into deciles. Groups
1 and 12 comprise the bottom and top 2 percent of lifetime wage income earners, and groups 2

and 11 the remaining 8 percent of the top and bottom deciles. All other groups constitute 10
percent of the population. For example, group 3 is the second decile of lifetime-wage income,
group four the third decile, and so on up to group 10.
The estimated earnings-ability profiles, scaled to include the effects of technical progress,
are shown in Figure 1. A detailed description of the procedure is provided in the Appendix.
Given our benchmark parameterization, peak hourly wages valued in 1996 dollars are $4.00,
$14.70, and $79.50 for individuals in classes 1, 6, and 12, respectively.

More generally,

steady-state annual labor incomes derived from the model's assumptions and from the
endogenous labor supply choices range from $9,000 to $130,000. These calculations include
labor compensation in the form of fringe benefits (discussed below).

Government Spending and Debt
The model includes government purchases of goods and services, government debt, and
distortionary taxes. The level of government purchases, Gt, was chosen so that the benchmark
steady-state ratio of government purchases to national income equals 0.214. The level of
government debt, Dt, was chosen such that the associated real interest payments equal about 3.5
percent of national income in the initial steady state. These values match the corresponding 1996
values for the combined local, state, and federal government in the United States.

The Benchmark Tax System
The benchmark tax system in our initial steady state is designed to approximate the
salient aspects of the 1996 U.S. (federal, state, and local) tax and transfer system. It features a
hybrid tax system (incorporating wage-income, capital-income, and consumption tax elements)
and payroll taxation for the Social Security and Medicare programs. To adjust for tax evasion,
we reduce income taxes by 2.6 percent. This adjustment is consistent with the degree of tax
evasion reported in Slemrod and Bakija (1996).

In the various alternative tax structure

experiments we assume that evasion reduces the post-reform tax base (income net of deductions
and exemptions) by the same percentage as before the reform. Thus, the level of tax evasion falls
when the tax base shrinks.
We approximate the hybrid current U.S. tax system by specifying a progressive
wage-income tax, a flat capital-income tax, a flat state income tax, and a flat consumption tax.

Wage Income Taxation
The wage-income tax structure has four elements: 1) a progressive marginal rate structure
derived from a quadratic approximation to the 1996 federal statutory tax rates for individuals, 2)
a standard deduction of $4000 and exemptions of $5660 (which assumes 1.2 children per agent,
consistent with the model's population growth assumption), 3) Itemized deductions—applied
only when they exceed the amount of the standard deduction—that are a positive linear function
of income estimated from data reported in the Statistics of Income,8 and 4) Earnings-ability
profiles that are scaled up to incorporate pension and fringe components of labor compensation.9

The data used in this estimation was taken from all taxable returns in tax year 1993. The function was

Capital Income Taxation
Following Auerbach (1996), we assume that income from residential capital and nonresidential capital are taxed at flat rates of 6 percent and 26 percent, respectively. Given the
roughly equal amounts of these two forms of capital, the effective federal marginal tax rate on
total capital income is 16 percent. However, this rate applies only to new capital. Existing
capital faces a higher tax rate which, given depreciation schedules, is estimated to be 20 percent.
We model this gap by assuming that all capital income faces a 20 percent tax, but that 20 percent
of new capital may be expensed, thereby generating a 16 percent effective rate on new capital. In
addition to the federal taxation, both capital and wage income are subject to a proportional state
income tax of 3.7 percent.

Consumption Taxation

obtained by regressing deductions exclusive of mortgage interest expense on the midpoints of reported income
ranges. (The deduction of interest expense on home mortgages was included in our calculation of the capital-income
tax rate, as we will subsequently describe.) The regression yielded a coefficient of 0.0755 with an R2 equal to 0.99.
9

Benefits as a function of adjusted gross income were kindly provided by Jane Gravelle of the
Congressional Research Service and Judy Xanthopoulos of the Joint Committee on Taxation, respectively. Based on
this information we regressed total benefits on AGI. The regression yielded a coefficient of 0.11295 with an R2 equal
to 0.99. In defining the wage-tax base, we therefore exempt roughly 11 percent of labor compensation from the base
calculations.

Consumption taxes in the initial steady state reflect two elements of the existing tax
structure. First we impose an 8.8 percent tax on consumption expenditures consistent with
values reported in the National Income and Product Accounts on indirect business and excise
revenues. However, because contributions to both defined benefit and defined contribution
pension plans receive consumption tax treatment, we levy an additional 2.5 percent tax on
household consumption goods expenditures to account for the indirect taxation of labor
compensation in the form of pension benefits (Auerbach 1996). This 2.5 percent tax replaces the
wage tax that otherwise would apply if pension contributions were taxed as income.

Solving the Model
The model is solved with a Gauss-Seidel algorithm. The calculation starts with a guess
for certain key variables and then iterates on those variables until a convergence criterion is met.
The identifying restrictions of the model are used to compute the remaining economic variables
as well as the updates for the iterations. The solution involves several steps and inner loops that
solve for household-level variables before moving to an outer loop which solves for the timepaths of aggregate variables including the capital stock and aggregate labor supply.
The household optimization problem is subject to the constraint that leisure not exceed
the endowment of time (equation (2)). For those households who would violate the constraint,
the model calculates shadow wage rates at which they exactly consume their full-time
endowment.
The household's budget constraint is kinked due to the tax deductions applied against
wage income. A household with wage income below the deduction level faces marginal and
16

average tax rates equal to zero. A household with wage income above the deduction level faces
positive marginal and average tax rates. Due to the discontinuity of the marginal tax rates, it may
be optimal for some households to locate exactly at the kink. Our algorithm deals with this
problem as follows. We identify households that choose to locate at the kink by evaluating their
leisure choice and corresponding wage income above and below the kink. We then calculate a
shadow marginal tax rate from the first-order conditions that puts those households exactly at the
kink. This procedure generates optimal forward-looking leisure and consumption choices for all
periods of life.
The payroll tax ceiling introduces additional complexity by creating a non-convexity in
the budget constraint. For those above the payroll tax ceiling, the marginal tax rate on labor falls
to zero. We evaluate the utility on both sides of the non-convex section and put households on
the side that generates highest utility.
Aggregate variables of the model are solved with a forward-looking algorithm that
iterates on the capital stock and labor supply over the entire transition path. An initial guess is
made for the time-paths of these variables as well as for the shadow wage rates, shadow tax rates,
endogenous tax rates, the payroll tax rate and the Social Security and Medicare wealth levels.
For an initial guess of the time-path of these variables, the model calculates the corresponding
factor prices and forward-looking consumption, asset and leisure choices for all income classes
in each current and future cohort. Shadow wages and shadow taxes are calculated to ensure that
the time endowment and the tax constraints discussed above are satisfied.

Households’ labor

supply and assets are then aggregated by both age and lifetime income class at each period in
time. This aggregation generates a new guess for the time-paths of the capital stock and labor
17

supply. The tax rate which is endogenous for the particular simulation, is updated to meet the
revenue-neutrality requirement. The payroll tax is also updated to preserve the pay-as-you-go
financing of Social Security and Medicare benefits.10 The algorithm then iterates until the capital
stock and labor supply time-paths each converge.

The Benchmark Equilibrium
Choices for the remaining technology, preference, and demographic parameters are
summarized in Table 1. The benchmark values for ä, ã, ñ, and n are those in Auerbach and
Kotlikoff (1987). The parameter á is chosen so that agents devote, on average, about 40 percent
of their available time endowment (of 16 hours per day) to labor during their prime working
years (real-life ages of roughly 21-55). The parameters ì j are chosen to match bequests as a
fraction of income in the initial steady state based on estimates by Menchik and David (1982)
reported in Fullerton and Rogers (1993). Summary statistics for the initial steady state are
provided in Table 2.
Given our parameter choices, the model generates a pre-tax, pre-expensing interest rate of
9.3 percent, a net national saving rate of 5.3 percent, and a capital/national-income ratio of 2.6.
Consumption accounts for 73.4 percent of national income, net investment for 5.2 percent, and
government purchases of goods and services for 21.4 percent. These figures are close to their
respective 1996 NIPA values.

Note that the Social Security replacement rate and absolute level of Medicare benefits are exogenous.

The calibrated model's initial economy-wide average marginal tax rate on wage income is
21.4 percent, close to the figure obtained from the NBER's TAXSIM model reported in Auerbach
(1996). The average wage-income tax rate equals 12.1 percent. For all individuals in the highest
lifetime income class (group 12), the average effective marginal tax rate on labor income is 28.6
percent. The highest realized effective marginal tax rate is 34 percent. For lifetime income class
6—whose members have peak labor earnings of about $35,000—the average tax rate and average
marginal tax rate are 10.6 and 20.0 percent, respectively. For the poorest class (group 1), the
corresponding rates are zero and 5.5 percent.11

IV. Tax-Reform Experiments
The various tax-reform experiments were described in the introduction and are
summarized in Table 3.

Except for the indicated changes to federal income taxes, each

experiment leaves the elements of the benchmark tax structure intact. In all of the experiments,
we take 1996 as our initial steady state, consistent with our chosen initial tax schedules and tax
bases. This section abstracts from capital-stock adjustment costs (that is, we set b=0 in (7)).

The average marginal rate for people with the lowest income exceeds zero due to positive shadow tax
rates in peak earnings years.

A Clean Income Tax
Our first experiment replaces the progressive taxation of wage income with a single rate
that is also applied to capital income. In addition, the clean income tax eliminates the major
federal tax-base reductions including the standard deduction, personal and dependent
exemptions, itemized deductions, the deductibility of state income taxes at the federal level, and
preferential tax treatment of fringe benefits.

The latter is implemented by decreasing the

consumption tax rate by 0.025 and subjecting all compensation to the new proportional income
tax. The investment expensing rate remains at its initial 20 percent level.
Aggregate results from the clean income-tax reform are summarized in Table 4. The
marginal tax rates required to satisfy the government's budget constraint are close to 13 percent
over the entire transition path. This value lies below both the 21.4 percent average marginal rate
applied to labor income and the 16 percent rate applied to capital income in the benchmark
steady state. National income rises by 4.5 percent immediately and by 5.4 percent ultimately. In
the early years of the transition, these output changes are dominated by increased work effort
associated with the lower marginal tax rates. In the long run, higher wealth levels mitigate some
of the increase in labor supply.

However, the accumulated effects on saving from lower

capital-income rates more than compensate for the lower labor supply: In the long run the capital
stock increases by just over 7.5 percent.

The short-run decrease in the capital-labor ratio

produces the short-run increase in the before-tax interest rate and short-run decrease in before-tax
wage rate. The long-run increase in the capital-labor ratio produces the long-run reversal of these
variables. The effect of this tax reform on the value of stock market (measured via Tobin's q) is
small because the level of expensing has not changed and the effective tax rate on capital income
20

has decreased only slightly (housing capital is no longer exempt).
Figure 2 shows the effects of the tax reform on remaining lifetime utility for different
generations by lifetime-income group. For ease of exposition, the figure reports the utility gains
only for classes 1, 3, 6, 9 and 12. The horizontal axis of the figure measures the period of birth
for the relevant generation relative to the period of the regime shift (period 1). For example, 0
refers to the generation born just prior to the regime shift, 1 to the generation born in the period
of the shift, 2 in the following period , and so on. The change in remaining lifetime utility is
measured as the equivalent variation of remaining full lifetime income. In interpreting these
numbers, one should keep in mind that full lifetime income includes the value of leisure. Full
lifetime income, in our model, is more than twice the size of remaining actual lifetime earnings.
Hence, the utility gains or losses for any cohort will tend to be larger in magnitude if measured
relative to either realized earnings or relative to consumption.
In the long run, only members of lifetime-income groups 7 through 12 benefit from the
clean income-tax reform, the rise in aggregate output notwithstanding. The main reason is that
average tax rates increase for income classes 1 through 6 due to the loss of deductions and
exemptions. In the short run, however, all agents who are 50 years (real age 70) and older at the
time of the reform benefit slightly since the reform increases the after-tax return to capital.

A Clean Consumption Tax
Our clean consumption tax differs from the clean income tax by including full expensing
of investment expenditures. This produces a consumption-tax structure. Formally, we specify
the system as a combination of a labor-income tax and a business cash-flow tax. Table 5
summarizes aggregate effects. The clean consumption tax produces the equivalent of a one-time
tax on the existing capital stock. It does so by lowering the value of the existing capital stock
relative to new capital, as reflected in the large drop in q.
The wealth effects for holders of old capital associated with the drop in q work in
combination with lower marginal tax rates to bring about a substantial increase in aggregate
short-run labor supply. In the period just after the tax reform, labor supply increases by almost
8.5 percent. At the same time, the saving rate responds strongly to the capital levy and to the
removal of the capital-income tax on marginal investment. The saving rate rises immediately
from 5.3 percent to near 10 percent. As the initial negative wealth effects and labor supply
responses diminish over time, the accelerated capital accumulation leads to higher levels of
output. The saving rate eventually recedes to 6.2 percent. Five years after the reform, the capital
stock (per effective unit of labor) is more than 10 percent higher than its initial steady state value,
and output is 8 percent higher. In the long run, the capital stock exceeds its initial value by 31.1
percent, and output its initial value by almost 11 percent.

The strong response of output and labor income from the shift to consumption taxation
allows the replacement tax rate to fall over time. The initial replacement tax rate is 14 percent,
which is higher than any of the rates associated with the clean income tax. However, in the long
run, the consumption-tax rate falls to 12.5 percent, which is slightly lower than the long-run rate
for the clean income tax.
Figure 3 shows that, despite the large aggregate income gains, lower lifetime-income
groups are hurt by the reform. Although these losses are not as large as those in the clean
income-tax case—indeed, several groups switch from being long-run utility losers to long-run
utility winners—the regressive nature of the outcomes persists.

Figure 3 also reveals the

substantial welfare loss for the owners of old capital. The loss is larger for richer agents who
own the larger share of the capital stock. The exception to this finding are the poorest agents
(group 1) of age 45 and above (real-age 65 and above). Their welfare gains can be explained by
two factors. First, this group consumes almost entirely out of social security, which is protected
from the change in asset values. Second, the poorest borrow against some of their social security
benefits earlier in life and their slightly negative net worth shrinks due to the policy-induced fall
in the value of existing capital.

The Flat Tax
Our flat tax experiment modifies the clean consumption tax by including a standard
deduction of $9500. In addition, housing wealth, which equals about half of the capital stock, is
entirely exempt from taxation. The levy on housing wealth under the consumption tax played a
large role in explaining the sharp jump in the short-run labor supply. Exempting housing from
taxation is an important modification, however, because it is unlikely that policy makers would
seriously consider taxing housing.
Table 6 reports aggregate results. The need to finance the standard deduction and tax
sheltering of old housing capital increases the replacement tax rates above those of the clean
consumption tax. As a result, the output effects under the flat tax are reduced relative to its
proportional counterpart.

The long-run rise in the capital stock and level of output are,

respectively, only 68 and 56 percent as large as those under the clean consumption tax. The labor
supply response is lower as well, reflecting both the higher short- and long-run levels of marginal
tax rates and the much smaller wealth effect on labor supply that results from protecting the
existing housing stock from the cash flow tax.12 The revenue-neutral flat-tax rate equals 22
percent initially and reaches 19.4 percent in the long run. However, it takes 10 years for the tax
rate to fall below 21 percent and another 11 years for the tax rate to fall below 20 percent.
The flat tax generates long-run utility gains across-the-board. Interestingly, the highest
relative gains are for the richest and poorest lifetime-income groups. The utility changes for the
richest and poorest lifetime-income groups also differ from those of the middle groups

This latter effect can be seen by the less dramatic decline in the value of q.

throughout the entire transition path. Group 12 benefits most from reduced marginal and average
tax rates. Group 1, which pays very little taxes under either regime, benefits from the overall
increase in wages. For those in income groups 3 through 9, the marginal and average tax rates
initially change little or even rise. This stems from the revenue neutrality of the experiment
which requires a flat-tax marginal rate that initially exceeds the pre-reform tax rates for some
agents in the middle-income classes in order to finance the lower tax rates at the top end. Those
who belong to the lifetime middle-income range and enter the workforce close to the time of
reform suffer utility losses along the transition path. They face relatively high tax rates of 20 to
22 percent on labor income for 20 to 25 years of their working life before the growth of the
capital stock becomes fully effective. Once the economy grows, though, tax rates fall and wages
rise, which raises the lifetime utility levels of groups 3 through 9.
Neither the macroeconomic variables nor the welfare results of the flat tax experiment are
influenced by the existence of a joy-of-giving bequest motive. We repeated the simulation by
turning off bequests (setting the utility bequest weight ì j = 0 for all j) and found no significant
differences in the initial steady-state computations nor in the post-reform changes in output or
welfare.13

The results for this experiment, available from the authors, are not reported.

Flat Tax with Transition Relief
Our fourth experiment adds transition relief to the flat tax by extending pre-reform
depreciation rules for capital in place at the time of the tax reform. Since the present value of
depreciation allowances equals roughly 50 percent of the current capital stock, transition relief is
modeled by cutting the effective cash-flow tax rate in half.
As seen in Table 7, all of the salutary long-run aggregate effects of the standard flat tax
are mitigated by the introduction of transition relief. Still, the capital stock increases by over 15
percent in the long run, affording a 3.5 percent rise in the long-run level of output. Labor supply
changes little following this tax reform, and then actually declines below its initial steady-state
level, reflecting both higher marginal tax rates (on average) and smaller wealth effects.
Figure 5 shows that transition relief leads to smaller short-run welfare losses for current
wealth holders but at the cost of smaller welfare gains for future generations. The provision of
transition relief actually reinforces the utility losses for the mid-range lifetime-income groups
along the transition path, turns positive gains for some individuals in the no-transition-relief case
to losses, and reduces the utility gains for those groups for whom positive welfare effects remain.

The X tax
Bradford's X tax, using the present-law standard deduction, maintains the progressivity of
the present-law wage tax schedule but raises the levy on old capital by setting the cash flow tax
rate

to the highest marginal tax rate applied to labor income—in this case, 30 percent—along with
full expensing of new investment.14 The large wealth levy allows the elimination of capital
income from the tax base and the protection of housing wealth (which reduces the effective cashflow tax rate to 15 percent). Nonetheless, as shown in Table 8, this reform still produces large
long-run output gains despite maintaining progressive wage taxation.

Only the clean

consumption tax generates larger long-run output gains.
The long-run welfare effects of the X tax are quite progressive. As shown in Figure 6, the
long-run gains vary inversely with lifetime income. Over the short run, those who are older and
belong to the highest income class at the time of the reform suffer the largest welfare loss,
reaching almost 7 percent of remaining lifetime utility since they hold the largest amount of real
assets. The
poorest elderly, on the other hand, actually benefit from the capital levy since they live essentially
on their social security benefits which are, in fact, a source of a slight amount of borrowing.

Recall that marginal wage-tax rates are a linear function of taxable labor income. The adjustments
required to maintain budget balance are implemented by changing the intercept of this function, while holding the
slope constant.

We repeated this simulation with a flat replacement wage tax while maintaining the
present-law deduction. The cash-flow tax on capital income was held fixed at 30 percent in
order to capture the effects of only flattening the wage tax.15 We found an increase in national
income relative to the standard X tax (9.4 percent versus 7.5 percent) along with an increase in
the long-run utility levels for all the top half of the income classes along with smaller increases
for the bottom half. Agents born into income groups 3 - 5 around the time of the reform (year 1),
however, incur a slightly smaller increase in their lifetime utility under this reform relative to the
standard X tax (about a 0.1 percent decline). The long-run distribution of welfare gains however
becomes less progressive with class 12 being the biggest winner, followed by classes 1, 9, 6, and
3.

V. Some Sensitivity Analysis
This section considers three alternative parameterizations of the standard (no transition
relief) flat-tax reform. In the first simulation, we introduce investment adjustment costs. In the
second simulation, we consider a smaller intertemporal elasticity of substitution. In the third
simulation, we reduce the intratemporal elasticity of substitution. For each case, we recalibrate
the initial steady state by changing either the pure rate of time preference or the utility-weight on
leisure.

The recalibration is required to start from a steady state with the same essential

characteristics. The specifics of these changes are indicated in Table 9. The simulation results
are reported in Tables 10-12 and Figures 7-9. Each of these changes reduces the degree to which

The results for this experiment, available from the authors, are not reported.

agents react to changes in incentives, thereby dampening the macroeconomic impact of the tax
reform.
The importance of wealth effects is reinforced once again in the adjustment cost
experiment (Table 10; Figure 7). Because the presence of investment adjustment costs makes
new capital relatively less attractive, q does not drop as much following the introduction of full
expensing as in the benchmark scenario without such costs. This cuts the initial labor supply
response almost in half and leads to less growth in the capital stock in the long run.
The experiment with a smaller intratemporal elasticity of substitution looks quite similar
to the flat-tax case under our benchmark parameterization in the early stages of the transition
path (Table 11; Figure 8). However, in the long run, the decreased willingness to substitute
higher consumption for leisure results in a decline in aggregate labor supply. Nevertheless, due
to the sizable increase in the capital stock, the real-wage growth is as large as in the original
flat-tax experiment.
Finally, a smaller intertemporal elasticity of substitution makes people less willing to
reallocate consumption and leisure to different time periods after a change in wages and interest
rates (Table 12; Figure 9). As a consequence, the one-time capital levy and the corresponding
lower taxes on other factor income are less effective in inducing higher saving and labor supply
immediately after the reform and lead to less long-run capital accumulation and labor supply.
Notice that the smaller expansion of output in the case with adjustment costs and a lower
intertemporal elasticity of substitution transforms the long-run welfare gains for the groups with
middle incomes into long-run welfare losses.

VI. Concluding Remarks
Proponents and opponents of fundamental tax reform wrestle with the same question: Are
the gains to the winners worth the costs to the losers? This paper does not answer such questions.
But it does try to give both sides a better basis for their answers. The paper's method is to
simulate a much-improved version of the Auerbach-Kotlikoff model—one that considers intraas well as intergenerational equity and one that is closely calibrated to U.S. fiscal institutions and
tax policy.
The model predicts significant long-run macroeconomic gains, including an 11 percent
increase in output, from replacing the current U.S. federal tax system with a proportional
consumption tax. For middle- and upper-income classes alive in the long run, this policy is a big
winner. But older transition generations suffer from the imposition of an implicit capital levy,
and low-income individuals, even in the long run, suffer a loss equal to about 4 percent of their
full lifetime resources as growth fails to compensate for the decline in tax progressivity.
The flat tax, which modifies the basic consumption tax by exempting housing wealth
from taxation and by providing a large wage-tax deduction, makes all long-run cohort members
better off, but at a cost of nearly halving the economy's long-run output gain, from 11 percent to
6 percent. Even then, this reform leaves initial older generations worse off. Insulating these
generations with transition relief, in the form of maintaining present-law depreciation allowances
on existing capital, reduces the long-run output gain still further to 3.6 percent.
Other reforms produce similar tradeoffs. Switching to a clean proportional income tax is
a loser for current and future low lifetime earners but a winner for everyone else. It also raises
30

long-run output by over 5 percent. The X tax, which combines consumption-tax and progressive
wage-tax elements, makes everyone better off in the long run and also raises output by 7.5
percent. But this reform harms initial older generations who face an implicit tax on their wealth.
To conclude, fundamental reform of the current U.S. tax structure offers the possibility of
significant macroeconomic gains, but not without true sacrifice by certain groups. Adjustments
that attempt to prevent adverse distributional effects yield much more modest aggregate effects.
This, at least, is the view from a model that captures many, but certainly not all, of the
inefficiencies of the current system. Expanding the current model to incorporate inter-asset and
inter-sectoral tax distortions as well as enforcement and compliance costs could well alter this
view, but that task remains for future research.

References
Altig, David, and Charles T. Carlstrom, “Marginal Tax Rates and Income Inequality in a LifeCycle Model,” Working Paper, Federal Reserve Bank of Cleveland, June 1996.
Auerbach, Alan J., “Tax Reform, Capital Accumulation, Efficiency, and Growth,” in: Henry J.
Aaron and William G. Gale, eds., Economic Effects of Fundamental Tax Reform, The Brookings
Institution: Washington, D.C., 1996.
Auerbach, Alan J. and Laurence J. Kotlikoff, Dynamic Fiscal Policy, Cambridge University
Press: Cambridge, 1987.
Auerbach, Alan J., Laurence J. Kotlikoff, Robert P. Hagemann, and Giuseppe Nicoletti, “The
Economic Dynamics of an Ageing Population: The Case of Four OECD Countries,” OECD
Economic Studies, Spring 1989, 51-96.
Auerbach, Alan J. and Joel Slemrod, “The Economic Effects of the Tax Reform Act of 1986,”
Journal of Economic Literature, June 1997.
Bradford, David, Untangling the Income Tax, Harvard University Press: Cambridge, MA, 1986.
Congressional Budget Office, Comparing Income and Consumption Tax Bases, CBO Paper, July,
1997.
Fullerton, Don and Diane Lim Rogers, Who Bears the Lifetime Tax Burden? The Brookings
Institution: Washington, D.C., 1993.
Hall, Robert E. and Alvin Rabushka, The Flat Tax, Hoover Institution Press: Stanford, 1983.
Hall, Robert E. and Alvin Rabushka, The Flat Tax, 2nd edition, Hoover Institution Press:
Stanford, 1995.
Menchik, Paul L. and Martin David, “The Incidence of a Lifetime Consumption Tax.” National
Tax Journal, 35, 1982, 189-203.
Slemrod, Joel and Jon Bakija, Taxing Ourselves: A Citizen's Guide to the Great Debate over Tax
Reform, MIT Press: Cambridge, MA, 1996.

Table 1.
Symbol

Benchmark Parameter Definitions and Values
Definition

PREFERENCES
Utility weight on leisure
á
Rate of time preference
ä
Intertemporal substitution elasticity
ã
j
Utility weight placed on bequests by income class j
ì
Intratemporal substitution elasticity
ñ
HUMAN CAPITAL
j
Productivity of agent in income class j at age s.
DEMOGRAPHICS
n
Population growth
N
Number of children per adult, (1+n)20
Fraction of agents of income class j
öj

Value

1.00
0.015
0.25
[1]

0.80

[2]

0.01
1.22
[3]

TECHNOLOGY
Technological change
ë
b
Adjustment cost parameter
Net capital share
è
DEBT, TAXES, DEDUCTIONS IN INITIAL STEADY STATE
—
Debt service as fraction of National Income
—
Disability Insurance tax rate
—
Medicare (HI) tax rate
—
Social Security (OASI) tax rate
—
Social Security replacement rate
—
Social Security marginal tax-benefit linkage
—
Payroll tax ceiling
Proportional consumption tax
ôC
K
Proportional capital income tax
ô
W
Progressive wage tax with deductions and exemptions
ô (⋅)
Y
State proportional income tax less evasion adjustment
ô
—
Reduction of wage base from itemized deductions
—
Reduction of wage base from fringe benefits
z
Expensing[7]

0.01
0.00
0.25

0.0350
0.0190
0.0290
0.0970
[4]

0.25
$62,700
0.113
0.20
[5]

0.011
0.0755[6]
0.1129[6]
0.20

Footnotes:
[1] Calibrated endogenously in the initial state to match the level of bequests—as a fraction of mean
national income—in Fullerton and Rogers (1993, Table 3-8), in 1996 dollars.
[2] See Appendix for estimation procedure.
[3] ö1=0.02, ö2=0.08, öi=0.10 (3≤i≤10), ö11=0.08, ö12=0.02
[4] The statutory progressive bendpoint formula for 1996, scaled up by a factor of 2 to account for the fact
that other non-DI benefits (mainly spousal and survivors benefits) account for 50% of all benefits paid (see
1996 OASDI Trustees Report, Table II.C7).
[5] The 1996 statutory tax function for a single individual with a deduction equal to $9661 ($4,000
standard deduction, $2,550 personal exemption and $2,550⋅N exemption for dependents).
[6] Total proportional base reduction above the standard deduction therefore equals 0.18845.

[7] Deductions for new investment above economic depreciation and adjustment costs.

Table 2.

Key Endogenous Equilibrium Values for the Initial Steady State and the
Corresponding Empirical Values
Model

Concept

Empirical Estimate and Calculation
Value

Estimate Calculation (using NIPA unless indicated)

COMPOSITION OF NATIONAL INCOME (PERCENT)
Personal Consumption

0.734

0.720 Personal consumption expenditures - housing services

Net Saving Rate

0.053

0.056 (National saving - capital consumption allowance)/NI

Government Purchases

0.214

0.212 Consumption expenditures + gross investment for
federal (defense and nondefense) and state and local consumption of fixed capital

TAX RATES AND GOVERNMENT REVENUE
Avg. Marginal Wage Tax[1]

0.214

0.217 Auerbach (1996) based on the NBER TAXSIM
model.

Government Revenue

0.239

0.239 Total receipts - contributions for social insurance property taxes (state and local)

OASDHI Tax

0.145

0.147 1996 tax rate is 15.3 which includes trust fund
contributions equal to about 0.6.

CAPITAL-OUTPUT RATIO AND BEFORE-TAX INTEREST RATE
Capital-Income Ratio

2.564

2.660 1993 current-cost net stock of fixed reproducible
wealth in the Survey of Consumer Finance - gov't
owned fixed capital / 1993 National Income

Before-Tax Rate of Return[3]

0.097

0.093 The 1960-1994 average of the sum of interest,
dividends, retained earnings and all corporate taxes
divided by the replacement value of capital stock
(Rippe, 1995).

Footnotes:
[1] Does not include the payroll tax.
[2] The social marginal rate of return (i.e., before corporate taxes).

Table 3.

Key Elements of Tax Reform Experiments

Experiment

Description

"Clean" Income Tax

Eliminate all Tax Base Reductions
Eliminate the standard deduction, personal exemption,
exemptions for dependents, itemized deductions,
preferential tax treatment of all fringe benefits (the
consumption tax treatment of pension and the deductibility
of non-pension benefits), and the deductibility of state
income taxes at the federal level.[1]
Flattening of Tax Rates
Replace progressive wage tax and proportional capital
income tax with a proportional equal tax rate on wage and
capital income. Eliminate double taxation of capital income.

"Clean" Consumption Tax

Eliminate all Tax Base Reductions
Flattening of Tax Rates
Full Expensing
Allow the deductibility of all new investment.

Flat Tax (Standard)

Eliminate all Tax Base Reductions
Flattening of Tax Rates
Full Expensing
Protection of Housing Wealth
Housing (including consumer durables) remain untaxed.[2]
Standard Deduction
Allow for a deduction for a single individual equal to
$9,500.

Flat Tax (Transition Relief)

Eliminate all Tax Base Reductions
Flattening of Tax Rates
Full Expensing
Protection of Housing Wealth
Standard Deduction
Transition Relief
All existing assets continue to receive depreciation
allowances.[3]

X Tax

Eliminate all Tax Base Reductions
Preserve Current-Law Progressive Wage Tax[4]
Capital Income Tax Set at Highest Marginal Wage Tax Rate
Full Expensing
Protection of Housing Wealth[5]

Footnotes:
[1] The consumption tax treatment of pensions is eliminated by decreasing the consumption tax by 0.025 and subjecting all
compensation to the new proportional income tax.
[2] About 50% of the capital stock is composed of housing and consumer durables which will not be taxed. Hence, the
proportional tax rate on capital income is set to 1/2 of the tax rate on wage income.
[3] As noted in Auerbach (1996, footnote 46), the current-law (with current inflation) present value of remaining depreciation
allowances per dollar of net nonresidential capital is approximately half the value of the assets. Allowing for these
depreciation allowances has the same impact as forgiving half of the cash-flow tax on existing assets. Hence, the cash flow tax
on capital income is set to 1/4 of the replacement proportional wage tax rate.
[4] General equilibrium effects and the constant government revenue constraint requires proportional shifts in the wage tax
schedule (with an increase in the short run and a decrease in the long run). The average marginal tax rate is reported in Table
8.
[5] Since the highest marginal wage tax rate in the final steady state equals about 0.30, the capital income tax is set equal to
0.15.

Table 4.

"Clean" Flat Income Tax
1996

Composition of National Income
Consumption[1] +
0.734

1997

1998

1999

2000

2001

2002

2003

2004

2005

2010

2025

2055

2145

0.762

0.764

0.765

0.767

0.768

0.769

0.771

0.772

0.773

0.778

0.784

0.785

0.053

0.069

0.068

0.067

0.066

0.065

0.064

0.063

0.061

0.056

0.214

1.000

1.045

1.046

1.047

1.048

1.049

1.050

1.051

1.053

1.054

1.055

1.054

Capital Stock, Labor Supply and Total Labor Income
Capital Stock[2]
1.000
1.006
1.012

1.018

1.024

1.029

1.034

1.038

1.042

1.046

1.060

1.075

1.076

[1]

Net Investment

Government[1] =
[2]

National Income

[2]

1.000

1.058

1.057

1.056

1.055

1.054

1.053

1.051

1.048

[2]

1.000

1.045

1.046

1.047

1.049

1.050

1.053

1.055

0.053

0.066

0.065

0.064

0.063

0.062

0.061

0.060

0.058

0.054

0.053

Factor Prices: Wage Rate and Interest Rates
Before-Tax Wage[2]
1.000
0.988

0.989

0.991

0.992

0.994

0.995

0.996

0.997

0.998

1.002

1.006

1.007

Labor Supply

Labor Income

Net Saving Rate
Net Saving Rate

[3]

After-Tax Wage

0.775

0.827

0.828

0.831

0.832

0.834

0.835

0.836

0.837

0.838

0.843

0.847

0.848

Before-Tax Rate of Return

0.097

0.101

0.100

0.099

0.098

0.097

0.096

0.095

0.096

After-Tax Rate of Return

0.080

0.087

0.086

0.085

0.084

0.083

Unified Government Debt
Debt[2]

1.000

0.999

1.000

Dynamic Replacement Income Tax Rate
Tax Rate[4]
n/a
0.133

0.132

0.131

0.130

0.129

0.128

Tax Revenue and the Endogenous OASDI-HI Payroll Tax
Revenue[5]
0.239
0.240
0.240
0.240

0.239

0.238

Payroll Tax Rate

0.147

0.141

0.142

0.143

0.144

Tobin's Q
Normalized Tobin's Q

1.000

1.009

1.010

1.011

1.010

Footnotes:
[1] The components of national income (NI) sum to income (i.e., they are not percentages of NI except, of course, for year 1996 when NI = 1.0).
[2] These variables grow without bound along the balanced-path equilibrium and are represented per-effective labor unit. Hence, they remain constant in the baseline steady state. These variables are indexed with a
baseline value of 1.00 in 1996.
[3] The After-Tax Wage rate is computed as (1-ô)⋅(Before-Tax Wage) where ô is the economy-wide effective average marginal tax rate on wage income.
[4] Statutory rate, post evasion. Effective rate is about 0.01 smaller due to evasion. Cash flow on capital income also equals this value.
[5] Percent of National Income.

Table 5.

"Clean" Consumption Tax
1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2010

2025

2055

2145

Composition of National Income
Consumption[1] +
0.734
0.053
Net Investment[1] +
0.214
Government[1] =
1.000
National Income[2]

0.744
0.103
0.214
1.061

0.746
0.110
0.214
1.069

0.750
0.110
0.214
1.074

0.756
0.109
0.214
1.078

0.761
0.106
0.214
1.081

0.765
0.104
0.214
1.083

0.770
0.102
0.214
1.086

0.774
0.100
0.214
1.088

0.778
0.098
0.214
1.090

0.794
0.090
0.214
1.098

0.817
0.076
0.214
1.107

0.823
0.072
0.214
1.109

0.824
0.071
0.214
1.109

Capital Stock, Labor Supply and Total Labor Income
Capital Stock[2]
1.000
1.023
1.045
[2]
1.000
1.084
1.076
Labor Supply
[2]
1.000
1.069
1.068
Labor Income

1.065
1.072
1.070

1.084
1.069
1.073

1.102
1.067
1.076

1.119
1.065
1.078

1.134
1.064
1.081

1.148
1.062
1.083

1.162
1.061
1.085

1.216
1.056
1.094

1.289
1.048
1.103

1.311
1.045
1.106

Net Saving Rate
Net Saving Rate

0.053

0.098

0.103

0.101

0.098

0.096

0.094

0.092

0.090

0.082

0.069

0.065

0.064

Factor Prices: Wage Rate and Interest Rates
Before-Tax Wage[2]
1.000
0.986
0.775
0.818
After-Tax Wage[3]
Before-Tax Rate of Return
0.097
0.102
After-Tax Rate of Return
0.080
0.102

0.993
0.817
0.100
0.100

0.998
0.821
0.098
0.098

1.003
0.826
0.096
0.096

1.008
0.831
0.095
0.095

1.012
0.836
0.094
0.094

1.016
0.841
0.093
0.093

1.020
0.846
0.092
0.092

1.023
0.850
0.091
0.091

1.036
0.866
0.088
0.088

1.053
0.888
0.083
0.083

1.058
0.894
0.082
0.082

Unified Government Debt
Debt[2]

1.000

0.999

1.000

Dynamic Replacement Income Tax Rate and Static Replacement Income Tax Rate
Tax Rate[4]
n/a
0.140
0.147
0.148
0.147
0.145

0.144

0.142

0.141

0.139

0.134

0.127

0.125

Tax Revenue and the Endogeous OASDI-HI Payroll Tax
Revenue[5]
0.239
0.233
0.242
Payroll Tax Rate
0.147
0.138
0.138

0.244
0.138

0.243
0.138

0.242
0.138

0.240
0.139

0.238
0.140

0.238
0.141

Tobin's Q
Normalized Tobin's Q

0.858

0.859

0.861

0.862

0.864

0.865

0.867

0.873

0.880

0.882

1.000

0.866

0.859

Table 6.

Flat Tax (Standard)
1996

Composition of National Income
Consumption[1] +
0.734

1997

1998

1999

2000

2001

2002

2003

2004

2005

2010

2025

2055

2145

0.723

0.724

0.727

0.731

0.734

0.737

0.740

0.743

0.745

0.756

0.773

0.781

0.782

0.053

0.086

0.087

0.085

0.083

0.082

0.081

0.080

0.077

0.070

0.066

0.214

1.000

1.023

1.025

1.028

1.030

1.033

1.035

1.036

1.038

1.040

1.047

1.057

1.061

Capital Stock, Labor Supply and Total Labor Income
Capital Stock[2]
1.000
1.019
1.033

1.045

1.056

1.066

1.076

1.085

1.093

1.101

1.135

1.187

1.212

1.215

[1]

Net Investment

Government[1] =
[2]

National Income

[2]

1.000

1.030

1.020

1.018

1.017

1.016

1.015

1.013

1.012

[2]

1.000

1.027

1.023

1.024

1.026

1.029

1.031

1.033

1.035

1.036

1.044

1.054

1.059

0.053

0.084

0.085

0.084

0.083

0.082

0.081

0.080

0.078

0.077

0.073

0.066

0.062

Factor Prices: Wage Rate and Interest Rates
Before-Tax Wage[2]
1.000
0.997

1.003

1.006

1.009

1.012

1.014

1.016

1.018

1.020

1.028

1.040

1.046

1.047

Labor Supply

Labor Income

Net Saving Rate
Net Saving Rate

[3]

After-Tax Wage

0.775

0.754

0.751

0.753

0.757

0.761

0.764

0.767

0.770

0.773

0.785

0.803

0.811

0.813

Before-Tax Rate of Return

0.097

0.098

0.097

0.096

0.095

0.094

0.093

0.092

0.090

0.087

0.085

After-Tax Rate of Return

0.080

0.098

0.097

0.096

0.095

0.094

0.093

0.092

0.090

0.087

0.085

Unified Government Debt
Debt[2]

1.000

Dynamic Replacement Income Tax Rate
Tax Rate[4]
n/a
0.214

0.221

0.220

0.218

0.217

0.215

0.214

0.212

0.207

0.198

0.194

Tax Revenue and the Endogenous OASDI-HI Payroll Tax
Revenue[5]
0.239
0.235
0.241
0.242

0.242

0.241

0.240

0.238

Payroll Tax Rate

0.147

0.144

0.145

0.144

0.143

Tobin's Q
Normalized Tobin's Q

1.000

0.901

0.897

0.898

0.899

0.900

0.901

0.902

0.905

0.909

0.911

Footnotes:
[1] The components of national income (NI) sum to income (i.e., they are not percentages of NI except, of course, for year 1996 when NI = 1.0).
[2] These variables grow without bound along the balanced-path equilibrium and are represented per-effective labor unit. Hence, they remain constant in the baseline steady state. These variables are indexed with a
baseline value of 1.00 in 1996.
[3] The After-Tax Wage rate is computed as (1-ô)⋅(Before-Tax Wage) where ô is the economy-wide effective average marginal tax rate on wage income.
[4] Statutory rate, post evasion. Effective rate is about 0.01 smaller due to evasion. Cash flow on capital income equals half of this value.
[5] Percent of National Income.

Table 7.

Flat Tax (Transition Relief)
1996

Composition of National Income
Consumption[1] +
0.734

1997

1998

1999

2000

2001

2002

2003

2004

2005

2010

2025

2055

2145

0.715

0.717

0.720

0.722

0.725

0.727

0.729

0.731

0.733

0.741

0.754

0.759

0.761

0.053

0.076

0.075

0.074

0.073

0.072

0.071

0.068

0.064

0.062

0.061

0.214

1.000

1.005

1.006

1.008

1.010

1.012

1.013

1.015

1.016

1.018

1.023

1.032

1.036

Capital Stock, Labor Supply and Total Labor Income
Capital Stock[2]
1.000
1.014
1.023

1.031

1.038

1.045

1.051

1.057

1.063

1.068

1.091

1.129

1.151

1.153

[1]

Net Investment

Government[1] =
[2]

National Income

[2]

1.000

1.003

0.999

1.000

0.998

[2]

1.000

1.006

1.005

1.007

1.009

1.010

1.012

1.013

1.015

1.016

1.022

1.031

1.034

1.035

0.053

0.076

0.075

0.074

0.073

0.072

0.071

0.070

0.069

0.067

0.062

0.060

0.059

1.006

1.008

1.010

1.011

1.013

1.014

1.016

1.017

1.022

1.031

1.036

1.037

Labor Supply

Labor Income

Net Saving Rate
Net Saving Rate

Factor Prices: Wage Rate and Interest Rates
Before-Tax Wage[2]
1.000
1.003
[3]

After-Tax Wage

0.775

0.731

0.730

0.733

0.736

0.738

0.741

0.743

0.745

0.747

0.755

0.769

0.776

0.778

Before-Tax Rate of
Return

0.097

0.096

0.095

0.094

0.093

0.091

0.089

0.088

0.087

After-Tax Rate of Return

0.080

0.097

0.096

0.095

0.094

0.093

0.091

0.089

0.088

0.087

Unified Government Debt
Debt[2]

1.000

Dynamic Replacement Income Tax Rate
Tax Rate[4]
n/a
0.242

0.244

0.243

0.242

0.240

0.239

0.238

0.236

0.235

0.231

0.224

0.221

0.220

Tax Revenue and the Endogenous OASDI-HI Payroll Tax
Revenue[5]
0.239
0.238
0.240
0.240

0.240

0.239

0.238

0.237

Payroll Tax Rate

0.147

0.146

0.145

0.144

0.145

Tobin's Q
Normalized Tobin's Q

1.000

0.950

0.949

0.950

0.951

0.952

0.954

0.955

Footnotes:
[1] The components of national income (NI) sum to income (i.e., they are not percentages of NI except, of course, for year 1996 when NI = 1.0).
[2] These variables grow without bound along the balanced-path equilibrium and are represented per-effective labor unit. Hence, they remain constant in the baseline steady state. These variables are indexed with a
baseline value of 1.00 in 1996.
[3] The After-Tax Wage rate is computed as (1-ô)⋅(Before-Tax Wage) where ô is the economy-wide effective average marginal tax rate on wage income.
[4] Statutory rate, post evasion. Effective rate is about 0.01 smaller due to evasion. Cash flow on capital income equals one-fourth of this value. [5] Percent of National Income.

Table 8.

X Tax
1996

Composition of National Income
Consumption[1] +
0.734

1997

1998

1999

2000

2001

2002

2003

2004

2005

2010

2025

2055

2145

0.714

0.719

0.723

0.726

0.730

0.733

0.736

0.739

0.742

0.753

0.774

0.786

0.789

0.053

0.093

0.092

0.091

0.090

0.089

0.088

0.087

0.084

0.078

0.074

0.073

0.214

1.000

1.021

1.024

1.027

1.031

1.033

1.035

1.038

1.040

1.042

1.051

1.065

1.074

1.075

Capital Stock, Labor Supply and Total Labor Income
Capital Stock[2]
1.000
1.031
1.043

1.055

1.066

1.076

1.086

1.096

1.105

1.114

1.151

1.220

1.262

1.272

[1]

Net Investment

Government[1] =
[2]

National Income

[2]

1.000

1.012

1.013

1.014

1.013

1.012

[2]

1.000

1.017

1.020

1.022

1.026

1.028

1.032

1.033

1.036

1.038

1.046

1.061

1.070

1.072

0.053

0.091

0.090

0.089

0.088

0.087

0.086

0.085

0.084

0.083

0.080

0.073

0.069

0.068

1.008

1.010

1.013

1.015

1.018

1.020

1.022

1.024

1.032

1.047

1.057

1.059

Labor Supply

Labor Income

Net Saving Rate
Net Saving Rate

Factor Prices: Wage Rate and Interest Rates
Before-Tax Wage[2]
1.000
1.005
[3]

After-Tax Wage

0.775

0.766

0.771

0.775

0.780

0.784

0.788

0.791

0.795

0.799

0.812

0.836

0.851

0.855

Before-Tax Rate of
Return

0.097

0.096

0.095

0.094

0.093

0.092

0.091

0.088

0.085

0.082

After-Tax Rate of Return

0.080

0.096

0.095

0.094

0.093

0.092

0.091

0.088

0.085

0.082

Unified Government Debt
Debt[2]

1.000

Dynamic Replacement Income Tax Rate
Tax Rate[4]
0.214
0.208

0.205

0.203

0.200

0.198

0.196

0.194

0.192

0.190

0.183

0.171

0.165

0.163

Tax Revenue and the Endogeous OASDI-HI Payroll Tax
Revenue[5]
0.239
0.244
0.243
0.243

0.243

0.242

0.241

0.239

0.238

Payroll Tax Rate

0.147

0.145

0.144

0.143

0.142

Tobin's Q
Normalized Tobin's Q

1.000

0.856

Footnotes:
[1] The components of national income (NI) sum to income (i.e., they are not percentages of NI except, of course, for year 1996 when NI = 1.0).
[2] These variables grow without bound along the balanced-path equilibrium and are represented per-effective labor unit. Hence, they remain constant in the baseline steady state. These variables are indexed with a
baseline value of 1.00 in 1996.
[3] The After-Tax Wage rate is computed as (1-ô)⋅(Before-Tax Wage) where ô is the economy-wide effective average marginal tax rate on wage income.
[4] Not proportional for the X tax. The value shown equals the economy-wide effective average marginal tax rate on wage income which is also reported in this table for the initial steady
state. Statutory rate, post evasion. Effective rate is about 0.01 smaller due to evasion. Cash flow on capital income equals 0.15. [5] Percent of National Income.

Table 9.

Sensitivity Analysis for Hall-Rabushka (Standard)

Related Parameter Changed
Table/
Figure

Calibration
Parameter[1]

Paramet
er

From

To Purpose

10 / 7

0.00

11 / 8

0.80

0.40 Reduce the intratemporal elasticity

12 / 9

0.25

0.10 Reduce the intertemporal elasticity

10.00 Introduce adjustment costs

Footnotes:
[1] Parameter that is adjusted in order to target the same capital-output ratio in the initial steady state.

Table 10.

Flat Tax (Standard) with Adjustment Costs
1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2010

2025

2055

2145

Composition of National Income
Consumption[1] +
0.733

0.729

0.730

0.732

0.733

0.734

0.736

0.737

0.738

0.744

0.755

0.765

0.770

Net Investment[1] +

0.050

0.062

0.063

0.064

0.063

0.062

0.061

0.060

0.059

Government[1] =

0.218

National Income[2]

1.000

1.009

1.010

1.012

1.013

1.014

1.016

1.017

1.018

1.019

1.024

1.034

1.042

1.047

Capital Stock, Labor Supply and Total Labor Income
Capital Stock[2]
1.000
1.006
1.011

1.016

1.021

1.025

1.030

1.034

1.038

1.042

1.059

1.096

1.131

1.150

Labor Supply[2]

1.000

1.016

1.014

1.013

1.012

1.013

Labor Income[2]

1.000

1.013

1.014

1.015

1.017

1.018

1.019

1.020

1.024

1.034

1.041

1.045

Net Saving Rate
Net Saving Rate

0.050

0.062

0.063

0.062

0.061

0.059

0.057

0.056

Factor Prices: Wage Rate and Interest Rates
Before-Tax Wage[2]
1.000
0.997

0.999

1.001

1.002

1.003

1.004

1.005

1.006

1.007

1.011

1.020

1.028

1.032

After-Tax Wage[3]

0.775

0.754

0.753

0.754

0.755

0.756

0.758

0.759

0.760

0.762

0.767

0.780

0.791

0.796

Before-Tax Rate of

0.083

0.076

0.078

0.079

0.078

0.077

0.080

After-Tax Rate of Return

0.059

0.062

0.063

0.064

0.063

0.066

Unified Government Debt
Debt[2]

1.000

1.001

1.000

0.999

1.000

Return

Dynamic Replacement Income Tax Rate
n/a
0.214
Tax Rate[4]

0.217

0.216

0.215

0.214

0.211

0.206

0.201

0.199

Tax Revenue and the Endogenous OASDI-HI Payroll Tax
Revenue[5]
0.239
0.237
0.239
0.240

0.240

0.239

0.238

Payroll Tax Rate

0.146

0.145

0.146

0.145

0.144

Tobin's Q
Normalized Tobin's Q

1.000

0.964

0.965

0.964

0.963

0.962

0.961

0.958

0.951

0.944

0.941

Footnotes:
[1] The components of national income (NI) sum to income (i.e., they are not percentages of NI except, of course, for year 1996 when NI = 1.0).
[2] These variables grow without bound along the balanced-path equilibrium and are represented per-effective labor unit. Hence, they remain constant in the baseline steady state. These variables are indexed with a
baseline value of 1.00 in 1996.
[3] The After-Tax Wage rate is computed as (1-ô)⋅(Before-Tax Wage) where ô is the economy-wide effective average marginal tax rate on wage income.
[4] Statutory rate, post evasion. Effective rate is about 0.01 smaller due to evasion. Cash flow on capital income equals half of this value.
[5] Percent of National Income.

Table 11.

Flat Tax (Standard): Low Intratemporal Substitution Elasticity (ñ=0.40)
1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2010

2025

2055

2145

Composition of National Income
Consumption[1] +
0.738

0.726

0.728

0.730

0.733

0.735

0.737

0.739

0.741

0.743

0.750

0.761

0.765

0.766

Net Investment[1] +

0.053

0.086

0.088

0.087

0.085

0.084

0.083

0.081

0.080

0.079

0.075

0.068

0.065

Government[1] =

0.210

National Income[2]

1.000

1.022

1.025

1.027

1.028

1.029

1.030

1.031

1.032

1.035

1.038

1.040

Capital Stock, Labor Supply and Total Labor Income
Capital Stock[2]
1.000
1.018
1.032

1.044

1.055

1.066

1.075

1.084

1.092

1.099

1.130

1.174

1.190

1.196

Labor Supply[2]

1.000

1.029

1.021

1.017

1.015

1.013

1.011

1.009

1.008

1.007

1.001

0.993

0.991

0.990

Labor Income[2]

1.000

1.026

1.024

1.025

1.026

1.027

1.028

1.029

1.032

1.036

1.038

Net Saving Rate
Net Saving Rate

0.053

0.085

0.086

0.084

0.083

0.082

0.080

0.079

0.078

0.077

0.072

0.065

0.063

Factor Prices: Wage Rate and Interest Rates
Before-Tax Wage[2]
1.000
0.997

1.003

1.007

1.010

1.013

1.015

1.018

1.020

1.022

1.031

1.043

1.047

1.048

After-Tax Wage[3]

0.775

0.755

0.753

0.755

0.759

0.762

0.765

0.769

0.771

0.774

0.785

0.801

0.806

0.807

Before-Tax Rate of

0.097

0.098

0.096

0.095

0.094

0.093

0.092

0.091

0.089

0.085

0.084

After-Tax Rate of Return

0.080

0.098

0.096

0.095

0.094

0.093

0.092

0.091

0.089

0.085

0.084

Unified Government Debt
Debt[2]

1.000

Return

Dynamic Replacement Income Tax Rate
n/a
0.213
Tax Rate[4]

0.220

0.219

0.218

0.216

0.215

0.214

0.213

0.209

0.203

0.201

0.200

Tax Revenue and the Endogenous OASDI-HI Payroll Tax
Revenue[5]
0.235
0.231
0.236
0.238

0.238

0.237

0.236

0.235

0.234

0.233

Payroll Tax Rate

0.151

0.148

0.149

0.148

Tobin's Q
Normalized Tobin's Q

1.000

0.902

0.898

0.899

0.900

0.901

0.902

0.904

0.907

0.908

Footnotes:
[1] The components of national income (NI) sum to income (i.e., they are not percentages of NI except, of course, for year 1996 when NI = 1.0).
[2] These variables grow without bound along the balanced-path equilibrium and are represented per-effective labor unit. Hence, they remain constant in the baseline steady state. These variables are indexed with a
baseline value of 1.00 in 1996.
[3] The After-Tax Wage rate is computed as (1-ô)⋅(Before-Tax Wage) where ô is the economy-wide effective average marginal tax rate on wage income.
[4] Statutory rate, post evasion. Effective rate is about 0.01 smaller due to evasion. Cash flow on capital income equals half of this value.
[5] Percent of National Income.

Table 12.

Flat Tax (Standard): Low Intertemporal Substitution Elasticity (ã=0.10)
1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2010

2025

2055

2145

Composition of National Income
Consumption[1] +
0.734

0.729

0.728

0.729

0.730

0.732

0.733

0.734

0.735

0.736

0.741

0.751

0.755

0.758

Net Investment[1] +

0.053

0.065

0.068

0.067

0.066

0.064

0.062

0.061

Government[1] =

0.214

National Income[2]

1.000

1.009

1.010

1.011

1.012

1.013

1.014

1.015

1.016

1.020

1.026

1.030

1.032

Capital Stock, Labor Supply and Total Labor Income
Capital Stock[2]
1.000
1.010
1.016

1.021

1.025

1.029

1.033

1.036

1.040

1.043

1.056

1.079

1.097

1.105

Labor Supply[2]

1.000

1.013

1.005

1.003

1.002

1.003

1.004

1.006

1.005

Labor Income[2]

1.000

1.012

1.008

1.007

1.008

1.009

1.010

1.011

1.012

1.013

1.017

1.024

1.027

1.029

Net Saving Rate
Net Saving Rate

0.053

0.065

0.067

0.066

0.065

0.063

0.061

0.059

Factor Prices: Wage Rate and Interest Rates
Before-Tax Wage[2]
1.000
0.999

1.003

1.004

1.006

1.007

1.008

1.009

1.010

1.013

1.018

1.022

1.024

After-Tax Wage[3]

0.775

0.756

0.751

0.750

0.752

0.753

0.754

0.755

0.757

0.758

0.763

0.772

0.778

0.781

Before-Tax Rate of

0.097

0.096

0.095

0.094

0.092

0.091

After-Tax Rate of Return

0.080

0.097

0.096

0.095

0.094

0.092

0.091

Unified Government Debt
Debt[2]

1.000

Return

Dynamic Replacement Income Tax Rate
n/a
0.213
Tax Rate[4]

0.221

0.223

0.222

0.221

0.220

0.219

0.217

0.212

0.209

0.208

Tax Revenue and the Endogenous OASDI-HI Payroll Tax
Revenue[5]
0.239
0.234
0.240
0.242

0.242

0.241

0.240

Payroll Tax Rate

0.147

0.146

0.145

Tobin's Q
Normalized Tobin's Q

1.000

0.902

0.897

0.898

0.900

0.902

0.904

Footnotes:
[1] The components of national income (NI) sum to income (i.e., they are not percentages of NI except, of course, for year 1996 when NI = 1.0).
[2] These variables grow without bound along the balanced-path equilibrium and are represented per-effective labor unit. Hence, they remain constant in the baseline steady state. These variables are indexed with a
baseline value of 1.00 in 1996.
[3] The After-Tax Wage rate is computed as (1-ô)⋅(Before-Tax Wage) where ô is the economy-wide effective average marginal tax rate on wage income.
[4] Statutory rate, post evasion. Effective rate is about 0.01 smaller due to evasion. Cash flow on capital income equals half of this value.
[5] Percent of National Income.

Appendix: Calculation of Earnings-Ability Profiles
Our earnings-ability profiles are based on the individual files of the University of
Michigan's Panel Study of Income Dynamics from 1976-1988. These calculations generally
follow those of Fullerton and Rogers (1993).
The sample utilized contains 9335 observations on 891 individuals. Excluded were
individuals with imputed real hourly earnings of less than one dollar and those with clear
inconsistencies in levels of educational attainment over the time period. This sample differs
from that used by Fullerton and Rogers, who (1) aggregate individual observations into
household observations and (2) consider only households with stable marital histories.
The following procedure was used to obtain the profiles shown in Figure 1.
(i) First stage regressions were run on the entire data set using a common set of
explanatory variables. The specification is identical to that used by Fullerton and Rogers except a

w$it = α i + α 1 BY i + α 2 Ait + α 3 Ait2 + α 4 Ait3 + α 5 Ait E it +

∑3h=1 α i+5 Ait Dith + α 9 Ait2 E it + ∑3h=1 α i+9 Ait2 Dith + ε it
birth-year variable, which is added to control for age-cohort effects. It is given by
where
w$is = the log of the real hourly wage for person i in time t,
ái = fixed effect for person i,
Yi = the birth year of person i,
Ait = the age of person i in time t,
Eit = the education level (in years) of person i in time t,
Dit = dummy variable for the marital status of person i in time t,

Dit2 = dummy variable for the (constant) race of person i,
Dit3 = dummy variable for the (constant) sex of person i.
The resulting coefficient estimates are reported in Table A1.
(ii) The coefficient estimates obtained from step (i) were used to construct simulated
life-cycle wage profiles for each individual from age 21 through 80. Unlike Fullerton and Rogers,
we do not splice wage observations from the PSID with predicted values in generating the
profiles. Instead we simply use predicted values for all wage observations. In constructing the
profiles we set education to the highest reported level and assume that marital status is constant
and equal to married if the individual is married at any time over the PSID sample period.
(iii) Lifetime wage income (LI) levels are imputed from the profiles generated in step (ii)

(s21)
80
( w$is • 4000)
LI i = ∑ s=21 (1+ r )

according to the formula
where the discount rate r is set to 8 percent, w$is is the predicted wage of the individual at age s,
and 4000 is the potential full-time endowment of work hours. This calculation follows Fullerton
and Rogers, except for the choice of r.
All observations were next sorted in ascending order of lifetime wage income, and
divided into the twelve groups described in the text. Following the text and letting ãj be the
fraction of the population in group j, our division yields ãj = 0.02 for j = 1 and 12, ãj =0.08 for j
=2 and 11, and ãj = 0.1 for j = 3 through 10.
(iv) Finally, regressions of the predicted wage observations on a common group intercept

j
2
3
w$isj = a0j + a1j Aisj + a 2 ( Aisj ) + a 3j ( Aisj ) + ζ is .

and a cubic in age were run for each group:
The estimated coefficients from these regressions are reported in Table A2. Figure 1's profiles are

based on these estimates adjusted for annual efficiency growth of one percent.

Table A1: PSID Regression Results
Variable
Birth Year (BY)

Coefficient

T statistic

-0.0005

1.47

0.0883

3.46

Age-Squared

-0.0016

3.20

Age-Cubed

6.66E-6

2.07

Age x Education (A D1)

-0.0009

2.02

Age x Marital Status (A D2)

0.0081

3.37

Age x Race (A D3)

0.0119

2.81

Age x Sex (A D4)

0.0339

1.69

Age-Squared x Education ((A)2 D1)

2.16E-5

3.30

Age-Squared x Marital Status ((A)2 D2)

-0.0001

2.84

Age-Squared x Race ((A)2 D3)

-0.0002

2.70

Age-Squared x Sex ((A)2 D4)

-0.0004

2.00

0.9779

—

Age (A)

Adjusted R2

Table A2: Estimated Coefficients for Wage Profiles by Lifetime Income (LI) Group
LI Group

Intercept

Age

AgeSquared

Age-Cubed

-0.6421

0.0949

-0.0016

7E-06

-0.2294

0.0941

-0.0016

7E-06

0.1831

0.0929

-0.0016

7E-06

0.4693

0.0907

-0.0016

7E-06

0.6772

0.0882

-0.0015

7E-06

0.8865

0.0853

-0.0015

7E-06

0.9794

0.0884

-0.0015

7E-06

1.1606

0.0864

-0.0015

7E-06

1.3180

0.0855

-0.0015

7E-06

1.4814

0.0862

-0.0015

7E-06

1.8151

0.0856

-0.0015

7E-06

2.5745

0.0853

-0.0015

7E-06

Full text of Working Paper (Federal Reserve Bank of Cleveland) : Simulating U.S. Tax Reform, Working Paper 97-12

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