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THE INTERNATIONAL SPILLOVER EFFECTS OF US. TAX REFORM:
A COMPUTATIONAL GENERAL EQUILIBRIUM APPROACH
WITH A GLOBAL TRADE MODEL

By

Kiwon Kang

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Economics
2002

ABSTRACT

THE INTERNATIONAL SPILLOVER EFFECTS OF U.S. TAX REFORM:
A COMPUTATIONAL GENERAL EQUILIBRIUM APPROACH
WITH A GLOBAL TRADE MODEL

By

Kiwon Kang

I integrate trade modeling and tax modeling, by evaluating the international
spillover effects of changes in U.S. tax policy. I use both static and dynamic
computational general-equilibrium models that divide the world into four regions. The
data are from Global Trade Analysis Project for 1995. My model incorporates a
labor/leisure choice and international cross-ownership of assets. My simulations suggest
that unilateral elimination of U.S. capital taxes generates capital inflows. This policy
change encourages more efficient use of the capital stock, but it will also generate
negative effects on the terms of trade. Overall, the policy change generates welfare gains
for the United States. If the other regions do not respond to the U.S. policy change, they
suffer welfare losses. However, if all regions eliminate capital taxes, welfare gains
accrue for the entire world. The analysis of welfare gains for the United States indicates
that unilateral elimination of U.S. capital taxes yields an annual static welfare gain of
around $98 billion in 1995 dollars (which amounts to 1.4 percent of GDP), while it yields
dynamic gains, whose present values are around $4.0~$4.1 trillion (which amount to 2.2

percent of GDP stream).

Copyright by
Kiwon Kang

2002

Dedicated to

My father, Dong-Hyuk Kang
My mother, Young-Nam Kim

My mother-in-law, Myung-J a Jung

My wife, Chooyoung Lee
My daughter, Michelle Kang

iv

ACKNOWLEDGEMENTS

The work with this dissertation has been long and extensive. Without support and
encouragement from several people, this work could not have been accomplished.

First of all, I would like to express my sincerest gratitude to my advisor, Dr.
Charles L. Ballard. He has taught me innumerable lessons and guided my research in the
right direction. He also provided me deeper understanding of economics. His expert
guidance was essential to the completion of this dissertation. I also would like to thank to
all committee members, including Dr. John H. Goddeeris and Dr. Lawrence W. Martin,
for their invaluable commentary.

I also would like to give special thanks to Dr. Gill Chin Lim for his unconditional
understanding and support throughout my graduate studies in East Lansing. He has
always showed me his energy and enthusiasm. His genuine efforts will influence the rest
of my life. Thanks also go out to all my friends at the Department of Economics
(especially, room 4 in the Old Botany) and the Visiting International Professional
Program, Michigan State University.

Last, but not least, I would like to thank my family for their endless love and
support. I especially owe much to my parents for their dedication and patience. My wife,
Chooyoung, deserves to receive my deepest appreciation. Her love and devotion itself

was, in the end, what made this dissertation possible.

TABLE OF CONTENTS

LIST OF TABLES ................................................................................ vii
LIST OF FIGURES ............................................................................... ix
CHAPTER 1. INTRODUCTION ...................................................... 1
CHAPTER 2. RELEVANT STUDIES ................................................ 4
2.1. The Incidence of the Corporate Tax ............................................. 4
2.2. Efficiency Results from Simulation Models .................................... 6
CHAPTER 3. DESCRIPTION OF THE SIMULATION MODEL ............ 13
3.1. Overview ........................................................................... 13
3.2. Structure of the Static Model .................................................... 18
CHAPTER 4. MODEL CALIBRATION ............................................ 41
4.1. Exogenous Parameters ........................................................... 41
4.2. Calibration Issues ................................................................. 43
CHAPTER 5. DATA AND SIMULATION METHOD .......................... 57
5.1. Data Interpretation ............................................................... 57
5.2. Simulation Method ............................................................... 69
CHAPTER 6. SIMULATION RESULTS IN THE STATIC CASE ........... 70
6.1. Central-Case Simulation ......................................................... 70
6.2. Sensitivity Analyses .............................................................. 83
6.3. Alternative Scenarios ............................................................ 95
CHAPTER 7. DYNAMIC MODEL ................................................. 103
7.1. Model and Calibration Issues .................................................. 103
7.2. Simulation Results .............................................................. 109
CHAPTER 8. CONCLUSION ....................................................... 122
APPENDIX ........................................................................................ 124
BIBLIOGRAPHY ............................................................................... 139

vi

Table 4-1.
Table 4-2.
Table 4-3.
Table 4-4.

Table 4-5.
Table 5-1.
Table 5-2.
Table 5-3.
Table 5-4.
Table 5-5.
Table 5-6.

Table 5-7

Table 5-8.
Table 5-9.
Table 6-1.
Table 6-2.
Table 6-3.
Table 6-4.
Table 6-5.

Table 6-6

Table 6—7.
Table 6-8.

Table 6-9.

LIST OF TABLES

Exogenous Parameter Values ....................................................... 43
Calibrated Parameter Values ........................................................ 46
Elasticity of Capital Abroad and Calibrated Asset-Substitution Elasticity ...50

Price Elasticities of Import Demand and Calibrated Trade Elasticity of

Substitution ............................................................................ 55
The SALTER Trade Elasticities .................................................... 56
Levels of Economic Activity by Region .......................................... 57
Dataset Mapping of Regions from GTAP version 4 ............................. 58
Dataset Mapping of Sectors from GTAP version 4 .............................. 59
Factor Taxes in the Model ........................................................... 61
Capital Taxes in EU. ................................................................. 64
Consumption Tax Rates in the Model ............................................. 65
Import Tariffs by Sector ............................................................ 66
Total Value of Imports and Exports by Sector and Region ...................... 67
Bilateral Trade Flows by Sector .................................................... 68
Possible Effects of Reducing U.S. Capital Taxes ................................. 73
Effects on Capital Flows ............................................................ 74
Effects on the Terms of Trade ...................................................... 75
Domestic Effects of the Tax-Policy Change on the U.S. Economy ............ 77
Spillover Effects of the U.S. Tax-Policy Change on Foreign Economics .....79

U.S. Static Welfare Changes of Unilateral Case, As a Function of

the Trade and the Asset Parameters ............................................... 81
Decomposing the Static EVs ......................................................... 82
Sensitivity Analysis with Respect to the Elasticities of Substitution
between Domestic and Imported Goods I ......................................... 84
Sensitivity Analysis with Respect to the Elasticities of Substitution

between Domestic and Imported Good II ......................................... 85

Table 6—10.Sensitivity Analysis with Respect to the Elasticities of Substitution

among Different Imported Goods I ................................................. 88

vii

LIST OF TABLES (cont’d)

Table 6-11. Sensitivity Analysis with Respect to the Elasticities of Substitution
among Different Imported Goods II ............................................... 89
Table 6-12. Sensitivity Analysis with Respect to the Different Combinations of Trade

Elasticities of Substitution .......................................................... 90
Table 6-13. Sensitivity Analysis with Respect to the Asset-Substitution Elasticities .....93
Table 6-14. Domestic Effects of Non-Zero Equalization of U.S. Capital Taxes ........... 97
Table 6-15. Domestic Effects of U.S. Labor-Tax Replacement ............................. 98
Table 6-16. Sensitivity Analyses with Different Combinations of Labor-Supply

Elasticities and Goods Elasticity of Substitution ................................ 99
Table 6-17. U.S. Static Welfare Changes of Multilateral Case, As a Function of

the Trade and the Asset Parameters .............................................. 102

Table 7-1. The Impact and Long-Run Effects of Replacing of U.S. Capital Taxes ...112
Table 7-2. The Equivalent Variation I - Dynamic Simulation of Unilateral Case ......116
Table 7-3. The Equivalent Variation II - Dynamic Simulation of Unilateral Case .....117
Table 7-4. The Equivalent Variation III - Dynamic Simulation of Multilateral Case ..117
Table 7-5. The Equivalent Variation IV - Dynamic Simulation of Multilateral Case ..118
Table 7-6. U.S. Dynamic Welfare Changes of Unilateral Case, As a Function of

the Trade and the Asset Parameters .............................................. 118
Table 7-7. U.S. Dynamic Welfare Changes of Multilateral Case, As a Function of

the Trade and the Asset Parameters .............................................. 119
Table 7-8. Intertemporal Effects for the U.S. ................................................ 120
Table 7-9. Welfare Effects for Whole World ................................................ 120

viii

Figure 3-1.
Figure 3-2.
Figure 6-1.

Figure 6-2.

Figure 6—3.

Figure 6-4.
Figure 6-5.
Figure 7-1.
Figure 7-2.
Figure 7-3.
Figure 7-4.
Figure 7-5.
Figure 7-6.
Figure 7-7.

LIST OF FIGURES

The Structure of the Production ................................................... 17
The Structure of Utility ............................................................. 24
Terms-of-Trade Effects from Elimination of U.S. Capital Taxes, As a

Function of the Elasticity of Substitution Between Domestic and

Imported Goods ..................................................................... 86
Capital-Flow Effects from Elimination of U.S. Capital Taxes, As a

Function of the Elasticity of Substitution Between Domestic and Foreign
Assets ................................................................................. 92

Welfare Gains for the U.S. from Unilateral Elimination of Capital Taxes,

As a Function of Labor-Supply Elasticity ........................................ 95
Optimal Strategy for the United States ........................................... 96
Welfare Effects - Unilateral vs. Multilateral ................................... 101
Consumption Path - All Regions ................................................. 109
Leisure Path - All Regions ........................................................ 110
Utility Path - All Regions ......................................................... 110
Consumption Path - U.S. .......................................................... 112
Leisure Path - U.S. ................................................................. 113
Utility Path - U.S. .................................................................. 114
U.S. Consumption Path, As a Function of Savings Elasticity . . . . . . . . . 1 14

ix

CHAPTER 1

INTRODUCTION

The current tax-reform debate in the United States has focused attention on
proposals that would lead to reform of the taxation of capital income. In the current
debates, three proposals have received the most attention; the “flat tax” proposal, which
suggests cutting income-tax rates to a single rate, the “unlimited saving allowance”
proposal, which suggests providing deductions for all savings, and the “consumption-tax-
only” proposal, which asserts complete replacement of the federal income tax with a
value-added tax.1 Although they differ in some important details, each of these proposals
points toward reduced taxation of capital income generally (and corporate capital income
in particular), and toward increased consumption taxation.

Much of the discussion has focused on the effect of tax reforms on labor supply
and capital accumulation within the domestic economy. A number of authors have
simulated the effects of moving toward consumption taxation in closed-economy models,
and have generally found that heavier reliance on consumption taxation will lead to
welfare gains in the long run.2

International issues have been given relatively little attention. However, as the
world economy becomes increasingly integrated, it becomes increasingly appropriate to

focus on international issues. Recently, some researchers have begun to study the

 

1 See the papers in Mieszkowski and Zodrow (forthcoming, 2002), which discuss the effects of various
proposals that would move in the direction of greater reliance on consumption taxation.

2 These papers include Auerbach and Kotlikoff (1983), Fullerton, Shoven, and Whalley (1983), Ballard
(1990a), Auerbach, Kotlikoff, Smetters, and Walliser (1997), Engen and Gale (1997), Jorgenson and
Wilcoxen (1997), Rogers (1997), and Altig, Auerbach, Kotlikoff, Smetters, and Walliser (2001).

international implications of major tax reforms. In the early 19803, Whalley (1980) and
Goulder, Shoven, and Whalley (1983) analyze the effects of tax-policy changes, using
open-economy simulation models. More recently, in the 19903, Grubert and Newlon
(1995), Hines (1996), Thalrnann, Goulder, and DeLorme (1996), and Mendoza and Tesar
(1998) deal with the international considerations of tax reform.

Multi-region models, in which international trade is the key inter-regional link,
have been developed for analyzing global issues, especially multilateral trade policy
issues such as trade liberalization, other trade policies, or fiscal policies that may be
changed simultaneously in a number of countries.3 With an integrated world market for
goods, the effects of tax policies undertaken by a single country spill over to other
countries. Recognition of such international economic interdependence stimulates
interest in the international coordination of fiscal policies, in general, and of tax reforms,
in particular.

My study aims to integrate tax and trade issues, by evaluating the international
spillover effects of U.S. fimdamental tax reform, and examining the key elements
determining the magnitude of its effects, using a multi-region trade model. In this study,
international spillover effects, through both changes in commodity flows and changes in
capital flows, are considered. This paper begins with a description of previous studies,
which are summarized in Chapter 2. Chapter 3 describes the static simulation model,

which is mainly used for the analyses. Chapter 4 provides the model calibration. The

 

3 In the middle of the 19905, Hertel and Tsigas (1996) developed the standard GTAP, which is well suited
for analyzing the effects of trade policies. There have been a lot of studies that deal with trade issues, with
multi-region trade models. However, there are only a few papers that analyze the effects of fiscal-policy
changes, using multi-region trade models. Only a few works deal with both tax and trade issues
simultaneously: Whalley (1980) focuses on the global effects of domestic factor-tax systems, and Whalley
(1982) partly deals with tax policy, in addition to trade issues.

data and simulation method are discussed in Chapter 5. Chapter 6 presents and interprets
the simulation results in the static case. The issues on dynamic simulations are discussed

in Chapter 7. Lastly, Chapter 8 concludes.

CHAPTER 2

RELEVANT STUDIES

2.1. The Incidence of the Corporate Tax

Harberger (1962) constructs a perfectly competitive, static, closed-economy
model with two sectors and two factors of production. When a tax is levied on capital
income in the corporate sector, competitive forces lead to a re-allocation of the capital
stock. This re-allocation continues until the net-of—tax return to capital is the same in
each sector. This leads to the result that the burden of the tax is borne by all capital,
including capital that is not located in the corporate sector. The results of Harberger’s
model depend on the elasticities of substitution between capital and labor in the two
sectors, the elasticities of demand for the two outputs, and the factor intensities in
production. However, Harberger finds that his basic result is quite robust with respect to
changes in the parameters of the model.

Shoven (1976) extends the Harberger model to include 12 production sectors.
Shoven’s model is more elaborate than that of Harberger, but it retains the basic character
of the Harberger model by assuming perfect competition in a static context.
Consequently, it is not surprising that Shoven’s results are broadly supportive of
Harberger’s. However, the efficiency effects estimated by Shoven are larger than those
estimated by Harberger. In effect, the assumption that there are only two sectors leads to
an understatement of the intersectoral distortions caused by differential capital taxation.
When Shoven moves to a 12-sector model, the simulated efficiency effects increase

substantially.

Fullerton, King, Shoven, and Whalley (FKSW, 1981) continue to assume perfect
competition, and they continue to assume that there are no international capital flows.
However, they extend the model to 19 production sectors, and they make the model
dynamic. In the short to medium run, the results of FKSW are similar to those of
Harberger (1962) and Shoven (1976): When the corporate and personal income taxes are
integrated, the returns to capital increase throughout the economy. This implies that the
burden of the corporate tax is borne by capital. However, when FKSW trace out the
dynamic development of the economy, the incidence picture changes in dramatic fashion.
When the rate of return to capital is increased by the integration of the corporate tax, the
rate of capital accumulation is increased. Consequently, in the very long run, the capital
stock is substantially larger when there is no corporate tax than it would have been in the
presence of the corporate tax. This increased capital stock leads to higher real wage rates
for workers, which means that labor bears a substantial portion of the burden of the
corporate tax in the long run.

All of the studies described above have assumed a closed economy.4 When
international flows of goods and capital are allowed, the results can change significantly.
Harberger (1995) considers a static, perfectly competitive model in which there are
international flows of goods and capital. Harberger assumes that the world capital market
functions perfectly, in spite of the evidence of substantial international capital

immobility.5 For a small, open economy, the net-of—tax rate of return to capital is fixed in

 

‘ There have been many other studies of the quantitative effects of tax policy changes, using closed-
economy models. These include Shoven and Whalley (1972), Whalley (1975), Keller (1980), Slernrod
(1983), Piggott and Whalley (1985), and Ballard, Fullerton, Shoven, and Whalley (1985).

5 The evidence on international capital immobility is extensive. Feldstein and Horioka (1980) report
empirical evidence suggesting that capital is quite immobile internationally. Frankel (1990) and Obstfeld
(1993) provide a review of the literature that was spawned by F eldstein and Horioka. Several possible

the world capital market. Consequently, there is no way for domestic capital to bear the
burden of the tax. Instead, capital will flow out of the domestic economy, raising the
domestic gross-of-tax rate of return to capital, until the net rate of return to domestic
capital is once again equal to the net rate of return to capital in the rest of the world.
When the international flow of goods is also perfectly competitive, the brunt of the
corporate tax must be borne by domestic labor.6

Gravelle and Smetters (1998) build a model with imperfect substitutability
between domestic and foreign products, and imperfect portfolio substitution between
domestic and foreign capital. Gravelle and Smetters find that these imperfections play an
important role in limiting the amount of the corporate tax that is borne by domestic labor.
In some cases, the burden on labor is eliminated entirely. Gravelle and Smetters perform
a number of sensitivity analyses. Their results show a mild amount of sensitivity to
changes in the parameters. However, for the parameter combinations that seem most
reasonable, capital bears at least half of the burden of the tax, and often significantly

more.

2.2. Efficiency Results from Simulation Models
2.2.1. Closed-Economy Simulation Models
Among the many econometric studies of consumption functions, only a few

suggest that saving is highly responsive with respect to the net-of-tax rate of return.7

 

explanations have been discussed in Gordon and Bovenberg (1996). Especially, Gordon and Bovenberg
attribute international capital immobility to asymmetric information across countries.

6 Feldstein (1994) gives a similar argument.

7 One of the very few studies to find a really large elasticity is that of Taylor (1971). He finds elasticities in
the vicinity of 0.8 to 0.9 in some cases. Another study is that of Heien (1972).

Most studies find that the savings elasticity is not far fi'om zero, and some find that it is
negative. Thus, if a simulation model implies that the savings elasticity is enormous, the
results of the simulation study must be viewed with considerable caution.

Unfortunately, many simulation models do imply very large savings elasticities.
In a model that lacks uncertainty, or borrowing constraints, or any other rigidities, model
consumers find it very easy to re-allocate their consumption across time, even though
such re-allocations may be more difficult for real people in the real world. This problem
is especially severe in models with very long time horizons. In the extreme case, a large
number of researchers assume that consumers live forever. These infinite-horizon
models often imply savings responses that are extremely unrealistic. Even in an
overlapping- generations model, in which consumers live for a finite period, the problem
can still be severe. For example, Auerbach and Kotlikoff (1983) show that simulations of
the switch to a consumption tax involve an increase in the savings rate from 10 percent to
42 percent.

This extreme result is driven by a feature that is common to the infinite-horizon
models.8 In models of this type, the first step in the consumer’s decision-making process
is to calculate his full wealth. This involves calculating the present discounted value of
the infinite stream of the consumer’s labor time. For a fundamental tax reform, the net
rate of return will usually increase. This means that the consumer’s full wealth will be
smaller under the policy change than it was in the “base case”. Since the consumer is
poorer, and since consumption in every period is a normal good, the consumer will want

to reduce this first-period consumption. This can lead to a very large increase in saving,

 

8 See Ballard (1990a, 2001) for details.

even if labor supply does not change. However, if the single-period utility function is a
composite of consumption and leisure, the consumer will want to consume less leisure, in
addition to consuming fewer goods. Therefore, the consumer will work more. When the
consumer works more and consumes less, it is possible to have truly enormous increases
in savings. Unfortunately, the workings of this type of model can tell us very little about
what would actually happen in the real world, in response to a tax-policy change.

In recent years, researchers have made promising developments in the
specification of simulation models. Engen and Gale (1996, 1997) have developed
overlapping-generations simulation models in which consumers are uncertain about their
path of future earnings and their length of life. To a great extent, this uncertainty reduces
the excessive sensitivity of savings. For example, Engen and Gale (1996) suggest that, if
modeled within the context of a closed economy, fundamental tax reform would increase
the U.S. saving rate by 0.3 to 0.8 percentage points.

In these models, consumption is typically reduced in the first several years after
the move to a consumption tax. However, the additional saving leads to a higher rate of
capital accumulation, so that consumption is eventually higher under a consumption tax
than an income tax. The present value of the gain in consumption in the future is usually
large enough to outweigh the loss of consumption in the near term. Thus, virtually all of
the closed-economy simulation studies find that movements toward consumption taxation
would yield welfare improvements.

Even though some of the simulation models imply that saving is extremely,
unrealistically responsive, it does not necessarily follow that these models imply welfare

improvements that are dramatically different from the welfare improvements that are

simulated by models with more modest savings elasticities. As shown in Ballard
(1990a), very large increases in the savings elasticity are ofien only associated with small
increases in the simulated welfare gains from moving toward a consumption tax. With a
small saving elasticity, consumption drops when a consumption tax is instituted, and then
recovers. Consumption eventually approaches a new steady state, in which the level of
consumption is higher than in the base case, but the rate of growth is the same. With a
larger savings elasticity, consumption drops farther when a consumption tax is instituted,
and it recovers more quickly. However, consumption will approach the same steady state
for either value of the savings elasticity. Thus, the consumption profiles for the large-
elasticity case and the small-elasticity case are really quite similar. For the large-
elasticity case, consumption is lower at first, and then higher, and finally the levels of
consumption in the two cases will converge to the same steady state. Consequently, the

long-run welfare calculations may not be dramatically different.

2.2.2. Open-Economy Simulation Models

Whalley (1980) evaluates the effects of removing domestic factor taxes, using a
static trade model in which goods are mobile, but factors are immobile across regions,
and suggests that the current factor tax structure can produce significant terms-of—trade
gains. The result shows that significant welfare losses occur as a result of the elimination
of domestic factor taxes. This result, which contrasts with the result of conventional
closed-economy analysis, is explained by the fact that national terms-of—trade losses

outweigh the gains from removal of domestic distortions.

Goulder, Shoven, and Whalley (GSW, 1983) begin with the GEMTAP model,
which they developed over a period of years, along with Ballard, Fullerton, and others.9
The standard version of the GEMTAP model has a very cursory treatment of the foreign
sector, but GSW modify the GEMTAP model of the U.S. economy and tax system, to
include international capital flows.

Their results depend critically on whether a particular reform leads to an increase
or a decrease in the net rate of return to capital in the United States, as perceived by
foreign investors. For reforms that lead to an increase in this rate of return (such as
corporate tax integration), the model suggests that the U.S. will receive capital inflows.
As a result of these inflows of capital from abroad, the U.S. experiences significant
welfare gains. The welfare gains are driven partly by international capital flows, which
were ruled out by assumption in Whalley (1980). On the other hand, for reforms that
lead to a decrease in the rate of return in the long run (such as an increase in the
percentage of domestic saving that is taxed on a consumption-tax basis), the model
usually finds that capital will flow out of the U.S., and these capital outflows lead to
welfare losses. Even though the results are highly sensitive with respect to the values of
elasticity parameters that control the degree of international capital flows, they
demonstrate that our understanding of the effects of tax-policy changes may be altered
when we introduce international capital flows.

Thalrnann, Goulder, and DeLorme (1996) assess the effects on the U.S. economy

of tax-policy changes in foreign countries. They use an infinite-horizon model that

 

9 For a detailed description of a standard version of the GEMTAP model, see Ballard, Fullerton, Shoven,
and Whalley (1985). This model has the advantage that it can be calibrated to any desired savings elasticity
so that it avoids some of the problems of excessive intertemporal responsiveness.

10

displays a larger degree of intertemporal sensitivity than does the model of GSW.
However, their results are of some interest. For one thing, they explicitly incorporate
imperfect substitutability between foreign and domestic assets, which is consistent with
the econometric evidence on international capital mobility. Even for a fairly modest
policy change (an increase in depreciation allowances in the rest of the world), the model
of Thalrnann, et al., calculates a welfare improvement of 0.3 percent of GDP for the rest
of the world.

Mendoza and Tesar (1998) use a simulation model to assess the difference
between the effects of fundamental tax reform in a closed economy and in an Open
economy. Mendoza and Tesar employ some extreme assumptions. First, they use a
model with an infinitely-lived consumer. As mentioned above, a model of this type is
likely to produce simulated consumer behavior that is unrealistically responsive to
changes in rates of return. Indeed, when Mendoza and Tesar simulate the effects of
replacing the U.S. capital-income tax with a consumption tax in a closed-economy
setting, they find that the impact effect is for consumption to decline by 8.3 percent,
which seems extremely large and unrealistic. An infinite-horizon formulation tends to
overstate intertemporal effects. The second extreme assumption is that they consider a
world in which international capital markets are “fully integrated”; that is, capital is
assumed to be perfectly mobile, in spite of the evidence of substantial international
capital immobility. Thus, their simulations are likely to overstate the extent of the
international capital flow that would be caused by fundamental tax reform in the United

States.

11

Mendoza and Tesar suggest that the simulated welfare gains from replacing the
U.S. capital-income tax with a consumption tax are greater when the simulations are
carried out in an open-economy than in a closed-economy model. In the open-economy
model, the U.S. gains by 2.89 percent, which is about one-third larger than in the closed-
economy model.

Although these earlier studies shed some light, they can be improved upon in
several dimensions: (1) The papers mentioned above are based on models with only two
regions. (2) The model of Mendoza and Tesar has a fully integrated world capital
market, which greatly overstates the degree of international capital mobility. (3) The
models of Thalrnann, et al., and Mendoza and Tesar employ infinite-horizon formulation,
which tend to overstate the intertemporal effects of tax-policy changes. In this paper, I
address some of these issues. The model described in the next section is a static model
with four regions, in which capital is internationally mobile, but with incomplete
adjustment in the world capital market. The model is extended later to the dynamic

structure, which incorporates sequences of single-period equilibria.

12

CHAPTER 3

DESCRIPTION OF THE SIMULATION MODEL

3.1. Overview

The basic framework for my research originates with the Global Trade Analysis
Project (GTAP).lo The standard version of the GTAP model is a static, multi-sectoral,
and multi-regional model, in which each region’s final demand is determined by a
representative agent, who allocates expenditure across goods so as to maximize welfare.
The model described here is based primarily on Rutherford’s (1998) GTAP-data-based
CGE model.11

In some respects, the core model used here is essentially identical to the standard
GTAP model. First, the model is static.12 There is no capital accumulation in the model.
Consequently, in this version of the model, I may understate the distorting effects of
capital taxes, since the effects on saving decisions are not captured.13 Second, perfect

competition is assumed in all sectors and all regions. The production technology is

 

1° The Global Trade Analysis Project (GTAP) is a research program initiated in 1992 to provide the
economic research community with a global economic data set for use in quantitative analyses of
international economic issues.

it The standard programming language for GTAP data and modeling work has been GEMPACK. In the
GEMPACK framework (see Harrison and Pearson (1996)), the model is solved as a system of linearized
equations. Rutherford (1998) develops a GTAP-data-based model that is implemented as a nonlinear
complementarity problem in the GAMS programming language, and calls it the “GTAPinGAMS” model.
The database represents global production and trade for 45 countries, 50 connnodities, and five primary
factors. This database characterizes all transactions in 1995, and measures them in 1995 dollars.

'2 The model described here has the same time frame as the well-known model of Harberger (1962), which
is sometimes called a “medium-run” model. Since there is no capital accumulation, it is not a long-run
model. However, it allows reallocation of the existing world capital stock among all sectors in the world.
Thus, it is not a short-run model, either.

'3 The dynamic version of the model, in which consumers make a saving decision in each period, is

required to capture intertenrporal distortions. The model is extended later to the dynamic setting, along
lines of the model of Ballard, et al. (1985).

13

characterized as constant returns to scale (CRTS).l4 Third, trade is based on the
Armington assumption: Commodities are distinguished by their place or country of
origin. ‘5 The assumption of national product differentiation is particularly convenient,
because it allows us to use a very simple formulation to incorporate crosshauling (i.e., the
simultaneous export and import of goods in the same commodity category), which is an
important empirical feature of international trade. However, it should be noted that the
Armington assumption has weaknesses. Brown (1987) criticizes this approach to product
differentiation. She suggests that strong terms-of-trade effects can arise from the
monopoly power implicit in national product differentiation. Therefore, she suggests that
the Armington-type model may be fundamentally flawed for commercial policy analysis.
An alternative approach is firm-level product differentiation, in which products are
differentiated by firm, rather than by country of origin.16 (F inn-level product
differentiation implies imperfect competition. See footnote 14.)

However, the core model differs from the standard GTAP or GTAPinGAMS

model in some important ways. The model is modified in the following ways:

 

'4 The assumptions of perfect competition and CRTS have been criticized on grounds that they tend to
underestimate the welfare gains of trade liberalization. Recent work in international trade has focused on
imperfect competition and scale economies. Imperfect competition and scale economies are important
subjects for my future work.

'5 The products are nationally differentiated; for example, Japanese cars that are produced in Japan are
distinct from American cars. Refer to Armington (1969). Most empirical evidences support national
product differentiation: Jomini, Zeitsch, McDougall, Welsh, Brown, Hambley, and Kelly ( 1991) review the
literature on estimation of the elasticities of substitution between domestic and imported goods, and
conclude that those elasticities are low for almost all products. Reinert and Roland-Holst (1992) also
estimate Armington elasticities ranging a low of 0. l4 and a high of 3.49, which implies that commodities
are far from perfect substitutes.

'6 This approach is based on the work of Spence (1976) and Dixit and Stiglitz (1977). Brown and Stern
(1989) demonstrate that if the appropriate formulation is one of oligopoly with firm-level product
differentiation, the approach of national product differentiation will provide a poor approximation of the
welfare changes.

14

(1) Final demand in the standard GTAP is represented by the constant-difference-
elasticity demand system. In the GTAPinGAMS model, final demand is of the Cobb-
Douglas functional form. However, the utility function of the nested constant elasticity
of substitution (CBS) form is incorporated in the core model here. The elasticity of
substitution is allowed to vary between different groups of goods: the elasticity of
substitution is large for close substitutes, and small otherwise. As shown in Shoven and
Whalley (1992), the specific form chosen typically depends upon how elasticities are to
be used in the model. The demands derived from the Cobb-Douglas utility function have
the restrictions of unitary income and uncompensated own-price elasticities, and zero
uncompensated cross-price elasticities. These restrictions are typically implausible,
given empirical estimates of elasticities applicable to any particular model. However,
these can be relaxed by using a more general functional form, such as the CES form.

(2) The model incorporates a labor/leisure choice, by having leisure as an
argument of the utility function. Among many simulation studies, Auerbach and
Kotlikoff (1987), Ballard, Fullerton, Shoven, and Whalley (1985), Fullerton and Rogers
(1993), and Jorgenson and Wilcoxen (1998) have adopted this approach. It is not
possible to capture fully the distortionary effects of income taxes in a model with
exogenous labor supply (such as the standard GTAP model or the GTAPinGAMS
model). Since the model incorporates an endogenous labor-supply decision, the results
reflect the fact that the income tax is distortionary. In addition, consumption taxes have
an effect on the real wage rate, even if the net-of-tax nominal wage rate is unaffected.
The model also captures the fact that this effect on the real wage rate will lead to changes

in labor supply.

15

(3) The model incorporates a new method for calibrating the international capital
flows. In our model, investors hold internationally diversified portfolios.l7 Consumers
choose the portfolio shares of domestic and foreign assets, which are assumed to be
imperfect substitutes in portfolios. As a result of changes in the relative rates of return,
consumers are induced to alter the fractions of their financial wealth held in assets from
different countries.

(4) Various ad-valorem taxes are incorporated in the model, as in the
GTAPinGAMS model; these include output taxes, taxes levied on intermediate inputs,
export taxes, import tariff, and taxes levied on private demand. ‘8 Since there are no data
for factor taxes in either the GTAP or the GTAPinGAMS database, the data for capital
taxes and labor taxes, which are calculated on the basis of some statistics, are newly
incorporated in the dataset.19 The corporate income taxes and the property taxes are
treated as taxes on capital use by industry. The payroll taxes are treated as taxes on labor
use by industry. The commodity taxes and the selective excise taxes are treated as

consumer taxes on goods purchased.

 

17 The standard GTAP model assumes that international capital flows are allocated in response to changes
in regional rates of return. The GTAPinGAMS model assumes exogenous international capital flows: it
ignores the significant phenomenon of the expansion of international capital flows, so that it does not
account for the spillover effects of the tax policy initiated by a country.

'8 Since the GTAP database has no direct data for taxation, each tax rate is imputed, in the GTAPinGAMS
database, using the corresponding values that are measured at both the tax-free price and the tax-inclusive
price.

'9 I deal with the method of calculating factor-tax rates, in Chapter 5.

16

Figure 3-1. The Structure of the Production

D,-’ X ir

I” level: i if

Leontief technology over composite A
intermediate inputs and value added

 

2"dlevel: 101', 11);, 10'.-

CES function over capital
and labor inputs 0',

3rd level:

CES aggregation of domestic er' Kir

 

and imported intermediate inputs

CES aggregation of home-located
capital owned by home resident
and by foreigners

4'” level: ID 'I ID j; K," K 5’
CES aggregation of different

imported intermediate inputs 0'17

SI' 3" SI“
101.14%} ....... 1ng

l7

3.2. Structure of the Static Model
3.2.1. Production Sector

A “tree”, as shown in figure 3-1, represents the structure of the production side of
the model. There are two types of produced commodities, domestic outputs and exports,
which are assumed to be prefect substitutes. The assumption of perfect substitution is
based on the fact that the goods produced for domestic consumption are nearly the same

as those produced for exports: Toyota cars consumed in Japan are nearly the same as

those consumed in the United States. Thus, the production activity levels, Qir , are

represented as just the sums of domestic outputs and exports:
Q{ = D{ +X,-’, (3.1)

where the Dir are domestic outputs for good iproduced in region r, and the X ,-r are

exports for good iproduced in region r.

Composite intermediate inputs and value added are combined by a fixed-

coefficient technology to generate these outputs, Qir :

Q{ = miniIDfi,ID§,-, ....... ,ID;,,VA{(L;,K{)}, (3.2)

where the ID}- are the intermediate demands for good j used in producing good i in

region r, the VAl-r are the value-added functions, the L:- are the labor inputs used in the

18

production of good i in region r, and the K i" are the capital inputs used in the production
of good i in region r.

The primary factors, labor and capital, are combined according to a value-added
function. Labor inputs are assumed to be mobile between production sectors, but not
internationally. Capital inputs are assumed to be mobile across sectors and regions. For
each sector in each region, a CBS fimction is employed to describe the functional

relationship between the two primary factors:

0:
i—l Ui—l O'i—l

VA , VA .
VAl(L.’-.Kl)=wi a.-' Li“ +[1—ar )xr “1 , (3.3)

 

q

 

VA
where the w,- are scale parameters, the a: are share parameters, and the 0',- are the

elasticities of substitution between labor and capital in sector i.

Cross-ownership of capital is allowed in the model: both home residents and
foreigners may own domestic capital. Therefore, producers make decisions about
choosing capital owned by home residents and capital owned by foreigners. In the
analysis, home-located capital owned by home residents and home-located capital owned
by foreigners are assumed to be perfect substitutes, which means that producers are
indifferent regarding whether their capital is owned by domestic residents or by
foreigners. With infinite elasticities of substitution, the capital inputs are just the sums of

capital owned by home residents and capital owned by foreigners:

19

Ktr(Krrr’Kisr)=Ktrr+Kiv’ (3'4)

where the K i' r are home-located capital owned by home resident and used in sector i,

and the K ,5 r are home-located capital owned by foreigners and used in sector i.

The cost fimctions are represented as:
C,-r(L;-',K,-r)= wa +rKl-r, (3.5)

where the w are wage rates and the r are rental rates in region r.

Minimizing the cost function (3.5) subject to a given technology (3.3), and

manipulating some equations, gives us the unit cost functions, of (w, r):

 

VA 0" VA 0" l-Ur
cir(w,r)=i{[air ] wl—a’ +[1—air ) rl—a‘} , (3.6)

 

 

 

 

01
l l ‘l—Ui ‘ 1-0',
VA
r \ r
L? (w,r)=Q_li airVA +[l—afVAJ a, r f (3.7)
. VA
W' (l—air )w
_ J j

 

 

20

and

 

'- rVA “1‘01 l—O’i
l—ai W

l . (3.8)

r

r
K{(w,r)=—'i(1-a{ +a,
i 61,- f

 

VA ) VA

 

 

 

 

Under the Armington assumption, which treats products in different regions as

qualitatively different across countries, intermediate input demands, ID 1',- , are

represented by a CBS aggregation of domestic and imported intermediate inputs.

Off

 

0' ......

1 1
,- r ID ,7- yr r ID 5rd}: 01—1
ID-- =5}, a-- [DJ-,- a,-.- + 1—a-,- IDj. 0;.- , (3.9)

 

 

J1 J1 J

[D
where the 51-,- are scale parameters, the 01;, are share parameters, the ID},r are
domestically supplied intermediate input demands for good j used in producing good i in
region r, the ID if are imported (from all foreign regions 3) intermediate input demands

.. are the elasticities of

for good j used in producing good i in region r, and the 0'],

substitution between domestic and imported intermediate inputs.
The intermediate input demand functions, ID},r and ID"? have the same form as

J“

the factor-demand functions, (3.7) and (3.8):

 

20 See section 1 in the appendix for details.

21

 

 

 

 

 

 

 

 

ji

 

 

 

T1_Uji l—O'j,’
ID
D'-- ID ID) a'-- q‘-,-
10;; = 6" la},- +[1—a5, J 1' ID] i (3.10)
.. r r
1' (l-aji )jS
L L _
and
' ID ‘H’fii r—aj,
r 1‘61}: qji
v fl rm rm
IDji — i l—aji +aji i , (3.11)
511' r ID 3
aji qji
k h d J

 

 

where the q ;,- are the producer prices of the domestically produced intermediate inputs,

and the qj-i are the after-tariff producer prices of the foreign inputs.

Sf

Imported intermediate input demands, ID j,- , are also represented by a CES

aggregation of the imported intermediate inputs from different regions:

5
aji

ID if] Girl
sr _ s Sic" 5..
[Dji _;ji Zafl ([Dji J 0’}, ,
5k

 

(3.12)

22

where the [Di-fr are imported (from region sk) intermediate input demands for good j

used in producing good i in region r, and the oj-l- are the elasticities of substitution

among imported intermediate inputs from different regions.

As in the case of intermediate input demands, imported intermediate input

demands, IDjfr , are represented by the formula:

 

0'},
[D s ——s
[Djfr = {/1 J; 216,}. ) (qu) , (3.13)
.. k
jl q .. 5k
11

where the qj-f are the after-tariff produce prices of foreign country s k .

3.2.2. Demand Sector

A representative agent determines final demand in each region. Figure 3-2 shows
the structure of the decision-making process of the representative agent as a “tree”.

I introduce the asset-holding function, to allow the consumer’s internationally
diversified portfolio. On the first level, the consumer chooses the shares of domestic and

foreign assets, which are assumed to be imperfect substitutes in financial wealth.21 The

consumer’s asset holdings in region r, A’ , are represented by a CBS function:

 

2' The assumption that domestic and foreign assets are imperfect substitutes in the consumer’s portfolio is
consistent with observed home-country preference; home-counny assets typically make up the bulk of
portfolios, even when rates of return on foreign assets are comparable or higher. See Thalrnann, Goulder,
and DeLorme ( 1996). French and Poterba (1991) empirically examine the international asset-ownership
patterns, and find that most investors hold nearly all of their wealth in domestic assets.

23

Figure 3-2. The Structure of Utility

1" level. """""" g,
CES aggregation of income from domestic capital 5 A
and income from foreign capital '

2’” level: H r _____________________________

CES aggregation of aggregate
consumption and leisure //\>\od

3’“ level: Cr 2'
CES aggregation of consumption

demands among difi’erent sectors 0'“.

h .
4’ level. C,” c; of

CES aggregation of domestic
and imported commodities 03m

5"I level: C i” C ,3 r
CES aggregation of difi’erent

imported commodities 0mm

 

CW 032' cr‘k’

l l l

 

A
A at: -1 A . or: -1 0,5 -l
Ar(rK"',r*KrS)= ar (rKrr 0;; +[l—ar )(r Krsi 0;}. ,

A . .
where the or are share parameters, the of; are the elasticities of substrtutron between

domestic and foreign capital assets, the rK " are income from domestic assets (home-

located capital invested by home resident) in region r, and the r*K '3 are income from

foreign assets (foreign-located capital invested by home resident) in region r.22

The consumer maximizes the asset-holding function, Ar , subject to the

constraints, K = K ” + K rs , where K is fixed. The assumption of fixed number of

capital invested by domestic residents is consistent with Harberger-type assumptions.23
These asset-holding functions can be represented by 2’ , which is a monotonic

transformation of Ar :

 

22 In the model, the rK 's , not the K 'S themselves, are used as the arguments of the function, in a sense

that the consumer cares about flows of income he gets from capital, not the capital itself. The r‘K rs are
also the result of a CBS aggregation.

23 In the standard Harberger model of a closed economy, the total capital stock is fixed, but capital is
mobile across sectors. It is as though owners of capital have a certain number of machines and rent them
out to whichever sector offers the highest after-tax return. In that spirit, I assume that U.S. citizens own a

fixed number of machines: K = K n + K rs , and have some allocation between K rr and K rs in the
base case. When a policy change changes the after-tax returns on domestic and foreign investments, they
may want to reallocate. Literally, this means that if the after-tax return goes up domestically, they will take
some of the machines they were renting to frrm in Europe and bring them back to the U.S. to rent them to
firms here. This seems a little unrealistic, but it is consistent with Harberger-type assumptions.

25

 

 

(3.15)

Differentiating Z r with respect to the choice variable K '7 yields the first-order

condition:

 

Xi

 

 

04—1

 

i=0. (3.16)

 

Totally differentiating with respect to (r / r') and K " , and manipulating it, I get the

elasticity of demand for domestic capital with respect to the ratio of domestic and foreign

rental rates, 77KB:

26

 

 

 

 

 

 

 

-1 A
(r) ar Krr 4(CJGn D+0rs:r1
6K” * r K
771(1)E ” = 2 , (3.17)
a[—-] K BF—D
*
r
where
A W
A UrSA-l 04—1 _ 0;; 1
.r (1.) (Kw .4 .1...“ (Mn .4 .,
r 04—1 —1 _1‘
A — -
Dakar [ t 0,, Krrafs -(1—ar )(K—K” 0,1),
r
L J
r 04—1 W

A A —-l A _ —l
and F-=-<ar (4*) 0,, K"a;; +(l—a' )(K—K" 0;: w
r

 

 

The elasticity of demand for domestic capital, ’lKD , has a positive sign, under the

assumption of home asset preference.24 The formulation of (3.17) has the property that as

t . . .
(r / r ) Increases, the consumer chooses a larger K " . By the unrts conventron,

r = r’ =1, equation (3.17) can be written as:

 

2’ B and F have positive signs, but D is undetermined. In addition, the numerator and denominator are also
undetermined. However, for the analysis, home residents are assumed to prefer to invest more money on
home-county assets. In the benchmark, the share parameters for domestic assets are set to 0.92~0.96.

With the assumption of home-asset preference, D and the denominator have positive signs. If a ,1 is

greater than 1.0, the numerator is definitely positive. Even though 0' :1 is less than 1.0, the numerator can

be positive, under the assumption of home asset preference. Consequently, the sign of 77KB is positive.

27

-1 A

A -— 0' —l

a’ Kr’ag D+ ’3"
K

 

77KB = (3.18)

BF-DZ

Using equation (3.18), the asset-substitution elasticities, 01:, are calibrated to

match with desired levels of the elasticity of demand for domestic capital with respect to

the ratio of domestic and foreign rental rate.
On the second level, the consumer maximizes the utility function, H r , subject to
a budget constraint that takes K " and K '7 , which were deriving from maximization of

Ar , as given. He maximizes the utility function, which is a CBS aggregation of

consumption and leisure:

0c!

 

 

Oct—1 Oct—1 O'd-l
H'(C’,t’)= p’ Cr 0.. +(1—p’ )6” ac. , (3.19)

C
where the ,6 r are share parameters, the ac); are the elasticities of substitution between
consumption and leisure, the Pcr are the prices of the composite consumption goods in
region r, the P[ are the prices of leisure in region r, the C r are the composite

consumption goods in region r, the (3’ are the values of leisure in region r.

The consumer’s budget constraints are given by:

28

Pch' + Pflr = wE’ +71?” +7?" + TR’ a 17, (3.20)

where the er are region r’s expanded income, which includes the value of the

consumer’s labor endowments, the value of the consumer’s capital income from domestic

capital, the value of the consumer’s capital income from foreign capital, and transfer

payments (T Rr ).25 The government collects taxes and tariffs, and all tax and tariff
revenues are assumed to be transferred to the agent in each region, in lump-sum

fashion.26 The Oct parameters are calibrated to match with desired levels of the labor-
supply elasticities.

Constrained maximization of the sub-utility functions H r provides the demand

 

 

functions:
KC 0C! Yr
C’ = r 1 a (3.21)
P C001 1-0, C ct l—od
" Pg ‘ [1-[3’ ) P,
and

 

25 Shoven and Whalley ( 1992) distinguish “expanded income” (which includes the value of the total
endowment of time) from observed money income. On this level, rK rr and r*K rs are taken as given.

. . . . t
Of course, 1n general equrlrbrrum, r and r are endogenous, but they are exogenous from the consumer’s
point of view.

26 In the closed-economy model, as Ballard (1990b) points out, when taxes are rebated to the consumer in
lump-sum fashion, taxes in the model do not have any income effects. However, there is still a possibility
of income effects, to a small degree, if taxes are collected from both domestic and foreign agents, but the
revenues are rebated only to domestic consumers.

29

l—flr er
Pr Co‘ce 1- C 0c: H,
e r r 05 r r cl
,8 P +(1—[3 ) Pg

 

 

(3.22)

C

On the third level, the consumer maximizes the utility fi'om aggregate
consumption, which is represented by a CES aggregation of consumption demands

among the different sectors:

 

 

UCC
C U“ 1 ace—1
C'(C1’ , ..... ,C,-’ )= Zfil Cl 0.. , (3.23)
1'
subject to the constraint:
ZPJC,’ = Y{ — PM a H, (3.24)

l

C
where the ,8,’ are share parameters, the ace are the elasticities of substitution among
different commodities, the Pf are the prices of the consumption goods 1' in region r, and
the C i’ are the levels of consumption of good i in region r.

Constrained maximization of the sub-utility functions C r gives the demand

functions:

30

 

C,-' = —L— 2 . (3.25)

On the fourth level, the consumer decides whether to buy a commodity at home or
abroad. According to the Armington assumption, commodities are distinguished by their
place of origin. Under this assumption, the consmnption of good i is represented by a
CBS aggregation of domestic and imported goods. The consumer maximizes the utility

functions:

1'
0’dm

 

 

D Jilin-l Odin-1 0'51," -1
Cir (Cirr’CiV)= fiir Ci" 0:1»: +(1-I6ir )Ciw adm a (326)

subject to the constraint:

P,” C,” + gsrcf’ = V; — Z Pfcf a 13’, (3.27)

j¢i

D .
where the ,8; are share parameters, the 021m are the Armington elasticities of
substitution between domestic goods and imported goods in sector i, the P,” are the

consumer prices of domestically produced goods in sector i and region r, the Pi” are the

31

consumer prices of imported goods in sector i and region r, the C i" are the levels of

consumption of domestically supplied goods in sector i and region r, and the C ,3 r are the

levels of consumption of imported (from all foreign regions s) goods in sector i and

- 7
regron r.2

Constrained maximization of the sub-utility functions C l-r provides the demand

 

 

functions:
D 0'51»:
." Y;
C1" = —-—P',, ,- 1. (3.28)
- 0' i cdm i
z ,0 dm ”pad", ,0 ”lead",
1' Pi +[1- i Pi
and
r'
I'D adm Yr
Csr = 1— i 3
I P,” 003m r—af, D “rim 1-af,
r rr m r sr m
.3: Pi +(1‘16i ) Pi

(3.29)

Finally, on the fifth level, the consumer maximizes aggregate consumption of
imported goods, which are represented by a CBS aggregation of different imported

commodities:

 

27 In equation (3.27), the constraint states that the consumer’s expenditure on the goods in sector i cannot

exceed Y 3r . The Z P jr C 5 indicate the value of the consumption for the commodities in sector j, and
j ¢i

must be substracted from Y 2r to determine the amount of income available for the commodities in sector 1'.

32

1'
0mm

 

 

S Ufnm-‘l Jinn! —1
cf’(cf", ..... ,ka’) = Z [3,? Cf“ of... , (3.30)
k
subject to the constraint:
ZBs’rCf’r = Ysr -Pr”C.-” 5 Y4". (3.31)

k

where the [3,5 are share parameters, the aim are the Armington elasticities of

substitution among imported goods in sector i from different regions, the Pi” are the

skr

consumer prices of imported (from s k ) goods in sector i and region r, and the C ,- are

the levels of consumption of imported (from s k ) goods in sector i and region r.28

Constrained maximization of the sub-utility firnctions C ,5 r gives the demand

functions:

 

28 In equation (3.31), the constraint states that the consumer’s expenditure on irrrported goods cannot

exceed Y I . The Pi” C 1'” represent the value of consumption of domestically supplied commodities, and

must be subtracted from Y 3r to determine the amount of income available for imported goods.

33

(3.32)

 

3.2.3. Zero-Profit Conditions

In this model, competitive producers operate according to constant-returns
technology, and earn zero profit. For the producer, the market value of a unit of output
equals the unit cost of production. The market value of a unit of output is the value of
sales in the domestic and export markets, net of indirect taxes. The unit cost of

production includes the cost of primary factor inputs and intermediate inputs with taxes:
D D X X Q
[qr a: wt or )[1 -t.-' ]

,F

F F ID 1D
:20; qt (Ii-t; )4—2‘1} q;i[1+t;i ], (3.33)
F .

D X
where the a: are the unit supply fimctions of domestic outputs, the a ,r are the unit
. ,F , .
supply functrons of exports, the a ,- are the unrt factor-demand functrons for labor and

. ID . . . . Q
caprtal, the a 5,- are the coefficrents of 1ntermedrate Inputs, the t{ are the output tax

34

F [D , ,
rates, the t{ are the factor tax rates, and the t}- are the tax rates for rnterrnedrate

inputs.29
In equilibrium, the value of a unit of imports equals the PCB. price, gross of

export tax, the transportation margin, and the applicable tariff:30
pi = 2a? {A (1 )+ }[1 ), (3.34)
S

M X
where the pf are the domestic C.I.F. prices in region r, the p ,5 are the PCB. export
. . rs M . . . sr X
pnces from regron s, the a i are the unrt nnport-demand fiinctrons, the t i are the

M
export tax rates, the t," are the import tariff rates, the r,” are the unit transport cost

coefficients, and the pT are the unit costs of transportation on all commodity trade

flows.3 1

 

L

K
29 q :- = W, and ql-r = r. See the appendix for unit-supply and unit-demand functions in detail.

30 The import aggregation activity, which defines the aggregation of imports by trading partner, is the most
complex component of the model. The import activity applies export taxes and import tariffs on all
bilateral trades, and it also applies transportation margins on all bilateral trades. In this sense, in the model,
two types of inputs are set to be applied to the import activity: one is F.O.B. payments to producers in
different regions, and the other is inputs of transportation services. Many multi-region CGE models have
neglected the presence of international transportation costs, due to difficulty in data availability. However,
Tsigas, Hertel, and Binkley (1992) estimate these margins from pooled time-series/cross-section bilateral
trade data. This is further refined in Gehlhar, Gray, Hertel, Huff, Ianchovichina, MacDonald, McDougall,
Tsigas, and Wigle (1996), where a trade-margins function, depending on distance and volume, is explicitly
estimated. The resulting margins are incorporated in the GTAP database. In the dataset, the values of
transportation cost in the manufacturing sectors are about 3~5 percent of the values of commodity trades,
and those in the primary-material and agriculture sectors are about 7~8 percent of the values of commodity
trades. See Hertel, Ianchovichina, and MacDonald (1997).

3 l The model assumes that export tax applies on the F .08. prices, net of transport margins, while the
import tariff applies on the C.I.F. prices, gross of export tax and transport margins. See Rutherford (1998).

35

Armington aggregation functions transform domestic and imported goods into
composite goods for private demand and intermediate input demand. Zero profit for the

private goods provides the following equilibrium identities:

1
im 1_ [m [m 1__ int j—
B’={fll’”" It” 0" +(1—fltDlg" It” 0" }‘ 0"“. (3.35)

where the ,6? are share parameters, the 09m are the elasticities of substitution between
domestic goods and imported goods, the Pir are the prices of the consumption goods i,

the P,” are the consumer prices of domestically produced goods i, and the P,” are the

consumer prices of imported (from all foreign regions 3) goods i. Similarly, zero profit

for intermediate input demand gives the identities:

l

i i i i i
r 100d»: rrl'adm ID dm sr1“"dm l-Ud

where the q ;,- are the prices of the intermediate inputs, the qz are the prices of the

intermediate inputs which are produced domestically, and the q if are the prices of the

intermediate inputs which are imported (from all foreign regions 3).

36

3.2.4. Income-Balance Equations
Consumer expenditures are the sum of labor earnings and capital earnings (capital
income fi'om domestic capital plus capital income from foreign capital), and transfer

payments:32

. Y D X
CEr=wEr+rKrr+r KrS-l-Ztir (qu Dir+qir Xir)

l

[D [D F F F C
r r r r r r r r
+ E tij qlr [Di ‘1' E ti qi FDi + E ti pi Ci
.. i

y Fi
X M X X
+25“ Pr‘rsMirs +Zt'rs [‘01s Mlsr(1+tlsr ]+pT7}er, (3.37)
is is

ID ,
where the CE r are consumer expenditures, the ID,’ = Z Qfa} are intermedrate
f

L
demands for sector i in region r, the FD,’ are labor demands for sector i in region r, the

K C
FD; are capital demands for sector i in region r, the t ,r are the tax rates on private

demand for sector i in region r, the M i" S are import demands from region s, and the

 

’2 All tax and tariff revenues are assumed to be rebated to the consumer in lump-sum fashion.

37

Ti” (= If s M i' S ) are real transport costs (which are assumed to be proportional to trade)

for sector i in region r.

3.2.5. Market-Clearance Conditions

In the domestic market, domestic output equals the sum of domestic demand for

consumer goods, and domestic demand for intermediate inputs:
D{ = C,” + 1D,". (3.38)

Similarly, in the import market, the aggregate supply of imports equals aggregate import

demand for private consumption and intermediate inputs:
M,-' = C,” + IDg’r, (3.39)

where M i’ are the aggregate supply of imports. In addition, export supply equals import

demand across all trading partners, plus demands for international transport:

X,’ = 2M,” + To; . (3.40)

S

When perfect substitution between domestic outputs and exports is assumed (the
elasticity of transformation is infinity), the market-clearance condition for aggregate

demand is:

38

Q; = C,” +113,” +2114,” +TD{ . (3.41)

S

As previously stated, private demand and intermediate input demand are defined

as Armington aggregations of domestic and imported inputs:

Udm

 

 

 

 

D odm-l D Odin-1 O'dm-I
C.’(C.-"’,C:’)= A.- C.” 0),, +(1-fl1- is” 0,, (342)
and
O'j"
ID O'ji-1 D 0'], 1 01-1
ID},(ID§,F,IDj;-’)=gfl (1;,- IDjr-f 0)) +(1—afi)’ ID}; a). .
(3.43)

In factor markets, primary factor supply equals primary factor demand. Labor
inputs are mobile between sectors, but immobile between regions. Capital inputs are
mobile across sectors and regions. Therefore, the market-clearance conditions for these

factors are:

L’ = 21.; (3.44)

and

39

K' = 2(K," + K,” ), (3.45)

i

where the Lr are the labor supplies in region r, the K r are the capital supplies in region

r, the L; are the labor demands for sector i in region r, the K {r are the demands for

home-located capital owned by home residents for sector i, and the K ,5 r are the demands

for home-located capital owned by foreigners for sector i.

40

CHAPTER 4

MODEL CALIBRATION

In determining the results of policy simulations, the parameter values for the
functional forms are very crucial. The procedure most commonly used to select
as 33

parameter values is “calibration . The goal of calibration is for the researcher to

impose desired elasticities upon the model.

4.1. Exogenous Parameters

The benchmark data set is used for determination of parameter values, which are
consistent with that observation. However, for the CES function, the benchmark data set
alone is not sufficient to determine all parameter values of the model tmiquely. This
under-identification problem is solved by exogenously specifying a sufficient number of
parameters from the econometric literature. The exogenous parameters are summarized
in Table 4-1.

On the production side of the economy, the elasticities of substitution between

labor and capital, 0',- , are extraneously specified. I adopt the sector—specific SALTER

substitution elasticity values provided by J omini, Zeitsch, McDougall, Welsh, Brown,

Hambley, and Kelly (1991). They are based on a review of the international cross-

 

” Calibration involves a deterministic approach to specifying parameter values to be used in an applied
general equilibrium model. The parameter specification methods in CGE models, which use deterministic
calibration rather than stochastic estimation, are often troubling to econometricians. However, this
calibration approach is widely used, for several reasons: (1) In some applied models, many thousands of
parameters are involved, and to estimate simultaneously all of the model parameters using time-series
methods would require either unrealistically large numbers of observations or severe identifying
resnictions. (2) Benchmark data sets are formulated in value terms, and their decomposition into separate
price and quantity observations makes it difficult to sequence equilibrium observations with consistent
units through time. See Shoven and Whalley (1992) for details.

41

section studies which estimated these parameters for various industries: the values are
1.19 for the primary-material sector and non-durable manufactures, 0.56 for the
agriculture sector, 1.26 for durable manufactures, and 1.35 for the service sector.34 The
high degree of substitutability in the service sector is caused by the high value of 1.68 in
the sector of trade and transportation, which is a sub‘sector of the service sector.

On the demand side, home residents are assumed to prefer to invest more money
on home-country assets: In the benchmark, the U.S. consumer is assumed to hold 92
percent of total assets in domestic assets and 8 percent of total assets in foreign assets in
his portfolio; the consumers in other regions are assumed to hold 92~96 percent of their
domestic assets and 4~8 percent of foreign assets in their portfolio. This assumption is
based on the empirical examination of international asset-ownership patterns, provided
by French and Poterba (1991). They find that that most investors hold nearly all of their
wealth in domestic assets: The domestic ownership shares of the U.S., Japanese, and the
UK. investors are estimated as 92.2, 95.7, and 92 percent, respectively.

Based on the econometric literature, the uncompensated labor-supply elasticity,

77 L , is assumed to be 0.15 in every region.35 Simulations will be performed using these

central values, and then sensitivity tests with different sets of elasticities of substitution

will be run.

 

3" The values are modified to fit in the model, using a weight parameter. Whalley (1985) uses the value of
factor substitution elasticities: 0.6 for the primary-material and agricultural sectors, 0.8 for manufactures,
0.9 for non-durable manufactures, and 0.7 for the service sector.

3’ Surveys of the labor-supply literature can be found in Killingsworth (1983), Burtless (1987), and
Heckman (1993). See also Fuchs, Krueger, and Poterba (1998).

42

Table 4-1. Exogenous Parameter Values

 

 

 

 

U.S. E. (1., Japan, ROW
(Production Side)
Elasticity of Substitution between Labor and Capital (03-)
Agriculture 0.56 0.56
Primary Materials 1.19 1.19
Durable Manufactures 1.26 1.26
Non-durable Manufactures 1.19 1.19
Services 1.35 1.35
Share of Capital Owned by Home Resident (on-K ) 0'91 0'95
(Demand Sidel
Share of Domestic Assets in Portfolio (0!” ) 0‘92 0924196
Uncompensated Labor—Supply Elasticity (n L ) 0.15 0.15

 

 

4.2. Calibration Issues

On the demand side, the elasticity of substitution between consumption and

leisure, 0'0) , the asset-substitution elasticity, of, , the elasticity of substitution among

different domestic goods, occ , and the trade elasticities of substitution, 03m and aim ,

are calibrated, using some values specified exogenously. The calibrated parameters are

summarized in Table 4-2.

43

First, I consider the calibration of the elasticity of substitution between
consmnption and leisure. On the second level, the consumer decides on aggregate

consumption and leisure. The demand fimction for leisure is:

l
b
O
h<

 

_, 4.1
p, Q ( )

Cool l'act C cl l'acz .
where Q = ,6 PC + 1— ,6 Pg . Then, the uncompensated lersure-
demand elasticity, I” , is:

at P) _ PgE _ P)t(1—ac,.)_

E—— 0' . 4.2
’7! 6P3 5 Y1 Y1 c! ( )

 

The uncompensated labor-supply elasticity, r) L , can be expressed in terms the amount of

labor supplied, L , or in terms of the amount of leisure, i :

 

 

=a_L_1fg__a(r:—t) P) _ aE_at P) (43)
‘apgl. 6P) E—e a1?) 6P) E-e' '

44

. . . . 6E
Manipulatrng equation (4.2) and equatron (4.3), and usrng the fact that -a—P- : 0 , an
2

expression for the leisure-demand elasticity is derived in terms of the labor-supply

elasticity, and the time-endowment ratio, (13:36

E-Z l
=— ———=— —— . 4.4
772 771. g 77L[¢_1) ( )

Substituting equation (4.8) into equation (4.6), and solving it for Oct? gives:

 

0c! = - (4.5)

The elasticity of substitution between consumption and leisure depends on the

uncompensated labor-supply elasticity, and on the time-endowment ratio.

 

E
36 The “time-endowment ratio" is defined as (D = I , where E is the consumer’s endowment of time, and

L is the amount of labor that is supplied in the base case.

45

Table 4-2. Calibrated Parameter Values

 

 

U.S. E. (1., Japan, ROW

T ime-Endowment Ratio (CD) 1.32 1.35~1.41
Elasticities of Substitution:

Consumption and Leisure (ace) 1.13 0.92~1.08

Domestic and Foreign Assets (0'4) 1'92~2 '01 1'3 8~1 '53

Dzflerent Domestic Goods (ace) 3 0.25~1.55 0.25~1.55

Domestic and Imported Goods (051»: ) 0'50~3'10 0'50~3 '10

Diflerent Imported Goods (afnm) a 1°00~6°20 LOO~6°20

 

 

a. These values are arbitrarily chosen, based on the calibrated 02m .

Researchers have used an extraordinary variety of values for the time-endowment
ratio, (1). One strategy is to select a value for (D , based on an essentially arbitrary
assumption about the number of hours available. The value of (D is given as 1.75 in
Ballard, Fullerton, Shoven, and Whalley (1985), 2.5 in Auerbach and Kotlikoff (1987),
3.846 in Greenwood and Huffman (1991), and 5.0 in Mendoza and Tesar (1998). If the
value of the time-endowment ratio is specified exogenously, as in the literature above,

equation (4.5) can be used to calibrate the elasticity of substitution, ac) , very precisely to

a desired value of the uncompensated labor-supply elasticity, n L . However, as Ballard
(1999) points out, the values chosen arbitrarily (1.75 ~ 5.0) lead to exceptionally large

values of the total-income elasticity of labor supply, 77, , in absolute value. The value of

46

(D that is necessary to produce a reasonable value for 77 I is far lower than virtually all of

the values of (I) that have been chosen arbitrarily in the simulation literature.37
A better strategy is to choose the desired value of the total-income elasticity of

labor supply, 17 1 , and to solve for the value of (D that is consistent with that elasticity.38

By the Slutsky decomposition, the difference between the compensated and
uncompensated elasticities is equal to the absolute value of the total-income elasticity of

labor supply:

*
77L — 771, = ‘77] - (4-6)

Based on the econometric literature, a value of -0.1 for 77 I would be reasonable. Since

77 L is exogenously given as 0.15, the desired value of 772 would be 0.25.

Therefore, I begin with the expenditure function to derive the compensated labor-

supply elasticity.

1
E -_- V{s"cl Pcl—a“ + (1 - more Pg‘ad }1—0c( , (4.7)

 

37 In the model of Ballard (1990b), the value of (D that is consistent with the reasonable value of t], , is

calibrated as 1.213. He also shows that the values of (D chosen arbitrarily, 2.5 and 5.0, produce
respectively -0.4414 and -0.6787, which is far larger than the most of the econometric estimates of the
total-income elasticity, -0. 1.

38 This follows Ballard (2000) closely.

47

where V is indirect utility function. Shephard’s Lemma tells us that the compensated
leisure-demand function is the derivative of the expenditure function with respect to the

wage rate:

 

ac!
LE = 2* = V(1_ mace 10; ct {pace rug—“ct + (1 — mac! 102—“d il-ace . (4.8)
6P);
Then, the compensated leisure-demand elasticity, 77; , is:
20'“) —1 Oct

0'63 Pgdci'i'1 (1_ fl)0'c( P172001 0 1-0c( _ Pgad _IQ 1"Old

 

. ._. 24 a _
g _ 6Pg 3* ac!
Q l—act
(4.9)
L
where o = V{5°’ct 1061"” + (1 — mac! Pj’ac‘ }1-ae . Using equation (4.4), the
compensated leisure-demand elasticity converts to the compensated labor-supply
elasticity, 772 :
.. P l’
772 =(1—<D)ace[—;—— ] (4.10)
1

43

This equation can be used to calibrate the time-endowment ratio, (1) , that is consistent

with the desired value of the compensated labor-supply elasticity, n2 .39 The value of
172 will increase monotonically with the value of (1). Thus, the absolute value of 77, ,

which has a positive relationship with the value of 772 , will increase monotonically with

the value of (1).

Second, I calibrate the asset-substitution elasticity, which may play a relatively
large role in an open—economy model. The consumer’s share of domestic assets is
expected to increase when domestic rental rates are relatively higher. How much are
domestic assets in his portfolio increased? The responsiveness of the decision is

controlled by the elasticity of substitution between domestic and foreign assets, 0,1.

This elasticity of substitution is directly related to international capital mobility. A lower
value means greater immobility of international capital. The lower value is supported by
Feldstein and Horioka (1980), who report empirical evidence suggesting that capital is
quite immobile internationally. Previous papers have employed fairly arbitrary
assumptions regarding the value of this parameter. Gravelle and Smetters (1998) take the
asset-substitution elasticity as 3.0. Thalrnann, Goulder, and DeLorme (1996) take it as
4.0. My goal is to calibrate this parameter more precisely, based on the econometric

evidence.

 

39 Based on the calibrated time-endowment ratio, the elasticity of substitution between consumption and
leisure is re-calibrated.

49

Table 4-3. Elasticity of Capital Abroad and
Calibrated Asset-Substitution Elasticity

 

 

 

Elasticity of Capital Abroad (77101) a Elasticity 0f Calibrated
Domestic Capital 0. :19
(771(1)) b

(as)

Altshuler, Grubert, and Newlon (1998) 2.80 0.24 1.92

Grubert and Mutti (2000) 3.23 0.28 2.01

(E. U.. Japan. ROW)

Boskin and Gale (1987) 1.91 0.12 1.53

Slernrod (1990) 0.77 0.05 1.38

 

 

a. The UKA in the U.S. represents the elasticity of U.S. direct investment abroad,
and the UKA in other regions represents the elasticity of U.S. foreign direct
investment.

b. The elasticities are calculated, using 77KB = UKA x (1 — a A )/ a A , where (1’4 is the
share of domestic assets in portfolio.

In Chapter 3, the equation for the elasticity of demand for domestic capital with
respect to the ratio of domestic and foreign rental rates, ’7KD , was derived from the

consumer’s utility maximization. As shown in equation (3.18), the elasticity of demand
for domestic capital depends on the amount of domestic capital, K " , and the asset-
substitution elasticity, 0,1. Therefore, the asset-substitution elasticity can be calibrated,

using the value of 77KB , which is calculated based on the value of the elasticity of

demand for capital abroad, 77“ , which, in turn, is taken from the econometric literature.

50

As shown in Table 4-3, if I use the value of the elasticity of capital abroad
provided by Altshuler, Grubert, and Newlon (1998), I calibrate the asset-substitution
elasticity for the U.S. to be 1.92. If I use the elasticity estimated by Grubert and Mutti
(2000), the calibrated asset-substitution elasticity is 2.01.40 Similarly, the asset-
substitution elasticities in other regions of the world are calibrated as 1.38 and 1.53,
based on the values of the elasticity of capital abroad, provided by Slernrod (1990) and
Boskin and Gale (1987). Therefore, in this analysis, I take the central values of the asset-
substitution elasticity in the U.S. and other regions as 2.0 and 1.5, respectively, although I
will also perform sensitivity analysis.

Finally, I consider the calibration of the elasticities of substitution in the third,
fourth, and fifth level of consumer’s decision. On the third level, the consumer
maximizes aggregate consumption, which is represented by a CBS aggregation of

consumption demands among different sectors. The demand function for goods is:

C r
_ 2?; Y2 (4.11)

 

4° Only available one from the literature is the value of ”KA with respect to r* , not the value of ”M
with respect to (r‘ / r). For calibrating asset-substitution elasticity, I use this available one as a proxy for

the value of 77KA with respect to (r‘ / r), based on the idea that investment decision depends on the
relative size of each region’s r , rather than on the absolute size of it. Altshuler, Grubert, and Newlon
(1988) estimate the elasticity of real capital abroad with respect to after-tax returns (1] KA) as 2.80. Based

on this information, and considering the share of domestic assets ((1 A ) under the assumption of home-
country asset preference, I calculate the elasticity of domestic capital ( 77KB) as 0.24. I also calculate the

elasticity of domestic capital as 0.28, using the value of the elasticity of capital abroad, 3.23, which is
estimated by Gruber and Mutti (2000).

51

C ace

1— cc . . . .
where A = Z '6'. P[ a . Then, the demand elastrcrtres, p“ (z), are:
i

CC 053915: (”cc ‘1)PirCir _

 

= ace. (4.12)
6P; Cir er
P-'c-'
Substituting for the expenditure share, 6“ (i) = -—'Yr—'- , and arranging for ace give:
2
cc i +6“ i
6.0:” 0 0. (4.13)

 

6“(i)—1

The elasticity of (substitution among different domestic goods depends on the price
elasticity of demand for a given variety of domestic goods, p“ (i), and the expenditure
share, 6“ (i).

The trade elasticities are very crucial, especially in a global model that deals with
trade issues. The 0:1»: parameters represent the higher-level Armington elasticities
between domestic goods and imported goods, in the fourth level of the consumer’s

decision, and the of”, parameters represent the lower-level Armington elasticities

among imported goods from different regions, in the fifth level of the consumer’s
decision. These elasticity values are very important, because the magnitude of the terms-

of-trade effects varies substantially with these trade elasticities. According to Brown

52

(1987), lower trade-elasticities tend to produce strong terms-of-trade effects. Shiells and
Reinert (1993) suggest that higher values of Armington elasticities must be considered, in
order to avoid large terms-of-trade effects. It would be possible to calibrate the trade
elasticities on the basis of econometric evidence, as I have just done for the asset-

substitution elasticities.
The procedure for calibrating 0:1," and aim is similar to that for calibrating

occ. An equation for the elasticity of substitution between domestic and imported goods

is:

i _ .uidm(s)+6idm(s)

_ , (4.14)
dm gidm (S) _ 1

 

aClSr Pisr
aPiSI‘ CISI'

 

where the pf’m (s{a ] are the price elasticities of import demand, and the

P” C T" . . .
Bid“ (s{= 4;] are the expendrture shares of imported goods vs. domestically

,
Y3

produced goods. In addition, an equation for the elasticity of substitution among

 

different imported goods is:
. mm .mm
0;"); :fll (sk)+61 (5k), (415)
61mm (5k )- 1

53

- aClSkr P'skr

l

= are the price elasticities of import demand for a given
aPS/(I' Cskr
l l

 

where pfnm (sk

skr skr
= P.- C.-

,
Y4

variety of imported goods, and the 19;” (s k are the expenditure shares of

imported goods from different regions.

I conclude that the elasticities of substitution, occ , 02m , and aim , can be
calibrated by selecting the corresponding demand elasticities, p“ (i), pflm (s), and
aim" (sk ), from the econometric literature. Among them, I start with the elasticity of
substitution between domestic and imported goods, 02m , that relies on the price
elasticities of import demand, ,ufi'" (s), which are relatively more available in the

empirical trade literature."1 Then I arbitrarily choose the values of (ICC and 0'an , based

on the prior belief that the elasticity of substitution among different imported goods is

larger than the elasticity of substitution between domestic and imported goods, which in

turn, is larger than the elasticity of substitution among different domestic goods (occ <
02m < ofnm ). I choose this procedure, instead of the alternative procedure of calibrating

the values of a“. and aim , because the information necessary to calibrate ace and

i

am", is relatively less available in the econometric literature.42

 

" Sawyer and Sprinkle (1999) review the literature on empirical estimates of the income and price
elasticities of demand for irrrports and exports by county, which have been published since 1976.

’2 In other words, I assume that the price sensitivity when choosing between cars and machines is

absolutely lower than the price sensitivity when choosing between domestic and inrported cars, and that the
sensitivity when choosing between domestic and irrrported cars is probably less than the price sensitivity

54

I calibrate the elasticity of substitution between domestic and imported goods.

Table 4-4 shows the results. I have a very wide range of calibrated values for 0:1»: , from
a low value of 0.8 to a high value of 3.3. The values of 0:1»: depend completely on the

values of pflm , of which the econometric literature has an extremely wide range.

Table 4-4. Price Elasticities of Import Demand and
Calibrated Trade Elasticity of Substitution

 

 

Price Elasticities of Import Demand, yfb" Calibrated 03m
Stern, Baum, and Greene (1979) -2.18 2.7
Haynes and Stone (1984) -2.83 3.3
Moffett (1989) -0.68 1.2
Deyak, Sawyer, and Sprinkle (1990) -0.54 0.9
Carone (1996) -0.39 0.8
Deyak, Sawyer, and Sprinkle (1997) -1.32 1.9

 

 

Consequently, I defer to the judgment of J omini, et al. (1991), and use the
SALTER elasticities of substitution, which represent a compromise between econometric

evidence and prior belief, as the central values. In the SALTER setting, the values of

 

when choosing among various imported cars. For this reason, the arbitrary value of 0'3"," must be higher
than the calibrated value of 0:1»: , and the arbitrary value of ace must be smaller than 02m . Fehr,
Rosenberg, and Wiegard (1995) follow this procedure: They calibrate the value of 02m = 1.5, based on the
price elasticities of import demand, [1,4 m , which are provided by Stern, Francis, and Schumacher (1976).

And they arbitrarily take the values of 0'“. = 1.1 and 0'5"", = 2.0, based on the calibrated 0'51," .

55

0:1»: are based on preferred estimates from the econometric literature, with some upward

adjustment, and the values of Jim" are set at twice the values of 0:1»: .43 According to

Dimaranan, McDougall, and Hertel (1998), they are generally higher than those estimated
by the econometric literature, to avoid strong terms-of-trade effects, but still low enough
to generate terms-of-trade effects. The sector-specified SALTER trade elasticities are

shown in Table 4-5.

Table 4-5. The SALTER Trade Elasticities a

 

 

Sectors 0' g m 0.:nm
Agriculture 2.43 4.86
Primary Materials 2.60 5.20
Durable Manufactures 3.40 6.80
Non-durable Manufactures 2.75 5.50
Services 2.05 4.10

 

 

a. The SALTER values, which are provided by Jomini, et al. (1991), are modified to
fit my model, using a weight parameter.

 

’3 The estimated trade elasticities in econometric literature are: 0:1," = 0.14~3.49 in Reinert and Roland-

Holst (1992), 03m = 1.0 and dim" = 1.5 in Shiells and Reinert (1993), and Harrrilton and Whalley (1985).

56

CHAPTER 5

DATA AND SIMULATION METHOD

5.1. Data Interpretation
5.1.1. Data Aggregation

I begin by aggregating the 45 regions in the GTAP database into four regions; the
United States, the European Union, Japan, and the Rest of the World (hereafter ROW).
This four-region version of the model is well suited for analysis of the tax policies
affecting the major developed trading areas. Table 5-1 shows the levels of economic
activity for the four regions. The transactions are measured in billions of 1995 dollars.
The United States, the European Union, and Japan have more than 70 percent of the
world income, and jointly participate in a large fi'action (about 60 percent) of world trade.

The mappings of regions are shown in Table 5-2.

Table 5-1. Levels of Economic Activity by Region
(Unit: Billions of 1995 dollars)

 

 

Income Income % Trade a Trade %
U.S. 7,126.4 25.17 1,640.1 13.58
E. U. 7,852.5 27.73 4,424.6 36.64
Japan 5,091.7 17.98 976.9 8.89
ROW 8,243.7 29.12 5,035.2 41.69

 

 

a. The figures are calculated as the sum of the values of imports and exports.

57

Table 5-2. Dataset Mapping of Regions from GTAP version 4

 

 

Regions in GTAP Mapping Regions in GTAP Mapping
in the in the
Model Model
Australia ROW Argentina ROW
New Zealand ROW Brazil ROW
Chile ROW
Japan JPN Uruguay ROW
Rest of South America ROW
Republic of Korea ROW
Indonesia ROW United Kingdom TEU
Malaysia ROW Germany TEU
Philippines ROW Denmark TEU
Singapore ROW
Thailand ROW Sweden ROW
Vietnam ROW Finland ROW
China ROW
Hong Kong ROW Rest of EU ’ TEU
Taiwan ROW
India ROW European Free Trade Area b ROW
Sri Lanka ROW Central European Associates ROW
Rest of South Asia ROW Former Soviet Union ROW
Canada ROW Turkey ROW
Rest of Middle East ROW
United States of America USA Morocco ROW
Rest of North Africa ROW
Mexico ROW South Afiica ROW
Central America and ROW Rest of South Afiica ROW
Caribbean Rest of Sub-Saharan Afiica ROW
Venezuela ROW Rest of the World ROW
Colombia ROW
Rest of Andean Pact ROW

 

 

 

 

a. Rest of EU includes France, Greece, Italy, Portugal, Netherlands, Belgium, Spain,

Ireland, Luxembourg, and Austria.

b. EFT includes Norway and Switzerland.

The GTAP database originally has 50 sectors. These are aggregated to five

sectors for the analysis: agriculture, primary materials, durable manufactures, non-

durable manufactures, and services. The mappings of sectors are shown in Table 5-3.

58

Table 5-3. Dataset Mapping of Sectors from GTAP version 4 ’

 

 

Sectors in GTAP Mapping Sectors in GTAP Mapping
in the in the
Model Model
Paddy rice AGR Wearing apparel NMF
Wheat AGR Leather goods NMF
Grains (other than rice and AGR Lumber and wood NMF
wheat) Pulp and paper NMF
Vegetable fruit nuts AGR
Oil seeds AGR Petroleum and coal PRY
Sugar cane and beet AGR products
Plant-based fibers AGR Chemicals rubber and PRY
Crops n.e.c. AGR plastics
Bovine cattle - sheep and AGR Non-metallic mineral PRY
goats -horse products
Animal products n.e.c. AGR Primary ferrous metals PRY
Raw milk AGR Non-ferrous metals PRY
Wool AGR
Forestry AGR Fabricated metal products DMF
Fishing AGR Motor vehicles DMF
Other transport equipment DMF
Coal PRY Electronic equipment DMF
Oil PRY Machinery and equipment DMF
Natural gas PRY Other manufacturing DMF
Other minerals PRY products
Bovine cattle meat products NMF Electricity SVS
Meat products n.e.c. NMF Gas manufacturing and SVS
Vegetable oils NMF distribution
Dairy products NMF Water SVS
Processed rice NMF Construction SVS
Sugar NMF Trade and transport SVS
Other food products NMF Other services (private) SVS
Beverages and tobacco NMF Other services (public) SVS
Textiles NMF Dwellings SVS

 

 

 

 

a. AGR=agriculture, PRY=primary materials, NMF=non-durable manufactures,
DMF=durable manufactures, SVS=services

59

5.1.2. Tax Rates and Trade Data

In this section, the structures of factor taxes and consumption taxes are reviewed.
Table 5-4 shows the different factor-tax rates in each of three major trading areas.44

Table 5-4 indicates that the overall tax rates on capital income are not very
different across regions. In each region, capital income is taxed at about 35 percent.
However, capital-tax rates in each sector are much differentiated across regions. The tax
rate on durable manufacturers in the U.S. is 2~3 times as large as those in the EU. and
Japan. The tax rates on labor income are considerably more differentiated across regions.
The tax rates on labor income are significantly higher in the European Union. The tax
rates on capital income are much higher than those on labor income in the U.S. and
Japan, while the tax rates on capital income are much lower than those on labor income
in the European Union.

The effective tax rates on capital income in the United States are calculated by the

formula;45

Capital Tax Liabilities
(5.1)

 

T K = .
Net Payments to Capital

 

’4 The tax rates in the ROW are taken as arithmetic averages of the corresponding taxes in the United
States, the European Union, and Japan.

’5 Thus, we calculate the average tax rate, and then assume that marginal tax rates are equal to the average
rates. This is the procedure used by Harberger (1962), Fullerton, Shoven, and Whalley (1983), and others.
An alternative would be to calculate marginal effective tax rates, based on data and assumptions regarding
variables such as depreciation schedules, nominal tax rates, and discount rates, and then to assume that
average tax rates are equal to the marginal rates. This method, in the tradition of Hall and Jorgenson
(1967), is used by Jorgenson and Wilcoxen (1997). One of our reasons for choosing the former approach is
that the data requirements for the latter approach are very formidable in a global model such as ours.

60

Table 5-4. Factor Taxes in the Model “

 

 

 

(Unit: %)
U.S. b E. U. Japan c
Capital Labor Capital Labor Capital Labor
Taxes Taxes Taxes ° Taxes d Taxes Taxes
(1) (2) (3) (4) (5) (6)
AGR 8.53 12.57 18.05 48.50 34.69 18.20
PRY 22.26 13.38 27.74 48.50 21.18 22.61
DMF 93.11 13.15 43.45 59.45 31.95 23.42
NMF 53.01 13.24 41.19 50.50 34.73 24.09
SVS 30.00 17.32 33.69 51.28 34.85 24.18
Overall 35.74 16.27 33.57 51.66 34.25 22.59

 

 

Source: Author’s calculations.

a. These rates are all calculated as rates of tax on net-of—tax factor incomes.

b. 1995 data.

c. The rates are weighted averages of 1993 data for Germany, France, Italy, and the
UK.

(1. 1994 data for Italy.

e. 1998 data on capital taxes, and 1999 data on labor taxes.

The return to capital, net-of-factor taxes, includes corporate profits after tax with
inventory valuation adjustment, the return to unincorporated capital, capital consumption
adjustment, net rent paid, and net interest paid. The tax on capital income at the industry
level has three components: the corporation income tax levied by the federal government,
corporation franchise taxes levied by the state governments, and property taxes levied by
the state and local governments."6 The August 1998 Survey of Current Business (SCB)

gives us data on the capital income net-of—tax and capital tax liabilities, directly or

 

’6 For simplicity, corporation franchise taxes, which are relatively small, are assumed to be zero.

61

indirectly.47 The column (1) of Table 5-4 shows the U.S. tax rates on capital income.
The U.S. capital taxes have much variance across sectors: the tax rates are highest in
durable manufactures, and lowest in agriculture.

The effective tax rates on labor income in the United States are calculated by the

4
formula; 8

Labor Tax Liabilities
(5.2)

 

T L = .
Net Payments to Labor

The net-of-factor-tax return to labor is the sum of wages, salaries, and the
estimated return to the labor of self-employed individuals. The tax on labor income
includes employer contributions to social insurance, employer contributions to OASDHI
(Old Age, Survivors, Disability, and Hospital Insurance), and self-employed
contributions to OASDHI. The data on labor-tax liabilities, as well as the net-of-factor-
tax return to labor, are provided directly or indirectly by the August 1998 SCB, and
unpublished worksheets from NID.49 As shown in the column (2) of Table 5-4, the U.S.

labor taxes are close to the overall average of 16 percent.

 

’7 Since the August 1998 SCB provides us only the data on the aggregate of capital consumption
adjustment, the aggregate of net rent paid, and the aggregate of industrial property taxes, I distribute those
aggregate values to each sector, on the basis of the corporate capital consumption allowance by sectors, net
interest paid by sectors, and corporation income taxes by sectors, which are available in the August 1998
SCB and unpublished worksheet from National Income Division (N ID), respectively.

’8 This method is also followed in GEMTAP.

’9 Unpublished worksheets from NID are available in http://www.bea.doc. gov.

62

Among the EU. members, only four countries (Germany, France, Italy, and the
United Kingdom) are considered, in computing tax rates of the European Union. The
sum of GDP of those four countries consists of more than 70 percent of total GDP in the
European Union.

Each country’s rates of tax on net-of—tax capital income are calculated by dividing
the corresponding country’s capital-tax liabilities by the corresponding country’s after-
tax capital income. The taxes on capital income include household’s payments of capital
income taxes, the payments of capital income taxes made by corporations, all recurrent
taxes on immovable property, and taxes on financial and capital transactions, which are
available in National Accounts Statistics: Main Aggregates and Detailed Tables, 1995,
and Revenue Statistics of OECD Member Countries, 1965-1994. The after-tax capital
income can be replaced by the net-of-tax operating surplus of the economy as a whole,
which is defined as gross output less the sum of intermediate consumption, compensation
of employees, consumption of fixed capital, and indirect taxes.50 National Accounts
Statistics: Main Aggregates and Detailed Tables, 1995, gives us the data on operating
surplus.

To get sector-specific tax rates on capital income, I distribute the aggregate value
of the taxes on capital income to each sector, on the basis of the each sector’s share of
total investment, which is available in OE CD Economic Surveys, and divide those
distributed values over sector-specific operating surplus, which are provided by National

Accounts Statistics: Main Aggregates and Detailed Tables, 1995.

 

’0 See Mendoza, Razin, and Tesar (1994) for details.

63

The overall and sector-specific tax rates in the four countries are shown in Table

5-5. The capital-income tax is significantly higher in the United Kingdom than in the

other countries of the European Union. Generally, the sector of manufactures has the

highest tax rates in most countries.

Finally, I attach a weight on each country, on the basis of the level of each

country’s GDP, which are available in National Accounts, Main Aggregates, 1960-199 7,

to get the weighted average of tax rates of the European Union. The last column of Table

5-5 has the weighted average of tax rates on capital income in the European Union.

Table 5-5. Capital Taxes in EU.

 

 

(Unit: %)
Germany France Italy UK. EU. (weighted average)

AGR 26.29 5.25 12.28 25.91 18.05
PRY 26.29 32.80 12.28 42.96 27.74
DMF 54.20 17.67 27.15 75.35 43.45
NMF 54.20 7.96 27.15 75.35 41.19
S VS 25.38 20.96 34.26 63.27 33.69
Overall 29.60 18.12 31.60 61.79 33.57

 

 

Source: Author’s calculations.

Data on the sector-specific labor tax rates are sparse. Based on information in

Messere (ed., 1998), I calculate sector-specific tax rates for Italy. I use these rates for the

European Union as a whole. The column (4) of Table 5-4 shows the assumed E.U. rates

on labor income.

For Japan, the effective tax rates on capital income are computed by dividing
corporation tax by corporate income assessed, which are provided by Japan Statistical
Yearbook 2001 . The effective tax rates on labor income are calculated by dividing labor
cost, which includes the cost of retirement allowances, cost of obligatory welfare
services, and cost of non-obligatory welfare services, over the total value of cash
earnings. Japan Statistical Yearbook 2001 gives us data on labor cost and value of cash
earnings. The tax rates on net-of-tax factor income in Japan are shown in the coltunns (5)

and (6) of Table 5-4.

Table 5-6. Consumption Tax Rates in the Model "

 

 

(Unit: %)
U.S. E. U. Japan ROW
Consumption Taxes
Agriculture 1.66 2.72 - 1.40
Primary Materials 3.36 3.58 5.83 6.26
Durable Manufactures 0.72 2.53 3.19 6.35
Non-durable Manufactures 2.65 2.61 6.48 6.03
Services 7.86 2.45 3.16 3.05

 

 

a. Tax rates are calculated, based on dataset.

The consumer taxes on goods purchased are computed, based on the dataset for
the gross-of-tax values of goods purchased, and the net-of-tax values of goods purchased.
Indirect taxes, such as the commodity taxes and the selective excise taxes, are treated as

the consumer taxes on goods purchased. Table 5-6 reports the consumption tax rates in

65

the dataset.51 Generally, higher tax rates are levied on primary—material goods purchased.
In the U.S., the rates are very differentiated across sectors: the highest rates are on

services, and the lowest rates are on durable manufactures.

Table 5-7. Import Tariffs by Sector

 

 

 

 

 

 

 

(Unit: %)

Destination U.S. E. U. Japan ROW
Source
(Agriculture)
U.S. 11.64 164.56 24.56
E. U. 4.69 33.80 19.13
Japan 0.90 8.50 6.59
ROW 4.30 9.26 34.40 0.13
(Primary Materials)
U.S. 3.19 1.52 5.34
E.U. 3.49 2.12 8.22
Japan 3.38 4.85 10.79
ROW 1.24 1.21 0.78 0.09
@urable Manufactures)
U.S. 3.43 0.94 5.66
E. U. 2.69 0.42 10.65
Japan 2.76 5.29 13.03
ROW 1.09 3.01 0.51 0.11
(Non-durable Manufactures)
U.S. 7.97 17.70 10.64
E.U. 10.01 22.58 16.50
Japan 6.17 8.32 27.83
ROW 6.68 9.25 13.34 0.20
(Services)
U.S. - 3.00 0.19
E. U. - 2.99 0.32
Japan - - 0.15
ROW - - 2.99

 

 

5 ' Most European countries adopt the value-added tax (VAT). However, the VAT is not included in the
dataset. If the VAT is considered, the effective consumption tax rates for the EU. would be higher. In

order to maintain the overall balance of the data base, I do not simply change one region’s tax rates, leaving

the rest of the data base unchanged.

Next, I analyze the import tariffs and the patterns of trade. Table 5-7 reports the
import tariffs in the dataset. In most regions, there is considerable variation in tariff rates
across sectors. In Japan, import barriers for agriculture range from 33.8 to 164.6 percent.

The data on imports and exports are reported in Table 5-8, and the data on
bilateral trade flows by sectors are summarized in Table 5-9. The United States has a
trade deficit, whereas Japan has a trade surplus, and the European Union is almost in the
state of trade balance. The United States is a “net importer” in the sectors of primary
materials, durable manufactures, and non-durable manufactures, and is a “net exporter” in
the sectors of agriculture and services. Especially, in durable manufactures, the data on
bilateral trade flows say that the United States is an overall “net importer”, but is a “net

exporter” in a trade with the European Union.

Table 5-8. Total Value of Imports and Exports by Sector and Region ’

(Unit: Billions of 1995 dollars)

 

U.S. E. U. Japan ROW

 

Value by Sector
AGR 18.8/37.7 91.1/56.7 45.0/0.70 103.8/106.4
PRY 177.6/ 103.9 538.0/478.9 115.7/67.3 616.4/645.8
DMF 4357/3170 7773/8253 98.9/344.8 1,079.1/698.7
NMF 142.5/73.6 419.9/368.8 100.9/15.1 421.6/491.3
S VS 129.7/203.8 392.7/475.8 113.8/74.8 391.5/480.6

Total Value 904.2/735.9 2,219.1/2,205.5 474.3/502.6 2,612.4/2,422.8

 

 

a. The figures are imports/exports.

67

Table 5-9. Bilateral Trade Flows by Sector

(Unit: Billions of 1995 dollars)

 

  
 
 

 

 

 

 

 

 

Destination U.S. E. U. Japan ROW All

Exports

Source

(Agriculture)

U.S. 5.73 8.49 23.45 37.67

EU. 1.07 41.38 a 0.89 13.35 56.99

Japan 0.06 0.05 0.57 0.68

ROW 15.36 32.60 12.23 46.23 a 106.42

All Imports b 16.45 79.76 21.61 83.60

(Primary Materials)

U.S. 23.12 10.00 70.76 103.88

E. U. 30.95 296.70 a 10.37 140.84 478.86

Japan 10.26 6.83 50.16 67.25

ROW 120.42 172.10 85.23 268.04 a 645.79

All Imports b 161.63 498.75 105.60 529.80

(Durable Manufactures)

U.S. 69.08 30.54 217.33 316.95

E. U. 66.94 461.75 a 18.82 277.82 825.33

Japan 107.02 55.25 182.53 344.80

ROW 235.69 152.04 44.14 266.83 a 698.69

All Imports b 409.65 738.12 93.50 944.51

Won-durable Manufactures)

U.S. 11.21 13.92 48.49 73.62

E. U. 16.74 234.03 a 10.09 107.95 368.81

Japan 1.69 1.39 11.96 15.05

ROW 106.44 139.84 60.43 184.60 " 491.31

All Imports 1’ 124.87 386.47 84.44 353.00

(Services)

U.S. 75.48 19.85 73.77 169.10 °

E.U. 60.73 184.19 a 13.42 140.87 399.21 C

Japan 12.34 12.24 32.08 56.66 c

ROW 55.80 114.05 74.39 137.51 a 381.75 C

All Imports b 128.87 385.96 107.66 384.23

 

a. These figures are the values of the intra-region trades.
b. These figures are different from the gross-tariff values of total imports, in Table

5-8.

c. These figures are different from the values of total exports that include

international transport sales, in Table 5-8.

68

5.2. Simulation Method

Quasi-Newton Iterations are applied in this analysis. The Newton methods are
used in several recent applied general equilibrium models to compute counterfactual
equilibria associated with changes in polices. These methods solve the systems of
nonlinear equations characterizing equilibrium by using successive linear approximations
to the nonlinear system.52 The equation system that characterizes equilibrium cannot
typically be written in closed form, since market demands are the sum of individual agent
demands. As a result, point estimates of derivatives of market excess demand fimctions
are repeatedly calculated and used to estimate successive adj ustrnents to the initial guess
of the equilibrium prices. These Newton steps allow large initial adjustments to the
starting vector of prices. When successive adjustments produce divergence rather than
convergence in solution, the Jacobian matrix must be recalculated during the computation

process.

 

’2 See Shoven and Whalley (1992).

69

CHAPTER 6

SIMULATION RESULTS IN THE STATIC CASE

I analyze the international spillover effects of U.S. tax reform. Since many of the
proposals for tax reform point toward reduced taxation of capital income, and toward
increased consumption taxation, I consider here the extreme case of complete elimination
of capital taxes.53 The lost revenues are replaced with higher rates of consumption tax, so
that tax revenue remains unchanged.54 After eliminating capital taxes, a new competitive
equilibrium is calculated and compared with the benchmark equilibrium. The results,
such as changes in output, imports, terms of trade, consumption, and utility levels, are
measured in percentage changes from the benchmark equilibrium. The changes in utility

between the new and old equilibria are also measured by using the equivalent variation.55

6.1. Central-Case Simulation
A simulation, using the central values of parameters, begins with the analysis of

mrilateral replacement of U.S. capital taxes. The fiscal policy initiated by one country

 

’3 1 take “the complete elimination of capital taxes with a replacement of consunrption taxes” as the main
scenario in the analysis. Later in this chapter, I will deal with some alternative scenarios.

5’ I model the personal income tax on capital income as if it were paid at the industry level, for simplicity.
So, the sector-specific capital taxes, which include corporate-income taxes and property taxes, are
incorporated in the model.

55 The equivalent variation, in the case where preferences are linearly homogenous, is written as:

_ H N - H 0 10

EV
HO

9

where H N is the new utility level, H 0 is the old utility level, and I 0 is the old income level.

70

has important impacts on prices and resources allocation in other countries, as well as in
that country. The spillovers occur through both terms-of-trade changes and through
effects on international capital flows.

Unlike a conventional closed-economy analysis, the terms-of-trade effects must
be considered in the analysis of tax-policy changes in a global trade model, which takes
international trade flows into account.” In the international trade setting in this model,
which allows for changes in imports and exports, the terms-of-trade effects associated
with tax changes have effects on worldwide welfare: One region may improve its terms
of trade with another, giving an increase in welfare for one region and a decrease in
welfare for the other. In the analysis of elimination of the sector-specific capital taxes in
the U.S., negative terms-of-trade effects are expected for the United States. If the U.S.
eliminates capital taxes, there will be decreases in the gross-of-capital-tax prices of U.S.
output. Thus, there will be a decline in the prices of U.S. exports and in the prices of
U.S. output produced for the domestic market (the first-order effect). Since the prices of
domestic goods decrease, domestic consumers will consume more domestic goods and
fewer imports. The reduction in its demand for imports leads to a decrease in its import
prices (the second-order effect). The first-order effect typically dominates the second-
order effect, so that negative terms-of-trade effects are expected. These negative effects

reduce the U.S. welfare gains from the elimination of domestic distortions.57

 

56 A country’s terms of trade is measured by an index of the prices of its exports relative to the prices of its
imports. An improvement in the U.S. terms of trade means that each unit of U.S. exports yields more units
of imports available to the U.S. economy than previously.

’7 Whalley (1980) also explains the terms-of-trade effects of factor taxes. Since taxes on factors in the U.S.
operate in the form of origin-based taxes, which are not rebated on exports, factor taxes produce terms-of-
trade gains. He analyzes the effect of removing domestic factor taxes, and shows that the abolition of
factor taxes causes a deterioration in the terms of trade.

71

International capital flows must be also considered in the open-economy model,
in which investors hold internationally diversified portfolios, and exhibit sensitivity to
differentials in returns on assets from different national financial markets. A fiscal-policy
change initiated by a given country may alter investors’ share of domestic assets. As a
result of tax-policy changes, there is a reallocation of the existing world capital stock
among all of the sectors in the world. The reduction in U.S. capital taxes raises the after-
tax returns on U.S.—located capital, and thus leads investors to reallocate more capital
stocks in the U.S., out of other countries. The U.S. changes the tax rate on capital in its
five sectors, and this leads to a change in the amount of capital located in each of those
five sectors, as well as in each of the other 15 sectors (five sectors each in EU, Japan,
and ROW). This leads to a new equilibrium in which the rates of return on both domestic
and foreign assets have changed. This change can have significant welfare consequences.

In addition to both terms-of-trade and capital-flow effects, Harberger effects are
expected only for the United States that initiates the tax-policy changes, since the
equalization of capital tax rates leads to a more efficient allocation of the U.S. capital
stock.

Table 6-1 summarizes the possible effects of reducing U.S. capital taxes on the
entire world. Whether each country will have positive (or negative) welfare gains totally
depends on the relative sizes of those three effects. For the U.S., if the two positive
effects dominate the negative terms-of-trade effects, then positive welfare gains will
occur. For the other countries, the terms of trade will be improved, but the capital stocks
will flow out of those countries to the United States. If the positive terms-of-trade effects

dominate the negative capital-flow effects, then welfare gains will occur.

72

Table 6-1. Possible Effects of Reducing U.S. Capital Taxes

 

 

U.S. E. (1., Japan, ROW
A. Terms-of—Trade Ejfects — +
B. Capital-Flow Eflects + —
C. Harberger Efi'ects +
Overall Effects ? ?

 

 

 

6.1.1. Effects on Capital Flows and Terms of Trade

Table 6-2 and Table 6-3 show the results of two of the mechanisms that determine
the overall welfare effects. First, I consider the spillovers that occur as a result of
international capital flows. The reduction in U.S. capital taxes raises the after-tax returns
on U.S.-located capital, relative to the rate of return on foreign capital. Consequently, the
reduction of capital taxes in the U.S. will tend to be accompanied by a reallocation of
global capital, with a greater share of the world’s capital stock being located in the United
States.

Under our central-case parameters, the overall U.S. capital stock is increased by
8.5 percent.58 The largest increase in capital in the U.S. is in the durable-manufacturing
sector, because this is the sector that faced the highest capital-tax burden before the

policy change. However, capital in U.S. agriculture actually decreases, because

 

58 The model used here is essentially static, but has a “medium-run” time fiame, in which there is enough
time for capital to be reallocated among sectors or countries. This model, as the Harberger model, involves
a time frame of at least three years, but probably not as much as ten years. As a result, the amount of
capital that is reallocated is fairly large.

73

agriculture loses its tax-preferred position as a result of the tax reform. The overall

capital stock in other regions is decreased by 1.8~2.5 percent.

Table 6-2. Effects on Capital Flows

(Unit: % Changes ")

 

 

U.S. E. U. Japan ROW

Rental Price of Capital 8.86 -5.13 -5.64 -4.92
Capital Flows by Sector

Agriculture -0.26 0.24 -1.85 -0.74

Primary Materials 4.32 -2.03 -2.42 -2.37

Durable Manufactures 54.47 -3.66 -2.94 -5.83

Non-durable Manufactures 18.76 -2.46 -2.64 -3 .58

Services 3.82 -1.58 -2.80 -1.59

Qvgrlll 8.49 -l .84 -2.54 -2.13

 

 

a. The figures are deviations from the benchmark values, in percent.

International spillovers also occur through changes in terms-of-trade effects. If
the U.S. eliminates capital income taxes, the gross-of-capital-tax prices of the U.S. output
will decrease, and thus its prices of exports will decline: U.S. export prices decline by 8.8
percent in primary materials, 11.6~14.2 percent in non-durable and durable manufactures,
and 8.9 percent in services. The relatively higher change in the durable-manufacture
sector can be explained by the characteristics of the U.S. tax system, in which capital use
in the manufacturing sector (especially in durable manufacturing) is relatively heavily

taxed. (See Table 5-4.)

74

Table 6-3. Effects on the Terms of Trade

(Unit: % Changes a)

 

 

U.S. E. U. Japan ROW
Export Prices by Sector
Agriculture -6.22 -7.32 -8.10 -7.89
Primary Materials -8.81 -7.36 -8.29 -7.91
Durable Manufactures -14. l 9 -7.62 -8.79 -8.48
Non-durable Manufactures —1 1.56 -7.44 -8.56 -8.05
Services -8.94 -7.43 -8.43 -8.24
Import Prices by Sector
Agriculture -7.97 -7.05 -7.18 -7.55
Primary Materials -8.07 -7.25 -8. 14 -8.23
Durable Manufactures -8.61 -7.36 -10.71 -10.07
Non-durable Manufactures -8. 15 -7.39 -8.83 -8.73
Services -8.41 -7.77 -8.47 -8.52
Terms of Trade -1.51 0.12 0.23 0.44

 

 

a. The figures are deviations from the benchmark values, in percent.

On the other hand, as a result of the reduction in the price of domestic goods,

domestic consumers will consume fewer imports. This leads to a decrease in import
prices: U.S. import prices decrease by 8.0~8.6 percent in each sector. However, the
reduction in U.S. export prices is larger than the reduction in U.S. import prices, and this
causes a 1.5-percent deterioration in the terms of trade for the United States. After the

changes in U.S. tax policy, the other regions of the world have small changes in the terms

75

of trade, due to a larger reduction in their import prices: there is not much change in the

European Union, and improvements of 0.1~0.4 percent in Japan and ROW.

6.1.2. Aggregate Effects on the U.S. Economy

Table 6-4 reports the results for the United States, which is the policy-initiating
economy. Under the complete elimination of capital taxes, higher rates of consumption
tax are used to achieve equal tax-revenue yield for the government. I consider a
multiplicative increase in tax rates, as well as an additive increase.

The first column of Table 6-4 shows the results of the case where consumption-
tax rates are increased multiplicatively (i.e., all rates are increased by the same
percentage). The results show that the tax-policy changes lead to a 2.0-percent increase
in the overall U.S. output level: 5.9 percent in primary materials, 19.2 percent in durable
manufactures, and 7.3 percent in non-durable manufactures. Because of the larger
decreases in the gross-of-tax prices of the outputs in durable manufactures, the increases
in outputs are larger in that sector. The overall U.S. imports are increased by 1.7 percent:
U.S. imports are decreased by 4.0 percent in durable manufactures, 1.7 percent in non-
durable manufactures, and 2.6 percent in services, whereas they are increased by 5.3
percent in primary materials and 11.8 percent in agriculture.

The tax-policy changes cause U.S. consumption to rise by 1.1 percent. The
increase in U.S. output is much larger than the increase in U.S. consumption. This is
because U.S. exports are greatly stimulated by the change in the terms of trade.
Consequently, the tax-policy changes lead to U.S. welfare gains of around $98 billion per

year in 1995 dollars, which amounts to about 1.4 percent of GDP. The percentage

76

increase in welfare is larger than the percentage increase in consumption. This is

because, when I use the central-case labor-supply elasticities, the decrease in the net

wage rate leads to an increase in leisure.

Table 6-4. Domestic Effects of the Tax-Policy Change on the U.S. Economy

 

Changes in Consumption Tax

 

Output by Sector (% changes) 1’
Agriculture
Primary Materials
Durable Manufactures
Non-durable Manufactures
Services
Qua—al.]
Imports by Sector (% changes)
Agriculture
Primary Materials
Durable Manufactures
Non-durable Manufactures
Services
QM
Consumption (% changes)
Equivalent Variation (8 billions)
EV (as % of GDP)

 

Multiplicative Additive
3.14 3.15
5.93 6.17
19.17 20.51
7.34 7.47
0.34 -0.17
2.02 2.13
11.76 10.78
5.31 5.37
-3.99 -3.91
-1.72 -1.69
-2.56 -2.56
1.67 1.65
1.13 1.32
98.3 117.6
1.38 1.65

 

a. Units are in parentheses.

77

Under the multiplicative change in consumption-tax rates, the relative sizes of the
consumption-tax rates in different sectors are maintained. Since multiplicative
replacement does nothing to alleviate consumption distortion, it may lead to smaller
welfare gains than those that would occur under a different set of replacement taxes.
Therefore, I also consider an additive tax-rate change. The second column of Table 6-4
has the results of the case where consumption-tax rates are increased additively (i.e., all
rates are increased by the same absolute amount). With the “additive” tax-rate changes,
consumption in the U.S. increases by 1.3 percent (vs. 1.1 percent with multiplicative
scaling), and U.S. welfare gains are around $118 billion per year, which amounts to 1.7

percent of GDP (vs. 1.4 percent with multiplicative scaling).

6.1.3. Aggregate Effects on the Foreign Economics

The policy initiated by one country affects the allocation of resources across
regions. The spillovers occur through changes in both commodity flows and capital
flows. The results of the policy change in the U.S. on the foreign economies are reported
in Table 6-5.

The results show that the U.S. tax-policy change, which replaces capital taxes
with consmnption taxes, leads to lower outputs in the foreign regions. The overall
outputs in the foreign economy are decreased by 0.5~1.0 percent. The reduction of
output is primarily attributable to international capital outflows. As pointed out by
Thahnann, Goulder, and DeLorme (1996), the mechanisms that determine the overall

welfare impacts can be complex.

78

Table 6-5. Spillover Effects of the U.S. Tax-Policy Change on Foreign Economies

 

 

 

 

Foreign Economy
E. U. Japan ROW
(0" (2) ° (1) (2) (I) (2)

Output by Sector (% changes) 3
Agriculture -0.39 -0.42 -0.69 -0.61 -0.16 -0.14
Primary Materials -0.52 -0.63 -0.81 -0.85 -0.78 -0.79
Durable Manufactures -1.09 -1.11 -1.28 -1.32 -1.63 -1.69
Non-durable Manufactures -0.53 -0.62 -0.80 -0.82 -1.1 1 -1 .14
Services -0.41 -0.38 -0.75 -0.76 -0.34 -0.31
M -0.54 -0.56 -0.84 -0.87 -0.93 -0.95

Imports by Sector (% changes)
Agriculture -0.80 -0.82 -0.93 —0.99 -0.83 -0.99
Primary Materials -0.75 -0.79 -0.81 -l .08 -0.87 -1.01
Durable Manufactures 0.09 0.14 0.79 0.69 -0.47 -0.53
Non-durable Manufactures 0.53 0.52 0.24 0.34 -0.51 —0.54
Services -0.41 -0.42 -O.42 -0.46 0.31 0.21
Qv_er_all -0.47 -0.51 -0.53 -0.66 -0.60 -0.67
Consumption (% changes) -0.52 -0.53 -0.76 -0.79 -0.66 -0.71
Equivalent Variation (8 billions) -32.9 -35.3 -3 l .1 -32.0 —42.0 -48.6
EV (as % of GDP) -0.42 -0.45 -0.61 -0.63 -0.51 -0.59

 

a. Units are in parentheses.

b. Each column (1) shows the results from a simulation with multiplicative changes

in consumption-tax rates in the United States.

c. Each column (2) shows the results from a simulation with additive changes in
consumption-tax rates in the United States.

On the one hand, the U.S. tax policy raises after-tax returns on U.S.-located

capital, which benefits foreigners who own such capital. By raising these foreigners’

capital income, the tax policy generates revenues to the foreign government. On the
other hand, the higher returns in the United States tend to increase the attractiveness of
investment in U.S.-located capital, so there will be reallocation of capital from the foreign
economies to the United States. The reduction in foreign-located capital leads to a
negative impact on the welfare of the foreign economies. The latter negative effects are
partly offset by the former positive effects. Therefore, if I focus only on the capital
market, the foreign economies suffer welfare losses.

Due to the elimination of the U.S. capital taxes, the terms of trade for foreign
economies are improved, by small amounts of 0. 1~0.4 percent. However, the positive
terms-of-trade effects for the foreign economies are dominated by the negative capital-
flow effects. As a result, there is lower consumption and lower welfare in the foreign
economies. The levels of consumption in the European Union, Japan, and the ROW are
decreased by 0.5 percent, 0.8 percent, and 0.7 percent, respectively. The welfare losses

are 0.4~0.6 percent of their GDP.

6.1.4. Decomposing the Welfare Effects

In this section, the overall welfare effects are decomposed. Table 6-6 shows the
process of the decomposition for the U.S. welfare. The overall effects can be isolated,
with comparing of four different cases: the case with central values of the trade elasticity
of substitution and the asset-substitution elasticities, the case with zero value of the asset-
substitution elasticity (which has zero capital-flow effects), the case with big value of the
trade elasticity of substitution (which is big enough to have zero terms-of-trade effects),

and the case with zero asset-substitution elasticity and big trade elasticity of substitution.

80

Table 6-6. U.S. Static Welfare Changes of Unilateral Case,

As a Function of the Trade and the Asset Parameters

(Unit: % of GDP)

 

Trade Elasticity of Substitution

 

 

Central Big T erms-of- Trade Effects
Asset-Substitution Central 1.38 2.05 :> -0.67 c
Elasticity Zero 0.15 0.74 :5 :0._59_ d
U U
Capital-F low :Efjects 1.23 8 Q1 b

 

 

 

999‘!”

the case with holding constant trade parameters

the case with holding constant trade parameters, and terms-of-trade effects at zero
the case with holding constant asset parameters

the case with holding constant asset parameters, and capital-flow effects at zero

The capital-flow effects can be isolated from comparing the case with central and

zero asset-substitution elasticities, holding constant trade parameters and also terms-of-

trade effects at zero. In this simulation, the positive capital-flow effects are estimated as

1.3 percent of GDP. Similarly, the negative terms—of-trade effects, which lead to welfare

losses of 0.6 percent of GDP, are estimated from comparing the case with central and big

trade elasticities substitution, holding constant asset parameters and also capital-flow

effects at zero. Lastly, Harberger effects, which amount to 0.7 percent of GDP, are

estimated directly from the simulation with zero asset-substitution elasticity and big trade

elasticity of substitution.

Table 6-7 summarizes the results for other regions, as well as the United States.

As shown in Table 6-7, the numbers representing the overall effects are not necessarily

81

equalized to the numbers, which are the sums of three effects. This is because some
intersections among three effects are expected.59 The results show that the capital-flow
effects are relatively dominant everywhere. For the U.S., the positive effects (the capital-
flow effects and Harberger effects) dominate negative terms-of-trade effects. For other
regions, the bigger negative capital-flow effects, which are associated with welfare
changes of -0.9 percent of GDP, dominate the smaller positive terms-of-trade effects,

which are associated with welfare gains of 0.3~0.4 percent of GDP.

Table 6-7. Decomposing the Static EVs
(Unit: % of GDP)

 

 

U.S. E. U. Japan ROW
A. Terms-of-Trade Eflects -0.59 0.39 0.29 0.36
B. Capital-Flow Efl'ects 1.31 -0.87 -0.94 -0.91
C. Harberger Eflects 0.74
Overall Effects 1 .38 -0.42 -0.61 -0.51

 

 

 

 

’9 I find some intersections between the terms-of-trade effects and the capital-flow effects, in which the
terms-of—trade effects are partly controlled by the asset-substitution elasticity. As domestic assets and
foreign assets become closer substitutes, the terms-of-trade loss in the U.S. also becomes larger: The more
sensitive investors are, the greater will be the increase in the quantity of capital supplied to the United
States. As a result, a higher asset-substitution elasticity is associated with a larger decrease in the gross-of-
tax price of U.S. capital. Consequently, a higher asset-substitution elasticity will be associated with a
larger decrease in the price of U.S. exports, so that the deterioration of the terms of trade will be more
severe.

82

 

6.2. Sensitivity Analyses
In this section, I conduct sensitivity analyses for the key parameters: (1) trade
elasticities of substitution, (2) asset-substitution elasticities, and (3) labor-supply

elasticities.

6.2.1. Sensitivity Analysis with Respect to the Armington Elasticities
I start with a sensitivity analysis for the Armington trade elasticities of

substitution, in which four possible cases are considered. These are: (a) changes in
Udm (usa), (b) changes in O'dm (others) , (0) changes in 0mm (usa), and (d) changes in
0",", (others). The results are shown in Table 6-8 through 6-11, and briefly summarized
in Table 6-12.

(a) As the O'dm (usa) become larger, the terms-of-trade eflects become smaller."0

In other words, as imports become closer substitutes with domestically produced goods in
the U.S., the terms-of-trade loss in the U.S. becomes smaller. The more sensitive
domestic consumers are, the greater is the shift into domestically produced goods, and

hence the greater will be the decreases in import prices. As the ad»: (usa) increases by

50 percent and 100 percent, the U.S. terms-of-trade loss becomes smaller by 33.2 and

52.3 percent (relative to the revised case with central-case parameters), and this leads to

 

6° This differs from the result in Brown (1987). She evaluates how national product differentiation relates
to the terrns-of-trade effects of a tariff, and shows that the terms-of-trade effects would increase in
magnitude, as the elasticity of substitution between domestic and imported goods becomes larger.
However, we find that the terms-of-trade effects are smaller when the elasticity of substitution is larger.
This difference comes from the fact that imposing a tariff drives the export price up, whereas eliminating
capital-income taxation drives it down. Imposing a tariff leads to an increase in export prices and a
decrease in import prices, and thus generates terms-of-trade gains. When the elasticity of substitution is
larger, the import prices fall farther, so that the terms-of-trade gains are increased.

83

an increase in the U.S. welfare gain by 8.0 and 14.5 percent (relative to the revised case

with central-case parameters), respectively.

Table 6-8. Sensitivity Analysis with Respect to the Elasticities of Substitution between
Domestic and Imported Goods 1’I

 

 

 

 

 

 

 

o;m(usa)

-50% ml” 25% 50% 100%

(1.33) (2_._6_5) ° (3.31) (3.98) (5.30)

(1) -233 (1) _-_1_.51 (1) -1.21 (1) -1.01 (1) -072

U.S. (2) 0.94 (2) 143 (2) 1.20 (2) 1.25 (2) 1.36
(3) 1.17 (3) L3 (3) 1.45 (3) 1.49 (3) 1.58

(1) 0.14 (1) w (1) 0.10 (1) 0.09 (1) 0.06

EU. (2) -051 (2) ._052 (2) -0.52 (2) -053 (2) -053
(3) -0.41 (3) -0_.4; (3) -042 (3) 0.43 (3) -043

(1) 0.33 (1) 023 (1) 0.19 (1) 0.16 (1) 0.14

Japan (2) -074 (2) M (2) -O.78 (2) -0.80 (2) -0.81
(3) -0.55 (3) M (3) -0.63 (3) -0.64 (3) -0.66

(1) 0.50 (1) 0._44 (1) 0.40 (1) 0.36 (1) 0.28

ROW (2) -047 (2) -_0_.6_6 (2) -053 (2) -052 (2) -050
(3) -054 (3) 0.51 (3) -0.47 (3) -045 (3) -040

 

a. (1) = % changes in terms of trade
(2) = % changes in consumption level
(3) = equivalent variation (as % of GDP)
b. The central values of 02m are 2.43 for agriculture, 2.60 for primary materials,

3.40 for durable manufactures, 2.75 for non-durable manufactures, and 2.05 for
services.
c. The figures in the parentheses (of the column heading) are represented as the

weighted average of 03m .

84

Table 6-9. Sensitivity Analysis with Respect to the Elasticities of Substitution between

Domestic and Imported Good H ’

 

 

 

 

 

 

03m (teu) = 03m (ipn) = 02m (row)
-50% mil” 25% 50% 100%
(1.33) (2_._6_5_) ° (3.31 ) (3.98) (5.30)
(1) -1.64 (1) 1.5_1 (1) -1.44 (1) -1.41 (1) -135
U.S. (2) 1.11 (2) up (2) 1.15 (2) 1.16 (2) 1.17
(3) 1.33 (3) 1_.33 (3) 1.40 (3) 1.41 (3) 1.43
(1) 0.10 (1) 012 (1) 0.13 (1) 0.13 (1) 0.14
EU. (2) -053 (2) 052 (2) -052 (2) -051 (2) -051
’ (3) -044 (3) M (3) .042 (3) .041 (3) .041
(1) 0.23 (1) M (1) 0.23 (1) 0.23 (1) 0.23
Japan (2) -0.76 (2) ._076 (2) -0.76 (2) -0.76 (2) -0.76
(3) -0.61 (3) i)._6_1. (3) -0.61 (3) -O.61 (3) -0.61
(1) 0.47 (1) 0._44_ (1) 0.40 (1) 0.38 (1) 0.36
ROW (2) -0.65 (2) M0 (2) -0.67 (2) -0.67 (2) -0.68
(3) -0.51 (3) fl (3) -051 (3) .052 (3) -0.52

 

 

a. (1) = % changes in terms of trade
(2) = % changes in consumption level
(3) = equivalent variation (as % of GDP)

b. The central values of of)", are 2.43 for agriculture, 2.60 for primary

materials, 3.40 for durable manufactures, 2.75 for non-durable
manufactures, and 2.05 for services.
c. The figures in the parentheses (of the column heading) are represented as the

weighted average of 02m.

(b) As the cam (other) become larger, the terms-of-trade eflects become smaller.

In other words, as the domestically produced goods in the foreign regions become closer

substitutes with imports (i.e., with exports from the U.S.), the U.S. terms-of-trade loss

85

becomes smaller. After the change of the US tax policy, foreign consumers will
consume more imports and fewer of their domestically produced goods, due to relative
decline in the price of imports. The more sensitive foreign consumers are, the greater is
the shift out of their domestically produced goods and into imported goods. This leads to
decreases in U.S. import prices, and increases in US export prices, when compared with
a situation in which the elasticities are smaller. Both the reduction of U.S. import prices
and the rise in U.S. export prices will reduce the U.S. terms-of-trade loss. As the

adm (others) increases by 50 percent and 100 percent, the U.S. terms-of-trade loss

becomes smaller by 6.9 and 10.4 percent, and this leads to a small increase in the U.S.

welfare gains.

Figure 6-1. Terms-of-Trade Effects from Elimination of U.S. Capital
Taxes, As a Function of the Elasticity of Substitution Between
Domestic and Imported Goods

(16
0A.
(12

432
-OA
-06
-08

-1
-12
-1A

-16
cenUal 50% 100% 150% 200% 250% 300% 350%

Elasticities of Substitution between Domestic and Imported Goods

% Change of TOT

 

 

86

Based on (a) and (b), we can say that the terms-of-trade effects become smaller

when the ad”, (all) become larger. Figure 6-1 shows that higher elasticities tend to
produce weaker terms-of—trade effects. As the ad»: (all) are increased by near 350

percent, the terms—of-trade effects for the United States disappear.

(c) As the 0mm (usa) become larger, there are no substantial changes in the
terms-of-trade effects. The magnitudes of the elasticity of substitution among different
imports in the U.S. don’t have a significant effect on U.S. import and export prices. This
is to be expected. The terms-of-trade effects for the U.S. depend on the ease with which
consumers can substitute between U.S. goods and goods from other regions, not on the
ease with which U.S. consumers can substitute between goods from Germany and goods

from Japan. Therefore, the U.S. welfare gains don’t change fi'om 1.4 percent, even if
aim is increased.

((1) As the 0mm (others) become larger, the terms-of—trade effects become
smaller. In the model, the elasticity of substitution among different imported goods in
other regions, 0mm (others), has the same role as the elasticity of substitution between
domestic and imported goods in the U.S., ad", (usa). As the 0",", (others) increases by

50 percent and 100 percent, the U.S. terms-of-trade loss become smaller by 26.6 and 45.1
percent, and this leads to an increase in the U.S. welfare gain by 6.4 and 11.8 percent,

respectively.

87

Table 6-10. Sensitivity Analysis with Respect to the Elasticities of Substitution among

 

 

 

 

 

 

Different Imported Goods I ’
0.an (usa)

-50% ge_ntr_alb 25% 50% 100%

(2.66) (5_.3_0) ° (6.62) (7. 96) (10.60)

(1) -152 (1) -1_.51_ (1) -1.51 (1) -151 (1) -150

U.S. (2) 1.13 (2) 1._1_3 (2) 1.13 (2) 1.13 (2) 1.13
(3) 1.38 (3) L3_8 (3) 1.38 (3) 1.38 (3) 1.38

(1) 0.11 (1) 0._12_ (1) 0.12 (1) 0.12 (1) 0.13

EU. (2) -052 (2) 0.52 (2) -052 (2) -0.51 (2) -0.51
(3) -0.42 (3) 3M2. (3) -042 (3) -042 (3) -0.42

(1) 0.23 (1) 9; (1) 0.23 (1) 0.23 (1) 0.24

Japan (2) -O.76 (2) -()_.76_ (2) -0.76 (2) -0.76 (2) -0.76
(3) -0.61 (3) M (3) -0.61 (3) -0.61 (3) -0.61

(1) 0.45 (1) 0L4 (1) 0.43 (1) 0.42 (1) 0.42

ROW (2) —0.66 (2) -_0._6_6 (2) -0.67 (2) -0.67 (2) -0.67
(3) -051 (3) -0_.51_ (3) -0.51 (3) -052 (3) -052

 

 

 

a. (1) = % changes in terms of trade
(2) = % changes in consumption level
(3) = equivalent variation (as % of GDP)
b. The central values of of”, are 4.86 for agriculture, 5.20 for primary materials,

6.80 for durable manufactures, 5.50 for non-durable manufactures, and 4.10 for
services.
c. The figures in the parentheses (of the column heading) are represented as the

weighted average of aim .

88

 

 

 

 

 

 

Table 6-11. Sensitivity Analysis with Respect to the Elasticities of Substitution among
Different Imported Goods H "
ofnm (teu) = aim" (jpn) = aim (row)
-50% m“ 25% 50% 100%
(2.66) (5.30) c (6. 62) (7. 96) (10.60)
(1) -2.44 (l) _-_1_._5_1 (l) -1.27 (1) -1.11 (1) -0.83
U.S. (2) 0.95 (2) 1g (2) 1.18 (2) 1.23 (2) 1.34
(3) 1.21 (3) LE (3) 1.43 (3) 1.47 (3) 1.54
(1) 0.14 (1) 0._12_ (1) 0.10 (1) 0.09 (1) 0.09
EU. (2) -0.50 (2) £5; (2) -0.53 (2) -0.53 (2) -0.54
(3) -0.45 (3) flA_2 (3) -0.42 (3) -0.43 (3) -0.43
(1) 0.28 (1) L2; (1) 0.20 (1) 0.17 (1) 0.15
Japan (2) -0.74 (2) M (2) -0.77 (2) -0.77 (2) -0.78
(3) -0.60 (3) M (3) -0.61 (3) -0.62 (3) -0.62
(1) 0.49 (1) 0_.4_4 (1) 0.40 (1) 0.38 (1) 0.36
ROW (2) -0.63 (2) £416 (2) -0.70 (2) -0.72 (2) -0.74
(3) -0.48 (3) M (3) -0.54 (3) -0.55 (3) -0.58

 

 

a. (1) = % changes in terms of trade
(2) = % changes in consumption level
(3) = equivalent variation (as % of GDP)
b. The central values of Jim are 4.86 for agriculture, 5.20 for primary materials,

6.80 for durable manufactures, 5.50 for non-durable manufactures, and 4.10 for
services.
c. The figures in the parentheses (of the column heading) are represented as the

weighted average of Jim.

89

Table 6-12. Sensitivity Analysis with Respect to the Different Combinations of

Trade Elasticities of Substitution "

 

 

Elasticities of Substitution Changes
0.51m (usa) -50% m +50% +100%
U.S. T.O.T. (% changes) -2.33 i5; -l.01 -0.72
(-54.17) 0.00 (33.19) (52.32)
U.S. EV (as % ofGDP) 1.17 1A8 1.49 1.58
(-15.37) 0.00 (8.01) (14.49)
02m (tea): 0.2m (I'Pn)=0';m (row) -50% central +50% +100%
U.S. TOT. (% changes) -1.64 i5; -1.41 —1.35
(-9.21) 0.00 (6.87) (10.37)
U.S. EV (as % ofGDP) 1.33 138 1.41 1.43
(-3.91) 0.00 (2.34) (3.67)
of" m (us a) -50% central +50% +100%
U.S. T.O.T. (% changes) -l.52 ;l._51_ -l.51 -1.50
(-0.42) 0.00 (0.32) (0.59)
U.S. EV(as % ofGDP) 1.38 1._38 1.38 1.38
(0.00) 0.00 (0.00) (0.00)
0;m(teu)=01pm(ipn)=afnm (row) -50% central +50% +100%
U.S. T.O.T. (% changes) -2.44 _-1._51_ -1.11 -0.83
(-61.43) 0.00 (26.56) (45.12)
U.S. EV (as % ofGDP) 1.21 Q 1.47 1.54
(-12.03) 0.00 (6.39) (11.83)

 

 

a. Numbers in parentheses represent percentage changes with respect to the values

in the central case.

90

' -’..‘.’ L‘Lw ”(3.-F

 

6.2.2. Sensitivity Analysis with Respect to the Asset-Substitution Elasticities
Secondly, I conduct a sensitivity analysis with respect to the asset-substitution

elasticities. The elasticity of substitution between domestic and foreign assets in

portfolios, or”; , determines the ease of substitution between the two assets, and thus the

degree of international capital mobility. When these elasticities of substitution are
altered, there will be changes in the results of replacing the U.S. capital taxes.

Table 6-13 reports the results. I take the central values of the asset-substitution
elasticity as 2.0 for the U.S. and 1.5 for other regions. For the sensitivity analysis, the
values of these elasticities of substitution are increased by up to 100 percent, to 4.0 and
3.0, to represent a greater degree of international capital mobility, and they are decreased
by 100 percent, to zero, which represents no mobility of international capital. Under the
U.S. tax-policy changes, as the asset-substitution elasticities become larger, there are
more capital inflows into the United States. The more sensitive investors are, the more
domestic capital is demanded, due to the higher after-tax returns in the United States. If

0;: is increased by 100 percent, the capital stock located in the U.S. will increase by

11.9 percent, relative to the base case. This compares with an increase of 8.5 percent
when the central-case parameters are used. Consequently, the amount of capital outflow
from the other regions will be substantially greater when the asset-substitution elasticity

is larger than in the central case. (See Figure 6-2.)

91

Figure 6-2. Capital-F low Effects from Elimination of U.S. Capital
Taxes, As a Function of the Elasticity of Substitution
Between Domestic and Foreign Assets

 

 

% Change of Capital Stock

 

400% -50% central 50% 100%
Elasticities of Substitution between Domestic and Foreign Assets

Table 6-13 also shows that higher asset-substitution elasticities are associated

with larger increases in welfare gains in the United States. As of, is increased by 100%,

the U.S. welfare gains increase by 43.5 percent, relative to the revised case with central-

case parameters. However, the other regions experience more capital outflows, with

higher asset-substitution elasticities. As of, is increased by 100%, the welfare losses for

the other regions are increased by 33.3~40.5 percent.

92

Table 6-13. Sensitivity Analysis with Respect to the Asset-Substitution Elasticities a

 

 

 

 

Variables 0,4
-100% -5 0% c_en_tr_a_l b +5 0% +100%
Capital Flows (% changes)

U.S. 0.00 5.35 w 10.51 11.92
(-100.00) (-36.98) 0.00 (23.79) (40.40)

E. U. 0.00 -1.46 -_1.84 -2.03 -2.15
(100.00) (20.65) 0.00 (-10.33) (-16.85)

Japan 0.00 -2.00 M, -2.75 -2.93
(100.00) (21.26) 0.00 (-8.27) (-15.35)

ROW 0.00 -1 .61 :24; -2.42 -2.60
(100.00) (24.41) 0.00 (-13.62) (-22.07)

EV (as % of GDP)

U.S. 0.15 1.03 fl 1.70 1.98
(-89.13) (-25.36) 0.00 (23.19) (43.48)

E. U. 0.15 -O.14 i)._4_2_ -0.51 -0.59
(135.71) (66.67) 0.00 (-21.43) (-40.48)

Japan 0.12 -0.29 M -0.73 -0.83
(119.67) (52.46) 0.00 (-19.67) (-36.07)

ROW 0.17 -0.24 M -0.61 -0.68
(133.33) (52.94) 0.00 (-19.61) (-33.33)

 

 

a. Numbers in parentheses represent percentage changes with respect to the values
in the central case.

b. The central values of 0;: are 2.0 for U.S., and 1.5 for other regions.

93

 

6.2.3. Sensitivity Analysis with Respect to the Labor-Supply Elasticities

Next, I examine the implications of changing the uncompensated labor-supply
elasticities, 77 L , and the total-income elasticity of labor supply, 7],. After the unilateral
U.S. tax-policy changes, the demand for U.S. capital is expected to increase, due to the
relatively higher after-tax returns in the United States. The higher demand for capital
causes the wage rate to decrease. Also, the gross-of-tax prices of consumer goods in the
U.S. are increased, because consumption taxes are used to replace the revenue lost as a

result of the elimination of capital taxes. These price increases lead to decreases in the
real wage rate. The decrease in labor supply will be greater when 77 L is greater.

Labor supply can also be affected through the income effect, which is controlled
by r] I . After the tax-policy changes, the consumer’s net capital income will be larger.
Because of the increase in non-labor income, the consumer will enjoy more leisure, and
thus will supply less labor. This effect will be greater when 771 is greater in absolute
value. Thus, higher values of r] L and 771 (in absolute value) are associated with larger

decreases in labor supply, through both the wage effect and the income effect.
Consequently, a smaller welfare gain is expected when either of these labor elasticities is
larger in absolute value.

Figure 6-3 shows the effects of changes in the labor-supply elasticities on the

welfare gains from the tax-policy change for the United States. The central values of 77 L
and 771 are 0.15 and -0.1, respectively. As expected, the welfare gains for the U.S. are

smaller when the labor-supply elasticities are larger in absolute value. However, the

magnitude of this effect is relatively small. This indicates that other influences (such as

94

 

capital inflows, and the improvement in the efficiency of use of the capital stock) are

more important than labor-supply effects, in determining the welfare gains.“

Figure 6-3. Welfare Gains for the U.S. fiom Unilateral Elimination of
Capital Taxes, As a Function of Labor-Supply Elasticity

 

-I- Total-Income Elasticity of
Labor Supply = -0.01

+Total-Income Elasiticty of
1 .8 . Labor Supply = —0.05

-)(- Total-Income Elasticity of
1 6 ‘_ Labor Supply = -0.1 l
(.4. — . i Liz!

H.

 

 

 

 

f

 

 

 

 

 

 

 

 

Welfare Gains as % of GDP

 

0 0 .05 0 .1 0 .15
Uncompensated Labor-Supply Elasticities

6.3. Alternative Scenarios
6.3.1. U.S. Policy Changes of Different Sizes

I investigate the optimal strategy for the United States, by simulating the analysis
with alternative scenarios, in which U.S. government controls the size of the unilateral
tax policy change. Figure 6-4 plots the U.S. equivalent variations, which correspond to

policy changes of different sizes (from a 0% reduction to a 180% reduction in U.S.

 

6' Also, I note that I vary the labor-supply elasticities over a relatively small range, but this is because the
econometric literature has made substantial progress toward identifying the labor-supply parameters. Most
estimates of the elasticity of male labor supply fall within a fairly narrow range, and the range of estimates
of female labor supply has been reduced in the last two decades.

95

capital taxes). As the size of the policy change increases, the EV increases at a
diminishing rate. The EV reaches a maximum point at a 140% reduction in US capital
taxes, but it falls sharply with greater reductions of U.S. capital taxes. If the U.S. were to
reduce its capital taxes by 180%, it would actually suffer welfare losses. This is because
the continued reduction in capital tax rates leads to a need for ever-greater increases in
the consumption taxes that are used to replace the lost revenues. As the consumption-tax ?
rates increase, their distortionary effects become dramatically larger. I conclude that an
optimal strategy for the United States is to subsidize capital, if other countries don’t

respond. 1

 

Figure 6-4. Optimal Strategy for the United States

 

 

 

 

 

 

 

Welfare Gains as % of GDP

 

 

 

or. 30% 60% 90% 120% 150% 180%
Percent Reduction in U.S. Capital Taxes

6.3.2. Non-Zero Equalization of U.S. Capital Taxes
Consider the policy in which U.S. capital-tax rates are equalized at a non-zero

value. In this simulation, the rates are equalized at 32.2 percent, so that the revenues are

96

 

constant. Thus, U.S. consumption-tax rates are not increased in this case. Table 6—14

shows the U.S. domestic effects of non-zero equalization, and compares with the effects

of zero equalization (which means complete elimination of capital taxes).

Table 6—14. Domestic Effects of Non-Zero Equalization of U.S. Capital Taxes

 

 

Non-Zero Equalization Zero Equalization
Capital Flows by Sector (% changes)
Agriculture -3.17 -1.26
Primary Materials -1 .34 4.32
Durable Manufactures 36.57 54.47
Non-durable Manufactures 1 1.28 18.76
Services 1.13 3.82
QM 4.17 8.49
EV (as % ofGDP) 1.07 1.38

 

 

With the policy of non-zero equalization of U.S. capital taxes, positive U.S.

welfare gains are also expected. The equalized rates lead to a more efficient allocation of

the U.S. capital stock. This policy change also has a positive effect on capital flows, but

the size of the effect is smaller than in the case of complete elimination. The equalized

U.S. capital-tax rate is still lower than the overall capital-tax rates in other regions.

However, the equalized tax rates in some sectors, such as agriculture and primary

materials, are even higher than the capital-tax rates in those sectors in other regions. The

higher tax rates in those sectors lead the after-tax return on U.S.-located capital to move

97

 

downward in those sectors. This leads to capital outflows in those sectors (3.2 percent in
agriculture, and 1.3 percent in primary materials), and thus drives in the direction of
lessening the total amount of capital inflows in the United States. Consequently,
comparing to the policy of complete elimination, the U.S. welfare gains are reduced
(from 1.4 to 1.1 percent of GDP), since the capital inflows into the U.S. become smaller

(from 8.5 to 4.2 percent).

6.3.3. Labor-Tax Replacement

Consider the alternative scenario in which U.S. capital taxes are replaced by labor
taxes, rather than by consumption taxes. As shown in Table 6-15, in the case of using
labor taxes for equal revenue yield, the increase in the level of consumption and the
welfare gains for the U.S. become larger. This can be mainly explained by the fact that
the labor taxes are closer to uniform, while the consumption taxes are differentiated

across SCCtOI‘S.62

Table 6-15. Domestic Effects of U.S. Labor-Tax Replacement

 

 

Labor- Tax Consumption-T ax
Replacement Replacement
Consumption (% changes) 1.27 1.13
TOT (% changes) -0.96 -1.51
EV (as % ofGDP) 1.62 1.38

 

 

 

’2 The sector-specific labor taxes are not differentiated across regions: The rates are around 13 percent in
all sectors, except in services. See Chapter 5 for details.

98

In addition, the negative terms-of-trade effect becomes smaller, since the negative
terms-of-trade effect is partly canceled by the increase in the labor taxes: If the sector-
specific labor taxes are increased, there are increases in the gross-of—labor—tax prices of
U.S. output. Thus, there is an increase in the prices of U.S. exports (the first-order effect).
And there is also an increase in the prices of U.S. imports, due to higher demand for
imports (the second-order effect). The dominant first-order effect leads to improVe the

terms of trade in the United States.

Table 6-16. Sensitivity Analyses with Different Combinations of Labor-Supply
Elasticities and Goods Elasticity of Substitution

 

 

E V with Labor- Tax E V with Consumption-
Replacement Tax Replacement
r] L (with a central value of (ICC)
0.0 2.35 1.87
0.15 a 1.62 1.38
0.30 1.30 1.22
ace (with a central value of T1L)
0.8 1.68 1.56
1.3 a 1.62 1.38
1.8 1.58 1.23
Combinations (0'ch 77 L )
(1.3, 0.15) 1.62 1.38
(0.8, 0.30) 1.34 1.23
(0.3, 0.60) 1.16 1.11
(0.1, 0.90) 1.02 1.01

 

 

a. central values

99

 

Table 6-16 shows how the U.S. welfare gains for both replacements are affected
by the labor-supply elasticity and elasticity of substitution among goods. It is expected
that the welfare gains with labor-tax replacement are directly controlled more by the
labor-supply elasticity. If the uncompensated labor-supply elasticity becomes larger, we
expect that the welfare gains for both replacements would be decreased. However, since ..
the labor-supply elasticity has a more direct effect on the welfare gains with labor-tax
replacement, changing the value of the labor-supply elasticity would have a greater effect

on the welfare gains with labor-tax replacement, rather than on those with consumption-

 

I.

tax replacement.

In the simulation, if the central value of the uncompensated labor-supply elasticity
is doubled, the welfare gains with labor-tax replacement drop by 19.8 percent (from 1.6
percent of GDP to 1.3 percent of GDP), while those with consumption-tax replacement
drop by 11.6 percent (from 1.4 percent of GDP to 1.2 percent of GDP). However, even
though the absolute value of the change in EV is larger with labor-tax replacement, the
ratio of EV with consumption-tax replacement to EV with labor-tax replacement doesn’t
change much. Similarly, if the goods elasticity of substitution is larger, the decreases of
the welfare gains with consumption-tax replacement are bigger than the decreases of
those with labor-tax replacement. The last part of Table 6-16 shows that, if both a
smaller goods elasticity of substitution and a larger labor-supply elasticity are assumed,

the gaps between the welfare gains for both of these replacements become smaller.

100

6.3.4. Responses of Foreign Governments

Finally, I consider the case of multilateral policy changes, in which other regions
also eliminate their capital taxes. Figure 6-5 shows the comparison of the effects of
unilateral and multilateral policy changes. The multilateral policy changes produce
welfare gains for the entire world, whereas the unilateral policy changes produce a
welfare gain only for the United States, which is the country undertaking the policy W
changes. This is because the multilateral policy changes encourage more efficient use of

capital everywhere.

 

Figure 6-5. Welfare Effects - Unilateral vs. Multilateral

 

  
 

 

 

 

 

 

  

 

 

 

 

2 ,_ _ _ _ _ _ _ __ __ _. _.__._ ._..”
9d. 1.5
{D . .
80‘ 1 a I Unilateral Polrcy
a\° I Multilateral Policy
Q o 5
E '
8
b o
to _
«E
g -0.5

US EU JPN ROW
Region

Table 6-17 shows the decomposition of the U.S. overall effects. The multilateral

case produces less capital-flow effects, and less terms-of-trade effects, comparing to

101

unilateral case. Even though other regions also pursue same policy, the after-tax returns

on U.S.-located capital are still relatively higher than the after-tax returns on foreign-

located capital. This comes from the difference of characteristics of capital-tax structures

for each region. The simultaneous eliminating of capital taxes also leads to smaller U.S.

terms-of-trade losses. This is due to the fact that the terms-of-trade losses associated

with a unilateral policy change are partially offset by terms-of-trade gains to trading -_
partners, when the policy change occur on a multilateral basis. For the United States,
welfare losses associated with reduced capital inflows are almost offset by the extra

welfare gains from the improvement of terms of trade. Thus, the multilateral case doesn’t

 

lead to much change in U.S. welfare gains.

Table 6-17. U.S. Static Welfare Changes of Multilateral Case,

As a Function of the Trade and the Asset Parameters

(Unit: % of GDP)

 

Trade Elasticity of Substitution

 

 

 

 

 

Central Big T erms-of- Trade Effects
Asset-Substitution Central 1.42 1.49 => -0.07 c
Elasticity Zero 1.05 0.96 :> -0.09 d
U U
Capital-F low Effects 0.37 ’ Q._5_3 b
a. the case with holding constant trade parameters
b. the case with holding constant trade parameters, and terms-of-trade effects at zero
0. the case with holding constant asset parameters
(1. the case with holding constant asset parameters, and capital-flow effects at zero

102

 

CHAPTER 7

DYNAMIC MODEL

Thus far, I have analyzed the effect of U.S. tax reform with a static model, in
which tax-policy evaluations are based on single-period equilibria. In this static
framework, the distorting effects of capital taxes may be understated, since the effects on g
saving decisions are not captured. The dynamic version of the model, in which
consumers make a saving decision in each period, is required to capture intertemporal

distortions.

 

7.1. Model and Calibration Issues

The dynamic structure here involves multiple repetition of an essentially two-
period maximization problem, which was used in the GEMTAP model. An alternative
approach is the lifetime-utility—firnction approach, which involves maximization of a
lifetime utility function, subject to a multiperiod budget constraint. This approach, which
was used in Summers (1981) and Auerbach and Kotlikoff (1983), has become quite
popular in recent years. Despite the popularity and some advantages of lifetime-utility-
function approach, it has at least one serious problem.63 Under seemingly reasonable
assumptions about the important parameters, such as the rate of time preference and the
intertemporal substitution elasticity, the lifetime-utility-firnction approach can yield very
high responses of savings to changes in tax rates. This problem does not arise in the

GEMTAP model, which can be calibrated precisely to any desired savings elasticity.

 

’53 The problems of excessive intertemporal responsiveness were previously discussed in detail, in Chapter 2.
Also, see Ballard (1987, 1990a) for further discussion.

103

The first equilibrium in every sequence is for the 1995 benchmark year. The
equilibria in any sequence are connected to each other through capital accumulation. In
other words, saving in the current period will augment the capital-service endowment

available in the next period. The endowment of labor grows at a constant rate.

In every sequence, the utility levels in region r, U r , are represented by a CBS

fimction:

 

0115 _1 0h: -1 all: —1

F
U’(H',Cf’)= 0’ H’ a... +(1—p’ )Cf’ a)... , (7.1)

 

where the H r are current expenditure in region r, the C fr are future consumption in

region r, and the Uhs are the elasticities of substitution between H r and C fr. That is,

saving decisions are based on the maximization of a nested utility function, where the
outer nest is defined over current expenditure (a composite of leisure and present-
consumption goods) and the expected future-consumption stream made possible from
savings.

The consumer’s budget constraints are given by:

PH’H’ +PS’s’ = wEr +71?” +7?" + TR' 5 Y1", (7.3)

104

 

where the PHr are the composite prices of leisure and present-consumption goods, the

PS" Sr are the values of savings in region r, and the Y1" are region r’s expanded income,

which includes the value of the consumer’s labor endowments, the value of the
consumer’s capital income from domestic capital, the value of the consumer’s capital
income from foreign capital, and transfer payments.

As in the static framework, the allocation of capital between home and abroad is
viewed as prior to the decision about current consumption and future consumption. In .1

this sense, the consumer’s capital income in (7.3) is treated as given, since it was derived

 

from the maximization of Ar :

 

A

or:

A 04-1 A 04-1 04-1

Ar(rK",r*Krs)= ar (rK")a,’; +(1—ar )(r'IKrsiar’: .
(7.4)

A
where the 62’ are share parameters, the of, are the elasticities of substitution between

domestic and foreign capital assets, the rK ” are income fi'om domestic assets (home-

located capital invested by home resident) in region r, and the rTK ’5 are income from
foreign assets (foreign-located capital invested by home resident) in region r.

In this model, there is no financial intermediation between saving and investment.
That is, a consumer buys investment goods directly with his savings. The model assumes

that the consumer who buys S units of capital will realize a capital service flow of 75

105

per period,64 and each unit of capital services is expected to earn PK per period. This

yield of saving is, in turn, sold for future consumption. Let Per be the price of

consumption today. Under the assumption of static expectation, the consumer expects

that firture consumption, C fr , will cost Pcr in each future year. Therefore,

 

Pc'Cfr = PK’ySr. (7.5)
Rearranging this, then I have:
P rP r
PS'S’ =( f) r; )cf’. (7.6)
K

This states that the value of saving equals the discounted present value of the expected
future consumption that can be brought with that saving. Using (7.6), I can rewrite the

budget constraints:

P'P'
PH’H’ +[-—5——C-]Cf’ = If. (7.7)

\—

6‘ I assign to y the same value that I assign to r in the benchmark, 0.04. However, in GEMTAP, the
Value of 7 is not same as r , because of the effect of personal taxes.

106

 

Constrained maximization of the utility functions F r yields the demand

 

 

 

 

 

functions:
F ahs
Hr = —fl W (7 8)
PHr ,- ,- 1_0hs .
PKry r
I
and 1
( \Uhs
Cfr = 1_flF er
1—0' s '
PSrPcr F0713 rl—oh, F M PSrPcr h
—P . fl PH +1-fl ——
K K 7 J Ps'r
(7.9)

Now, I consider the calibration of the elasticity of substitution between current

expenditure and future consumption. Differentiating the demand function for firture

consumption in (7.9) with respect to PK yields:

 

 

as = (1—pF)"’”K _s(1-pf)a”(a,,,-1)+s(a,,,-1)

a 0' —1
6PK pKyWPSPCW ’“qj PK(PSPC) ’” ‘1' PK
Pc PKI’ PK)’

, (7.10)

 

107

PSPc

1-0’ hs
] . Manipulating the demand
PK)’

where ‘1’ =flFahs PHI—‘7’ls +(1—flF)ahs(

function for future consumption and substituting into (7.10) gives us a simple expression

for the saving elasticity:

_as_§,_(_ = PKK _ PSs(a,,, —1)

 

 

 

 

 

= + 0' -l . 7.11
p at), S ,1 Y1 ( h. ) ( )
Solving for O'hs gives: a
K+S
+1-— Y
6,, = s 1 . (7.12)
1__
Y1

The a h 5 parameters are calibrated to match with desired levels of the savings

elasticity. Regarding the savings elasticity, the empirical literature is kind of a mix.
Some articles give support for positive elasticities, but some also give support for
negative elasticities, or for responses that are not distinguished from zero. In this study, I
take the central value of the savings elasticity with respect to the return to capital (,0) to
be 0.4, which was found by Boskin (1978), and then a sensitivity test with different
values will be run. Boskin’s work has shifted the consensus toward the belief that the
savings elasticity is positive. And, his estimates are generally statistically significant, and

he suggests that they are economically significant, as well.

108

If constrained maximization of the utility function, U r , occurs repeatedly, then
utility depends on a stream of consumption that extends infinitely into the future. When I
move through the sequences, the capital stock grows because of saving. The growth rates

of capital and labor are chosen so that the base case is indeed on a balanced grth path.

7.2. Simulation Results

I analyze the dynamic effects of changes in U.S. tax policy on the global economy.

Here again, I consider the complete elimination of U.S. capital taxes. The lost revenues
are replaced with higher rates of consumption taxes. Under the dynamic framework, the
future path of the economy can be analyzed explicitly. Table 7-1 through 7-3 plot the
transitional dynamic paths of consumption, leisure, and utility in all regions. The vertical
axis represents the deviations from the pre-tax-reform equilibrium, in percentage terms.

The first 40 years of the sequence of equilibria are shown on the horizontal axis.

Figure 7-1. Constnnption Path - All Regions

 

 

Devrattons m %
(of Pre- T ax-Reform Eq 'm)

 

Period

109

. .l Aunt-L finals.”
1'

 

(_

 

Deviations in %
(of Pre- T ax—Reform Eq 'm)

Deviation in %
(of Pre- T ax-Reform Eq 'm)

1
o
'01

Figure 7-2. Leisure Path - All Regions

c.)
'01

 

—4 m
'cnm'oroo

 

o
o'tn

 

 

l
7‘ l
01 —L

Period

Figure 7-3. Utility Path - All Regions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

110

 

8......

 

The U.S. consumption and utility paths are shown to be growing at a stronger
pace, while the other regions have flatter paths of consumption and utility. This is
because of higher capital accumulation, along with capital inflows to the United States.

Now, I investigate the dynamic effects on the U.S. domestic economy in detail.
To investigate the transitional effects, I also consider the case in which lost revenues are
replaced with higher rates of labor taxes, and compare the results to the case with higher
rates of consumption taxes. Table 7-1 shows the dynamic results of impact and long-run

effects. Consider first the case in which capital taxes are replaced by higher consumption

 

taxes. The impact effects show that the consumption level drops by 1.6 percent, and the
utility level decreases by 0.6 percent, relative to the pre-tax-reform equilibrium. The
level of consumption falls sharply, since the increase in output level is surpassed by the
increase in the savings level. The decrease in the utility level is rather smaller, due to the
increase of leisure. The decrease in the net wage rate leads to a substantial increase in
leisure. In the long run, utility level increases by 4.0 percent, mostly due to higher
increases in consumption level.

In the second case, in which capital taxes are replaced by labor taxes, the impact
effects show that the utility level decreases by 0.1 percent, relative to the pre-tax-reform
equilibrium. This is due to small decreases in the consumption level, at the time of the
changes in tax policy. The level of consumption does not move so much in the case of
labor-tax replacement, while it falls sharply in the case of the replacement with
consumption taxes, since an increase in the output level is almost canceled by an increase

in the savings level. The increase in leisure is larger than that in the case of consumption-

111

tax replacement, since the increase in labor taxes directly leads to a increase in leisure. In

the long run, consumption and utility level increase by 4.5 and 3.9 percent, respectively.

Table 7-1. The Impact and Long-Run Effects of Replacing of U.S. Capital Taxes
(Unit: % Changes 8’)

 

 

Replacing by Consumption Tax Replacing by Labor Tax
Impact Eflect Long-Run Effect Impact Eflect Long-Run Efl'ect
Consumption -1 .62 5.60 -0.63 4.45
Leisure 2.97 0.70 3.12 1.20
Utility -0.55 4.00 -0.06 3.86

 

 

 

 

a. Figures are percentage changes relative to pre-tax-reform equilibrium.

Figure 7-4. Consumption Path - U.S.

 

or
1

01
D

 

 

 

h
T

 

 

ff— ' 1 ‘ 1.0-CTR
3 +LTR

 

l
l

 

 

 

 

 

Devratrons in %
(of Pre— T ax-Reform Eq ’m)

o ..L
I
p
..
_
b
..
-
_
h—
..
_
_
..
p-
_
)—
h
..
._
.
..
..
j-
p—
p-
)-
)-
..
b-
hr
)-
b
..
._
L-
)-
h

l

 

I
‘

 

 

I
N
1

Period

112

Figure 74 through 7-6 show the transitions of consumption, leisure, and utility
level in the United States, after the policy shock occurs in the first year. In the case of the
replacement with consumption taxes, the level of consumption is lower in the first year,
by around -1.6 percent. However, consumption then rises at a faster rate, as a result of
the greater amount of capital accumulation. The level of consumption approaches a new
balanced-growth path asymptotically, and reaches a gain of 5.6 percent from the base ff“
case beyond year 40. In the case of replacement with labor taxes, consumption rises at a
slower rate, and reaches a gain of 4.5 percent from the base case beyond year 40. The

paths of leisure in both cases have similar shapes: the level of leisure is higher at first

 

year, and then decreases as time goes on. With the labor tax replacement, labor decreases

more, and thus leisure increases more.

Figure 7-5. Leisure Path - U.S.

9°
01

 

w
2.4

 

N

CI
1
.11

 

 

" +CTR

um.“— +er

N

t

(I!
_J

 

 

 

_A
01
i

 

d
D

 

Devzatrons m %
(of Pre- T ax-Reform Eq ’m)

.0
U!
i

 

 

 

 

 

1 5 9 13 17 21 25 29 33 37 41
Period

113

 

Figure 7-6. Utility Path - U.S.

 

&

 

 

O)

 

 

 

 

 

 

 

Devratrons tn %
( of-Pre- T ax-Reform Eq 'm)
d N

 

 

O

 

 

Period

 

Figure 7-7. U.S. Consumption Path, As a Function of Savings
Elasticity

-0- savings elasticity=0.4
+ savings elasticity=0.2

+ savings elasticity=0.0

Devratrons in %
(of Pre-T ax-Reform Eq 'm)

 

Period

114

I also report the sensitivity analysis of the U.S. consumption path with respect to
savings elasticity. As shown in Figure 7-7, for a larger savings elasticity, consumption
drops farther at first, and then it recovers more quickly, and the level of consumption
finally reaches at higher point at year 40, compared to the lower-elasticity case.

Last, I calculate the dynamic welfare gains, using the present value of the stream
of the equivalent variation over 40 years and more.65 Although the economy approaches 3‘
the new steady state closely by the end of 40 years, I use longer periods to ensure that the
approach to the new steady state is very close.66 The approximation is involved in

calculations of the termination term.67 Table 7-2 and 7-3 show the results of a unilateral

 

nl-n-v—v 1‘; -u.-—A._-I _-

policy change. The results show that a 100-year simulation provides a U.S. welfare gain
of around $4.0 trillion, while a 200-year simulation provides around $4.1 trillion. These
amount to about 2.2 percent of GDP stream, which are discounted over the simulation
period (vs. 1.4 percent of GDP in static simulation). The welfare losses for the European
Union, Japan, and the Rest of World are 0.4~0.7 percent of their GDP streams (vs.
0.4~0.6 percent of their GDP in static simulation).

The welfare gains of a multilateral policy change are shown in Table 7-4 and 7-5.

The results show that a 100-year simulation yields a U.S. welfare gain of around $3.3

 

65 For dynamic welfare evaluation, I use the H r function, not the U r function. If savings are included in
the evaluation of utility in the current period, the “double counting” problem would happen, since savings
are used to buy future consumption.

66 The dynamic procedure here does not guarantee that the change in welfare will be invariant with respect
to the numbers of years between first and last equilibrium. In general, the longer is the numbers of years,
the closer is the equivalent variation to the actual steady-state value. See Ballard, et al. (1985) for details.

67 Over 40 years in a revised-case calculation, the economy asymptotically approaches a new steady state.
However, it will not actually reach the new steady state. As far as a policy is designed to increase saving,
the economy will still be experiencing a small amount of capital deepening, even after many years. For
calculating the termination term, I assume a slight decrease in saving from the amount that I actually
calculated for the termination year.

115

trillion, while a ZOO-year simulation yields around $3.4 trillion. These amount to about
1.8 percent of GDP stream, which are discounted over the simulation period (vs. 1.4
percent of GDP in static simulation). Under a multilateral policy change, other regions
also have welfare gains, which amount to about l.1~1.2 percent of their GDP streams (vs.

0.5~0.6 percent of their GDP in static simulation).

Table 7-2. The Equivalent Variation I - Dynamic Simulation of Unilateral Case
(Unit: Billions of 1995 Dollars)

 

 

Simulation Period U.S. E. U. Japan ROW

40 2,735.38 -88l.81 -888.58 -1,165.95

60 3,475.34 -872.91 —887.14 -1,159.94
80 3,813.35 -868.85 -886.48 -1,156.75
100 3,967.75 -866.99 -886.18 -1,155.29
120 4,038.28 -866.15 -886.05 -1,154.62
140 4,070.50 -865.76 885.98 -l,154.32
160 4,085.22 -865.58 -885.96 -1,154.18
180 4,091.94 —865.50 -885.94 -1,154. 12
200 4,095.01 -865.46 -885.94 -1,154.09

 

 

 

116

Table 7-3. The Equivalent Variation II - Dynamic Simulation of Unilateral Case

(Unit: % of GDP Stream)

 

 

Simulation Period U.S. E. U. Japan ROW
40 1.84 -0.54 -0.84 -0.68
60 2.06 -0.47 -0.74 -0.60
80 2.15 -0.44 -0.70 -0.56
100 2.18 -0.43 -0.68 -0.55
120 2.19 -0.43 -0.68 -0.54
140 2.20 -0.43 -0.67 -0.54
160 2.21 -0.43 -O.67 -0.54
180 2.21 -0.42 -0.67 -0.54
200 2.21 -0.42 -0.67 -0.54

 

 

Table 7-4. The Equivalent Variation III - Dynamic Simulation of Multilateral Case

(Unit: Billions of 1995 Dollars)

 

 

 

Simulation Period U.S. E. U. Japan ROW
40 2,329.59 1,524.93 826.99 1,418.34
60 2,905.79 1,978.86 1,147.78 1,892.14
80 3,169.00 2,186.13 1,294.07 2,108.40
100 3,289.24 2,280.76 1,360.79 2,207.11
120 3,344.16 2,323.97 1,391.21 2,252.16
140 3,369.25 2,343.69 1,405.83 2,272.72
160 3,380.71 2,352.70 1,411.41 2,282.11
180 3,385.94 2,356.81 1,414.30 2,286.39
200 3,388.33 2,358.69 1,415.61 2,288.35

 

117

 

 

Table 7-5. The Equivalent Variation IV - Dynamic Simulation of Multilateral Case
(Unit: % of GDP Stream)

 

 

Simulation Period U.S. E. U. Japan ROW
40 1.57 0.93 0.78 0.83
60 1.72 1.11 0.95 0.97
80 1.78 1.11 1.03 1.03
100 1.81 1.14 1.05 1.05
120 1.82 1.15 1.06 1.06
140 1.82 1.15 1.07 1.06
160 1.83 1.15 1.07 1.07
180 1.83 1.15 1.07 1.07
200 1.83 1.16 1.07 1.07

 

 

Table 7-6. U.S. Dynamic Welfare Changes of Unilateral Case,
As a Function of the Trade and the Asset Parameters

(Unit: % of GDP)

 

 

 

Trade Elasticity of Substitution
Central Big T erms-of- Trade Efi'ects
Asset-Substitution Central 2.22 2.54 :> -0.32 c
Elasticity Zero 1.01 1.24 :> fl d
U U
Capital-F low Effects 1.21 a fig b

 

 

 

the case with holding constant trade parameters

the case with holding constant trade parameters, and terms-of-trade effects at zero
the case with holding constant asset parameters

the case with holding constant asset parameters, and capital-flow effects at zero

9*? 9‘1”

118

 

Next, the overall U.S. welfare effects of a 200-year simulation are decomposed. I
consider both a unilateral case and a multilateral case. The results are shown in Table 7-6
and 7-7. The capital-flow effects and the terms-of-trade effects can be isolated, through
the same process used in the static case. The method of isolating Harberger effects is
different. In the static case, the numbers being estimated directly from the simulation
with zero asset-substitution elasticity and big trade elasticity of substitution simply F
represent Harberger effects (0.74 in Table 6-6, and 0.96 in Table 6-17). However, in the l
dynamic case, they can’t be interpreted as only Harberger effects (1.24 in Table 7-6, and r

1.58 in Table 7-7). Since they include the positive effects on saving decision, which are

 

not captured in the static framework, they must be interpreted as the sum of Harberger
effects and the intertemporal effects. As shown in Table 7-8, the intertemporal effects are

estimated as 0.5~0.6 percent of GDP.

Table 7-7. U.S. Dynamic Welfare Changes of Multilateral Case,
As a Function of the Trade and the Asset Parameters
(Unit: % of GDP)

 

 

 

Trade Elasticity of Substitution
Central Big Terms-of— Trade Effects
Asset—Substitution Central 1.83 1.84 :> -0.01 c
Elasticity Zero 1.49 1.58 :5 002 d
U U
Capital-F low Effects 0.34 a M b

 

 

 

the case with holding constant trade parameters

the case with holding constant trade parameters, and terms-of-trade effects at zero
the case with holding constant asset parameters

the case with holding constant asset parameters, and capital-flow effects at zero

999'?”

119

 

Table 7-8. Intertemporal Effects for the U.S.
(Unit: % of QD_P_)

 

 

 

 

 

Static Dynamic Intertemporal Effects
Unilateral Ca_sg a
E V 0.74 1 .24 :5 0.50
Multilateral Case 3
EV 0.96 1.58 :5 0.62 5""?

 

 

a. the case with zero asset-substitution elasticity and big trade elasticity of
substitution

 

Table 7 -9. Welfare Effects for Whole World

 

 

 

 

 

U.S E. U. Japan ROW W_orlg'
Unilateral Case
EV ($ billions) ’ 4,095.01 -865 .46 -885.94 -1,154.09 1,189.52
EV (% of World GDP Stream) 0.16
Multilateral Case
EV ($ billions) 3,388.33 2,358.69 1,415.61 2,288.35 9,450.98
EV (% of World GDP Stream) 1.28

 

a. Units are in parentheses.

So far, I focused on each region’s welfare gains or losses, rather than welfare
effects for whole world. Now, I calculate the overall welfare gains in both unilateral and
multilateral case, using a ZOO-year simulation. Table 7-9 shows that a unilateral policy

change yields world welfare gains of around $1.2 trillion. These amount to about only

120

 

0.2 percent of world GDP stream, which are discounted over the simulation period.
However, under a multilateral policy change, the world enjoys tremendous welfare gains
of $9.5 trillion, which amount to about 1.3 percent of world GDP stream. The results
show that a worldwide tax reform is superior over a unilateral tax reform, in a sense that a

worldwide reform leads to larger world welfare gains.

121

CHAPTER 8

CONCLUSION

This paper has described a global trade model in which international spillover
effects can occur through changes in commodity flows and changes in capital flows. I
use both static and dynamic computational general-equilibrium models that divide the
world into four regions. The data are from Global Trade Analysis Project for 1995. My
model incorporates a labor/leisure choice and international cross-ownership of assets. I
report and interpret the results of simulations of changes in U.S. tax policy.

In the static simulation, I find that unilateral elimination of U.S. capital taxes
generates welfare gains for the United States. The tax-policy changes improve the
allocation of the domestic capital stock, and they generate capital inflows, but they also
generate negative effects on the terms of trade. The positive effects dominate the
negative effects, so that U.S. welfare is improved. Conversely, foreign economies
experience capital outflows, along with positive terms-of-trade effects. Since the positive
terms-of-trade effects are dominated by the negative capital-flow effects, the foreign
economies have welfare losses. However, when all regions remove their capital taxes,
the entire world experiences welfare gains.

As the trade elasticities of substitution become larger, the terms-of-trade effects
become smaller. A larger asset-substitution elasticity causes larger capital-flow effects,
and it also causes larger terms-of-trade effects. When labor supply is more elastic, the

welfare gains are reduced.

122

 

 

Under the dynamic framework, the future path of the economy is analyzed
explicitly. The consumption path for the United States is shown to be growing at
relatively stronger pace, while the other regions have a flatter path of consumption,
because of higher capital accumulation, along with capital inflows to the United States:
The U.S. consumption is decreased in the first year when the policy shock occurs.
However, the level of consumption then rises at a faster rate, and finally approaches a
new balanced-growth path asymptotically. With a larger savings elasticity, consumption
drops farther at first, and it recovers more quickly.

The analysis of welfare gains for the United States indicates that unilateral
elimination of U.S. capital taxes yields dynamic gains, whose present values are around
$4.0~$4.1 trillion, while it yields an annual static welfare gain of around $98 billion in
1995 dollars. The dynamic gains are estimated as 2.2 percent of GDP stream, while the
static gain is estimated as 1.4 percent of GDP. If all regions adopt the policy changes, the
dynamic gains for the United States are 1.8 percent of GDP stream, compared with 1.4

percent of GDP in the static case.

123

 

Illa,
L

 

APPENDIX

1. Factor Demand Functions with CES

A firm with CES technologi demands quantities 35,- of factor i when market prices
are p,- and taxes are ti. Assuming an elasticity of substitution equal to 0', find the

compensated demand for the ith factor when market prices and taxes are given by p j

and tj

 

5'"

The production function is CES, so it can be written:

1
y=r/J{axlp +0—61ka ,where p=OI—c;l

The compensated demand functions for this production function can be then

derived using standard Lagrangean techniques:

Q
L
Q
..L

Tilq

L=P1(1+11)X1 +P2(1+’2)x2 +4 y-l/I an" +(1—alx20

 

 

If this is differentiated with respect to x1 and x2 ,

124

 

 

 

o—l
__ __ _1 _
p1(1+tl)=Ay/(;3_—l) axl" +(1—a)x20 0(00 )x10 (1)
1
9:1 0_-1 E 1 :1.
p2(1+tz)=Aw(}E_—1) 66.10 +(1—a)x2" (1—a{0; )x20 (2)

Dividing (1) by (2), and arranging for x2 ,

x2 {fill—”21.000231, (3)

P2(1+’2) 0

Putting (3) into the cost ftmction,

C=P1(1+’1)X1+P2(1+12)x2

=(,1(1,,1».{a001(1+n)1rAlgerian-(2)50 W

a

Therefore, compensated demand functions can be written:

125

 

 

C

=ip1(1+t1)} “0(P1(1+’1))1-0 +(1—a)a(Pz(l+t2))l-a

 

 

(4)

and

C

_ l-a 0
x2 _ {P2(1+t2 )} aa(p1 (1+t1))1"’ +(1—a)a(p2 (1+t2 ))1’0 (5)

 

For simplicity, let a“ (pl (1 + t1))1"a + (1 — a)” (p2 (1 + t2 ))1_‘7 s A , and putting

(4) and (5) into the production function,

 

mv‘

 

 

 

9;] 3;] 0-1
y_,,a(__a_]a£ " ,(1_a(__1_1_]a£ " ,
) P104411 A P204421 A
L
=l/ICA0‘1
Now, we can get the unit cost function:

C C _1__
cE—z =I/I—1A1—0 (6)

y L

126

 

1

fibres not-0 + (1 -a)"(pz(1 “Zr-“F

Putting (6) into equations (4) and (5), we get associated demand functions:

+18%)

and
y (1 - all/'6 a
x, = _ (8)
ll! P2 (1 + ’2)
Next step is to calibrate functional parameters to a single benchmark
equilibrium.68 From (3), we get the value of a:

1
171(13‘1-1181" _ 51(13‘5117711—‘0
1 1 _ _ - —1-p _ - ...1-p
- — - — P1(1+t1)x1 +P2(1+12)x2
171(1+t1)3510 +P2(1+12)ff

 

 

If we define 0 as the value share of x1 at the benchmark point:

 

6’ In most large-scale applied general-equilibrium models, we have many function parameters to specify
with relatively few observations. The conventional approach is to calibrate functional parameters to a
single benchmark equilibrium. See GAMS Development Corporation (1998).

127

 

'[u
(VHF-‘3-

 

51044-031
§1(1+t—1)31+§2(1+52)52

6:

 

then the relationship between 6 and a is presented:

—p
“*1

ail” + (1 — 61);;

9:

 

And, we get the value of w from the production function:

V] = fézi’lp +(1—a)5f2p}_%

Using these calibrated parameters, the cost and demand functions can be
expressed as the calibrated share from. In the calibrated form, the cost and demand
functions explicitly incorporate benchmark demands, benchmark factor price, benchmark
tax rate, the elasticity of substitution, benchmark cost, benchmark output, and benchmark
value share. First, the production fimction in the calibrated share form is presented, using

the value of 52' and (9:

l
p p _
y=5i 6E1] duet—2] p (9)
x1 12

128

 

Qnfi

 

Next, using the value of E and 0 , the unit cost function in the calibrated share form is

presented:

1

c = EMMY—G + (1 — oiMJI-o I; (10)

510+?” 52(1+t.2)

Lastly, the compensated demand fianction in the calibrated share form is presented:

and

Therefore, in general, the unit compensated demand function in the calibrated share form

(37 = 5 =1) can be expressed:

1

—. -. a . . 1-0 E
xizfi[£l-(-l+—tlk] ,where C= 26i(£_l_(_lit_12] (11)

Pi(1+ti) 51'0“?)

i

129

 

 

 

 

2. Compensated Demand Functions with CES

A consumer with CES utility consumes quantities 1?,- when market prices are pi.
Assuming an elasticity of substitution equal to 0', find the compensated demand for the

ith good when market prices are given by p j-

The utility function is CES, so it can be written:

1
U={mlp+(1—a)x§}; ,where [3:931

Constrained maximization of the utility function U yields the compensated

demand functions:

 

a a Y
x1 = {_} 0' 1—0 0' 1—0' (1)
pl 0: p1 + (1 — a) p2

and

 

a
l—a Y

x2={ } 0' 1—0' a 1—0' (2)
P2 (1 p1 +(1—a) [)2

For simplicity, let (zapll-U + (1 — or)"r p21—0 a A , and putting (1) and (2) into the

utility function, we have the indirect utility function:

130

 

rm! fi‘

“—3.

 

 

 

 

0'
' 2:1 91‘ :1
0' a _ a 0'
V=Ta[£) Z +(1—a(1—a-] Z >
P1 A P2 A
L J
L
= YAC"1
So, the expenditure function is expressed:
...L
E = VAl“I
1
=V(a0p11'0 +(1_a)0p21-01-o (3)

Next step is to calibrate functional parameters to a single benchmark equilibrium.

We get the value of a:

l

_ __ _ _1—
Plxla _ P1X] p
' 1 1 ‘ _ —l-p _ —l—p
__ _; _ _; Plxl +p2x2
Pix] +p2x2

 

 

If we define 9 as the value share of x1 at the benchmark point:

131

P1x1

FIE] + 52372

 

then the relationship between 6 and a is presented:

Cit-1p F ‘m "

._.—

_ ail” + (1 —a)ff

 

And, we get the value of (7 from the utility function:

 

l

mama—w

Using these calibrated parameters, the demand functions can be expressed as the

calibrated share from. First, the utility function in the calibrated share form is presented,

using the value of (7(=1) and 6:

 

1
p p —
U: 6(9) 4149(9) p (4)
x1 x2

Next, using the value of E(= 1) and 19 , the unit expenditure function in the calibrated

share form is presented:

132

1—0 1-0' 1;
e: 19%?) +(1—0(€—2] (5)

And, lastly, using the relationship between the expenditure and the indirect utility

functions:

 

the compensated demand function in the calibrated share form is presented:

and

 

Therefore, in general, the unit compensated demand function in the calibrated share form

((7 = E =1) can be expressed:

133

e_- 0' . 1—0' 1-0
x,- = 3V [—11] , where e: 2 6(35] and V =
Pi

i

3. Supply Functions with CET

A firm with a CE T technology produces joint products (outputs) 1?,- when market

prices are [7,- and output tax is ty. Assuming a constant elasticity of transformation

 

equal to 77 , let ’s find the supply functions of the ith output when market prices and taxes

are given by p 1- and ty.

The production function is CET, so it can be written:

L
1:1 L“ n+1

y=y1 axl" +(1—a)x2'7

 

Constrained maximization yields the supply fimctions (assuming same output

taxes on two products):

of" C
p"7(1—z ) a"? 1+”441—01)"? “’7
1 y P1 P2

(1)

 

 

XI:

134

 

and

1— W C
x2 = (‘77 a) -—77 1+7; —77 1+7; (2)
p2 (l-ty) a p1 +(1—a) p2

 

For simplicity, let of” p11“? + (1 — a)_'7 p?" a A , and putting (1) and (2) into the

production function,

 

 

 

,L
’7_+.1 ’7_"1 0+1
-0 '1 _ --n '7
W1 ,7 :2 +1-: —“.,,“) % >
P (1'0) P2(1'ty)
“L
l-ty
Now, we can get the unit cost function:
1
_C C —1 fl
c=;= _;_ =w A 6—9) a)
WCA 0+1 ._1_
l—ty

135

.. ML «ILLIY

 

 

Putting (3) into equations (1) and (2), we get associated supply functions:

“’7
x1 = {l){ all/C } (4)
V’ pl 1—ty

and
-n
y (1 - QWC
x, = ._ (5)
[wllpzll -ty )}
Next step is to calibrate functional parameters to a single benchmark equilibrium.
We get the value of a:

l

— - r7
P1X]

1 l

 

—— 77 — — 7)
Plxl +P2x2

If we define 6 as the value share of x1 at the benchmark point:

1713‘]

Eli] + 523-2

6:

 

then the relationship between 6 and a is presented:

136

 

1.}

 

 

n+1 17:1
air—1'7 + (1 ——a)fz'7

And, we get the value of 1/1 from the production fimction:

.1
0+1 n+1 "+1

111:; 0551" +(1—a)5c’2'7

Using these calibrated parameters, the cost and demand functions can be
expressed as the calibrated share form. First, the production function in the calibrated

share form is presented, using the value of 5; and 6:

2:1 17:1 5
y=y 6(—’§‘— " +(1-49)(i‘.—2 ” (6)

11 J‘2

Next, using the value of E and 0 , the unit cost function in the calibrated share form is

presented:

1+7; 1+1; 1? _
c=E 9(9) +04%?) ’7 (1 t’) (7)

137

 

 

Lastly, the supply function in the calibrated share form is presented:

and

Therefore, in general, the unit supply function in the calibrated share form (y = E =1)

can be expressed:

01'

x. z . (8)

 

~
~
H

 

 

138

 

 

 

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