Journal of International Economics 50 (2000) 497–517
www.elsevier.nl / locate / econbase
Trade liberalisation and endogenous growth
A q-theory approach
Richard E. Baldwin a , *, Rikard Forslid b
a
Graduate Institute of International Studies, 11 a Ave de la Paix, CH-1202 Geneva, Switzerland
b
Department of Economics, University of Lund, Box 7082, S-220 07 Lund, Sweden
Received 24 February 1997; received in revised form 5 October 1998; accepted 8 October 1998
Abstract
This paper introduces a new approach to the analysis of endogenous growth effects and
uses it to illustrate two novel trade-and-growth links. The approach’s simplicity allows us to
introduce scale economies and imperfect competition into the R&D and financial intermediation sectors of a Romer–Grossman–Helpman endogenous growth model. We show
that trade liberalisation can stimulate growth via a procompetitive effect in the R&D sector
and / or financial sector.  2000 Elsevier Science B.V. All rights reserved.
Keywords: Endogenous growth; Trade and growth; Trade liberalisation; Tobin’s q
JEL classification: F43; F13; F12; F36; 04
1. Introduction
The pro-growth effects of openness have long been recognised, yet tools for
formally evaluating the impact of trade on long-run growth have only appeared in
the past decade. The early literature here includes Rivera-Batiz and Romer
(1991a,b), Grossman and Helpman (1991), Segerstrom et al. (1990) and Krugman
(1988).
Our paper builds on this literature in two ways, by introducing a new approach
*Corresponding author. Tel.: 141-22-734-8950; fax: 141-22-733-3049.
E-mail address: [email protected] (R.E. Baldwin)
0022-1996 / 00 / $ – see front matter  2000 Elsevier Science B.V. All rights reserved.
PII: S0022-1996( 99 )00008-2
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R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
to the analysis of growth effects, and by using this approach to illustrate two novel
openness-and-growth links.
The analytic approach, which relies on Tobin’s q-theory of investment, is
simple to motivate. Long-run per-capita growth is driven by the perpetual
accumulation of physical, human, and / or knowledge capital (depending upon
model details). In mainstream growth models – such as Lucas (1988), Romer
(1986, 1990), Rebelo (1991), Grossman and Helpman (1991), and Aghion and
Howitt (1992) – capital accumulation is driven by the investment decisions of
self-interested agents. Consequently, solving an endogenous growth model boils
down to characterising investment in a general equilibrium setting. Many solution
strategies are possible, but the powerful, well-known, and intuitive ‘q-theory’
method of Tobin (1969) turns out to be the simplest.1
The value of any novel method of analysis lies in its ability to permit study of
richer, more complex, models. To illustrate the usefulness of the q-approach, we
enrich the basic Romer–Grossman–Helpman endogenous growth model in two
interesting directions.
First, we allow for imperfect competition and scale economies in the R&D
sector. Standard endogenous growth models – Lucas (1988), Romer (1986, 1990),
Rebelo (1991), Grossman and Helpman (1991), Aghion and Howitt (1992) and
Young (1998) – assume that firms are atomistic and perfectly competitive in the
sectors that drive growth, namely the innovation and / or education sectors. When it
comes to innovative firms, these assumptions are surely too strong. It is hard, for
instance, to think of Sony, Microsoft and Phillips as atomistic. Similarly, it is hard
to think of innovation as subject to private constant returns. After all, developing a
new product or process is not like driving a taxi. Developers must learn the
state-of-the-art before coming up with new advancements. Additionally, it seems
reasonable that innovation involves sunk costs such as laboratories and databases.
Besides being unrealistic, these Walrasian assumptions rule out a wide range of
important effects (scale effects, procompetitive effects, variety effects, etc.) that
have proved important in the new trade theory. We show that enriching the model
in this direction opens the door to a novel trade-and-growth link based on the
pro-competitive effect of trade. The enrichment also allows study of links between
growth and market concentration in the R&D sector.
The second enrichment introduces non-trivial financial intermediation between
savers and investors. Specifically, we allow for scale economies and imperfect
competition in a banking sector; this enables us to endogenously determine the
mark-up between the rate that borrowers pay and savers receive. It also allows us
to show that liberalising trade in financial services has a pro-competitive effect on
the mark-up and that this tends to be pro-growth.
1
q is the ratio of capital’s market value (marginal benefit) to replacement cost (marginal cost).
R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
499
The remainder of the paper is in three sections. Section 2 presents the basic
model and introduces the q-theory approach, including welfare and policy
analysis. Section 3 first presents an organising framework for trade-and-growth
links and uses it to classify the links illustrated in the early literature. The section
then enriches the basic Romer–Grossman–Helpman product-innovation model in
the directions described above. Finally, it uses the enriched model to illustrate two
novel trade-and-growth links and two novel competition-and-growth links. Section
4 presents our concluding remarks.
2. The basic model and q-theory analysis
In the seminal Romer (1990) model – and its open-economy version RiveraBatiz and Romer (1991a,b) – long-run growth is driven by the ceaseless
accumulation of knowledge capital. These models include four factors: knowledge
and physical capital, and skilled and unskilled labour. Including four factors brings
out the full implications of Romer’s approach, but his basic insight can be shown
more directly. To present the q-approach as cleanly as possible, we work with a
bare-bones product-innovation endogenous growth model that is a slight generalisation of Grossman and Helpman (1991), Chapter 3.
2.1. Assumptions and intermediate results
Consider a world of two identical countries, each with two sectors (manufacturing X and innovation I) and two factors of production (labour L and knowledge
capital K). Firms in the X-sector face Dixit–Stiglitz monopolistic competition and
increasing returns. Specifically, each differentiated variety is produced by a single
X-firm using labour (the variable input) and one unit of knowledge capital (the
fixed cost). The cost function is p 1 wa X x i , where p and w are the factor rewards
of K and L, a X is the unit input coefficient, and x i is variety-i output. Trade in
X-varieties is subject to frictional (iceberg) barriers so t $ 1 units must be shipped
to sell one unit abroad.2 Factors (L and K) are not traded.
National labour stocks are fixed, but each nation’s K is the cumulative output of
its innovation sector (I-sector). The I-sector is perfectly competitive and firms
produce one unit of K with a I units of L. To individual I-firms a I is a parameter,
but, following Romer (1990) and Grossman and Helpman (1991), we assume a
sector-wide learning curve – i.e. that the marginal cost a I declines as the sector’s
2
Frictional barriers are interpreted as technical barriers that inhibit trade without generating tariff
revenue, or as specific tariffs when the tariff revenue’s equilibrium impact is ignorable.
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cumulative output rises.3 The precise I-sector production and marginal cost
functions are:
LI
1
Q K 5 ], F 5 wa I ; a I ; ]]], 0 # l # 1
aI
K 1 lK *
(1)
where Q K is the flow of new K, LI is I-sector employment, F is the marginal cost
of K (i.e. the X-sector’s fixed cost in equilibrium), K and K* are domestic and
foreign cumulative I-sector production. The parameter l governs the internationalisation of learning effects; see Eaton and Kortum (1996) for evidence that
0 , l , 1.
As in Romer (1990), depreciation is ignored, so K~ 5 Q K . Because each Xvariety requires one unit of K, K is also the number (mass) of X-varieties produced
by each nation. From Eq. (1) and symmetry, the growth rate of K (call this g) is
related to I-sector employment by:
QK
K~
g ; ] 5 ] 5 (1 1 l)LI
K
K
(2)
This is the growth-rate form of the I-sector production function.
Romer (1990), and Grossman and Helpman (1991) view units of K as ‘designs’
(Romer) or ‘blueprints’ (Grossman and Helpman). The model’s logic, however,
permits a broader interpretation. For instance, the knowledge might be embedded
in labour (making K variety-specific human capital) or in a variety-specific
machine, as suggested in Romer (1986). The corresponding I-sectors would be (i)
the innovation sector (knowledge capital), (ii) the investment-goods sector
(physical capital), or (iii) the instruction sector (human capital). Rationalisations
of the I-sector learning curve may be quite different for physical, human and
knowledge capital, yet these differences have no impact on the model’s mechanics.
To encourage agnostic interpretation, the generic symbols K and I are adopted.
Preferences of the infinitely lived representative consumer in each nation are:
`
Ee
t50
K 1K *
2r t
ln(Ct ) dt; Ct 5 Et /Pt ; Pt ;
1E
i50
1 / (12 s )
p
12 s
it
di
2
(3)
where r . 0 is the time-preference parameter, C and E are the consumption
aggregate and consumption expenditure, pi is variety-i’s consumer price, and
s . 1 is the elasticity of substitution (time subscripts are dropped, clarity
permitting). The representative consumer owns all her nation’s K and L.
Utility optimisation yields a CES demand function for each variety, a trans-
3
These authors implicitly assume a learning curve, but do not refer to it as such. Rather, falling
marginal costs are justified by reference to knowledge spillovers (Grossman–Helpman), or knowledge’s
non-rival nature (Romer).
R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
501
versality condition, and the Euler equation E~ /E 5 r 2 r, where r is the rate of
return to savings.4 On the supply side, I-sector competition ensures PK 5 F 5 wa I
where PK is the price (replacement cost) of capital. X-sector profit maximisation is
characterised by the well-known mark-up pricing conditions:
p(1 2 1 /s ) 5 aw, p * (1 2 1 /s ) 5 awt
(4)
where p and p* are the local-market and export-market consumer prices,
respectively.
Each firm’s capital is variety specific and therefore firm specific, so K’s reward
is not set in a capital market. Rather, K is paid its Ricardian surplus (i.e. operating
profit). Operating profit depends upon the operating profit margin (equal to 1 /s
with mark-up pricing), and sales. Specifically:
p 5 E /s K
(5)
since, by symmetry of varieties and nations, per-variety sales equal E /K.
2.2. Dynamic analysis with Tobin’ s q
The difficulty of analysing any dynamic model is influenced by the choice of
state variables, the choice of numeraire and the choice of solution methodology.
Given the basic logic of the product-innovation model (investment determines the
rate of knowledge accumulation which in turn determines the rate of growth), the
natural state variable is the amount of resources devoted to investment, namely LI .
Since the model has only one primary factor, L, expenditure allocation is
tantamount to resource allocation, so labour is the natural numeraire. This brings
us to the solution method.
Investment is the key to endogenous growth, so the solution method must allow
us to characterise investment in a general equilibrium setting. Tobin (1969)
provides a powerful and well-known method for doing just this. As we shall see, q
is a simple function of the level of real investment, so Tobin’s famous q51
condition allows us to solve directly for the steady-state level of real investment,
namely LI , and thereby for the steady-state growth rate.
Our use of Tobin’s q differs slightly from that of macro economists. A standard
macroeconomic proposition is that investment stops when q51 (see Blanchard and
Fischer, 1989 p. 62, and Turnovsky, 1996), yet in our model, positive investment
does occur when q51. Indeed, the investment level jumps to enforce the equality.
This apparent contradiction is easily resolved. q51 defines the steady-state
investment level. In a neoclassical model, diminishing returns to K imply that
steady-state investment is zero (assuming no depreciation, or exogenous growth
4
Detailed derivations of these and other results are available from the authors (e-mail
[email protected]).
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R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
factors). In an endogenous growth model, however, capital’s rate of return is
independent of K, so q51 is perfectly consistent with positive investment.5
2.2.1. Solving for steady-state growth
Taking real investment LI as the state variable when the Euler equation involves
E requires a change-of-variable transformation. Denoting nominal investment
spending as I, nominal income Y equals E 1 I. Because I-sector competition
eliminates pure profits, the value of I-sector output and input match, so E 5 wL 1
p K 2 wLI . Employing Eq. (5) we have:
w(L 2 LI )
E 5 ]]]
1 2 1 /s
(6)
Taking L as numeraire and using the fact that L~ I 5 0 in steady state (by definition
of a state variable), Eq. (6) implies E~ 5 0 in steady state. From the Euler equation,
E~ 5 0 implies:
r5r
(7)
in steady state. Moreover, L~ I 5 0 and Eq. (2) mean that the steady-state g is time
invariant. Because the system is always in steady state (see Appendix A), r always
equals r. Intuitively, the model lacks transitional dynamics since the only state
variable is a ‘jumper’.6
We first calculate the numerator of Tobin’s q. Ruling out bubbles, the stockmarket value of a unit of capital (call this V ) is the present value of its associated
income stream pt . The time-invariance of g and E, together with Eq. (5), imply
that p falls at the rate g. Since this income stream is discounted at r, the integral
solves to:
`
Vt ;
Ee
2r(s 2t )
pt
ps ds 5 ]]
r 1g
(8)
s 5t
5
More specifically, in Blanchard–Fischer chapter 2.4 the marginal cost of producing and installing a
unit of capital is F(1 1 T ), where the constant production cost F is unity (by choice of units) and the
installation cost T is a convex function of the investment-capital ratio, I /K. With a quadratic T function,
the first order condition is V 5 F(1 1 g I /K), where V is the present value of K’s reward and g
parameterises T. Solving, I /K 5 (V/F 2 1) /g ; hence the standard result that I 5 0 when q ;V/F is
unity. However, as g limits to zero (as in our model), I . 0 is consistent with V/F arbitrarily close to
unity. Moreover, if one interprets Tobin’s ‘replacement cost’ as including installation charges, q equals
V/ [F(1 1 g I /K)] and the q 5 1 condition determines the investment level even in the Blanchard–
Fischer model.
6
Hirsch and Smale (1974, p. 22) define a system’s state as the information characterising it at a given
time. The state vector lists such information and its elements are state variables. In this sense LI is a
state variable. Economists often distinguish between state vector elements that represent stocks and
flows, labelling the former ‘state variables’ and the latter ‘control variables’, but both are state variables
under the Hirsch–Smale definition.
R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
503
The denominator of q is PK 5 F, so q5 p / [F( r 1 g)]. Using Eqs. (8), (5), (6), (1)
and (2) yields:
(1 1 l)(L 2 LI )
q[LI ] 5 ]]]]]]]
(s 2 1)( r 1 (1 1 l)LI )
(9)
Notice that Tobin’s q is a simple decreasing function of real investment LI for two
reasons. Raising investment reduces expenditure (see Eq. (6)) and this harms
profits (see Eq. (5)). Also, a higher LI means competing varieties are introduced
more rapidly, so p falls faster. Both effects lower V.
Tobin’s famous q51 condition – assuming countries are large enough for an
interior solution, i.e. L . r [s 2 1] / [1 1 l] – implies that the steady-state sectoral
allocation of L is:
L r (1 2 1 /s )
L¯ I 5 ] 2 ]]], L¯ X 5 L 2 L¯ I
s
11l
(10)
where ‘bars’ denote steady-state values.
Mechanically, Tobin’s q is forced to unity by price-taking behaviour and free
entry. Atomistic I-firms price K at its marginal cost F and atomistic X-firms, who
take PK as given, exit or enter until V equals F. Intuitively, a unit of K is worth V,
so pure profits would be earned if q . 1. Thus, we can view q . 1 as the market’s
signal to shift more resources to I-sector production.
All dynamic features of the model follow from L¯ I . Using Eqs. (2) and (10), we
find:
(1 1 l)L 2 r (s 2 1)
g¯ 5 ]]]]]]
s
(11)
Moreover, real income growth is g¯ /(s 2 1) because real income is Y /P (P is the
Eq. (3) perfect-price index), and K grows at g.7 From Eq. (2), g¯ is increasing in L¯ I .
In the basic model, growth only depends upon the parameters l, s, r and L, so, as
in Grossman–Helpman, trade in goods and the level of protection have no
influence on growth (see Rivera-Batiz and Romer, 1991b, or Baldwin and Forslid,
1998 for model where tariffs affect growth). The steady-state rate of investment
and saving, I /Y, equals L¯ I / [L 1 (L 2 L¯ I ) /(s 2 1)] and this too is increasing in L¯ I .
The fact that we can first solve for the static allocation of resources and then
characterise the dynamics illustrates the block recursiveness of the model. Tobin’s
q helps bring this out since q is a contemporaneous sufficient statistic for all
growth aspects.
Although analytic concepts are clearest when expressing q in terms of LI , q can
be written as a simple, monotonically decreasing function of g by using g 5 (1 1
l)LI . Namely:
7
This growth is akin to a perpetual variety gains-from-trade in a monopolistic competition trade
model.
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R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
(1 1 l)L 2 g
q[g] 5 ]]]]
(s 2 1)s r 1 gd
(12)
In this form, q 5 1 defines g¯ directly.8
2.2.2. Static-economy representation and policy analysis
The model’s steady-state equilibrium has what might be called a ‘staticeconomy representation’. That is to say, along the steady-state growth path, the
division of primary resources is time-invariant and the amount of L employed in
the I-sector determines all of the model’s dynamics features. We can, therefore,
fully represent the steady-state growth equilibrium and evaluate the growth effects
of policy and parameter changes using concepts and diagrams from static
equilibrium analysis. It also helps show that analysing trade and growth models is
not much more difficult than analysing static new trade models.
Capital is variety-specific so the model’s static-economy representation is
similar to the specific-factor model (see Neary, 1978 for a modern treatment), as
Fig. 1 shows. In the diagram, L is the length of the horizontal axis with LI
Fig. 1. Static economy representation.
8
The q-approach differs from that of Grossman and Helpman (1991). The hallmarks of the
Grossman–Helpman approach are: (i) unorthodox choices of numeraire (E 5 1) and state variable (the
inverse value of the stock market), and (ii) identification of g from the solution of two simultaneous
equations, namely the ‘labour-market clearing condition’, viz. L 5 n~ 1 E /p where n is the number of
varieties and the ‘no-arbitrage condition’, viz. n~ /n 5 n /s 2 g 2 r where n ; 1 /KV is the inverse value
of the stock market. The q-approach is closer to the approach that focuses on ‘r’. q 5 1 implies
(p /F ) 2 g 5 r, where the left-hand side is the flow return to K, namely r. K drops out of p /F and g
depends only on LI , so finding g¯ from q[g¯ ] 5 1 is like solving r[g¯ ] 5 r.
R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
505
measured from the left and LX from the right. Every point defines a sectoral
division of labour.
Tobin’s q is the value of the marginal product of labour in the I-sector (VMPLI )
because I-firms face private constant returns (i.e. labour’s average product 1 /F
equals its marginal product) and a unit of K is worth V. From Eq. (9), VMPLI
declines in LI . Since the X-sector is imperfectly competitive, the proper concept is
the value of the marginal revenue product of LX (VMRPLX ) and this is graphed as
VMRPLX 5 1. To understand why it is flat, note that the marginal physical product
of LX is 1 /a X , implying that the marginal revenue product is p(1 2 1 /s ) /a X . The
optimal producer price always equals a X /(1 2 1 /s ), so VMRPLX 5 1 for any LX .
As usual the intersection of VMPLI and VMRPLX identifies the equilibrium
division of L. The steady-state growth rate g¯ is found from Eq. (2), as graphed in
the lower quadrant.
The static-economy representation opens the door to a simple and systematic
approach to analysing the growth effects of policy and parameter changes. We
illustrate the approach diagrammatically before presenting it more formally. Due
to the lack of transitional dynamics, q 5 1, but policy or parameter changes can
lead to incipient changes in q. For instance, increasing international knowledge
spillovers (i.e. dl . 0) decreases F without altering V. This shifts up the qschedule to the dashed line in Fig. 1. If LI were unchanged, V would exceed F and
I-firms would earn pure profits. The incipient profit induces them to hire LI up to
the point where V is restored to F. The rise in L¯ I raises g¯ and the long-run growth
rate of real income. Since LI can jump, the growth effects occur instantaneously.9
Formally, we introduce Q as the vector of parameters and policies, and write q
as an implicit function of g and Q. Totally differentiating q[g;Q ] 5 1 with respect
to g and Qi , we find dg / dQi 5 (≠q / ≠Qi ) /(2≠q / ≠g). Plainly, the incipient impact of
dQi on q is a sufficient statistic for its growth effect since q declines with g. A
more detailed result is found by writing p as an implicit function of g and Q, and
writing PK and r as implicit functions of Q.10 Totally differentiating:
≠PK
≠p
≠r
] 2 ]]
(r 1 g) 2 ]PK
≠Qi ≠Qi
≠Qi
dg
] 5 ]]]]]]]]
dQi
PK 2 ≠p / ≠g
(13)
Since PK . 0 and faster growth lowers p, the denominator is everywhere positive.
The sign of the growth effect of dQi therefore depends only upon the sign of the
numerator. Thus:
9
Assuming quadratic adjustment costs in I-sector hiring would introduce transitional dynamics, and
allow q to deviate from unity in transition. Specifically, if the adjustment costs were d (dLI / dt)2 / 2, then
at all points along the transition we would have V 2 F 2 d (dLI / dt) 5 0.
10
Using Eqs. (2), (5) and (6), p ( g;u ) 5 [L 2 g /(1 1 l)] / [(s 2 1)K].
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R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
Proposition 1. The sign of the growth effect of a policy or parameter change
depends only upon the sign of (≠p / ≠Qi ) 2 (≠PK / ≠Qi )(r 1 g) 2 (≠r / ≠Qi )PK where
Qi is the particular change under study.
For most parameters or policy changes, only one of the three partial derivatives
in the numerator is non-zero. Thus, growth effects can often be signed by signing a
single partial derivative.
Proposition 1 suggests a means of easily expanding the range of trade and
growth links that have been formally demonstrated in the literature. International
economists know a great deal about the links between trade policy and p (see
Helpman and Krugman, 1989 for examples), and between trade policy and sectoral
prices (PK being the particular one of interest here). The working paper version of
our paper, Baldwin and Forslid (1996), used this shortcut to study six trade-andgrowth links. To keep the paper focused, we present only two examples of how
this shortcut can be applied to sign the growth effects of various trade liberalisations; see Baldwin and Forslid (1998), and Baldwin et al. (1998) for further
applications.
2.2.3. Welfare Analysis
Tobin’s q also provides an intuitive approach to welfare analysis. Private agents
choose LI such that V 5 F, yet learning externalities lower the labour cost of all
future innovation. The value of this labour saving is the gap between the public
and private return to knowledge creation. To calculate the gap, we totally
differentiate the production function K~ 5 (1 1 l)LI K with respect to K and LI and
set dK~ to zero. The result implies that boosting K by one unit at time 0 means it
takes (LI /Kt ) less labour at time t to reproduce the same K path. The present value
of the labour savings is thus (LI /K0 ) /( r 1 g) when K rises at g (K0 is the initial
stock). Plainly, the global planner should choose LI such that the private value of
innovation V and the social value of the externality (LI /K0 ) /( r 1 g) sum to the
marginal cost, namely F. Since Eq. (1) implies 1 /K 5 (1 1 l)F and g 5 (1 1 l)LI ,
the socially optimal K growth rate g s is characterised by:
S
gs
]]
q5 12
r 1 gs
D
(14)
Since ≠q / ≠g , 0, Eq. (14) says that the laissez-faire economy grows too slowly.
Positive welfare effects therefore tend to be associated with pro-growth effects.
Plainly an I-sector ad valorem production subsidy of g s /( r 1 g s ) is the first-best
policy.
3. Openness and growth links
This section employs Proposition 1 to illustrate two novel openness-and-growth
links and two novel competition-and-growth links in an enriched version of the
R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
507
basic model. Before this, however, we develop an organising framework for
trade-and-growth links that permits us to place our new links in the context of the
links from the early trade and endogenous growth literature.
3.1. Links in the seminal trade-and-endogenous growth literature
The defining contributions in trade-and-new-growth theory are Rivera-Batiz and
Romer (1991a,b), and Grossman and Helpman (1991). Rivera-Batiz and Romer
list three trade and growth effects: (1) The redundancy effect (by eliminating
international duplication of innovative activities, trade permits a more efficient use
of I-sector resources and this is pro-growth), (2) the integration effect (if the
I-sector is subject to economy-wide scale economies, trade boosts I-sector labour
productivity and growth by increasing market size), and (3), the reallocation effect
(market opening alters the sectoral allocation of resources, which can be pro- or
anti-growth). Grossman and Helpman (1991, Chapter 9) suggest an alternative
classification of effects by listing four ways in which international integration
affects growth: Market size, redundancy, international knowledge spillovers, and
the allocation effect. These four and the three Rivera-Batiz–Romer effects are
simply two ways of categorising the same set of mechanisms. As it turns out, it is
easier to illustrate the internal logic of the Rivera-Batiz–Romer classification.
3.1.1. An organising framework for openness-and-growth links
To capture the three effects, consider (1) and (2) modified to allow for the
possibility that without trade some foreign innovations are not distinct from
existing domestic varieties. This is captured by a non-redundancy parameter j , i.e.
the fraction of foreign innovations that are not identical to existing home
innovation. Since no extra learning accrues from redundant foreign innovations,
the I-sector production function in growth rate terms is g 5 LI (1 1 lj ). Total
differentiation yields:
dg 5 lLI dj 1 LI j dl 1 (1 1 lj )dLI
(15)
The rate of real income growth is proportional to g, so this is also a decomposition
of real income growth changes.
The first right-hand term shows the redundancy effect. Specifically, enriching
the basic model by replacing (1) with a I 5 1 /(K 1 lj K*), Proposition 1 shows
that a reduction in redundancy (dj . 0) is pro-growth because ≠PK / ≠j , 0 and all
the other partials are zero. The second term reflects the integration effect. Changes
in l may reflect better communications, or freer trade in I-sector intermediates (as
in the Rivera-Batiz–Romer ‘lab equipment’ model), or freer overall trade when
trade in goods is a conduit of knowledge (as in Grossman and Helpman, 1991).
Given that freer trade raises l (possibly from zero under autarky), Proposition 1
shows that dl . 0 is pro-growth because ≠PK / ≠l , 0 and all the other partials are
zero. The last term captures the reallocation effect.
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R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
International integration may increase or decrease real investment, so the growth
effect may be pro- or anti-growth. Since the reallocation effect focuses on the
change in an endogenous variable rather than the causes of its change, Proposition
1 is not useful.
The three effects are very uneven. The redundancy and integration effects refer
to very specific economic mechanisms that shift I-sector labour productivity. The
third effect, however, is an amalgamation that includes anything that changes the
level of real investment in knowledge creation. The four new links illustrated
below (two involve trade liberalisation and two involve changes in competition)
are examples that provide microfoundations for the reallocation effect.
3.2. A Portmanteau model
This section enriches the basic model in ways that open the door to two novel
interactions between trade and growth. All the Section 2 assumptions are
maintained except those dealing with the I-sector, and financial intermediation
between savers and investors.
3.2.1. Enriching I-sector market structure and technology
Since innovation is the key to growth, the simplistic modelling of the I-sector in
the basic model is unsatisfactory. In particular, perfect competition and constant
private returns in the I-sector strike us as assumptions that require more than the
usual suspense of disbelief. Much innovation gets done by very large companies.
Similarly, it is hard to think of innovation as subject to private constant returns.
The assumptions of constant returns and perfect competition rule out a wide range
of important effects emphasised by the new trade theory (Helpman and Krugman,
1989). To capture some of these aspects, we introduce simple forms of scale
economies and imperfect competition into the I-sector. Specifically, we assume a
one-time sunk cost in the I-sector. Thus the present value of the cost of producing
a constant flow of designs Q Ki is:
`
Ee
2r t
Ft Q Ki dt 1 G; G $ 0
(16)
t50
where the sunk cost comprises G units of L (w 5 1).
The second enrichment is to permit trade in I-sector output (designs). Trade in
designs, however, is assumed to be hindered by cost-raising barriers of which
product standards provide a concrete example. Most new products need to be
certified as meeting industrial, health, safety and / or environmental standards.
Certifying boards are typically influenced by local industries (directly by industry
representatives, or indirectly via political pressure). Since local industry must
compete with the new products, national standards commonly discriminate de
facto against foreign varieties. In keeping with the certification example, we
R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
509
assume that it costs G times F (G $ 1) to develop and certify a design for sale
abroad, but only F for sale at home.
Lastly, consider I-sector market structure. Designs correspond to unique
varieties, but each design is as good as the next to buyers (X-firms) since each
variety is as good as the next to consumers. With designs as perfect substitutes, we
assume the most natural market structure, namely oligopoly with segmented
markets. The number of I-firms per country is exogenous (equal to m I ) in our
policy analysis. An interesting extension would be to endogenise the number of
I-firms, m I , using a free entry condition with fixed entry costs. We conjecture –
based on results in the ‘new’ trade theory, e.g., Helpman and Krugman (1989,
Chapter 7.5) – that even with entry, liberalisation would have a procompetitive
effect and thus be pro-growth.
I-firms play Nash in the output capacities devoted to local and export sales. With
segmented markets, these capacities – denoted as Q Kj and Q *Kj – are chosen
independently. Thus, for established I-firms, the problem is:
`
max
Q Kj ,Q *Kj
Ee
2rt
s(PK 2 F )Q Kj 1 (P K* 2 G F )Q *Kjd dt
(17)
t 50
where PK and P *K are local and export market prices and G indicates the severity
of the cost-raising trade barriers (G 5 1 for non-discrimination in certification).
3.2.2. Enriching the financial sector
One of the many simplifications adopted in the early trade and endogenous
growth literature was the assumption of costless intermediation between savers and
investors. While convenient, this assumption is not innocuous. Investment is the
key to endogenous growth, so financial intermediation affects growth except under
the basic model’s extreme assumptions. This extreme assumption also seems
unrealistic since Rajan and Zingales (1996) provide empirical evidence of a
connection between nations’ growth rates and the level of development of their
financial markets.
Finally, given the rapid expansion of international trade in financial services, it
seems appropriate to investigate a model where such trade might have growth
effects. As we shall see, adding a nontrivial financial intermediation sector creates
a novel trade-and-growth link related to the closed-economy financial repression
and growth links in Roubini and Sala-i-Martin (1992).
To illustrate this link simply, the financial sector is enriched by assuming
riskless bonds (in fixed supply) and assuming investors (new X-firms) borrow from
banks. Banking involves a fixed, sunk cost of H labour units. Interpreting the
representative consumer as a continuum of agents, atomistic savers will not cut out
banks by incurring H themselves. Moreover, this nonconvexity creates imperfect
competition and we again assume an oligopoly market structure since loans are a
homogenous product. The number of banks per country mB is fixed.
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R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
Trade in financial services (lending) is possible, but national markets are
assumed to be segmented and international lending assumed to involve a
proportional flow cost. This cost, which reflects real and regulatory barriers to
international lending, is measured by the policy parameter c (c 5 1 indicates free
trade in financial services). The objective function for an established bank is:
`
max
I i ,I i*
Ee
2rt
f(R 2 r) Ii 1 (R* 2 c r)I i*g dt
(18)
t50
where Ii and I *i are the local and export market lending flows (time invariant in
equilibrium since L is numeraire), and R and R* are the respective lending rates.
Banks are price-takers in the savings market due to competition from bonds; r is
the interest rate paid to savers.
3.3. New trade-and-growth links
Intuition is served by isolating effects, so we make parameter assumptions that
highlight one trade-and-growth link at a time in the following subsections.
3.3.1. Procompetitive effects in the I-sector
In the standard product innovation model, I-sector price-cost mark-ups always
equal unity due to perfect competition. Here we show that when the price-cost
mark-ups are endogenous, increasing I-sector competition can lower the equilibrium price of capital by lowering these mark-ups. This tends to raise national q’s
and thereby increases investment and long-run growth.11
We study two distinct sources of increased I-sector competition. The first is an
increase in the number of I-firms holding trade barriers constant. This might be
thought of as corresponding to more rigorous enforcement of antitrust regulations.
The second is a liberalisation of I-sector trade barriers holding the number of
I-firms constant. This corresponds to harmonisation or mutual recognition of
product standards – what trade specialists call a mutual recognition agreement –
or any other policy that reduces discrimination against foreign-developed product
varieties. As we shall see, increasing the number of competitors lowers equilibrium price-cost margins. Liberalising I-sector trade also lowers these margins via
the well-known procompetitive effect demonstrated in static models by Markusen
(1981), and Smith and Venables (1988), inter alia.
To explore these links as simply as possible, the Section 3.2 model is simplified
in two ways. We assume that financial intermediation is perfect and costless, and
that I-sector learning effects are perfectly transmitted internationally, i.e. l 5 1.
The first step is to show that the typical I-firm’s intertemporal problem can be
11
In a process-innovation (i.e. quality ladders) model, Baldwin (1992) demonstrates that autarky-tofree-trade liberalisation can stimulate growth via a procompetitive effect in the I-sector.
R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
511
reduced to an equivalent static problem. Since firms play Nash in capacity, and
* F,
capacity can be measured in terms of labour, namely LIi 5 Q Ki F and L Ii* 5 Q Ki
the equilibrium capacities imply that total I-sector employment is time-invariant in
steady state. As explained in Section 2, this implies that the equilibrium discount
rate always equals r. Consequently, an I-firm’s choices boil down to a sequence of
identical static choices of LIi and L Ii* . Thus, the typical I-firm’s problem is:
max
L Ii , L *Ii
P*
S]PF 2 1D L 1S]
2 GD L *
F
K
K
Ii
Ii
(19)
The next step is to find the inverse demand function for new innovations.
Investors (new X-firms) will pay V for a new design, so the inverse demand
function is PK 5V 5 p /( r 1 g) from q 5 1. Utilising symmetry, Eqs. (1), (2) and
(5), we have:
PK
2E
]
5 ]]]]]
mI
F
s( r 1 2
L )
O
i 51
(20)
Ii
Assuming I-firms ignore their impact on aggregate expenditure E but not their
impact on the I-sector output, the elasticity of PK /F with respect to LIi is the
elasticity of 1 /( r 1 2LI ) with respect to LI (this equals g /( r 1 g) since g 5 2LI
when l 5 1) times the I-firm’s capacity share denoted as s I ; LIi /LI . Using an
analogous formula for the elasticity of P *K /F with respect to L Ii* , the first order
conditions are:
S
D
PK
sI
P K*
s I*
1
g
]
1 2 ] 5 1, ] 1 2 ] 5 G ; ] ; ]]
F
e
F
e
e
r 1g
S
D
(21)
where s I* ; L *Ii /LI (by symmetry LI 5 L *I ).
As usual, oligopolistic prices and market shares are simultaneously determined.
Utilising symmetry and the adding up constraint m I (s I 1 s *I ) 5 1, we have:
G 2 m I e (G 2 1)
1 1 m I e (G 2 1)
s * 5 ]]]]], s 5 ]]]]]
m I (1 1 G )
m I (1 1 G )
(22)
where m I is the number of I-firms. Substituting Eq. (22) into Eq. (21), K’s
equilibrium replacement cost is:
PK 5 mI F;
11G
mI ; ]]]]]]
2 2 1 / [m I (1 1 r /g)]
(23)
where mI is the endogenous price-marginal cost mark-up and P K* 5 PK .
We turn now to showing that there are growth effects from a marginal increase
in I-sector competition – namely, dm I . 0 – and from a marginal liberalisation of
trade in designs – namely, dG , 0.
Proposition 1 tells us that demonstrating trade-and-growth links is only slightly
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R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
more difficult than analysing a static model of imperfect competition and trade. In
particular, the demonstration only requires us to establish that q is diminishing in
g, and to sign the partial derivatives of q with respect to G and m I . Since m I and G
only enter the system via mI , signing ≠q / ≠G and ≠q / ≠m I only requires us to sign
≠mI / ≠G and ≠mI / ≠m I .
By definition, q 5V/PK where V 5 p /( r 1 g) and p 5 E /s K as usual. The
expression for E is still given by Eq. (5) despite the possibility of pure profits in
the I-sector. Defining PI as equilibrium pure profit of a typical I-firm, E equals
L 1 p K 1 PI m I 2 I, but I equals pure profits plus payments to I-sector labour, i.e.
I 5 PI m I 1 LI , so E equals (L 2 LI ) /(1 2 1 /s ), as in the basic model. Combining
these facts:
(L 2 g / 2)(2 2 1 / [m I (1 1 r /g)])
J
q 5 ]] 5 ]]]]]]]]]
mI F
(s 2 1)( r 1 g)(1 1 G )
(24)
By inspection of Eq. (24), ≠q / ≠g , 0 and by inspection of Eq. (23), ≠PK / ≠G . 0
and ≠PK / ≠m I , 0.
Having signed the partials, Proposition 1 tells us that increasing I-sector
competition and liberalising trade in designs both enhance long-run growth.
This is our first example of how the q-approach simplifies analysis of growth
effects. Proposition 1 tells us that signing growth effects only involves signing
partial derivatives in the growth model’s static economy representation. The static
economy representation here is related to the Brander and Krugman (1983) model
of two-way trade in an oligopolistic industry. Given this analogy, intuition for the
two links is straightforward. The replacement cost of capital depends upon I-sector
marginal cost and equilibrium mark-up mI . In an oligopoly (and indeed most forms
of imperfect competition), more competitors means lower mark-ups. Plainly, then,
more competition lowers PK . This favours investment and stimulates long-run
growth. More directly, lowering PK means higher output (demand slopes downward and the equilibrium flow supply of K equals equilibrium demand). Because
this is I-sector output, higher output means faster growth.
Intuition for the trade liberalisation result follows a similar path, the key being
that liberalisation lowers the equilibrium mark-up via a procompetitive effect.
Reciprocal liberalisation ‘defragments’ both design markets. That is, when G . 1,
markets are fragmented in the sense that I-firms in both nations have larger shares
in their local market than they do in their export market, i.e. s I . 1 /(2m I ) . s *I
where 1 / 2m I is the average market share. Lowering G pushes both s I and s I*
towards the average, and this market ‘defragmentation’ raises the degree of
competition as measured by, say, the Herfindahl index of concentration.
3.3.2. Procompetitive effect in banking
Very similar logic can be used to demonstrate that liberalisation of financial
services trade can have a pro-growth effect via its impact on the equilibrium
R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
513
mark-up in the financial sector competition. To illustrate this simply, the Section
3.2 model is modified by restoring perfect I-sector competition and setting l 5 1.
Finding the dependence of Tobin’s q on market structure and trade barriers in
the financial sector is facilitated by the derivation of a number of intermediate
results. First, because banks play a game in lending capacity, whatever level of
capacity they choose entails a time-invariant level of aggregate lending and
investment. This has three significant ramifications. First, the steady condition
L~ I 5 0 and Eq. (2) imply that K grows at the time-invariant rate of g 5 2LI .
Second, this time-invariant rate and Eq. (1) means that F falls at a constant rate of
2LI . Finally, L~ I 5 0 and the Euler equation imply that the rate paid to savers ‘r’
must equal r.
New X-firms enter up to the point where V 5 PK , and since I-sector competition
fixes PK 5 F, the rate of return to owning a design is p /F 2 F~ /F 5 p /F 2 g.
X-firms, which are assumed to borrow their set-up cost F from banks, are willing
to pay any borrowing rate up to this rate on their loan. Oligopolistic banks
therefore charge R 5 p /F 2 g. This defines the inverse demand function for loans
since g 5 2o i Ii (i51, . . . , 2mB ) is the sum of loans made by all banks. Employing
Eqs. (1), (2) and (5), we see that:
2E
R 5 ] 2 2Q B ; Q B ;
s
SO O D
mB
mB
I i*
Ii 1
i 51
(25)
i 51
where Q B is the total of loans made in the home market and R is the lending rate.
Observe that the inverse demand function is linear. The expression for R* is
isomorphic.
As above, a bank’s problem can be reduced to an equivalent static problem,
namely:
max (R 2 r )LIj 1 (R* 2 cr )L Ij*
I j , I j*
(26)
where measuring loans in units of labour means Ij 5 LIj and I *j 5 L *Ij . The first
order conditions are:
S
D
sB
s B*
R 1 2 ] 5 r, R 1 2 ] 5 cr
u
u
S
D
(27)
where u ; (2E /s g) 2 1, and sB ; LIi /LI and s B* ; L *Ii /LI are the local and export
market shares of a typical bank. Here we use the fact that r 5 r in steady state to
set the rate paid to savers equal to r. The formula for equilibrium sB and s B* are as
in Eq. (22), with u, c and mB substituted for e, G and m I .
Given this set-up, it is obvious Brander–Krugman reciprocal dumping of
financial services occurs. As above, reciprocal liberalisation of financial services
trade (i.e. dc , 0) and / or an increase in mB will have a procompetitive effect that
lowers the equilibrium mark-up of R over r. Since:
514
R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
2L 2 g
q 5 ]]]]];
(s 2 1)( mB r 1 g)
11c
mB ; ]]]]]]
s
2 2 ]]]]
mB (2L /g 2 s )
(28)
The mark-up is increasing in c and diminishing in mB , so liberalisation and / or an
increase in the number of banks will lead to an incipient rise in both countries’ q.
Since q is diminishing in g (observe that mB is increasing in g), Proposition 1
implies that worldwide growth would rise when international markets for loans
become less fragmented and / or more competitive.
4. Concluding remarks
Using the q-theory approach, this paper illustrates two novel openness-andgrowth links. To summarise the links, note that one link operates via its impact on
q’s denominator and the other via q’s numerator. The first link affects the
denominator and it arises in a product-innovation endogenous growth model
generalised to include the possibility of imperfect competition in the I-sector. As is
well known, trade liberalisation can – via the procompetitive effect – alter market
structure and equilibrium mark-ups. We show that liberalisation reduces I-sector
mark-ups, thereby lowering capital’s replacement cost. The resulting incipient
increase in q leads to faster growth.
The second link deals with q’s numerator, i.e. the value of introducing a new
innovation. The link appears when we allow imperfect competition in financial
intermediation. Namely reciprocal liberalisation of trade in financial services
lowers the mark-up between savers’ and investors’ interest rates via a procompetitive effect. With lower borrowing costs, firms discount future operating profit at a
lower rate and this increases the value of introducing new capital. The resulting
incipient rise in Tobin’s q (which is the value of the marginal product of I-sector
labour) draws more resources into both nations’ I-sectors and growth rises.
In addition to these two openness-and-growth links, we demonstrate that
increased competition in the I-sector and the banking sector are pro-growth.
Proposition 1 suggests that many other openness-and-growth links could be
modelled. In particular, Proposition 1 should allow researchers to hook easily into
well-known results concerning the incipient impact of trade liberalisation on
operating profits. For examples of such applications, see the working paper version
of our paper, Baldwin and Forslid (1996). Moreover, the realisation that we can
study growth effects by studying the impact of policy changes on the static
economy representation of the growth model should allow researchers to investigate the growth effects in the many trade-and-imperfect-competition models
developed in the past two decades.
One particularly important area of research would be to enrich further the
I-sector market structure and technology. For instance, the modelling of the
R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
515
innovation process in the Romer–Grossman–Helpman product innovation models
is extremely rudimentary, yet innovation is at the heart of the model. It would
seem important to evaluate the effects found in partial equilibrium innovation
models (e.g. Tirole, 1988 Chapter 10) in the context of trade and endogenous
growth models.
Acknowledgements
This is a substantial revision of our NBER and CEPR working papers (5549 and
1397, respectively). We thank Elhanan Helpman and Gene Grossman for inspiration and comments, and Victor Norman, Elena Seghezza, Philippe Martin, Phil
Lane and Don Davis for helpful comments on earlier drafts. Support came from
Swiss NSF grant 1214-043580.95 / 1, and Ford Foundation support of CEPR’s
GARP project. Forslid acknowledges the Swedish Council for Research in
Humanities and Social Sciences (subsidy [F59 / 95).
Appendix A. Understanding the lack of transitional dynamics
Here we prove that the model is always in steady state without using any of the
conclusions that depend upon that result. The proof follows the standard line of
reasoning used to show that a dynamic system jumps to its saddle path and then
evolves along the saddle path until the steady state is attained.
The system is characterised by a transversality condition and one differential
equation – the Euler equation:
Fig. 2. Showing the lack of transitional dynamics.
516
R.E. Baldwin, R. Forslid / Journal of International Economics 50 (2000) 497 – 517
S
(1 1 l)L (1 1 l)LI
L~ I 5 ( L 2 LI ) r 2 ]]] 1 ]]]
s 21
1 2 1 /s
D
(A.1)
which can be derived without assuming that transitional dynamics are absent. Fig.
2 plots this differential equation, ignoring the non-negativity constraint on LI .
Clearly, there is a unique, interior steady-state value of LI at EE, and clearly the
equation is saddle-path unstable (LI enters the differential equation with a positive
sign) where the saddle path is the point EE. As usual, the optimising representative
consumer will always choose LI 5 EE to avoid violating necessary conditions for
utility maximisation.
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