W?s gj1D
POLICY RESEARCH WORKING PAPER 1970
Trade Liberalization and Although trade liberalization
has been linked
Endogenous Growth in a econometrically and through
Small Open Economy casual empiricism to large
income increases, attempts to
quantify its impact in static
A Quantitative Assessment simulation models have
shown estimated gains. This
paper shows that when the
Thomas F. Rutherford endogenous dynamic effects
David G. Tarr of trade liberalization are built
into simulation models, the
estimated gains are indeed
very large. But complementary
regulatory, financial market,
and macroeconomic reforms
are important to realize the
largest gains.
The World Bank
Development Research Group
Trade H
September 1998
POLICY RESEARCH WORKING PAPER 1970
Summary findings
Rutherford and Tarr develop a numerical endogenous their central model, where the economy is assumed to be
growth model approximating an infinite horizon, which unable to borrow on international financial markets. If
allows them to investigate the relationship between trade macroeconomic and financial reforms are in place that
liberalization and economic growth. would allow international borrowing, however, the same
Economic theory generally implies that trade tariff cut is estimated to result in a 37 percent increase in
liberalization will improve economic growth, and the Hicksian equivalent variation. On the other hand, if
two phenomena are positively correlated in empirical inefficient replacement taxes must be used in an
tests, but the connection is not well-substantiated in economy without the capacity to borrow internationally,
numerical general equilibrium models. the gains would be reduced to 4.7 percent. Larger tariff
In the authors' model, an intermediate input affects cuts - typical of those in many developing countries
aggregate output through a Dixit-Stiglitz function. over the past 30 years - produce larger estimated
Additional varieties provide the engine of growth in this welfare gains at least proportionate to the size of the cut.
framework and the existence of this mechanism The authors apply the model to five developing
magnifies the welfare costs. In this model with lump sum countries and estimate the impact of the tariff changes
revenue replacement, reducing a tariff from 20 percent those countries plan to undertake as part of Uruguay
to 10 percent produces a welfare increase (in terms of Round commitments. Because of the dynamic effects,
Hicksian equivalent variation over the infinite horizon) estimated gains are considerably larger than those found
of 10.7 percent of the present value of consumption in in the literature on the impact of the Uruguay Round.
This paper - a product of Trade, Development Research Group - is part of a larger effort in the group to assess the impact
of trade and investment on economic growth. The study was funded by the Bank's Research Support Budget under the
research project "The Dynamic Impact of Trade Liberalization in Developing Countries" (RPO 681-40). Copies of this
paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Lili Tabada, room
MC3-333, telephone 202-473-6896, fax 202-522-1159, Internet address Itabada@worldbank.org. David Tarr may be
contacted at dtarr@worldbank.org. September 1998. (49 pages)
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about
development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The
papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this
paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the
countries they represent.
Produced by the Policy Research Dissemination Center
Trade Liberalization and Endogenous Growth
in a Small Open Economy: A Quantitative Assessment
by
Thomas F. Rutherford and David G. Tarr*
* Associate Professor, Department of Economics, University of Colorado; and Lead Economist,
The World Bank. 'We would like to thank Richard Baldwin, Glenn Harrison and seminar
participants at the April 1997 conference in Milan Italy on Technology Diffusion and
Developing Countries for helpful comments. Research support was provided by the World Bank
under RPO No. 68140, "The Dynamic Impact of Trade Liberalization in Developing Countries."
1. Introduction
Intemational trade economists have typically argued that an opentrade regime is very important for
economic development. This view has been based partly on neoclassical trade theory, which generally finds
that a country improves its welfare from trade liberalization, partly on casual empirical observation that
countries which remain highly protected for long periods of time appear to suffer significantly and perhaps
cumulatively, and partly on systematic empirical work that also finds trade liberalization beneficial to welfan
and growth (e.g., Sachs and Warner, 1995).') What has been troubling is that the numerical modeling
estimates of the impact of trade liberalization have generally found that trade liberalization increases the
welfare of a country by only about one-half to one percent of GDP, gains which are very small in relation
to the paradigm.2' For many years authors have claimed that the welfare gains from trade liberalization wou!d
be much larger if the dynamic impact of trade liberalizationwere taken into account, but heretofore no such
models have been developed.3)
')Of course, all aspects of the paradigm that trade liberalization leads to faster growth have been subject to criticism.
For example, Rodrik (1992) has developed models in which trade liberalization is immiserizing, and causality has
been questioned in the Sachs and Warner results.
')See, for example, de Melo and Tarr (1990; 1992; 1993); Harrison, Rutherford and Tarr (1993; 1997a; 1997b); Morkre
and Tarr (1980; 1995); and Tarr and Morkre (1984). The consistently small estimated gains in constant returns to scale
models came to be known as "the Harberger constant." While some estimates with increasing returns to scale models
(such as Harris, 1984) have been larger (up to 10 percent of GDP), these estimates have been more controversial, often
based on regime switching (see Harrison, Jones et al., 1993; and Harrison, Rutherford and Tarr, 1997a). In our view,
the results are less than convincing for a strong version of the paradigm.
3'Moreover, we have shown, see Rutherford and Tarr (1997), that a comparative static model may be a close
approximation to the annual welfare gains from trade liberalization in a dynamic model, if the dynamic model is
simply Ramsey based, i.e., if there is no endogenous growth.
Some numerical general equilibrium modelers have produced comparative "steady state" estimates of the welfare
gains which are two to four times the comparative static estimates of their models (e.g., Harrison, Rutherford and
Tarr, 1996, 1997; Francois, McDonald and Nordstom, 1996; and Baldwin, Francois and Portes, 1997). These are
multi-sector quantifications of the Baldwin (1989) 'medium term growth bonus," which hold the rental rate on
capital constant and allow the capital stock to vary. Harrison, Rutherford and Tarr (1996; 1997a) and Rodrik (1997)
have explained, however, that these estimates overestimate the gains from trade liberalization in a Ramsey type
model because they fail to adjust for the foregone consumption cost of achieving the higher capital stock.
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With the development of endogenous growth theory (for example, Romer (1990), Romerand Rivera-
Batiz (1991), Grossman and Helpman (1991) and Segerstrom, Anant and Dinopoulos (1990)) a clear
theoretical link has been provided from trade liberalization to economic growth. Due to the complexity of
the models, however, the theoretical literature has necessarily focused on a comparison of the steady-state
growth paths, and been based on rather aggregated models. Since two policies that achieve the same steady-
state growth path could have very different welfare consequences, it is important to develop models that
derive the dynamic adjustment path and evaluate the welfare effect.
In this paper we develop a dynamic small open economy model defined over a 54 year horizon, frnm
1997 to 2050 with terminal constraints which approximate an infinite horizon. There are two sectors Xand
Y. The Y sector produces goods for domestic and export markets under constant returns to scale (CRTS).
Inputs into Yare labor and a pure intermediate goodX. The good Xis produced by both foreign and domestic
firms under the large group monopolistic competition assumption and increasing returns to scale (IRTS).4)
We employ the by now standard assumption that inputs ofXaffect the production of Yaccording to
a Dixit-Stiglitz function. This means that additional varieties of X reduce the cost of producing Y. Firms in
the IRTS sector must incur a once and for all fixed cost of a "blueprint" in order to introduce a new product;
and firms also incur a fixed cost in any period in which they operate. Domestic firms use relatively more
local inputs and relatively less imported inputs. Product development costs are lower for foreign firms under
the assumption that in relation to the size of the domestic market there is an infinite stock of varieties of
Nonetheless, the estimates for Hicksian equivalent variation remain less than five percent of GDP, except for the
Baldwin, Francois and Portes paper; and Rodrik (1997) has estimated that after adjusting for the foregone
consumption cost of investment, the estimated equivalent variation in the Baldwin, Francois and Porter paper would
also be less than five percent.
')Our analysis can be viewed as an extension of Ethier (1982) and Markusen (1989, 1991). Markusen investigated
the implications of the substantial trade in imported intermediate inputs using static and two period models. A
previous model of ours, Rutherford and Tarr (1996), also employed an Ethier-Dixit-Stiglitz framework to evaluate
the impact of trade liberalization. In that paper, however, the growth rate was not affected endogenously, so the
additional welfare gains from the variety effect were derived from transitional dynamics.
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products on international markets; thus, their development costs represent solely the cost of adapting and
introducing a Product from the international market to the domestic economy. All agents in the model,
including firms in the IRTS sector, optimize over the infinite horizon with perfect foresight apart from
unanticipated policy changes.
In our central model, the country cannot borrow on international capital markets, so that the value
of imports must be covered by exports in each period of the model. We investigate the impact of allowing
capital flows in the sensitivity analysis.
The onl-v tax distortion in the economy in the benchmark data set is a twenty percent tariff on
imports. We first construct a steady state growthpath with which we can compare results of counterfactual
experiments. We then reduce the tariff to ten percent and compare all variables to their values in the
benchmark steady-state.
We construct a series of counterfactual scenarios to determine the sensitivityof the results to tax, macro and
financial policies, as well as to different tariff cuts and parameter specification. We evaluate the welfare
consequences of a change in policies, i.e., we report the Hicksian equivalent variationfor the infinitely-lived
representative agent.
Some of our mnost important results are as follows: with lump sum revenue replacement,
reducing a tariff from 20% to 10% produces a welfare increase (in terms of Hicksian equivalent
variation over the infinite horizon) of 10.7 percent of the present value of consumption in our central
model. We investigated the sensitivity of our results to all of the key parameters in the model and
found that the welfare estimates for the same tariff cuts ranged up to 37 percent with capital flows,
and down to 4.7 percent with inefficient replacement taxes. Doubling or quadrupling the size of the
tariff cuts, which would characterized the experience of many developing countries in the past 30
years, resulted in estimates of the welfare gains that were at least twice or four times, respectively,
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the size of the cut. We applied the model to five developing countries and estimated the impact of the tarif
changes which they plan to undertake as part of their Uruguay Round commitments. Our estimatedgains are
large in relation to the literature estimates of the impact of the Uruguay Round.
Our results illustrate the crucial importance of complementary reforms to fully realize the potential
gains from the trade reform. Notably, with the ability to access international capital markets, the gains are
more than doubled. Moreover, use of inefficient replacement taxes will significantlyreduce the gains. These
combined results show that complementary macroeconomic, regulatory, and financial market reforms to
allow capital flows and efficient alternate tax collection are crucial to realize the pDtentially large gains from
trade liberalization.
Large welfare gains in the model arise because the economy benefits from increased varieties of
foreign X in the short run, and increased varieties of domesticX after several years. In order to assess the
importance of variety gains, we perform the tariff reform in a constant returns to scale, perfect competition
Ramsey model; then additional varieties do not increase total factorproductivity. In this model the Harberger
constant reemerges, as welfare gains are about 0.5 percent of the present value of consumption.
We apply our model to datasets for five countries: Argentina, Brazil, Korea, Malaysiaand Thailand,
and assess the effects on these economies of the tariff changes they agreed as part of their Uruguay Round
commitments. The relatively large welfare gains that we estimate for these five countries relative to the
literature estimates ofthe gains from the Uruguay Round for these countries, suggest that the large welfare
gains in our stylized model are not based on implausible parameter values.
Although estimates of equivalent variation have been widely seen as too small, some may question
whether our estimates are too large. To put these numbers in perspective, in appendix A we have
analytically derived the relationship between a permanent increase in the steady state growth rate and
equivalent variation. A welfare gain of between 10 and 35 percent of consumption corresponds to a
permanent increase in the growth rate of between 0.4 and I percent. A policy induced change in the growth
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rate of this magnitude is quite plausible in the context of the actual long term per capita growth rates overthe
25-30 year period beginning in 1962. The highest average long term annual growth rates are for the four
"East Asian tigers," with rates over 6 percent (Korea at 6.7 percent is the highest). At the other extreme theie
are 17 countries, largely in Africa, with negative growth rates, three of which are less than negative 2
percent. The average per capita growth rate for developing (developed) countries as a whole is 1.6 (2.9)
percent with a standard deviation of the growth rate of 2 (1).5)
Sachs and Warner (1995) maintain that this large range and standard deviation of the growth rates
across developing countries is explained in large part by trade liberalizatbn. Based on cross-country growth
regressions, they estimate that open economies have grown about 2.45 percent faster than clcsed economies,
with even greater differences for open versus closed economies among developing countries. They note that
trade liberalization is often accompanied by macro stabilization and other market reforms, and their open
economy variable can be picking up these other effects as well.6) But they argue that trade liberalization is
the sine qua non of the overall reform process, because other interventions such as state subsidies often are
unsustainable in an open economy. While, like Sachs and Warner, our results show that trade liberalization
can have an important impact on growth, we also find that the benefits of trade liberalization can be dissipatad
without complementary reforms in the macroeconomic, financial and tax areas.
These econometric estimates suggest that our estimate of equivalent variation, which corresponds
in our central model to a growth rate change of 0.4 percent, may still be too small. But larger tariff changes
5)These estimates are taken from Pritchett (1997), who performed the calculations based on the Summers and Heston
(1991) data.
6OBecause trade policy may be endogenous, some have criticized the Sachs and Warner OLS estimates as suffering
from simultaneity bias. Ann Harrison and Dani Rodrik (1997) have provided preliminary estimates, however, that
show that the impact of trade liberalization on growth is even larger when the simultaneity bias is taken into
account; in particular, a ten percent reduction in the tariff as we have simulated above, is estimated to increase the
growth rate by considerably more than our estimate of 0.3 percent. In addition, they show that the black market
premium plays an equally important role as tariff reduction. Although Sachs and Warner take the black market
premium as part of their openness measure, Harrison and Rodrik separate it and prefer to think of it as a proxy for
macro stabilization.
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than our ten percent cut produce larger welfare gains and correspond to higher changes in the growth rates.
On the other hand, Young (1995) has estimated that the majority of the growth amorg the four East
Asian tigers is explained by factor accumulation, not increases in total factor productivity. But even Young
has found that average annual total factor productivity growth was equal to 1.7 percent in South Korea, 2.1
percent for Taiwan and 2.3 percent for Hong Kong. Only Singapore had virtually zero growth in total factor
productivity according to Young's estimates. Using Young's data,) however, but correcting for a bias in the
estimation procedure, Rodriguez-Clare (1997) estimates that a much larger share (almost 60 percent ) of the
growth among these four countries is due to an increase in TFP. We ccnclude that a detailed examination of
the East Asian tigers leaves a sufficient role for policy in explaining growth that our equivalent variation
estimates are not excessive.
Since our model employs the Chamberlinian large group assumption, the markup over fixed costs
remains unchanged, so there are no rationalization gains. Thus, these calculations show that the Ethier-Dixit
Stiglitz characterization of production, where additional varieties lowers costs, is sufficient to generate the
large welfare gains and increase in per-capita income. We have also developed a model in which there are
positive spillovers from additional foreign varieties on the costs of introducing new domestic varieties.
Although the domestic industry recovers more rapidly, the welfare gains are mt significantly affected, since
additional domestic varieties come largely at the expense of foreign varieties. Since the existence of
spillovers is somewhat controversial, the robustness of our results with respect to spillovers provicbs support
for the variety-trade liberalization paradigm.
The remainder of this paper is organized as follows. Section 2 outlines essential features of our
model. Section 3 presents results and sensitivity analysis with respect to model structure. The application
7)For Singapore, Rodriguez-Clare corrected for inconsistencies in the data.
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of the model to the Uruguay Round commitments of five developing countries is presented in Section 5.
Section 6 concludes. Appendix A provides further details on welfare calculations over an infinite horizon,
relating changes in the economic growth rate to infinite-horizon welfare and then show how we apply these
results to approximate infinite horizon welfare. Appendix B describes the stylized benchmark data set and
model calibration.
2. Model Formulation
We consider a two sector economy. The Y sector produces exports and final goods for the domestic
market under constant returns to scale (CRTS) and perfect competiticn. The X sector which is composed of
both domestic and foreign firms produces intermediate goods under increasing returns to scale (IRTS) and
imperfect competition with a Dixit-Stiglitz representation of the impact ofincreases in the number of products
on total factor productivity. Markups on goods in the IRTS sector are based on the Chamberlinian large
group assumption--that is, the elasticity of demand facing the representative firm is equal to the compensatel
elasticity of substitution between varieties. Final demand arises from an infinitely-lived epresentative agent
who is at the margin indifferent between an additional unit of consumption and an additional unit of
investment. In this section we outline the key features of the model in terms of the objectives and constraint
facing various agents.
2.1 Consumer Behavior
The intertemporal utility function of the infinitely lived representative consumer is the discounted
sum of the utility of consumption over the horizon:
u = ( E A' Cf P
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In this equation the parameter p controls the intertemporal elasticity of substitutioti) and A is the single
period discount factor. Aggregate consumption in a given period (Q is a Cobb-Douglas aggregate of
consumption of domestic and imported final goods:
C =CD D CM D
t I f
We assume that imported final goods cannot be produced in the home market, due to technical
limitations of the domestic final goods sector. The agent's intertemporal and within-period consumption
decisions are weakly separable. Thus, the typical static first order condition applies on consumption decisions
within a time period, given a decision on how much b spend on consumption in any period. In the standard
manner, the intertemporal decision is based on the maximization of the utility function subject to the
constraint that the present value of consumption equals the present value of income:
max U = ( E A CD, CM t" P)p
s.t.
(1 + c) ( P t CD,t s j PM CM) = WI L + II
In this expression, all prices are defined in present value terms, discounted to period 0 (=1997). The
right side of the constraint, which is the present value of income, includes the present value of wage incomeO
together with profits from existing capital stocks and patents. T is the consumption tax, discussed below.
In a steady-state equilibrium, there are no pure profits, but along an adjustment path moving to a new steady
state there may be returns associated with existing capital and markups over marginal cost. In other words,
S) The intertemporal elasticity of substitution (T = 1/l-p- See table I for the assumed values of elasticities in
different sectors.
9) Note that population is fixed over the time horizon. Economic growth results solely from productivity
improvements due to the accumulation of varieties, and the real wage increases over time relative to the prices of
domestic output and imports.
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pure profits and losses are only associated with current (extant) firms. All firms formedduring the model
horizon earn zero economic profit.
2.2 Government Revenue and Expenditure
The government provides public goods and services at an exogenous level through the infinite
horizon. While we presume that these goods are provided because they generate net benefits for the
representative consumer, we do not formally model the impactof public provision on consumer well-being.
Instead, we account for the cost of providing public sector services through the imposition of an equal-yield
constraint asserting that any change in tariff rates must be compensated by a permanent change in one of
three alternative domestic tax instruments. The government purchases domestic final output (GD) and
imported final output (GM,) to assure that a given level of public provision is maintained, i.e.
GDD GM 1 G
I
The public sector budget constraint (which determines the replacement tax rate) is then written in present
value terms as:
(p,D GD, + p,M GM,) = E ( T,M(ttM) + T,C(Tc) + T,K(CK) + T7Y(rY) )
In this equation the sum on the left represents the cost of public expenditures, and the sum on the right
represents tax revenue from tariffs, consumption taxes, capital income taxes and final output taxes,
respectively. The tariff rates (tQM) are exogenously specified policy variables, whereas the tax rates on
consumption, capital income and output are determined endogenously to assure that the government budget
constraint is satisfied.10)
10) In any equilibrium only one of the replacement tax instruments is non-zero, depending on the scenario-specific
replacement tax option.
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2.3 Sales and Production of the Final Good
Good Y is produced as differentiated products for sale in the domestic and international markets. TIB
shares of sales at home and abroad are determined by relative prices. This iseffectively an Armington-style
differentiation of products in the export market. A constant elasticity of transformation (CET) function
relates the composite output level in a given period to domestic andexport sales. Firms producing the final
good maximize profit subject to the constraint:
y f (DJ + (1-T1D) (-| f
_~~~~ E
In this equation parameters D and E are the base year (1997) levels of output to the domestic and export
markets, and lD is the baseline value share of domestic sales in total sales (the base year production level is
scaled to unity).
Production of the Y composite is associated with a nested production function based on inputs of
labor (L) and differentiated intermediate inputs (xi ). Given prices of intermediate goods and labor, the
aggregate production sector operates so to minimize the costs of producing a given output subject to the
constraint:
IN a/p i ND P NF a/p
L- i= -I- x PDS X
In this function, the intermediate inputs and labor enter in a Cobb-Douglas aggregate with value
shares determined by base year demands. It is evident from the production function that we have firm level
rather than national product differentiation. Since costs of varieties can differby foreign or domestic origin,
at the second level, within the intermediate input (X) nest, we account for substitution between domestic and
foreign varieties according to a constant-elasticity-of-substitution aggregation. The inputs of intermediates
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from domestic and foreign firms represent the effective supply of X from these firm types. The effective
supply of all typef firms is described by:
( \ iipIp 1-p
Xf -- 1 ( X = (nfxf )XiP = nf Xf f E {D,F}
in which Xjf = Xf (by symmetry) is output of a representative typef firm, Xf = nff x,f is the total output from
typeffirms. Holding total output from type f firms constant, effective supply from type f firms increases wih
,-p I
nf P = nf,_ which is the "variety effect multiplier." The multiplier increases with 17 and increases as o
decreases toward 1 ( a >1). (The second equation in this expression reflects our assumption of symmetric
firm structure.) We then may express the aggregate production function as:
Y Li-a nL + p P _p COP
Following Romer and others, we assume that the value share ofX in aggregate production is related
to the elasticity of substitution between varietiesso that a=p, which implies that the elasticity itself is definel
by the value share as a = I/(1 -a). Making this substitution, we have the following expression for aggregate
output:
Y = (n L)I a * + ( L)a ?
2.4 Market Clearance Conditions
Output ofthe good Ysupplied to the domestic market can be consumed or invested. Investment in
XD andXF sectors involve forgone consumption of domestic output. The market clearance for macro output
sold in the domestic market is given by:
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D~ = CD~ +GD + p'DBf+ tnt( +D X,)
D,C,G, E t MDF), ( , ,n, ( a,
This equation states that domestic output is purchased by households (CD,), government (GD ) and firms.
In turn, each firm type has four sources of demand for domestic output: (i) inputs to blue-print design
(D Bf), (ii) inputs to physical capital formation (I,), (iii) recurring fixed costs (np cD) and (iv) variable
costs of production (n a D X ). Both firm types (domestic and foreign) are treated symmetricaly, although
ft p f
we adopt parameters reflecting a relatively larger share of domestic inputs for the domestic firm. Domestic
firms are assumed to make investmnents in plant and equipment, whereas foreign firns who generally import
all the key components invest solely in distribution facilities such as warehouses and transportation
equipment.
The corresponding supply-demand balance for imported goods is as follows:
Mt CM, + GM, + (f ft aft xft)
Thus, imports enter into final demand by consumers and government and intermediate demand by firms.
Imported inputs ( p Bf) are required to establish either a domestic or foreign firm and are also required
for the fixed costs of operation (n afM xf,).
ft p
2.5 Capital Stock Evolution
In our model, capital is firm-specific following installatbn, and investment rates may fall to zero as
a consequence of unanticipated changes in policy parameters. Following a standard Solow growth model,
investment in period t produces a unit of additional capital in the following year which may be used for
production in the future. Physical capital stock depreciates at a constant geometric rate:
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K =XK + f e {D,F}
ft+1 ft if,
whereas the number of blueprints (=number of firms) of each type are permanently in the market after they
are produced:
nf =n +Bf, f e {D,F}
2.6 Firms and Production Varieties
In sector Xthere is a one to one correspondence between firms and product varieties. The production
of good X involves both fixed and variable costs. Variable costs include inputs of aggregate output (domestb
and imported) and capital. Fixed costs can have two components: (i) "overhead", a recurring fixed capital
cost which is incurred in every period that the firm operates, and (ii) "setup costs", a one time research and
development (or blueprint) cost that must be incurred in order to design and market a new product. The
relative importance of blueprint and overhead costs are different for domestic and foreign firms. We asume
that foreign firms sell products which have been designed abroad, so their setup costs represert only the cost
of adapting an existing design to the domestic market. We model the productbn of blueprints by both types
of firm through the input of domestic and imported aggregates in fixed proportion. We assume in the present
model that there is no international trade in blueprints. Hence domestic firms may notlicense designs but
must purchase resources to develop new products from scratch.
We assume that most of the costs for foreign firms selling inthe domestic market are associated with
capital services and imported goods. In this setting the foreign firm's fixed costs of production may be
interpreted as the cost of maintaining a distribution system within the country.
The model is deterministicand firms have perfect (point) expectations of future prices. Hence, a new
firms will enter at time t if and only if there are positive net quasi-rents. This happens when the present value
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of markup revenue"') over marginal costs into the future is equal to or greater than the present value of the
fixed costs of operation, including fixed operating costs (for foreign and domestic firms) and the fixed costs
of product development (for domestic firms). It is possible to interpret this decision using Tobin's q theory
(see Baldwin and Forslid, 1996). The rate of investment in blueprints occurs to the point that the stock marke
value of the net income (i.e., the present value of net surplus) equals the replacement costs, namely the
marginal cost of a blueprint, since R&D is perfectly competitive.
The Dixit-Stiglitz production function for good Xis perfectly symmetric with respect to domestic ard
foreign firms, i.e, we have firm level product differentiation, with no brand ornational preferences. Varieties
of different vintages are equally preferred but differentiated. In this framework, all domestic firms that
operate sell the same quantity of outputand their varieties sell for the same markup-inclusive price. Likewis
all foreign firms which operate sell the same quantity at the same price. Domestic and foreign firms enter
symmetrically in the final goods production function so the derived demand for domestic and foreign
intermediates is symmetric; but they remain differentiated and their prices may therefore differ. Since foreigi
and domestic firms are treated differently regarding their cost structures, their prices usually differ.
Furthermore, we assume that any firm producing at time t produces the same quantity as all other
firms irrespective of vintage, but differing according to whether it is foreign or domestic. This implies that
the share of total output produced by firms of vintage v is equal to the share of vintage v firms in the total
number of firms. These life cycle assumptions impose a symmetric structure on the equilibrium which maka
it possible to account for the share of markup revenue available in any period received by firms of vintage
V.
Unlike our previous model in which we tracked the level of investment for all vintages through the
model horizon, in the present model we achieve a considerable simplification byintroducing a state variable
This may be called "operating surplus", "operating profit" or "Ricardian surplus" by different authors.
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for each firm type which tracks the present value of future markup earnings. This effectively treats the
human capital embodied in blueprint designs in the same analytic framework as is conventionally applied to
physical capital fornation. The underlying logic in unchanged from the previous model - the free-entry
assumption assures zero profit over the infinite horizon, and the time path of future prices affect not only
investment activity but the decisions by firms to enter markets and undertake product development.
Optimization over the infinite horizon applies not only to consumers and competitive firms, but also to the
managers of monopolistically competitive firms.
Our model is one of a small open economy. In particular, we assume that the small open economy
has only a negligible impact on the number of varieties available on world markets, and the cost of blueprint
for foreign firms. In general, we observe that there are many more varieties of products available on world
markets than are available in the small open economies. Accordingly, we assume that the decision facing
foreign firms is how many of the products for which blueprints akeady exist can be profitably introduced in
the local economy. The cost of the blueprint is a much smaller component of the cost of production for
foreign firms than for domestic firms -- and a larger fraction of the fixed costs of operation are associated
with recurring fixed costs of selling in the domestic market.
In the next section we investigate the properties of our model using numerical methods in vhich we
calibrate coefficients of utility and production functions to a reference growth path. Inthe results that follow,
we have assumed baseline data corresponding to table 1. These input parameters are reconciled to produce
the benchmark social accounts shown in table 2. For details on the translation of input data to model
parameters, see Appendix B.
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3. Model Results
We consider a 54 year model horizon, defined over the years 1997-2050. Initially there is only one
distortion in the economy: a twenty percent tariff on imports of both goodX, the pure intermediate good
produced under IRTS and monopolistic competition, as well as the final good, produced under CRTS. In
order to establish a point of reference we calibrate a model to a "benchmark" steady-state equilibrium. In our
central counterfactual scenarios, we reduce the tariff from 20% to 10% on an ad valorem (net) basis and
compare the results in all scenarios to the benchmark steady-state equilibrium with the initial tariff in place.
Unless otherwise indicated, all key variables are reported as a percentage of their values in the benchmark
steady-state equilibrium.
In table 3 we present six model variants or scenarios. In our central model, we assume there are no
spillovers from the entry of foreign firms and that the lost tariff revenue is replaced by a lump sum tax on
consumption. In our second model, we allow for spillover effects of the entry of foreign firms which reduce
the costs of developing blueprints by domestic firms. In the third model, we assume all sectors opeate under
constant returns to scale and perfect competition; then there is no productivity boost in the Y sector as a resut
of additional varieties of the X good.
In all of our models we impose an "equal yield constraint" regarding government revenue. Unless
otherwise stated, the reduction in tariff revenue if offset by a consumption tax. Given he absence of a labor-
leisure choice, this is equivalent to a lump sum tax. We examine the impact of employing a final output tax
or a tax on capital as the replacement tax in the fourth and fifth models presented in table 3.
In our central model and unless otherwise stated, we assume thatthe country has difficulty accessing
international capital markets. This may be because it has imposed rstrictions on financial flows, or because
macroeconomic conditions in the country are such that it can not attract international investors. We takea
polar version of this assumption and assume that the country faces a balance of trade constraint in each
-16-
period, i.e., the value of its exports must equal the value of its imports (both a world prices) in each period.
We relax this constraint in the sixth model, where we allow the home country to borrow on international
capital markets provided any borrowing is repaid within the model horizon. Then,the present value of exports
must equal the present value of imports over the model horizon.
In all scenarios we present the Hicksian equivalent variation (EV). The EV is based on the
intertemporal utility function optimized over the 54 year model horizon, with an approximation for the
infinite horizon. We present EV in percentage terms, where the denominator is the present value of
benchmark consumption over the infinite horizon. In the figures, we present the 54 year time path for key
variables in percentage change relative to the steady-state. The variables we report are as follows: Figure 1:
Final Consumption, composite of domestic and imported final goods Figure 2: Real Exchange Rate; Figure
3: Rental Rate on Capital; Figure 4 and 5: Number of Domestic and Foreign Firms, respectively; Figure 6:
Consumption Paths for Alternate Replacement Taxes.
3.1 Tariff Reduction with Central Assumptions
We first consider the scenario in which we cut all tariffs from 20% to 10%. In this scenario, Hicksiai
equivalent variation (EV) increases by 10.7 percent of the present value of consumption over the infinite
horizon.
What is driving these results is the following. The removal of the tariff on imported intermediates
results in an increase in the tariff ridden demand curve for imports and an increase in the price foreign firms
receive for their products. This increases the present value of quasi-rents for foreign firms. Entry by foreign
firms occurs in any period until the present value of the quasi-rents are driven down to the one time start up
costs of establishing a domestic presence for the foreign firm plus present value of the fixed costs of
operating the domestic subsidiary. After about 1O years, the number of foreign varieties stabilizes for the
duration of the model horizon at about 30% more than in the steady state. (See figure 5.) The increase in
-17-
imports, however, results in a substitution effect that reduces the demand for and price ofdomestic varieties;
this shuts down investment and firm creation for the domestic variety for a period of about 6 years.
Although the increase in foreign varieties has the impact of decreasing the demand for domestic
varieties of the intertnediate good X, the domestic industry eventually stabilizes after 8 years rather than
progressively going into demise. (See figure 4.) The principal reason for this is that the marginal productivity
of domestic X in Y production increases as use of domestic X in Y declines. The entire labor force is
employed in the production of Y, and it is not possible to reduce labor usage applied to domestic Xwithout
also reducing labor usage in imported X. Thus, as domestic X declines due to substitution toward cheaper
imported X, its marginal product increases to eventually arrest the further decline of the dometic X industry.
The transitional dynamics of the model in the early years are dominated by theincrease in the number
of foreign firms. The increase in the number of firms has an immediate impact on theproductivity in the final
good sector inducing output of the final good sector to increase in the first year. This immediate increase in
productivity and output of the final goods sector allows the economy to satisfy two constraints painlessly:
(1) the economy is able to invest more in intermediate goods(it takes capital to produce the foreign variety)
without reducing consumption in the short run relative to the steady state. Although the economy facesa
Ramsey problem of determining the optimal tradeoff between consumption and investment, the tradeoff is
within the framework of an expanded choice set relative b the steady state. In fact, the economy consumes
about 7 percent more in the initial years compared with the benchmark steady state (see figure 1); and (2)
despite the period by period balance of trade constraint, the economy is able to import more foreign
intermediate varieties, without reducing its imports of final goods. The economy meets its balance of trade
constraint by exporting more of the final good. Thus, reducing the tariff does not result in any adjustment
costs in this model except for the losses that accrue to the specific capital owners in the domestic intermediat
goods sector. The surge in productivity results in both a 'level" effect and a growth effect regarding the
increase in consumption. The level effect can be observed by the jump in consumption in the first year. In
-18-
addition, however, due to an increase in the rental rate on capital (figure 3), the long run growth rate increases
from 2 to 2.1 percent.'2)
3.2 Tariff Reduction with Spillovers
In this scenario, we cut the tariff on both final and intermediate inports from 20% to 10%, starting
in the initial period. Crucially, we allow an increase in the nunber of foreign firms to decrease the blueprint
costs for domestic firms, with a spillover elasticity equal to four percent. The equivalent variation of this
scenario is 10.9 percent of the present value of consumption, which differs by only a smal amount from the
10.7 percent for EV in the central model without spillovers.
The decrease in the tariff has the effect of increasing the number of foreign varieties, just as it does
in the central model. With spillovers, however, an increase in the number of foreign varieties has two
competing effects on investment in the domestic variety of X. On the one hand, as the number of foreign
varieties increases, the demand for the domestic variety decreases, so the quasi-rents available for domestic
firms decreases--decreasing the likelihood of domestic investment. On the other hand, the costs of domestic
blueprints decreases with the number of varieties--increasing the likelihood of investment. Inour formulation
of spillover effects, a 100 percent increase in the number of foreign varieties relative to the steady state,
reduces the blueprint costs of domestic firms by roughly 4 percent relative to the steady state blueprint costs
With these parameters, the spillover effect dominates after about 6 years, after which investnent h domestic
firms resumes. Relative to their steady state value, the number of domestic firms bottoms out at about 90
percent of their steady state value after about 7 years, and climbs to the benchmark steady state value by
'2) In this model the domestic and international rental rates on capital are decoupled, so a tariff reform produces a
permanent increase in the domestic interest rate and a larger long-run increase in the growth rate. The domestic
interest rate is computed using the price of final consumption. This rate can temporarily depart from the
international rental rate on capital in the model with perfect capital markets due to Armington differentiation of
domestic and imported goods. In the long run, the domestic interest rate and the international rate converge
aymptotically.
-19-
2050.
It may appear puzzling that with spillovers, where the domestic industry has its costs reduced by
foreign varieties, the economy does not gain a significantly larger amount. The reason is that what is most
important to the welfare increase is the number of varieties rather than tin geographic source of them. With
spillovers, once the profitability of investment is restoredfor the domestic industry producing goodX, growth
of new foreign varieties falls-so there are more domestic firms and varieties, but fewer foreign varieties. TIC
loss of productivity due to the loss of foreign varieties almost fully offsets the gain in welfare due to the
increased number of domestic varieties.
3.3 Constant Returns to Scale (No Variety Multiplier)
In this model, we replace increasing returns to scale and imperfect competition in the intermediate
sector with constant returns to scale and perfect competition. Then only total output of the intermediate is
important (numbers of varieties are not counted), so there is no variety productivity effect. Although
consumers and decisions by investors optimize the consumption-capitd stock choice as in a Ramsey model,
there is no endogenous growth.
Equivalent variation for this scenario drops to 0.5 percent of the present value of consumption over
the infinite horizon. Without the variety multiplier, there is neither the initial "level" effect in consumption
nor the growth rate effect that obtained in our central and spillover models. Transitional dynamics are then
more painful, since in order to finance the additional investment in the earlier period, consumption falls in
the early years relative to the steady state. This result is similar to the results of Rutherford and Tarr (1997)
who showed that a Ramsey multisector model with constant returns to scale is insufficient to generate the
large welfare gains claimed for the trade liberalization paradigm .
3.4 Impact of Alternate Replacement Taxes
-20-
Except for the scenarios discussed in this subsection, we have employed a consumption tax as our
replacement tax. In the scenarios described here, we use two alternate taxes as the replacement tax for the
lost tariff revenue: a tax on output; and a tax on capital. The impact on the path of consumption, as a functicn
of the three replacement taxes, are presented in figure 10.
The curve labeled Consumption Tax is the same curve as in figure 1. Consumption increases to
between 7 and 12 percent of benchmark consumption during the model horizon. The consumption tax is a
Lump Sum distortionless tax in our model, but a tax on dormstic output introduces certain inefficiencies. In
particular, a domestic output tax discriminates against dometic output in favor of imports, and against final
output in favor of intermediate production. As a result of the relative inefficiency ofthe domestic output tax,
the path of consumption is cut by about 40-50 percent relative to the one with a tax on consumption and the
equivalent variation is reduced to a gain of 6.7 percent of the present value of consumption..
Finally, the tax on capital produces a consumption path that is inferior to the one with an cutput tax,
but preferable to the benchmark path with the tariff in place, i.e., the tax on capital is the most inefficient of
our three replacement taxes, but is better than a tariff in our model. In our model, the intermediate good X
uses capital intensively since only intermediate production uses capital as a primary input and only final
goods use labor as a primary input.'3) A tax on capital then discourages the introduction of new varieties
since it discourages the investment required for the introduction of new varieties of products and discourages
the production of intermediates relative to the production of final goods. The economy loses tie productivity
boost from the varieties and the gain in equivalent variation is less than only 4.7 percent of the value of
consumption. These results illustrate the importance of efficient tax replacement. With inappropriate
replacement tax mechanisms, the gains from trade liberalization can be drastically cut.
'3)Each good is used as an internediate input in production of the other good, and thus both goods use both
primary factors of production indirectly.
-21-
3.5 Capital Flows
In this scenario, the tariff is reduced from 20% to 10%, but the country is assumed to be able to
borrow on international capital markets provided that the borrowing is repaid within the model horizon. Tha
the period-by-period balance of payments constraint is replaced by the constraint that the present value of
its exports less imports is zero over the model horizon, and all other assumptions in the central model
remained unchanged. In this scenario Hicksian equivalent variation (EV) is 37 percent of the present value
of benchmark consumption over the infinite horizon. There is an initial jump in consumption of about 23
percent, and relative to the steady state, the wage rate increases by about 110 percent by the year 2050.
Why is the increase in EV with capital flows more than three times the EV value without capital
flows? The decrease in the tariff implies that there is an incentive for new foregn firms to enter, as in the no
capital flows model. The ability of the country to borrow, however, allows the country to run trade deficits
and import much more in the periods immediately following tariff reduction. These additional imports are
used to finance the start up capital of new foreign firms and to pay for the additional imports of foreign
varieties. Foreign firms increase by almost 100 percent of their steady state value with capital flows by the
year 2003, as opposed to an increase of about 35 percent of their steady state value without capital flows. Tie
larger increase in foreign firms leads to a considerably larger increase in labor productivity and the wage rat
in the early years.
What is interesting is that there is a much larger increase in the number of domestic firmswith capital
flows-in fact, the number of domestic firms increases dramatically relative to the steady state value by the
end of the model horizon. This is explained by a real exchange rate effect. The economy finds it optimal to
run trade deficits in the early years of the model. These trade deficits finance additional inport varieties and
additional consumption in the early years."4) The capital inflows in the early years result in less real exchanW.
'4)The latter occurs because consumers optimize consumption over the model horizon subject to their lifetime
income constraint or permanent income. With the ability to borrow on intemational capital markets, consumers can
-22-
rate depreciation in the early years of the model (in fact, they result in real exchange rate appreciation in the
first two years); but the capital outflows in the later years of the model result in a strong real exchange rate
depreciation in those years. (See figure 2.) The steeper real exchange rate depreciation with capital flows
in the years following 2020 (compared with central assumptions) raises the costs of importing foreign
varieties in those years, and shifts demand toward domestic varieties. Domestic agents, who fully anticipate
future real exchange rate movements, recognize profit opportunities and begin to invest by the year 2003.
Among the models we consider, it is perhaps ironic that the model with capital flows, where we see the
largest initial increase of foreign firms, ultimately leads to by far the strongest resurgence of domesic firms,
even compared to the model with spillovers.
3.5 Sensitivity Analysis
In table 4 we present the results of our sensitivity analysis for the key parameters in our model, and
we investigate the impact of different tariff changes. We present the Hicksian equivalent variation for each
scenario (with the approximation for the infinite horizon), and the growth rates calculated over three time
horizons: 1997-2010; 1997-2050; and 2049-2050, which is the projected growth rate into the infinite horizon
Except for the last three rows, in all scenarios the tariff rate is reduced from 20 to 10 percent.
As a point of reference, in row 0 we present the,results obtained with our central assumptions,
previously presented in row 1 of table 3. The result from row I illustrates that the larger the share of imported
in intermediate use (0), the larger the EV gains. The reason is that for a given ten percent cut in the tafiff, the
same proportional effect on the share of imports, generates more imported varieties, with the consequent
productivity boost, when this share is high. For the share of intermediates in final production (a), there are
offsetting effects: a higher share of intermediates in final production shotld increase the number of varieties
smooth consumption more easily.
-23-
because again the proportional change induced by a ten percent tariff cut should induce a larger increase in
the number of varieties; but the larger is a, the smaller is the variety multiplier for any number of varieties.
Thus, the impact of a change in this parameter on EV is ambiguous, and our two simulations presented in
rows 2 and 3 along with the central model show that EV as a function of a is not monotonic in the range of
our central elasticity values.
In the benchmark steady state, the rental rate on capital is 5 percent and thegrowth rate is 2 percent.
It is shown in appendix A that as these two rates approach each other, a given permanent increase in
consumption over the infinite horizon yields a larger EV. In rows 4 and 5, we illustrate the magnitude of the
change by varying each of these rates by one percent from the benchmark.
The results in row 6 indicate that, as is typical in comparative static models, themore elastic are the
substitution possibilities, the greater the gains. In particular, with a larger elasticity of transformation, the
economy is able to export more in response to a real exchange rate depreciation following tariff reduction,
which allows it to pay for more imports; and the additional intermediate imports provide a productivity b@st
through the additional varieties. The impact of this parameter is quite strong, as EV increases from 10.7 to
17.1 percent with a doubling of the elasticity of transformation.
Given that many developing countries in the past 30 years have started from protection levels well
above 20 percent and have implemented trade liberalizations considerably in excess of a ten percent tariff
cut, in rows 7, 8 and 9 we examine the impact of cutting the tariff from 2O percent to zero, from 40 percent
to 30 percent and from 40 percent to zero. For the results in rows 8 and 9, we generated a new baseline
steady state growth path with a 40 percent tariff in place. The results of rows 7 and 9 show that the gains are
very substantial for larger tariff cuts-the increase in EV from cutting the tariff from 40 percent to zero is moie
than 50 percent, which is more than double the gain of a cut from 20 percent to 0. Based on measurement
of Harberger triangles, comparative static models also produce the result that the gains increase more than
proportionately with the size of the tariff cut; but the result here is based on the fact that in our simulations
-24-
the number of varieties more tlhan doubles with a doubling of the tariff cut.
5. Application to the Uruguay Round Tariff Cuts of Five Developing Economies
In order to assess whether the large welfare results obtained above are dependent on possibly
unrealistic parameter values, we aply this model to five countries: Argentina, Brazil, Korea, Malaysia and
Thailand. We simulate the impact of the tariff cuts only on the intermediate products that these countries
agreed to as part of their Uruguay Round commitments. That is,we ignore the tariff cuts they made on final
products, as well as any liberalization in services.
For these countries., we employ the "GTAP" dataset (see Gelhar et al., 1997) and aggregate the
following GTAP sectors into our single intermediate goods sector: pulp and paper; chemicals, rubber and
plastics, non-metailic mineral products, primary ferrous metals, non-ferrous metals, fabricated metal
products, transport industries, machinery and equipment, other manufacturing products, and other services
(private). The resulting parameter values, including the tariff cuts are presented in table 5. Although all
countries have a share of intermediates over 60 percent, the share of imports in intermediates varies from 7
percent in Brazil to 71 percent in Malaysia. Tariff cuts on intermediates varies from 2 percent for Malaysia
to 8 percent for Brazil.
We examine the impact of these Uruguay Round tariff cuts in two models: first in our endogenous
growth model with central assumptions; and next in a constant returns to scale Ramsey model. In our central
model, the Hicksian equivalent variation increase ranges from 1.4 to 7.8 percent of the present value of
consumption over time. The largest value is in Thailand, which is theonly country of the five with a large
share of imported intermediates, and a relatively large tariff cut of seven percent. Argentina's low share of
imported intermrnediates and only five percent tariff cut explains its relatively low welfare gain.
These results are not intended to be a precise estimate of the gains from the Uruguay Round for these
economies (see Hlarrison, Rutherford and Tarr, 1 997a). Rather they suggest that the our large welfare gains
-25-
are not based on implausible parameter values. In the Ramsey model, the lack of variety induced productivity
increases results in quite small welfare increases, ranging from 0.1 percent in Korea and Malaysia to 0.4
percent in Thailand. Again, this indicates that estimated welfare gains are inthe range of the estimates from
competitive, static model.
5. Summary and Conclusions
This paper has investigated the effects of tariff liberalization in a small open economy in which
endogenous growth is linked to the introduction of new products by domestic or foreign firms. We have
developed a dynamic numerical model which allows us to trace out the dynamic adjustment path of all
variables and approximate the infinite-horizon welfare consequences of a change in policies. In our central
scenario, the tariff is cut from 20 percent to 10 percent, and we consider the impact both when the country
can access international capital markets and when it cannot.
We found that the welfare gain (Hicksian equivalentvariation) from tariff reform is 10.7 percent of
the present value of consumption in our central model,, a significant increase considering that the benchmak
tariff rate is only cut from 20 percent to 10 percent. We investigated the sensitivity of our results to all of
the key parameters in the model and found that the welfare estimates for the same briff cuts ranged up to 37
percent with capital flows, and down to 4.7 percent with inefficient replacement taxes. Larger tariff cuts,
which have characterized the experience of many developing countries in the past 30 years, resulted in
increases in the estimates of the welfare gains that were at least proportionate to the size of the cut.
We applied the model to five developing countries and estimated the impact of the tariff changes
which they plan to undertake as part of their Uruguay Round commitments. The gains of 0.7 percent to 7.8
percent that we estimate for these countries are large in relation to the comparative static or comparative
steady state estimates of the effects of the Uruguay Round for these countries.
Clearly these results support the paradigm that trade liberalization leads to significant income
-26-
increases, but they also illustrate the crucial importance of complementary reforms to fully realize the
potential gains from the trade reform. Notably, with the ability to access international capital markets, the
gains are more than doubled. Moreover, use of inefficient replacement taxes will significantly reduce the
gains. These combined results show that while there are indeed large gains possible from trade liberalizatioii
complementary macroeconomic, regulatory, and financial market reforms to allow capitalflows and efficient
alternate tax collection are crucial to realize the large gains.
-27-
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Table 1: Input Assumptions for Stylized Model
Value Shares Other Parameters
Intermediate value share (a) 66 % Baseline Interest Rate 5 %
Import Value Shares Baseline Growth Rate 2 %
Intermediate Demand (0X) 50 % Capital Depreciation Rate 7 %
Final Demand (O9 ) 20 % Baseline Tariff Rate 20 %
Domestic intermediate 0 % Elasticities of Substitution
Imported intermediate 75 % Intertemporal 0.5
Domestic intermediate capital 50 % Export Supply I
Imported intermediate capital 75 % Import Demand I
Capital Value Shares
Domestic intermediate 75 %
Imported intermediate 25 %
Blueprint Share of Fixed Cost
Domestic intermediate 90 %
Imported intermediate 10 %
Table 2: Benchmark Social Accounts (steady-state equilibrium)
L Y XD XM M I FD
PD 0.76 -0.11 -0.25 -0.40
PM -0.16 0.29 -0.02 -0.10
PX -0.66 0.33 0.33
PI 0.28 -0.28
PFX 0.24 -0.24
PL -0.34 _ 0.34
RK -0.11 -0.05 0.16
IMK I -0.11 -0.11 0.22
T I I I -0.05 0.05
Key:
Y Production of final PD Final goods
XD Domestic PM Final goods (imports)
XM Imported intermediate PX Final goods (exports)
M Imports PI Investment
I Investment PF Foreign exchange
FD Final Demand PL Wage rate
RK Return to capital
M Markup revenue
T Tariff revenue
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Table 3: Estimated Welfare and Growth Effects of Tariff Reduction*
Model EV- G2010 G2050 Gterm
1. Central Assumptions 10.7 2.6 2.2 2.1
2. Spillovers 10.9 2.6 2.2 2.1
3. Constant Returns to Scale 0.5 2.0 2.0 2.0
4. Output Tax Replacement 6.7 2.5 2.1 2.0
5. Capital Income Tax Replacement 4.7 2.4 2.1 2.0
6. Capital Flows 37.0 4.2 2.7 2.2
* Parameter choices for all models are shown in table 1. Unless otherwise
indicated, all models include: lump sum replacement taxes, no spillover effect of
new foreign varieties on the domestic cost of new blueprints, and period by period
balance of trade constraint..
EVo Hicksian equivalent variation over the infinite horizon as a percent
the present value of benchmark steady state consumption
G2010 Average consumption growth 1997-2010
G2050 Average consumption growth 1997-2050
Gterm Terminal growth rate (from 2049 to 2050)
-33-
Table 4: Sensitivity Analysis
Parameter* Central Sensitivity Balance of trade constraint for each period:
Value Value EVoo G2010 G2050 Gterm
0 10.7 2.6 2.2 2.1
1. 01 0.5 0.25 4.6 2.3 2.1 2.1
2. a 0.66 0.80 11.0 2.5 2.3 2.2
3. a 0.66 0.50 11.3 2.8 2.2 2.0
4. G 0.02 0.03 14.6 3.8 3.3 3.1
5. R 0.05 0.04 13.0 2.7 2.2 2.1
6. qtDX 1 2 17.1 3.1 2.3 2.1
7. Tariff change 20% to 0% 23.7 3.4 2.5 2.2
8. Tariff change 40% to 30% 9.1 2.6 2.2 2.1
9.Tariff change 40%to0% 51.6 4.4 3.1 2.1
* The counterfactual scenarios use the sensitivity value. The central value is listed for reference only.
Key:
EV°o Hicksian equivalent variation over the infinite horizon
G2010 Average consumption growth 1997-2010
G2050 Average consumption growth 1997-2050
Gterm Terminal growth rate (from 2049 to 2050)
0e Import share of intermediate inputs
a Intermediate share of aggregate cost
G Baseline growth rate
R Baseline interest rate
TlDX Elasticity of transformation in aggregate production (domestic versus exports)
Tariff Alternative pre-existing tariff rates and tariff reform programs (in the reference case, 20% is cut to 10%)
-34-
Table 5: Evaluation of the Uruguay Round Tariff Cuts for Five Developing Countries,
with and without Product Variety Productivity Impacts
Data Welfare and Growth Estimates
import post-
Country and Model intermediate share of benchmark Uruguay
value share intermediates ltariff Round tariff EV°o G20 10 G2050 Gterm
I Product Variety Productivity
and Capital Flows
A. Korea 0.6 0.2 15.0 8.0 2.6 2.2 2.1 2.0
B. Malaysia 0.7 0.7 8.0 6.0 4.0 2.3 2.1 2.0
C. Thailand 0.6 0.6 32.0 25.0 7.8 2.5 2.2 2.0
D. Argentina 0.9 0.1 28.0 23.0 0.7 2.0 2.0 2.0
E. Brazil 0.6 0.1 30.0 22.0 1.4 2.1 2.0 2.0
II Constant Returns to Scale
and Capital Flows
A. Korea 0.1 2.0 2.0 2.0
B. Malaysia 0.1 2.0 2.0 2.0
C. Thailand - same as above - 0.4 2.0 2.0 2.0
D. Argentina 0.2 2.0 2.0 2.0
E. Brazil 0.1 2.0 2.0 2.0
Key : See table 3.
Source : GTAP dataset for data, see Gehihar et al. (1997); and authors' estimates.
-35-
Appendix A: Growth and Welfare over the Infinite Horizon
This appendix derives algebraic relations relating changes in the growth rate of consumption to the
equivalent variation in infinite-horizon consumption. Itthen shows how these formula may be employed to
provide consistent estimates of infinite horizon welfare based on equilibrium choices over a finite horizon.
These functions relating growth to welfare are interesting for two reasons. First, they providesome intuition
as to the importance of changes in growth rates vis-a-vis the more conventional static efficiency estimates
of the welfare cost of protection. Second, these equations are required for estimating the infinite-horizon
welfare change, given welfare changes over the time horizon of the model, the terminal consumption level
and the terminal (steady-state) consumption growth rate.
We begin with a constant-elasticity of substitution utility function:
U(C) = Alc jl/p
The elasticity of intertemporal substitution is given by c=l/(l -p). The model is based on ordinal utility, so
the optimal consumer choices are unaffected by monotonic transformations of the utility function. For
example, this utility function is equivalent to:
U(C) =
t=o 1-1/
The advantage of the former function is that because it is linearly homogeneous in consumption levels
(U(IC) = U(C)), a one percent change in U corresponds to a one percent equivalent variation in income.
If we let C denote a reference consumption path, and let C denote an alternative time path of consumption
levels, the equivalent variation in infinite-horizon welfare then corresponds to:
-36-
EV = ° - I
We now evaluate the equivalent variation of a permanent change in the consumption growth rate, assuming
that the initial level of consumption in period t=O is held constant. Take C, I( + g )' and
c, = ( 1 + g )'. It then follows that the equivalent variation in income is:
Er=tI - a (I +g)P I/P_I
EV = - A(--)1" I
I - a (i +g)P
In order to relate this expression to the calibrated equilibrium calculations such as those conducted in our
paper, it is helpful to replace the utility discount parameter, 4 by an expression based on the baseline growth
rate and interest rate. In other words, in order to compute a baseline equilibrium, we do not begin with a
given value of the utility dscountfactor. We instead assume a balanced baseline growth path with agiven
growth rate (g), and a given interest rate (r). It is then a simple matter to show that the utility discount
factor is given by:
l+r
Substituting into the equivalent variation equation, we then have:
_ _ l~~~~/p
r - ( 1
EV= r-I
+- ~ +g
I+9
This expression provides us with a useful check on the magnitude of welfare gains arising from our
calculations. Figure Al simply computes the Hicksian welfare metric for growth rate increases rangingfran
-37-
O to 1%. Two lines correspond to baseline growth rates of 1% and 2%. Both functions are based on a
baseline interest rate of 5% and an intertemporal elasticity of substitution equal to one half We see that
growth rate changes of a 0.5% produce welfare changes on the order of 10 to 15%, depending on the initial
growth rate. Holding constant the baseline interest rate, the welfare change increases in thebaseline growth
rate.
Figure A2 investigates the sensitivity of thisfunction to the baseline interest rate. As expected, the
higher the interest rate, the lower the welfare gain associated with a permanent change in the growth rate.
A higher interest rate implies a larger discount on future consumption increases, so that future gains in
consumption are less important.
Figure A3 illustrates the relationship between the intertemporal elasticity of substitution and the
welfare gain associated with a hafa percentage increase in the consumption growth rate. Again, the resuls
are intuitive. The higher the elasticiy of intertemporal substitution, the larger the achievable gain from an
increase in future consumption. When the intertemporal elasticity is close to zero, an increase in the growth
rate has not effect on welfare because period 0 consumption does not change. However, as the intertempord
elasticity increase from zero, the consumer benefits more as she is able to more easily substitute current
consumption for future consumption.
In our model calculations, we adopt afinite-horizon model which approximates the infinite-horizon
equilibrium. We apply terminal conditions which assure that terminal period investment is positive and
increasing with aggregate GDP (See Lau, Palke and Rutherford 1997 for details on the terminal
approximation.) Having computed equilibrium values for period 0 to T, we have an explicit utilityindex over
consumption in these periods, but this indexfails to accountfor consumption increase in the post-terminal
period We can approximate the infinite horizon welfare index, however, based on the followingfunctions
of thefinite-horizon model: (i) the welfare indexfor periods 0 to T, u ., (ii) terminalperiod consumption,
-38-
C7 and (iii) post-terminal growth, g. We produce an infinite-horizon welfareindex based on the assumption
that the economy exhibits steady-state growth at ratet from period T+l to the infinite horizon.
In order to lay out the formulae for this approximation, we begin by splitting the infinite-horizon
welfareintotwoperiods,t=0toTand t>T Weassumeagrowthrateofo_= Tc Tforthepost-termind
CT
period, then:'5)
. . I/p~~~~~~~~~~~/
U(C) = E ' cfP
= [ AE d' C P + CA' { C (1 +g)()}P Ij
A L 'C p + C P /
- = A' T I-A(I +g,f }
When working with a calibrated model, it may be easier to begin from a reference balanced growth path.
SubstitutingforA as above, and denoting the average consumption growth rate through period t as 0,, the
equivalent variation in income can be written:
EV(f= ){ [4 -_±~
I l +r) I =° t=O +r +g
+ T 1 g( r ) 1T1 I +g p- - I 1/
I+r JI I +r +g
Alternatively, this expression can be written in terms of the wefare level through period T and the level and
In the finite horizon model we use a utility function,
UT = ( S /vt CP)
in which there is no additional 'weight' on period T consumption. In the finite horizon model, a constraint on the
terminal capital stock such that investment follows a steady-state growth path. Having computed the finite horizon
equilibrium, we then compute the infinite horizon welfare index.
-39-
growth rate of consumption in the post-terminalperiod, i.e.
EV { 3 Up + (Ir-) I, }
In which we define: . = -b, where 0 = - and.
y (gX g) = 1
1+i V
In a constant growth rate model, the term y (g., g) is always unity, so the welfare then depends solely on
the utility index through model horizon and the terminal consumption level relative to the original steady-
state growth rate.
-40-
Appendix B: Benchmark Assumptions and Calibration
Consider the input data as outlined in Table 1. Scaling base yearfinal goods output to unity, we then
define imported and domestic intermediate inputs as:
x,W=o a and xD=(I -1) a'
Labor inputs for final goods production may then be inferred through exhaustion of product:
LM = ei (I-a) and L. = (1-01) (I-a).
Base year wage income is the sum of these values, L =LD +LM.
The interrnediate value share determines markups over marginal cost, and this in turn defines markip
revenues given assumed sales by firm type:
mkf = xf (1 -a), f e {D,M}
Capital returns in intermediate goods production are defined as a fraction of variable cost:
vkf = kvsf (xf - mk)
Imported inputs to intermediate goods production are also defined as a fraction of variable cost:
mxf = mvsf (xf - m9k)
Domestic inputs to intermediate production are determined by exhaustion of product:
dxf = (I-kvs,-mvs) (x,-mkp
The user cost of capital equals interest plus depreciation, so the initial capital stock in can then be inferred
from capital returns:
-41-
vk
kx = f
f r+8
Fixed costs of intermediate goods production equal the sum of recurring fixed costs and blueprints. We use
a parameter fcshrf to define how these shares are separated:
fcOf = fcshr1 mkr
Blueprints do not depreciate, so the value of a firm's equity is related to the base year dividends through the
interest rate:
(1-fcshrf) mkf
ff - r
Base year furm creation is determined by the steady-state growth ram (there is no depreciation of blue-prints
in this model):
if = g f
Domestic and intermediate inputs to investment are based on the import value share in investment:
imjf = mvsIf if idf = (I-mvsi) if .
Base year capital investment in firms is sufficient to cover growth plus depreciation of the capital stock:
ixf = kxf (g + o) .
Net investment by households in the intermediate goods sector equals the total vahe of blueprint and capital
formation, less the value of markup revenue net of recurring fixed costs:
I = F_f if + ixf - (mkf + mkf - fc?
As we assume that tariff revenues are returned to the consumer in a lump sum, me must determine base year
tariff revenue and imports to final demand simultaneously. The following system of equations then
determine base year tariff revenue (7) and imports (c):
-42-
T = I +t ( C. + Efmxf im)
and
C. = 0c (L - I + 7)
Solving, we have
T=t ( (L-1) + ;,mx,+im,)
1 +t (1 -0)
Domestic consumption is then
Cd = (1-0c) (L-I+T)
Total demand for domestic output is equal to the sum of final demand, inputs to intermediate production,
recurring fixed costs for intermediate demand, inputs to new firms and investment in capital
goods for new firms:
D = cd + Er dxf + fcf + idf + ixf
We assume that both firm types supply to the domestic and import markets in the same proportions, we
therefore use market share to define production to the domestic and export market by firm type.
dD = (1-OX) D, dM =Ox D
Imports include those for final consumption, X production and X-sector investment:
M = cm + E, mx,f - im,
I +t
The value of total exports equals the net of tariff value of imports. Imposing trade balance, the value of
exports equals the value of imports deflated by the base year tariff: And then from our assumption of
symmetry of export shares across domestic and foreign firms, we have:
e = M, eD = ( 1- ) M
-43-
Figure 1: Consumption Path following Tariff Reform
40
35
30 - CENTRAL
, . CAPITAL FLOWS
25 CRTS
@ 25/ SPILLOVERS ---
a< 20
a L
00
15
n . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
2000 2010 2020 2030 2040 2050
.~~~~~~~~~~~~~~~~~~~~~~~~~~
Figure 2: The Real Exchange Rate following Tariff Reform
25 I -
20 -,
CENTRAL
CAPITAL FLOWS
15 CRTS
. . . . . .= =. . . .........SPILLOVERS -
10 7
0
I
01
-10 1i0 0 20 ,
2000 2010 2020 2030 2040 2050
Figure 3: Interest Rate following Tariff Reform
8.5 , . .
CENTRAL
7.5 l CAPITAL FLOWS
CRTS
2 7 i, SPILLOVERS
6.5 A
64
5.5 IIt
5 ; ;: -- ------,----------------------- --,--
2000 2010 2020 2030 2040
Figure 4: Domestic Firms following Tariff Reform
250-------
200
CENTRAL
CAPITAL FLOWS
150 CRTS
SPELLOVERS
a)
100
0 50
-50
2000 2010 2020 2030 2040 2050
Figure 5: Foreign Firms following Tariff Reform
100 ,/\ . .
I 00~~~~
80 /
| ''\\ ~~~~~~~~CENTAGrL
60 ~~~~~~~~~~~CAPITAL FLOWS
60 , , |CRTS
., SPILLOVERS --
40l
20
X g ~~.. ... . . .. ... ....,,,..... .. . ....... ..... .... ..,...:.,j. .... . .. ... .. . .
-20X
-20,
-40 , , ,
2000 2010 2020 2030 2040 2050
Figure 6: Consumption Paths for
Alternative Replacement Taxes
40 1 - - ,
35
CENTRAL
30 CAPITAL FLOWS
25" !OUTPUT TAX
CAPITAL TAX
20
0 20
X15
10
15
10 __ _
2000 2010 2020 2030 2040 2050
Policy Research Working Paper Series
Contact
Title Author Date for paper
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Transition Econor.iss 33722
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Ni?nane vab.;i,ri
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and Why
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