Trade liberalisation and endogenous growth A q-theory approach

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).


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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).


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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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.


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.

504


(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.


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].

506


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


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.

508


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


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.

510


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.


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

512


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


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


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


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


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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