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THESIS

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dissertation entitled

AN ASSESSMENT OF THE VALUE-ADDED TAX,
USING COMPUTATIONAL GENERATIONAL EQUILIBRIUM MODEL
WITH OVERLAPPING GENERATIONS

presented by

JAE-JIN KIM

 

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in Economics

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AN ASSESSMENT OF THE VALUE-ADDED TAX,
USING COMPUTATIONAL GENERAL EQUILIBRIUM MODEL
WITH OVERLAPPING GENERATIONS

By

Jae-Jin Kim

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

1996

ABSTRACT

AN ASSESSMENT OF THE VALUE-ADDED TAX,
USING COMPUTATIONAL GENERAL EQUILIBRIUM MODEL
WITH OVERLAPPING GENERATIONS

By
Jae-Jin Kim

Auerbach and Kotlikoff (1983) found that a consumption taxation would lead to long-run
welfare gains, at the expense of the cohorts that are elderly during the transition. Their
model has no bequests, and no government transfers. However, bequests explain a large
portion of the capital stock, and transfer payments make up a large fraction of the income
of the elderly. The inclusion of bequests and transfer payments may affect the results
substantially, since they can significantly alter the wealth profile of the elderly. We have
incorporated these important factors into a computational general equilibrium model of
the United Stated economy and tax system. Our model has bequests, a realistic profile of
government transfers, a labor/leisure choice, and a number of other features, including a
detailed treatment of the many components of the tax system. Taken together, these
factors help to produce a fairly flat wealth profile over the life cycle, which is much more
realistic than the extremely humped wealth profiles of Auerbach and Kotlikoff. Our main
result is that a consumption tax may lead to welfare gains for all cohorts, including the

elderly.

Copyright by
Jae-J in Kim
1 996

Dedicated to

My father, You-Kyung Kim
My mother, Bong-Sup Shim

My father-in-law, Tae-Young Kim
My mother-in—law, Bong-Soon Lim

My aunt, Choon Sup Shim
My aunt, Ha Sup Shim

My wife, Hye-Kyung
My daughter, Tae-Won

ACKNOWLEDGEMENTS

I would like to express my thanks to all committee members, Charles L. Ballard,
Leslie E. Papke, and John H. Goddeeris. I could not have finished my dissertation
without their help, encouragement, and patience to its completion. I would like to
express my special thanks to my mentor and advisor Dr. Charles L. Ballard. His
encouragement always bolstered my spirits and kept me going. He has spent endless
hours guiding me and reading my dissertation. Without his support and encouragement, I
could never gotten this far. He is a model of teacher, scholar, advisor, and human being'
to me.

The road to the completion of my dissertation has been filled with countless
challenges. Numerous people helped me at various stages of this road. I am especially
deeply grateful to Dr. Gill-Chin Lim for his vision and guidance. He has shown me
support, concern, and encouragement all the time.

I have met many good friends at Michigan State University. I would like to thank
all of them, especially Sang Ho Lee, Young-Beurn Lee, and Michael F. Miller.

I reserve special thanks for my family, especially for my parents, parents in law
and aunts. Without their unconditional love, support, understanding, and patience over
the years, I would not have enjoyed the victory today.

Finally, my deepest gratitude goes to a very special person in my life, my wife,
Hye-Kyung. I thank her from the bottom of my heart for all the love she has shown and

countless sacrifices she has made to help me complete my dissertation.

TABLE OF CONTENTS

 

 

List Of Tab|98IIII IIIIIIIII IIIIIII ...... II ........ I IIIIIIII II IIIIIII III IIIIIIII IIIII IIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIiv
List Of Figures IIIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIII I IIIII I IIIIIIIIIIIIIIIIII IIIII IIIIIIII IIIIIIIIIIIIIIIIIIIIIIII Vi
CHAPTER 1 INTRODUCTION ................................. ....................... . ....... .1
1.1 Introduction ....................................................................................................................................... 1

1.2 Review of the literature ..................................................................................................................... 2
1.2.1 The Role of Bequests .............................................................................................................. 9

1.3 Plan for this Research ................................................. . -- - ........................................... 10
CHAPTER 2 DESCRIPTION OF THE SIMULATION MODEL... .......... ..... ...13
2.1 Model Structure ............................................................................................................................... 13
2.1.1 The household Sector ............................................................................................................ 13

2.1.2 The Production Sector ........................................................................................................... 23

2.1.3 The Foreign Sector ................................................................................................................ 24

2.1.4 The Government Sector ........................................................................................................ 28
CHAPTER 3 DATA AND PARAMETERS" ............................................ ..........39
3.1 New Data ......................................................................................................................................... 39
3.1.1 Bequest and Transfer Proportions Without Demographic Adjustment ................................. 41

3.1.2 Bequest and Transfer Proportions With Demographic Adjustment ...................................... 44

3.2 Parameter Selection ......................................................................................................................... 51
3.2.1 Parameterization of the Elasticities of Substitution ............................................................... 53

3.2.2 Parameterization of the Leisure Intensity .............................................................................. 54

3.2.3 Parameterization of the Labor Efficiency Ratio .................................................................... 55
CHAPTER 4 SIMULATION RESULTS...... ................................. .. ................. ...58
4.1 Solution Process ............. - ._ ............................................................................ 58
4.1.1 Base Case .............................................................................................................................. 59

4.1.2 Revised Case ......................................................................................................................... 60

4.1 Results in the Aggregated Model .................................................................................................... 60
4.2.1 Case Without Demographic Adjustment ............................................................................... 61

4.2.2 Case With Demographic Adjustment .................................................................................... 84

4.3 Results in the Disaggregated Model .............................................................................................. 106
4.3.1 Case Without Demographic Adjustment ............................................................................. 106

4.3.2 Case With Demographic Adjustment .................................................................................. 107

4.4 Results When Tax on Bequests is Positive .................................................................................... 119

4.5 Conclusion .................................................................................................................................... 127
APPENDIX ................................................ . ..... . ............... 129
BIBLIOGRAPHY ..... . ..... . ................ ............ ...154

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Table 8
Table 9

Table 10

Table 11

Table 12

Table 13

Table 14

Table 15

Table 16

Table 17

Table 18

Table 19

LIST OF TABLES

Difference Between My Model and Auerbach and Kotlikoff’s ............. 12
Classification of Industries and Consumer Expenditures .................... 25
US. Taxes and Their Treatment in the Model .................................... 32
Inheritances Per Household, 1973 (in dollars) .................................... 40
Public Transfers Per Household, 1973 (in dollars) .............................. 41
Adjusted Inheritances Per Household, 1973 (in dollars) ..................... 42
Adjusted Public Transfers Per Transfers Per Household, 1973

(in dollars) ........................................................................................... 42
Adjusted Inheritances and Transfers Per Each Age Group ................ 43
Proportion of Inheritances and Transfers ............................................ 43
Number of Household (in dollars) ....................................................... 44
Adjusted NH Within Each Age Group (in $thousands) ....................... 45
Total Inheritances for Each Income and Age Group

(in $thousands) ................................................................................... 46
Total Transfers for Each Income and Age Group

(in $thousands) ................................................................................... 46
Proportion of Inheritances for Each Income and Age Group .............. 47
Proportion of Transfers for Each Income and Age Group ................... 47
Proportion of Inheritances and Transfers ............................................ 48
Proportions of Inheritances and Transfers in Both Cases .................. 51

Newcomer Cohort’s Saving Profile When C*=0
($billion/5 year Period) ........................................................................ 62

Aggregate K/L Ratio When C*=0, No Demographic Adjustment,
Aggregated Model .............................................................................. 70

iv

LIST OF TABLES (cont’d)

Table 20 Real Rental Prices of Capital in Revised Case When C*=0,

No Demographic Adjustment, Aggregated Model ............................... 71
Table 21 Newcomer Cohort’s Saving Profile When C*=0

($billionsl5 year period) ...................................................................... 84
Table 22 Aggregate K/L Ratio When C*=0, with Demographic Adjustment,

Aggregated Model .............................................................................. 88
Table 23 Real Rental Price of Capital in Revised Case When C*=0,

with Demographic Adjustment, Aggregated Model ............................. 89
Table 24 Aggregate K/L Ratio without Demographic Adjustment,

Disaggregated Model ........................................................................ 109
Table 25 Real Rental Price of Capital without Demographic Adjustment,

Disaggregated Model ........................................................................ 110
Table 26 Aggregate K/l. Ratio with Demographic Adjustment,

Disaggregated Model ........................................................................ 1 1 1
Table 27 Real Rental Price of Capital with Demographic Adjustment,

Disaggregated Model ........................................................................ 112
Table 28 Investment Goods Purchasing When BK=50%, C*=20%,

with No Demographic Adjustment, Aggregated Model ..................... 121
Table 29 Investment Goods Purchased When BK=50%, C*=20%,

with Demographic Adjustment, Aggregated Model ........................... 122

Figure 1
Figure 2
Figure 3

Figure 4A

Figure 4B

Figure 40

Figure 4D

Figure 5A

Figure 5B

Figure SC

Figure 50

Figure 6A

Figure 6B

Figure 6C

Figure 6D

LIST OF FIGURES

Proportions of Inheritances .............................................................. 49
Proportions of Transfers .................................................................. 50
Labor Supply Profile of Newcomer Cohort When *=0, without
Demographic Adjustment, Aggregate Model ................................... 69
Wealth Profile of Newcomer Cohort When C*=0, without
Demographic Adjustment, Aggregated Model ................................ 72
Rental Price of Capital When C*=0, without Demographic
Adjustment, Aggregated Model ....................................................... 73
Present Value of Equivalent Variation When C*=0, without
Demographic Adjustment, Aggregated Model ................................ 74
Equivalent variation as Proportion of Lifetime resources When

C*=0, without Demographic Adjustment, Aggregated Model .......... 75
Wealth Profile of Newcomer Cohort When C*=10%, without
Demographic Adjustment, Aggregated Model ................................ 76

Rental Price of Capital When C*=10%, without Demographic
Adjustment, Aggregated Model ....................................................... 77

Present Value of Equivalent Variation When C*=10%, without
Demographic Adjustment, Aggregated Model ................................ 78

Equivalent variation as Proportion of Lifetime resources
When C*=10%, without Demographic Adjustment,

Aggregated Model ........................................................................... 79
Wealth Profile of Newcomer Cohort When C*=20%, without
Demographic Adjustment, Aggregated Model ................................ 80

Rental Price of Capital When *=20%, without Demographic
Adjustment, Aggregated Model ....................................................... 81

Present Value of Equivalent Variation When C*=20%, without
Demographic Adjustment, Aggregated Model ................................ 82

Equivalent variation as Proportion of Lifetime resources
When C*=20%, without Demographic Adjustment,
Aggregated Model ........................................................................... 83

vi

Figure 7A

Figure 7B

Figure 7C

Figure 70

Figure 8A

Figure 8B

Figure BC

Figure BD

Figure 9A

Figure 9B

Figure 90

Figure 90

Figure 10A

Figure 108

Figure 10C

LIST or FIGURES (cont’d)

Wealth Profile of Newcomer Cohort When C*=0, with

Demographic Adjustment, Aggregated Model ................................ 90
Rental Price of Capital When C*=0, with Demographic

Adjustment, Aggregated Model ....................................................... 91
Present Value of Equivalent Variation When C*=0, with
Demographic Adjustment, Aggregated Model ................................ 92
Equivalent variation as Proportion of Lifetime resources When

C*=0, with Demographic Adjustment, Aggregated Model ............... 93
Wealth Profile of Newcomer Cohort When C*=10%, with
Demographic Adjustment, Aggregated Model ................................ 94
Rental Price of Capital When C*=10%, with Demographic
Adjustment, Aggregated Model ....................................................... 95
Present Value of Equivalent Variation When C*=10%, with
Demographic Adjustment, Aggregated Model ................................ 96
Equivalent variation as Proportion of Lifetime resources When
C*=10%, with Demographic Adjustment, Aggregated Model .......... 97
Wealth Profile of Newcomer Cohort When C*=20%, with
Demographic Adjustment, Aggregated Model ................................ 98

Rental Price of Capital When C*=20%, with Demographic
Adjustment, Aggregated Model ....................................................... 99

Present Value of Equivalent Variation When C*=20%, with
Demographic Adjustment, Aggregated Model .............................. 100

Equivalent variation as Proportion of Lifetime resources When
C*=20%, with Demographic Adjustment, Aggregated Model ........ 101

Wealth Profile of Newcomer Cohort When C*=30%, with

Demographic Adjustment, Aggregated Model .............................. 102
Rental Price of Capital When C*=30%, with Demographic
Adjustment, Aggregated Model .................................................... 103

Present Value of Equivalent Variation When C*=30%, with
Demographic Adjustment, Aggregated Model .............................. 104

vii

Figure 100

Figure 11A

Figure 118

Figure 110

Figure 12A

Figure 128

Figure 120

Figure 13A

Figure 138

Figure 14A

Figure 143

LIST OF FIGURES (cont’d)

Equivalent variation as Proportion of Lifetime resources When
C*=30%, with Demographic Adjustment, Aggregated Model ....... 105

Rental Price of Capital When C*=0 and BK=70%, without

Demographic Adjustment ............................................................. 1 13
Present Value of Equivalent Variation When C*=0 and BK=70%,
without Demographic Adjustment ................................................. 114
Equivalent Variation as Proportion of Lifetime Resources When
C*=0 and BK=70%, without Demographic Adjustment ................. 1 15
Rental Price of Capital When C*=0 and BK=50%, with

Demographic Adjustment ............................................................. 1 16
Present Value of Equivalent Variation When

C*=0 and BK=50%, with Demographic Adjustment ...................... 117
Equivalent Variation as Proportion of Lifetime Resources When
C*=0 and BK=50%, with Demographic Adjustment ...................... 118
Investment Share of GNP When C*=0, BK=50%,and No
Demographic Adjustment ............................................................. 123
Equivalent Variation as Proportion of Lifetime Resources When
C*=0, BK=50%, and No Demographic Adjustment ....................... 124
Investment Share of GNP When C*=20%, BK=50%, and with
Demographic Adjustment ............................................................. 125

Equivalent Variation as Proportion of Lifetime Resources When
C*=20%, BK=50%, and with Demographic Adjustment ................ 126

viii

Chapter 1

INTRODUCTION

1.1. Introduction

The question of whether consumption or income is the appropriate tax base is an
important one with a long history of study. Henry Simons (1938) was an eloquent
advocate of income taxation, while consumption taxation has been advocated by such

distinguished economists as Irving Fisher (1942) and Nicholas Kaldor (1957).

There are two different ways to tax consumption. One method involves indirect
taxation, with, for example, a general sales tax or value-added tax (VAT). The second
method involves taxing consumption directly by allowing a deduction for saving from the
income tax base. The latter approach is sometimes called “personal consumption

taxation.”

Since the Second World War, value-added taxes have become standard in the
European Community, and similar structures have been adopted in recent years in Japan,
Canada, and New Zealand. The US. Treasury Department’s Blueprints for Basic Tax
Reform (1977) advocated a personal consumption tax. A VAT has not yet been adopted
in the United States, nor has the US. moved fully toward personal consumption taxation.

Nevertheless, it seems unlikely that the debate will end soon. For example, the Chairman

of the House Ways and Means Committee, Bill Archer, has advocated the adoption of a

national consumption tax.

Besides this tax proposal, there are several other proposals for alternative federal
taxes. Senators Pete Domenici (R-N. M.) and Sam Nunn (D-Ga.) proposed the USA (or
unlimited saving account) Tax. It levies an 11% VAT on all businesses. It allows
exemptions of $17,600 for a family of four. There is a full tax credit for payroll tax
payments for both personal and business taxes. It has graduated tax rates for the personal
tax, starting at 19% and rising to 40%. Robert Hall and Alvin Rabushka of the Hoover
Institution have proposed a 19% flat tax on all businesses, with the deduction of wages
and pension contributions from the tax base along with material costs and capital
investments. House Majority Leader Richard Armey (R-Texas) and Senator Richard
Shelby (R-Ala.) proposed a 20 percent flat tax rate with a $31,400 exemption for a family
of four. David Bradford has proposed an X-tax which is similar to Hall-Rabushka, but
with graduated tax rates on household wage income to raise progressivity. In this study, I
consider the effects of adopting a uniform VAT or national sales tax in the United States.
In my simulations, the revenues from this tax will be used to lower the marginal income

tax rates.

1.2. Review of the Literature

In a two-period model of consumption choice with no labor supply decision, a
consumer chooses between present and future consumption. In this model, a
consumption tax has an efficiency advantage over an income tax, since the consumption

tax does not generate a substitution effect. Feldstein (1978) shows that this argument

neglects the effect of taxes on the individual’s choice between leisure and consumption.
Since the individual consumes three distinct goods (i. e., first-period leisure, first-period
consumption, and second-period consumption), the choice between an income tax and a

consumption tax will depend upon the complementarity among all three goods.

In response to the limitations of two-period models, three types of simulation
model were developed in the late 19705 and 19808: the family of “GEMTAP” models,

infinite-horizon models, and overlapping-generations life-cycle models.

Summers (1981) studies intertemporal taxation using a simulation model with
overlapping generations of life-cycle consumers. Summers’s model has no bequests, no
labor/leisure choice, no uncertainty, and no borrowing constraints, and there is perfect
foresight. Also, the structure of utility is extremely simple, with additively separable,
isoelastic utility functions. He takes an entirely different approach from the previous
studies, i. e., he chooses parameter values from a variety of sources rather than calibrating
them based on real data. This approach generates large estimates of the saving elasticity,
which range as high as 3.71. Thus, it is not surprising that he finds very large welfare
gains from moving to a consumption tax. Summers explains the high savings elasticities
in terms of a “human wealth effect”.' It should also be emphasized that Summers only
looks at steady states. This means that he ignores the possibility of losses during the

transition to a new tax regime.

 

1 When the net rate of return goes up as a result of a change in tax policy, the present value of
lifetime wealth goes down. The consumer is now poorer, and reduces his first-period
consumption. Thus, saving increases.

Starrett (1982, 1988) points out that the Summers model implies unusual swings
in the pattern of consumption. He also shows that some of Summers’s parameterizations
are associated with highly unrealistic capital/labor ratios for the economy. He suggests
two changes in the Summers formulation to control the large saving elasticities. The first
change introduces a minimum required level of consumption. The second involves “big-
ticket items”, that lead to a change in the desired consumption path once these changes
are made. Following the suggestion of Starrett, I incorporate minimum required
consumption level in my model, in an effort to reduce the intertemporal responses to a

more realistic level.

Auerbach and Kotlikoff (1983, 1987) expand this approach by focusing on
transition and intergenerational distribution issues. They examine how dynamic tax
policy changes such as a change in the tax rate on saving can shift the overall burden of
taxes from one generation to another, using assumptions similar to Summers’. They find
that the shift to consumption taxation would lead to large long-run welfare gains.
However, the large long-run gains come at the cost of harming the cohorts that are old at
the time of the policy change. This is explained partly in terms of the inelastic behavior
of the old in a simple life-cycle model with no bequests.2 Auerbach and Kotlikoff find
that it is very difficult (but theoretically possible) to establish tax rates that will benefit all

age groups.

Fullerton, Shoven, and Whalley (1983) use the “GEMTAP” model, in which

infinitely-lived consumers make repeated choices between present and future

consumption. Thus, consumption is only affected by current income, not by lifetime
wealth. However, the strength of this model is that it can be calibrated precisely to any
desired intertemporal elasticity. The welfare gains from the adoption of a full
consumption tax are on the order of one percent of wealth, when the transition is
evaluated explicitly. These results are broadly similar for savings elasticities between 0.0

and 0.4.

Goulder, Shoven, and Whalley (1983) consider the effect of adopting four
alternative forms of VAT in the United States. These include income-type VATS and
consumption-type VATS, on both destination and origin bases. Some believe the
destination-based VAT in Europe restricts trade, since exports leave Europe tax-free but
imports are taxed as they enter. Thus, they have prompted the discussion of adopting
VAT in the United Stated for reasons of international competitiveness reason. However,
the results of Goulder, Shoven, and Whalley Show that foreign trade concerns regarding
destination- versus origin-based taxes do not provide a legitimate reason for the United

States to introduce a VAT, but a broadly based VAT may lead to welfare gains.

Ballard and Goulder (1985) explore how consumers’ expectations can influence
the attractiveness of adopting a personal consumption tax in the United States. Using the
infinite-horizon model, they find that the welfare gain from adopting a consumption tax is

reduced by about ten percent when moving from myopia to a great deal of foresight.

 

2 When each cohort begins and ends its life with zero capital, it must be true that cohorts are
dissaving rapidly late in life. Thus, such dissaving is penalized by the consumption tax.

Ballard and Shoven (1987) use the GEMTAP model to examine the efficiency
properties of introducing a VAT in the United States. They compute the efficiency-
equity trade-off offered by a VAT, using a computational general equilibritun (CGE)
model of the US. economy and tax system. Their contribution to the literature is the
introduction of Stone-Geary inner nest in the consumer utility functions. This closes off a
portion of each consumer’s income, and thus reduces the overall degree of responsiveness
of consumption choice. They consider three types of VAT: an ideal consumption-type
VAT, an ideal income-type VAT, and a more politically realistic ‘mean European VAT’.3

However, my model has the same marginal tax rate for all commodities.

In addition to looking at three types of VAT, Ballard and Shoven perform
simulations reducing the income tax using additive replacement and multiplicative
replacement, which are two different ways in which the income tax could be scaled.
They find that the simulation results are very sensitive to the manner of replacement.
Additive replacement means additive changes to the marginal income tax rate, i. e., the
same number of percentage points is subtracted from (or added to) each household’s
marginal income tax rate. With multiplicative replacement, each household’s marginal
tax rate is multiplied by a constant, so that equal government revenue yield is achieved.
When tax increases are necessary for equal revenue yield, additive replacement is more
efficient. However, when tax reductions are necessary for equal yield, multiplicative

replacement is more efficient. The simulation results of Ballard and Shoven show that,

 

3 The primary distinguishing characteristics of the European VATS are the consumption base, the
destination base, and differentiated rate structure. See Aaron (1981) and Cnossen (1982) for a
discussion of rate structures of the European VATS.

even though rate differentiation does reduce the regressiveness of the VAT somewhat, the
VATS are generally regressive, and that rate differentiation is not a very efficient way to
redistribute income. Although their results are interesting, they cannot look at some

important issues such as the intergenerational distribution.

Ballard, Scholz, and Shoven (1987) study three types of consumption-based tax:
an ideal flat consumption VAT, a stylized European VAT, and a progressive expenditure
tax. They find that the adoption of a flat consumption-based equal-revenue-yield VAT
leads to modest welfare gains in the aggregate. For their central-case simulations, they
have larger welfare gains when multiplicative replacement rather than additive
replacement is used. This fact reminds us that the method of tax replacement can be just
as important as the tax policy change itself. Although rate differentiation like that of the
European VATS reduces its regressivity on the VAT, it leads to substantial reductions in
the welfare gains at the same time. Thus, there is a trade-off between equity and

efficiency.

Ballard, Scholz, and Shoven also consider the welfare effects of replacing the
corporate income tax with these three types of VAT. This replacement produces fairly
substantial welfare gains, regardless of the type of replacement for equal revenue yield.
The attractiveness of the policies ultimately depends on what kind of a social welfare
function is used. Their results Show that a Bentharnite would favor all three types of
VAT, while a Rawlsian would advocate a differentiated VAT with additive replacement,

or the progressive expenditure tax with either additive or multiplicative replacement.

Finally, their sensitivity analysis says that a greater saving elasticity always leads to

larger welfare gains, as expected.

Feldstein and Krugman (1990) use a simple three-good, two-period model to
explore the international trade effects of a VAT. They Show that the widespread belief
that VATS give the traded goods sectors of countries with VATS an advantage over the
corresponding sectors of countries that rely on income taxation, is incorrect. They argue
that a VAT may improve competitiveness in the short run by offering less bias against
saving than an income tax, and this tends to improve the trade of balance, other things
being equal. However, an offsetting effect is that, a VAT tends to be levied more heavily
on traded goods, thus reducing rather than increasing the Size of a country’s traded-goods
sector. Thus, on balance, we have an uncertain effect on a nation’s net exports in the
Short run. However, in the long run, imports may increase in excess of exports as a result
of the accumulation of foreign investment. Feldstein and Krugman conclude that the
common belief that a VAT is a kind of disguised protectionist policy is based on a

misunderstanding.

Jorgenson and Yun (1990) use an infmite-horizon model with an intertemporally
additive utility function to evaluate the impact of the Tax Reform Act of 1986 on US.
economic growth. They find that the welfare gain from moving to a consumption tax
from an income tax is much larger than the gain from the Tax Reform Act of 1986.
However, since the infinite-horizon models are usually characterized by a very large
intertemporal responsiveness, we must be careful in interpreting the welfare results of

these simulation models. In addition, since these models abstract from the simultaneous

existence of many generations of different ages, they can not consider intergenerational

issues.

1.2.1. The Role of Bequests

Many of the models discussed above leave out intergenerational issues, which are
important for many reasons. At this point, I will discuss some of the empirical literature

on bequests.

Using cross-section Social Security data, Mirer (1979) finds that the wealth of the
aged does not decrease during their lifetimes, and adds that “Precautionary, bequest, or
other motives must be taken into account if the theory is to explain the wealth holding
behavior of persons toward the end of their lives.” White (1978) uses a simulation
approach, and finds that the simple life-cycle theory without bequests cannot explain the
total amount of observed aggregate personal saving. Her simulated values of aggregate

saving represent no more than about 60 percent of the observed values.

Kotlikoff and Summers (1981) estimate historic age-earnings and age-
consumption profiles. These profiles are combined with data on rates of return to
calculate a stock of life-cycle wealth. They compare this stock of life-cycle wealth with
aggregate wealth holdings in the United States, to see whether any intergenerational
transfers occur. They conclude that the simple life-cycle theory of saving with no
intergenerational transfers is a very poor description of the process of capital
accumulation in the US. economy. In other words, intergenerational transfers are

responsible for a sizable amount of wealth accumulation in the US.

10

Gale and Scholz (1994b) conclude that inter vivos transfers and bequests may
account for about 51 percent of net wealth accumulation. This implies that an
overlapping-generations model will have great difficulty in capturing the stylized facts of

the economy, unless it incorporates intergenerational transfers in an explicit way.

In fact, without bequests, consumers are born with no capital and die without
leaving any capital. If the model is to generate a large capital stock (like the one actually
observed), this requires consumers to save a tremendous amount early in life, followed by
very rapid dissaving late in life. Thus, we observe a very steep wealth profile during their
working years, and a very rapid decrease in wealth during the retirement period. This fact
leads to the widely-publicized results of Auerbach and Kotlikoff that the move to
consumption taxation would lead to large welfare gains at the cost of banning the cohorts

that are elderly at the time of the policy change.

1.3. Plan for this Research

In the GEMTAP model, the consumer makes a choice in every period between
present and future consumption. Thus, the model is basically an infinitely repeated two-
period model. The advantage of this model is that it can be calibrated to any desired
intertemporal elasticity. However, it is not attractive theoretically, since consumers make
their decisions subject to a constraint on current income, rather than an entire lifetime

wealth stream. It also ignores issues of intergenerational distribution.

11

In infinite-horizon models, such as those of Jorgenson-Yun and Ballard-Goulder
(1985), a single consumer maximizes the utility from an infinite stream of consumption,
subject to an infinite stream of wealth. This type of model tends to produce an
unrealistically large saving elasticity, which will tend to lead to overstated welfare gains.
In addition, since these models abstract from the simultaneous existence of many

generations of different ages, they cannot consider intergenerational issues.

An overlapping generations life-cycle model is attractive because it can explore
intergenerational issues. However, it does not necessarily remove the possibility of very

high intertemporal elasticities.

The purpose of my dissertation is to build a model that not only addresses the
intergenerational issues that first came to our attention with Auerbach and Kotlikoff, but
also overcomes some of the problems of that model. First of all, I want to lower the
elasticity, so that the overall size of the intertemporal responses is reasonable. Just as
important, however, I want to deal with one of most widely-publicized results of
Auerbach and Kotlikoff, the story that the elderly are badly hurt during the transition
period in the movement from an income tax to a consumption tax. Since Auerbach-
Kotlikoff do not incorporate either bequests or government transfers, they generate
unusual wealth profiles. All of the evidence (e. g., White, Mirer, Kotlikoff-Summers,
Gale and Scholz) shows that wealth profiles are fairly flat. Thus, I want to incorporate

bequests and government transfers in order to create flatter, more realistic wealth profiles.

Since the purpose of my model is to improve on some of the problems of

Auerbach and Kotlikoff, it is worthwhile to compare the major differences between two

 

12

models. Table 1 shows the differences between my model and that of Auerbach and

Kotlikoff.

Table 1. Difference Betweeg My Model 93d Auerbach and Kotlikoff’s

 

 

 

 

 

 

 

 

 

A-K (1983) A-K (1987) My Model

5 No 0.25 0.4

E 1 0.8 0.8

p 0.02 0.015 0.01

Foresight Perfect Foresight Perfect Foresight Myopia

Bequests No No Yes
Government Transfers No No Yes
Labor/leisure Choice No Yes Yes
C. No No Yes

 

 

 

 

5 =lntertemporal Elasticity of Substitution Between Consumption and Leisure
5 =Intratemporal Elasticity of Substitution Between Consumption and Leisure

p =The Rate of Time Preference

C'=Minirnum Required Consumption Level

 

Chapter 2

DESCRIPTION OF THE SIMULATION MODEL

2.1. Model Structure

2.1.1. The Household Sector

We assume that, in every period, aggregate consumption, saving, and labor supply
are derived from the intertemporal optimizing behavior of individual generations. Each
generation or cohort has an economic life of 55 years (for example, from age 21 through
age 75), and a new cohort is “born” each period (one period is five years).4 Thus, in any

period, there are 11 cohorts of different ages making household decisions.

Households derive utility from consumption, leisure, and bequest-giving. The

utility function for any given cohort takes the following additively separable formz’

.. . «Ii-1 1
{( C.—C) +w(H —H,)}+ ———,'b B,

U—l T
(1)U_5,Z_:( 5(1+p)T

1+p)”

In the above expression, t is the period, T is the index for the last period of life, C, is

consumption in period t, C. is minimum required consumption", H. is potential labor

 

4 Auerbach and Kotlikoff also assumed an economic lifetime of 55 years. However, they
calculate equilibria every year. The assumption of a five-year period reduces computational
expense, without sacrificing a great deal of information.

5 This kind of intertemporal additively separable utility function is used by virtually all
researchers in the field. However, it should be emphasized that it is not used primarily because
of realism, but because it is tractable. Lifetime utility functions of this sort can be found in
Ballard (1983), Auerbach and Kotlikoff (1983), and Ballard and Goulder (1987). The bequest
formulation is discussed in Blinder (1974).

13

14

time, and H, is labor supply in period t. Thus, leisure in period t, which we call 1:], or 1,,
is defined as H ' - H,. The parameter p is the rate of time preference.7 The parameter
0' 51—1 / 5' , where E is the elasticity of substitution between C and l in a given period.

The parameter 6 E 1 - l / 3', where 5‘ is the elasticity of substitution between bundles of

C and I across periods. To maintain dynamic consistency, the elasticity of substitution

between consumption/leisure bundles and bequests is also 3’. The distribution parameter

a influences the intensity of demand for leisure at given relative prices.

B7. is the bequest left at the end of year T.8 The parameter b determines the
strength of the bequest motive. When b is zero, individuals derive no benefits from
bequest-giving. Thus, since length of life is assumed to be known with certainty, such
that accidental bequests are ruled out, the consumers will not leave any bequests when
b=0. The larger the value of b, the more bequests individuals leave, thus the greater the

fraction of lifetime resources left by individuals to succeeding generations. This type of

 

5 Note that, even though I include C“ (minimum required consumption level) in the model, it
does not mean that tax base is changed.

7 We assume that p is constant, in order to maintain dynamic consistency in the sense of Strotz
(1955-1956).

3 We assume certain date of death, as Auerbach and Kotlikoff did, but others relax this
assumption. We also assume that all bequests come at end of life. We abstract from gifts
inter-vivos. Gale and Scholz (1994b) distinguish between intended transfers and unintended
transfers using the 1983-86 Survey of Consumer Finances. Their estimate shows that intended
transfers (i.e., inter-vivos transfers) account for at least 20% of net worth. Their results show
that bequests account for an additional 15% of net worth. Thus, intergenerational transfers
account for at least 35%, and probably around 50% of net worth. We collapse inter vivos gifts
into bequests in our model.

15

bequest theory has been used, for example, by Blinder (1974). However, it should be

noted that other plausible explanations for bequests have been proposed.9

Each cohort maximizes utility subject to an intertemporal wealth constraint.
Suppressing taxes for expositional convenience, we can write the lifetime wealth

constraint as:
T

(2) PK,K1+ Z{W,'(H‘ —1,)+ TR, + 1N, — P,C, }d, — PBTBTdT = 0,
(:1

where PK, is the current price of a unit of nonhuman capital, Kl is the current capital

endowment, W ' is the hourly wage, TR is transfers, and IN represents inheritances. The
variable Pt refers to the price index for consumption, which is a weighted average of the
price of specific consumption goods purchased in the given period. The discounting

operator for period t, d,, is defined by

 

9 Davies (1981) takes the importance of bequests as given, and attempts to explain why bequests
take place. He suggests that consumers do not gain utility from bequests, but rather that they
are forced to leave accidental bequests as a result of the lack of well-functioning annuities
markets. He finds that uncertainty about length of life can indeed depress consumption if the
intertemporal substitution elasticity is sufficiently small. Bemheim, Shleifer, and Summers
(1985) suggest that bequests are a device by which parents manipulate the behavior of their
children. Barro (1974) regards bequests as arising from the intertemporal utility maximization
decision of intergenerationally altruistic individuals. Such individuals maximize a utility
stream which includes the utilities of their immediate descendants as well as themselves.
Wolfe and Goddeeris (1987) emphasize uncertainty about future health status as a possible
additional reason for accidental bequests. Kotlikoff (1986) shows that uncertain health
expenditures represent a strong motive for saving. However, this motive may be greatly
influenced by the availability of private insurance and the presence of government programs
such as Medicaid. Hubbard, Skinner, and Zeldes (1995) find that the presence of asset-based
means-tested social insurance leads to a non-monotonic relationship between wealth and
consumption for lifetime low-income families, which is inconsistent with the orthodox life-
cycle model. They suggest that a properly specified life-cycle model with precautionary
saving and social insurance can explain the heterogeneity in motives for saving. Carroll and
Samwick (1992) provide some evidence that wealth is higher for consumers with greater
income uncertainty. They find that the pattern of precautionary saving is more consistent with
the “buffer-stock” models of saving, in which consumers hold wealth to buffer consumption
against near-term fluctuations in income, and are far less concerned about uncertainty in
lifetime income than in the standard model.

16

I 1
"IT——

“(1+rs)

3:1
I , t=l

,Vt>l

‘9.
III

 

where rs is the expected rate of return between period s and period (3+1). Equation (2)
thus states that the sum of current non-human wealth and the present value of prospective

lifetime labor income, transfers, and inheritances must equal the present value of

consumption plus bequests.

We can write the labor supply constraint as:
(3) (H. —1,)20 forallt.
Equation (3) states that the labor supply cannot be negative in any period.

Each cohort has a given endowment of potential labor time (H °), which is
allocated to working and leisure: H ' = H, +1,. The value of HT is constant over the

lifetime of a given cohort. The hourly wage (W,') can be written as

(4) W,'= WM. ,

where W t is the prevailing wage per unit of effective labor, and eh is the ratio of effective

labor to labor hours for a cohort of age h. The labor efficiency ratio (eh) changes over

the lifetime of a given cohort, reflecting changes in skills as a result of experience and

age.

17

Some key aspects of the solution to the consumer’s lifetime utility maximization
will be discussed here. Details are provided in part I of the Appendix. The consumer’s
choice variables are consumption (C t) and leisure (1,,or H i - H,) in each period, and the

size of the bequest (37’). We can form the Lagrangean function by combining equations

(1), (2), and (3):

i—1 {(C — C")" +w(H‘ —H)"}3 4.1—1 5:535
I t 6(1+p)T T

+ AP), K, + i{W/(H‘ —1,)+ TR, + 1N, — P,C,}d, — PBTBTdT]

where A. is the Lagrange multiplier and represents the marginal utility of lifetime

resources, and the ”’3 are the Kuhn-Tucker multipliers on the constraints on labor

supply.

Taking the first-order conditions for consumption and leisure, and rearranging,

gives us the following expressions:

(6) ——1——(é° + a 10);"1 (3‘0“ = ith
(1+ p)(—l I l I I

ll’

18

and

b’

(7) (6,0 + 71,40)?" 01,1," = A(W,'+ ,u,)d, .

___l___
(1+ p)"'

Equation (6) indicates that the marginal utility of consumption at time I must equal the
marginal cost of consumption, and equation (7) shows that the marginal utility of the

leisure must equal its marginal opportunity cost.

Dividing (6) by (7) and arranging, we solve for I, (leisure in period t) as a function

of consumption in period t and various parameters:

(8) l, = C35, ,

l

W' 5

where 5, =[—'t1%) .
a

I I

Substituting (8) into (6) and manipulating terms gives us:

(9) 6 =,13‘1-—'Pfi ———(l+p) (1+a,g°)("‘3)(3'—TJ.

Dividing (9) for period t by (9) for period (t-l) yields:

l9

. L ,
6—] a

9 =(,,,,l)[i) [2L] ,
C.-. Pr—l 1 ‘1' ar—I 61—1

I

(10)

 

 

1
1+ p ‘5" . -
77, = 1+ — l, r. e. , the reference growth rate of consumptron,
’14

where ( and

,-(.-g)(,:—,)=(”;il(.ill=% °

 

 

By recursively applying (10) over successive periods and manipulating, we can express

C, in terms of C, and the parameters of the problem:

(11) 6 =C,o

I

l
3: 0 V
where Q, = {(5)0 +p)'-ld,} [w] .
P1 ““15?

Equation (11) represents an optimal consumption path. Once the optimal C, is known,
we can obtain an optimal consumption path conditional on expected prices and interest

rates.

Differentiating the Lagrangean function with respect to bequests (3,) yields:

(12) ——1———b'""B;’" = my, ,

(1 +p)T

20

which indicates that the marginal utility of the bequest must equal its marginal

opportunity cost. Rearranging (6) gives us:

I l

13 =
( ) PrdT (1 + p)T-l

 

6
x ——l x
a a 0—1
(c,.+a,z,)a c, .

Substituting (8) and (11) into (13) and rearranging terms yields the following expression:

6 A

(14) ,1 = ((1 + p)"'P,.d,)"(1+ (21T1§,“,’.)3—l(GETTY—l .

Substituting (14) into (12) and rearranging terms gives us an expression for the optimal

bequest in terms of discretionary consumption in the base period:

(15) B, = b¢é,o,,

_l_

+ p)PBT ] 6-1 6—0
P

where ¢=[(l (1+aréflm.

T

Equation (15) implies that bequests are equal to zero when the bequest intensity
parameter (b) is zero, and that bequests increase with b. Although equation (15) suggests
a linear relationship between bequests and b, this is not the case, since higher values of b
entail lower discretionary consumption. (We have to reduce consumption in order to

leave a larger bequest.)

21

Substituting (11) into (8), we have
(m) L=GQRP

From equation (1 1), we have

(17) C, =C +(C, —C’)o,.

Substituting (11), (15), (16), and (17) into (2), and rearranging terms, gives us an initial

optimal consumption:

T
PK, Kl + Z {(W,'+ 11,)H' + TR, + IN, — Rc‘ }d,
(18) C, = c‘ + '=‘

T

20, {UV/+14); + 10,}.1, +P3,b¢ordr

r=I

 

In the above equation, first-period consumption (C,) is linearly homogeneous in lifetime

resources (initial wealth plus the present value of lifetime potential labor time, transfers,
and inheritances). Equations (18) and (10) imply that, for given lifetime resources and

prices, a lower b indicates higher consumption at each point in time.

Once we get the initial equilibrium consumption level (C, ) , we can calculate an
equilibrium consumption path according to (1 1). By substituting this equilibrium
consumption path into (8) and the leisure constraint, we can get the equilibrium leisure

path and thus the equilibrium labor path:

22

PC, = C' +(C, - c‘)o,
(19) I. = (C. —C‘)é.
LH, = H' —1, .

 

From equation (10), the rate of consumption growth is negatively related to the

growth rate of prices (P, / P,_,) and positively related to the interest rate (r,) and to the

growth rate in the real wage. In the steady-state, P, = P and r, = F , and the consumption

growth equation becomes:

 

(20) C! .._. (1 + fii—M—‘j

1Tait-15:1

9
.3

where the steady-state reference growth rate of consumption (7)) is:

 

(21) fiJleJT—l.

Thus, lower values for time preference (p) or higher values for the intertemporal elasticity

of substitution (3), which is inversely related to 6, imply a steeper consumption profile in
the steady state. Although the growth rate of aggregate consumption is a constant in the
steady state, the growth rate of individual consumption is not. Individual consumption
growth will depend positively on the hourly wage, W,’ (or W,e,,), and this in turn will vary

over one’s lifetime according to changes in eh. These variations imply that the bracketed

23

component of equation (20) will not be constant over time. Thus the growth rate of

individual consumption changes over the lifetime.

From (8), leisure is related to discretionary consumption according to:

L
a -(C, 41%“) .

I I

Thus, with o<l, leisure in period t is positively related to P, and negatively related to

W,'. The optimal labor path (H1) is negatively related to P, and positively related to W,',

since H, = H. —l, .

2.1.2. The Production Sector

The structure of the production submodel is Similar to that of the GEMTAP model
of Fullerton, Shoven, and Whalley. (The reader may refer to Ballard et al. (1985) for
detail.) This model includes 19 profit-maximizing industries, which produce value added
with capital and labor. In addition, a portion of the output of each of the 19 industries is
used as intermediate input. Each industry uses labor and capital in a constant elasticity of
substitution (CES) value-added function. The industries also use the outputs of other

industries through a matrix of fixed input-output coefficients.

24

Since each industry purchases outputs from other industries, the output of a given
industry meets both final demand and the intermediate goods demands of industry. Each
of the 19 industries creates a producer good that can be used as an intermediate input, or
can be transformed into 17 consumer goods and one capital investment good that are
demanded directly by households. The goods classification of the consumer expenditure
data is different from the classification of the outputs of the production sectors. Thus, the
19 goods produced by industry do not correspond to the commodities purchased by
consumers. To accommodate these different classifications, we convert these 19
producer goods into 18 consumer goods by a fixed-coefficient “Z” matrix. The 18 goods
include 17 consumption categories, plus one “savings/investment good”, which is a
composite of the producer goods that are used in the investment process. The 19

producer goods and the 17 consumer goods other than saving are listed in Table 2.

2.1.3. The Foreign Sector
For each of the 19 producer goods, we specify foreign export demand and import

supply functions. These functions incorporate parameters that determine constant price

elasticities of import supply and export demand:

M.=M.° P". 6' O<0<oo, '=1,...., 19,
(22) [ l I( MI) I

E, = 15,9057)” -—00 < v < 0, i: 1,...., 19.
where M, and E, are import demand and export supply, M? and E? are constants, P,‘,', is

the world price of imports, PE? is the world price of US. exports, and I9 and v are the
price elasticities of import supply and export demand. These equations imply that the 1‘“

commodity can be both imported and exported.

25

Table 2. Classification of Industries and Consumer Expenditures

 

” ' " Proaaeei‘coaa; ‘ "

(Industries).

’ ConsumerGoods

(Expenditure Categories)

 

 

 

Agriculture, forestry, and fisheries
Mining

Crude petroleum and gas

Contract construction

Food and tobacco

Textile, apparel, and leather
Paper and printing

Petroleum

Chemicals, rubber, and plastics

Lumber, furniture, stone, clay, and glass

Metals, machinery, instruments, and

miscellaneous manufacturing

Transportation equipment and ordnance

Motor vehicles

Transportation, and

utilities

communications,

Trade

Finance and insurance

Real estate

Services

Government enterprises

 

 

Food

Alcohol

Tobacco

Household food and utilities
Shelter

Furnishing

Application

Apparel

Public transportation

New and used cars, fees and maintenance

Cash contributions and personal care

Financial services
Reading and entertainment

Household operations

Gasoline and motor oil
Health care

Education

 

 

 

26

The model allows for the phenomenon of crosshauling, which means that a given
commodity can be both exported and imported. There can be many reasons for this
phenomenon. Armington (1969) asserts that foreign commodities are qualitatively
different from domestic goods. This imperfect substitutability is often referred to as the
Armington assumption. In this model, however, we explain crosshauling by reference to

geography and transportation costs.10

In order to close the system and solve the general equilibrium model, we add the

trade balance constraint:
1‘) I9
(23) ZPAZM1=ZPETET °
i=1 i=1
If we substitute equation (22) into equation (23), we have
l9 0 l9 0 v
(24) 2PM (P3) = ZPE‘rE. (Pg) .
i=1 r'=l

We define the relationship between US. and world prices through an exchange
rate term, e, as

US _ 10
P151 _ 3P5:

US_ w
PMi _ePMr"

(25)

The model is, of course, a real model and has no financial exchange rate variable, but the

use of this construct enables us to write foreign import supply and export demand as

 

10 Ballard et al. (1985) give an example: “It may be perfectly sensible for the United States to
export Alaskan oil to Japan and at the same time import the identical product through ports on
the East Coast and the Gulf of Mexico, given the cost of delivering Alaskan oil to the eastern
United States.”

 

\l

27

functions of US. prices rather than of world prices. US. prices are determined

endogenously in the model. If we substitute these prices into (24) and rearrange terms,

we have:
_'_
v—6
(26) e = [141) ,
wl
F 9 US 9” 0
WI = 2(PM1' ) M
where '3'

19

W2 = zlPéiSYH Eio‘

L r'=l

 

Finally, substituting equations (25) and (26) into equation (22), gives

(27)

 

Note that w, and w2 are themselves fimctions of US. import and export prices.

Equations (27), thus, can be thought of as foreign import supply and export demand

functions, written as functions of US. prices, and incorporating zero trade balance.

I treat the foreign trade activity of the United States in a simple manner, so as to
close the model: We do not deal with capital flows (i. e. , while the economy in this model
is open to balanced international flows of goods and services, it is not open to
international capital flows). However, as foreign trade has increased rapidly as a fraction

of GNP and capital markets have become more international for the last few decades,

28

there has been growing interest in open-economy models for analyzing the effect of
changes in tax policies. Several studies have investigated the effects of international
capital flows in the context of general-equilibrium tax models.‘l Second, I do not
differentiate between commodities on the basis of origin (i.e., we do not employ the

assumption of Armington (1969)).

Despite these simplifying assumptions, foreign trade has an effect on the model.
Foreign trade introduces a difference between the aggregate demands of consuming
groups in the United States (broadly defined to include business investment and
government purchases) and the demands for products faced by US. domestic industries.
The demand for US. exports by foreigners has a negative price elasticity, while the
supply of imports to the United States has a positive price elasticity. The relative prices
of traded goods are determined endogenously in the model. Trade balance is assured,

since the export demand and import supply functions satisfy budget balance.

2.1.4. The Government Sector

General Features:
The model represents in detail the taxation, production, consumption, and transfer

roles of the government. In the base case, the model generates a steady-state growth path.

 

llGoulder, Shoven, and Whalley (1983) found that the allowance for international capital service
flows can either greatly increase the efficiency gain of a tax policy in the case of corporate tax
integration, or turn a significant gain to a large loss as we move to a consumption tax. Their
results indicate that the evaluation of domestic tax policy is very sensitive to the functioning of
international capital markets. Goulder (1989) pointed out that, for a small open economy,
subsidizing saving would not increase welfare as most of the increased saving will spill into
the foreign capital market. The nation thus will lose revenue without augmenting its own
capital. He found that the welfare effects of investment subsidies are muted, since some of the
returns from the additional capital will be paid to foreign investors. His results depend, in part,
upon his use of an infinite-horizon model, which tends to give large intertemporal welfare
effects.

29

Relative prices remain constant through time, and all outputs and aggregate incomes
grow at the growth rate of the overall economy. In addition, government spending, tax
revenue, government deficits, and government debt all remain in constant proportion to
GNP. In the revised case, we maintain the same growth of government debt as in the
base case, but examine the effects of changing the configuration of tax rates, while

holding the profiles of real government spending and bond issue fixed.l2

We divide government activities into three broad categories: general government

activities, government enterprises, and transfer payments.

1) General Government Activities: Government offers some goods and services
to the public, free of charge. These goods and services may be true public goods, or they
may be private in nature. Expenditures by government, other than those for public
enterprises, are an element of final demand. These expenditures include payments for
capital and labor services and purchases of industry outputs. We model the government
as if it were a single consumer, with a Cobb-Douglas utility function defined over all 19

producer goods, capital, and labor.‘3

These government expenditures do not enter the
utility functions of consumers as public goods. When tax rates are changed for a

simulation, an alternative source of tax revenue is changed, so that government

 

12The model of bonds and debt used in this study is essentially the same as that described in a
paper by Goulder (1985), which allows for alternative government financing and contains the
overlapping-generations features described in this paper. With the exception of the treatment
of bond issuance and debt, the modeling of government is similar to that in Ballard, Fullerton,
Shoven, and Whalley (1985), and in Ballard and Goulder (1987).

13We do not really claim that government is a Cobb-Douglas consumer. The main purpose of
this assumption is to allow for some responsiveness to output price changes. In any case, it
does not greatly affect the results of the model when we simulate the effects of the structural
tax reforms. We Simply use the government utility function, and the corresponding
expenditure function, to hold constant the govemment’s revenue jg gal terms. Thus, what is
important is the concept of equal-revenue-yield equilibrium.

30

expenditures are held constant in real terms, and the government budget remains in
balance. Consequently, we only need to be concerned with changes in consumer utility

when we want to calculate the total welfare change from some policy.

2) Government Enterprises: Government produces certain goods and services that
are sold in private markets. The government enterprises (e. g., postal services and some
utilities) provide the goods and services subject to user charges, even though the charges
may not cover costs. The model treats government enterprises as an industry (number
19); thus it operates like the other private industries. It uses primary factors and
intermediate inputs and earns zero economic profits. This industry receives a large
subsidy, such that its output is sold substantially below cost. This means that the

effective output tax rate for government enterprises in the model is negative.

3) Transfer Payments: The government makes redistributive transfer payments
directly to consumers in a lump-sum fashion in each period. We use data for Social
Security, Supplemental Security Income, Food Stamps, Aid to Families with Dependent
Children, and other welfare programs to determine the amount of transfers payments.
These transfers are held constant in real terms during simulations, using a Laspeyres price

index.

The government collects taxes on capital, labor, outputs, income, intermediate
goods purchases, and consumer purchases. The government uses its revenue to make
transfer payments to consumers, and to subsidize government enterprises. The

government uses the remaining revenues to buy producer goods at the prices of Pi

31

(i=1,...,19), to buy labor at the gross-of-tax price, P,,(1+tf) , and to buy capital at the

gross-of-tax price, PK(1 + I?) .

Since the gross-of-tax capital price in the private sector equals the marginal
product of capital, a capital flow from the public to the private sector would imply
(possibly large) welfare gains, which would lead to the miscalculation of the welfare
effects of distorting taxes. Therefore, we assume that the entire government sector faces
a price for capital that is equal to PK(1+ (D) , where (I) is the weighted-average tax rate on
capital used in industry. Then, if the industry tax rates were to change, the govemment’s
price would change accordingly. The new price of capital faced by the government
would be PK (1 + the new weighted average industry tax rate). Thus, capital would not

flow from the government to the private sector.

The model is calibrated to generate a steady-state growth path in the base (or
status uo case. Relative prices remain constant through time, and all outputs and
aggregate incomes grow at the rate of growth of the overall economy. In addition, base-
case government spending, tax revenues, government deficits, and government debt all
remain in constant proportion to GNP. In revised-case (or policy change) simulations, we
maintain the same growth of government debt as in the base case, but alter the

configuration of taxes.

Model Treatment of Taxes:
The model incorporates each of the major taxes in the United States. In Table 3, I

outline the ways in which these are modeled. My goal is to assess the entire system of

32

distortionary taxes. Therefore, the disaggregated treatment of production is important,

since it allows us to consider intersectoral as well as intertemporal distortions.

Table 3 US. Taxes and Their Treatment in the Model

 

Tax Treatment

 

1 Corporate taxes (including state and Ad valorem tax on use of capital
local) and corporate franchise taxes services by industry

 

2 Property taxes Ad valorem tax on use of capital
services by industry

 

3 Social Security taxes, unemployment Ad valorem tax on use of labor services
insurance taxes, and workmen’s by industry
compensation taxes

 

4 Motor vehicles taxes Ad valorem tax on use of motor
vehicles by producers

 

5 Retail sales taxes Ad valorem tax on purchases of
producer goods

 

6 Excise taxes Ad valorem tax on output of producer
goods

 

7 Other indirect business taxes and non- Ad valorem tax on output of producer
tax payments to government goods

 

 

8 Personal income taxes (including state Linear function for each consumer;
and local) 30% of saving currently tax sheltered

 

 

 

The treatment of each tax in the model reflects certain assumptions about the tax
system. We combine the corporate and property taxes to produce an overall tax rate on
capital income originating in each industry. One important feature of this model is the
personal factor tax, which is designed to capture the different proportion of each sector’s
capital income subjected to full personal income taxation. This proportion will differ

across industries, depending on variations in dividend/retention policies and differences

 

33

in the amount of unincorporated capital which qualifies for the investment tax credit. At

the industry level, capital income is taxed at rate T, the overall capital-weighted average
marginal income tax rate." In order to derive the amount of “personal factor tax” in each
industry, we calculate the parameter f, (the fraction of the ith industry’s payment for
capital). When all capital taxes are subtracted from capital income, we have net income
to capital." The effective tax rates that we use in this model are the ratios of all capital
taxes to net capital income in each industry. Since the effective tax rate is defined as
taxes relative to _r_1_et capital income, rather than to the more common use of gm income,
the rates can exceed unity. The average tax rate on capital income at the industry level is

.97, which corresponds to a tax rate on gross capital income of just under 50%.

1) The Corporate Tax: We follow the tradition of Harberger (1962, 1966), who
treated the corporate tax as a partial factor tax, even though this has been the subject of
active debate.'6 We follow Harberger’s procedure of treating the corporate tax as an ad
valorem tax on capital, with average and marginal tax rates the same. As a result,

differences in capital income tax rates cause capital to be misallocated across industries.

 

14This feature captures the favorable treatment of industries with a high proportion of retained
earnings, industries that receive large amounts of noncorporate investment tax credits, and the
housing industry. However, it leads to distortion of the interindustry capital allocation.

15Net income to capital is equal to the gross income to capital, minus corporate and property
taxes, minus the personal factor tax, where the personal factor tax is CAPirf,‘ (gross income to
capital minus corporate and property tax). ‘I' is capital-weighted average of the consumers’
marginal tax rates. CAP,- is the Capital payments from the ith industry, net of corporate and
property taxes. f,’ is the proportion of the ith sector’s CAP) that is subject to the personal
income tax.

16For instance, Stiglitz (1973) points out that, if all marginal investments by firms are debt-
financed, the corporate tax operates as a lump—sum tax. Gravelle and Kotlikoff (1989) explore
the misallocation of capital between corporate and noncorporate firms within the same sector.
Their results show that the coexistence of corporate and noncorporate capital in the same
sector makes the distortion larger. They find a high elasticity of incorporation with respect to
tax parameter changes in their model. However, Gordon and MacKie-Mason (1990) find that

34

In addition, the corporate tax affects savings decisions, since savers who acquire
corporate equity pay these taxes indirectly on the rettun to their savings. Through the tax
treatment of depreciation and the investment tax credit, we have a pattern of tax rates by

industry which is highly discriminatory.

The advantage of this approach is that it replicates the tax revenue that is actually
observed in the economy. The weakness, however, is that it abstracts from the details of

the tax system such as the investment tax credit, depreciation, differences in tax rates, and

property tax.

While our model bases incentives to invest on average tax rates, the cost-of-
capital approach bases incentives to invest on marginal tax rates, and it indicates that
marginal tax rates may not be the same as average tax rates. In other words, while the
Harberger model uses average tax rates measured for existing assets, the cost-of—capital
approach uses marginal tax rates for the incremental uses of capital, Since the concept of

the tax on a new investment is preferred as a measure of the incentive to invest.

Fullerton and Henderson (1989) use a cost-of-capital approach to measure the
incentives to invest in each combination of asset, sector, and industry. Their model
encompasses inter-asset, inter-sectoral, and inter-industry distortions into a single general
equilibrium model of the US. tax system. They find that intersectoral distortions are

much smaller than those in Harberger-type models, such as the model of Fullerton,

 

this elasticity of incorporation is small, which casts doubt upon the validity of the Gravelle-
Kotlikoff model.

35

Shoven, and Whalley. In contrast, interasset distortions dominate the two other

misallocations.

Fullerton and Gordon (1983) take account of uncertainty, the flexibility of
corporate financial policy, and inflation in the cost-of-capital framework. They argue that
recipients of capital income receive benefits which largely compensate them for the taxes
they pay, and often more than compensate them. These recipients are able to reduce
some of the risk in the return on their investments by transferring it to the government
through risky tax revenue. They find that corporate tax integration actually reduces
welfare, because the welfare gains of lessening tax distortions through integration are
more than offset by the welfare losses resulting from raising tax rates on labor income to

replace the lost revenue, and because the government no longer provides this insurance.

However, Bulow and Summers (1984) challenge this, by dividing the riskiness of
an investment into “income risk” (i. e., variation in the return from capital goods) and
“capital risk” (i. e., variation in the price of capital assets). They argue that most of the
risk borne by owners of corporate capital pertains not to income risk (which is hedged by
the corporate income tax), but to capital risk (which is not hedged by the corporate

income tax). Therefore, the Fullerton-Gordon story does not work well.‘7

Ballentine (1987) points out that all of the studies with cost-of-capital calculations
are incomplete in modeling the tax system. Those studies usually take account of the
investment tax credit, depreciation schedule, indexing, dividend deduction, corporate and

personal marginal tax rates, and property taxes. However, they omit multiperiod

36

accounting rules, industry-specific incentives, international tax charges, and many other

aspects that are difficult to model.

The advantage of the cost-of—capital approach is that it is more consistent with
microeconometric theory, and it captures some important details of the tax system. The
disadvantage is that it neither gets the revenue correct nor captures the extreme

complexity of the tax system, as mentioned above by Ballentine (1987).18

2) The Property Tax: We treat this as a differential tax on capital by sector
(similarly to the corporate tax). This falls most heavily on residential housing, but
structures in other capital-using industries in the economy are also liable for the tax. As

with the corporate income tax, both static and dynamic distortions occur.

3) The Income Tax: We specify income taxes as linear functions of income with
a negative intercept and a single positive marginal tax rate. Although each consumer
faces a constant marginal tax rate, the average tax rate increases with income due to the
negative intercepts. Thus, this model captures the fact that US. tax system is
progressive, although it does not capture the details of the graduated tax rate structure.
We do not model many of the deductions and exemptions that exist in the US. tax
system. The key distortions caused by the income tax have to do with factor supply
decisions. It is widely recognized that the income tax distorts labor supply. In addition,
the supply of new capital through saving is affected by the double taxation of saving,

although these effects are partially offset by the tax treatment of pensions and housing.

 

l7See Slemrod (1982, 1983) for further details.

37

We assume that 30% of saving is sheltered in this way.I9 In addition to distorting factor-
supply decisions, the income tax also has important features which distort choices among
industries and commodities. The most prominent of these is the preferential treatment of
housing that results from the absence of tax on the imputed income of owner-occupied

housing. This is compounded by the preferential treatment for capital gains on houses.

4) Sales and Excise Taxes: We model sales and excise taxes as consumer
purchase taxes on the 17 consumer goods. The average tax rates are about 5.2% in this
model, and rates for most goods are reasonably low. Consumer sales taxes have a variety
of effects. Even if the sales tax system covers all commodities evenly, it still distorts
labor supply decisions. Additional distortions come from the nontaxation of food and
services in most States. Also, the specific excises on alcohol, tobacco, and gasoline are
discriminatory in our model, since we treat them (along with sales taxes) as ad valorem

taxes.

5) The Social Security Payroll Tax: We model Social Security payroll taxes as ad
valorem taxes on the use of labor services by industry, and we treat Social Security

benefits as lump-sum transfers.

The tax rate on labor for each industry is derived by taking payroll taxes and other
contributions as a proportion of labor income. The tax rate on capital for each industry is
obtained by taking three components - the corporate income tax levied by the federal

government, corporate franchise taxes levied by the state governments, and property taxes

 

13As an example of how the cost-of-capital approach can give unusual results, see Fullerton and
Rogers (1993).

38

levied at the state and local levels. We use capital income as the tax base for all three
taxes, even though the legal tax bases for the latter two are capital stock and capital

assets, respectively.20

The labor tax rate used by government (If) is based on Social Security and

railroad retirement taxes paid by the government and its employees. When the
government pays these taxes on its use of labor, it pays the taxes to itself. Consequently,
the income effects cancel out. However, the price effects measure correctly the

opportunity cost to government of hiring additional labor.

The capital tax rate used by government (1,?) is more disputable. Governments in

the US. pay neither corporate income taxes nor property taxes. If we were to model t: as
only the personal tax on that capital income, the government’s tax rate on K would be
substantially less than the private sector’s tax rate. The benchmark equilibrium would
imply a misallocation of capital in favor of government use. Any reduction in the capital
taxes faced by the private sector would imply reallocation flows from the government

sector to the private sector.

 

19This assumption is based on calculations using the 1976 Flow of Funds Accounts.

20Even though we use capital income net of all taxes to reflect the use of capital in each industry,
we should note that measuring the industrial use of capital services by capital income is not the
only method available. See Kendrick (1976) and Jorgenson and Sullivan (1981).

Chapter 3

DATA AND PARAMETERS

Several important aspects of our model are shared by the GEMTAP model
described in Ballard et al. (1985). The data set used in that model contains valuable
information on industry interactions and taxes. However, the original GEMTAP model
(which was based on 1973 data) consisted of 12 infinitely-lived consumers, and thus
could not address the intergenerational issues that concern us here. A fundamental
challenge in the development of the model used here was to link consistently an
overlapping-generations treatment of households with the detailed and disaggregated data

from the GEMTAP model.

3.1. New Data
The basic source of the data is Karl Scholz (1987). Scholz’s original data set

provides information for 14 consumer groups, which are distinguished on the basis of
their incomes in 1983. I begin by aggregating them into a single consumer group. Then,

I re-divide them into 11 groups, which are distinguished by age.

It is necessary to make some adjustments to create a data set for inheritances and
government transfers. The bequest left by one cohort is assumed to be divided among the
11 cohorts that are alive during the next period. Therefore, we need to calculate the
proportions of total bequests that are received by the next 11 cohorts. We derive these

proportions based on Consumer Expenditure Survey data showing the value of bequests
,/

39

40

received per year. The aggregated version of the 1972-1973 data was issued by the
Bureau of Labor Statistics. These values are reported in per-household terms in Table 4.
We also need the proportions of government transfers that are received by the different
cohorts at a given time. These proportions are derived from Michigan Panel Studies of
Income Dynamics Survey data (PSID, 1973). These data were collated by Charles
Becker, and reported in Fullerton, Shoven, and Whalley (1980). These values are

reported in per household terms in Table 5.

However, the problem is that the data are from the real world, which does not
conform neatly to the structure of my steady-state model. So, I need to adjust the data so

that I can use them in my model. Here are two ways to approach this problem.

Table 4. Inheritances Per Household, 1973 (in dollars)

 

 

 

 

, , Age ofHead

Income Class 18-24 25-34 35-44 45-54 55-54 - 65+_ SUM

$0 - 84,000 151 49 0 18 4 30 '252
84,000 - 87,000 60 21 7 27 193 74 , 382
137,000-310,000 99 204 15 14 133 132 l ”597?.“
810,000-815,000 87 62 38 25 117 124 453' ' .
815,000-825,000 0 98 186 165 123 606 -, 11,178.
825,000+ . 0 191 456 272 418 364 1,701

SUM _ 397 625 , 702 _ 521 988 p 1330 _ 4,563

 

 

 

 

 

 

 

 

 

 

41

Table 5. Public Transfers Per Household, 1973 (in dollars)

 

 

 

 

 

 

 

 

 

 

 

 

Ageof Head . ‘ .
. Income-Class 18-24 25-34 :35-44. 45-54 -1 55-64 . 1165+ SUM
Ail-"ii155180-841000 462 1,124 1,530". 1,152 1,0041 1683 6955
$4,000 - $7,000 178 875 1,444 980 1,114 2,476 . 7,067..
$7,000-$10,000 157 210 917 906 876 2,487 5,553
$10,000-$l$,000 54 101 397 462 501 2,627 4,142
I $15,000-$25,000 5 7 87 178 238 2,320 2,835
825,000+ 1 l 145 49 99 46 1.077 1,427
A SUM 867 2,462 4,424 3,777 3,779 12,670 27,979

 

3.1.1. Bequest and Transfer Proportions Without Demographic Adjustment

While the age of the youngest group in Table 4 and Table 5 is between 18 and 24,

the youngest cohort in my model is between 20 and 24. Thus I multiply the first column

of Table 4 and Table 5 by 5/7 to get the data that conform to the data set of my model.

Since the model’s cohorts are 5 years apart rather than 10 years apart, I average the above

data for every group except the youngest one to get the inheritance and transfer amounts

for my model. Table 6 and Table 7 show the adjusted inheritances and transfers per

household.

Except for the youngest age group in Table 6 and Table 7, I divide the total of

inheritances and transfers for each of the ten-year cohorts into two equal pieces, so that

they conform to the five-year cohorts of my model. Table 8 shows the results of these

manipulations.

 

42

Table 6. Adjusted Inheritances Per Household, 1973 (in dollars)

 

 

 

 

 

 

Age of Head ‘ ,. .

Income Class 20-24 25-34 35-44 45-54 55-64 65+ ' SUM
$0 - $4,000 108 49 0 18 4 30 252
$4,000 - $7,000 43 21 7 27 193 74 382
$7,000-$10,000 71 204 15 14 133 132 597
$10,000-$15,000 62 62 38 25 117 124 453

$15,000-$25,000 0 98 186 165 123 606 1,178
$25,000+ 0 191 456 272 418 364 1,701

- :1 SUM I 284 625 702 521' "‘ 988 - .7 _ , 173-30 ,4 jf’Efl-4g'536'3-I '

 

 

 

 

 

 

 

 

Table 7. Adjusted Public Transfers Per Household, 1973 (in dollars)

 

 

 

 

 

 

 

 

 

 

 

 

Age of Head

1 Income Class 2024 25-34 35-44 45-54 55-64 165+ SUM
80 - $4,000 330 1,124 1,530 1,152 1,004 1,683 6,955
84,000 - $7,000 127 875 1,444 980 1,114 2,476 7,067
$7,000-$10,000 112 210 917 906 876 2,487 5,553
810,000-815,000 39 101 397 462 501 2,627 4,142
815,000-825,000 . 4 7 87 178 238 2,320 2,835
825,000+ ‘ 8 145 49 99 46 1.077 1,427
SUM ‘ ' 620 52,462 ' .-4,424 3,777 3,779 I 12,670 L 27,979

 

 

 

43

Table 8. Adjusted Inheritances and Transfers Per Each Age Group

 

 

 

 

AGE Inheritances Transfers
20-24 284 620
25-29 3 12 1,23 1
30-34 3 1 3 1,23 1
35-39 351 2,212
40-44 351 2,212
45-49 260 1 ,889
50-54 261 1,888
55-59 494 1,889
60-64 494 1 ,890
65-69 665 6,335
70-74 665 6,335
TOTAL 4,450 27,732

 

 

 

Table 9 shows the actual bequest and transfer proportions I use in my model.

This table shows that most inheritances and government transfers are received later in

 

 

 

 

 

life.
Table 9. Pronortions of Inheritances and Transfers
AGE“ INPROP" TRPROP°
1 0.064 0.022
2 0.070 0.044
3 0.070 0.044
4 0.080 0.080
5 0,080 0.080
6 0.058 0.068
7 0.058 0.068
8 0.111 0.069
9 0.111 0.069
10 0.149 0.228
11 0.149 0.228
TOTAL 1 .000 1 .000

 

 

 

 

 

'AGE = Period of life. Each period is five years in length, so that the 11 periods of life cover a total of 55
years. When AGE=1, the cohort has just entered the model, and the cohort’s last period of life
occurs when AGE=1 l.
bINPROP = the proportion of the total bequest that is received by each of the 11 living cohorts in the
benchmark.
cTRPROP = the proportion of total government transfers that is received by each of the 1 1 living cohorts
in the benchmark.

44

3.1.2. Bequest and Transfer Proportions With Demographic Adjustment"
First, Table 10 shows that the number of households (NH) of each age group is

irregular, while I assume that the population grows steadily at the rate of (1+G), where G
= 0.267562984.22 If we use NH of the oldest age group as the base, NH of the other
groups should grow by (HG), starting at 13881 (which is NH of the oldest age group)

keeping the proportion of NH within each age group constant.23

Table 10. Number of Households (in thousands)

 

fl Age ofHead _

 

“Income Class 18-24 25-34 35-44 45-54 55-64 65+ I SUM

 

80 - 84,000 1,239 1,202 810 1,153 1,815 6,059 12,278
84,000 - 87,000 1,451 1,676 1,096 1,290 1,644 3,589 10,746
,....37'2900'319-000 1,354 2,505 1,497 1,568 1,629 1,629 10,182
. 810,000-815,000 1,266 4,619 3,101 2,990 2,484 1,345 1 15,805
. 815,000-825,000 494 3,640 3,886 4,025 2,483 879 15,407
$25,091“, A I , 54 683 1,318 1,904 1,079 380 5,418

 

 

 

 

 

 

 

 

 

SUM ~ 5,858“ "14,325?'11,708’=*~12,9301=“11,1314 -1~3;881- 69,836

 

l multiply 13881 by (1+6), raised to various powers to calculate the total number

of households in each age group which I have to use in my model:

 

21Note that, even in this case, the population growth rate is constant over time. We just apply
this fixed population growth rate to derive bequests and transfers proportions across cohorts in
each period.

22The economy is on a balanced growth path if the capital endowment grows at the same rate as
the effective labor force. G is a steady-state growth rate and the endowment of labor must
grow at this rate to be on a balanced grth path. G=0.022284497 for one year,
G=0.121064355 for five years, and G=0.267562984 for ten years. See Ballard, Fullerton,
Shoven, and Whalley (1985) for further information.

 

Generation 2:
Generation 3:
Generation 4:
Generation 5:
Generation 6:

45

13881(1+G)l = 17595
13881(1+G)2 = 22303
13881(1+G)3 = 28270
13881(1+G)‘ = 35834
35824(1+G)‘ = 40172

where G = 0.267562984
where G = 0.267562984
where G = 0.267562984
where G = 0.267562984
where G = 0.121064355

For generation 6, G is 0.121064355 rather than 0.267562984 because we need to

calculate the number of households whose age is between 20 and 24. We multiply the

first column of Table 10 by 40172/5858, the second column by 35834/14325, etc, in

order to calculate NH which I can actually use in my steady-state model. Table 11 shows

this adjusted NH within each age group, when we take into account the demographic

change.

 

 

 

 

 

 

 

Ipble ll. Adiu_sted NH Within Each Age Group (in thousands)
Age Group

Income Class 2024 25-34 35-44 45-54 55-64 65+
80 - $4,000 1..;8.497;7f 3,007 1,956 1,989 2,868 6,059
$4,000-$7,000 9,950 4,193 2,646 2,225 2,598 3,589
$7,000-$10,000 1+: 9,28541-122‘: 6,266 3,615 2,705 2,574 1,629
810,000-815,000 : 8,682 11,554 7,488 5,157 3,926 1,345
815,000-825,000 0 3,388 9,105 9,383 6,943 3,924 879
825,000+ , 370 1,709 3,182 3,284 1,705 380
SUM 40,172? 35,834 28,270 22,303 17,595 13,881

 

 

 

 

 

 

 

We multiply both the adjusted inheritances per household (Table 6) and public

transfers per household (Table 7) by these adjusted numbers of households (Table 11), to

get the total inheritances and transfers for each income and age group (Table 12 and

Table 13). If we add up the last row of the Tables 12 and 13, we can get the total

 

23Allowing irregular demographics would be an interesting and important extension of this
model. See chapter 3 of Ballard (1983) and chapter 11 of Auerbach and Kotlikoff (1987) for

 

46

inheritances and transfers which are $15,856,868 and $80,369,858 each. We divide each
figure for inheritances and transfers by these total inheritances and transfers, to get the
proportion of inheritances and transfers that is received by each income class/age group
cell. Table 14 and Table 15 show the inheritance and transfer proportions for each

income and age group.

Table 12. Total Inheritances for Each Income and A e Grou in thousands

 

 

 

 

 

 

. Age Group '

flin'comc Class 20-24 25-34 354114 45-54 55:64 ’ 625-rs
$0 . $4,000 917,676 147,343 0 35,802 1 1,472 181,770
' $4,000-37,000 427,850 88,053 18,522 60,075 501,414 265,586
$7,ooo-$1o,ooo 659,235 1,278,264 54,225 37,870 342,342 215,028
. 310000415300 538,284 716,348 284,544 128,925 459,342 166,780
815,000-325,000 0 892,290 1,745,238 1,145,595 482,652 532,674
825,000+ 0 326,419 1,450,992 893,248 712,690 138,320
SUM 2.543.045 32448717 5:.3‘.553-,s»_2=1=¥221.2-2,301,515,; 2,569,912, 11,500,158?

 

 

 

 

 

 

Table 13. Total Transfers for Each Income and A e Grou in thousands

 

Age Group

 

Income Class 20-24 25-34 35-44 45-54 55-64 65+

 

$0 - $4,000 2,804,010 3,379,868 2,992,680 2,291,328 2,879,472 10,197,297
$4,000 - $7,000 1,263,650 3,668,875 3,820,824 2,180,500 2,894,172 8,886,364
$7,ooo-$1o,ooo 1,039,920 1,315,860 3,314,955 2,450,730 2,254,824 4,051,323
$10,000-$15,000 338,598 1,166,954 2,972,736 2,382,534 1,966,926 3,533,315

 

 

$15,000-$25,000 13,552 63,735 816,321 1,235,854 933,912 2,039,280
$25,000+ 2,960 247,805 155,918 325,1 16 78,430 409,260
SUM 5,462,690 9,843,097 14,073,434 10,866,062 1 1,007,736 29,1 16,839

 

 

 

 

 

 

 

 

further discussion.

 

 

47

Table 14. Proportion of Inheritances for Each Income and Age Group

 

Age Group

 

Income Class 20-24 25-34 35-44 . 45-54 ' 55-64. 65+

 

’ . .80 -._$4,000 0.057 0.009 0 0.002 f i H 0.001 0.011
" $4,000 - $7,000 0.026 0.006 0.001 0.004 0.032 0.017
$7,000-$10,000 0.042 0.081 0.003 0.002 0.022 0.014
$10,000-$15,000 0.034 0.045 0.018 0.008 0.029 0.011

$15,000-$25,000 0 0.056 0.1 10 0.072 0.030 0.034
825,000+ 0 0.021 0.092 0.056 0.045 0.009

 

 

 

 

 

 

 

 

SUM 0159 0.218 0.224 0.144 0.1259 . 0.096

 

Table 15. Proportion of Transfers for Each Income and Age Group

 

Agevaroup

 

IncomeClass 20-24 "25-34 235.44 ‘ . '45-54- _ 55-64 65+

 

$0 - $4,000 0.035 0.042 70.037 0.029 0.036 0.127
$4,0002-: $7,000 0.016 0.046 0.048 0.027 0.036 0.11 1

. $7,000-$10,000, 0.013 0.016 0.041 0.030 0.028 0.050
-§194999’$.15'49°9 0.004 0.015 0.037 0.030 0.024 0.044

 

 

 

 

 

 

 

 

 

 

815,000-825,000 0 0.001 0.010 0.015 0.012 0.025
8225,0003; . i 0 0.003 0.002 0.004 0.001 0.005

 

Since the age groups are 5 years apart in my model, rather than 10 years, I average

the above data for every age group except the youngest, to get the inheritance and transfer

 

48

proportions for my model. Table 16 presents the proportions I use for inheritances and

transfers when we take into account the demographic change.

Table 16. Proportions of Inheritances and Transfers

 

 

 

 

AGE” INPROPb TRPROPc

1 0.159 0.068

2 0.108 0.062

3 0.1 10 0.061

4 0.1 12 0.088

5 0.1 12 0.087

6 0.072 0.068

7 0.072 0.067

8 0.080 0.068

9 0.079 0.069
10 0.049 0.182

1 1 0.047 0.180
TOTAL 1 .000 1 .000

 

 

 

 

'AGE = Period of life. Each period is five years in length, so that the 11 periods of life cover a total of 55
years. When AGE=1, the cohort has just entered the model, and the cohort’s last period of life
occurs when AGE=1L

bINPROP = the proportion of the total bequest that is received by each of the 11 living cohorts in the

benchmark.

°TRPROP = the proportion of total government transfers that is received by each of the 11 living cohorts

in the benchmark.

We put Table 9 and Table 16 together so that we can easily compare the
difference in inheritances and transfers proportions between the two cases. Table 17
shows these results. Figure 1 tells us that inheritances are heavily concentrated later in
life in case 1, while they are heavily concentrated early in life in case 2, since we assume
that the population grows steadily across cohorts. However, we do not observe such a big

difference in proportions of transfers in general. Figure 2 shows these differences.

9

4

wa<0
wmw<o

III
I61

ou<

 

moons-tog... u.o 6:03.395 ._. 952“.

N90

8
c

a
Q
o

".
O

soon-mow] to womodoid

Figure 2. Proportions of Transfers

CASE 1
CASE 2

 

uqsuu; p IllOflJOdOJd

51

Table 17. Proportions of Inheritances and Transfers in Both Cases

 

 

 

 

Inheritances Transfers

AGE CASE 1 CA§E 2 (35813 1 CKS—E 2
1 0.064 0.159 0.022 0.068
2 0.070 0.108 0.044 0.062
3 0.070 0.110 0.044 0.061
4 0.080 0.112 0.080 0.088
5 0.080 0.112 0.080 0.087
6 0.058 0.072 0.068 0.068
7 0.058 0.072 0.068 0.067
8 0.111 0.080 0.069 0.068
9 0.111 0.079 0.069 0.069
10 0.149 0.049 0.228 0.182
11 0.149 0.047 0.228

 

 

 

 

   

 

 

 

 

 

3.2. Parameter Selection

We have chosen 3=0.4, 6'=0.8, and p=0.01 (for one year) for the central case.

Since the bequest weighting parameter, b, has no intrinsic meaning itself, I will focus on

BK, which represents the percentage of current total capital that can be explained by

bequests.

In order to perform simulations, we need parameter values that would describe the

behavior of consumers, producers, and the government. We determine parameter values

for the equations in the model, using a non-stochastic calibration method.24

 

24An alternative procedure would be to estimate the parameters of the model econometrically.
Unfortunately, our model is much too large to be estimated as an econometric system of

52

The assumptions that producers minimize cost and receive zero economic profits
allow us to choose the values of the production function parameters. Similarly, the
assumption that households maximize their utility subject to a budget constraint has
implications that allow us to choose the parameters of the inner nest of the utility
function, which govern the allocation of aggregate consumption in each period among the
17 consumer goods. Similar logic applies to the choice of parameters in the

government’s utility functions.

Even afier the above procedures, we still have free parameters to determine. To

deal with this problem, we specify the consumer’s elasticity of substitution parameters
(3, 3) on the basis of estimates from the econometric literature. Thus, the

parameterization procedures involve, first, selecting certain parameters from outside
econometric estimates, and, second, identifying the remaining parameters for the
overlapping generations of life-cycle households, on the basis of the restrictions implied
by the two requirements discussed in the paragraphs that follow. (A detailed description

of this procedure is explained in part 1 of the appendix: we offer only a sketch here.)

 

simultaneous equations. On the other hand, if we were to use single-equation methods to
estimate the parameters, and then calculate an equilibrium solution for the economy, the
solution would not match the adjusted benchmark data. Mansur and Whalley (1984) say that
the deterministic calibration method that we use for large-scale general equilibrium models has
weaknesses, since it requires preselection of elasticities, and it does not provide any basis for a
test of the specification, because it fits perfectly the single data point used. They consider
whether stochastic estimation procedures can be used for small-scale general equilibrium
models. They find that, even though stochastic estimation of complete models may be
infeasible for large-scale models, time-series econometric estimation appears feasible for
smaller-scale variants. Jorgenson (1984) estimates the parameters of nonlinear general
Equilibrium models using econometric methods. Thus he makes some progress in this
irection.

53

l. Replication Reguirement:

In the first period of the base case, the integrated model must generate an equilibrium
solution that matches the Scholz data (1987). In particular, the aggregate labor supply,
wage income, capital income, consumption, and saving that emerge from the
overlapping-generations model must be identical to the aggregate labor demand, wage
payments, capital income payments, consumption, and saving contained in the GEMTAP

data set.

2. Balanced-Growth Requirement:

In the base case, the model must generate a steady-state growth path.

3.2.1. Parameterization of the Elasticities of Substitution

The parameters of 3' and 3 are set exogenously. Friend and Blume (1975),
examining portfolio decisions, suggest that :5 is less than or equal to 0.5. Summers
(1982) favored a value for 3 of around 0.33, and Ghez and Becker (1975) estimate that 3'

should be at most 0.28. Hall (1988) finds that 3‘ is indistinguishable fiom 0. Hansen and

Singleton (1983) and Weber (1970, 1975), however, call for values equal to or greater

than 0.5 for 3.

It is important to recognize, however, that the choice of :5 (the intertemporal
elasticity of substitution between consumption and leisure) cannot be made independently
of the choices of other parameters, especially 3 (the elasticity of substitution of

substitution between consumption and leisure in any period) and b (the bequest

parameter). Moreover, even for seemingly reasonable values for :3, models of this type

54

5 This is because of the “human

can generate unrealistically large saving elasticities.2
wealth effect”. From equation (8), we know that leisure decreases as well when

consumption decreases. Thus, not only does the consumer buy fewer goods, but he also

works more and earns more labor income. These two effects can generate very large

saving elasticities. In our simulation model, we want to use values for 5' and 3 that are
reasonably in line with those from the econometric literature. However, we are also

mindful of the need for implied elasticities of behavioral response to be reasonable.
Equation (21) indicates that the steady-state reference growth rate of consumption (if) is

determined by 5, p, and F . We have chosen 3:04, 3:08, and p=0.01 (for one year) for
the central case. These exogenous parameters imply a value of approximately 0.0129 for

77 for one year, and 0.0664 for five years.

3.2.2. Parameterization of the Leisure Intensity

Given these parameter values taken exogenously from outside econometric

estimates, it is necessary to define the leisure intensity parameter (01,) and benchmark

endowment of labor time and capital for each of the 11 cohorts alive in the benchmark
year (first equilibrium period). This must be done in a way that assures that both the
replication and balanced-growth requirements are satisfied. The problem is tractable by
the assumption of balanced growth and the fact that the utility-function parameters of all
cohorts are specified to be the same. Under these circumstances, in the steady state, the

pattern across time of a given cohort’s consumption (or leisure) will be closely linked to

 

25Auerbach and Kotlikoff (1983) produced the bizarre results that the immediate effect of an
unanticipated switch to a consumption tax is an increase in the saving rate from 10% to about
42%.

55

the pattern across cohorts of consumption (or leisure) at a given point in time. In other
words, in a steady state, we can infer information about individual profiles on the basis of
cross-section information. In the case of consumption, the following relationship must

hold in the steady state:

C

nJ+1

(:28) (:h-Il :: l'
' (1+8)

 

Thus, the total consumption of cohort n-t (born t years before cohort n) in period 1

(Cu—1,1) must be the same as the total consumption of cohort n in period t+1 (Cum),
adjusted for the growth rate of population (g). Thus, for purposes of calibration, equation
(28) allows the expression of the behavior of all cohorts in terms of the behavior of a
single representative cohort. Once the paths of consumption and leisure for the
representative cohort are identified, one can determine fairly directly the benchmark
endowments of labor time and capital for all cohorts alive in that period, because these

endowments are translations of the representative cohort’s endowments at different points

in time.

3.2.3. Parameterization of the Labor Efficiency Ratio (e,)

The “human capital earnings function” of Mincer (1970, 1974), in which earnings
are expressed as a quadratic in potential experience, has been one of the most widely-
accepted empirical specifications in economics. Mincer expresses the natural logarithm
of earnings per hour, week, or year as a linear function of the number of years of school

completed and as a quadratic function of years since leaving school (or potential work

56

experience). The quadratic in experience has been adopted very widely, since most
researchers believed that it provides a reasonable approximation to the actual earnings
profile. Since the pioneering work by Mincer, several studies have been done on this

subj ect.26

Murphy and Welch (1990) found that, in spite of its widespread acceptance, the
quadratic human capital earnings function provides a poor approximation of the true
empirical relationship between earnings and experience. They noted that the standard
quadratic function in experience understates early career earnings growth by about 30% -
50%, and overstates midcareer growth by 20% - 50%. They suggest that a quartic
specification provides a reasonably good approximation to the “true” earnings function.
The model used here incorporates exogenous values for eh based on a quartic function

estimated by Murphy and Welch:

(29) eh = e’ ,

 

26Oaxaca (1973) included a quadratic experience variable in the wage equation, in accordance
with the post schooling investment model of human capital formation as developed by Johnson
(1970) and Mincer (1970). His study indicates that 8 follows a hump-shaped pattern over the
life-cycle, rising over most of economic life but falling in the last portion. Welch (1979)
added an early career spline to experience and experience squared, to explain the evidence that
early career wage growth is more rapid for those with more schooling. This splined
experience coefficient generally implies more rapid growth in earnings during the early years
of the career than can be captured in the experience quadratic alone.

57

where x = b, +b2h+ b,h" +b4h3 +b,h‘ .

I use bl = -0.465218, b2 = 0.584478, b3 = -0.1319, b4 = 0.014343, and b5 = -0.000624.

Chapter 4

SIMULATION RESULTS

4.1. Solution Process

Since the original raw data are taken from many different sources, they are not
mutually consistent, so that quantities supplied are not equal to quantities demanded.
However, to generate counterfactual simulations, we must begin with a consistent
benchmark equilibrium data set, where quantities demanded equal quantities supplied for
every good and factor. Thus, we first make a series of consistency adjustments for the
1983 data set. Given this equilibrium data set and any exogenously specified parameters,
we use the nonstochastic calibration techniques to determine the remaining parameters.
This calibration process ensures that the model replicates the 1983 data set in the absence
of any policy change. Dynamic calibration procedures further ensure that, in a base-case

sequence, the economy is on a steady-state, balanced growth path.

In the solution process, several equilibrium conditions must be met. In each
period, demand must equal supply for every good and factor, and tax revenues plus net
revenue from bond sales must equal government expenditures. The model is solved in
each period, using the téi tonnement algorithm developed by Kimbell and Harrison
(1986). An initial guess is made regarding the current price of labor services, the price of

capital services, and tax rates. Based on these values and expectations of future prices,

58

59

each cohort determines lifetime wealth and the optimal path of consumption, leisure, and
saving. If excess demand is found in any factor market, prices are adjusted, and iterations
are continued until no excess demand is found. Thus, equilibrium is achieved when total
factor demands equal total factor supplies, and the government budget is balanced. I
calculate equilibria over 31 successive periods, spaced five years apart. I employ the

assumption of myopic expectations regarding prices.27

4.1.1. Base Case

With this consistent data set and parameters, we are ready to perform simulations.
In the base-case simulation, the model replicates the original Scholz (1987) data set, and
it produces a steady-state growth path. Various data on prices and quantities from the
base-case simulation are saved and used later in comparisons with the data from a
revised-case simulation. The revised-case simulation is based on the same behavioral
parameters, but with a different configuration of taxes. Figure 3 shows the labor supply
profile of a newcomer cohort for various values of BK, when C *=O% in the case of no
demographic adjustment. As we increase the BK value, we have a smaller increase in
labor supply early in life, and the consumer retires later in life. This shape of labor
supply profile depends on the quartic earnings function of Murphy and Welch (1990).
All of these profiles show a slow decrease in labor supply for 25-30 years, even though

we observe a sharp drop of labor supply afier retirement in reality. However, we have to

 

27Ba|lard and Goulder (1985) and Ballard (1987) discuss the effects of future price expectations,
in an infinite-horizon model and in the GEMTAP model. They show that the differences
between perfect foresight and myopia are not very large. However, Auerbach and Kotlikoff
(1987) and Judd (1985) show that the nature of expectations may be important if an
announcement effect is involved, or if the policy change is only temporary. However, in this
dissertation, l concentrate exclusively on permanent, unanticipated policy changes, so that

60

admit that any simulation model of this kind cannot duplicate the true labor supply profile

exactly.

4.1.2. Revised Case

For the revised—case simulation, we specify a tax policy that replaces a portion of
the current income tax with a 10% uniform VAT.28 My analysis here takes a differential
incidence approach.29 As we change a tax policy, the level of government exhaustive
expenditure is held constant in real terms. If government expenditures are to remain
unchanged, and if we are to maintain budget balance, we have to alter some tax rates to
maintain equal government revenue yield. In the experiments performed here, a 10%
uniform value-added tax is instituted, and the revenue from this tax is used to lower the

marginal income tax rates.

4.2. Results in the Aggregated Model

It has long been asserted that a move toward consumption taxation would result in
welfare gains in the aggregate. Auerbach and Kotlikoff (1983) did indeed find long-run

welfare gains, using a perfect-foresight general equilibrium simulation model. However,

 

announcement effects are not relevant. I plan to incorporate perfect foresight in a future
version of the model.

28Consumption taxation can be accomplished either by taxing consumption itself (as with a VAT
we consider here) or by offering deductions for saving within the income tax (as studied by
Fullerton, Shoven, and Whalley (1983)). However, the latter treatment has problems in the
transition: First, consumers may have other assets that can simply be transferred into their
qualified accounts to avoid taxation without actually undertaking any saving. Second, the
present system has a ceiling on the amount that can be deducted in any one year. Thus, if
consumers plan to save more than the ceiling, the government would lose revenue without
providing any marginal incentive to save. Empirical evidence suggests that these problems are
very substantial. See Gale and Scholz (1994a) and Engen and Gale (1993).

29See Musgrave (1959) for different ways of calculating tax incidence.

61

the Auerbach-Kotlikoff model, with no bequests, produces unrealistic wealth profiles.30
In addition to this, their model has no labor/leisure choice31 and no government transfer
payments. The presence of transfer payments may affect the results, since it can

significantly alter the consumption profile of the elderly.

1 have built these important factors into my model. Thus, my model has bequests,

a labor/leisure choice, and a “realistic”32

profile of government transfers. I also use a
Stone-Geary form of the instantaneous utility function in order to control the
intertemporal elasticities. Taken together, these factors help to produce a fairly flat
wealth profile, which is much more realistic than the extremely humped wealth profiles
of Auerbach and Kotlikoff. We get different results depending on the inheritance and
transfer proportions we use in the calibration process. Thus, I report two results, one

without demographic adjustments of the inheritance and transfer profiles, and the other

with demographic adjustment.

4.2.1. Case Without Demographic Adjustment
In this case, I use the original data on the number of households (NH) of each age

group as they are, even though they are irregular and do not conform to the assumption of

constant population growth in my model.

 

30See Seidman (1984) and Ballard (1990). See also Mirer (1967), White (1978), and Kotlikoff
and Summers (1981) for discussion of this problem.

31However, in another paper, Auerbach, Kotlikoff, and Skinner (1983) do include a labor/leisure
choice in the model.

321t means that the elderly receive more transfers than the young. We derive the transfer profile
from data on the government transfers from the Michigan Panel Studies of Income Dynamics
(PSID, 1973).

62

In the revised-case simulation, we replace a portion of the current income tax with
a 10% uniform VAT, and compare the results with various data on prices and quantities
saved in the base-case simulation. We begin with a model that is similar to that of
Auerbach and Kotlikoff, in that bequests are zero and there is no minimum required level

of consumption.

Table 18 shows that, when BK=2%33 and C. =0, each cohort dissaves in the first
period of its economic life, and turns to rapid increases in saving until the fourth of the
five-year periods of the life. Thereafier, saving begins to drop. Finally, saving goes
negative in the seventh period and beyond. Because of these huge swings of the saving
profile, the elderly are harmed during the transition as we move toward greater reliance

on consumption taxation, which is the result of Auerbach and Kotlikoff.

Table 18. Newcomer Cohort’s Savin Profile When C*=0 billions/5 ear eriod

 

 

 

T BK=2% BK=15% BK=25% BK=50% BK=70%
1 -105.0 —109.7 -113.6 -124.4 -l35.4
2 650.6 593.9 551.0 458.9 396.2
3 1041.1 965.8 909.0 787.3 704.6
4 1227.3 1169.2 1125.2 1028.0 956.2
5 967 5 953.4 941.9 907.5 865.8
6 357.3 424.8 474.3 561.6 586.4
7 -510.0 -301.3 -145.5 162.3 320.5
8 -967.8 -871.7 -796.4 -558.8 -249.6
9 -l411.4 -1258.1 -1137.4 —845.3 -608.0
10 -462.2 -254.9 -91.1 305.0 624.4
11 -680.2 -509.2 -372.4 -39.5 225.5

 

 

 

 

 

 

 

 

33Even though it is possible to run simulations for a wide variety of values of BK, I have
encountered some numerical problems in calibrating the model when BK=0% which is the
same case as the model of Auerbach and Kotlikoff. In this model with a labor/leisure choice,
we use the leisure intensity parameter (01) to achieve calibration. The a parameter is very
sensitive, and it has not been possible to calibrate the model when BK<2%. However, BK=2%
is low enough that we can compare these results with those of Auerbach and Kotlikoff. I did
run the simulation successfully when BK=0% in the case with demographic adjustment.

63

While there is wide consensus among economists that intergenerational transfers
explain a large portion of total wealth accumulation, there is no clear consensus about the
exact proportion of total wealth accumulation that can be explained by bequest. Kotlikoff
and Summers (1981) divide total wealth into life-cycle wealth and transfer wealth. They
come to the result that transfer wealth can explain from 46% to 80% of the total wealth
accumulation, depending on definitions and methodology. Modigliani (1988) says that
the reported evidence indicates that the share of wealth received does not exceed 25% of
the total wealth. Reviewing six types of evidence concerning the importance of
intergenerational transfers to savings, Kotlikoff (1988) finds that intergenerational
transfers play a very important and dominant role in US. wealth accmnulation. Recently
Gale and Scholz (1994b) conclude that inter vivos transfers and bequests may account for

about 51% of net wealth accumulation.

Figure 4A shows that, as BK increases, we have a flatter and flatter profile of
wealth. In other words, we observe smaller and smaller swings in savings, as bequests
become more important in the model. When BK=70% and C ‘ =0, we observe less rapid
saving early in life, and less rapid dissaving later. Saving is even positive in the last two

periods. This result is actually not unusual considering some of the empirical studies.34

The adoption of a VAT or a national sales tax leads to capital deepening, and thus

to a decrease in the relative price of capital services over time. As we can see in Table

 

34Mirer (1979) found that wealth tends to increase with age after adjusting for intercohort
differences in wealth at retirement. Bemheim (1986) found that a large portion of singles as
well as couples continue to accumulate wealth afier retirement.

64

19, the K/L ratio starts at 0.243 and eventually increases to 0.28235 when BK=2%, as
capital deepening occurs. This amounts to a 16% increase in the K/L ratio. Even though
we increase BK, the eventual steady-state K/L ratio is the same in each case, and it

converges so fast because the elasticities are high.

As the K/L ratio changes, the prices of capital and labor services also change
accordingly. For example, Table 20 shows that, when BK=2% and C*=0, the price of
capital services (which was 1.0 in the base case) increases to 1.065 in the first period,36
but it decreases to 0.926 in the final period as capital deepening occurs. When BK=70%
and C*=0, the price of capital increases to 1.036 in the first period, but it decreases to
0.929 in the last period. If we take a look at Figures 4B, 5B, and 6B, we find that the
rental price of capital fluctuates a lot before it converges to a new steady-state level. This
happens mainly because we assume myopia in my model. If we assume perfect foresight
in my model, the rental price of capital may not fluctuate as much as a result of a policy

change.

Auerbach and Kotlikoff (1983) find that the shift to consumption taxation would
lead to large long-run welfare gains at the cost of harming the cohorts that are old at the
time of policy change. Auerbach, Kotlikoff and Skinner (1983) come to a similar result:

They find that a consumption tax offers efficiency gains, chiefly due to the replacement

 

35Capital here is being measured in terms of service flows. Since capital service flows are only a
fraction of the value of the capital stock, these numbers for capital/labor ratios are much
smaller than those reported elsewhere. However, there is no fundamental conceptual
difference between the different numbers.

36This can be explained by Summers’ Human Wealth Effect. The present value of human
wealth decreases as the interest rates goes up when we adopt a VAT. Then consumers would
want to consumer less, and enjoy less leisure. Consequently, labor supply increases, and this
pushes up the relative price of capital services in the first period.

65

of large marginal tax burdens on the relatively inelastic elderly. However, they
acknowledge that, since their model does not incorporate a number of important factors
which might influence saving behavior (e.g., bequest, risk, etc. ), the results must be

regarded with some caution.

The simulation results of my model with bequests confirm their caution. As we
can see in Figure 4D, when bequests are this large, even the cohorts that are elderly
during the transition have welfare gains. Figure 4D shows that, as BK increases, the
elderly are hurt less and less, and finally, every generation including the elderly is better
off for a reasonably large value of BK. From Figures 4D, 5D, and 6D, we can tell that

this result is valid for various values of C *.

Auerbach and Kotlikoff (1983) find that the equivalent variation for cohorts living
in the new long-run equilibrium under the consumption tax is 2.32% of the lifetime
resources. In my model, when C *=0 and BK=2%, which is close to their case, I obserVe a
1.6% increase in welfare as a proportion of lifetime resources for the cohorts in the new
steady-state equilibrium. Figures 4D, 5D, and 6D tell us that these values increase as we
increase the BK value. For example, the welfare gains in the new steady-state is about
1.92% of lifetime resources when C*=0 and BK=50%, and it rises to 2.06% when C*=0
and BK=70% in my model. We also observe that the long-run welfare increase becomes
smaller as we increase the C“ value. For example, the welfare increase is about 1.92%
when C*=0% and BK=50%, 1.81% when C*=10% and BK=50%. The welfare gains are

smaller than those of Auerbach and Kotlikoff (1983).

C0

re:

Ct

11

(D

r1

66

This can be explained by two factors: First, as I incorporate minimum required
consumption and bequests into the model, consumer behavior becomes less elastic with
respect to the policy change. Second, my model assumes a more realistic policy change,
i. e. , we begin with a model with taxes on incomes, consumer purchases, capital use, labor
use, outputs, and bequests. We then introduce a 10% uniform VAT on top of existing
sales and excise tax and reduce income tax rates, while maintaining all of the other
features of the model’s treatment of taxes. Auerbach and Kotlikoff assume that the
model starts with a complete income tax and no other taxes and then they replace it with a
complete consumption tax. Another factor is that, in calculating the welfare change as a
proportion of lifetime resources, I use a definition of lifetime resources that differs from
the definition of Auerbach and Kotlikoff. In my model, the lifetime resources are defined
as initial wealth plus the present value of lifetime labor time (excluding leisure), plus

transfers, and inheritances.

There are several ways to define the lifetime resources. For example, we can
either include or exclude leisure in the definition of lifetime resources. Here, I exclude
leisure. There are some legitimate reasons to exclude leisure in the definition of lifetime
resources in my model: First, the amount of leisure is chosen in an arbitrary way in most
models of this kind. In my model, the calibration procedures are such that the amount of
leisure is very large in most simulations. This makes the value of the welfare change as a
proportion of lifetime resources so small that it is very hard to give any economic
meaning to the number. Second, we exclude leisure in the definition of lifetime

resources, so that it will be possible to compare our results with any model with no

 

 

 

a1

67

labor/leisure choice. (Later, I intend to develop a model with no labor/leisure choice. In

this case, of course, leisure will not be included in the definition of lifetime resources.)

However, Auerbach and Kotlikoff include leisure in their definition of lifetime

resources. They say (1987, p.74);

“One measure of these utility differences is the equivalent percentage increase in
full lifetime resources (assets plus the present value of earnings based on
working fill] time) needed in the original income tax regime to produce each
cohort’s realized level of utility under the specified alternative tax regimes.”

In the initial steady-state of Auerbach and Kotlikoff model, about 51% of lifetime
resources are spent on leisure. Since the denominator of my model is smaller than that of
Auerbach and Kotlikoff, the welfare change as a proportion of lifetime resources in my
model will be bigger than that of their model, ceteris paribus. Thus, the true difference in
the welfare change as a result of the policy change between my model and their model is

actually bigger than it would appear, based on these figures.

I have performed some sensitivity analysis with respect to changes in C' (the
minimum required level of consumption) and BK. The results are reported in Figure 4A
to Figure 6D. As we increase C. , the intertemporal responsiveness decreases. However,
the pattern of the wealth profile, the present value of the welfare change, the path of the
rental price of capital, and the equivalent variation as a proportion of lifetime resources
are quite similar. For a low value of BK with C‘=0%, I have results that are similar to
those of Auerbach and Kotlikoff (1983). However, with a reasonably large value of BK,
every cohort has welfare gains for various values of C. , even though the elderly have

smaller welfare gains than the younger or future cohorts.

68

This can be explained by two factors: First, since the elderly have less dissaving,
they are penalized less by the move toward consumption taxation. Second, even though
the policy change leads to capital deepening, and thus to a decrease in the relative price of
capital services over time, initially it leads to an increase in the price of capital services,
which helps to increase the welfare of the elderly (who have more capital income than

labor income). For example, in the first period, the rental price of capital increases to
1.065 when BK=2% and C. =0 (relative to a base-case value of 1.0), and 1.036 when

BK=70% and C. =0. The reason for the increase in the price of capital services is as
follows: When we adopt a VAT, we use the revenue to decrease the income tax rates. As
a result, the net-of-tax interest rate goes up, and the present value of human wealth
decreases. Then, consumers in the model desire to consume less, and to enjoy less
leisure. Consequently, labor supply increases, and this pushes up the relative price of
capital services in the first period.37 As we increase C. , we can reduce the intertemporal

elasticities. For each value of C‘, the rental price of capital fluctuates less as BK

increases.

 

37Another effect we may consider is that the reduction in consumption and leisure induce more
investment demand. Since investment goods are relatively labor intensive, the demand for
labor increases, leading to an increase in the price of labor. However, the fact that the price of
capital services increases in the first period means that the labor supply effect (which increases
the price of capital services) is greater than this labor demand effect (which decreases the price
of capital services).

 

oEnEooEoo «305.3 ...xoouio coc>> tocoo L02.09502 co eEEQ 2:55.. ..ccu . r. 5:50.

Figure 3. Labor Supply Profile of Newcomer Cohort When C*=0%, without Demographi

Adjustment, Aggregate Model

 

---BK=2%

 

 

 

 

KIddns :0qu

Period

70

Table 19. Amate K/L Ratio When C*=0, No Demogr_aphic Adjustment,
Aggrggate Model

 

 

 
     

 

 

T _ , ,, .. BK=2%” 2'
Vii-'1' 0.267 0.243 0.248 V 0.249 I H 0.251
2» " 0.267 0.306 0.292 0.288 0.284
3» .. 0.267 0.277 0.283 0.282 0.282
4 1 0.267 0.289 0.285 0.286 0.285
'5' 0.267 0.281 0.283 0.284 0.285
,6 ' 0.267 0.283 0.282 0.283 0.283
. 7- 0.267 0.281 0.281 0.282 0.283
{,8 0.267 0.282 0.282 0.281 0.282
'9 ‘ 0.267 0.284 0.283 0.281 0.282
3101 0.267 0.282 0.282 0.282 0.282
' 9‘11 0.267 0.283 0.282 0.282 0.282
'42 . 0.267 0.282 0.282 0.282 0.282
13 [ 0.267 0.283 0.282 0.283 0.282
14 0.267 0.282 0.282 0.282 0.282
51'5- 0.267 0.282 0.282 0.282 0.282
161" 0.267 0.282 0.282 0.282 0.282
'_‘1‘7 ' 0.267 0.282 0.282 0.282 0.282
‘ 2,184: i. 0.267 0.282 0.282 0.282 0.282
'19 0.267 0.282 0.282 0.282 0.282
220 g 0.267 0.282 0.282 0.282 0.282
21], 1' 0.267 0.282 0.282 0.282 0.282
“22 0.267 0.282 0.282 0.282 0.282
I. 23'- '] 0.267 0.282 0.282 0.282 0.282
524‘ 0.267 0.282 0.282 0.282 0.282
”25 0.267 0.282 0.282 0.282 0.282
1.262 0.267 0.282 0.282 0.282 0.282
1’ 2,7" 0.267 0.282 0.282 0.282 0.282
28 0.267 0.282 0.282 0.282 0.282
0.267 0.282 0.282 0.282 0.282
, 0.267 0.282 0.282 0.282 0.282
31 0.267 0.282 0.282 0.282 0.282

 

 

 

 

 

 

 

 

71

Table 20. Real Rental Price of Capital in Revised Case When C*=0, No

Demoggaphic Adjustment, Aggregate Model

 

 

 

T BK=2% BK=25% BK=50% BK=70%
1 1.065 1.047 1.043 1.036
2 0.858 0.895 0.910 0.921
3 0.944 0.924 0.927 0.927
4 0.907 0.917 0.918 0.919
5 0.930 0.925 0.922 0.921
6 0.924 0.926 0.926 0.924
7 0.930 0.929 0.928 0.927
8 0.927 0.929 0.930 0.929
9 0.921 0.925 0.930 0.930
10 0.928 0.927 0.927 0.928
11 0.924 0.927 0.928 0.929
12 0.927 0.927 0.928 0.929
13 0.925 0.927 0.929 0.930
14 0.926 0.927 0.928 0.929
15 0.925 0.927 0.929 0.929
16 0.926 0.927 0.929 0.929
17 0.926 0.927 0.929 0.929
18 0.926 0.927 0.929 0.929
19 0.926 0.927 0.929 0.929
20 0.926 0.927 0.929 0.929
21 0.926 0.927 0.929 0.929
22 0.926 0.927 0.929 0.929
23 0.926 0.927 0.929 0.929
24 . 0.926 0.927 0.929 0.929
25 0.926 0.927 0.929 0.929
26 0.926 0.927 0.929 0.929
27 0.926 0.927 0.929 0.929
28 0.926 0.927 0.929 0.929
29 0.926 0.927 0.929 0.929
30 0.926 0.927 0.929 0.929
31 0.926 0.927 0.929 0.929

 

 

 

 

 

 

 

   

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84

4.2.2. Case With Demographic Adjustment
The number of households (NH) of each age group in the original data is irregular

while I assume that the population grows steadily at the rate of (1+G), where G =
0.267562984. Thus in this case, I adjust the original data set base on NH of the oldest age

group so that it conforms to the assumption of constant population growth in my model.

Table 21 shows that, when BK=0%, each cohort begins to save fi'om the first
period of its economic life, and saving increases until the fourth of the five-year periods
of life. Thereafter, saving begins to drop and becomes negative in the seventh period.
However, in this case, we do not observe positive saving at the end of life, even when BK
is increased to very high values. However, as with case of no demographic adjustment,

we observe smaller and smaller swings in savings as BK increases.

Table 21. Newcomer Cohort’s Saving Profile When C*=0 (Sbfllions/S year period}

 

 

 

 

 

 

 

 

 

T BK=0% BK=25% BK=31% BK=50% BK=60%
1 25.6 17.4 14.9 5.5 0.9
2 614.0 515.7 494.3 433.8 406.1
3 947.5 816.9 788.5 708.2 671.4
4 1166.3 1062.7 1039.3 968.5 935.6
5 887.2 862.3 854.3 817.6 799.5
6 377.6 492.8 512.7 542.9 554.3
7 -383.9 -52.1 11.7 151.4 211.6
8 -983.7 -839.8 -773.7 -492.2 -368.7
9 -1312.3 -1130.3 -1093.5 -957.9 -886.5
10 -649.4 -402.6 -350.2 -165.6 -70.6
11 -689.0 -418.8 -358.7 -156.9 —54.6
SUM 0.0 924.2 ‘ 1139.6 1855.3 . 2199.0:-

 

 

85

In this case, we also observe capital deepening. Table 22 shows that the K/L ratio
decreases to 0.254 in the first period, and eventually increases to 0.281 when BK=0%.
This amounts to a 10.6% increase in the K/L ratio. Table 23 shows that the real rental
price of capital also changes in this case, and reaches almost the same level in the final
period. However, we observe smaller fluctuations of the capital price for the first few
periods compared with former case. Figures 7B, 8B, 9B, and ICE show these results for

different values of C*.

I have also performed the same sensitivity analysis with respect to changes in C *
and BK, and the results are reported in Figures 7A to 10D. The results are similar to
those from the case of no demographic adjustment. As Figures 7C, 8C, 9C, and 10C
show, we see less fluctuation of the welfare change as we increase the BK values. The
same thing can be observed in Figures 7D, 8D, 9D, and 10D, where we express the

welfare change as a proportion of lifetime resources.

As in the former case with no demographic adjustment, we observe smaller and
smaller welfare gains as we increase 0". While we observe larger welfare increases as
we increase the BK value in the case with no demographic adjustment, we observe
m; welfare increases in this case as we increase the BK values. We have 1.6%
welfare gains in the new steady state when C*=0% and BK=0%, but only 1.0% welfare
gains when C*=O% and BK=50%. When C*=30% and BK=50%, we have 0.76% welfare
gains in the new steady state. Therefore, the effect of BK on the long-run welfare gains

depends on the profile of transfer payments and bequests over the life cycle.

86

In all cases, I find that a move toward consumption taxation leads to long-run
welfare gains. However, my results in the transition are somewhat different from those of
Auerbach and Kotlikoff. I find that the losses to the elderly become smaller and smaller
when we increase the BK values. (In some cases, the elderly actually gain.) The big
difference between the case with demographic adjustment and the case without
demographic adjustment is that we do not observe positive welfare gains for all cohorts in
the case with demographic adjustment, even when we increase the BK values to very high

levels.

By comparing the simulation results of this case with those of no demographic
adjustment, I find that we have different results depending on the bequest and transfer
proportions we are using in this model, although, in my opinion, the results with no
demographic adjustment are more realistic. Although we do not observe such a big
difference in the proportion of transfers between the two cases, we observe a big
difference in the proportion of inheritances between the two cases. As we observed in
Figure 1, with demographic adjustment, inheritances are more heavily distributed in early
life. In reality, however, inheritances are bunched up in the later years of life. To tell
which case is more realistic, I run simulations with demographic adjustment for transfers,
but with no adjustment for inheritances. I find that the results are more close to the case
without demographic adjustment for either transfers or inheritances. Thus we know that
the basic difference in the results between the two cases comes from the proportion of
inheritances which are heavily concentrated in early life in the case with demographic

adjustment.

87

I also believe that bequests are large. Therefore, the results with BK much higher
than zero are most believable. Some of these yield the result that all cohorts gain. Some
do not. However, all have the result that, with a higher value of BK, the losses of the

elderly become substantially smaller.

Table 22. Aggrggate K/L Ratio When C*=0, with Demographic Adjustment,

Aggregate Model

 

 

 

 

BASE CASE REVISED. CASE ‘. .
T BK=0% WWW
1 0.267 0.254 0.249 10.252 1 0.253 I
2 0.267 0.278 0.286 0.281 0.279
3 0.267 0.282 0.286 0.283 0.283
4 0.267 0.284 0.287 0.284 0.284
5 0.267 0.284 0.285 0.284 0.284
6 0.267 0.283 0.283 0.283 0.283
7 0.267 0.282 0.282 0.282 0.282
8 0.267 0.281 0.282 0.281 0.282
9 0.267 0.281 0.283 0.281 0.28I
10 0.267 0.281 0.283 0.281 0.282
11‘ 0.267 0.282 0.283 0.282 0.282
12 0.267 0.282 0.283 0.281 0.282
13 0.267 0.281 0.283 0.28I 0.282
14 0.267 0.281 0.283 0.281 0.282
15 0.267 0.281 0.283 0.281 0.282
16 0.267 0.281 0.283 0.281 0.282
17 0.267 0.281 0.283 0.281 0.282
18 0.267 0.281 0.283 0.281 0.282
19 0.267 0.281 0.283 0.28I 0.282
20 0.267 0.28] 0.283 0.281 0.282
21 . 0.267 0.281 0.283 0.281 0.282
22 0.267 0.281 0.283 0.281 0.282
23 0.267 0.281 0.283 0.281 0.282
24 0.267 0.231 0.283 0.281 0.282
25 0.267 0.281 0.283 0.281 0.282
26 0.267 0.281 0.283 0.28I 0.282
27 0.267 0.281 0.283 0.281 0.282
28 0.267 0.281 0.283 0.28I 0.282
29 0.267 0.281 0.283 0.281 0.282
30 0.267 0.281 0.283 0.281 0.282
31 0.267 0.281 0.283 0.281 0.282

 

 

 

 

 

 

 

89

Table 23. Real Rental Price of Capital in Revised Case When C*=0, with

Demographic Adjustment, Aggregate Model

 

 

 

T BK=0% BK=25% BK=50% BK=60%
1 1.022 1.041 1.031 1.028
2 0.934 0.911 0.927 0.932
3 0.925 0.917 0.925 0.925
4 0.921 0.914 0.921 0.921
5 0.922 0.919 0.923 0.922
6 0.925 0.924 0.926 0.925
7 0.927 0.926 0.929 0.927
8 0.930 0.927 0.931 0.930
9 0.930 0.924 0.931 0.930
10 0.929 0.924 0.929 0.929
11 0.929 0.924 0.929 0.928
12 0.928 0.925 0.929 0.928
13 0.929 0.925 0.929 0.928
14 0.928 0.925 0.929 0.928
15 0.929 0.925 0.929 0.928
16 0.929 0.924 0.929 0.928
17 0.929 0.925 0.929 0.929
18 0.929 0.925 0.929 0.929
19 0.929 0.925 0.929 0.929
20 0.929 0.925 0.929 0.929
21 0.929 0.925 0.929 0.929
22 0.929 0.925 0.929 0.929
23 0.929 0.925 0.929 0.929
24 0.929 0.925 0.929 0.929
25' * 0.929 0.925 0.929 0.929
26 0.929 0.925 0.929 0.929
27 0.929 0.925 0.929 0.929
28 0.929 0.925 0.929 0.929
29 0.929 0.925 0.930 0.929
30 0.929 0.925 0.930 0.929
31 0.929 0.925 0.930 0.929

 

 

 

 

 

 

 

 

 

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106

4.3. Results in the Disaggregated Model

As Table 2 shows, I disaggregate this model into 19 sectors and 18 consumer
goods in this case, and run the simulations again. I am several simulations for the
disaggregated model, and compare these results with those of the aggregated model for

the same values of BK and C*, to see the effects of VAT on each sector.

4.3.1. Case Without Demographic Adjustment
The saving and wealth profiles from the disaggregated model are the same as

those of the aggregated model. Table 24 shows that the aggregate K/L ratio starts at
0.250 and eventually increases to 0.280 in the disaggregated model when C*=0 and
BK=50%, as capital deepening occurs. This amounts to a 12.0% increase in the K/L ratio,
while we can see a 13.3% increase in the aggregated model. For various values of C‘" and
BK, the increase in the ratio of K/L is smaller in the disaggregated model than in the

aggregated model.

Since the K/L ratio changes somewhat less in the disaggregated model, we see
slightly less fluctuation in the price of capital services. In Table 25, we can observe this
difference. For example, when C*=0 and BK=50% in the disaggregated model, the real
rental price of capital increases to 1.027 (vs. 1.043 in the aggregated model) in the first
period, but it decreases to 0.933 (vs. 0.929 in the aggregated model) in the final period as
capital deepening occurs. This difference is also shown in Figure 11A for C*=0 and

BK=70%.

Figures 113 and 11C show the difference in the welfare change between the

disaggregated model and the aggregated model. When C*=0% and BK=70%, we have

107

2.06% welfare gains as a proportion of lifetime resources in the aggregated model. When
the same parameters are used in the disaggregated model, we have 1.89% welfare gains.
For various values of C* and BK, we do not observe any big difference in welfare change
between the aggregated and disaggregated model. This is not a surprising result, because
I have assumed a uniform VAT on 19 production sectors. If we levy a differentiated
VAT on each sector, we would expect to see a bigger difference in the welfare change

between the aggregated model and the disaggregated model.

4.3.2. Case With Demographic Adjustment
Generally speaking, we observe almost the same results in this case as in the case

of the disaggregated model without demographic adjustment. The results are reported in
Tables 26 and 27, and also in Figures 12A, 12B, and 12C. However, in this case, we do
not observe much overshooting in the rental price of capital for various values of C“ and
BK. The capital service price converges more quickly, without much fluctuation, to the

new steady state than in the aggregated model.

Since there are only a consumption good and an investment good in the
aggregated model, there is no relative price change among goods, even when factor prices
change. However, in the disaggregated model, relative prices of the consumption goods
can change, since each price is a weighted average of the prices of the 19 goods. In the
revised case with the disaggregated model, there is a big shift of investment toward
contract construction (4th industry) and metals, machinery, instruments, and
miscellaneous manufacturing (5th industry). This leads to a price change of these two

industries.

108

However, as we can observe in figure 11A, 11B, 11C, 12A, 123 and 12C, there is
only a small change between the results of the disaggregated model and those of the
aggregated model. Thus, the disaggregated model does not tell us a great deal more

about the dynamics of this model.

109

Table 24. Aggrggate K/L Ratio without Demographic Adiustment,
Disaggregated Model

 

 

 

 

C*=0 and BK=50%
T Aggregated Disaggregated
1 0.249 0.250
2 0.288 0.290
3 0.282 0.279
4 0.286 0.283
5 0.284 0.281
6 0.283 0.280
7 0.282 0.280
8 0.281 0.279
9 0.281 0.280
10 0.282 0.280
11 0.282 0.280
12 0.282 0.280
13 0.282 0.280
14 0.282 0.280
15 0.282 0.280
16 0.282 0.280
17 0.282 0.280
18 0.282 0.280
19 0.282 0.280
20 0.282 0.280
21 0.282 0.280
22 0.282 0.280
23 0.282 0.280
24 0.282 0.280
25 0.282 0.280
26 0.282 0.280
27 0.282 0.280
28 0.282 0.280
29 0.282 0.280
30 0.282 0.280
31 0.282 0.280

 

 

 

 

 

 

 

110

Table 25. Real Rental Price of Capital without Demographic Adjustment,
Disaggregated Model

 

 

 

 

C*=0 and BK=50% c*=1o% and§k=50%

T Aggregated Disaggregated Aggregated Fisaggregated
1 1.043 1.027 1.040 1.026
2 0.910 0.903 0.907 0.900
3 0.927 0.934 0.925 0.932
4 0.918 0.924 0.919 0.925
5 0.922 0.930 0.924 0.930
6 0.926 0.932 0.926 0.932
7 0.928 0.933 0.929 0.933
8 0.930 0.934 0.929 0.933
9 0.930 0.934 0.926 0.931
10 0.927 0.932 0.927 0.932
11 0.928 0.933 0.928 0.932
12 0.928 0.933 0.928 0.932
13 0.929 0.933 0.929 0.933
14 0.928 0.933 0.928 0.932
15 0.929 0.933 0.928 0.932
16 0.929 0.933 0.928 0.932
17 0.929 0.933 0.928 0.932
18 0.929 0.933 0.928 0.932
19 0.929 0.933 0.928 0.932
20 0.929 0.933 0.928 0.932
21 0.929 0.933 0.928 0.932
22 0.929 0.933 0.928 0.932
23 0.929 0.933 0.928 0.932
24 0.929 0.933 0.928 0.932
25 0.929 0.933 0.928 0.932
26 0.929 0.933 0.928 0.932
27 0.929 0.933 0.928 0.932
28 0.929 0.933 0.928 0.932
29 0.929 0.933 0.928 0.932
30 0.929 0.933 0.928 0.932
31 0.929 0.933 0.928 0.932

 

 

 

 

 

 

111

Table 26. Aggpegate K/L Ratio with Demographic Adjustment, Disaggrggated
Model

 

 
 

 

 

 

 

 

 

C=0and ifiéo/ .
T Aggregated Disaggregated Aggregated..- 7 f .
I 0.251 0.251 0.254 0.254
2 0.284 0.286 0.279 0.281
3 0.286 0.283 0.285 0.283
4 0.286 0.283 0.286 0.282
5 0.285 0.281 0.285 0.282
6 0.283 0.281 0.283 0.280
7 0.282 0.280 0.282 0.280
8 0.282 0.280 0.281 0.280
9 0.283 0.281 0.281 0.280
10 0.283 0.281 0.282 0.280
11 0.283 0.281 0.282 0.280
12 0.283 0.281 0.282 0.280
13 0.283 0.281 0.282 0.280
14 0.283 0.281 0.282 0.280
15 0.283 0.281 0.282 0.280
16 0.283 0.281 0.282 0.280
17 0.283 0.281 0.282 0.280
18 0.283 0.281 0.282 0.280
19 0.283 0.281 0.282 0.280
20 0.283 0.281 0.282 0.280
21 0.283 0.281 0.282 0.280
22 0.283 0.281 0.282 0.280
23 0.283 0.281 0.282 0.280
24 0.283 0.281 0.282 0.280
25 0.283 0.281 0.282 0.280
26 0.283 0.281 0.282 0.280
27 0.283 0.281 0.282 0.280
28 0.283 0.281 0.282 0.280
29 0.283 0.281 0.282 0.280
30 0.283 0.281 0.282 0.280

31 0.283 0.281 0.282 0.280

 

 

 

112

Table 27. Real Rental Price of Capital with Demographic Adjustment,

Disaggpegated Model

 

 

 

 

 

 

 

 

 

C*=0 and BK=0% C*=30% mam——

T Aggregated Disaggregated Aggregated Disaggr 98,919.11 3
1 1.033 1.018 1.023 1.013
2 0.917 0.909 0.932 0.921
3 0.914 0.921 0.918 0.922
4 0.915 0.923 0.916 0.924
5 0.919 0.927 0.919 0.926
6 0.923 0.929 0.923 0.929
7 0.926 0.931 0.926 0.931
8 0.927 0.931 0.928 0.932
9 0.924 0.928 0.928 0.932
10 0.924 0.929 0.926 0.930
11 0.924 0.929 0.925 0.930
12 0.924 0.929 0.925 0.930
13 0.924 0.929 0.926 0.930
14 0.924 0.929 0.926 0.930
15 0.924 0.929 0.926 0.930
16 0.924 0.929 0.926 0.930
17 0.924 0.929 0.926 0.930
18 0.924 0.929 0.926 0.930
19 0.924 0.929 0.926 0.930
20 0.924 0.929 0.926 0.930
21 0.924 0.929 0.926 0.930
22 0.924 0.929 0.926 0.930
23 0.924 0.929 0.926 0.930
24 0.924 0.929 0.926 0.930
25 0.924 0.929 0.926 0.930
26 0.924 0.929 0.926 0.930
27 0.924 0.929 0.926 0.930
28 0.924 0.929 0.926 0.930
29 0.925 0.929 0.926 0.930
30 0.925 0.929 0.926 0.930
g 31 0.925 0.929 0.926 0.930

 

 

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4.4. Results When Tax on Bequests ls Positive
One of the issues of shifting to a consumption tax is how to tax bequests and gifts.

There are pros and cons on whether we should tax bequests. While some economists say
that bequests should not be taxed until they are consumed by the recipients, others argue
that they should be treated as consumption at the time of death.38 So far, I have assumed
that there are no taxes on bequests in my model. However, it is interesting to see how the
results change as we levy a positive tax rate on bequests. I run the simulation model for
certain values of BK and C“ in the aggregated model, both with and without demographic
adjustment. I observe how the results might change as we levy different tax rates on

bequests.

Table 28 shows that investment goods purchased increase as we increase the tax
rate on bequests. In the last period, we have about 14.9% more investment goods
purchased when the tax rate on bequests is 20% than when there is no tax on bequests.
This ratio is almost constant from the first period of the simulation. Table 29 reports how
investment goods purchased change as we increase the tax rate on bequests when
BK=50%, C*=20%, and with demographic adjustment. In this case, we observe a smaller
increase in the amount of investment goods purchased as we increase the tax rate on

bequests.

Figures 13A and 14A show that the investment share of GNP increases as we

increase the tax rate on bequests. Consumers have to save more, in order to leave the

 

388ee Bradford (1984) and Aaron and Galper (1985) for further discussion. This debate turns on
distributional and administrative issues, more than on efficiency issues.

120

same amount of bequests as the tax on bequests increases.” Figures 138 and 14B show
how the equivalent variation as a proportion of lifetime resources changes as we change
the tax rate on bequests. We do not observe a big difference in the welfare change as we
levy a positive tax on bequests. For example, in the case of no demographic adjustment,
if the tax on bequests is 0%, we have welfare gains of 1.92% of lifetime resources in the
long-run when C*=0, BK=50%. If we increase the tax rate on bequests to 10%, we have
long-run welfare gains of 1.87%. Thus, the effect of the estate tax on the welfare change
is small in the long run. In addition, the effect is small in the short run, as shown in
Figures 133 and 143. This result can be explained by the fact that tax revenue from
bequests makes up only about 1.4% of the total tax revenue when the tax rate on bequests
is l0%. As long as the tax revenue from bequests explains such a small portion of the
total tax revenue, we do not expect a big difference in the welfare change as we levy a
positive tax on bequests. Since we only observe a small efficiency difference as we
change the tax rate on bequests, the estate tax debate appears to turn primarily on

distributional and administrative concerns.

39However, this is not a Barro/Ricardian model, because we assume that the households derive
utility from their own consumption, leisure, and bequests, not from those of their descendants.

121

Table 28. Investment Goods Purchased When C*=20% BK=50%
with No Demographic Adjustment, Aggregated Model

 

 

    

 

 

 

 

 

 

 

T ggu=0 Btax=5% Max .. .. .
1 1915 1914 1915 1914 1914
2 1275 1385 1494 1603 1711
3 1564 1628 1688 1754 1818
4 1623 1698 1765 1840 1909
5 1834 1904 1965 2036 2102
6 2069 2145 2211 2288 2359
7 2342 2427 2500 2586 2666
8 2655 2751 2836 2933 3025
9 2988 3099 3197 3310 3416
10 3275 3404 3518 3650 3774
11 3697 3839 3965 4110 4248
12 4149 4309 4452 4617 4771
13 4688 4865 5022 5203 5374
14 5225 5427 5606 5812 6006
15 5869 6092 6291 6520 6735
16 6570 6822 7045 7303 7545
17 7365 7646 7896 8184 8456
18 8253 8569 8845 9173 9478
19 9257 9611 9925 10288 10630
20 10380 10777 11130 11537 11921
21 11639 12083 12479 12936 13366
22 13043 13542 13986 14499 14982
23 14624 15183 15681 16255 16797
24 16393 17020 17579 18223 18830
25 18379 19082 19707 20429 21110
26 20603 21391 22092 22902 23665
27 23098 23981 24768 25676 26531
28 25895 26885 17766 28784 29744
29 29029 30139 31128 32269 33345
30 32543 33788 34896 36179 37482
:31“,‘ N 36483 37879 39121 40556 41908

 

 

122

Table 29. Investment Goods Purchased When C*=20%, BK=50%,

with Demographic Adjustment, Aggregated Model

 

 

 

 

 

 

 

T Btax=0 Btax=5% Btax=1j0°éfl
1 1724 1699 1696
2 1487 1530 1577
3 1533 1571 1611
4 1647 1687 1727
5 1820 1862 1905
6 2053 2097 2143
7 2328 2375 2426
8 2641 2694 2751
9 2982 3042 3108
10 3309 3380 3455
11 3699 3778 3868
12 4151 4240 4335
13 4662 4761 4867
14 5224 5335 5453
15 5857 5981 6113
16 6568 6705 6854
17 7361 7517 7683
18 8251 8425 8612
19 9250 9445 9655
20 10370 10590 10825
21 11626 11872 12136
22 13034 13309 13605
23 14611 14921 15252
24 16380 16727 17093
25 18363 18752 19168
26 20586 21022 21489
27 23079 23567 24090
28 25873 26420 27006
29 29005 29619 30277
30 32517 33205 33942
_31 36453 37224 38051

1627
1653
1769
1950
2192
2480
2812
3178
3535
3953
4436
4980
5580
6255
7013
7861
8812
9879
11076
12418
13921
15607
17496
19614
21988
24650
27635
30981
34731
38936

 

 

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1694
1810
1993
2238
2531
2870
3244
3611
4039
4533
5087
5700
6390
7164
8031
9002
10092
11316
12687
14222
15944
17876
20038
22464
25184
28233
31652
35484
39780

 

 

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127

Currently, I am using a steady-state model, in order to be more comparable with
the work of others. However, I am interested in doing some work with non-steady-state
models in the future. Although I have only one group per cohort in the model to generate

the results reported thus far, I will extend this to a multigroup model in the future.

4.5. Conclusion
Auerbach and Kotlikoff (1983) focused attention on the transitional problems that

could occur, if we were to move substantially toward consumption taxation in the United
States. They found that a move toward consumption taxation would lead to long-run
welfare gains, at the expense of the cohorts that are elderly during the transition. Their
model has no bequests, and no government transfers. Thus, in a model like that of
Auerbach and Kotlikoff, the elderly have to accumulate wealth rapidly during their
working years, in order to consume during their retirement period. Consequently, their
wealth decreases rapidly during retirement. Thus, in the Auerbach-Kotlikoff model, the
elderly would be hurt when we adopt a VAT or a national sales tax, since they have to
consume so rapidly out of their accumulated wealth. However, as many empirical studies
have shown, bequests explain a large portion of the capital stock. In addition, transfer
payments make up a 1arge fraction of the income of the elderly. This may affect the
results substantially, since it can significantly alter the wealth profile of the elderly.

I have incorporated these important factors into a computational general
equilibrium model of the United Stated economy and tax system. My model has
bequests, a realistic profile of government transfers, a labor/leisure choice, and a number

of other features, including a detailed treatment of the many components of the tax

128

system. Taken together, these factors help to produce a fairly flat wealth profile, which is
much more realistic than the extremely humped wealth profiles of Auerbach and
Kotlikoff. As a result, it is sometimes possible for all cohorts to have welfare gains from
a move toward greater reliance on consumption taxation. Even when all cohorts do not
gain from this policy change, the losses to the elderly are still mitigated when we assume
the presence of substantial bequests. Thus, both bequests and government transfer
payments (which make up a large proportion of the income of the elderly), are important
factors to have these results. I find that these results are sensitive to the assumption about
the profile of transfer payments and bequests over the life cycle.

As Starrett (1988) suggested, I have incorporated a minimum required level of
consumption into the utility function. However, this factor has only a modest effect on
the results. I disaggregate this model into 19 sector and 18 consumer goods and I run the
simulations again. However, I find that this also has little effect. Another surprising
result I find is that, even when the tax on bequests is positive, it only has a small effect on
the welfare change.

My main result is that the transition losses to the elderly as a result of the move
toward consumption taxation are greatly reduced. Under some sets of parameters that are
not unreasonable, the policy change may lead to welfare gains for all cohorts, including

the elderly.

APPENDIX

APPENDIX

This appendix relies on an appendix to Ballard and Goulder (1987). However, my
model has some nice features that their model lacks. Even though their model has
bequests in it, the bequest parameter was always set to zero during their simulations.
However, my model has positive bequests and I add a minimum required consumption to
control the intertemporal elasticities. 1 also add a positive labor supply constraint to their
model. While bequests and government transfers are assumed to be distributed evenly
across cohorts in their model, I use realistic bequest and transfer proportions across
cohorts based on the real data. I use a quartic specification of human capital earnings
based on Murphy and Welch (1990) to derive the labor efficiency ratio (eh ). Ballard and
Goulder, however, use the quadratic human capital earnings function of Oaxaca(1973).
As shown by Murphy and Welch, the quartic fiinction describes actual earnings profiles

much more accurately than does the quadratic.

1. SOLUTION QF HOUSEHOLD’S MAXIMQATION PROBLEM

Let C.=C.—C°‘°and 174:1): H‘ —H..

 

40David Starrett (1982) first suggested that a Stone-Geary formulation of the instantaneous
utility or felicity function would be useful in studying the behavior of life-cycle consumers.

129

130

PC, = consumption at year t,
C ° = minimum consumption level,
where H, (= 1,) = leisure,

H, = amount of labor supply, and

 

H ° = potential labor time given endowment.

The utility function for any given cohort takes the following additively separable form:

6

1 T :11 a 3 1 1
(1-1) U:gz-(—1+lp)- [{(C -C1)a +a1(H —H,) } +3Wb163g,

"T is the index for the final year of life,
I, is leisure at year t,
B, is the bequest left at the end of year T,

3 is the elasticity of substitution between bundles of C and 1 across periods,

5 E l — i,
where 5
Bis the elasticity of substitution between C and l in a given period,
1
0- E - Z 9
0'

p is the rate of time preference,
or is the leisure intensity parameter, and

 

Lb is the bequest parameter.

The intertemporal wealth constraint is:

(..2) P IK+Z{W (H -1,,)+TR +IN— —P,C,,-}d —P BHd =0“

 

41Taxes have been suppressed for notational convenience. Inclusion of taxes is straightforward.

131

PK, is the price of initial nonhuman capital,

K 1 is the initial capital endowment,

W,’ is the wage rate for period t,

H, is the hours worked for period t,

where TR, is transfers for period 1,

IN, is inheritances for period t,

P, is the price index for consumption for period t,

d, is the discounting factor for period 1, defined below, and

 

P8, is the price of bequest for period t.

h

and
M) W.'= W191. ,

W, is the prevailing wage per unit of effective labor for period t
e
w re e,, is the ratio of effective labor to labor hours for a cohort of age h.

The intertemporal labor supply constraint is:
(1-4) (H‘ -1,) 20 for all 1,
Finally,

We assume that bequests are all given at end of life.

‘__l___1___
“(1+r,)

5:1
1 , {=1

,Vt>1

‘Q.
Ill

 

From expressions (1-1), (1-2), and (1-4), we can write the Lagrangean function for the

consumer’s maximization problem as

132

.a . .3- 1 1
(1-5)L=%Z(-1—1——+p),_C,{( _c) +a.(H -111} +3(_,1+p) 1.....

+ 1[P,,,K, + i {W,"(H — 1,) + TR, + IN, - PC,}d, - 5713,11,]

=1
T I
+ ,1 2
(=1

(11" —l,)d,} ,

where A is the Lagrange multiplier and represents the marginal utility of lifetime

3:

resources, and 11,5 are the Kuhn-Tucker multipliers on the constraints on labor supply.

If we take the first-order condition from equation (1-5) with respect to

consumption, leisure, ,1, and ,ut, we get the following expressions:

 

3L __l_ l 5 a- a' :4 At7-1_ _
(1-6) 5-5—7(1+p)— (C, +a,,l ) 0C, 213d, -0,
d _g;_ 1___}____6 a a 6 0-1 _ r _ _
(1-7) a1‘1,(— 07,]: 6(1+p)" ;(C, +a,,l )3' 612,1, 2W,d, 211,11, -0
01 T .
’57: PKIK,+ZI{W,’(H -l,)+TR,+IN,—P,C,}d,—PBTBTdT
(1'8) +ifl,(H. _ll)dl =0 ’
1-1
and
(1-9) i=(H’-1,)20.

133

1.12., if (H‘ —1,) >0, then .1, = 0
if (H‘-1,)=0, then p, >0

In other words, if we have positive labor supply, then pf—‘O, and W,’ is the effective wage.

If we have zero labor supply, then ,u,>0, and W,’ + ,u, is the reservation wage at which the

consumer chooses to supply exactly zero labor.

Rearranging terms of (1-6) and (1-7) gives us the following equations, indicating

that the marginal utility of the consumption at time I must equal the marginal cost of

consumption, and marginal utility of the leisure must equal its marginal opportunity cost:

2. .
(1-10) mfiy + 01,13), 1C,“ =
and
1 A0' a g“! o-l _
(1-11) Wk, +a,1,) 01,1, _

Dividing (1-10) by (1-11) yields

C‘"l _ P

I I

W.'+ 11. '

 

0,1,0—1

APd

I I

1(W' +p,)d

I I'

We rearrange terms to get the path of leisure as a function of discretionary consumption

and parameters.

134

aP

I I

la-l = ( ”ll’+ #:Jéa-i

I

I —[VVI'+#1)a—l "

I alP’ I '
Thus
(Ln) L=é6,

l
W '+ E
where 4‘, = [—L—EL) .
0J3

Substituting (1-12) into (1-10) gives an expression in terms of C,, 21, Pt, 5;, and

parameters such as p, o, and 5.

Zfiiyjfik+angfy’Crth¢=o

We rearrange terms to get an expression of C, in terms of other terms and parameters.

5— ,
W(C,”(l+a,§f))° le—l = APd

I I

I I

1 a i” A -aAa'—
Wot-0,6,)ale C, l=lPd

C*'-2Pd0+-'” “(“g
1 - 11 ,0) (It-(1,5,) a

135

67" = Apt M0 WHO-3)
“(1+rs)
l l H 4 a 1
(1-13) (21:15133-7 79:91—— (1+a, 7)("3)(fi).

From the equation (1-13), we get

(SI—l
_'_ _'_ "2 6 I
(1_14) CM 2 164103;] 79741" (1+a:*1§:|)(1—;)(fl) ‘

HUM)

s=l

Dividing (1-13) by (1-14), and rearranging gives us the ratio of C”, over é,_,:
I l 5 I

C‘, (3)5(1+p)fi[ 1+a,§j’ )(1'ZXETI)

A — PM 1+r,_, Liar—15:1

6 1

A6, =[l+[l+p]5_—T—l][i]s-1(1+atgf]('-Z)(ET)
:_1 1+ rI-l Pt—l 1+ 61,4574

A 3.71 a' at
(1-15) s=(1+,,,)[_a) (1.1L) ,
C PI-l 1 + at-lgl-l

 

 

 

 

136

 

1
1+ p 54 , _
77, = 1+ — 1, 1. e. , the reference growth rate of consumptlon,
rI—l

where < and

W=(1-§)(3‘.—J=(";5)(51J=§£5-

 

 

L

Recursive application of (1-1 5) over successive periods yields
1

— W
6-1
{-1 =(1+ nt—l)(11:l-l ] (11+ aI-lgl-l) ,
1—2 + at-th—Z

I—2

('3)

 

)

If we multiply successively the above equations, we get

.1- _._
5-l£‘*pl(‘“’l~~(—‘”Udell—”Ml"
(‘3, 1+rl 1+r2 1+r,_l P, 1mg: '

We rearrange terms to get the expression of C“, in terms of 6', and the parameters of the

 

problem:

6-l

I
Q- (1+p)"‘ [QECMW
A H Pl 1+algr

l H(1+rs)

s=l

137

04m é=qo

l

P "l 3:] l I '0‘ V
where Q,={[—I;:-)(l+p) (1,} (fig—é?) .

Equation (1-16) represents an optimal consumption path. Once optimal C" is known, we
can obtain an optimal consumption path, conditional on expected prices and interest rates.
Differentiating the Lagrangean function with respect to the consumer’s bequests

(8,) yields an expression indicating that the marginal utility of the bequest must equal

its marginal opportunity cost:

01 = 1
53¢ (l+p)T

 

b'-“B;‘.-' = 110,761,.

Rearranging terms yields:

(1-17) (—l—+'lprl—63¥_l =R‘PBTdT'

From equation (1-10),

138

l l A 3,4,.
= C°+a 1° a C04.
PPM-«r n) ,

 

From (1-12), 1;? = (C,P§T)a = C375; ; thus, substituting this into the above equation gives

US:

1 1 A A i—l P.
= CC? C0 0P a C04.
PPPP-t rm ,

 

Rearranging terms:
- A 52. A
,1 = ((1 + p)“l PTdT) l(c;’(1 + a,5;))v 'Cyr'

T—l “‘ é-| A _
,1 =((1+p) PTdT) (l+a,.§‘,’.)a C: '.

From (1-16), 6‘, = 6,0,. Substituting this expression into the above equation yields:

_ —l 55. A 6—1
(1-18) l=((1+p)TlPTdT) (1+aT§;)0‘(C,QT) .
Substitute (1-18) into (1-17)
1 5 5-1

 

(1+p)’ b““Bi" = ((1+p)"'PPdP)"(1 + aP:;)3“(éPoP) PPdP

Rearranging this gives us an expression for the optimal bequest in terms of discretionary

consumption in the base period.

139

._ 1+pTd ._ 0 §__ , (H
Bo I = (l(+,0)2'PTd bbl(1+“"5r)° I(CIQT) P3P
T T

 

 

B?" = (1:0) PBTb‘H (1 + (m1)ELI (630,)“1

T

BT =[m]6-lb(1+ aT§;)(é§g)(fi) éIQT
Pr

Thus,

(1-19) B, = [weigh

l
1 P 5i" .52:
fight] (1+ (1,6?)09-1) .
T

where ¢ = (
Equation (1-19) implies that bequests are equal to zero when the bequest intensity
parameter (b) is zero. Bequests increase with b. Although (1-19) suggests a linear
relationship between bequests and b, this is not the case, since a higher value of b entails
lower discretionary consumption (we have to reduce consumption in order to leave more

bequest).

140

Now substitute (1-16) into (1-12):

04m L=éogr
From (1-16),

C, —C’ = (C, —C‘)o,.
Rearranging terms gives us:

C, =C‘+(CI —C’)o,.

(1-21)

Substitute (1-16), (1-19), (1-20), and(1-21) into (1-8):

PK. K, + i[W,"(H — é,o,§,)+ TR, + IN, — P,(C° + é,o,)]d, — P,Tb¢é,o,d,

(=1

T
+ 2411‘ - C‘,Q,§,)d, = 0 .

I=l

Rearranging terms gives us an equation for initial consumption:

PKIKI + Zr; {(W,’+ ,u,)H° + TR, + IN, - P,C'}d, =
12!

PKI K, + Zr; {(W,'+ y,)H' + TR, + IN, - gc‘ }d =

I
(:1

T

ZWQPad, +p.nP5.d, + max.

l=l

+ P3,b¢0rdrél

{(W.'+ mam + Pod, }é.

+PPb¢oPdPéP

1
=1

s

141

PPK. +i{(WP'+y.)H‘ + TR. + IN. — PPC'}dP = (in. {UV/wag, +PP}d.

Is! In]

+PP,b¢nPdP]é‘P

PK, K, + i {(W,'+ p,)H‘ + TR, + IN, - Rc‘ }d,
6] = l=l

T

ZQ.{(W.'+#P)§. +PP}d, +PPb¢oPdP

l=l

 

Thus

7'
PK, K, +Z{(W,’+ p,)H’ + TR, + IN, — P,C'}d,
(1-22) C, = c' + '='

T

20, {(W.'+#.)é‘. +P.}d, + PPmedP

l=l

 

In the above equation, base-period consumption is linearly homogeneous in lifetime
resources (initial wealth plus the present value of lifetime labor time, transfers, and
inheritances). Equations (1-22) and (1-15) imply that, for given lifetime resources and

prices, a lower b indicates higher consumption at each point in time.

Once we get the initial equilibrium consumption level ((3, ) , we can calculate an
equilibrium consumption path according to (1-16). By substituting this equilibrium
consumption path into (1-12) and the leisure constraint, we can get the equilibrium

leisure path and thus the equilibrium labor path:

l'

C, = c‘ +(C, —C‘)o,
II = (CI _C.);r
(H, = H' —I,

 

142

2. PROCEDURES FOR DETERMINING THE
INTERGENERATION_AL ALLOCATION OF ENDOWMENTS
CONSISTENT WITH OBSERVED AGGiEGATE DATA
(CALIBRATION PROCESS)

We assume that each generation or cohort has an economic life of 55 years. In
addition, we calculate equilibria for five-year periods. Since a new cohort is born each
period, there are 11 living cohorts, with different endowments of labor and capital. We
describe the procedure for calculating the labor and capital endowments for each cohort,
based on aggregate data. This parameterization procedure must satisfy two kinds of
requirements: a replication requirement and a balanced-growth requirement. The labor
and capital endowments of each cohort must be such as to generate individual cohort
behavior which, when aggregated, replicates observed aggregate values and leads to

steady-state growth of the economy.

2.1. Exogenous Parameters

The critical exogenous parameters here are 8, the intertemporal substitution
parameter, c, the intratemporal substitution parameter, and b, the bequest intensity
parameter. The growth rate of population, g, is also exogenous here, although this growth
rate is actually determined in a separate data consistency program based on the observed

rate of net capital accumulation. Finally, the reference steady-state growth rate of

143

I
— . .. _ 1+ 3:1
consumption, 77, IS exogenous. From the defimtion of 77 [=( p ) —1], we

 

1+r

determine the rate of time preference (p).

2.2. Individual Consumption Paths

Let C", denote consumption of cohort n at time t. At t=1 (which represents the
benchmark year), the living cohorts are indexed from 1 to N, where N=11. Cohort N is

the “newcomer” cohort, i.e., the youngest cohort alive in the benchmark year.

The endowment allocation for each cohort begins with the consumption
aggregation condition, i.e., the total of the consumption of the cohorts living during the

benchmark year must be equal to the observed aggregate consumption ( C A). Thus,

(2-1) ZC,, = C,

where C A is observed aggregate consumption.

From equation (1-16),

A

CnJ = finial,
for the newcomer cohort “N”, it implies that:
CNJ = CNJQI

Thus

144

O O

Cm - Cm = (CNJ - CN.I)QI a
01'
(2-2) C... =0}... +(CP,. —C;..)a.P

where Q, is a fimction of prices, interest rates, and parameters such as 5, o, p, and a,.
The steady-state values for the prices and interest rates are known (B = F and r, = 7).

Therefore, in the steady-state,
_'_
Q _ (1+pj'4 5"(1+a,(§,"j”
’ - 1+ F 1+ emf,"
since P, and P, cancel each other out. The parameter values 8, o, and p are chosen
exogenously. The only relevant parameter that is unknown is (1,. For the purpose of this

exposition, it will be convenient to proceed as if a, were known here; in fact, a is

calculated by an iterative procedure which will be described below.

In the steady state, per-capita consumption is a function of age (k) only.

6‘ ,9

However, cohort size increases at the rate of g over time, implying that when cohort

n+j reaches age k, its consumption will be (1+ g)j times larger than cohort n’s

consumption at age k. This in turn implies that

(2'3) CN—j,l = CN.j+I(1 + g)-j -

From (2-2), we have

145

(2‘4) CNJ+I = CN.j+l + (CNJ_ CM 1 )0

j+l'

Substituting (2-4) into (2-3) yields

(2-5) GP-.. = [CPPP + (CPP — CI...)0P.. ](1 + g)".
N N—l

Since 2C", = 2C N_ 1,, , by substituting (2-5) into (2-1), we can rewrite the consumption
n=I j=0

aggregate condition (2-1) in terms of the consumption of the newcomer cohort, and the

minimum consumption level of the newcomer cohort over his lifetime:

N-l .
ZJCNJH + (CM! " C;.,)Q,,,](l + 8)-! = CA -
,.

Rearranging terms in the above equation gives the value of the newcomer cohort’s initial

consumption, C M, :

N' .N- l
ZCN1+I(1+g)—j + (CNJ C'NJ)Q j+1(1+g)—j =CA
J=0 j=0
.N—l All
20(CNI— —CNJ)QJ+I(1+g)j =CA 'OCN,+1(1+g)
F J:
. N-l -j N—l
(C‘Nl CNI)Z;QJ+1(1+g) = CA _ZOCN J+l(1+g)
J= j=

Thus

146

 

 

N-l
CA - --0 CN.j+l(1+ g) 1
(2'6) (CNJ — Cm) = N—lj— j a
a,” (1 + g)

j=0
Of

N-l . —,

CA — -._0 CN,j+l(1+ g)
(2'7) Cm = CNJ + N-lj- _
(2,,, (1 + g)

The newcomer cohort’s initial consumption, C NJ, is expressed as a function of C A, g, Q,

C L P and CL”. Once CM, is determined by (2—7), the benchmark consumption of other

cohorts can be calculated by substituting (2-6) into (2-5).

CN—jJ :

 

2

-1

CA — CN,j+l(1 + g)—j

O

 

J
N-l ,
Z Qj+l (1 + g)—j

J=0

2.3. Cohort Labor Time Endowments

Q

j+l

—

 

The benchmark leisure for each cohort can be calculated based on

(2'8) In,l = énJgnJ ’

147

l

5'” :[nlleml +Iun,I];:l-

amll’l

where e", is labor efficiency parameter for cohort n at time 1

a is leisure intensity parameter for cohort n at time 1

ml

 

The parameters em, and a”, are based on age only, and the age profiles of e and or are

identical for all cohorts. Thus, the leisure path for each cohort is calculated as follows:

(2-9) 1 = ‘

",1 mt n,t '

Aggregate labor time (H3) is determined by

(210) H; = H, Pufil,” .

n=l

To determine HL, we have to know H A and 1”,. While 1",, is determined above by (2-8),

H A will be determined by the iterative procedure which will be explained below.

Individual cohort time endowments (H;,1) must satisfy the aggregate condition:

(2-11) 2H; =HP-

n=l

Cohort labor time endowments increase from cohort to cohort at the steady-state grth
rate (g), but per-capita endowments of labor time are constant within each cohort’s

lifetime. Since

I48

0

. _ HNJ
(2'12) HnJ-(l+g)N-n '

Substituting (2-12) into (2-11) yields

 

N H .
(2-13) N‘N-n - HA ’
n=l (1+g)
01'
. H.
(2'14) HNJ = N A

Equation (2-14) shows the labor time endowment for the newcomer cohort. By
substituting (2-14) into (2-12), we can get the time endowments of all other cohorts

(I'LL):

(2-15) H‘ = N H‘ (1+g)"‘”.

 

2.4. Capital Endowment in the Benchmark

The capital owned by each cohort in the benchmark year is a reflection of the time
path of capital ownership over a given cohort’s lifetime. We consider two cases: 1) b=0

(the no-bequest scenario) and 2) b>O, in which case there will be positive bequests.

149

In the case of b=0, we calculate the newcomer cohort’s capital path from birth,
using income and the saving path, and the assumption of zero initial wealth. This time
path of capital for the newcomer cohort translates into the benchmark capital of other

cohorts according to

K .+
(2-16) KN-jJ = (1 :éij '

 

In the positive-bequest case, the procedure is a bit more complex. An initial guess
is made of the benchmark bequest. We assume that each cohort’s bequest is divided to
the 11 living cohorts according to the actual data.42 Thus, we can get the initial
inheritance, i. e., initial wealth of the newcomer cohort. Using the income path and the
saving path for the newcomer cohort, we calculate the time path of non-human wealth, as
well as the eventual bequest, which is equal to the value of wealth of the newcomer
cohort at death. Since bequests increase at the rate of population growth (g) over time, if

we divide the eventual bequest by the newcomer cohort at the end of his lifetime by

(1+ g)n , we can calculate the bequest lefi to all 11 living cohorts at the benchmark

period. The guess of the initial bequest (which is divided among the 11 living cohorts) at
the benchmark is adjusted by an iterative procedure until this initial bequest value is

equal to the eventual bequest left by the newcomer cohort at the end of his lifetime

divided by (1+ g)”.

 

42The division of total bequests among 11 living cohorts in the benchmark is based on Consumer
Expenditure Survey data, which Projector and Weiss (1966) used in their unpublished work
sheet. However, since these data do not conform to the age brackets of my model, I smoothed
the data.

150
2.5. Qualification

The procedure described above neglected two significant details. First, from
equation (2-2), the calculation of individual consumption path (Cm) depends on the or
profile, since 0, is a function of or. The shape of or profile is given exogenously:
a, = (Thar0 (h=1, ..., 11). We assume that leisure intensity is constant across cohorts
(a, =1). Thus, we have a, = a0 and a, is defined for the range of h. However, a, must
be determined in the calibration procedure. From (2-7), we know that, for any do , there
is a unique value of Cm which is consistent with the aggregation requirements.
However, the newcomer’s initial consumption (CM) must also be consistent with its
lifetime resources, as expressed by equation (1-22). Equation (1-22) implicitly poses a
second relationship between or and C M, , and an iterative procedure is employed to find

the combination of or and C N, satisfying both equations of (1-22) and (2-7):

From (1-22), we have

T T T
PKlK, + Z IN,d, + Z {(W,’+ p,)H‘ + TR,}d, - ZRC'd,
(2-17) C1 — C. = TH I=l T 1:!
29,047+ ”Aid: + ZQIPIdI + PBrmedT
I=l

Isl

 

Now, let

T
T, = PK, K, + Z IN,d,

Isl

T
T. = Z{(W.'+M)H' + TR.}d.

(=1

151

T: = PBTmedT

Ts = 0.1361.

7’
(=1

Then, we can rewrite the equation (2-17) by using these values:

. T T—T
(2-18) C,—C = , '+ 2 3

Zn.(W.'+u.) ed. M. +T. ’

(=1

 

l

T T ( :
where ZQ,(W,'+,u,)§d, =ZQ,(W,'+;1,)(M) Id, .
(=1

(=1 a( P(

Rearranging terms gives us:

1
T

:2. WM. :d. = T :2. Wm. m a. '(Eld.
P

(=1 (=1 (

Since a, = a, a0 and we assumed that a, = l, a, = a0. Thus, the above expression can

be rewritten:

T T W' cT—i _
§Q.(W('+ mam. = gum... P)(_;_#) (Pat...) ,1,

I

Rearranging terms:

152

I

T T r g.-
ZQ.(W.’+#.)§d.= 9.(PK'+#.)(V-V’,¥L) ' ‘
(=1 (=1 (
T 1

(2-19) Zo,(W,'+ p,)§d, =T,a,-(;),

(=1

T W' o—-l
where T7 = ZQ,(W,'+;(,)[—’;—’u’-) d, .

(=1 (

Substituting (2-19) into (2-18), we have

. T+T-T
C1-C= 1'2 3

T,*a,,'(fi) +T5 +T4

 

We rearrange terms to isolate a0:

-4 T+T—T
T7*ao (a-l)+7;+n=—J‘C'l—:éT—3'

 

Thus,

 

153
We do the iterative procedure until 05,, value satisfies both equations (1-22) and (2-7).

The second qualification is that, although H A (aggregate labor supplied) is used in

equation (2-10) to determine H; (aggregate labor time), it is not a component of the
benchmark data. However, the “value” of labor supply (VHA) is part of the benchmark

data, and VHA and H A are related to each other according to

 

 

VH
2-20 H = f ,
( ) A W
where
N
Z PLenJHnJ
2-21 W ' = "=1
( ) HA

Since P, = 1 in steady-state, we can rewrite the above equation as:

N

. 2 cm] HnJ

2-22 W ="—='-———
( ) H.

The wage index W' is necessary to calculate H A from observed VHA, but W ' itself
depends on H A and Hm (benchmark labor supplies of individual cohorts). Since H .4 and
W' are dependent each other, it is necessary to employ an iterative procedure which

adjusts guesses of W’ until the conditions in (2-20) and (2-22) are simultaneously

satisfied.

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