Technical Paper Series

Congressional Budget Office

Washington, DC

Analyzing Tax Policy Changes Using a Stochastic

OLG Model with Heterogeneous Households

Shinichi Nishiyama

Congressional Budget Office

Washington, DC

E-mail: shinichi.nishiyama@cbo.gov

December 2003

2003-12

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

critical comment. These papers are not subject to CBO’s formal review and editing processes.

The analysis and conclusions expressed in them are those of the authors and should not be interpreted as those of the Congressional Budget Office. References in publications should be cleared

with the authors. Papers in this series can be obtained at www.cbo.gov (select Publications and

then Technical Papers).
Abstract

This paper describes a stochastic overlapping generations (OLG) model with heterogeneous agents, which is one of five models used at the Congressional Budget Office for recent

fiscal policy analyses. In this model economy, households are heterogeneous with respect

to their age, wealth holding, working ability, and working history, and households face individual shocks to their ability to earn income every year. The paper also explains the choice

of parameters, the characteristics of the baseline economy, and the features of the model

through policy experiments under several different assumptions. The solution algorithm is

also shown in the Appendix.

Journal of Economic Literature Classification Numbers: D9, H3, H6.

Key Words: overlapping generations; dynamic general equilibrium.

Helpful comments and suggestions were received from Robert Dennis and Douglas Hamilton.
1 Introduction

This paper describes a stochastic overlapping generations (OLG) model, which is one of

five macroeconomic models used in “An Analysis of the President’s Budgetary Proposals for

Fiscal Year 2004” (Congressional Budget Office, 2003a) and for several other fiscal policy

analyses at the Congressional Budget Office (CBO).1

The model is a life-cycle general equilibrium growth model, in which households are

heterogeneous with respect to their ages, working abilities (measured by hourly wages),

wealth holdings, and earnings histories (which determine their Social Security benefits). A

household is assumed to be a married couple with some children. Every year, a large number

of households with parents aged 20 enter the model economy. At the beginning of each year,

households below age 80 receive idiosyncratic working ability shocks (which follow a firstorder Markov process). There are 8 distinct working ability levels for each age below 80. At

the end of each age, a fraction of households die, according to the mortality rate of each age.

Households can live at most 110 years, that is, the mortality rate at the end of age 109 is one.

Each household (with different age, working ability, wealth holding, and earnings history) chooses its optimal consumption, labor supply (working hours), and savings, taking

current and future factor prices (such as the interest rate and wage rate) and policy variables

(such as marginal income tax rates) as given. Households in the model are forward looking

and have model-consistent expectations of future factor prices and policy variables. Because

there are no aggregate shocks in the model, households have perfect foresight about those

future factor prices and policy variables. Yet, they still do not know their own future working

ability and mortality.

The utility function of a household is a combination of Cobb-Douglas and constant relative risk aversion (CRRA). Government consumption is not included in the utility function,

so it is assumed to have no value. However, this assumption is not as restrictive as it may

first appear. One could interpret simulations that cut lump-sum transfers as also illustrating

the economic effects of cutting government consumption that is valued by consumers and

viewed as a perfect substitute for private goods. Thus, the model can be used to illustrate

1

The other four macroeconomic models used at CBO are a Solow growth model, an infinite-horizon (Ramsey)

growth model, the Global Insight model, and the Macroeconomic Advisers model.

1
polar views about the value of government consumption.

The model has a representative (but perfectly-competitive) firm with Cobb-Douglas production technology. Regarding the openness of the economy, the model assumes two polar

cases—a closed economy and a small open economy. In a closed economy, no international

capital flow is assumed, and trade surplus (deficit) is assumed to be zero. The interest rate

and the wage rate are determined by domestic capital stock (which is equal to the sum of

total private wealth and net government wealth) and labor supply. In a small open economy,

a perfectly flexible international capital flow is assumed. The interest rate and the wage rate

are fixed at their international levels. Domestic capital stock is determined by the labor supply of the economy, and the difference between domestic capital and national wealth (the

sum of private wealth and net government wealth) is filled up by international capital inflow

(or outflow).

The model includes progressive federal income tax, flat state income tax, a payroll tax,

and OASDI benefits calibrated to those of the United States. For federal income tax, the

statutory marginal tax rates are modified by two adjustment factors so that the effective tax

rates on labor income and capital income are roughly the same as those in the U.S. economy.

In the model, no intergenerational altruism is assumed. All of the bequests in the model

are accidental, due to uncertain life span. For simplicity, the wealth left by the deceased

households are collected and distributed to the working-age households (ages 20 to 64) in

a lump-sum manner. Each working-age households expect rationally the future accidental

inheritances when it makes a decision on consumption, labor supply, and savings.

To illustrate the properties of the model, this paper examines the economic effects of

cutting all federal individual income tax rates by 10 percent. Because the model imposes the

government’s intertemporal budget constraint, the tax cut must eventually be financed by either cutting spending or raising taxes. The paper explores five alternative assumptions about

financing. Two of the alternatives assume that the tax cut is financed contemporaneously

by reducing government consumption or lump-sum transfers. Under those assumptions, the

policy experiment is budget neutral. The remaining three financing alternatives assume that

the tax cut is deficit financed for 10 years. After that, the simulations assume that the government gradually adjusts fiscal policy so that the debt-output ratio is stabilized in 20 years.

2
The policy adjustments involve one of three changes: reducing the government consumption,

cutting transfers, or raising individual income tax rates.

The rest of the paper is laid out as follows: Section 2 describes the model, Section

3 explains the calibration of the model, Section 4 shows the results of cutting individual

income tax rates by 10 percent, Appendix A explains the algorithm of computing equilibria,

and Appendix B shows the detailed results of the policy experiments in Section 4.

2 Model

The model is a standard general equilibrium growth model with uninsurable idiosyncratic shocks (also known as Bewley model), which is similar to the models in Aiyagari

(1994), Huggett (1996), and many others. The present model is also an extension of those in

Nishiyama (2002) and Nishiyama and Smetters (2003).2

The economy consists of three sectors: heterogeneous households with elastic labor supply; a perfectly competitive representative firm with constant-returns-to-scale production

technology; and a government with a full commitment technology. Time is discrete, and

a period of the model corresponds to a year.

2.1 The Household Sector

Households are heterogeneous with respect to ages i, working abilities ei (measured by

their hourly wages), beginning-of-period wealth holdings ai, and average historical earnings

bi that determine their Social Security benefits. Every year, a large number (normalized to

unity) of new households of age 20 enter into the economy. The population of this economy

grows at a constant rate of ν. A household of age i observes an idiosyncratic working ability

shock, ei, at the beginning of each year and chooses its optimal consumption ci, working

hours hi, and end-of-period wealth holding ai+1, taking the government’s policy rule and

series of factor prices and the government’s policy variables as given.3 At the end of each

year, a fraction of households die based on the mortality tables. The model assumes that no

2

The model is also influenced by Auerbach and Kotlikoff (1987) in many aspects. 3

Because there are no aggregate shocks in the present model, households can perfectly foresee these factor

prices and policy variables, using the current distribution of households and the current policy variables. Yet,

their own future working ability and mortality are uncertain.

3
one lives longer than 110 years. For simplicity, all households are assumed to be two-earner

married couples of the same age.

2.1.1 The Household’s Problem

Let si denote the state of an age i household,

si = (i, ei, ai, bi), (1)

where i ∈ I = {20, ..., 109} is the household’s age, ei ∈ E = [emin, emax] is its working

ability (measured by hourly wage), ai ∈ A = [amin, amax] is its beginning-of-period wealth,

and bi ∈ B = [bmin, bmax] is its average historical earnings.4 Let St denote the state of the

economy at the beginning of year t,

St = (xt (si),WG,t), (2)

where xt (si) is the joint distribution of households with si ∈ I × E × A × B, and WG,t

is the beginning-of-period net government’s wealth. Let Ψt denote a series of government

policy rules known at the beginning of year t,

5

Ψt = {WG,s+1, CG,s, trLS,s, τI,s (.), τP,s (.), trSS,s (.)}∞

s=t , (3)

where CG,s is government’s consumption, trLS,s is lump-sum transfers (lump-sum tax if negative), τI,s (.) is an income tax function, τP,s (.) is a payroll tax function for Social Security,

and trSS,s (.) is a Social Security benefit function.6

4

The average historical earnings are used to calculate the Social Security benefits of each household. The

variable bi approximates the average indexed monthly earnings (AIME) multiplied by 12 as of age i. 5

In this model economy, the government does not solve an optimization problem. The government’s policy

rule is described as a set of tax and spending functions, in which functional forms are possibly time variant, and

a financing rule must satisfy an intertemporal budget constraint. At least one of the series in Ψt is unknown to

the households. Households form rational expectations of the series based on the government’s policy rule, the

intertemporal budget constraint, and the structure of the model. 6

In this paper, the payroll tax function covers taxes for the Old-Age, Survivors, and Disability Insurance

(OASDI) and Hospital Insurance (HI). For computational convenience, the function τP,t(.) denotes the OASDIHI tax levied on employees (a married couple) only. The rest of payroll tax is levied on their employers. See

equations (19) and (23). For simplicity, the Social Security benefit function trSS,s (.) includes the OASDI

benefits only and does not include Medicare and Medicaid (HI) benefits.

4
The household’s problem is

v (si, St; Ψt) = max ci,hi,ai+1

ui (ci, hi) + β φiE [v (si+1,St+1; Ψt+1) | ei] (4)

subject to

ai+1 = 1

1 + μ {wteihi + (1 + rt)ai − τI,t (wteihi, rtai, trSS,t (i, bi)) (5)

−τP,t (wteihi) + trSS,t (i, bi) + trLS,t − ci} ≥ amin,

a20 = 0, a110 ≥ 0,

where ui(.) is a period utility function of an age i household, β is the time-preference factor,

φi is the survival rate, wt is the wage rate per efficiency unit of labor, and rt is the interest

rate (the rate of return to capital).7 Individual variables of the model are normalized by the

steady-state per capita growth rate μ. Let πi,i+1 (ei+1 | ei) denote the conditional probability

for the age i + 1 working ability being ei+1 when the age i working ability is ei. Then,

E [v (si+1,St+1; Ψt+1) | ei] = ]

E

v (si+1,St+1; Ψt+1) πi,i+1 (ei+1 | ei) d ei+1. (6)

At the beginning of the next period, the state of the household, the state of the economy,

and the government policy rule become

si+1 = (i + 1, ei+1, ai+1 + qt, bi+1) with πi,i+1 (ei+1 | ei), (7)

St+1 = (xt+1 (.),WG,t+1), (8)

Ψt+1 = {WG,s+1, CG,s, trLS,s, τI,s (.), τP,s (.), trSS,s (.)}∞

s=t+1 , (9)

where qt denotes accidental bequests that a household receives at the end of the period, and

net government wealth WG,t+1 is determined by the government budget constraint. The

average historical earnings bi follows

bi+1 =







0 if i ≤ 24

1

i−24 {(i − 25)bi wtwt−1 + min (wteihi/2, wehmax

t )} if 25 ≤ i ≤ 59

bi/(1 + μ) if i ≥ 60,

7

So, wteihi is the earnings of a household of age i with working ability ei in year t.

5
where wehmax

t is the Old-Age, Survivors, and Disability Insurance (OASDI) tax cap, which

is $80,400 in 2001. For simplicity, the model assumes that the highest 35 years of earnings

correspond to those in ages between 25 and 59.8

2.1.2 The Measure of Households

Let xt (si) denote the measure of households, and let Xt (si) be the corresponding cumulative measure. The measure of households is adjusted by the steady-state population

growth rate ν. The population of age 20 households is normalized to be unity in the baseline

economy on the balanced growth path, that is,

]

E

dXt (20, e20, 0, 0) = 1. (11)

Let 1[a=y] be an indicator function that returns 1 if a = y and 0 if a 9= y. Then, the law of

motion of the measure of households is, for i ∈ I = {20, ..., 109} ,

xt+1 (si+1) = φi

1 + ν

]

E×A×B

1[ai+1=ai+1(si,St;Ψt)+qt] (12)

×1[bi+1=bi+1(wteihi(si,St;Ψ),bi)] πi,i+1(ei+1 | ei) dXt (si).

For simplicity, accidental bequests due to uncertain life span are captured by the government and distributed to all surviving working-age households in a lump-sum manner. The

accidental bequests per household at the end of year t is

qt =

S109

i=20(1 − φi)

U

E×A×B ai+1(si,St; Ψt) dXt (si)

S64

i=20 φi

U

E×A×B dXt (si) .

The steady-state condition is

St+1 = St (14)

for all t and si ∈ I × E × A × B.

8

Social Security benefits in the United States are computed on the basis of the highest 35 years of earnings,

adding an additional state variable to the model. Earnings before age 60 are wage indexed and earnings after age

60 are price indexed.

6
2.2 The Firm

National wealth Wt is the sum of total private wealth and government’s net wealth WG,t.

Total labor supply Lt is measured in efficiency units.

Wt = [

109

i=20

]

E×A×B

ai dXt (si) + WG,t, (15)

Lt = [

109

i=20

]

E×A×B

ei hi(si,St; Ψt) dXt (si). (16)

There is a perfectly competitive representative firm in this economy. In a closed economy,

capital stock is equal to national wealth, that is, Kt = Wt, and gross national product Yt is

determined by a constant-returns-to-scale production function,

Yt = F(Kt, Lt). (17)

The profit-maximizing condition of the firm is

rt + δ = FK(Kt, Lt), (18)

(1 + τ

P,t)wt = FL(Kt, Lt), (19)

where δ is the depreciation rate of capital, and τ

P,t is the employer’s portion of the marginal

payroll tax rate.9

In a small open economy, factor prices, r∗

t and w∗t are fixed at international levels, and

domestic capital stock KD,t and labor supply Lt are determined so that the firm’s profit

maximizing condition satisfies,

r∗

t + δ = FK(KD,t, Lt), (20)

(1 + τ

P,t)w∗t = FL(KD,t, Lt). (21)

Gross domestic product YD,t is determined by the production function,

YD,t = F(KD,t, Lt),

9

U.S. payroll taxes are divided equally between firms and employees. While the incidence of the tax does not

depend on this division, the present model explicitly includes the division for calibration purposes.

7
and gross national product Yt is determined by

Yt = (r∗

t + δ) Wt + (1 + τP,t)w∗t Lt.

Net foreign investment is shown by the difference between national wealth and domestic

capital stock, that is, Wt − KD,t.

2.3 The Government

Government tax revenue consists of federal income tax TI,t and payroll tax for Social

Security TP,t. These revenues are

TI,t = [

109

i=20

]

E×A×B

τI,t (wteihi(si, St; Ψt), rtai, trSS,t (i, bi)) dXt (si), (22)

TP,t = 2 × [

109

i=20

]

E×A×B

τp,t (wteihi(si,St; Ψt)) dXt (si). (23)

Total lump-sum transfer T rLS,t is

T rLS,t = trLC,t [

109

i=20

]

E×A×B

dXt (si), (24)

and Social Security (OASDI) benefit expenditure T rSS,t is

T rSS,t = [

109

i=20

]

E×A×B

trSS,t (i, bi) dXt (si). (25)

The law of motion of the government wealth (normalized by productivity growth and population growth) is

WG,t+1 = 1

(1 + μ) (1 + ν)

{(1 + rt)WG,t + TI,t + TP,t − TLS,t − T rSS,t − CG,t} , (26)

where CG,t is government consumption.

8
2.4 Recursive Competitive Equilibrium

Definition Recursive Competitive Equilibrium (Steady State): Let si = (i, ei, ai, bi) be

the individual state of households and let Ψ be the time-invariant government policy rules,

Ψ = {WG, CG, trLS, τI (.), τP (.), trSS(.)} .

Factor prices (r, w); accidental bequests q; the policy variables (WG, CG, τLS); the parameters φ of policy functions (τI (.), τP (.), trSS(.)); the value function of households, v (si; Ψ) ;

the decision rule of households,

d(si; Ψ) = {ci(si; Ψ), hi(si; Ψ), ai+1(si; Ψ)};

and the measure of households, x (si), are in a steady-state recursive competitive equilibrium

if, in every period, each household solves the utility maximization problem (1) – (5) taking Ψ

as given; the firm solves the profit maximization problem, and the capital and labor markets

clear, that is, (15) – (21) hold; the government policy rules satisfy (22) – (26); the goods

market clears; and the measure of households is constant, that is, (14) holds.

Definition Recursive Competitive Equilibrium (Equilibrium Transition Path): Let si =

(i, ei, ai, bi) be the individual state of households, let St = (xt(si), WG,t) be the aggregate

state of the economy, and let Ψt be the government policy rules known at the beginning of

year t,

Ψt = {WG,s+1, CG,s, trLS,s, τI,s(.), τP,s(.), trSS,s(.)}∞

s=t.

A series of factor prices, accidental bequests, the policy variables, and the parameters of

policy functions,

Ω ={rs, ws, qs,WG,s+1, CG,s, τLS,s,φs}∞

s=t;

the value function of households,{v (si,Ss; Ψs)}∞

s=t; the decision rule of households,

{d(si,Ss; Ψs)}∞

s=t = {ci(si, Ss; Ψs), hi(si,Ss; Ψs), ai+1(si,Ss; Ψs)}∞s=t;

9
and a series of the measure of households, {xs(si)}∞

s=t, are in a recursive competitive equilibrium if, in every period s = t, ...,∞, each household solves the utility maximization

problem (1) – (5) taking Ψt as given; the firm solves the profit maximization problem, and

the capital and labor markets clear, that is, (15) – (21) hold; the government policy rules

satisfy (22) – (26); and the goods market clears.

3 Calibration

The model is calibrated to broad features of the economy. For the baseline economy on

a balanced growth path, the degree of time preference β is chosen so that the capital-output

ratio is 2.74; the share parameter of consumption α is chosen so that the average annual

working hours of married couples (aged 20 to 64) in the initial steady state are consistent with

U.S. data. In addition, total factor productivity A is chosen so that the wage rate equals unity.

The coefficient or relative risk aversion γ is set to either 2.0 or 4.0, following the previous

literature. As explained below, a Cobb-Douglas-CRRA utility function and a Cobb-Douglas

production function are used for the calibration.10

Table 1 summarizes the parameter choices. The first column presents the set of parameters that CBO used in its March 2003 “Analysis of the President’s Budget (Congressional

Budget Office, 2003a).” The second column presents an alternative set of assumptions. Differences between the two columns stem largely from the assumptions about the coefficient

of relative risk aversion and the maximum number of hours that a household could work per

year. Both sets of assumptions are within reasonable bounds given the empirical research.

The parameter choices are interrelated. If the coefficient of relative risk aversion or

maximum hours is changed, it will alter the time preference parameter needed to produce a

capital-output ratio of 2.74 in the baseline. Changing those parameters will also affect the

share parameter of consumption needed to target the average hours of work.

The following sections describe the choice of functional forms and parameter values, the

choice of four target variables and values.

10The calibration strategy is similar to those in Nishiyama (2002) and Nishiyama and Smetters (2003), but

many parameters in this analysis are revised.

10
Table 1: Parameters

Assumptions

March 2003 Alternative

Time preference parameter β 0.984 1.012

Share parameter for consumption α 0.454 0.694

Maximum working hours hmax

i 8,760 5,460

Coefficient of relative risk aversion γ 2.0 4.0

Capital share of output θ 0.30 0.30

Depreciation rate of capital stock δ 0.047 0.047

Long-term per capita real growth rate μ 0.018 0.018

Population growth rate ν 0.010 0.010

Total factor productivity A 0.988 0.988

3.1 Households

Utility Function. The model has elastic labor supply and uses the following Cobb-Douglas

utility function with constant relative risk aversion (CRRA),

u(ci, hi) =

q

((1 + ni/2)−ζ ci)α(hmax

i − hi)1−α

r1−γ

1 − γ ,

where γ is the coefficient of relative risk aversion, α is the share parameter for consumption,

ni is the number of dependent children, ζ is the consumption adjustment parameter for children, and hmax

i is the maximum working hours.11 The coefficient of relative risk aversion

is assumed to be either 2.0 or 4.0. The numbers of dependent children by age cohorts are

calculated from the Panel Study of Income Dynamics (PSID) 1993 Family Data (see Table

2). The consumption adjustment parameter for children is assumed to be 0.6.12

The annual working hours in the model are the sum of the working hours of a husband

and a wife. The average working hours of married households between ages 20 and 64 are

3,368 hours in the 1998 Survey of Consumer Finances (SCF). In the March 2003 assumption, hmax

i is set to be 8,760 per household, which is simply calculated as 12 hours times 365

days times 2 people. In the alternative parameterization, hmax

i is set to be 5,460 hours per

11In this setting, the growth-adjusted β becomes β(1 + μ)α(1−γ)

. 12When ζ = 0.6, since 20.6 = 1.517, a married couple with two dependent children needs to consume 52

percent more than a married couple with no children does to attain the same level of utility if other things are

equal.

11
Table 2: Number of People Under 18 Years of Age in a Married Household

Age cohorts Number of people Age cohorts Number of people

under age 18 under age 18

20-24 0.895 45-49 1.011

25-29 1.149 50-54 0.445

30-34 1.617 55-59 0.188

35-39 1.905 60-64 0.094

40-44 1.649 65-plus 0.000∗

Source: Nishiyama and Smetters (2003). The authors’ calculations from the

Panel Study of Income Dynamics (PSID) 1993 Family Data.

∗The number 0.000 for ages 65-plus is an assumption and not from PSID data.

couple, which is the 95th percentile of working hours in the 1998 SCF. Given those alternative assumptions about maximum hours, the parameter α is chosen so that average working

hours of households of age 20 to age 64 is 3,368 hours in the steady-state baseline economy.

In March 2003 assumptions, α is 0.454, in the alternative assumption, it is 0.694.

Working Ability. The working ability in this calibration corresponds to the hourly wage

(labor income per hour) of each household in the 1998 SCF. The average hourly wage of a

married couple (family members #1 and #2 in SCF) used for the calibration is calculated by

Hourly Wage = Regular and Additional Salaries (#1 + #2) + Welfare or Assistance

max {Working Hours (#1 + #2), 520} .

To capture the household’s exposure to earnings risk more precisely, unemployment or worker’s

compensation, Temporary Assistance for Needy Families (TANF), food stamps, and other

forms of welfare or assistance are added to the salaries before calculating the hourly wage.

Table 3 shows the eight discrete levels of working abilities of five-year age cohorts.13 Using a shape-preserving cubic spline interpolation, the working ability of each age cohort is

obtained. The average hourly earnings of production workers have increased by 16.7 percent during the years from 1997 to 2001.14 In the calibration, the numbers in the table are

13The hourly wage of a household that works less than 520 hours (10 hours a week per couple) is calculated as

its adjusted labor income divided by 520 hours. Accordingly, the hourly wage of a household that does not work

at all is assumed to be zero. In the real economy, some households have fairly high working ability but choose

not to work (for example, because of schooling). One observation of the age 20-24 cohort, which has an hourly

wage of $193.01, is ignored. 14Source: Department of Commerce, Bureau of Labor Statistics.

12
Table 3: Working Abilities of a Household (in U.S. Dollars per Hour)

Percentile Age cohorts

20-24 25-29 30-34 35-39 40-44 45-49

e1 0-20th 3.83 5.42 5.42 6.93 6.12 6.59

e2 20-40th 7.07 8.64 9.76 11.28 11.36 12.70

e3 40-60th 8.68 10.91 13.46 15.01 15.59 17.22

e4 60-80th 10.67 14.01 18.08 19.96 22.09 23.22

e5 80-90th 14.05 17.52 27.17 25.27 30.89 31.58

e6 90-95th 18.20 22.48 33.71 33.38 48.59 44.31

e7 95-99th 28.43 32.64 54.11 52.16 76.13 86.50

e8 99-100th 36.81 46.09 167.15 186.47 221.34 301.99

Percentile Age cohorts

50-54 55-59 60-64 65-69 70-74 75-79

e1 0-20th 5.48 3.52 0.00 0.00 0.00 0.00

e2 20-40th 11.53 10.06 4.54 0.00 0.00 0.00

e3 40-60th 16.16 14.26 11.18 2.82 0.00 0.00

e4 60-80th 23.44 21.28 18.16 10.37 1.81 0.00

e5 80-90th 32.14 30.93 28.56 19.48 12.57 0.00

e6 90-95th 43.01 44.10 59.36 27.68 29.03 1.96

e7 95-99th 78.61 85.29 96.22 59.34 64.91 14.25

e8 99-100th 314.59 379.44 421.55 299.25 195.73 146.14

Source: Nishiyama and Smetters (2003). The authors’ calculations from

the 1998 SCF data.

multiplied by 1.167 to convert the hourly wages in 1997 into those in 2001.

Markov Transition Matrix. The Markov transition matrix, Γ, of working ability is calculated from the hourly wage of people ages 30-39 in 1991 in the PSID individual data. To

make the working ability process more persistent, the matrix is calculated as the transition

from the average of years 1989 and 1990 to the average of years 1990 and 1991.

Γ =





0.7674 0.2049 0.0183 0.0045 0.0049 0.0000 0.0000 0.0000

0.1810 0.6033 0.1844 0.0129 0.0000 0.0086 0.0046 0.0052

0.0388 0.1517 0.6768 0.1220 0.0011 0.0046 0.0050 0.0000

0.0126 0.0361 0.1039 0.7210 0.0980 0.0139 0.0145 0.0000

0.0000 0.0081 0.0332 0.2360 0.6306 0.0676 0.0145 0.0100

0.0000 0.0000 0.0000 0.0582 0.3224 0.5303 0.0891 0.0000

0.0007 0.0000 0.0000 0.0354 0.0000 0.2827 0.6433 0.0379

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.3553 0.6447





,

13
Table 4: Survival Rates in the United States in 1998 (Weighted Average of Males and

Females of Each Age)

Age Survival Age Survival Age Survival Age Survival Age Survival

Rate Rate Rate Rate Rate

20 0.999113 40 0.997978 60 0.989365 80 0.938048 100 0.676941

21 0.999066 41 0.997820 61 0.988361 81 0.931804 101 0.658846

22 0.999037 42 0.997654 62 0.987195 82 0.924980 102 0.639629

23 0.999028 43 0.997465 63 0.985840 83 0.917566 103 0.619216

24 0.999032 44 0.997267 64 0.984324 84 0.909481 104 0.597532

25 0.999043 45 0.997044 65 0.982631 85 0.900623 105 0.574495

26 0.999049 46 0.996797 66 0.980851 86 0.890904 106 0.550021

27 0.999041 47 0.996534 67 0.979101 87 0.880258 107 0.524022

28 0.999014 48 0.996258 68 0.977433 88 0.868650 108 0.496402

29 0.998970 49 0.995960 69 0.975763 89 0.856070 109 0.467066

30 0.998919 50 0.995626 70 0.973892 90 0.842518

31 0.998865 51 0.995247 71 0.971745 91 0.828007

32 0.998804 52 0.994823 72 0.969406 92 0.812554

33 0.998735 53 0.994352 73 0.966856 93 0.796181

34 0.998660 54 0.993826 74 0.964033 94 0.778913

35 0.998573 55 0.993231 75 0.960839 95 0.761457

36 0.998475 56 0.992570 76 0.957219 96 0.744011

37 0.998368 57 0.991857 77 0.953175 97 0.726790

38 0.998250 58 0.991094 78 0.948673 98 0.710031

39 0.998122 59 0.990263 79 0.943665 99 0.693980

Source: Nishiyama and Smetters (2003). The authors’ calculations from the Social Security

Administration (2001). In the calibration, the survival rate at the end of age 109 is set to zero.

where Γ(j, k) = π(ei+1 = ek

i+1 | ei = e

j

i).

15

Population Growth and Mortality. The population growth rate ν is assumed to be 1.0

percent per year in a balanced growth path. The survival rates φi at the end of age i =

{20, ..., 109} are the weighted average of males and females in 1998 from Social Security

Administration (2001).16 (See Table 4.) The survival rate at the end of age 109 is replaced

by zero.

15The Markov transition matrix is fairly stable across age cohorts, although the diagonal elements tend to be

smaller in age 20s and slightly larger in age 50s. 16The numbers are calculated from Table 4.C6 in the Social Security Administration (2001).

14
3.2 The Firm

Production Function. Production takes the Cobb-Douglas form,

F(Kt, Lt) = AtKθ

t L1−θ

t .

To compute GNP, the model uses the sum of working hours in efficiency units as total labor

supply Lt. The capital share of output θ is chosen by

θ = 1 − Compensation of Employees + (1 − θ) × Proprietors’ Income

National Income + Consumption of Fixed Capital .

The number of θ in 2000 is 0.30.17 The annual per-capita growth rate μ is assumed to be

1.8 percent. The annual population growth rate ν is assumed to be 1.0 percent. Total factor

productivity A is chosen to be 0.988 so that the wage per unit of efficient labor is normalized

to be unity.

Fixed Capital and Private Wealth. Fixed capital K in the calibration is the sum of private

fixed assets and government fixed assets. In 2000, private fixed assets were $21,165 billion,

government fixed assets were $5,743 billion, and the government debt held by the public is

$3,410 billion.18 From these numbers, the government net wealth is set at 9.5 percent of

total private wealth in the initial steady-state economy. In 2000, the capital-GDP ratio is

2.74. The time preference parameter β is chosen so that the capital-GDP ratio of the steady

state economy (a balanced growth path) is 2.74.

The Depreciation Rate of Fixed Capital. The depreciation rate of fixed capital δ is chosen

by the steady-state condition,

δ = Total Gross Investment

Fixed Capital − μ − ν.

In 2000, private gross fixed investment accounted for 17.2 percent of GDP, and government

(federal and state) gross investment accounted for 3.3 percent of GDP.19 When the capital17Source: Department of Commerce, Bureau of Economic Analysis. The average of θ in years between 1996

and 2000 is 0.31. 18ibid. 19ibid.

15
Table 5: Marginal Individual Income Tax Rates in 2001 (Married Household, Filed Jointly)

Taxable Income Marginal Income Tax Rate (%)

In 2001 Income (Model) In 2006 (Projected)

$0 – $9,523 $0 – $12,000 10 × φτI

$9,523 – $45,908 $12,000 – $57,850 15 × φτI

$45,908 – $99,116 $57,850 – $124,900 25 × φτI

$99,116 – $151,015 $124,900 – $190,300 28 × φτI

$151,015 – $269,692 $190,300 – $339,850 33 × φτI

$269,692 – $339,850 – 35 × φτI

Note: The tax brackets corresponding to the 2001 income level are calculated from the projected

tax brackets for 2006 in House of Representatives (2001).

output ratio is 2.74, the ratio of gross investment to fixed capital is 7.5 percent. Subtracting

the productivity and population growth rates, the annual depreciation rate is 4.7 percent.

3.3 Government

Income Taxes. The model assumes a progressive income tax schedule, standard deduction, and personal exemptions for self, spouse, and dependent children. For simplicity, all

households in the model are assumed to be married households that file tax returns jointly,

and corporate income is included into the capital income of households. The individual income tax schedule in the baseline economy is matched to the projected one for 2006 in the

“Economic Growth and Tax Relief Reconciliation Act of 2001 (House of Representatives,

2001).” Because the model uses the 2001 working-ability profile, the tax brackets are adjusted to the 2001 income level. Table 5 shows the statutory marginal tax rates. In 2001,

the standard deduction for a married household was $7,600, and the exemption was $2,900

per person. The exemptions for dependent children follow Table 2. All of the tax brackets,

standard deduction, and exemption are assumed to be growth adjusted so that there is no real

bracket creep.

To adjust the effective capital income tax rates at lower levels than labor income tax

rates, the taxable capital income ratio 0.768 is multiplied to the capital income.20 For elderly

households, a part of Social Security benefits are taxable and included to the adjusted gross

20Table 10 shows that the effective tax rate on capital income in 2004 (projected by CBO) is about 23 percent

lower than effective tax late on labor income.

16
income.21 Because economic income is higher than taxable income, the effective marginal

tax rates are lower than the statutory ones. All statutory rates are proportionately adjusted by

φτI , which equals 0.673 under the March 2003 assumption and 0.705 under the alternative

assumption, so that federal income tax revenue, including corporate income tax revenue, is

10.2 percent of GDP in the baseline economy. In addition, refundable child tax credits ($500

per child, reduced if taxable income is above $110,000) are applied. State and local income

taxes in the model are 4.0 percent of income (excluding Social Security benefits) above the

same standard deduction and exemptions.

Social Security. The tax rate levied on both employers and employees for Old-Age, Survivors, and Disability Insurance (OASDI) is 6.2 percent, and the tax rate for Medicare (HI) is

1.45 percent. In 2001, employee compensation above $80,400 was not taxable for OASDI.

(See Table 6.) So, the firm’s profit-maximization problem becomes

w × (1 + Marginal Payroll Tax Rate) = AFL(K, L),

where the marginal payroll tax rate is either 0.0765 or 0.0145 for high-earnings workers.

Because the marginal payroll tax rates are not uniform across households, the calibration

uses the average payroll tax rate (total payroll tax paid by employers divided by total labor

income) instead.22

Social Security benefits are based on each worker’s Average Indexed Monthly Earnings

(AIME), bi/12, and the replacement rate schedule in the United States. The replacement

rates are 90 percent for the first $561, 32 percent for amounts between $561 and $3,381, and

15 percent for amounts above $3,381.

The benefits received by retired workers accounted for 69.1 percent of total OASDI benefits in December 2000.23 The calibration simply assumes that each elderly household re21See Table 2.A32 in Social Security Administration (2001).

22The marginal payroll tax rate faced by a representative firm depends on how the firm increases one additional

unit of labor input. If the firm hires an additional set of workers of the same earnings distribution of existing

workers, the marginal labor cost for the firm is the market wage rate plus the average payroll tax rate. If the

firm does not increase its workers but make them work an additional hour, then, the marginal labor cost is the

market wage rate plus the weighted average of marginal payroll tax rates, which will likely be lower than the

average payroll tax rate. The calibration uses the average payroll tax rate, which is 5.94 percent in the baseline,

to calculate the marginal cost for the firm for simplicity. 23See Table 5.A1 in Social Security Administration (2001).

17
Table 6: Marginal Payroll Tax Rates in 2001

Labor Income per Marginal Tax Rate (%)

worker (wteihi/2) OASDI HI

$0 – $80,400 6.2 × τP,Adj 1.45

$80,400 – 0.0 × τP,Adj 1.45

Note: The same taxes are levied to employers. The payroll tax

adjustment factor τP,Adj is assumed to be 1.0.

Table 7: OASDI Replacement Rates in 2001

AIME (b/12) Marginal Replacement Rate (%)

$0 – $561 90.0 × trSS,Adj

$561 – $3,381 32.0 × trSS,Adj

$3,381 – 15.0 × trSS,Adj

Note: The OASDI benefit adjustment factor trSS,Adj is assumed to be 1.448

to reflect disability insurance and survivors insurance.

ceives other benefits—those for spouses, children, and disabled workers—proportionally.

Benefits calculated from AIME are multiplied uniformly by 1.448 (=1/0.691). For simplicity, the model assumes that the government consumes the difference between the OASDI

payroll tax revenue and the OASDI benefits in the initial steady-state economy.24

Government Bond Yields. In the baseline economy, the real rate of return to capital, before corporate and individual income taxes, is about 6.25 percent, so the real rate on government debt is 3.25 percent. Because aggregate uncertainty does not exist in the model, it does

not endogenously generate a risk premium between capital and government bonds. However, assuming that the risk premium is zero would cause government debt to accumulate

too fast in simulations where tax cuts were temporarily financed through budget deficits. To

overcome this problem, the model assumes an exogenous risk premium, ρ = 0.03 (or 300

basis points), between the market rate of return and the government bond yield.25

The procedure of applying the premium is implemented as follows. Let WG, KG, and

DG be the government’s net wealth, capital stock, and debt held by public, respectively, and

24In the real economy, the surplus is added to the Social Security trust fund after subtracting administration

costs. 25There is a criticism on this ad hoc treatment of government bond yields, however.

18
let WP and KP be private (households’) net wealth and private capital stock, respectively.26

Then, we have WG = KG − DG and WP = KP + DG. National wealth W and capital

stock K are defined as W = WP + WG and K = KP + KG. In a closed economy we have

W = K. The market rate of return r is determined by the marginal product of capital, that

is, r = FK(K, L) − δ.

Suppose that the government bond yield rG is defined as rG = r − ρ, where ρ > 0 is

a risk premium. If the market rate of return r is not stochastic, no households will purchase

government bonds. One of the simplest ways to avoid this problem is, by assumption, making

the households hold government bonds proportionally to their wealth levels.

The share of government bonds in a household’s portfolio, sB, is calculated as

sB = DG

WP

= DG

KP + DG

.

The average rate of return to the household’s portfolio, rh, is

rh = (1 − sB) r + sBrG = (1 − sB) r + sB (r − ρ).

This average rate of return rhwill be used to find the household’s decision rules. For example,

the capital income of a household becomes smaller if ρ > 0 and sB > 0. In the government’s

intertemporal budget constraint, the market rate r will be used for the rate of return to the

government capital stock KG, but rG = r − ρ will be used for the cost of the government

debt. When the debt-GDP ratio goes up, and sB goes up, the market interest rate r will go

up because of the crowding out, but the average interest rate rh will not go up as much and it

discourage private savings further.

3.4 How Well Does the Model Match the Data?

Tables 8 and 9 show the distribution statistics of the overlapping generation models and

those in the U.S. data. The model roughly capture the distributions in earnings, income, and

wealth. In terms of Gini coefficients, the earnings and wealth inequalities under March 2003

assumptions are about the same as those in the U.S. data, and the inequalities under the alternative assumptions are slightly lower. However, the model does not replicate the wealth

26In the baseline economy, the ratio of KG to GDP is set at 0.586 and the ratio of DG to GDP is 0.348.

19
Table 8: The Gini Coefficients in the Baseline Economy

Earnings Income Wealth

All Ages 20-64

March 2003 Assumptions 0.608 0.531 0.581 0.748

Alternative Assumptions 0.566 0.499 0.545 0.706

U.S. data (married households)∗ 0.60 – – 0.75

∗The author’s calculation using data from the 1998 Survey of Consumer Finances.

Table 9: The Wealth Distribution in the Baseline Economy

Percentage of wealth held by top

1% 5% 10% 20% 40%

March 2003 Assumptions 18.6 46.3 61.4 77.5 92.5

Alternative Assumptions 16.6 41.9 56.6 73.0 89.5

U.S. data (married households)∗ 30.5 53.9 64.9 77.2 90.4 ∗The author’s calculation using data from the 1998 Survey of Consumer Finances.

inequality completely. For example, the share of wealth held by top 1 percent of households is 18.6 percent under March 2003 assumptions and 16.6 percent under the alternative

assumptions, and the numbers are significantly lower than 30.5 percent calculated from the

1998 Survey of Consumer Finances.

4 Policy Experiments

This section describes the economic effects of cutting all statutory federal income tax

rates by 10 percent. The tax cut is assumed to be unanticipated and be enacted in year 1.

Table 10 shows the impact on the average effective marginal tax rates on capital and labor.

The effective tax rate on capital declines by only 3 to 4 percent because the policy does not

change corporate income tax rates.

The policy experiment was implemented in two steps:

First, the changes in average effective marginal income tax rates are calculated outside

the model. Then, the percent changes in marginal tax rates on labor income and capital

income were incorporated in the model by proportionately adjusting the model’s tax rates on

labor and capital so that the percentage changes in effective marginal rates were similar to

20
Table 10: Effective Marginal Tax Rates on Labor Income and Capital Income (%)

Model Calendar Tax Rate on Labor Income Rate on Capital Income

Year Year Current Law Proposal %ch Current Law Proposal %ch

1 2004 18.1 16.3 -9.7 13.9 13.5 -3.1

2 2005 19.0 17.1 -9.7 13.9 13.5 -3.2

3 2006 19.0 17.2 -9.7 14.0 13.5 -3.2

4 2007 19.3 17.4 -10.0 14.0 13.6 -3.2

5 2008 19.5 17.6 -9.8 13.9 13.5 -3.1

6 2009 19.8 17.8 -9.7 14.9 14.3 -3.5

7 2010 20.0 18.1 -9.6 14.9 14.3 -3.6

8 2011 21.8 19.7 -9.6 15.5 14.9 -3.9

9 2012 22.0 19.8 -9.8 15.5 14.9 -3.9

10- 2013- 22.0 19.8 -10.2 15.5 14.9 -3.9

the numbers in Table 10.

Second, adjustments were made in lump-sum transfers so that the model’s prediction of

the revenue loss without macroeconomic feedbacks matched the estimates provided by the

Joint Committee on Taxation (JCT). See Table 11.

Because the model imposes the government’s intertemporal budget constraint, tax cuts

must eventually be financed by either cutting spending or raising taxes. This paper considers

five alternatives:

1. Government consumption (waste) CG,t reduced contemporaneously;

2. Lump-sum transfers trLS,t reduced contemporaneously;

3. Government consumption CG,t reduced gradually after 10 years;

4. Lump-sum transfers trLS,t reduced gradually after 10 years;

5. Income tax rates φτI raised gradually after 10 years.

The ratio of government debt (net wealth) to the baseline GDP is fixed throughout the

transition path in first two alternatives. In the remaining alternatives, the debt-GDP ratio is

stabilized after 20 years.

21
Table 11: Matching JCT’s Revenue Estimates

Model Calendar Static Revenue Change Lump-sum Transfer AdYear Year (as % of GDP) justment (in 2001 dollars)

JCT Estimate∗1 OLG Model∗2 March 2003 Alternative

1 2004 -0.65 -0.90 -262 -234

2 2005 -0.76 -0.90 -136 -115

3 2006 -0.81 -0.90 -89 -71

4 2007 -0.82 -0.92 -98 -79

5 2008 -0.85 -0.91 -53 -36

6 2009 -0.86 -0.90 -40 -25

7 2010 -0.93 -0.90 51 60

8 2011 -1.02 -0.90 135 138

9 2012 -0.99 -0.92 87 93

10- 2013- -1.01 -0.96 75 83

∗1Converted to calender year from fiscal year.

∗2Before lump-sum transfer adjustments; without macroeconomic feedbacks.

4.1 March 2003 Assumptions

Table 12 show the results of the experiment in selected macroeconomic variables. The

numbers are percent changes from the baseline economy.

(1) Contemporaneous reductions in government consumption. When the marginal tax

rate on labor income was reduced by 10 percent, labor supply would increase both in the short

run and in the long run. National wealth would also increase, because the marginal tax rate on

capital income was reduced by 3 to 4 percent by assumption, and because after-tax earnings

would be higher. Except for the first 5 years, the percent increase in national wealth is larger

than the percent increase in labor supply, and the wage rate would be higher and the interest

rate would be lower in a closed economy. So, the long-run change in national wealth would

be smaller and the long-run change in labor supply would be larger in a closed economy than

in a small open economy. The increase in GNP is simply calculated from the production

function. Throughout the transition path, the percent increase in private consumption would

be larger than the percent increase in GNP, because government consumption was reduced

to make the government budget balanced, and more resources were allocated to households.

22
Table 12: Income Tax Rates Reduced by 10 Percent Proportionally—March 2003 Assumptions (Percent Changes from the Baseline)

Closed Economy Small Open Economy

Years Long Years Long

1-5 6-10 1-10 Run 1-5 6-10 1-10 Run

(1) Contemporaneous reductions in government consumption

National Wealth 0.3 1.0 0.6 2.2 0.4 1.3 0.9 3.7

Labor Supply 0.7 0.5 0.6 0.4 0.8 0.5 0.7 0.2

GNP 0.6 0.6 0.6 1.0 0.7 0.8 0.7 1.2

Consumption 1.1 1.5 1.3 2.2 1.0 1.3 1.2 2.1

(2) Contemporaneous reductions in lump-sum transfers

National Wealth 0.5 1.8 1.2 3.0 0.7 2.3 1.5 4.6

Labor Supply 0.9 0.9 0.9 1.0 1.1 0.9 1.0 0.8

GNP 0.8 1.2 1.0 1.6 1.0 1.3 1.2 1.9

Consumption 0.9 1.2 1.0 1.6 0.7 0.9 0.8 1.6

(3) Deficit finance for 10 years then phased-in reductions in government consumption

National Wealth 0.1 -0.2 -0.1 -1.2 -0.1 -0.7 -0.4 -2.5

Labor Supply 0.8 0.5 0.7 0.2 0.8 0.5 0.6 0.4

GNP 0.6 0.3 0.4 -0.2 0.5 0.1 0.3 -0.4

Consumption 0.9 1.2 1.0 1.7 1.1 1.4 1.3 1.7

(4) Deficit finance for 10 years then phased-in reductions in lump-sum transfers

National Wealth 0.2 0.4 0.3 0.1 0.2 0.2 0.2 -0.6

Labor Supply 1.0 0.8 0.9 1.0 1.0 0.8 0.9 1.1

GNP 0.8 0.7 0.7 0.7 0.8 0.6 0.7 0.6

Consumption 0.8 1.0 0.9 1.1 0.9 1.1 1.0 1.1

(5) Deficit finance for 10 years then phased-in increases in income tax rates

National Wealth 0.1 0.0 0.0 -4.4 0.0 -0.5 -0.2 -7.6

Labor Supply 0.8 0.7 0.8 -0.3 0.8 0.6 0.7 0.3

GNP 0.6 0.5 0.5 -1.6 0.6 0.3 0.4 -2.1

Consumption 0.9 1.1 1.0 -1.0 1.1 1.3 1.2 -0.8

When the effective marginal tax rate on labor income is on average 19 percent, marginal

payroll tax rate is on average 6 percent, and marginal state and local tax rate is 4 percent,

the after-tax wage goes up by 2.7 percent by a 10 percent marginal income tax rate cut if

the market wage rate does not change. In a small open economy, where the wage rate was

not assumed to change, labor supply would increase by 0.7 percent on average in the first 10

years. From these two numbers, the model implies that the uncompensated wage elasticity

of labor supply is about 0.26 under this assumption.

23
(2) Contemporaneous reductions in lump-sum transfers. Compared to the financing assumption (1), both labor supply and national wealth would be larger throughout the transition

path. Because the reductions in lump-sum transfers were applied to both working-age households and retired households, households would have to accumulate higher life-cycle savings

to prepare for the period after retirement and, accordingly, they would have to work more under this financing assumption. Since government consumption was not reduced, the percent

increase in private consumption would be smaller under this assumption than the financing

assumption (1).

(3) Deficit finance for 10 years then phased-in reductions in government consumption.

Compared to the financing assumption (1), the government debt would increase for the first

20 years, because the phased-in reductions in government consumption took 10 more years.

By assumption, households would have to hold a larger share of government bonds, which

rate of return was lower than the market rate of return. So, in a small open economy, private

savings would be smaller and private consumption would be slightly larger. National wealth

would decrease mostly due to the increase in government debt, and the interest rate would

be higher in a closed economy. The percent decrease in national wealth would be smaller in

a closed economy than in a small open economy because of the general equilibrium effect.

In the long run, the increased government debt would push down national wealth and GNP,

and the percent changes in those two variables would be negative. The increase in private

consumption would also be smaller than the financing assumption (1).

(4) Deficit finance for 10 years then phased-in reductions in lump-sum transfers. Compared to the financing assumption (2), national wealth would be smaller because of the increased government debt, and labor supply would be slightly smaller in a small open economy. Consumption in a small open economy would be slightly larger in the short run, because the average rate of return would be lower, but the increase in consumption is smaller in

the long run due to the larger reduction of lump-sum transfers. Compared to the small open

economy case, the interest rate would be slightly higher in a closed economy, so would be

national wealth and GNP. Private consumption would be slightly lower in a closed economy

24
than in a small open economy.

(5) Deficit finance for 10 years then phased-in increases in income tax rates. The effect

of a 10 percent tax cut would be larger than the financing assumption (3) but less than the

financing assumption (4) in the short run. Because an income tax rate increase after 10 years

would hurt retired households less than working-age households, compared to the financing assumption (4), households would have to accumulate less wealth for the period after

retirement. In the long run, the negative effect of the government debt increase would be

the largest among the five government-financing assumptions. Higher marginal tax rates on

capital income would reduce national wealth and GNP in the long run. Private consumption

would decrease, too.27

4.2 Alternative Assumptions

Under the alternative assumptions, the share parameter for consumption is increased from

0.454 to 0.694, and the wage elasticity of labor supply is lower than that under the March

2003 assumptions. In addition, the coefficient of relative risk aversion is increased from

2.0 to 4.0 (or, equivalently, the intertemporal elasticity of substitution of the composite of

consumption and leisure is reduced from 0.5 to 0.25).

So, in all financing assumptions and in both a closed economy and a small open economy,

percent increases in labor supply under the alternative assumptions would be smaller than

those under the March 2003 assumptions. Labor supply would increase by 0.4 percent for

the first 10 years in a small open economy under the financing assumption (1). This result

implies that the uncompensated wage elasticity of labor supply is around 0.15 in the short run.

Compared to the March 2003 assumptions, the percent increase in GNP would be smaller in

the short run.

27The present policy experiment reduces the marginal tax rates on labor income by 10 percent, but it reduces

the marginal tax rates on capital income by only 3 to 4 percent. After 10 years, the policy experiment assumes

that the tax rates on both labor income tax and capital income tax would be increased proportionally from the

level in year 10. This assumption makes the negative effect on national wealth larger than that on labor supply

in the long run.

25
Table 13: Income Tax Rates Reduced by 10 Percent Proportionally—Alternative Assumptions (Percent Changes from the Baseline)

Closed Economy Small Open Economy

Years Long Years Long

1-5 6-10 1-10 Run 1-5 6-10 1-10 Run

(1) Contemporaneous reductions in government consumption

National Wealth 0.3 1.0 0.6 2.8 0.3 1.0 0.6 3.2

Labor Supply 0.5 0.4 0.4 0.4 0.5 0.3 0.4 0.1

GNP 0.4 0.6 0.5 1.1 0.4 0.5 0.5 1.1

Consumption 1.0 1.3 1.1 2.1 1.0 1.2 1.1 2.0

(2) Contemporaneous reductions in lump-sum transfers

National Wealth 0.6 2.1 1.3 3.8 0.6 2.3 1.5 4.5

Labor Supply 0.7 0.7 0.7 0.8 0.7 0.6 0.6 0.5

GNP 0.7 1.1 0.9 1.7 0.7 1.1 0.9 1.7

Consumption 0.5 0.8 0.7 1.4 0.4 0.6 0.5 1.2

(3) Deficit finance for 10 years then phased-in reductions in government consumption

National Wealth -0.2 -0.9 -0.5 -1.8 -0.2 -1.0 -0.6 -1.9

Labor Supply 0.4 0.2 0.3 0.0 0.5 0.3 0.4 0.1

GNP 0.2 -0.1 0.1 -0.6 0.3 0.0 0.1 -0.5

Consumption 0.9 1.1 1.0 2.0 1.0 1.2 1.1 2.0

(4) Deficit finance for 10 years then phased-in reductions in lump-sum transfers

National Wealth 0.2 0.4 0.3 0.6 0.2 0.4 0.3 0.6

Labor Supply 0.7 0.6 0.6 0.7 0.7 0.6 0.6 0.7

GNP 0.5 0.5 0.5 0.6 0.5 0.5 0.5 0.7

Consumption 0.4 0.6 0.5 0.8 0.5 0.7 0.6 0.8

(5) Deficit finance for 10 years then phased-in increases in income tax rates

National Wealth -0.1 -0.7 -0.4 -7.1 -0.1 -0.7 -0.4 -7.4

Labor Supply 0.5 0.3 0.4 -0.7 0.5 0.4 0.5 0.0

GNP 0.3 0.0 0.2 -2.6 0.3 0.1 0.2 -2.2

Consumption 0.8 1.0 0.9 -1.9 0.9 1.1 1.0 -1.1

In the long run, the sizes (absolute values) of percent changes from the baseline would be

smaller in a small open economy than the March 2003 assumption, but the sizes of percent

changes would be larger in a closed economy. In other words, the difference between a closed

economy and a small open economy would be smaller under the alternative assumptions than

the March 2003 assumptions.

26
Appendices

A The Computation of Equilibria

The algorithm to solve the model for a steady-state equilibrium and an equilibrium transition path is similar to those in Conesa and Krueger (1999), Nishiyama (2002), and Nishiyama

and Smetters (2003).28

A.1 The Discretization of the State Space

The state of a household is si = (i, ei, ai, bi) ∈ I ×E×A×B, where I = {20, ..., 109},

E = [emin, emax], A = 

amin, amax

, and B = [bmin, bmax]. To compute an equilibrium, the

state space of a household is discretized as esi ∈ I ×Ee×Ae×B, e where Ee = {e1, e2, ..., eNe },

Ae = {a1, a2, ..., aNa}, and Be = {b1, b2, ..., bNb }.

29 For all these discrete points, the model

computes the optimal decision of households, d(esi,St; Ψt)=(ci (.), hi (.), ai+1 (.)) ∈

(0, cmax] × [0, hmax

i ] × A, the marginal values, ∂

∂a v(esi,St; Ψt) and ∂∂bv(esi,St; Ψt), and the

values v(esi,St; Ψt), given the expected factor prices and policy variables.30

To find the optimal end-of-period wealth, the model uses the Euler equation and bilinear

interpolation (with respect to a and b) of marginal values at the beginning of the next period.31

In this paper, Ne, Na, and Nb are 8, 35, and 8, respectively. Since there are 90 different ages,

the total number of discrete states is 201,600.32

A.2 A Steady-State Equilibrium

The algorithm to compute a steady-state equilibrium is as follows. Let Ψ denote the

time-invariant government policy rule Ψ = (WG, CG, trLS, τI (.), τP (.), trSS(.)).

28The author is grateful to José Víctor Ríos-Rull for his teaching of the computational procedure of heterogeneous agent models. 29The grid points on the wealth space A is not equally spaced. The present calibration assumes aj = $100 ×

j3.5 for j = 2, ..., Na and a1 = $0. 30Because the marginal value with respect to historical earnings, ∂

∂b v(esi, St; Ψt), is difficult to obtain analytically, it is approximated by (v(., bj+1, St; Ψt) − v(., bj

, St; Ψt))/(bj+1 − b

j ) where j = 1, 2, ..., Nb. 31The marginal values with respect to wealth, ∂

∂a v(esi, St; Ψt), are used in the Euler equation to obtain optimal

savings, the marginal values with respect to historical earnings, ∂

∂b v(esi, St; Ψt), are used in the marginal rate of

substitution condition of consumption for leisure to obtain optimal working hours, and the values, v(esi, St; Ψt),

are used to calculate welfare changes measured by compensating variations in wealth. 32When the number of grid points is 201,600, it takes AMD Athron(TM) XP 2600+ about 48 minutes to

calculate one loop of iteration (120 years). It usually takes 5 to 10 loops, depending on the complexity of the

experiment, to calculate an equilibrium transition path of 120 years.

27
1. Set the initial values of factor prices (r0, w0), accidental bequests q0, the policy variables(W0

G, C0G, tr0LS), and the parameters φ0 of policy functions(τI (.), τP (.), trSS(.))

if these are determined endogenously.33

2. Given Ω0 = (r0, w0, q0, W0

G, C0G, tr0LS, φ0), find the decision rule of a household

d(esi; Ψ, Ω0) for all esi ∈ I × Ee × Ae × Be.

34

(a) For age i = 109, find the decision rule d(es109; Ψ, Ω0). Since the survival rate

φ109 = 0, the end-of-period wealth ai+1(es109; .)=0 for all es109. Compute consumption and working hours (ci(es109; .), hi(es109; .)) and, then, marginal values

∂

∂a v(es109; Ψ, Ω0) and values v(es109; Ψ, Ω0) for all es109.

35

(b) For age i = 108, ..., 20, find the decision rule d(esi; Ψ, Ω0), marginal values

∂

∂a v(esi; Ψ, Ω0), and values v(esi; Ψ, Ω0)for all esi, using ∂∂av(esi+1; Ψ, Ω0) and

∂

∂bv(esi+1; Ψ, Ω0) recursively.36

i. Set the initial guess of a0

i+1(esi; .).

ii. Given a0

i+1(esi; .), compute (ci(esi; .), hi(esi; .)), using ∂

∂bv(esi+1; Ψ, Ω0). Plug

these into the Euler equation with ∂

∂av(esi+1; Ψ, Ω0).

iii. If the Euler error is sufficiently small, then stop. Otherwise, update a0

i+1(esi; .)

and return to Step ii.

3. Find the steady-state measure of households x(esi; Ω0) using the decision rule obtained

in Step 2. This computation is done forward from age 20 to age 109. Repeat this step

to iterate q for q1.

4. Compute new factor prices (r1, w1), the policy variables (W1

G, C1G, tr1LS), and the

parameters φ1 of policy functions.37

33Actually, if we find the capital-labor ratio, both r and w are calculated from the given production function

and depreciation rate. 34In the steady-state economy, the decision rule of a household d(esi; Ψ, Ω0) is not a function of the aggregate

state of economy Se = (x(esi), WG). The measure of household x(esi) is determined uniquely by the steady-state

condition, and the government’s wealth WG is determined by the policy rule Ψ. 35The marginal value with respect to historical earnings, ∂

∂b v(esi; Ψ, Ω0), is zero when i > 60 in this paper. 36Again, ∂

∂b v(esi; Ψ, Ω0), is obtained by (v(., bj+1; Ψ, Ω0) − v(., bj ; Ψ, Ω0))/(bj+1 − bj ). 37In many cases, only one of the policy variables and parameters, (W1

G, C1G, tr1LS, φ1), is assumed to be

endogenous (by the government’s financing rule), and it is calculated from the government’s intertemporal budget

constraint.

28
5. Compare Ω1 = (r1, w1, q1, W1

G, C1G, tr1LS, φ1) with Ω0. If the difference is sufficiently small, then stop. Otherwise, update Ω0 and return to Step 2.

A.3 An Equilibrium Transition Path

Let’s assume that the economy is in the initial steady state in period 0, and that the

new policy schedule (rule) Ψ1, which was not expected in period 0, is announced at the

beginning of period 1, where Ψ1 = {WG,t+1, CG,t, trLS,t, τI,t (.), τP,t (.), trSS,t (.)}∞

t=1.

Let Se1 = (x1(esi), WG,1) be the state of the economy at the beginning of period 1. The

state of the economy Se1 is usually equal to that of the initial steady state. The algorithm

to compute a transition path to a new steady-state equilibrium (thereafter, final steady-state

equilibrium) is as follows.

1. Choose a sufficiently large number, T, such that the economy is said to reach the

new steady state within T periods.38 Set the initial guess, {Ω0

t }T

t=1, on factor prices

(r0

t , w0t), accidental bequests q0t , the policy variables (W0

G,t+1, C0G,t, tr0LS,t), and the

parameters φ0

t of policy functions for t = 1, 2, ..., T.

2. Given Ω0

T = (r0T , w0T , q0T , W0G,T , C0G,T , tr0LS,T ,φ0T ), find the final steady-state decision rule d(esi, SeT ; ΨT ; Ω0

T ), marginal values, ∂

∂a v(esi,SeT ; ΨT ; Ω0

T ), and values

v(esi, SeT ; ΨT ; Ω0

T ) for all esi ∈ I × Ee × Ae × Be. (See the algorithm for a steadystate equilibrium.)

3. For period t = T −1, T −2, ..., 1, based on the guess, Ω0

t , find backward the decision

rule d(esi,Set; Ψt; Ω0

t), marginal values ∂

∂av(esi, Set; Ψt; Ω0

t), and values v(esi,Set; Ψt;

Ω0

t) for all esi ∈ I ×Ee×Ae×Be, using the next period marginal values ∂

∂av(esi+1, Set+1;

Ψt+1; Ω0

t+1) and values v(esi+1, Set+1; Ψt+1; Ω0t+1) recursively.

(a) For age i = 109, find the decision rule d(es109,Set; Ψt; Ω0

t) and compute the marginal values ∂

∂av(es109,Set; Ψt; Ω0

t) and values v(es109, Set; Ψt; Ω0t) for all es109.

(b) For age i = 108, ..., 20, find the decision rule d(esi,Set; Ψt; Ω0

t) and compute

∂

∂a v(esi,Set; Ψt; Ω0

t) and v(esi,Set; Ψt; Ω0t) for all esi, using ∂

∂av(esi+1,Set+1; Ψt+1;

Ω0

t+1) and v(esi+1,Set+1; Ψt+1; Ω0

t+1) previously computed.39

38For this to be the case, the government’s policy rule has to be time-invariant sufficiently before period T,

that is, Ψs = ΨT for 1 ≤ s<T. 39Note that this step does not use ∂

∂a v(esi+1, Set; Ψt; Ω0

t ) recursively.

29
i. Set the initial guess of a0

i+1(esi; .).

ii. Given a0

i+1(esi; .), compute (ci(esi; .), hi(esi; .)), using ∂

∂bv(esi+1,Set+1; Ψt+1;

Ω0

t+1) calculated from v(esi+1,Set+1; Ψt+1; Ω0

t+1). Plug these into the Euler

equation with ∂

∂a v(esi+1, Set+1; Ψt+1; Ω0

t+1).

iii. If the Euler error is sufficiently small, then stop. Otherwise, update a0

i+1(esi; .)

and return to Step ii.

4. For period t = 1, 2, ..., T−1, compute forward Ω1

t = (r1t , w1t , q1t ,W1

G,t+1, C1G,t, tr1LS,t,

φ1

t) and the measure of households xt+1(esi), using the decision rule d(esi,Set; Ψt; Ω0

t)

obtained in Step 3 and using the state of economy Set = (xt(esi), WG,t) recursively.

5. Compare {Ω1

t }T

t=1 with {Ω0

t }T

t=1. If the difference is sufficiently small, then stop.

Otherwise, update {Ω0

t }T

t=1 and return to Step 2. If the final steady-state equilibrium

is known, return to Step 3 instead.40

B Detailed Tables and Figures

March 2003 Assumptions. Tables A.1 (a) to A.5 (a) show the effects of a 10 percent marginal rate cut on macroeconomic variables in selected years; Tables A.1 (b) to A.5 (b) show

the welfare gains or losses of households of selected age cohorts and temporary working

abilities; and Figures A.1 to A.5 also show the effects of a 10 percent marginal rate cut

throughout the transition paths.

Alternative Assumptions. Similarly, Tables A.6 (a) to A.10 (a) show the effects of a 10

percent marginal rate cut on macroeconomic variables; Tables A.6 (b) to A.10 (b) show the

welfare gains or losses; and Figures A.1 to A.5 also show the effects of a 10 percent marginal

rate cut throughout the transition paths.

40For example, for a policy experiment with balanced budget assumption, the final steady state needs to be

calculated only once, because the government wealth (debt) level in T is known and fixed. If deficit financing is

assumed for the first several years, the government wealth level in T changes, and the final steady state needs to

be calculated in every iteration.

30
Table A.1 (a). Income Tax Rates Reduced by 10 Percent Proportionally; Government Consumption Reduced Contemporaneously

Changes in Macroeconomic Indicators from the Baseline-- M- arch 2003 Assumptions

Year Average

1 2 3 4 5 6 7 8 9 10 15 20 25 30 40 120 01-05 06-10 01-10

C( losed Economy)

%ch N( ational Wealth) 0.0 0.2 0.3 0.5 0.6 0.7 0.9 1.0 1.1 1.2 1.6 1.9 2.0 2.1 2.2 2.2 0.3 1.0 0.6

%ch(Labor) 0.8 0.7 0.6 0.6 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.4 0.4 0.7 0.5 0.6

%ch G( NP=GDP) 0.5 0.5 0.5 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.8 0.9 0.9 0.9 1.0 1.0 0.6 0.6 0.6

%ch(Consumption) 0.9 1.0 1.1 1.2 1.3 1.4 1.4 1.5 1.6 1.6 1.8 2.0 2.1 2.1 2.2 2.2 1.1 1.5 1.3

%ch G( ross Investment) 2.2 2.4 2.4 2.4 2.3 2.2 2.4 2.7 2.5 2.7 2.5 2.4 2.3 2.3 2.2 2.2 2.4 2.5 2.4

ch(Lump-Sum Transfer/GDP%) -0.24 -0.12 -0.08 -0.09 -0.05 -0.04 0.05 0.12 0.08 0.07 0.07 0.07 0.07 0.07 0.07 0.07 -0.12 0.06 -0.03

ch G( ov't Consumption/GDP%) -0.49 -0.61 -0.66 -0.67 -0.70 -0.71 -0.80 -0.87 -0.84 -0.85 -0.85 -0.84 -0.85 -0.85 -0.85 -0.86 -0.63 -0.82 -0.72

ch(Income Tax/GDP%) -0.80 -0.80 -0.81 -0.83 -0.81 -0.81 -0.80 -0.81 -0.82 -0.84 -0.84 -0.83 -0.83 -0.82 -0.82 -0.82 -0.81 -0.82 -0.81

ch(Interest Rate%) 0.06 0.04 0.02 0.01 0.00 -0.02 -0.03 -0.04 -0.05 -0.05 -0.09 -0.11 -0.12 -0.13 -0.13 -0.13 0.03 -0.04 0.00

%ch W( age Rate) -0.2 -0.2 -0.1 0.0 0.0 0.1 0.1 0.1 0.2 0.2 0.3 0.4 0.5 0.5 0.5 0.5 -0.1 0.1 0.0

ch(Private Wealth G/ DP%) 0.0 0.4 0.9 1.3 1.7 2.0 2.3 2.6 3.0 3.3 4.5 5.2 5.6 5.8 6.0 6.0 0.9 2.7 1.8

ch G( ov't Wealth/GDP%) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

ch(Budget Deficit G/ DP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

(Small Open Economy)

%ch N( ational Wealth) 0.0 0.2 0.4 0.6 0.8 1.0 1.1 1.3 1.5 1.6 2.3 2.8 3.1 3.4 3.6 3.7 0.4 1.3 0.9

%ch(Labor) 1.0 0.9 0.8 0.8 0.7 0.6 0.5 0.5 0.5 0.5 0.4 0.3 0.3 0.2 0.2 0.2 0.8 0.5 0.7

%ch G( NP) 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.9 1.0 1.1 1.1 1.2 1.2 1.2 0.7 0.8 0.7

%ch G( DP) 1.0 0.9 0.8 0.8 0.7 0.6 0.5 0.5 0.5 0.5 0.4 0.3 0.3 0.2 0.2 0.2 0.8 0.5 0.7

%ch(Consumption) 0.9 1.0 1.0 1.1 1.2 1.2 1.3 1.3 1.4 1.4 1.7 1.8 1.9 2.0 2.1 2.1 1.0 1.3 1.2

%ch G( ross Dom. Investment) 1.0 0.9 0.8 0.8 0.7 0.6 0.5 0.5 0.5 0.5 0.4 0.3 0.3 0.2 0.2 0.2 0.8 0.5 0.7

ch(Lump-Sum Transfer/GDP%) -0.24 -0.12 -0.08 -0.09 -0.05 -0.04 0.05 0.12 0.08 0.07 0.07 0.07 0.07 0.07 0.07 0.07 -0.12 0.06 -0.03

ch G( ov't Consumption/GDP%) -0.44 -0.57 -0.63 -0.64 -0.67 -0.69 -0.78 -0.87 -0.84 -0.85 -0.86 -0.86 -0.86 -0.87 -0.87 -0.86 -0.59 -0.81 -0.70

ch(Income Tax/GDP%) -0.78 -0.78 -0.79 -0.81 -0.79 -0.80 -0.79 -0.80 -0.81 -0.84 -0.84 -0.83 -0.83 -0.83 -0.83 -0.83 -0.79 -0.81 -0.80

ch N( et Foreign Assets G/ DP%) -2.6 -1.8 -1.0 -0.4 0.3 1.0 1.6 2.2 2.7 3.0 5.3 6.9 7.9 8.5 9.2 9.6 -1.1 2.1 0.5

ch(Private Wealth G/ DP%) 0.0 0.5 1.1 1.7 2.2 2.7 3.1 3.6 4.1 4.5 6.4 7.7 8.6 9.2 9.8 10.1 1.1 3.6 2.3

ch G( ov't Wealth/GDP%) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

ch(Budget Deficit G/ DP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

31
Table A.1 (b). Income Tax Rates Reduced by 10 Percent Proportionally; Government Consumption Reduced Contemporaneously

Compensating Variations in Wealth as Percentages of Per-Household GDP-- M- arch 2003 Assumptions

The Year When Age 20 (Top) / the Age in Year 1 (Bottom)

-88 -79 -69 -59 -49 -39 -29 -19 -9 1 11 21 41 61 81 101 120

109 100 90 80 70 60 50 40 30 20 10 0 -20 -40 -60 -80 -99

(Closed Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.4 -0.4 0.0 0.1 0.3 2.6 4.5 4.2 2.4 3.9 4.1 4.3 4.3 4.3 4.3 4.3

20-40 percentile 0.2 0.9 4.2 7.6 7.8 5.6 7.7 8.2 8.5 8.5 8.5 8.5 8.540-60 percentile 0.2 1.6 6.0 9.7 10.6 7.5 9.9 10.5 10.8 10.8 10.9 10.9 10.960-80 percentile 0.4 3.1 9.0 13.1 14.4 10.2 12.9 13.6 14.0 14.0 14.0 14.1 14.080-90 percentile 1.1 5.4 11.9 16.4 17.7 13.1 16.1 16.9 17.2 17.3 17.3 17.4 17.490-95 percentile 3.5 11.3 15.2 21.4 21.0 16.2 19.5 20.4 20.8 20.8 20.9 21.0 20.995-99 percentile 12.2 25.9 27.1 31.5 28.5 21.0 24.6 25.5 26.0 26.0 26.1 26.2 26.299-100 percentile 52.9 111.9 88.9 69.3 52.8 27.6 31.7 32.8 33.3 33.4 33.4 33.6 33.6

Average -0.3 -0.4 -0.4 0.0 1.5 4.4 8.3 11.6 11.9 8.4 10.8 11.4 11.6 11.7 11.7 11.7 11.7(Small Open Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.4 -0.4 -0.1 0.3 0.6 2.9 4.7 4.3 2.5 3.7 4.0 4.2 4.2 4.2 4.2 4.2

20-40 percentile 0.4 1.3 4.8 8.0 8.0 5.7 7.4 7.9 8.3 8.3 8.3 8.3 8.340-60 percentile 0.5 2.4 6.9 10.5 11.1 7.6 9.5 10.0 10.5 10.6 10.6 10.6 10.660-80 percentile 1.0 4.8 10.8 15.0 15.6 10.5 12.5 13.1 13.6 13.7 13.7 13.7 13.780-90 percentile 2.1 8.2 15.1 19.7 20.2 13.7 15.7 16.4 17.0 17.1 17.1 17.1 17.090-95 percentile 5.2 16.6 20.9 27.5 25.0 17.3 19.6 20.3 20.8 20.9 20.9 20.9 20.995-99 percentile 15.5 35.5 38.3 43.1 36.1 23.6 26.1 26.9 27.4 27.5 27.5 27.5 27.599-100 percentile 62.5 142.6 122.8 100.7 73.8 32.6 35.6 36.4 37.0 37.1 37.1 37.1 37.1

Average -0.3 -0.4 -0.4 -0.1 2.1 6.3 10.4 13.7 13.3 8.8 10.5 11.1 11.5 11.6 11.6 11.6 11.6

32
Figure A.1. Income Tax Rates Reduced by 10 Percent Proportionally; Government Consumption Reduced

Contemporaneously---March 2003 Assumptions

(a) GNP

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(b) National Wealth

-1

0

1

1

2

2

3

3

4

4

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(c) Labor Supply

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(d) Private Consumption

0.0

0.5

1.0

1.5

2.0

2.5

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(f) Interest Rate

-0.15

-0.10

-0.05

0.00

0.05

0.10

0 10 20 30 40 50 60 70 80 90 100

Year

Ch from the Baseline

(g) Wage Rate

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(e) Income Tax Revenue

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0 10 20 30 40 50 60 70 80 90 100

Year

Ch as a % of the

Baseline GDP

(h) Welfare Gain / Loss (Avg. of Each Age)

-2

0

2

4

6

8

10

12

14

16

-80 -60 -40 -20 0 20 40 60 80 100 120

Year When Age 20

ch as a % of perHousehold GDP

Closed Economy Small Open Economy

33
Table A.2 (a). Income Tax Rates Reduced by 10 Percent Proportionally; Lump-Sum Transfers Reduced Contemporaneously

Changes in Macroeconomic Indicators from the Baseline-- M- arch 2003 Assumptions

Year Average

1 2 3 4 5 6 7 8 9 10 15 20 25 30 40 120 01-05 06-10 01-10

C( losed Economy)

%ch N( ational Wealth) 0.0 0.3 0.5 0.8 1.1 1.3 1.5 1.8 2.1 2.3 2.6 2.8 2.9 3.0 3.0 3.0 0.5 1.8 1.2

%ch(Labor) 1.0 0.9 0.9 0.9 0.9 0.9 0.8 0.9 0.9 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.9 0.9%ch G( NP=GDP) 0.7 0.7 0.8 0.9 0.9 1.0 1.1 1.1 1.3 1.4 1.5 1.6 1.6 1.6 1.6 1.6 0.8 1.2 1.0%ch(Consumption) 0.6 0.8 0.9 1.0 1.0 1.1 1.2 1.2 1.2 1.2 1.4 1.4 1.5 1.6 1.6 1.6 0.9 1.2 1.0%ch G( ross Investment) 3.6 4.0 4.1 4.3 4.4 4.5 5.0 5.6 5.9 3.2 3.2 3.1 3.1 3.1 3.0 3.0 4.1 4.8 4.5ch(Lump-Sum Transfer/GDP%) -0.68 -0.68 -0.68 -0.69 -0.67 -0.67 -0.65 -0.64 -0.64 -0.64 -0.64 -0.64 -0.64 -0.65 -0.66 -0.67 -0.68 -0.65 -0.67ch G( ov't Consumption/GDP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00ch(Income Tax/GDP%) -0.78 -0.78 -0.78 -0.79 -0.77 -0.76 -0.75 -0.75 -0.75 -0.77 -0.77 -0.76 -0.76 -0.75 -0.75 -0.75 -0.78 -0.76 -0.77ch(Interest Rate%) 0.08 0.05 0.03 0.01 -0.01 -0.03 -0.05 -0.07 -0.09 -0.10 -0.12 -0.13 -0.14 -0.14 -0.15 -0.15 0.03 -0.07 -0.02%ch W( age Rate) -0.3 -0.2 -0.1 0.0 0.1 0.1 0.2 0.3 0.3 0.4 0.5 0.5 0.5 0.6 0.6 0.6 -0.1 0.3 0.1ch(Private Wealth G/ DP%) 0.0 0.7 1.5 2.2 2.9 3.5 4.2 4.9 5.7 6.4 7.1 7.6 7.9 8.1 8.2 8.2 1.5 4.9 3.2ch G( ov't Wealth/GDP%) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0ch(Budget Deficit G/ DP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00(Small Open Economy)

%ch N( ational Wealth) 0.0 0.3 0.7 1.0 1.3 1.7 2.0 2.3 2.7 3.0 3.6 4.0 4.2 4.4 4.6 4.6 0.7 2.3 1.5

%ch(Labor) 1.3 1.2 1.1 1.1 1.0 1.0 0.9 0.9 0.9 1.0 0.9 0.9 0.8 0.8 0.8 0.8 1.1 0.9 1.0%ch G( NP) 0.9 0.9 1.0 1.1 1.1 1.2 1.2 1.3 1.4 1.6 1.7 1.8 1.8 1.9 1.9 1.9 1.0 1.3 1.2%ch G( DP) 1.3 1.2 1.1 1.1 1.0 1.0 0.9 0.9 0.9 1.0 0.9 0.9 0.8 0.8 0.8 0.8 1.1 0.9 1.0%ch(Consumption) 0.6 0.6 0.7 0.8 0.8 0.9 0.9 0.9 1.0 1.0 1.1 1.3 1.4 1.4 1.5 1.6 0.7 0.9 0.8%ch G( ross Dom. Investment) 1.3 1.2 1.1 1.1 1.0 1.0 0.9 0.9 0.9 1.0 0.9 0.9 0.8 0.8 0.8 0.8 1.1 0.9 1.0ch(Lump-Sum Transfer/GDP%) -0.61 -0.62 -0.63 -0.65 -0.64 -0.64 -0.64 -0.64 -0.64 -0.65 -0.66 -0.66 -0.66 -0.66 -0.67 -0.68 -0.63 -0.64 -0.64ch G( ov't Consumption/GDP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00ch(Income Tax/GDP%) -0.74 -0.74 -0.75 -0.77 -0.75 -0.75 -0.74 -0.74 -0.75 -0.77 -0.77 -0.77 -0.77 -0.76 -0.76 -0.76 -0.75 -0.75 -0.75ch N( et Foreign Assets G/ DP%) -3.5 -2.4 -1.2 -0.3 0.9 1.9 2.9 3.9 4.9 5.6 7.3 8.5 9.4 9.9 10.4 10.5 -1.3 3.8 1.3ch(Private Wealth G/ DP%) 0.0 0.9 1.8 2.7 3.6 4.5 5.4 6.3 7.3 8.2 9.8 10.9 11.6 12.1 12.5 12.7 1.8 6.4 4.1ch G( ov't Wealth/GDP%) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0ch(Budget Deficit G/ DP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

34
Table A.2 (b). Income Tax Rates Reduced by 10 Percent Proportionally; Lump-Sum Transfers Reduced Contemporaneously

Compensating Variations in Wealth as Percentages of Per-Household GDP-- M- arch 2003 Assumptions

The Year When Age 20 (Top) / the Age in Year 1 (Bottom)

-88 -79 -69 -59 -49 -39 -29 -19 -9 1 11 21 41 61 81 101 120

109 100 90 80 70 60 50 40 30 20 10 0 -20 -40 -60 -80 -99

(Closed Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.4 -1.0 -3.8 -6.3 -6.3 -4.9 -2.6 -1.1 -0.7 -2.6 -2.5 -2.5 -2.6 -2.6 -2.6 -2.5

20-40 percentile -6.4 -7.3 -4.5 -2.2 -0.5 -0.6 -3.3 -3.0 -3.0 -3.1 -3.1 -3.1 -3.140-60 percentile -6.8 -8.0 -3.6 -1.2 0.4 -0.1 -2.8 -2.4 -2.5 -2.6 -2.6 -2.5 -2.560-80 percentile -7.7 -7.7 -1.7 1.4 2.5 1.1 -1.4 -1.0 -1.0 -1.1 -1.1 -1.1 -1.180-90 percentile -8.0 -6.4 0.0 3.8 4.7 2.3 -0.1 0.4 0.4 0.3 0.3 0.3 0.390-95 percentile -6.5 -2.0 1.6 7.0 7.1 4.1 2.0 2.5 2.5 2.4 2.4 2.4 2.495-99 percentile 1.1 10.5 11.0 14.9 13.0 7.4 6.0 6.5 6.5 6.4 6.4 6.4 6.599-100 percentile 38.1 87.8 64.6 46.0 32.8 12.4 11.8 12.4 12.5 12.4 12.4 12.4 12.4

Average -0.3 -0.4 -1.0 -3.8 -6.1 -5.3 -1.8 0.9 1.9 0.8 -1.6 -1.2 -1.3 -1.3 -1.4 -1.3 -1.3(Small Open Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.4 -1.0 -3.8 -6.1 -6.0 -4.8 -2.7 -1.3 -0.9 -3.0 -2.8 -2.7 -2.7 -2.7 -2.7 -2.7

20-40 percentile -6.0 -6.7 -4.0 -1.9 -0.6 -0.8 -4.0 -3.5 -3.3 -3.3 -3.3 -3.3 -3.340-60 percentile -6.3 -6.7 -2.6 -0.4 0.6 -0.3 -3.6 -3.1 -2.9 -2.9 -2.9 -2.9 -2.960-80 percentile -6.6 -5.0 0.6 3.6 3.7 1.0 -2.3 -1.8 -1.5 -1.6 -1.6 -1.5 -1.580-90 percentile -6.1 -1.8 4.2 7.8 7.4 2.5 -0.9 -0.3 0.0 0.0 0.0 0.0 0.090-95 percentile -3.2 6.1 9.4 15.0 11.8 4.8 1.6 2.2 2.5 2.5 2.5 2.5 2.595-99 percentile 6.8 24.4 26.2 30.0 22.3 10.1 7.1 7.8 8.1 8.1 8.1 8.1 8.199-100 percentile 52.9 131.6 110.6 87.2 59.4 18.1 15.4 16.1 16.4 16.4 16.4 16.4 16.5

Average -0.3 -0.4 -1.0 -3.8 -5.0 -2.5 0.9 3.4 3.3 0.9 -2.2 -1.7 -1.5 -1.5 -1.5 -1.5 -1.5

35
Figure A.2. Income Tax Rates Reduced by 10 Percent Proportionally; Lump-Sum Transfers Reduced

Contemporaneously---March 2003 Assumptions

(a) GNP

0.0

0.5

1.0

1.5

2.0

2.5

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(b) National Wealth

-1

0

1

2

3

4

5

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(c) Labor Supply

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(d) Private Consumption

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(f) Interest Rate

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0 10 20 30 40 50 60 70 80 90 100

Year

Ch from the Baseline

(g) Wage Rate

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(e) Income Tax Revenue

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0 10 20 30 40 50 60 70 80 90 100

Year

Ch as a % of the

Baseline GDP

(h) Welfare Gain / Loss (Avg. of Each Age)

-8

-6

-4

-2

0

2

4

-80 -60 -40 -20 0 20 40 60 80 100 120

Year When Age 20

ch as a % of perHousehold GDP

Closed Economy Small Open Economy

36
Table A.3 (a). Income Tax Rates Reduced by 10 Percent Proportionally; Government Consumption Reduced Gradually After 10 Years

Changes in Macroeconomic Indicators from the Baseline-- M- arch 2003 Assumptions

Year Average

1 2 3 4 5 6 7 8 9 10 15 20 25 30 40 120 01-05 06-10 01-10

C( losed Economy)

%ch N( ational Wealth) 0.0 0.1 0.1 0.1 0.1 0.0 -0.1 -0.2 -0.4 -0.5 -1.3 -1.5 -1.4 -1.3 -1.3 -1.2 0.1 -0.2 -0.1

%ch(Labor) 0.9 0.8 0.8 0.8 0.7 0.6 0.6 0.5 0.5 0.5 0.3 0.2 0.2 0.2 0.2 0.2 0.8 0.5 0.7%ch G( NP=GDP) 0.7 0.6 0.6 0.6 0.5 0.4 0.4 0.3 0.2 0.2 -0.2 -0.3 -0.2 -0.2 -0.2 -0.2 0.6 0.3 0.4%ch(Consumption) 0.7 0.8 0.9 1.0 1.0 1.1 1.1 1.2 1.2 1.3 1.4 1.5 1.6 1.6 1.7 1.7 0.9 1.2 1.0%ch G( ross Investment) 1.0 0.4 0.0 -0.3 -0.8 -1.2 -1.7 -2.2 -2.6 -2.9 -2.6 -1.0 -1.1 -1.2 -1.2 -1.2 0.0 -2.1 -1.0ch(Lump-Sum Transfer/GDP%) -0.24 -0.12 -0.08 -0.09 -0.05 -0.04 0.05 0.12 0.08 0.07 0.07 0.07 0.07 0.07 0.07 0.07 -0.12 0.06 -0.03ch G( ov't Consumption/GDP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.50 -1.02 -1.01 -1.00 -1.00 -1.00 0.00 0.00 0.00ch(Income Tax/GDP%) -0.79 -0.79 -0.80 -0.82 -0.81 -0.81 -0.81 -0.82 -0.84 -0.87 -0.90 -0.91 -0.90 -0.90 -0.90 -0.90 -0.80 -0.83 -0.82ch(Interest Rate%) 0.07 0.06 0.05 0.05 0.05 0.05 0.05 0.06 0.07 0.08 0.12 0.14 0.12 0.12 0.11 0.11 0.06 0.06 0.06%ch W( age Rate) -0.3 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.3 -0.3 -0.5 -0.5 -0.5 -0.5 -0.4 -0.4 -0.2 -0.2 -0.2ch(Private Wealth G/ DP%) 0.0 0.6 1.3 1.9 2.4 3.0 3.4 3.9 4.4 4.8 6.4 7.2 7.6 7.8 8.0 8.0 1.2 3.9 2.6ch G( ov't Wealth/GDP%) 0.0 -0.4 -1.0 -1.6 -2.3 -3.0 -3.7 -4.5 -5.4 -6.2 -9.9 -11.4 -11.4 -11.4 -11.4 -11.4 -1.1 -4.5 -2.8ch(Budget Deficit G/ DP%) 0.46 0.60 0.67 0.71 0.77 0.81 0.92 1.04 1.04 1.10 0.77 0.32 0.32 0.32 0.32 0.32 0.64 0.98 0.81(Small Open Economy)

%ch N( ational Wealth) 0.0 0.0 0.0 -0.1 -0.2 -0.3 -0.5 -0.7 -0.9 -1.1 -2.2 -2.6 -2.6 -2.5 -2.5 -2.5 -0.1 -0.7 -0.4

%ch(Labor) 0.9 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.4 0.4 0.8 0.5 0.6%ch G( NP) 0.6 0.6 0.5 0.5 0.4 0.3 0.2 0.1 0.1 0.0 -0.3 -0.5 -0.4 -0.4 -0.4 -0.4 0.5 0.1 0.3%ch G( DP) 0.9 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.4 0.4 0.8 0.5 0.6%ch(Consumption) 1.0 1.1 1.1 1.2 1.2 1.3 1.3 1.4 1.4 1.5 1.6 1.6 1.7 1.7 1.7 1.7 1.1 1.4 1.3%ch G( ross Dom. Investment) 12.3 -0.5 -0.2 0.5 -0.5 -0.2 -0.2 0.0 0.6 1.0 0.4 0.4 0.5 0.4 0.4 0.4 2.3 0.2 1.3ch(Lump-Sum Transfer/GDP%) -0.24 -0.12 -0.08 -0.09 -0.05 -0.04 0.05 0.12 0.08 0.07 0.07 0.07 0.07 0.07 0.07 0.07 -0.12 0.06 -0.03ch G( ov't Consumption/GDP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.48 -0.98 -0.98 -0.98 -0.98 -0.98 0.00 0.00 0.00ch(Income Tax/GDP%) -0.78 -0.79 -0.80 -0.82 -0.81 -0.82 -0.82 -0.83 -0.85 -0.88 -0.89 -0.89 -0.89 -0.89 -0.89 -0.89 -0.80 -0.84 -0.82ch N( et Foreign Assets G/ DP%) -2.5 -2.2 -2.1 -2.2 -2.3 -2.4 -2.7 -3.2 -3.8 -4.5 -7.2 -8.4 -8.3 -8.2 -8.1 -8.1 -2.2 -3.3 -2.8ch(Private Wealth G/ DP%) 0.0 0.5 0.9 1.4 1.7 2.1 2.4 2.6 2.9 3.2 4.0 4.2 4.4 4.4 4.5 4.5 0.9 2.6 1.8ch G( ov't Wealth/GDP%) 0.0 -0.4 -1.0 -1.6 -2.3 -3.0 -3.7 -4.5 -5.4 -6.3 -10.0 -11.4 -11.4 -11.4 -11.4 -11.4 -1.1 -4.6 -2.8ch(Budget Deficit G/ DP%) 0.46 0.60 0.68 0.72 0.78 0.82 0.94 1.05 1.05 1.10 0.76 0.32 0.32 0.32 0.32 0.32 0.65 0.99 0.82

37
Table A.3 (b). Income Tax Rates Reduced by 10 Percent Proportionally; Government Consumption Reduced Gradually After 10 Years

Compensating Variations in Wealth as Percentages of Per-Household GDP-- M- arch 2003 Assumptions

The Year When Age 20 (Top) / the Age in Year 1 (Bottom)

-88 -79 -69 -59 -49 -39 -29 -19 -9 1 11 21 41 61 81 101 120

109 100 90 80 70 60 50 40 30 20 10 0 -20 -40 -60 -80 -99

(Closed Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.4 -0.4 0.3 0.6 0.8 2.2 3.4 2.9 1.5 2.4 2.6 2.8 2.8 2.8 2.8 2.8

20-40 percentile 0.8 1.5 3.9 6.0 5.7 3.8 4.9 5.3 5.6 5.6 5.6 5.6 5.640-60 percentile 1.0 2.6 5.8 8.1 8.2 5.3 6.4 6.8 7.1 7.1 7.1 7.1 7.160-80 percentile 1.8 5.2 9.6 12.3 12.1 7.5 8.6 9.0 9.3 9.3 9.3 9.3 9.380-90 percentile 3.2 8.7 13.7 16.7 16.2 9.9 11.0 11.4 11.8 11.8 11.8 11.8 11.890-95 percentile 6.7 17.3 19.8 24.3 20.7 13.0 13.9 14.3 14.7 14.7 14.7 14.7 14.795-99 percentile 17.1 36.3 36.9 39.3 31.0 18.5 19.2 19.3 19.8 19.8 19.8 19.8 19.799-100 percentile 63.0 140.4 118.8 94.7 66.8 26.5 26.8 26.7 27.2 27.3 27.3 27.2 27.2

Average -0.3 -0.4 -0.4 0.3 2.8 6.6 9.3 11.4 10.3 6.3 7.3 7.6 7.9 7.9 7.9 7.9 7.9(Small Open Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.4 -0.5 -0.6 -0.4 -0.2 1.8 3.4 3.1 1.7 2.7 2.8 2.8 2.8 2.8 2.8 2.8

20-40 percentile -0.3 0.2 3.2 5.8 5.9 4.2 5.4 5.5 5.6 5.6 5.6 5.6 5.640-60 percentile -0.6 0.7 4.6 7.5 8.3 5.7 7.0 7.1 7.2 7.2 7.2 7.2 7.260-80 percentile -0.8 1.6 6.8 10.3 11.3 7.9 9.2 9.4 9.5 9.5 9.5 9.5 9.580-90 percentile -0.6 3.2 8.9 12.9 14.1 10.2 11.6 11.7 11.8 11.8 11.8 11.8 11.890-95 percentile 1.0 7.9 10.8 16.8 16.8 12.9 14.2 14.3 14.4 14.4 14.4 14.4 14.495-99 percentile 8.9 20.7 20.9 25.4 23.5 17.1 18.1 18.2 18.3 18.3 18.3 18.3 18.399-100 percentile 48.4 102.6 78.0 59.5 46.1 23.0 23.7 23.7 23.9 23.9 23.9 23.9 23.8

Average -0.3 -0.4 -0.5 -0.6 0.4 3.0 6.3 9.2 9.4 6.5 7.7 7.8 7.9 7.9 7.9 7.9 7.9

38
Figure A.3. Income Tax Rates Reduced by 10 Percent Proportionally; Government Consumption Reduced

Gradually After 10 Years---March 2003 Assumptions

(a) GNP

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(b) National Wealth

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(c) Labor Supply

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(d) Private Consumption

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(f) Interest Rate

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0 10 20 30 40 50 60 70 80 90 100

Year

Ch from the Baseline

(g) Wage Rate

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(e) Income Tax Revenue

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0 10 20 30 40 50 60 70 80 90 100

Year

Ch as a % of the

Baseline GDP

(h) Welfare Gain / Loss (Avg. of Each Age)

-2

0

2

4

6

8

10

12

-80 -60 -40 -20 0 20 40 60 80 100 120

Year When Age 20

ch as a % of perHousehold GDP

Closed Economy Small Open Economy

39
Table A.4 (a). Income Tax Rates Reduced by 10 Percent Proportionally; Lump-Sum Transfers Reduced Gradually After 10 Years

Changes in Macroeconomic Indicators from the Baseline-- M- arch 2003 Assumptions

Year Average

1 2 3 4 5 6 7 8 9 10 15 20 25 30 40 120 01-05 06-10 01-10

C( losed Economy)

%ch N( ational Wealth) 0.0 0.1 0.2 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0.2 0.1 0.2 0.4 0.3

%ch(Labor) 1.1 1.0 0.9 1.0 0.9 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 1.0 1.0 0.8 0.9%ch G( NP=GDP) 0.8 0.7 0.7 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.7 0.7%ch(Consumption) 0.6 0.7 0.8 0.8 0.9 0.9 1.0 1.0 1.1 1.1 1.1 1.0 1.1 1.1 1.1 1.1 0.8 1.0 0.9%ch G( ross Investment) 2.0 1.6 1.3 1.1 0.8 0.6 0.3 0.1 0.0 0.0 0.0 0.2 0.2 0.2 0.1 0.1 1.4 0.2 0.8ch(Lump-Sum Transfer/GDP%) -0.24 -0.12 -0.08 -0.09 -0.05 -0.04 0.05 0.12 0.08 0.07 -0.38 -0.76 -0.75 -0.75 -0.76 -0.77 -0.12 0.06 -0.03ch G( ov't Consumption/GDP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00ch(Income Tax/GDP%) -0.77 -0.77 -0.78 -0.79 -0.78 -0.78 -0.77 -0.78 -0.79 -0.82 -0.82 -0.81 -0.81 -0.81 -0.81 -0.81 -0.78 -0.79 -0.78ch(Interest Rate%) 0.08 0.07 0.05 0.05 0.04 0.03 0.03 0.03 0.03 0.04 0.05 0.06 0.06 0.06 0.06 0.06 0.06 0.03 0.04%ch W( age Rate) -0.3 -0.3 -0.2 -0.2 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.1 -0.2ch(Private Wealth G/ DP%) 0.0 0.8 1.6 2.4 3.2 3.9 4.6 5.3 6.0 6.7 9.4 10.3 10.3 10.3 10.3 10.2 1.6 5.3 3.4ch G( ov't Wealth/GDP%) 0.0 -0.4 -0.9 -1.5 -2.1 -2.8 -3.4 -4.1 -4.9 -5.7 -8.7 -9.8 -9.8 -9.8 -9.8 -9.8 -1.0 -4.2 -2.6ch(Budget Deficit G/ DP%) 0.42 0.56 0.63 0.66 0.71 0.74 0.84 0.95 0.94 0.98 0.63 0.28 0.28 0.28 0.28 0.28 0.60 0.89 0.74(Small Open Economy)

%ch N( ational Wealth) 0.0 0.1 0.2 0.2 0.3 0.3 0.3 0.2 0.2 0.1 -0.1 -0.3 -0.4 -0.4 -0.5 -0.6 0.2 0.2 0.2

%ch(Labor) 1.2 1.1 1.0 1.0 0.9 0.8 0.8 0.8 0.8 0.8 0.9 1.0 1.0 1.0 1.1 1.1 1.0 0.8 0.9%ch G( NP) 0.8 0.8 0.7 0.8 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.8 0.6 0.7%ch G( DP) 1.2 1.1 1.0 1.0 0.9 0.8 0.8 0.8 0.8 0.8 0.9 1.0 1.0 1.0 1.1 1.1 1.0 0.8 0.9%ch(Consumption) 0.8 0.8 0.9 1.0 1.0 1.1 1.1 1.1 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 0.9 1.1 1.0%ch G( ross Dom. Investment) 15.8 0.0 -0.1 1.0 -0.3 0.3 0.0 0.6 0.9 1.7 1.0 1.3 1.0 1.2 1.2 1.1 3.3 0.7 2.0ch(Lump-Sum Transfer/GDP%) -0.24 -0.12 -0.08 -0.09 -0.05 -0.04 0.05 0.12 0.08 0.07 -0.38 -0.74 -0.74 -0.74 -0.75 -0.76 -0.12 0.06 -0.03ch G( ov't Consumption/GDP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00ch(Income Tax/GDP%) -0.75 -0.76 -0.77 -0.79 -0.78 -0.78 -0.78 -0.78 -0.79 -0.82 -0.82 -0.81 -0.81 -0.81 -0.81 -0.81 -0.77 -0.79 -0.78ch N( et Foreign Assets G/ DP%) -3.2 -2.6 -2.2 -2.0 -1.7 -1.5 -1.4 -1.5 -1.6 -2.0 -2.8 -3.5 -3.8 -4.0 -4.2 -4.5 -2.3 -1.6 -2.0ch(Private Wealth G/ DP%) 0.0 0.7 1.4 2.2 2.8 3.5 4.1 4.7 5.4 6.0 8.3 9.0 8.8 8.7 8.5 8.2 1.4 4.7 3.1ch G( ov't Wealth/GDP%) 0.0 -0.4 -0.9 -1.5 -2.1 -2.7 -3.3 -4.1 -4.9 -5.7 -8.7 -9.8 -9.8 -9.8 -9.8 -9.8 -1.0 -4.1 -2.5ch(Budget Deficit G/ DP%) 0.40 0.54 0.61 0.64 0.70 0.74 0.85 0.95 0.95 0.98 0.62 0.28 0.28 0.28 0.28 0.28 0.58 0.89 0.74

40
Table A.4 (b). Income Tax Rates Reduced by 10 Percent Proportionally; Lump-Sum Transfers Reduced Gradually After 10 Years

Compensating Variations in Wealth as Percentages of Per-Household GDP-- M- arch 2003 Assumptions

The Year When Age 20 (Top) / the Age in Year 1 (Bottom)

-88 -79 -69 -59 -49 -39 -29 -19 -9 1 11 21 41 61 81 101 120

109 100 90 80 70 60 50 40 30 20 10 0 -20 -40 -60 -80 -99

(Closed Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.4 -0.5 -1.6 -3.9 -4.7 -3.8 -3.0 -1.9 -1.1 -2.7 -4.8 -4.7 -4.8 -4.9 -4.9 -4.9

20-40 percentile -3.9 -5.3 -3.5 -2.6 -1.7 -1.4 -4.5 -7.1 -7.1 -7.3 -7.3 -7.3 -7.340-60 percentile -4.1 -5.5 -2.6 -1.5 -1.0 -1.2 -4.8 -7.5 -7.5 -7.6 -7.7 -7.7 -7.760-80 percentile -4.3 -4.2 -0.2 1.6 1.3 -0.5 -4.3 -7.0 -7.1 -7.2 -7.3 -7.3 -7.380-90 percentile -3.9 -1.6 2.5 4.8 4.1 0.4 -3.7 -6.5 -6.5 -6.7 -6.7 -6.7 -6.790-95 percentile -1.3 4.9 6.4 10.2 7.3 2.0 -2.3 -5.1 -5.2 -5.3 -5.4 -5.4 -5.495-99 percentile 7.5 20.6 19.9 21.9 15.5 5.8 1.6 -1.3 -1.4 -1.5 -1.6 -1.6 -1.699-100 percentile 48.8 113.2 89.9 67.3 44.3 11.7 7.5 4.5 4.5 4.3 4.3 4.3 4.3

Average -0.3 -0.4 -0.5 -1.6 -2.9 -1.9 0.2 1.4 1.2 -0.4 -3.6 -6.2 -6.2 -6.3 -6.4 -6.4 -6.4(Small Open Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.4 -0.6 -2.4 -4.7 -5.4 -4.0 -2.9 -1.7 -1.0 -2.6 -4.5 -4.6 -4.7 -4.7 -4.8 -4.7

20-40 percentile -4.8 -6.1 -3.8 -2.6 -1.4 -1.1 -4.2 -6.9 -6.9 -7.1 -7.1 -7.1 -7.140-60 percentile -5.2 -6.7 -3.2 -1.7 -0.8 -0.9 -4.4 -7.1 -7.2 -7.4 -7.4 -7.4 -7.460-80 percentile -6.2 -6.4 -1.7 0.8 1.1 -0.1 -3.9 -6.7 -6.8 -7.0 -7.0 -7.0 -7.080-90 percentile -6.6 -5.0 0.0 3.2 3.4 0.8 -3.4 -6.2 -6.3 -6.5 -6.5 -6.5 -6.590-95 percentile -5.3 -0.2 1.7 6.9 5.9 2.3 -2.2 -5.0 -5.1 -5.3 -5.4 -5.4 -5.495-99 percentile 2.5 13.0 12.2 15.9 12.6 5.6 1.0 -1.8 -2.0 -2.2 -2.2 -2.3 -2.299-100 percentile 42.1 98.2 73.1 52.9 36.7 10.8 5.9 3.0 2.8 2.6 2.6 2.5 2.6

Average -0.3 -0.4 -0.6 -2.4 -4.6 -3.9 -1.2 0.6 1.0 -0.1 -3.4 -5.9 -6.1 -6.2 -6.2 -6.3 -6.2

41
Figure A.4. Income Tax Rates Reduced by 10 Percent Proportionally; Lump-Sum Transfers Reduced

Gradually After 10 Years---March 2003 Assumptions

(a) GNP

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(b) National Wealth

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(c) Labor Supply

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(d) Private Consumption

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(f) Interest Rate

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 10 20 30 40 50 60 70 80 90 100

Year

Ch from the Baseline

(g) Wage Rate

-0.4

-0.3

-0.2

-0.1

0.0

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(e) Income Tax Revenue

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0 10 20 30 40 50 60 70 80 90 100

Year

Ch as a % of the

Baseline GDP

(h) Welfare Gain / Loss (Avg. of Each Age)

-7

-6

-5

-4

-3

-2

-1

0

1

2

-80 -60 -40 -20 0 20 40 60 80 100 120

Year When Age 20

ch as a % of perHousehold GDP

Closed Economy Small Open Economy

42
Table A.5 (a). Income Tax Rates Reduced by 10 Percent Proportionally; Income Tax Rates Increased Gradually After 10 Years

Changes in Macroeconomic Indicators from the Baseline-- M- arch 2003 Assumptions

Year Average

1 2 3 4 5 6 7 8 9 10 15 20 25 30 40 120 01-05 06-10 01-10

C( losed Economy)

%ch N( ational Wealth) 0.0 0.1 0.1 0.1 0.1 0.1 0.1 0.0 -0.1 -0.2 -0.9 -1.9 -2.9 -3.5 -4.1 -4.4 0.1 0.0 0.0

%ch(Labor) 1.0 0.9 0.8 0.8 0.7 0.7 0.7 0.6 0.6 0.7 0.1 -0.6 -0.5 -0.4 -0.4 -0.3 0.8 0.7 0.8%ch G( NP=GDP) 0.7 0.6 0.6 0.6 0.6 0.5 0.5 0.4 0.4 0.4 -0.2 -1.0 -1.2 -1.3 -1.5 -1.6 0.6 0.5 0.5%ch(Consumption) 0.7 0.8 0.9 0.9 1.0 1.0 1.1 1.1 1.1 1.2 0.8 0.1 -0.3 -0.6 -0.9 -1.0 0.9 1.1 1.0%ch G( ross Investment) 1.2 0.7 0.3 0.1 -0.3 -0.6 -1.0 -1.3 -1.4 -1.5 -3.5 -5.2 -4.9 -4.7 -4.5 -4.4 0.4 -1.2 -0.4ch(Lump-Sum Transfer/GDP%) -0.24 -0.12 -0.08 -0.09 -0.05 -0.04 0.05 0.12 0.08 0.07 0.07 0.07 0.07 0.07 0.07 0.07 -0.12 0.06 -0.03ch G( ov't Consumption/GDP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00ch(Income Tax/GDP%) -0.78 -0.79 -0.79 -0.81 -0.80 -0.80 -0.80 -0.80 -0.82 -0.85 -0.40 0.19 0.20 0.20 0.19 0.16 -0.79 -0.81 -0.80ch(Interest Rate%) 0.07 0.06 0.05 0.05 0.05 0.05 0.05 0.05 0.06 0.07 0.08 0.11 0.19 0.25 0.30 0.32 0.06 0.05 0.06%ch W( age Rate) -0.3 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.3 -0.3 -0.4 -0.7 -0.9 -1.1 -1.2 -0.2 -0.2 -0.2ch(Private Wealth G/ DP%) 0.0 0.7 1.4 2.0 2.6 3.2 3.8 4.3 4.9 5.5 7.1 5.8 3.1 1.5 -0.1 -0.9 1.3 4.3 2.8ch G( ov't Wealth/GDP%) 0.0 -0.4 -1.0 -1.6 -2.2 -2.9 -3.6 -4.4 -5.2 -6.0 -9.6 -11.1 -11.1 -11.1 -11.1 -11.1 -1.1 -4.4 -2.7ch(Budget Deficit G/ DP%) 0.45 0.59 0.66 0.69 0.75 0.78 0.89 1.00 1.00 1.04 0.77 0.31 0.31 0.31 0.31 0.31 0.63 0.94 0.79(Small Open Economy)

%ch N( ational Wealth) 0.0 0.0 0.0 0.0 -0.1 -0.2 -0.3 -0.5 -0.6 -0.8 -1.8 -3.4 -4.8 -5.8 -6.9 -7.6 0.0 -0.5 -0.2

%ch(Labor) 1.0 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.6 0.7 0.1 -0.6 -0.2 0.0 0.2 0.3 0.8 0.6 0.7%ch G( NP) 0.7 0.6 0.6 0.5 0.5 0.4 0.3 0.3 0.3 0.3 -0.5 -1.4 -1.6 -1.8 -1.9 -2.1 0.6 0.3 0.4%ch G( DP) 1.0 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.6 0.7 0.1 -0.6 -0.2 0.0 0.2 0.3 0.8 0.6 0.7%ch(Consumption) 1.0 1.0 1.1 1.2 1.2 1.2 1.3 1.3 1.3 1.4 1.0 0.4 0.1 -0.2 -0.6 -0.8 1.1 1.3 1.2%ch G( ross Dom. Investment) 13.1 -0.3 -0.1 0.8 -0.3 0.1 0.0 0.4 0.9 1.6 -1.4 -2.7 0.4 0.4 0.4 0.3 2.6 0.6 1.6ch(Lump-Sum Transfer/GDP%) -0.24 -0.12 -0.08 -0.09 -0.05 -0.04 0.05 0.12 0.08 0.07 0.07 0.07 0.07 0.07 0.07 0.07 -0.12 0.06 -0.03ch G( ov't Consumption/GDP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00ch(Income Tax/GDP%) -0.78 -0.78 -0.79 -0.81 -0.80 -0.80 -0.80 -0.81 -0.82 -0.85 -0.40 0.19 0.16 0.15 0.13 0.13 -0.79 -0.82 -0.81ch N( et Foreign Assets G/ DP%) -2.6 -2.3 -2.2 -2.3 -2.2 -2.4 -2.6 -2.9 -3.4 -4.1 -5.3 -7.6 -12.6 -15.9 -19.3 -21.6 -2.3 -3.1 -2.7ch(Private Wealth G/ DP%) 0.0 0.5 1.0 1.5 2.0 2.4 2.7 3.1 3.6 3.9 4.6 2.0 -2.0 -4.7 -7.6 -9.6 1.0 3.1 2.1ch G( ov't Wealth/GDP%) 0.0 -0.4 -1.0 -1.6 -2.2 -2.9 -3.6 -4.4 -5.3 -6.1 -9.7 -11.2 -11.2 -11.2 -11.2 -11.2 -1.1 -4.4 -2.8ch(Budget Deficit G/ DP%) 0.44 0.59 0.66 0.70 0.75 0.79 0.90 1.01 1.01 1.05 0.78 0.32 0.32 0.32 0.32 0.32 0.63 0.95 0.79

43
Table A.5 (b). Income Tax Rates Reduced by 10 Percent Proportionally; Income Tax Rates Increased Gradually After 10 Years

Compensating Variations in Wealth as Percentages of Per-Household GDP-- M- arch 2003 Assumptions

The Year When Age 20 (Top) / the Age in Year 1 (Bottom)

-88 -79 -69 -59 -49 -39 -29 -19 -9 1 11 21 41 61 81 101 120

109 100 90 80 70 60 50 40 30 20 10 0 -20 -40 -60 -80 -99

(Closed Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.4 -0.4 0.3 0.5 0.6 1.9 2.0 0.6 -0.3 -0.4 -1.3 -2.0 -2.0 -2.1 -2.1 -2.1

20-40 percentile 0.7 1.2 3.3 3.9 1.8 0.1 -0.9 -2.8 -4.0 -4.1 -4.1 -4.1 -4.140-60 percentile 0.8 2.2 4.9 5.5 3.0 0.5 -1.2 -3.7 -5.2 -5.3 -5.4 -5.4 -5.460-80 percentile 1.4 4.3 8.0 8.7 5.4 1.4 -1.6 -5.0 -6.8 -6.9 -6.9 -7.0 -7.080-90 percentile 2.6 7.2 11.3 12.3 8.5 2.4 -1.9 -6.1 -8.1 -8.2 -8.3 -8.3 -8.390-95 percentile 5.7 14.4 15.8 18.6 12.0 4.0 -1.5 -7.2 -9.5 -9.6 -9.6 -9.7 -9.695-99 percentile 15.4 30.6 29.5 31.2 20.9 8.0 0.5 -8.4 -11.0 -11.0 -11.0 -11.1 -11.199-100 percentile 58.7 121.9 97.2 77.4 52.9 14.2 3.3 -10.1 -13.1 -13.1 -13.0 -13.1 -13.1

Average -0.3 -0.4 -0.4 0.3 2.4 5.5 7.7 8.2 5.0 1.2 -1.1 -4.0 -5.5 -5.6 -5.6 -5.6 -5.6(Small Open Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.4 -0.5 -0.5 -0.4 -0.3 1.3 1.6 0.5 -0.2 -0.2 -0.8 -1.6 -1.8 -1.8 -1.8 -1.9

20-40 percentile -0.3 0.0 2.4 3.1 1.4 0.2 -0.6 -1.9 -3.2 -3.5 -3.6 -3.6 -3.640-60 percentile -0.6 0.4 3.5 4.1 2.3 0.5 -0.9 -2.6 -4.0 -4.4 -4.5 -4.5 -4.660-80 percentile -0.9 1.0 4.9 5.8 3.7 1.1 -1.5 -3.8 -5.4 -5.9 -5.9 -6.0 -6.080-90 percentile -0.8 2.1 6.0 7.3 5.2 1.8 -2.2 -5.3 -7.0 -7.5 -7.6 -7.6 -7.690-95 percentile 0.7 5.7 6.1 9.2 6.5 2.7 -2.8 -7.4 -9.2 -9.6 -9.7 -9.8 -9.895-99 percentile 8.3 16.2 12.2 14.2 10.7 4.8 -3.8 -12.1 -13.8 -14.3 -14.4 -14.5 -14.599-100 percentile 46.6 87.6 54.3 35.6 25.8 7.7 -5.8 -19.0 -20.7 -21.3 -21.4 -21.5 -21.5

Average -0.3 -0.4 -0.5 -0.5 0.3 2.2 4.3 5.0 3.1 0.9 -1.2 -3.4 -4.8 -5.1 -5.2 -5.2 -5.2

44
Figure A.5. Income Tax Rates Reduced by 10 Percent Proportionally; Income Tax Rates Increased

Gradually After 10 Years---March 2003 Assumptions

(a) GNP

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(b) National Wealth

-8

-7

-6

-5

-4

-3

-2

-1

0

1

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(c) Labor Supply

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(d) Private Consumption

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(f) Interest Rate

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0 10 20 30 40 50 60 70 80 90 100

Year

Ch from the Baseline

(g) Wage Rate

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(e) Income Tax Revenue

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0 10 20 30 40 50 60 70 80 90 100

Year

Ch as a % of the

Baseline GDP

(h) Welfare Gain / Loss (Avg. of Each Age)

-8

-6

-4

-2

0

2

4

6

8

10

-80 -60 -40 -20 0 20 40 60 80 100 120

Year When Age 20

ch as a % of perHousehold GDP

Closed Economy Small Open Economy

45
Table A.6 (a). Income Tax Rates Reduced by 10 Percent Proportionally; Government Consumption Reduced Contemporaneously

Changes in Macroeconomic Indicators from the Baseline-- A- lternative Assumptions

Year Average

1 2 3 4 5 6 7 8 9 10 15 20 25 30 40 120 01-05 06-10 01-10

C( losed Economy)

%ch N( ational Wealth) 0.0 0.1 0.3 0.4 0.6 0.7 0.8 1.0 1.1 1.2 1.8 2.1 2.4 2.5 2.7 2.8 0.3 1.0 0.6

%ch(Labor) 0.5 0.5 0.4 0.5 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.4 0.4%ch G( NP=GDP) 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.6 0.6 0.7 0.8 0.9 1.0 1.0 1.1 1.1 0.4 0.6 0.5%ch(Consumption) 0.8 0.9 1.0 1.1 1.1 1.2 1.2 1.3 1.4 1.4 1.6 1.8 1.9 2.0 2.1 2.1 1.0 1.3 1.1%ch G( ross Investment) 1.8 2.2 2.3 2.3 2.4 2.3 2.6 3.0 2.9 3.0 3.0 2.9 2.9 2.8 2.8 2.8 2.2 2.7 2.5ch(Lump-Sum Transfer/GDP%) -0.23 -0.11 -0.07 -0.08 -0.04 -0.02 0.06 0.13 0.09 0.08 0.08 0.08 0.08 0.08 0.08 0.08 -0.10 0.07 -0.02ch G( ov't Consumption/GDP%) -0.54 -0.66 -0.70 -0.71 -0.73 -0.74 -0.81 -0.89 -0.85 -0.87 -0.85 -0.84 -0.84 -0.84 -0.84 -0.85 -0.67 -0.83 -0.75ch(Income Tax/GDP%) -0.82 -0.82 -0.81 -0.83 -0.81 -0.81 -0.80 -0.80 -0.81 -0.84 -0.83 -0.82 -0.81 -0.80 -0.80 -0.80 -0.82 -0.81 -0.82ch(Interest Rate%) 0.04 0.03 0.01 0.00 -0.01 -0.02 -0.03 -0.04 -0.05 -0.06 -0.10 -0.13 -0.15 -0.16 -0.17 -0.18 0.01 -0.04 -0.01%ch W( age Rate) -0.2 -0.1 0.0 0.0 0.0 0.1 0.1 0.2 0.2 0.2 0.4 0.5 0.6 0.6 0.7 0.7 -0.1 0.2 0.1ch(Private Wealth G/ DP%) 0.0 0.4 0.8 1.2 1.6 1.9 2.3 2.6 3.0 3.4 4.9 5.9 6.5 7.0 7.4 7.7 0.8 2.6 1.7ch G( ov't Wealth/GDP%) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0ch(Budget Deficit G/ DP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00(Small Open Economy)

%ch N( ational Wealth) 0.0 0.1 0.3 0.4 0.6 0.7 0.8 1.0 1.1 1.3 1.9 2.3 2.6 2.8 3.0 3.2 0.3 1.0 0.6

%ch(Labor) 0.5 0.5 0.5 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.1 0.5 0.3 0.4%ch G( NP) 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.6 0.6 0.8 0.9 0.9 1.0 1.0 1.1 0.4 0.5 0.5%ch G( DP) 0.5 0.5 0.5 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.1 0.5 0.3 0.4%ch(Consumption) 0.8 0.9 1.0 1.0 1.1 1.1 1.2 1.2 1.3 1.3 1.5 1.7 1.8 1.9 2.0 2.0 1.0 1.2 1.1%ch G( ross Dom. Investment) 0.5 0.5 0.5 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.1 0.5 0.3 0.4ch(Lump-Sum Transfer/GDP%) -0.23 -0.11 -0.07 -0.08 -0.04 -0.02 0.06 0.13 0.09 0.08 0.08 0.08 0.08 0.08 0.08 0.08 -0.10 0.07 -0.02ch G( ov't Consumption/GDP%) -0.53 -0.65 -0.70 -0.71 -0.74 -0.75 -0.83 -0.91 -0.88 -0.90 -0.89 -0.89 -0.89 -0.89 -0.89 -0.89 -0.66 -0.85 -0.76ch(Income Tax/GDP%) -0.81 -0.81 -0.81 -0.84 -0.82 -0.82 -0.81 -0.82 -0.83 -0.86 -0.85 -0.84 -0.84 -0.84 -0.83 -0.83 -0.82 -0.83 -0.82ch N( et Foreign Assets G/ DP%) -1.4 -1.0 -0.5 0.0 0.5 0.9 1.4 1.8 2.2 2.6 4.4 5.7 6.6 7.2 7.9 8.3 -0.5 1.8 0.6ch(Private Wealth G/ DP%) 0.0 0.4 0.8 1.2 1.6 2.0 2.3 2.7 3.1 3.5 5.2 6.3 7.2 7.7 8.3 8.7 0.8 2.7 1.7ch G( ov't Wealth/GDP%) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0ch(Budget Deficit G/ DP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 24.44 0.00 0.00 0.00

46
Table A.6 (b). Income Tax Rates Reduced by 10 Percent Proportionally; Government Consumption Reduced Contemporaneously

Compensating Variations in Wealth as Percentages of Per H- ousehold GDP---Alternative Assumptions

The Year When Age 20 (Top) / the Age in Year 1 (Bottom)

-88 -79 -69 -59 -49 -39 -29 -19 -9 1 11 21 41 61 81 101 120

109 100 90 80 70 60 50 40 30 20 10 0 -20 -40 -60 -80 -99

(Closed Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.5 -0.2 -0.4 -0.4 -1.7 1.5 2.7 2.0 0.2 1.4 1.6 1.7 1.8 1.8 1.8 1.8

20-40 percentile -0.5 -0.2 2.6 5.0 4.7 2.6 4.8 5.5 5.9 6.0 6.0 6.0 6.040-60 percentile -0.7 0.4 3.8 6.6 7.3 4.3 6.9 7.7 8.3 8.4 8.4 8.4 8.460-80 percentile -1.2 1.5 5.9 9.0 10.2 6.5 9.4 10.5 11.1 11.2 11.2 11.2 11.380-90 percentile -0.4 2.9 8.2 11.6 13.1 9.5 12.9 14.1 14.9 15.0 15.0 15.1 15.190-95 percentile 1.4 7.4 10.8 15.9 15.9 11.8 15.3 16.7 17.5 17.6 17.6 17.6 17.795-99 percentile 9.0 18.2 18.9 23.4 21.7 16.1 20.0 21.6 22.5 22.6 22.6 22.7 22.799-100 percentile 41.6 77.5 59.4 49.9 40.0 22.1 26.3 27.9 28.9 29.0 29.0 29.0 29.0

Average -0.3 -0.5 -0.2 -0.4 0.2 2.1 5.5 8.1 8.2 5.1 7.6 8.4 9.0 9.0 9.1 9.1 9.1(Small Open Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.5 -0.2 0.1 0.4 -1.1 1.8 2.6 1.8 0.2 1.1 1.2 1.3 1.4 1.4 1.4 1.4

20-40 percentile 0.5 0.8 3.1 5.0 4.3 2.2 3.8 4.3 4.8 4.8 4.9 4.9 4.940-60 percentile 0.5 2.1 4.6 6.9 6.9 3.8 5.6 6.2 6.7 6.8 6.8 6.8 6.860-80 percentile 0.9 4.5 7.8 10.0 10.2 5.9 7.8 8.5 9.1 9.2 9.3 9.3 9.380-90 percentile 2.6 7.6 11.6 13.6 13.9 8.8 11.0 11.8 12.5 12.7 12.7 12.7 12.790-95 percentile 5.7 15.4 17.2 20.2 17.7 11.3 13.6 14.4 15.1 15.3 15.3 15.3 15.395-99 percentile 15.7 31.6 31.0 32.0 25.6 16.5 19.1 20.0 20.7 20.9 20.9 20.9 20.999-100 percentile 56.6 113.9 93.6 75.2 52.9 23.9 26.7 27.6 28.4 28.5 28.6 28.5 28.5

Average -0.3 -0.5 -0.2 0.1 2.2 5.2 7.7 9.3 8.5 4.8 6.5 7.0 7.5 7.6 7.6 7.6 7.6

47
Figure A.6. Income Tax Rates Reduced by 10 Percent Proportionally; Government Consumption Reduced

Contemporaneously---Alternative Assumptions

(a) GNP

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(b) National Wealth

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(c) Labor Supply

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(d) Private Consumption

0.0

0.5

1.0

1.5

2.0

2.5

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(f) Interest Rate

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0 10 20 30 40 50 60 70 80 90 100

Year

Ch from the Baseline

(g) Wage Rate

-0.2

0.0

0.2

0.4

0.6

0.8

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(e) Income Tax Revenue

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0 10 20 30 40 50 60 70 80 90 100

Year

Ch as a % of the

Baseline GDP

(h) Welfare Gain / Loss (Avg. of Each Age)

-2

0

2

4

6

8

10

-80 -60 -40 -20 0 20 40 60 80 100 120

Year When Age 20

ch as a % of perHousehold GDP

Closed Economy Small Open Economy

48
Table A.7 (a). Income Tax Rates Reduced by 10 Percent Proportionally; Lump-Sum Transfers Reduced Contemporaneously

Changes in Macroeconomic Indicators from the Baseline-- A- lternative Assumptions

Year Average

1 2 3 4 5 6 7 8 9 10 15 20 25 30 40 120 01-05 06-10 01-10

C( losed Economy)

%ch N( ational Wealth) 0.0 0.3 0.6 0.9 1.2 1.5 1.7 2.0 2.4 2.7 3.1 3.3 3.5 3.7 3.8 3.8 0.6 2.1 1.3

%ch(Labor) 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7%ch G( NP=GDP) 0.5 0.6 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.5 1.5 1.6 1.6 1.7 1.7 0.7 1.1 0.9%ch(Consumption) 0.3 0.4 0.5 0.6 0.7 0.7 0.8 0.8 0.9 0.9 1.0 1.1 1.2 1.3 1.3 1.4 0.5 0.8 0.7%ch G( ross Investment) 3.8 4.3 4.7 4.9 5.1 5.3 5.9 6.6 6.8 3.8 3.9 4.0 4.0 4.0 4.0 3.8 4.6 5.7 5.1ch(Lump-Sum Transfer/GDP%) -0.73 -0.72 -0.71 -0.72 -0.69 -0.68 -0.66 -0.66 -0.65 -0.67 -0.65 -0.65 -0.65 -0.66 -0.66 -0.67 -0.71 -0.66 -0.69ch G( ov't Consumption/GDP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00ch(Income Tax/GDP%) -0.80 -0.79 -0.79 -0.80 -0.77 -0.76 -0.75 -0.75 -0.75 -0.77 -0.76 -0.75 -0.75 -0.74 -0.74 -0.74 -0.79 -0.76 -0.77ch(Interest Rate%) 0.05 0.03 0.01 -0.01 -0.04 -0.06 -0.08 -0.10 -0.13 -0.14 -0.17 -0.19 -0.21 -0.22 -0.23 -0.22 0.01 -0.10 -0.05%ch W( age Rate) -0.2 -0.1 0.0 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.8 0.9 0.9 0.9 0.0 0.4 0.2ch(Private Wealth G/ DP%) 0.0 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.5 7.4 8.4 9.2 9.7 10.1 10.5 10.4 1.6 5.7 3.6ch G( ov't Wealth/GDP%) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0ch(Budget Deficit G/ DP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00(Small Open Economy)

%ch N( ational Wealth) 0.0 0.3 0.6 0.9 1.3 1.6 1.9 2.3 2.6 3.0 3.5 3.8 4.1 4.3 4.4 4.5 0.6 2.3 1.5

%ch(Labor) 0.8 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.5 0.5 0.5 0.5 0.5 0.7 0.6 0.6%ch G( NP) 0.5 0.6 0.7 0.8 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.6 1.7 1.7 0.7 1.1 0.9%ch G( DP) 0.8 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.5 0.5 0.5 0.5 0.5 0.7 0.6 0.6%ch(Consumption) 0.3 0.3 0.4 0.5 0.5 0.5 0.6 0.6 0.6 0.6 0.8 0.9 1.0 1.1 1.2 1.2 0.4 0.6 0.5%ch G( ross Dom. Investment) 0.8 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.5 0.5 0.5 0.5 0.5 0.7 0.6 0.6ch(Lump-Sum Transfer/GDP%) -0.71 -0.71 -0.71 -0.72 -0.70 -0.70 -0.69 -0.69 -0.70 -0.72 -0.71 -0.71 -0.71 -0.71 -0.71 -0.71 -0.71 -0.70 -0.70ch G( ov't Consumption/GDP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00ch(Income Tax/GDP%) -0.79 -0.79 -0.78 -0.80 -0.78 -0.78 -0.77 -0.77 -0.78 -0.80 -0.79 -0.79 -0.78 -0.78 -0.78 -0.78 -0.79 -0.78 -0.78ch N( et Foreign Assets G/ DP%) -2.1 -1.1 -0.2 0.7 1.8 2.7 3.7 4.6 5.6 6.5 8.0 9.0 9.8 10.3 10.8 11.1 -0.2 4.6 2.2ch(Private Wealth G/ DP%) 0.0 0.8 1.7 2.6 3.5 4.4 5.2 6.2 7.2 8.2 9.5 10.5 11.2 11.7 12.2 12.4 1.7 6.2 4.0ch G( ov't Wealth/GDP%) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0ch(Budget Deficit G/ DP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 24.44 0.00 0.00 0.00

49
Table A.7 (b). Income Tax Rates Reduced by 10 Percent Proportionally; Lump-Sum Transfers Reduced Contemporaneously

Compensating Variations in Wealth as Percentages of Per H- ousehold GDP---Alternative Assumptions

The Year When Age 20 (Top) / the Age in Year 1 (Bottom)

-88 -79 -69 -59 -49 -39 -29 -19 -9 1 11 21 41 61 81 101 120

109 100 90 80 70 60 50 40 30 20 10 0 -20 -40 -60 -80 -99

(Closed Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.5 -2.9 -8.6 -10.4 -9.8 -9.0 -5.3 -1.9 -0.6 -1.9 -1.8 -1.7 -1.6 -1.6 -1.6 -1.6

20-40 percentile -10.9 -10.9 -8.4 -6.2 -2.4 -0.9 -3.8 -3.3 -3.1 -2.6 -2.6 -2.5 -2.640-60 percentile -12.0 -12.6 -7.4 -5.9 -2.7 -0.9 -4.0 -3.4 -3.1 -2.3 -2.3 -2.2 -2.360-80 percentile -14.9 -14.2 -6.4 -4.1 -2.0 -0.5 -3.8 -3.1 -2.7 -1.6 -1.5 -1.5 -1.680-90 percentile -16.4 -15.1 -5.8 -2.2 -0.7 -0.2 -3.7 -2.8 -2.4 -0.8 -0.8 -0.7 -0.990-95 percentile -17.3 -14.0 -6.7 -0.1 1.1 0.7 -2.6 -1.7 -1.2 0.6 0.7 0.7 0.595-99 percentile -11.5 -7.1 -3.5 3.7 5.1 2.7 -0.4 0.6 1.1 3.2 3.3 3.4 3.299-100 percentile 15.5 37.2 23.7 19.7 17.2 6.2 3.7 4.7 5.3 7.5 7.5 7.6 7.5

Average -0.3 -0.5 -2.9 -8.6 -12.4 -11.6 -7.1 -4.2 -1.4 -0.4 -3.2 -2.6 -2.3 -1.5 -1.4 -1.4 -1.5(Small Open Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.6 -2.9 -7.5 -9.0 -8.8 -14.6 -9.6 -4.1 -0.9 -2.5 -2.4 -2.3 -2.3 -2.3 -2.3 -2.3

20-40 percentile -9.1 -9.2 -12.2 -11.2 -5.9 -2.3 -5.8 -5.2 -4.7 -4.7 -4.7 -4.7 -4.740-60 percentile -9.6 -9.6 -9.2 -10.2 -6.8 -2.9 -6.6 -5.9 -5.3 -5.3 -5.3 -5.3 -5.360-80 percentile -10.5 -8.0 -4.6 -6.1 -5.8 -3.1 -6.8 -6.0 -5.4 -5.4 -5.4 -5.4 -5.480-90 percentile -9.7 -5.2 -0.2 -1.4 -3.1 -3.3 -6.9 -6.1 -5.5 -5.5 -5.4 -5.4 -5.490-95 percentile -6.7 2.5 4.3 5.4 0.7 -2.3 -5.7 -4.8 -4.2 -4.2 -4.2 -4.2 -4.295-99 percentile 3.8 17.2 16.6 16.8 8.5 0.7 -2.5 -1.6 -1.0 -1.0 -0.9 -0.9 -1.099-100 percentile 42.2 96.9 76.7 58.3 35.3 6.2 3.3 4.2 4.8 4.9 4.9 4.9 4.9

Average -0.3 -0.6 -2.9 -7.5 -8.4 -5.9 -6.5 -6.0 -4.1 -2.2 -5.4 -4.8 -4.3 -4.3 -4.3 -4.3 -4.3

50
Figure A.7. Income Tax Rates Reduced by 10 Percent Proportionally; Lump-Sum Transfers Reduced

Contemporaneously---Alternative Assumptions

(a) GNP

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(b) National Wealth

0

1

2

3

4

5

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(c) Labor Supply

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(d) Private Consumption

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(f) Interest Rate

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0 10 20 30 40 50 60 70 80 90 100

Year

Ch from the Baseline

(g) Wage Rate

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(e) Income Tax Revenue

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0 10 20 30 40 50 60 70 80 90 100

Year

Ch as a % of the

Baseline GDP

(h) Welfare Gain / Loss (Avg. of Each Age)

-14

-12

-10

-8

-6

-4

-2

0

-80 -60 -40 -20 0 20 40 60 80 100 120

Year When Age 20

ch as a % of perHousehold GDP

Closed Economy Small Open Economy

51
Table A.8 (a). Income Tax Rates Reduced by 10 Percent Proportionally; Government Consumption Reduced Gradually After 10 Years

Changes in Macroeconomic Indicators from the Baseline-- A- lternative Assumptions

Year Average

1 2 3 4 5 6 7 8 9 10 15 20 25 30 40 120 01-05 06-10 01-10

C( losed Economy)

%ch N( ational Wealth) 0.0 -0.1 -0.1 -0.2 -0.4 -0.5 -0.7 -0.9 -1.1 -1.4 -2.5 -2.7 -2.3 -2.1 -1.9 -1.8 -0.2 -0.9 -0.5

%ch(Labor) 0.5 0.4 0.4 0.4 0.3 0.3 0.3 0.2 0.2 0.2 0.1 0.0 0.0 0.0 0.0 0.0 0.4 0.2 0.3%ch G( NP=GDP) 0.3 0.3 0.2 0.2 0.1 0.1 0.0 -0.1 -0.2 -0.3 -0.7 -0.8 -0.7 -0.6 -0.6 -0.6 0.2 -0.1 0.1%ch(Consumption) 0.8 0.8 0.9 1.0 1.0 1.0 1.1 1.1 1.2 1.2 1.4 1.5 1.7 1.8 1.9 2.0 0.9 1.1 1.0%ch G( ross Investment) -0.7 -1.1 -1.6 -2.0 -2.4 -2.9 -3.4 -4.0 -4.5 -5.0 -4.2 -1.5 -1.6 -1.7 -1.7 -1.8 -1.6 -4.0 -2.8ch(Lump-Sum Transfer/GDP%) -0.23 -0.11 -0.07 -0.08 -0.04 -0.02 0.06 0.13 0.09 0.08 0.08 0.08 0.08 0.08 0.08 0.08 -0.10 0.07 -0.02ch G( ov't Consumption/GDP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.70 -1.48 -1.46 -1.45 -1.44 -1.43 0.00 0.00 0.00ch(Income Tax/GDP%) -0.82 -0.82 -0.82 -0.85 -0.83 -0.83 -0.83 -0.83 -0.85 -0.88 -0.89 -0.88 -0.87 -0.87 -0.86 -0.86 -0.83 -0.84 -0.84ch(Interest Rate%) 0.04 0.04 0.04 0.05 0.05 0.06 0.07 0.09 0.10 0.12 0.20 0.21 0.18 0.16 0.15 0.14 0.04 0.09 0.07%ch W( age Rate) -0.1 -0.1 -0.2 -0.2 -0.2 -0.2 -0.3 -0.3 -0.4 -0.5 -0.8 -0.8 -0.7 -0.6 -0.6 -0.5 -0.2 -0.3 -0.3ch(Private Wealth G/ DP%) 0.0 0.4 0.8 1.3 1.7 2.1 2.5 2.9 3.4 3.9 5.9 7.3 8.3 8.9 9.5 9.8 0.8 3.0 1.9ch G( ov't Wealth/GDP%) 0.0 -0.5 -1.2 -1.9 -2.7 -3.5 -4.4 -5.4 -6.5 -7.6 -12.6 -14.7 -14.7 -14.7 -14.7 -14.7 -1.3 -5.5 -3.4ch(Budget Deficit G/ DP%) 0.54 0.70 0.79 0.85 0.93 0.99 1.13 1.28 1.32 1.42 1.06 0.41 0.41 0.41 0.41 0.41 0.76 1.23 1.00(Small Open Economy)

%ch N( ational Wealth) 0.0 -0.1 -0.1 -0.3 -0.4 -0.5 -0.7 -0.9 -1.2 -1.4 -2.5 -2.8 -2.5 -2.3 -2.1 -1.9 -0.2 -1.0 -0.6

%ch(Labor) 0.5 0.5 0.5 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.1 0.5 0.3 0.4%ch G( NP) 0.4 0.3 0.3 0.2 0.2 0.1 0.0 -0.1 -0.1 -0.2 -0.6 -0.7 -0.6 -0.6 -0.5 -0.5 0.3 0.0 0.1%ch G( DP) 0.5 0.5 0.5 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.1 0.5 0.3 0.4%ch(Consumption) 0.8 0.9 1.0 1.0 1.1 1.1 1.2 1.2 1.3 1.3 1.5 1.7 1.8 1.9 2.0 2.0 1.0 1.2 1.1%ch G( ross Dom. Investment) 7.2 0.0 0.1 0.3 -0.1 0.0 0.0 0.0 0.3 0.5 0.2 0.1 0.2 0.1 0.1 0.1 1.5 0.2 0.8ch(Lump-Sum Transfer/GDP%) -0.23 -0.11 -0.07 -0.08 -0.04 -0.02 0.06 0.13 0.09 0.08 0.08 0.08 0.08 0.08 0.08 0.08 -0.10 0.07 -0.02ch G( ov't Consumption/GDP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.65 -1.37 -1.37 -1.37 -1.37 -1.36 0.00 0.00 0.00ch(Income Tax/GDP%) -0.81 -0.81 -0.81 -0.84 -0.82 -0.82 -0.81 -0.82 -0.83 -0.86 -0.85 -0.84 -0.84 -0.84 -0.83 -0.83 -0.82 -0.83 -0.82ch N( et Foreign Assets G/ DP%) -1.4 -1.5 -1.6 -1.9 -2.2 -2.5 -2.9 -3.4 -4.1 -4.8 -7.6 -8.3 -7.4 -6.8 -6.1 -5.7 -1.7 -3.5 -2.6ch(Private Wealth G/ DP%) 0.0 0.4 0.8 1.2 1.6 2.0 2.3 2.7 3.1 3.5 5.2 6.3 7.2 7.7 8.3 8.7 0.8 2.7 1.7ch G( ov't Wealth/GDP%) 0.0 -0.5 -1.2 -1.9 -2.6 -3.4 -4.3 -5.2 -6.3 -7.4 -12.1 -14.0 -14.0 -14.0 -14.0 -14.0 -1.2 -5.3 -3.3ch(Budget Deficit G/ DP%) 0.53 0.68 0.77 0.83 0.90 0.96 1.10 1.24 1.27 1.36 0.99 0.39 0.39 0.39 0.39 0.39 0.74 1.18 0.96

52
Table A.8 (b). Income Tax Rates Reduced by 10 Percent Proportionally; Government Consumption Reduced Gradually After 10 Years

Compensating Variations in Wealth as Percentages of Per H- ousehold GDP---Alternative Assumptions

The Year When Age 20 (Top) / the Age in Year 1 (Bottom)

-88 -79 -69 -59 -49 -39 -29 -19 -9 1 11 21 41 61 81 101 120

109 100 90 80 70 60 50 40 30 20 10 0 -20 -40 -60 -80 -99

(Closed Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.5 0.1 1.7 2.2 0.2 2.2 2.4 1.3 0.0 0.7 0.8 1.1 1.1 1.1 1.1 1.1

20-40 percentile 2.6 2.6 3.8 4.8 3.5 1.5 2.6 3.3 4.0 4.1 4.1 4.1 4.140-60 percentile 3.1 5.0 5.9 7.1 6.0 2.8 3.9 4.8 5.7 5.8 5.8 5.8 5.860-80 percentile 5.2 10.0 10.7 11.4 9.9 4.6 5.8 6.8 7.9 8.0 8.0 8.0 8.080-90 percentile 8.8 15.9 16.8 16.5 14.7 7.4 8.6 9.8 11.0 11.1 11.2 11.2 11.190-95 percentile 14.9 29.3 27.1 26.4 20.0 10.1 11.3 12.4 13.7 13.8 13.8 13.8 13.895-99 percentile 29.6 54.5 49.6 44.2 30.8 16.3 17.4 18.3 19.7 19.9 19.9 19.9 19.999-100 percentile 83.6 171.2 143.4 109.9 69.3 25.4 26.2 26.9 28.4 28.5 28.6 28.6 28.5

Average -0.3 -0.5 0.1 1.7 6.3 10.5 11.0 11.0 8.5 3.9 5.0 5.8 6.6 6.7 6.7 6.7 6.7(Small Open Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.5 -0.2 0.1 0.4 -1.1 1.8 2.6 1.8 0.2 1.1 1.2 1.3 1.4 1.4 1.4 1.4

20-40 percentile 0.5 0.8 3.0 5.0 4.3 2.2 3.8 4.3 4.8 4.8 4.9 4.9 4.940-60 percentile 0.5 2.1 4.6 6.9 6.9 3.8 5.6 6.2 6.7 6.8 6.8 6.8 6.860-80 percentile 0.9 4.5 7.8 10.0 10.2 5.9 7.8 8.5 9.1 9.2 9.3 9.3 9.380-90 percentile 2.6 7.6 11.6 13.6 13.9 8.8 11.0 11.8 12.5 12.7 12.7 12.7 12.790-95 percentile 5.7 15.4 17.2 20.2 17.7 11.3 13.6 14.4 15.1 15.3 15.3 15.3 15.395-99 percentile 15.7 31.6 31.0 32.0 25.6 16.5 19.1 19.9 20.7 20.9 20.9 20.9 20.999-100 percentile 56.6 113.9 93.6 75.2 52.9 23.9 26.7 27.6 28.4 28.5 28.5 28.5 28.5

Average -0.3 -0.5 -0.2 0.1 2.2 5.2 7.7 9.3 8.5 4.8 6.4 7.0 7.5 7.6 7.6 7.6 7.6

53
Figure A.8. Income Tax Rates Reduced by 10 Percent Proportionally; Government Consumption Reduced

Gradually After 10 Years---Alternative Assumptions

(a) GNP

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(b) National Wealth

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(c) Labor Supply

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(d) Private Consumption

0.0

0.5

1.0

1.5

2.0

2.5

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(f) Interest Rate

0.00

0.05

0.10

0.15

0.20

0.25

0 10 20 30 40 50 60 70 80 90 100

Year

Ch from the Baseline

(g) Wage Rate

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(e) Income Tax Revenue

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0 10 20 30 40 50 60 70 80 90 100

Year

Ch as a % of the

Baseline GDP

(h) Welfare Gain / Loss (Avg. of Each Age)

-2

0

2

4

6

8

10

12

-80 -60 -40 -20 0 20 40 60 80 100 120

Year When Age 20

ch as a % of perHousehold GDP

Closed Economy Small Open Economy

54
Table A.9 (a). Income Tax Rates Reduced by 10 Percent Proportionally; Lump-Sum Transfers Reduced Gradually After 10 Years

Changes in Macroeconomic Indicators from the Baseline-- A- lternative Assumptions

Year Average

1 2 3 4 5 6 7 8 9 10 15 20 25 30 40 120 01-05 06-10 01-10

C( losed Economy)

%ch N( ational Wealth) 0.0 0.1 0.2 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.6 0.6 0.6 0.6 0.2 0.4 0.3

%ch(Labor) 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.6 0.6%ch G( NP=GDP) 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.6 0.6 0.6 0.7 0.6 0.5 0.5 0.5%ch(Consumption) 0.3 0.4 0.4 0.5 0.5 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.4 0.6 0.5%ch G( ross Investment) 1.5 1.3 1.2 1.1 0.9 0.8 0.6 0.5 0.5 0.5 0.5 0.7 0.7 0.7 0.7 0.6 1.2 0.6 0.9ch(Lump-Sum Transfer/GDP%) -0.23 -0.11 -0.07 -0.08 -0.04 -0.02 0.06 0.13 0.09 0.08 -0.52 -1.08 -1.08 -1.08 -1.08 -1.09 -0.10 0.07 -0.02ch G( ov't Consumption/GDP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00ch(Income Tax/GDP%) -0.80 -0.79 -0.79 -0.81 -0.78 -0.78 -0.77 -0.77 -0.78 -0.80 -0.77 -0.76 -0.76 -0.75 -0.75 -0.75 -0.79 -0.78 -0.79ch(Interest Rate%) 0.05 0.04 0.03 0.03 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.00 0.04 0.01 0.02%ch W( age Rate) -0.2 -0.2 -0.1 -0.1 -0.1 -0.1 -0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.1 0.0 -0.1ch(Private Wealth G/ DP%) 0.0 0.8 1.6 2.5 3.4 4.2 5.1 6.0 7.0 8.0 11.9 13.6 13.8 13.9 14.0 13.9 1.7 6.0 3.9ch G( ov't Wealth/GDP%) 0.0 -0.5 -1.1 -1.8 -2.5 -3.2 -4.0 -4.8 -5.8 -6.8 -10.7 -12.2 -12.2 -12.2 -12.2 -12.2 -1.2 -4.9 -3.0ch(Budget Deficit G/ DP%) 0.50 0.64 0.72 0.77 0.83 0.88 1.00 1.13 1.15 1.22 0.83 0.35 0.35 0.35 0.35 0.35 0.69 1.08 0.88(Small Open Economy)

%ch N( ational Wealth) 0.0 0.1 0.2 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.6 0.6 0.7 0.6 0.2 0.4 0.3

%ch(Labor) 0.8 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.6 0.6%ch G( NP) 0.5 0.5 0.5 0.6 0.5 0.5 0.5 0.5 0.5 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.5 0.5 0.5%ch G( DP) 0.8 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.6 0.6%ch(Consumption) 0.3 0.4 0.5 0.5 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.5 0.7 0.6%ch G( ross Dom. Investment) 10.4 0.2 0.2 0.6 0.1 0.3 0.3 0.4 0.6 0.9 0.7 0.7 0.7 0.7 0.7 0.7 2.3 0.5 1.4ch(Lump-Sum Transfer/GDP%) -0.23 -0.11 -0.07 -0.08 -0.04 -0.02 0.06 0.13 0.09 0.08 -0.52 -1.08 -1.07 -1.07 -1.08 -1.09 -0.10 0.07 -0.02ch G( ov't Consumption/GDP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00ch(Income Tax/GDP%) -0.79 -0.78 -0.78 -0.80 -0.78 -0.78 -0.77 -0.77 -0.77 -0.80 -0.77 -0.76 -0.76 -0.75 -0.75 -0.75 -0.79 -0.78 -0.78ch N( et Foreign Assets G/ DP%) -2.1 -1.7 -1.3 -1.1 -0.8 -0.6 -0.5 -0.4 -0.4 -0.4 -0.4 -0.4 -0.2 -0.1 0.1 0.0 -1.4 -0.5 -0.9ch(Private Wealth G/ DP%) 0.0 0.8 1.6 2.5 3.3 4.2 5.0 5.9 6.9 7.9 11.8 13.5 13.7 13.9 14.0 13.9 1.6 6.0 3.8ch G( ov't Wealth/GDP%) 0.0 -0.5 -1.1 -1.7 -2.4 -3.1 -3.9 -4.8 -5.7 -6.7 -10.6 -12.1 -12.1 -12.1 -12.1 -12.1 -1.1 -4.8 -3.0ch(Budget Deficit G/ DP%) 0.48 0.62 0.70 0.75 0.82 0.87 0.99 1.12 1.14 1.22 0.82 0.34 0.34 0.34 0.34 0.34 0.68 1.07 0.87

55
Table A.9 (b). Income Tax Rates Reduced by 10 Percent Proportionally; Lump-Sum Transfers Reduced Gradually After 10 Years

Compensating Variations in Wealth as Percentages of Per H- ousehold GDP---Alternative Assumptions

The Year When Age 20 (Top) / the Age in Year 1 (Bottom)

-88 -79 -69 -59 -49 -39 -29 -19 -9 1 11 21 41 61 81 101 120

109 100 90 80 70 60 50 40 30 20 10 0 -20 -40 -60 -80 -99

(Closed Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.5 -1.2 -5.3 -8.2 -9.0 -7.3 -10.7 -4.7 -1.0 -1.8 -3.8 -3.7 -3.7 -3.7 -3.7 -3.7

20-40 percentile -8.4 -9.6 -7.0 -12.7 -7.0 -2.5 -6.0 -9.6 -9.3 -9.3 -9.4 -9.4 -9.440-60 percentile -8.8 -10.2 -6.2 -11.9 -8.6 -3.3 -7.8 -11.3 -10.9 -11.0 -11.1 -11.1 -11.160-80 percentile -9.6 -8.6 -3.9 -7.9 -8.2 -3.9 -9.0 -12.5 -12.1 -12.2 -12.2 -12.2 -12.280-90 percentile -8.6 -5.7 -0.9 -3.2 -5.9 -4.8 -10.1 -13.5 -13.1 -13.2 -13.2 -13.2 -13.290-95 percentile -5.5 2.2 3.4 3.8 -2.0 -4.3 -9.9 -13.3 -12.9 -13.0 -13.0 -13.0 -13.095-99 percentile 4.6 17.1 15.5 14.9 5.8 -2.1 -7.4 -10.9 -10.4 -10.5 -10.6 -10.6 -10.699-100 percentile 42.4 96.7 75.6 56.1 32.0 2.7 -2.1 -5.5 -5.0 -5.2 -5.2 -5.2 -5.2

Average -0.3 -0.5 -1.2 -5.3 -7.5 -6.3 -3.4 -7.6 -5.9 -2.9 -6.8 -9.9 -9.6 -9.7 -9.7 -9.7 -9.7(Small Open Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.5 -1.5 -6.1 -8.8 -9.5 -7.5 -10.6 -4.6 -0.9 -1.8 -3.8 -3.7 -3.7 -3.7 -3.7 -3.7

20-40 percentile -9.1 -10.1 -7.2 -12.6 -6.9 -2.3 -5.9 -9.5 -9.2 -9.3 -9.3 -9.3 -9.340-60 percentile -9.7 -10.8 -6.4 -11.9 -8.4 -3.1 -7.7 -11.3 -10.9 -10.9 -11.0 -11.0 -11.060-80 percentile -10.9 -9.5 -4.4 -8.0 -8.0 -3.7 -8.9 -12.4 -12.0 -12.1 -12.1 -12.1 -12.180-90 percentile -10.4 -7.0 -1.6 -3.4 -5.7 -4.5 -10.0 -13.4 -13.0 -13.1 -13.1 -13.1 -13.190-95 percentile -7.9 0.6 2.4 3.5 -2.0 -4.0 -9.7 -13.2 -12.8 -12.9 -12.9 -12.9 -12.995-99 percentile 2.5 14.9 14.0 14.3 5.8 -1.7 -7.2 -10.7 -10.3 -10.4 -10.4 -10.4 -10.499-100 percentile 40.0 93.5 73.2 55.0 32.2 3.3 -2.0 -5.4 -5.0 -5.1 -5.1 -5.1 -5.1

Average -0.3 -0.5 -1.5 -6.1 -8.6 -7.1 -3.8 -7.7 -5.7 -2.7 -6.7 -9.9 -9.6 -9.6 -9.6 -9.6 -9.6

56
Figure A.9. Income Tax Rates Reduced by 10 Percent Proportionally; Lump-Sum Transfers Reduced

Gradually After 10 Years---Alternative Assumptions

(a) GNP

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(b) National Wealth

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(c) Labor Supply

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(d) Private Consumption

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(f) Interest Rate

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0 10 20 30 40 50 60 70 80 90 100

Year

Ch from the Baseline

(g) Wage Rate

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(e) Income Tax Revenue

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0 10 20 30 40 50 60 70 80 90 100

Year

Ch as a % of the

Baseline GDP

(h) Welfare Gain / Loss (Avg. of Each Age)

-12

-10

-8

-6

-4

-2

0

-80 -60 -40 -20 0 20 40 60 80 100 120

Year When Age 20

ch as a % of perHousehold GDP

Closed Economy Small Open Economy

57
Table A.10 (a). Income Tax Rates Reduced by 10 Percent Proportionally; Income Tax Rates Increased Gradually After 10 Years

Changes in Macroeconomic Indicators from the Baseline-- A- lternative Assumptions

Year Average

1 2 3 4 5 6 7 8 9 10 15 20 25 30 40 120 01-05 06-10 01-10

C( losed Economy)

%ch N( ational Wealth) 0.0 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.7 -0.8 -1.0 -2.1 -3.3 -4.4 -5.3 -6.3 -7.1 -0.1 -0.7 -0.4

%ch(Labor) 0.5 0.5 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 -0.2 -0.8 -0.7 -0.7 -0.7 -0.7 0.5 0.3 0.4%ch G( NP=GDP) 0.4 0.3 0.3 0.3 0.2 0.1 0.1 0.0 0.0 -0.1 -0.8 -1.5 -1.9 -2.1 -2.4 -2.6 0.3 0.0 0.2%ch(Consumption) 0.7 0.8 0.8 0.9 0.9 0.9 1.0 1.0 1.0 1.0 0.6 -0.2 -0.7 -1.0 -1.4 -1.9 0.8 1.0 0.9%ch G( ross Investment) -0.4 -0.8 -1.1 -1.5 -1.8 -2.2 -2.6 -2.9 -3.2 -3.5 -5.4 -6.8 -7.0 -7.1 -7.2 -7.1 -1.1 -2.9 -2.0ch(Lump-Sum Transfer/GDP%) -0.23 -0.11 -0.07 -0.08 -0.04 -0.02 0.06 0.13 0.09 0.08 0.08 0.08 0.08 0.08 0.08 0.08 -0.10 0.07 -0.02ch G( ov't Consumption/GDP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00ch(Income Tax/GDP%) -0.82 -0.82 -0.82 -0.84 -0.82 -0.82 -0.81 -0.82 -0.83 -0.86 -0.18 0.68 0.69 0.70 0.70 0.67 -0.82 -0.83 -0.83ch(Interest Rate%) 0.04 0.04 0.04 0.05 0.05 0.06 0.06 0.07 0.09 0.10 0.15 0.20 0.30 0.37 0.45 0.52 0.04 0.08 0.06%ch W( age Rate) -0.2 -0.1 -0.2 -0.2 -0.2 -0.2 -0.3 -0.3 -0.3 -0.4 -0.6 -0.8 -1.1 -1.4 -1.7 -2.0 -0.2 -0.3 -0.2ch(Private Wealth G/ DP%) 0.0 0.4 0.9 1.5 2.0 2.5 3.0 3.5 4.1 4.7 6.6 5.3 2.2 0.0 -2.8 -5.0 1.0 3.5 2.3ch G( ov't Wealth/GDP%) 0.0 -0.5 -1.2 -1.9 -2.7 -3.5 -4.3 -5.3 -6.4 -7.4 -12.3 -14.4 -14.4 -14.4 -14.4 -14.4 -1.3 -5.4 -3.3ch(Budget Deficit G/ DP%) 0.54 0.69 0.78 0.84 0.91 0.97 1.11 1.25 1.28 1.37 1.05 0.41 0.41 0.41 0.41 0.41 0.75 1.20 0.97(Small Open Economy)

%ch N( ational Wealth) 0.0 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.7 -0.9 -1.0 -2.1 -3.4 -4.5 -5.4 -6.4 -7.4 -0.1 -0.7 -0.4

%ch(Labor) 0.6 0.5 0.5 0.5 0.5 0.4 0.4 0.4 0.4 0.4 0.0 -0.5 -0.3 -0.2 -0.1 0.0 0.5 0.4 0.5%ch G( NP) 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 -0.6 -1.3 -1.6 -1.8 -2.0 -2.2 0.3 0.1 0.2%ch G( DP) 0.6 0.5 0.5 0.5 0.5 0.4 0.4 0.4 0.4 0.4 0.0 -0.5 -0.3 -0.2 -0.1 0.0 0.5 0.4 0.5%ch(Consumption) 0.8 0.8 0.9 1.0 1.0 1.0 1.1 1.1 1.1 1.2 0.8 0.1 -0.2 -0.4 -0.8 -1.1 0.9 1.1 1.0%ch G( ross Dom. Investment) 7.7 0.1 0.2 0.5 0.0 0.1 0.2 0.3 0.6 0.8 -1.1 -1.8 0.1 -0.1 -0.1 -0.1 1.7 0.4 1.0ch(Lump-Sum Transfer/GDP%) -0.23 -0.11 -0.07 -0.08 -0.04 -0.02 0.06 0.13 0.09 0.08 0.08 0.08 0.08 0.08 0.08 0.08 -0.10 0.07 -0.02ch G( ov't Consumption/GDP%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00ch(Income Tax/GDP%) -0.81 -0.81 -0.81 -0.83 -0.81 -0.81 -0.80 -0.80 -0.81 -0.84 -0.19 0.60 0.59 0.59 0.58 0.57 -0.81 -0.81 -0.81ch N( et Foreign Assets G/ DP%) -1.5 -1.5 -1.6 -1.8 -2.0 -2.3 -2.6 -3.0 -3.5 -4.1 -5.9 -8.0 -11.6 -14.1 -17.3 -20.0 -1.7 -3.1 -2.4ch(Private Wealth G/ DP%) 0.0 0.4 0.9 1.4 1.8 2.3 2.7 3.2 3.8 4.3 6.0 4.5 1.4 -1.0 -3.9 -6.4 0.9 3.3 2.1ch G( ov't Wealth/GDP%) 0.0 -0.5 -1.1 -1.9 -2.6 -3.4 -4.2 -5.1 -6.2 -7.2 -11.8 -13.8 -13.8 -13.8 -13.8 -13.8 -1.2 -5.2 -3.2ch(Budget Deficit G/ DP%) 0.52 0.67 0.76 0.81 0.88 0.94 1.07 1.21 1.23 1.31 0.99 0.39 0.39 0.39 0.39 0.39 0.73 1.15 0.94

58
Table A.10 (b). Income Tax Rates Reduced by 10 Percent Proportionally; Income Tax Rates Increased Gradually After 10 Years

Compensating Variations in Wealth as Percentages of Per H- ousehold GDP---Alternative Assumptions

The Year When Age 20 (Top) / the Age in Year 1 (Bottom)

-88 -79 -69 -59 -49 -39 -29 -19 -9 1 11 21 41 61 81 101 120

109 100 90 80 70 60 50 40 30 20 10 0 -20 -40 -60 -80 -99

(Closed Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.5 0.1 1.5 1.9 0.0 2.1 1.8 0.3 -0.4 -0.1 -0.6 -1.2 -1.4 -1.4 -1.4 -1.5

20-40 percentile 2.2 2.3 3.7 3.7 1.4 -0.1 -0.6 -2.5 -4.3 -4.8 -4.9 -4.9 -5.040-60 percentile 2.6 4.5 5.7 5.6 2.7 0.4 -1.1 -3.9 -6.4 -7.0 -7.1 -7.1 -7.260-80 percentile 4.4 9.0 10.0 9.2 5.3 1.1 -1.7 -5.6 -8.7 -9.5 -9.5 -9.6 -9.680-90 percentile 7.5 14.1 15.3 13.6 8.9 2.1 -2.3 -7.5 -11.0 -11.7 -11.8 -11.8 -11.990-95 percentile 12.8 25.4 23.8 22.1 13.1 3.7 -2.0 -8.9 -12.8 -13.7 -13.8 -13.8 -13.995-99 percentile 26.0 46.7 42.4 37.7 22.3 7.9 0.1 -10.4 -14.7 -15.6 -15.7 -15.8 -15.999-100 percentile 74.9 145.7 119.8 94.5 56.4 14.7 3.3 -12.2 -17.0 -17.9 -18.0 -18.1 -18.2

Average -0.3 -0.5 0.1 1.5 5.4 9.2 9.9 9.0 4.9 1.1 -1.0 -4.3 -6.6 -7.2 -7.3 -7.3 -7.3(Small Open Economy)Temporary Hourly Wage Class

0-20 percentile -0.3 -0.5 -0.2 0.1 0.3 -1.2 1.6 1.8 0.8 -0.2 0.4 0.2 -0.1 -0.3 -0.3 -0.3 -0.3

20-40 percentile 0.4 0.5 2.7 3.6 2.2 0.8 1.1 0.2 -1.0 -1.5 -1.6 -1.6 -1.640-60 percentile 0.3 1.7 4.0 5.0 3.6 1.6 1.3 -0.3 -1.7 -2.3 -2.4 -2.4 -2.460-80 percentile 0.6 3.6 6.3 7.3 5.5 2.5 1.2 -1.0 -2.8 -3.4 -3.5 -3.5 -3.580-90 percentile 2.0 5.9 8.9 9.8 7.9 3.8 1.2 -2.2 -4.2 -4.9 -5.1 -5.1 -5.190-95 percentile 4.6 11.6 12.1 14.3 10.4 5.1 1.2 -3.5 -5.7 -6.5 -6.7 -6.7 -6.795-99 percentile 13.7 23.9 20.9 22.3 16.0 8.1 1.7 -6.5 -9.0 -9.8 -10.0 -10.0 -10.099-100 percentile 50.8 88.9 64.0 51.5 35.7 12.4 1.9 -11.2 -13.8 -14.6 -14.8 -14.8 -14.8

Average -0.3 -0.5 -0.2 0.1 1.8 3.9 5.9 6.6 4.7 2.0 1.1 -0.9 -2.3 -2.8 -2.9 -3.0 -3.0

59
Figure A.10. Income Tax Rates Reduced by 10 Percent Proportionally; Income Tax Rates Increased

Gradually After 10 Years---Alternative Assumptions

(a) GNP

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(b) National Wealth

-8

-7

-6

-5

-4

-3

-2

-1

0

1

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(c) Labor Supply

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(d) Private Consumption

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(f) Interest Rate

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50 60 70 80 90 100

Year

Ch from the Baseline

(g) Wage Rate

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0 10 20 30 40 50 60 70 80 90 100

Year

%ch from the Baseline

(e) Income Tax Revenue

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

0 10 20 30 40 50 60 70 80 90 100

Year

Ch as a % of the

Baseline GDP

(h) Welfare Gain / Loss (Avg. of Each Age)

-10

-5

0

5

10

15

-80 -60 -40 -20 0 20 40 60 80 100 120

Year When Age 20

ch as a % of perHousehold GDP

Closed Economy Small Open Economy

60
References

[1] Aiyagari, S. Rao (1994), “Uninsured Idiosyncratic Risk and Aggregate Saving,” Quarterly Journal of Economics, 109, 659-684.

[2] Auerbach, Alan and Laurence Kotlikoff (1987), Dynamic Fiscal Policy, Cambridge University Press.

[3] Conesa, Juan and Dirk Krueger (1999), “Social Security Reform with Heterogeneous

Agents,” Review of Economic Dynamics, 2, 757-795.

[4] Congressional Budget Office (2003a), “An Analysis of the President’s Budgetary Proposals for Fiscal Year 2004,” March 2003.

[5] Congressional Budget Office (2003b), “The Budget and Economic Outlook: An Update,” August 2003.

[6] House of Representatives (2001), “Economic Growth and Tax Relief Reconciliation Act

of 2001—Conference Report to Accompany H.R. 1836,” 107th Congress, First Session,

Report 107-84.

[7] Huggett, Mark (1996), “Wealth Distribution in Life-Cycle Economies,” Journal of Monetary Economics, 38, 469-494.

[8] Huggett, Mark and Gustavo Ventura (1999), “On the Distributional Effects of Social

Security Reform,” Review of Economic Dynamics, 2, 498-531.

[9] Nishiyama, Shinichi (2002), “Bequests, Inter Vivos Transfers, and Wealth Distribution,”

Review of Economic Dynamics, 5, 892-931.

[10] Nishiyama, Shinichi and Kent Smetters (2003), “Consumption Taxes and Economic Efficiency in a Stochastic OLG Economy,” Working Paper 2002-6, Congressional Budget

Office, and NBER Working Paper 9492.

[11] Social Security Administration (2001), Social Security Bulletin: Annual Statistical Supplement, available at http://www.ssa.gov/statistics/supplement/2001/index.html.

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