The Dynamic Effects of Contingent Tariffs
Elias Dinopoulos
Paul S. Segerstrom
Department of Economics
Department of Economics
University of Florida
Michigan State University
Gainesville, FL 32611
East Lansing, MI 48824
[email protected]fl.edu
[email protected]
November 11, 1997
Abstract
This paper develops a specific-factor variant of the “quality ladders” model without the
scale effect property. We analyze the dynamic effects of contingent tariffs that are imposed
on imports whenever domestic firms lose their global technological leadership positions to
foreign firms. Small “rent-extracting” contingent tariffs do not benefit domestic firms that
fall behind and are negatively related to the global rate of technological change in the short
run. Large “protective” contingent tariffs allow domestic technological laggards to capture
the domestic market and are positively related to the global rate of technological change in
the short run.
JEL classification numbers: O32, O41. Key words: growth, R&D, tariffs.
*The authors would like to thank Paul Pecorino, Rod Ludema, other conference participants at the Spring 1996 Midwest International Economics Conference and the 1996 Allied
Social Science Annual Meetings, and two anonymous referees for helpful comments. Of
course, any errors that remain are our own responsibility.
1
Introduction
The past five decades have been characterized by rapid technological change. In many
cases, firms that were technological leaders have fallen behind in global technological
races. As a result, shifts in comparative advantage and structural changes in trade patterns have occurred. For example, in the 1950’s, U.S. firms were technological leaders
in the automobile, steel and machine tool industries, and the U.S. was a net exporter of
these products. But the successful adoption of industrial robots and American managerial
techniques (quality circles) enabled Japanese automobile manufacturers to produce higher
quality cars. Due to the incorporation of continuous-casting and oxygen furnaces, Japanese
steel producers gained a competitive advantage over their U.S. rivals. And the adoption of
numerically controlled (computer based) technology enabled Japanese firms to produce
higher quality machine tools. In all these industries, Japanese exports increased substantially and U.S. firms experienced significant losses.
Shifts in comparative advantage increase the effectiveness of protectionist demands
from domestic firms and workers.1 In many instances governments respond to these protectionist demands by considering and even granting tariff protection to domestic firms that
fail to keep pace by innovating. For instance, countervailing duties (CVD) and antidumping
(AD) provisions that are protective in nature fall into the category of contingent tariff protection. This type of protection was considered in all of the above mentioned industries.2
Prusa [1997] has analyzed the trade effects of U.S. antidumping actions by considering 428
1
See Bhagwati [1982] and Dinopoulos [1983] for analyses of the interactions between shifts in compara-
tive advantage and lobbying responses.
2
The U.S.-Japan auto VER was preceded by a safeguards case that involved requests from U.S. automobile
producers for relief due to market disruption. The U.S. steel VER in the early eighties followed a series of
AD and CVD petitions. The U.S. machine tool industry petitioned the government for relief from imported
machine tools on several occasions before the imposition of the VER. An additional example is provided
by the semiconductor industry, where U.S. firms dominated the global market until the late 1970s. The
semiconductor agreement between the U.S. and Japan occurred after several AD petitions against Japanese
manufacturers (see Bhagwati [1988], p.53). Although protection took the form of quantity restrictions instead
of tariffs in these industries, the popularity of AD and CVD has been increasing recently, whereas the Uruguay
multilateral trade agreement calls for gradual reduction and eventual elimination of VERs.
1
AD cases filed by domestic firms between 1980 and 1988. One third of these cases resulted
in duties with those in the top quartile exceeding 36%.3 According to Prusa, these tariffs
had substantial effects on domestic prices and trade volumes: the imposition of duties over
36% resulted in an average increase of the unit values of imported goods by more than
100% and in a reduction in the volume of trade by 47%. Moreover, in some instances the
imposition of AD duties has eliminated trade in narrowly defined products due to substantial trade diversion effects.
If one views technological change as an endogenous process that is affected by trade
policies, then it is natural to ask the question: what are the dynamic effects of protecting
domestic firms that fall behind in global technological races? This question has received
surprisingly little attention in the theoretical literature on endogenous growth and international trade. Rivera-Batiz and Romer [1991b] show that higher common tariffs between
two structurally identical countries slow technological change and economic growth at the
margin, except at extremely high tariff levels. Allowing for cross-country differences in
factor productivity, Grossman and Helpman [1990] find that a small import tariff on final
goods increases economic growth if and only if the policy-active country has a comparative
disadvantage in R&D. In both of these papers, though, because innovations are new horizontally differentiated products, domestic firms never fall behind in global technological
races and shifts in comparative advantage for particular products never occur. More closely
related to the present paper, Grossman and Helpman [1991, section 10.4] analyze a two
country “quality ladders” model where firms produce different quality products and there
exist domestic firms with lower quality products that could potentially benefit from tariff
protection. However, they only consider the effects of “small departures from free trade”
3
The following examples illustrate the high levels of tariffs that resulted from U.S. AD investigations in
the 1980s: the U.S. imposed a 57% tariff on Japanese cast-iron pipe imports; there was a 64% duty and a
119% duty levied against Brazilian and Argentinean carbon steel wire rod respectively; and an ad valorem
tariff of 124% was imposed against Italian tapered roller bearings as well. We are indebted to Tom Prusa
for providing this information. In addition, Feenstra [1992] describes the details of a temporary tariff on
heavyweight motorcycle imports to the U.S. during the period 1983-87 in order to protect the only U.S.
producer – Harley Davidson – based on a “threat of serious injury” to the domestic industry. This tariff was
removed at the request of Harley Davidson.
2
(p. 273), that is, tariffs on imported products that are too small to benefit domestic firms
that have fallen behind technologically.4
In this paper, we follow Rivera-Batiz and Romer [1991a,b] in studying the dynamic
effects of tariff barriers between two structurally identical countries (Home and Foreign).
However, we assume a “quality ladders” structure as in Segerstrom, Anant and Dinopoulos
[1990], and Grossman and Helpman [1991]. In each industry, firms engage in research
activities aimed at improving the quality of existing products. There are complete international knowledge spillovers and firms that experience R&D success earn temporary
monopoly profits as a reward for their past R&D efforts. The rates at which technological change and economic growth occur are endogenously determined based on the profit
maximizing behavior of firms in both countries.
In this model, R&D investment generates knowledge-driven trade between the two
countries. Because of the uncertainly associated with research activities, each industry
experiences random shifts in competitiveness and there are always firms in each country
producing inferior quality products that would directly benefit from appropriately targeted
protectionist policies. We study the effects of tariffs which are contingent to innovations
that trigger changes in trade patterns because the likelihood of protection is higher in these
industries due to resource-reallocation considerations. More precisely, under contingent
tariffs, each country imposes an ad valorem tariff on imports only in those industries where
a domestic firm has recently lost its global technological leadership to a foreign firm (i.e.
a trade pattern switch has occurred). In industries where a domestic technological leader
has been recently replaced by another domestic firm, free trade prevails by assumption. We
follow the standard practice of studying the effects of tariffs first, leaving the corresponding
analysis of other trade restrictions to future research.
With both countries imposing contingent tariffs on imported goods, the incentives to
innovate differ across industries in each country. For example, in a Home exporting indus4
Several recent studies have analyzed the dynamic effects of across-the-board (as opposed to contingent)
tariffs in a variety of settings (i.e. Brock and Turnovsky [1993], Galor [1994], Osang and Pereira [1996],
Dinopoulos and Syropoulos [1997]). These studies have found that tariffs have ambiguous effects on welfare
and growth.
3
try where the current quality leader is a Home firm, Home innovation means that the new
quality leader’s main competitor is also a Home firm (the previous Home quality leader).
Because no Foreign firm is adversely affected by the Home innovation, the new Home quality leader earns profits from selling to domestic consumers and earns profits from exporting
without the hinderance of tariff barriers. In contrast, in a Home importing industry where
the current quality leader is a Foreign firm, Home innovation means that the new Home
quality leader’s main competitor is a Foreign firm (the previous quality leader). Because
the Foreign government imposes a tariff on imports in such an industry, the new quality
leader earns lower profits from exporting, implying that the reward for innovating is lower
in importing industries. Profit-maximizing firms respond to these incentives by devoting
more resources to R&D in exporting industries than in importing industries. Consequently,
the imposition of tariffs generates a misallocation of resources compared to the free trade
equilibrium given the structural symmetry of the model and the assumption of industryspecific factors.
When the contingent tariff rate is small, Foreign quality leader firms appropriately lower
their prices so that Home quality follower firms continue to be priced out of business. Likewise, Home quality leaders appropriately lower their prices so that Foreign quality followers continue to be priced out of business. We refer to these tariffs as “rent-extracting”
contingent tariffs because they transfer rents from foreign quality leaders to domestic governments in both countries. Technologically backward domestic firms (followers) that are
threatened by import competition do not benefit from small “rent-extracting” contingent
tariffs. However, when the contingent tariff rate is large, in particular, large enough to
offset the technological advantages of foreign rivals, then Home (Foreign) quality leaders
cannot profitably export to Foreign (Home) consumers in industries where contingent tariffs are imposed. We refer to these tariffs as “protective” contingent tariffs because they
enable domestic firms that are threatened by import competition to survive. The technologically backward domestic firms that are protected earn positive economic profits from
selling to domestic consumers, but of course, do not export their products.5 To summa5
Because products within each industry are identical when adjusted for quality by assumption, protective
contingent tariffs segment the market but are not strictly prohibitive in the following sense: an increase in
4
rize, in the rent-extracting contingent tariff case, foreign leaders drive domestic firms out
of business and in the protective contingent tariff case, domestic firms drive foreign leaders
out of the domestic market. We analyze both cases in this paper.
When the tariff rate is small (the rent-extracting contingent tariff case), a permanent
increase in the tariff rate leads to a temporary decrease in the global rate of technological
change. This “productivity slowdown” occurs for two reasons. First, there is the R&D
incentive effect. If a domestic firm innovates in an industry with a foreign leader (an importing industry), the new domestic quality leader earns lower profits from exporting when
the rent-extracting tariff rate is higher. By extracting more of the rents innovators earn,
higher rent-extracting tariffs discourage firms from investing in R&D in importing industries while having no direct effect on the reward for innovating in exporting industries.
Second, there is the resource utilization effect. By making it more attractive to innovate
in exporting industries, higher rent-extracting tariffs increase the imbalance in R&D effort
across industries in each country. Given our assumption of diminishing returns to R&D at
the industry level, greater imbalance in R&D effort across industries implies that resources
are used less efficiently in the R&D sector, which also contributes to the productivity slowdown.
In contrast, when the tariff rate is large (the protective contingent tariff case), a permanent increase in the tariff rate has the opposite effect on technological progress. A
permanent increase in the protective contingent tariff rate leads to a temporary increase in
the global rate of technological change. There are three reasons why this occurs. First,
the previously mentioned R&D incentive effect now works in the opposite direction. Industry leaders calculate that they will be the beneficiaries of protectionism after a foreign
firm innovates in their industry. Since higher tariffs on imports generate higher profits for
protected domestic firms, the rewards for innovating directly increase in both importing
and exporting industries as a result of higher protective contingent tariffs. Second, the
previously mentioned resource utilization effect also works in the opposite direction. With
protective tariffs allows protected domestic firms to raise their prices and earn higher profits, whereas changes
in prohibitive tariffs do not generate any such effects. In other words, protective tariffs segment the market
but do not eliminate potential competition from global quality leaders.
5
protective contingent tariffs in place, firms in both countries devote more resources to R&D
in exporting industries than in importing industries. Firms in importing industries benefit
relatively more from higher protective contingent tariffs since such firms do not earn as
large profits immediately from innovating. By making it relatively more attractive to innovate in importing industries, higher protective contingent tariffs reduce the imbalance in
R&D effort across industries in each country. Given the assumed diminishing returns to
R&D at the industry level, resources are used more efficiently in the R&D sector when
R&D effort is more balanced across industries. Third, there is a labor market effect that
is not present with rent-extracting contingent tariff rate increases. By driving up the prices
consumers pay in protected markets, higher protective contingent tariffs reduce the overall demand for workers in manufacturing and free up labor for employment in the R&D
sector. Given that all three effects point in the same direction, protective contingent tariffs
unambiguously promote technological progress at the margin.
The rest of this paper is organized as follows: In section 2, the two country model with
contingent tariffs is presented. The dynamic effects of higher rent-extracting contingent
tariffs are analyzed in section 3 and section 4 covers the protective contingent tariff case.
Section 5 offers concluding comments. Some of the more technically involved arguments
are presented in Appendix A at the end of the paper.
2
The Model
The model developed in this section is a two-country version of Grossman and Helpmans’
[1991,chap.4] “quality ladders” growth model with two important modifications that drive
the main results of the analysis. First, we assume that R&D difficulty (i.e. the inverse
of total factor productivity in the production of R&D services) increases with cumulative
R&D effort in each industry. Second, we assume that each industry uses one mobile and
one industry-specific factor in the production of R&D services.
The first modification is adopted in order to rule out the “scale effect” property of early
R&D-griven growth models which share the counterfactual prediction that a permanent
6
increase in R&D resources should lead to a permanent increase in economic growth rates.6
Jones [1995a] has argued persuasively against the empirical validity of this prediction by
pointing out that measures of R&D resources (such as R&D expenditure or the number
of scientists and engineers in R&D) exhibit exponential growth in sharp contrast to the
stationarity of per capita output and total factor productivity growth rates. In addition,
Kortum [1997] has presented time-series evidence that shows a stationary flow of patents
over the last 50 years which implies that the R&D resources per patent ratio (a rough
measure of R&D difficulty) has been increasing over time.
The assumption that R&D difficulty increases with cumulative R&D effort removes the
scale effects from the quality ladders growth model and generates a steady state equilibrium
with strictly positive and constant utility growth coupled with exponential growth in R&D
resources. This assumption also generates an increasing R&D resources per patent ratio
over time.7 There are two important implications of this modification. First, the long-run
rate of technological change is proportional to the exogenous rate of population growth and
therefore tariffs are ineffective in the long run. This implication is common in other models of growth without scale effects (e.g. Jones [1995b] and Kortum [1997]). In a previous
version of this paper, Dinopoulos and Segerstrom [1996], we have shown that if R&D difficulty is proportional to world population as proposed in Dinopoulos and Thompson [1996],
then tariffs influence the long-run rate of technological change, and the main results of our
analysis are robust to this modification. Second, this assumption allows us to analyze the
transitional effects of tariffs on technological progress by comparing the steady-state values of relative R&D difficulty (before and after permanent increases in tariff rates) without
6
See, for example, Romer [1990], Segerstrom, et al. [1990], Grossman and Helpman [1991] and Aghion
and Howitt [1992].
7
Other recently developed models of R&D-driven growth without scale effects include Jones [1995b],
Young [1995], Segerstrom [1996], Dinopoulos and Thompson [1996], and Kortum [1997]. The empirical
relevance of these models has not been established unequivocally yet. For instance, the models of Jones and
Young have implications for patent statistics that are less satisfactory than the ones of the present model. The
number of researchers per patent decreases over time in Jones’ model and remains constant in Young’s model.
Kortum’s model is similar to the present one although much more complicated and provides microfoundations
for our approach by tracing the increasing R&D difficulty to declining technological opportunities over time.
7
formally analyzing the transitional dynamics of the model.
If all factors are perfectly mobile across industries and activities, then contingent tariffs have no effects on the margin, as we will show in section 4. Firms in both countries
immediately specialize by only doing R&D in exporting industries. Shifts in comparative
advantage never occur and contingent tariffs do not generate any tariff revenues in equilibrium. In order to obtain more interesting and empirically relevant results, we assume that
R&D utilizes both workers with general skills (which are mobile across industries) and
workers with highly specialized R&D skills (which are industry-specific factors). We have
in mind that many researchers undergo extensive training to do particular types of research
and cannot easily switch to other occupations without years of retraining. For simplicity, we do not model these training decisions and instead assume that some factors are
industry-specific. With less than perfect factor mobility, firms continue to do some R&D
in importing industries when there are positive tariffs on imported products, implying that
shifts in comparative advantage occur. Thus, some firms in each country receive contingent
tariff protection in equilibrium.
We refer to the two countries in the model as “Home” and “Foreign”. As in Rivera-Batiz
and Romer [1991a,b], we assume symmetry throughout our analysis, both in the endowments and technologies faced by each country, and in the policies that are implemented.
The assumption of two symmetric countries is obviously unrealistic, but simplifies the
analysis considerably and is dictated by tractability considerations.
In the model, there is a continuum of industries producing final goods indexed by ω ∈
[0, 1]. Thus, there also is a continuum of specific factors, the specialized R&D workers that
cannot move across industries. In each industry, firms are distinguished by the quality j
of the products they produce. Higher values of integer j denote higher quality. At time
t = 0, the state-of-the-art quality product in each industry is j = 0, that is, one firm in
each industry knows how to produce a j = 0 quality product and no firm knows how to
produce any higher quality product. A firm that produces a state-of-the-art quality product
is called a “quality leader.” A firm that produces a product one step below the state-of-theart quality product (in each industry) is called a “quality follower.” At time t = 0, one half
of the industries have Home quality leaders and the other half have Foreign quality leaders.
8
Firms in both countries can engage in R&D to discover the next-generation product in each
industry and all firms possess the same R&D technology. When the state-of-the-art quality
in an industry is j, the next winner of a R&D race becomes the sole producer of a j + 1
quality product. Thus, over time, products improve as innovations push each industry up
its “quality ladder.”
2.1
Consumers and Workers
Each country has a fixed number of identical households that provide labor services in exchange for wages. Each household is modelled as a dynastic family whose size grows over
time at an exogenous rate n which also equals the population growth rate.8 We normalize
the total number of individuals in each country at time t = 0 to equal unity. Thus, the
population of workers in each country at time t is N (t) = ent . Each household maximizes
the discounted utility
U≡
∞
ent e−ρt log u(t) dt
(1)
0
where ρ > 0 is the common subjective discount rate, and u(t) is the utility per person at
time t, which is given by
log u(t) ≡
1


log  λj d(j, ω, t) dω.
0
(2)
j
In equation (2), d(j, ω, t) denotes the quantity consumed of a product of quality j produced
in industry ω at time t, and λ > 1 measures the size of quality improvements.
At each point in time t, each household allocates expenditure to maximize u(t) given
the prevailing market prices. Solving this optimal control problem yields a unit elastic
demand function (d = c/p where d is quantity demanded, c is per capita consumption
expenditure and p is the relevant market price) for the product in each industry with the
lowest quality adjusted price. The quantity demanded for all other products is zero. To
break ties, we assume that when quality adjusted prices are the same for two products of
different quality, a consumer only buys the higher quality product.
8
Barro and Sala-i-Martin [1995, chapter 2] discuss in greater detail this formulation of household behavior
within the context of the Ramsey model of growth.
9
Given this static demand behavior, maximizing (1) subject to the household’s intertemporal budget constraint yields the well-known differential equation
ċ(t)
= r(t) − ρ,
c(t)
(3)
where r(t) is the market interest rate at time t. This intertemporal optimization condition
implies that a constant per capita expenditure path is optimal when the market interest
rate is ρ. A higher market interest rate induces consumers to save more now and spend
more later, resulting in increasing per capita consumption over time. In a balanced growth
equilibrium where c is constant over time, (3) implies that the equilibrium interest rate must
equal ρ.
On the production side, individuals are classified as either having general skills or specialized R&D skills. At time t, the endowment of workers with specialized R&D skills is
given by H(t) = sN (t), where s ∈ (0, 1) is the fixed fraction of the population that is specialized, and the endowment of workers with general skills is given by L(t) = (1 − s)N (t).
=
Both populations of workers grow at the same exogenous rate ( Ḣ(t)
H(t)
L̇(t)
L(t)
=
Ṅ (t)
N (t)
= n).
General and specialized labor constitute the only two factors of production in the economy. Specialized workers have industry-specific skills for doing research and only do research. Workers with general skills, on the other hand, can engage in either manufacturing
of final products or R&D and are perfectly mobile across industries and activities.9 Assuming symmetry across industries in the endowments of specialized workers and a measure
one of industries, H(·) represents both the employment of specialized R&D workers in
each industry and the total employment of specialized R&D workers in each country (aggregated across industries). Full employment prevails for all types of workers throughout
time.
2.2
Product Markets
In each industry, one unit of general labor is required to produce one unit of output, regardless of quality. Labor markets are perfectly competitive and the wage of workers with
9
The assumption that R&D utilizes both general and specialized factors is also made in Aghion and Howitt
[1992].
10
general skills is used as the numeraire. Consequently, each firm has a constant marginal
cost of production equal to one. Firms compete in prices.
We assume that both countries impose a common ad-valorem tariff τ on imports. However, instead of looking at across-the-board tariffs on all imports, we analyze the common
government practice of protecting domestic firms that have recently fallen behind foreign
firms in global technological races. These are often the firms that lobby vigorously and
successfully for import restrictions. The quality ladders growth model is ideally suited for
studying this type of government intervention. Protection for technologically backward
firms cannot be analyzed using Romer’s [1990] endogenous growth model because growth
is based on the sequential introduction of horizontally differentiated products, and there are
no technologically backward firms to protect.
The Home country government imposes the ad-valorem tariff τ on imports in all industries where a Foreign quality leader competes against a Home quality follower (one step
down in the quality ladder). These are the industries where Home firms have recently lost
market share to Foreign firms. In industries where a Foreign leader competes against a
Foreign follower, we assume for simplicity that free trade prevails. Likewise, the Foreign
country government imposes the ad-valorem tariff τ on imports in those industries where
a Home quality leader competes against a Foreign quality follower (one step down in the
quality ladder). Free trade prevails in industries where a Home quality leader competes
against a Home quality follower. Thus, both governments help out domestic firms that
are technologically backward (quality follower firms that one step down in their industry’s quality ladder) and threatened by international competition (compete against foreign
quality leaders). Each domestic industry experiences random cycles of “contingent” tariff
protection based on when a shift occurs in its competitiveness.10
To determine static Nash equilibrium prices and profits, consider first the profits earned
10
With this formulation, if a Home firm is a quality leader and a Foreign firm innovates, then the Home
firm receives tariff protection. But if another Foreign firm subsequently innovates and becomes the quality
leader, then the tariff is removed, since the Home firm has fallen two steps behind the current quality leader.
Our focus in this paper is on studying protection that is temporary in nature, not protection that is given to
firms no matter how far behind they have fallen technologically.
11
by a Home leader from selling to Home consumers when competing against a Home follower. With the Home follower charging a price of one, the lowest price it can charge and
not lose money, the Home quality leader earns the profit flow π(p) = (p − 1)c(t)N (t)/p
from charging the price p if p ≤ λ, and zero profits otherwise. These profits are maximized by choosing the limit price p = λ > 1. Thus the Home quality leader earns the
profit flow π L ≡
λ−1
λ
c(t)N (t) at time t from selling to Home consumers and none of
the other firms in the industry can do better than break even (by selling nothing at all).
When a Home leader competes against a Home follower (or when a Foreign leader competes against a Foreign follower), tariffs are not imposed by either country, and therefore
the leader earns the profit flow π L from selling in each of the two countries.
In industries where a Home leader competes against a Foreign follower, the Foreign
government imposes the tariff τ on imports. The Home leader still earns the profit flow
π L from selling in the Home market. However, in the Foreign market, with the Foreign
follower charging a price pF = 1 (the lowest price it can charge without losing money), the
Home leader cannot charge a price higher than pL = λ to Foreign consumers. Since the
Home leader has to pay a tariff to the Foreign government, the “after tax” price p∗L that the
leader receives is given by p∗L (1 + τ ) = λ or p∗L = λ/(1 + τ ), and the leader earns per unit
profits λ/(1 + τ ) − 1 from selling to the Foreign market. Since demand is unit elastic and
Foreign consumers pay the “before tax” price λ for the leader’s product, the quantity that
the Home leader sells is
c(t)N (t)
.
λ
(t)
Thus, the Home leader earns profits [λ/(1 + τ ) − 1] c(t)N
λ
from selling to the Foreign market. This profit expression is valid when the tariff rate τ is in
the range 0 ≤ τ < λ − 1. We call contingent tariffs in this range “rent-extracting” tariffs.11
Such tariffs do not prevent technological leaders from driving their foreign competitors out
of business, but they do reduce profit flows by shifting rents from technological pioneers to
governments in both countries.
Consider next the case where a Home leader competes against a Foreign follower and
the Foreign government imposes a tariff τ on imports that is in the range λ−1 ≤ τ < λ2 −1.
The lowest price the Home leader can charge in the Foreign market and still break even is
pL = 1 + τ . The Foreign follower can then price the Home leader out of the Foreign mar11
The classic article on rent-extracting tariffs is Brander and Spencer [1981].
12
ket by charging the limit price pF = (1 + τ )/λ. The restriction λ − 1 ≤ τ ensures that
pF = (1 + τ )/λ ≥ 1, implying that the follower’s price covers its constant unit cost in the
Foreign market. The restriction τ < λ2 − 1 implies that pF = (1 + τ )/λ < λ, and consequently the protected follower cannot be undersold by any Foreign firm two steps down
in the quality ladder. We call contingent tariffs in this range “protective” tariffs since they
allow follower firms to successfully compete against foreign leaders. Under a protective
(t)
=
tariff, a Home (Foreign) follower earns the positive profit flow π F (t) ≡ (pF − 1) c(t)N
pF
1−
λ
1+τ
c(t)N (t) from selling to Home (Foreign) consumers. Protected followers do not
export their products in equilibrium, so leaders are always able to earn positive profits from
selling to domestic consumers. Higher protective tariffs allow domestic quality followers
to raise their prices and profits even though markets are segmented in equilibrium. We
analyze both the rent-extracting and protective contingent tariff cases in this paper.12
2.3
R&D Races
All firms in an industry have the same R&D technology13 and there is free entry into each
R&D race. In industry ω at time t, a firm engaged in R&D that employs i (ω, t) workers with general skills and hi (ω, t) workers with specialized R&D skills is successful in
discovering the next higher quality product with instantaneous probability
Ii (ω, t) =
12
Ai (ω, t)α hi (ω, t)1−α
X(ω, t)
(4)
If tariffs are sufficiently high (τ ≥ λ2 − 1), then Home followers earn at least as much as Home leaders
(in other industries) from selling to Home consumers and firms two or more steps down in an industry’s
quality ladder may find it profitable to produce. We do not study these possibilities on the grounds that the
analysis would become taxonomic.
13
Although this assumption is standard in the R&D-driven endogenous growth literature, it would probably
be more realistic to assume that industry leaders can improve their own products more easily than can other
firms (e.g. Intel appears to be the prime candidate to invent the next generation of microprocessors). The
implications of leader R&D cost advantages are studied in Segerstrom and Zolnierek [1997]. Introducing
these R&D cost advantages into the present trade model would reduce the likelihood of market turnover, but
we do not think the qualitative properties of the model would change.
13
where A > 0 and α > 0 are given technology parameters, and X(ω, t) is a function
that captures the difficulty of conducting R&D which each individual firm takes as given.
By instantaneous probability, we mean that Ii (ω, t) dt is the probability that the firm will
innovate by time t + dt conditional on not having innovated by time t, where dt is an
infinitesimal increment of time. We assume that α ≤ 1/2, that is, workers with specialized
R&D skills are at least as important as workers with general skills in R&D activities.14 The
returns to engaging in R&D are independently distributed across firms, across industries,
and over time, and thus, the instantaneous probability of R&D success in industry ω at
time t is given by I(ω, t) =
i Ii (ω, t)
= Ix (ω, t) + Im (ω, t). Variable Ix (ω, t) is the
instantaneous probability of R&D success by firms in the country where the current quality
leader resides (the country that would currently export under free trade), and Im (ω, t) is the
instantaneous probability of R&D success by firms in the other country (the country that
would currently import under free trade).15
In each R&D race, all firms in a country face the same factor prices, and each R&D
“production function” is strictly concave and homogenous of degree one. It follows that
each R&D firm participating in a race from the same country must choose the same i /hi input ratio. Thus we can conveniently aggregrate across firms to obtain per country industrylevel innovation rates. For the exporting country in industry ω at time t, we obtain
Ix (ω, t) =
where LIx (ω, t) =
and H(t) =
i
i i (ω, t)
ALIx (ω, t)α H(t)1−α
X(ω, t)
(5)
is the exporting country’s R&D employment of general labor
hi (ω, t) is the exporting country’s industry-level employment of specialized
R&D labor (because there is symmetry across industries in the endowments of specialized
factors, H(·) is not a function of ω). A similar expression holds for the importing country.
To remove the “scale effect” property of earlier endogenous growth models, we assume
14
As is demonstrated in Appendix A, the assumption α ≤ 1/2 is a sufficient but not necessary condition
for the conclusions derived in this paper. This assumption rules out the case where α is close to one and
R&D technologies are almost linear. Then quality ladders models become much harder to analyze since they
typically have multiple steady state equilibria (see Davidson and Segerstrom [1997]).
15
When I is constant over time, which we will show holds in the balanced growth equilibrium, the time
duration of each R&D race is an exponentially distributed random variable with parameter I.
14
that R&D starts off being equally difficult in all industries [X(ω, 0) = 1 for all ω] and
R&D difficulty grows in each industry with cumulative R&D effort:
Ẋ(ω, t)
= µ · [Ix (ω, t) + Im (ω, t)]
X(ω, t)
(6)
where µ > 0. Equation (6) captures in a simple way the idea that as each country grows and
X(ω, t) increases over time, innovating becomes more difficult in each industry. Although
we do not explicitly model the process that leads to increasing R&D difficulty, we think of
firms choosing among an infinite array of R&D projects with varying degrees of expected
difficulty. In such a setting, projects with lower degrees of expected difficulty would be
explored first, leaving the more difficult research projects to be explored later. The specification (6) was proposed in Segerstrom [1996] and generates a quality ladders model with
similar properties to Jones’ [1995b] variety-based growth model.16
Given the symmetric structure of the model, we focus on equilibrium behavior where
the R&D intensities Ix (·) and Im (·) do not vary across industries ω at any given point in
time t. Thus the ω argument of functions is dropped in the remainder of the paper.
Let vx (t) be the expected discounted reward for R&D success by a Home firm in an
exporting industry at time t (an industry where the current quality leader is a Home firm).
In such an industry, Home R&D firm i chooses its employment of workers with general
and specialized skills to maximize its expected discounted profits
vx (t)
Ai (t)α hi (t)1−α
− i (t) − w(t)hi (t),
X(t)
(7)
where w is the relative wage rate of specialized workers in this industry. Since all Home
R&D firms in this industry face the same factor prices and choose the same factor ratio in
equilibrium, profit maximization yields the first order condition
vx (t) =
16
x(t)1/α Ix (t)(1−α)/α N (t)
α·θ
(8)
In the earlier version of this paper, Dinopoulos and Segerstrom [1996], we also explore the implications
of an alternative specification for how R&D difficulty increases over time:
Ẋ(ω,t)
X(ω,t)
= n. This specification
captures the notion that it is more difficult to introduce new products and replace old ones in a larger market
due to informational, organizational, marketing and transportation costs. All of the results derived in the
paper continue to hold with the alternative specification except the effects of tariff increases on the rate of
technological change are permanent instead of temporary.
15
where x(t) ≡ X(t)/N (t) is a measure of relative R&D difficulty and θ ≡ A1/α s(1−α)/α is a
positive constant. Likewise, let vm (t) be the expected discounted reward for R&D success
by a Home firm in an importing industry at time t (an industry where the current quality
leader is a Foreign firm). In such an industry, R&D profit maximization by Home firms
yields the corresponding first order condition
vm (t) =
Given that
1−α
α
x(t)1/α Im (t)(1−α)/α N (t)
.
α·θ
(9)
> 0, (8) and (9) imply that the innovation rate in exporting (importing)
industries is higher when the reward for innovating in exporting (importing) industries is
higher, other things being equal.
This completes the description of the two country model with contingent tariffs.
3
Rent-Extracting Contingent Tariffs
We begin our analysis of rent-extracting contingent tariffs by solving for the reward for
innovating in an exporting industry vx (t).
When a Home firm innovates in an industry with a Home leader, the new Home leader
competes against a Home follower (the previous Home leader). Because innovation does
not switch the trade pattern of this industry, tariffs are not imposed and the new Home
leader earns profits 2π L = 2(λ − 1)c(t)N (t)/λ from selling to both Home and Foreign
consumers. After further innovation occurs, this firm will be driven out of business.
Now consider things from the perspective of the owners of the Home firm. Over a
time interval dt, the shareholders receive a dividend 2π L (t) dt, and the value of the firm
appreciates by v̇x (t) dt. Because the Home quality leader is targeted by other firms that
conduct R&D to discover the next higher quality product, the shareholder suffers a loss
of vx (t) if further innovation occurs. This event occurs with probability I(t) dt, whereas
no innovation occurs with probabillity 1 − I(t) dt. Efficiency in financial markets requires
that the expected rate of return from holding a stock of the Home quality leader is equal
to the riskless rate of return r(t) dt that can be obtained through complete diversification:
2π L (t)
dt
vx (t)
+
v̇x (t)
[1
vx (t)
− I(t) dt] dt −
vx (t)−0
vx (t)
I(t) dt = r(t) dt. Taking limits as dt approaches
16
zero, and substituting for
v̇x (t)
vx (t)
vx (t) =
using (8) yields
2 λ−1
c(t)N (t)
λ
r(t) + Ix (t) + Im (t) −
1 ẋ(t)
α x(t)
1−α I˙x (t)
α Ix (t)
−
−n
.
(10)
The profits earned by the Home quality leader 2π L are appropriately discounted using the
interest rate r and the instantaneous probability I = Ix + Im of being driven out of business
by further innovation. Also taken into account in (10) is the possibility that these discounted
profits grow over time.
The reward for innovating in an importing industry vm (t) can be similarly calculated.
When a Home firm innovates in an industry with a Foreign leader, the new Home leader
competes against a Foreign follower (the previous Foreign leader). Since rent-extracting
contingent tariffs are imposed by the Foreign government, the Home leader earns profits
(t)
λ−1
λ
c(t)N (t) from selling to Home consumers and earns profits [ 1+τ
−1] c(t)N
λ
λ
from selling
to Foreign consumers. After further innovation occurs, this Home firm will be driven out
of business. Consequently, the reward for innovating in an importing industry at time t is
vm (t) =
λ−1
c(t)N (t)
λ
(t)
λ
+ [ 1+τ
− 1] c(t)N
λ
r(t) + Ix (t) + Im (t) −
1 ẋ(t)
α x(t)
Note that in a balanced growth equilibrium where
ẋ
x
=
−
1−α I˙m (t)
α Im (t)
ċ
c
=
I˙x
Ix
=
−n
I˙m
Im
.
(11)
= 0, vx (t) > vm (t)
when τ > 0. Rent-extracting contingent tariffs make it more attractive for firms to innovate
in exporting industries than in importing industries. Note also that vm (t) is a decreasing
function of τ , holding all other endogenous variables fixed. Higher rent-extracting contingent tariffs directly reduce the reward for innovating in importing industries.
Combining (8) and (10), as well as (9) and (11) yields two R&D profit maximization
conditions for exporting and importing industries, respectively:
c(t)
2 λ−1
λ
r(t) + Ix (t) + Im (t) −
λ−1
c(t)
λ
1 ẋ(t)
α x(t)
−
1−α I˙x (t)
α Ix (t)
x(t)1/α Ix (t)(1−α)/α
=
αθ
−n
(12)
x(t)1/α Im (t)(1−α)/α
αθ
(13)
λ
+ [ 1+τ
− 1] c(t)
λ
r(t) + Ix (t) + Im (t) −
1 ẋ(t)
α x(t)
−
1−α I˙m (t)
α Im (t)
−n
=
For both exporting and importing industries, R&D profit maximization implies that the
discounted marginal revenue product of an innovation must equal its marginal cost at each
point in time.
17
Consider next the Home labor market for workers with general skills. The supply of
workers with general skills is (1 − s)N (t) and the demand for these workers consists of
two components: manufacturing and R&D. Rent-extracting tariffs do not affect the prices
consumers face, and the Home country accounts for half of the world’s leaders due to
symmetry. Each Home leader produces
c(t)N (t)
λ
units for Home consumers and
c(t)N (t)
λ
units
(t)
=
for Foreign consumers. Thus, total Home demand for manufacturing labor is 12 · 2c(t)N
λ
c(t)N (t)
.
λ
Equation (5) implies that the demand for R&D workers with general skills in
industries with a Home leader is [Ix (t)X(t)/AH(t)1−α ]1/α . Correspondingly, the demand
for R&D workers with general skills in importing industries (industries with a Foreign
leader) is [Im (t)X(t)/AH(t)1−α ]1/α . Since one half of industries have Home leaders and
one half have Foreign leaders, full employment of labor implies that
1−s=
c(t) x(t)1/α
+
[Ix (t)1/α + Im (t)1/α ].
λ
2θ
(14)
Any equilibrium path for the model must simultaneously satisfy (3), (6), (12), (13) and
(14) for all t. We will now proceed to show that the model has a unique balanced growth
equilibrium where all endogenous variables grow over time at constant (not necessarily the
same) rates and analyze how permanent increases in contingent tariff rates affect the balanced growth equilibrium. Appendix B shows that this equilibrium as well as the free-trade
equilibrium are locally saddle-path stable, that is, if the state variable x is initially close to
its balanced growth value, then there exists an equilibrium transition path [satisfying (3),
(6), (12), (13) and (14) for all t] that converges asymptotically over time to the balanced
growth equilibrium path.17
In any balanced growth equilibrium, (6) implies that
that
ẋ
x
=
−
α) Ḣ
H
ċ
c
Ẋ
.
X
I˙x
Ix
=
I˙m
Im
= 0 and then (14) implies
= 0 as well. Differentiating (5) with respect to time yields
I˙x
Ix
= α L̇LIx
+ (1 −
Ix
Using (6) and setting I˙x (t) = 0, yields
I ≡ Ix + Im =
n
.
µ
(15)
Equation (15) implies that the balanced growth global innovation rate in each industry
is completely determined by the world population growth rate n and the R&D difficulty
17
Appendix B is available from the authors upon request.
18
growth parameter µ. Equation (15) has three interesting implications which we will discuss
in turn.
First, given that the world population growth rate n is positive, the assumption of increasing R&D difficulty (µ > 0) is needed to solve the model. When µ ≤ 0, (15) implies
that a balanced growth equilibrium does not exist. As the world economy becomes larger
and the reward for innovating increases over time, the increase in R&D difficulty serves as
a counterbalancing force in the model.18
Second, higher population growth is good for R&D investment. The mechanism at
work is as follows: When the population growth rate is higher, aggregate consumer expenditure growth is also higher, which implies that the profit flows earned by industry leader
=
firms grow more rapidly over time ( v̇vxx (t)
(t)
v̇m (t)
vm (t)
= n). Faster population growth means a
larger expected discounted reward for innovating and firms naturally respond by devoting
more resources to R&D activities.19
Third, world population growth (n > 0) is necessary to sustain economic growth. If
world population growth ever comes to an end (n = 0), the model predicts that the rate
of technological change will gradually fall to zero over time. Although we do not view
this prediction about the future to be implausible, at the same time we do not want to
give it undue emphasis. It is worth stressing that we have not modelled either fertility or
human capital accumulation decisions. Incorporating into the model a negative relationship
between fertility and human capital accumulation could make economic growth sustainable
even without population growth.
Taking into account that
18
I˙x
Ix
=
I˙m
Im
=
ẋ
x
=
ċ
c
= 0 and that r(t) = ρ is implied by
We conjecture that when µ ≤ 0, the economic growth rate in each country increases without bound over
time.
19
An interesting topic for future research is to analyze the case of asymmetric countries with different pop-
ulation growth rates. We conjecture that countries with higher population growth rates would not necessarily
experience higher rates of technological change within the context of our model. For one thing, when free
trade prevails, the reward for innovating is the same across countries even when population growth rates differ. The profits of firms depend on the time path of world consumer expenditure, not on how this consumer
expenditure is distributed across countries, and therefore the reward for innovating would be the same across
countries even when population growth rates differ.
19
(3), equations (12), (13), (14) and (15) represent a system of four equations in four unknowns Ix , Im , c and x. These equation allow us to uniquely determine balanced growth
equilibrium values for all endogenous variables.
By definition, the growth rate of each consumer’s utility is constant in a balanced growth
equilibrium. We can obtain an explicit expression for this growth rate by substituting for
consumer demand (d = c/p) and the market price p = λ into the representative consumer’s
static utility function (2), and differentiating with respect to time (see Grossman and Helpman [1991,chap.4] for further details). These calculations imply that in a balanced growth
equilibrium, each consumer’s utility grows over time at the rate
gu ≡
u̇(t)
= (Ix + Im ) log λ.
u(t)
(16)
Solving (12) for c and substituting into (13), we obtain a balanced growth R&D condition in (Im ,Ix ) space:
Ix
2λ − 2
=
λ
Im
λ + 1+τ − 2
(1−α)/α
.
(17)
The R&D condition is an upward-sloping line that goes through the origin and pivots counterclockwise with any increase in the tariff rate τ . Notice that the R&D condition can only
be satisfied if Ix ≥ Im .
The upward sloping R&D condition is illustrated in Figure 1, together with the downward sloping iso-growth line given by (15). Since these two curves have only one intersection, the balanced growth equilibrium innovation rates Ix and Im are uniquely determined.
Starting from an initial balanced growth equilibrium given by point A, an increase in the
rent-extracting contingent tariff leads to a new balanced growth equilibrium given by point
B. Consequently, we conclude that a higher rent-extracting contingent tariff τ increases Ix
and decreases Im , but has no effect on the long-run growth rate gu , which is proportional
to Ix + Im . Higher rent-extracting contingent tariffs increase the relative profitability of
exporting industries vx /vm and shift R&D resources toward exporting industries in both
countries. Higher rent-extracting contingent tariffs also increase the imbalance in R&D
effort across industries in both countries (measured by Ix /Im ).
Solving (12) for c and then substituting into (14) yields a third balanced growth condi-
20
Final R&D Condition
Ix
Initial R&D Condition
Ix=Im
B
A
Final Resource Condition
Initial Resource Condition
Iso-Growth Line
Im
Figure 1: Long-run effects of rent-extracting contingent tariffs
tion in (Im ,Ix ) space, a resource condition:
2(1 − s) =
x1/α Ix(1−α)/α
x1/α 1/α
1/α
+ Im
).
(ρ + Ix + Im − n) +
(I
αθ(λ − 1)
2θ x
(18)
Given equilibrium values of Ix and Im , (18) uniquely determines the balanced growth equilibrium value of x. Substituting equilibrium values of Ix , Im and x back into (14) allows
us to pin down c as well. Thus the model has a unique balanced growth equilibrium.
Since the RHS of (18) is increasing in both Ix and Im , the resource condition is globally
downward-sloping in (Im ,Ix ) space, holding x fixed. The RHS of (18) is also increasing in
Ix holding Ix + Im and x fixed in the relevant region where Ix > Im . It follows that the
resource condition has a flatter slope than any iso-growth line. As illustrated in Figure 1,
the initial balanced growth equilibrium point A is given by the common intersection of the
R&D, constant growth and resource conditions (with x set equal to the balanced growth
equilibrium value in the resource condition).
The relatively flat slope of the resource condition plays a critical role in our comparative
steady-state analysis. A permanent increase in the rent-extracting contingent tariff rate τ
causes the R&D condition to shift leftward and the resource condition to remain fixed
[τ does not appear in (18)]. A new common intersection of the three balanced growth
conditions at point B is only achieved if x decreases and the resource condition shifts up
21
[the RHS of (18) is increasing in x and increasing in Ix ]. For x(t) ≡
X(t)
N (t)
to decrease,
X(t) must temporarily grow at a slower rate than the population N (t). Given (6), this
only occurs if the overall innovation rate Ix (t) + Im (t) temporarily falls below the balanced
growth level given by (15).
The following theorem summarizes the effects of rent-extracting contingent tariffs.
Theorem 1 A permanent increase in the rent-extracting contingent tariff rate (τ )
(i) permanently increases each country’s R&D intensity in exporting industries (Ix ),
(ii) permanently decreases each country’s R&D intensity in importing industries (Im ),
(iii) temporarily decreases the global rate of technological change (x decreases) and
(iv) has no effect on the long-run growth rate gu .
There are two reasons why rent-extracting contingent tariffs contribute to a “productivity slowdown.” First, there is the R&D incentive effect. If a domestic firm innovates in
an industry with a foreign leader (an importing industry), the new domestic quality leader
earns lower profits from exporting when the rent-extracting tariff rate is higher. By extracting more of the rents innovators earn, rent-extracting tariff rate increases discourage firms
from investing in R&D in importing industries while having no direct effect on the reward
for innovating in exporting industries [holding all other variables fixed, an increase in τ
reduces vm while leaving vx unaffected]. Second, there is the resource utilization effect.
By making it relatively more attractive to innovate in exporting industries, higher rentextracting tariffs increase the imbalance in R&D effort across industries in each country.
Given that there are decreasing returns to R&D at the industry level (which is implied by
our assumption of industry-specific factors), more imbalance in R&D effort across industries implies that resources are used less efficiently in the R&D sector [the resource condition has a flatter slope than any iso-growth line]. For both of these reasons, rent-extracting
contingent tariffs retard technological progress at the margin.
4
Protective Contingent Tariffs
Having already analyzed the effects of smaller rent-extracting contingent tariffs (0 < τ <
λ − 1), in this section we examine the effects of larger protective contingent tariffs (λ − 1 <
22
τ < λ2 − 1). Following the methodology of section 3, we will analyze the transitional effects of protective tariffs by focusing on steady-state changes in the relative R&D difficulty
variable x.
Consider first the Home labor market for workers with general skills. The supply of
workers with general skills is (1 − s)N (t), and the demand for these workers consists of
two components; manufacturing and R&D. Protective contingent tariffs affect consumer
prices and therefore the demand for manufacturing labor. Given the model’s symmetric
structure, at any point in time, half of all industries have Home leaders and half of all industries have Foreign leaders. Let β denote the proportion of industries with Home leaders
and Home followers. Because the global innovation rate in each industry is Ix + Im due
to symmetry, β =
1 Ix
.
2 Ix +Im
In industries with a Home leader and a Home follower, no
tariff is imposed and the Home leader employs 2cN (t)/λ manufacturing workers. When a
Home leader competes against a Foreign follower ( 12 − β industries), the Foreign follower
is protected and the Home leader only produces for Home consumers, using cN (t)/λ manufacturing workers. There are also
1
2
− β industries (due to symmetry) where a Home
follower competes against a Foreign leader. Protection is granted to the Home follower
who employs cN (t)/pF = cN (t)λ/(1 + τ ) manufacturing workers to supply the Home
market. Equation (5) implies that the demand for R&D workers with general skills in industries with a Home leader is [Ix X(t)/AH(t)1−α ]1/α . Correspondingly, the demand for
R&D workers with general skills in importing industries is [Im X(t)/AH(t)1−α ]1/α . Since
one half of industries have Home leaders and one half of industries have Foreign leaders, H(t) = sN (t), and x = X(t)/N (t), the Home demand for R&D workers with general
1/α
)/2θ. Full employment of labor in the Home country requires
skills is x1/α N (t)(Ix1/α + Im
that
2(1 − s) =
Ix c
Im λc
x1/α 1/α
c
1/α
+
+
+
[I
+ Im
].
λ λ(Ix + Im ) (1 + τ )(Im + Ix )
θ x
(19)
Note that higher protective contingent tariffs reduce the demand for workers in manufacturing and have a tendency to shift resources from production of final goods to R&D investment.
Next consider the incentives to innovate in exporting industries. When a Home firm
innovates in an industry with a Home leader, the new successful Home leader competes
23
against a Home follower (the previous Home leader). Because innovation does not switch
the trade pattern of this industry, tariffs are not imposed and the new Home leader earns
profits 2(λ − 1)cN (t)/λ from selling in both the Home and Foreign markets. After further
innovation occurs, this firm will continue to earn profits if a Foreign firm wins the R&D
race, because there will be a switch in the trade pattern and the Home firm will qualify for
contingent tariff protection. Thus with instantaneous probability Im , a Home leader is succeeded by a Foreign leader and then the protected Home follower earns profits π F (t) until
it is driven out of business by further innovation. Consequently, the reward for innovating
in an exporting industry is
vx (t) ≡
2 λ−1
cN (t) +
λ
λ
Im (1− 1+τ
)cN (t)
ρ+Im +Ix −n
ρ + Im + Ix − n
.
(20)
In (20), the profits 2(λ − 1)cN (t)/λ earned by an innovative firm are appropriately discounted using the balanced growth interest rate ρ, and the instantaneous probability that
the firm loses its leadership position Ix + Im . By subtracting n, we also take into account
that, due to population growth, aggregate consumer expenditure and profits earned by innovative firms grow over time at the rate n.
The reward for innovating in an importing industry vm (t) can be similarly calculated.
When a Home firm innovates in an industry with a Foreign leader, the new successful
Home leader competes against a Foreign follower (the previous Foreign leader). Since the
Foreign government imposes the tariff τ on imports in this industry, the Home leader only
earns profits (λ − 1)cN (t)/λ from selling to Home consumers. After further innovation
occurs, this Home firm will still earn profits if the innovator is a Foreign firm, because then
the Home follower (previous Home leader) will qualify for tariff protection. Consequently,
the reward for innovating in an importing industry at time t is
vm (t) ≡
λ−1
cN (t)
λ
+
λ
Im (1− 1+τ
)cN (t)
ρ+Im +Ix −n
ρ + Im + Ix − n
.
(21)
Note that vx (t) > vm (t) for all t. Protective contingent tariffs make it relatively more
attractive to innovate in exporting industries than in importing industries. Note also that
vx (t) and vm (t) are both increasing functions of τ (holding all other endogenous variables
24
fixed). Higher protective contingent tariffs directly increase the rewards for R&D success
because firms anticipate that they may benefit from being protected in the future.
Combining (8) and (20), as well as (9) and (21) yields two balanced growth R&D profit
maximization conditions for exporting and importing industries, respectively:


Im 1 −
λ
1+τ

2(λ − 1)
x1/α Ix(1−α)/α
c =
+
(ρ + Ix + Im − n)
λ
ρ + Im + Ix − n
αθ


Im 1 −
λ
1+τ
(22)

(1−α)/α
λ−1
x1/α Im
c =
+
(ρ + Ix + Im − n)
λ
ρ + Im + Ix − n
αθ
(23)
For both exporting and importing industries, R&D profit maximization implies that the
discounted marginal revenue product of an innovation must equal its marginal cost at each
point in time.
Equations (22), (23), (19) and (15) represent a system of four equations in four unknowns Ix , Im , c and x. These equation allow us to uniquely determine balanced growth
equilibrium values for all endogenous variables. In the protective tariff case, innovative
firms earn profits after further innovation occurs (making for more complicated expected
discounted profit calculations) and there are two state variables, x and β, that gradually
adjust over time (instead of the one state variable x in the rent-extracting tariff case). Because of these additional complicating features, analysis of out-of-steady-state transition
paths appears to be intractable and thus we focus exclusively on the model’s steady state
equilibrium properties in the protective tariff case.
Solving (22) for c and then substituting into (23), we obtain a balanced growth R&D
condition in (Im , Ix ) space:
(ρ + Ix + Im − n) + Im 1 −
2 λ−1
λ
λ−1
(ρ
λ
+ Ix + Im − n) + Im 1 −
λ
1+τ
λ
1+τ
=
Ix
Im
(1−α)/α
.
(24)
Since the LHS of (24) is greater than one, the R&D condition can only be satisfied if
Ix > Im . In Appendix A, it is shown that the R&D condition is globally upward sloping
in (Im , Ix ) space and shifts to the right as τ increases (for Ix > 0). The upward sloping
R&D condition is illustrated in Figure 2, together with the downward sloping iso-growth
line given by (15). Since these two curves have only one intersection, the balanced growth
equilibrium innovation rates Ix and Im are uniquely determined. Starting from an initial
25
balanced growth equilibrium given by point A, an increase in the level of protection leads
to a new balanced growth equilibrium given by point B. Consequently, we conclude that a
higher protective tariff rate τ increases Im and decreases Ix , but has no effect on the longrun growth rate gu , which is proportional to Ix + Im . Higher protective tariffs decrease
the relative profitability of exporting industries vx /vm and shift R&D resources toward
protected industries in each country. Since Ix > Im at both points A and B in Figure 2,
higher protective tariffs also reduce the imbalance in R&D effort across industries
Ix
Im
in
each country.
Solving (22) for c, then substituting into (19) yields a third balanced growth condition
in (Im ,Ix ) space, a resource condition:
2(1 − s) =

1/α

x
Ix1/α
Im Ix(1−α)/α λ
Ix(1−α)/α
 αθ (ρ + Ix + Im − n) 
+
+


λ
Im (1− 1+τ
)
λ
λ(Ix + Im ) (1 + τ )(Ix + Im )
2(λ−1)
+
λ
ρ+Ix +Im −n
x1/α 1/α
1/α
+
) .
(Ix + Im
θ
(25)
Given equilibrium values for Ix and Im , (25) uniquely determines the balanced growth
equilibrium value of x. In Appendix A, it is shown that the resource condition is globally
downward-sloping in (Im , Ix ) space and has a flatter slope than each iso-growth line in the
relevant region where Ix ≥ Im .
The relatively flat slope of the resource condition has important implications for technological change. As is illustrated in Figure 2, the initial balanced growth equilibrium at
point A is determined by the common intersection of the R&D, the resource and the constant growth conditions. A permanent increase in the protective tariff rate τ causes the
R&D condition to shift rightward and the resource condition to shift up. The only way
that a new common intersection of the three balanced growth conditions can be achieved
is if x increases. The endogenous variable x appears in the resource condition, but not in
either the R&D or constant growth conditions. Since the resource condition shifts down
when x increases [the RHS of (25) is increasing in x and increasing in Ix ], to reach a new
balanced growth equilibrium, x must increase enough so that the final resource condition
goes through point B, as is illustrated in Figure 2. For x(t) ≡
X(t)
N (t)
to increase, X(t) must
temporarily grow at a faster rate than the population N (t). Given (6), this only occurs if the
26
Initial R&D Condition
Final R&D Condition
Ix
Ix=Im
A
Higher Tariff
Initial Resource Condition
Final Resource Condition
B
Iso-Growth Line
Im
Figure 2: Long run effects of protective contingent tariffs
global innovation rate Ix (t) + Im (t) temporarily exceeds the balanced growth level given
by (15). Thus, permanently higher protective tariffs generate a temporarily faster rate of
technological change.
We have established the following theorem:
Theorem 2 A permanent increase in the protective contingent tariff rate (τ )
(i) permanently increases each country’s R&D intensity in importing industries (Im ),
(ii) permanently decreases each country’s R&D intensity in exporting industries (Ix ),
(iii) temporarily increases the global rate of technological change (x increases) and
(iv) has no effect on the long-run growth rate (gu ).
Higher protective contingent tariffs increase the global rate of technological change at
the margin for three reasons. First, there is the R&D incentive effect. Under protective
tariffs, when a domestic firm innovates in an industry with a foreign quality leader, the foreign leader becomes a “protected” foreign follower, and the new leader cannot profitably
sell to foreign consumers. Nevertheless, the new leader gains from higher protective tariffs
because, after further innovation, it sometimes is the beneficiary of these higher tariffs. A
domestic R&D firm targeting a domestic leader also benefits from higher protective tariffs
27
because if successful, it sells to both the Home and Foreign markets, and after further innovation, it sometimes is the beneficiary of these higher tariffs. Higher protective tariffs
directly increase the expected discounted profits earned from R&D success and this encourages firms to employ more R&D workers (vx and vm are both increasing functions of
τ holding all other variables fixed). Second, there is the resource utilization effect. With
higher R&D investment in exporting industries initially (Ix > Im ), an increase in protective
tariffs reduces the imbalance in R&D effort across industries within each country by reducing Ix and increasing Im . Higher protective tariffs reduce the relative R&D profitability of
exporting industries and make it relatively more attractive for domestic R&D firms to innovate in industries with foreign leaders. Given our assumption of industry-specific R&D
factors, less imbalance in R&D effort across industries implies that resources are used more
efficiently in the R&D sector (the resource condition has a flatter slope than any iso-growth
line). Third, there is the labor market effect. Higher protective tariffs allow protected firms
to charge higher prices and reduce the demand for manufacturing labor. By raising prices
and lowering consumption, protective tariffs free up labor from production activities to be
employed in the R&D sector (the resource condition shifts out when τ increases). For all
three reasons, higher protective contingent tariffs increase the rate of technological change
in the short run.
A key assumption underlying Theorems 1 and 2 is that the workers with specialized
R&D skills in each industry are industry-specific factors and cannot move across industries.
It is worth considering more carefully the role that this assumption plays in the analysis.
With contingent tariffs in place, the reward for innovating is greater in exporting industries
than in importing industries, as we have shown. Profit maximizing firms respond to these
incentives by hiring more R&D workers with general skills in exporting industries. These
firms also want to hire more R&D workers with specialized R&D skills in exporting industries. However, with fixed endowments of specialized R&D workers, the increased demand
only serves to bid up the wages of these workers in exporting industries. If workers could
spend time studying and acquiring specialized R&D skills, then in response to the higher
wages, not only would more workers with general skills choose R&D employment, but
also more workers would choose to study and acquire specialized R&D skills in exporting
28
industries. Since acquiring skills takes time, we would expect to see the number of workers
with specialized R&D skills gradually rise over time in exporting industries (and gradually
fall over time in importing industries). Thus, allowing for skill accumulation would appear to magnify over time the difference between R&D effort in exporting and importing
industries that is derived in this paper.
Consider now how the effects of higher protective contingent tariffs would change if
workers could acquire specialized skills by studying. Higher protective contingent tariffs
directly increase the rewards for innovating in both exporting and importing industries, as
we have shown. When firms try to hire more specialized R&D workers, this serves to
bid up the wages of these worker in both exporting and importing industries. In response
to these higher wages, more workers would choose to acquire specialized R&D skills.
Thus, allowing for skill accumulation, we would still expect to see that higher protective
contingent tariffs increase both R&D employment and the rate of technological change.
However, the effects of contingent tariff protection would gradually disappear over time,
as the numbers of both general and specialized R&D workers in importing industries go to
zero.
If all workers are perfectly mobile across industries and activities (α = 1), the number
of R&D workers in each importing industry goes to zero immediately in response to contingent tariff protection. Equation (24) cannot be satisfied, implying that countries completely
specialize in R&D (Ix > 0, Im = 0). With complete R&D specialization, Home leaders
always compete against Home followers and Foreign leaders always compete against Foreign followers in equilibrium. Since no firm benefits from contingent tariff protection in
equilibrium, higher protective tariffs have no effects. We have assumed a continuum of
industry-specific R&D factors in order to rule out this extreme possibility.
5
Conclusions
In this paper, we have developed a two country endogenous growth model where the profitmaximizing R&D behavior of firms determines the rate of technological change. In the
model, trade patterns change over time as new technological leaders appear in both coun29
tries. We use the model to analyze the dynamic effects of contingent tariffs, tariffs that are
imposed on imports whenever domestic firms lose their technological leadership positions
to foreign firms.
When governments help out domestic firms that fall behind foreign firms in global
technological races by offering them contingent tariff protection, this temporarily increases
the global rate of technological change at the margin. Higher protective contingent tariffs
shift resources toward the free-trade equilibrium and improve the overall efficiency of R&D
resource utilization. In addition, higher protective contingent tariffs allow domestic firms
to charge higher prices to domestic consumers and shift resources from the manufacturing
sector to the R&D sector.
A very different picture emerges when the contingent tariffs on imported products are
too small to benefit technologically backward domestic firms. Small contingent tariffs that
merely shift rents from domestic technological leaders to foreign goverments temporarily
decrease the global rate of technological change at the margin. Rent-extracting contingent
tariffs directly reduce the reward for innovating in importing industries and shift resources
from importing industries to exporting industries in both countries, reducing the efficiency
of R&D resource utilization.
Because higher rent-extracting contingent tariffs decrease the rate of technological
change and higher protective contingent tariffs have the opposite effect, the overall relationship between contingent tariffs and technological progress is non-monotonic. RiveraBatiz and Romer [1991b] also derive a non-monotonic relationship between tariffs and
technological change.20 Starting from free trade, they find that an increase in the common tariff rate initially retards but eventually stimulates technological change. However,
Rivera-Batiz and Romer find that the common tariff rate has to be astronomically large (in
excess of 200 percent) before higher tariffs stimulate technological change at the margin
(see p.985). In contrast, we find that the contingent tariff rate only has to be high enough to
benefit protected firms for higher tariffs to promote technological progress at the margin. If
innovations represent 10 percent improvements in product quality, then contingent tariffs
20
It is worth stressing that tariff rate changes have temporary effects in our model and permanent effects in
Rivera-Batiz and Romer [1991b].
30
exceeding 10 percent promote technological progress at the margin.
Although higher protective tariffs temporarily increase the rate of technological change,
given the non-monotonic overall relationship between tariffs and innovation, it does not
follow that a move from free trade to contingent tariff protection increases the rate of technological change in the short run. In fact, since higher tariffs hurt innovative firms initially
by reducing the profits earned from exporting and only generate benefits later after these
firms have lost their leadership positions (benefits that are appropriately discounted), the
general presumption should be that trade liberalization promotes technological progress.
Computer simulations of the model provide support for this case. For plausible parameter values, moving from contingent tariff protection to free trade in all industries increases
the rate of technological change in the short run. (See the earlier version of this paper,
Dinopoulos and Segerstrom [1996], for the computer simulation analysis.)
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32
Appendix A: Protective Contingent Tariffs
First, we derive properties of the balanced growth R&D condition (24), which can be
rewritten as
(1−α)/α
2 λ−1
(ρ + Ix + Im − n) + Im 1 −
Im
λ
λ−1
(ρ
λ
+ Ix + Im − n) + Im 1 −
λ
1+τ
λ
1+τ
= Ix(1−α)/α .
(A1)
Let D denote the denominator of the LHS of (A1). Differentiating the LHS of (A1) yields
(1−α)/α
1−α
1−α
∂D
Im
+ λ−1
(ρ+Ix +Im −n)( αI
D− ∂I
[D λ−1
)+D2 αI
]
∂LHS
λ
λ
m
m
m
=
> 0, since α ≤ 12 guarantees
∂Im
D2
that
1−α
D
αIm
>
∂D
.
∂Im
Likewise,
∂LHS
∂Ix
=
(1−α)/α
Im
D2
λ−1
I
λ m
1−
λ
1+τ
∂LHS
/
∂Im
function theorem, the slope of the R&D condition dIx /dIm =
is positive if
1−α (1−2α)/α
I
α x
−
2
λ−1 (1−2α)/α Im
I
λ m
D2
1−
λ
1+τ
> 0. Using the implicit
∂RHS
∂Ix
−
∂LHS
∂Ix
> 0. The assumption α ≤
1
2
guarantees that this holds in the relevant region where Ix ≥ Im . Thus, the R&D condition
(1−α)/α
is globally upward-sloping in (Im , Ix ) space. Since
∂LHS
∂τ
=
− λ−1
(ρ+Ix +Im −n)Im
λ
λIm
(1+τ )2
D2
< 0 and the R&D condition always goes through the origin, an increase in τ causes the
R&D condition to rotate clockwise.
Second, we derive properties of the balanced growth resource condition. This condition
can be written as 2(1 − s) = A · B + C where A, B and C are defined by the bracketed
expressions on the RHS of (25). Differentiating each bracketed expression, we obtain
∂A
∂Ix
=
1−α (1−2α)/α
I
αλ x
since α ≤
∂B
∂Im
=
x1/α
αθ
1
2
(1−α)/α
+
Im Ix
1/α
+Ix (1−α)
αλ(Ix +Im )2
implies that 1 − 2α ≥ 0,
2(λ−1)
λ
+
λ
Im (1− 1+τ
)
ρ+Ix +Im −n
−2 ∂A
∂Im
(1−2α)/α
+
=
2(λ−1)
λ
2 (1−α)I
λIm
x
1/α
Ix
(Ix +Im )2
− 1−
since τ < λ2 − 1 for protective tariffs. Since
(1−α)/α
+λIm Ix
(1+τ )α(Ix +Im )2
λ
1+τ
λ
1+τ
∂B ∂C
,
,
∂Ix ∂Ix
−
+
and
1
λ
>0
> 0 and
Im (1− λ )
2 ρ+Ix +I1+τ
m −n
∂C
∂Im
(1−2α)
>0
are all obviously positive,
the balanced growth resource condition is globally downward-sloping in (Im , Ix ) space.
Furthermore, since the RHS of (25) is increasing in x and decreasing in τ , the resource
condition shifts up when τ increases and shifts down when x increases.
Consider now what happens when Ix increases and there is a corresponding decrease in
Im . Given that α ≤
1
2
and λ − 1 ≤ τ < λ2 − 1
Ix(1−α)/α 1 − α Ix + Im
1
λ
dA =
+
·
+
dIx dIm =−dIx
Ix + Im
αλ
Ix
αλ 1 + τ
I (1−α)/α 1 − α
1
λ
≥ x
+
−
Ix + Im
αλ
αλ 1 + τ
33
1 − α Im
−1
·
α
Ix
Ix(1−α)/α 2 − α − αλ
≥
>0
Ix + Im
αλ
when λ < 3. We will assume that the innovation size parameter λ is less than 3 since
this corresponds to markups of price over marginal cost that are less than 200% under free
trade, which is certainly the main case of interest. Also
x1/α
1 − 1+τ
dB αθ
=
≥ 0 and
λ
dIx dIm =−dIx
Im (1− 1+τ
) 2
λ−1
2 λ + ρ+Ix +Im −n
λ
x1/α (1−α)/α
dC (1−α)/α
=
I
−
I
≥0
x
m
dIx dIm =−dIx
αθ
in the relevant region where Ix ≥ Im . We have established that the RHS of the resource
condition increases when Ix increases and there is a corresponding decrease in Im (so that
Ix + Im remains constant). It follows that after this change, we need to decrease Im to get
back to satisfying the resource condition. Thus the resource condition has a slope less than
one (in absolute value) in the relevant region where Ix ≥ Im .
Appendix B: Stability of Equilibrium
We want to show that there exists an equilibrium transition path satisfying (3), (6), (12),
(13) and (14) for all t that converges to the balanced growth equilibrium. Equation (17)
implies that on the balanced growth equilibrium path,
conjecture that
Ix (t)
Im (t)
Ix
Im
= k ≡
2λ−2
λ
λ+ 1+τ
−2
α
1−α
. We
= k also holds for all t outside the steady-state (along an equilibrium
transition path) and will verify that this conjecture is correct. If so, then (6) implies that
ẋ(t)
= µ(1 + k)Im (t) − n
x(t)
(B1)
and (14) can be rewritten as becomes

Im (t) = 
2θ 1 − s −
c(t)
λ
k 1/α + 1
α

1
.
x(t)
(B2)
Taking logs of both sides, then differentiating (B2) with respect to time t and substituting
˙
(t)
ẋ(t)
for ċ using (3) yields IIm
= −c(t) λx(t)1/α[r(t)−ρ]2θα
− x(t)
. Substituting this expression
Im (t)1/α (k1/α +1)
m (t)
34
and Ix (t) = kIm (t) into (12) yields
r(t) + (1 − µ)(1 + k)Im (t) +
(1 − α)c(t)[r(t) − ρ]
λ 1−s−
c(t)
λ
λ − 1 αIm (t)c(t) k 1/α + 1
=
. (B3)
λ 1 − s − c(t)
k (1−α)/α
λ
Equation (B2) implies that Im is just a function of c and x and taking this into account,
(B3) implies that r is also just a function of c and x. Thus (3) and (B1) [where Im (t) is
given by (B2) and r(t) is given by (B3)] represent a system of two nonlinear autonomous
differential equations which can be written in general form as ċ = F (c, x) and ẋ = G(c, x).
At the unique balanced growth equilibrium (c∗ , x∗ ), ċ = 0 and ẋ = 0. We will show that
this balanced growth equilibrium is a saddle-point equilibrium by establishing that21
∂F (c∗ ,x∗ )
∂c
∂G(c∗ ,x∗ )
∂c
∂G(c∗ ,x∗ ) ∂x
∂F (c∗ ,x∗ )
∂x
∗
= c µ(1 + k)x
∗
=
∂Im (c∗ ,x∗ ) ∗
x µ(1 + k) ∂x
∗ ∗
c∗ ∂r(c∂c,x )
∗ ∗
c∗ ∂r(c∂x,x )
∗
,x
x∗ µ(1 + k) ∂Im (c
∂c
∗)
(B4)
∂r(c∗ , x∗ ) ∂Im (c∗ , x∗ ) ∂r(c∗ , x∗ ) ∂Im (c∗ , x∗ )
<0
−
∂c
∂x
∂x
∂c
Differentiating (B3) with respect to x and c yields
∂r
=
∂c
∂Im
∂c
(µ − 1)(k + 1) +
λ−1 k1/α +1
αc
λ k(1−α)/α 1−s− λc
1+
and
∂r
=
∂x
+
λ−1 αIm (1−s) k1/α +1
λ (1−s− λc )2 k(1−α)/α
1−α
c
λ 1−s− λc
∂Im
∂x
(µ − 1)(k + 1) +
1+
λ−1 k1/α +1
αc
λ k(1−α)/α 1−s− λc
c
1−α
λ 1−s− λc
(B5)
.
(B6)
Substituting (B5) and (B6) back into (B4), we find that some major cancelation occurs and
the inequality in (B4) holds if and only if
∂Im
∂x
But (B7) holds since
∂Im
∂x
λ−1 αIm (1−s) k1/α +1
λ (1−s− λc )2 k(1−α)/α
c
1 + 1−α
λ 1−s− λc
< 0.
(B7)
< 0 follows from (B2) and all the other terms are strictly positive.
Thus the balanced growth equilibrium is locally saddlepath stable, as is illustrated in Figure
3.22 The proof of stability of the free trade balanced growth equilibrium is obtained by
21
See Theorems 24.6 and 24.7 in Hoy, et al [1996].
22
Figure 3 is drawn for the case where
∂F
∂c
> 0. If
∂F
∂c
< 0, then Figure 3 must be redrawn with a
downward sloping ċ = 0. However, in both cases, the saddlepath is upward sloping and the same story can
be told about how the economy adjusts over time.
35
c
.
c=0
Saddlepath
B
.
x=0
x
Figure 3: Stability of the balanced growth equilibrium
setting τ = 0. Q. E. D.
When x(t) is higher than its balanced growth equilibrium value (an unanticipated permanent increase in the rent-extracting tariff rate has just occured), then the equilibrium saddlepath involves a gradually declining x(t) as the economy converges to the new balanced
growth equilibrium (point B in Figure 3). Along this equilibrium transition path, consumer
expenditure c(t) temporarily exceeds its new balanced growth equilibrium value, and the
additional resources going to produce consumer goods come at the expense of R&D investment. For x(t) to decline over time, equation (6) implies that the global innovation rate
in each industry Ix (t) + Im (t) temporarily falls below its balanced growth value nµ . Thus,
permanently higher rent-extracting contingent tariffs generate a temporarily slower rate of
technological change.
36