North-South Technological Diffusion: A New Case for Dynamic Gains from Trade Michelle P. Connolly1

Diego Valderrama2

1 Department

of Economics Duke University

2 Economic Research Federal Reserve Bank of San Francisco

UC Davis

Outline Introduction Previous Literature What We Do In This Paper Basic Setup of Model Consumers’ Problem Final Goods Production Industrial Structure Innovation and Imitation Bertrand price competition Transitional Dynamics Results Southern Trade Liberalization High Rate of Technical Diffusion Trade liberalization concurrent with licensing Conclusions

Dynamic implications of North-South trade

Focuses on the transitional dynamics for North and South resulting from technological diffusion through reverse engineering of traded intermediate goods

Principal contributions to existing literature

I

Derive the transitional dynamics of a quality ladder for both North and South

I

Welfare analysis shows crucial importance of considering the transition path rather than just comparing steady states

I

Introduces the notion of learning-to-learn in research

I

Trade and infrastructure are considered in a more explicit modeling of imitation

I

The concept of learning-to-learn is incorporated into both imitative and innovative processes, which in turn drive domestic technological progress for both countries.

Relation to previous literature

1. Dynamic consequences to the South if trade with the North causes it to specialize in industries lacking positive externalities (e.g., Young (1991)) I

We consider what happens if the South specializes in imitation, an activity with less benefits from learning to learn than innovation

2. Effect of North-South trade on technological progress and diffusion (e.g.,Grossman and Helpman (1991a, 1991b), Barro and Sala-i-Martin (1997)) I

I

Here, North-South trade causes a feedback effect between Northern and Southern research Feedback effect affects the transition path and steady-state for both the North and the South

What we do in this paper

I

I

Introduce N-S model of technological diffusion through trade and imitation. International trade with reverse engineering of intermediate goods I I

I

Feedback effects between N. innovators and S. imitators Both regions face transition paths dependent on their relative technologies

Find welfare implications of trade and intellectual property right (IPR) policy: I

I

Southern Trade liberalization can be welfare reducing for the North, even though it is welfare enhancing in steady-state. IPRs can be potentially welfare enhancing for both countries.

Basic setup of model I

Perfectly competitive final goods production in each region (dep. on quality of intermediate goods)

I

Both countries consume both final goods

I

Research determines who knows how to make the latest technology

I

Monopolistic competition with Bertrand pricing in the intermediates goods sectors determines which firm (among those with the technology) will capture the world market. This will depend on marginal costs of production, and trade frictions.

I

Balanced trade: there is no intertemporal substitution across countries.

Northern Consumers’ problem Consumers maximize PDV of lifetime utility. They consume both domestic goods, CN , and imported goods, CS∗ : Z ∞ ¯ N )e −ρt dt max u(C (1a) {CN ,CS∗ ,v}t→∞ 0 ! ¯ 1−θ − 1 C N ¯N ) = u(C (1b) 1−θ ¯ N = C κ C ∗ 1−κ C N S

(1c)

v˙ = w + rN v − EN

(1d)

EN = PN CN +

PS∗ CS∗ .

(1e)

¯ N , is defined as the The consumption-based price index, P minimum expenditure, EN , such that the composite good index, ¯ N = 1, for a given set of prices: C ¯N = P



PN κ

κ 

PS∗ 1−κ

1−κ .

(2)

We obtain two expressions for consumer demands: ¯N P ¯N C PN ¯N P ¯N . CS∗ = (1 − κ) ∗ C PS CN = κ

(3) (4)

Consumption Growth

¯˙ N C 1 = ¯ θ CN

! ¯˙ N P rN − ¯ − ρ . PN

(5)

Quality ladder model of growth with technology embodied in intermediate goods

Yi = Ai Liα

J  X

q kNj xˆikj

1−α

, i ∈ {N , S}

j=1 I

Uses domestic and foreign intermediates in production

I

Final goods are costlessly transformed into consumption goods, intermediate goods, and research goods

(6)

Intermediate goods

I

Limit prices determined by closest competitor

I

N. innovators compete with either previous N. innovators or S immitators. 3 types of Firms: J = nNN + nNS + nS

I

1. nNN = N. innovators facing N. competition 2. nNS = N. innovators facing S. competition 3. nS = S. imitators facing N. competition I

3 limit prices

I

3 entry-exit conditions dependent upon pC , pI

Probability of innovation

pIkNj = zIkNj ϑkNj ϕIkNj , ϑkNj = βI q kNj , 1 −kNj ϕIkNj = q α . ζI and it depends on I

resources devoted to research

I

past learning-to-learn

I

the difficulty of innovation

I

ζI , fixed cost of innovation

and

where

Probability of imitation

pCkNj = zCkNj ϑkSj ϕIkNj , kSj

ϑkNj = max(βC q , βI q e ω −kNj q α ϕCkNj = for ζC qˆjσ q kSj , and q kNj   M η ω= . QN

qˆj =

and it depends on I

resources devoted to research

I

past learning-to-learn in industry j

I

the difficulty of imitation

where kNj

), σ > 1,

Probability of imitation pCkNj = zCkNj ϑkSj ϕIkNj ,

where

ϑkNj = max(βC q kSj , βI q kNj ), e ω −kNj q α for σ > 1, ϕCkNj = ζC qˆjσ q kSj , and q kNj   M η ω= . QN

qˆj =

and it depends I

negatively on the sector j South/North technology ratio, qˆj , and reflects the increasing cost of imitation as Southern technology approaches that of the North.

I

positively on the interaction, ω, between the two countries.

Assumptions

I

In equilibrium, we choose parameters so that the marginal cost of production in South less than in North.

I

Spillover from past innovative experience, βI , is greater than that from imitation, βC .

I

Fixed cost of imitation, ζC , less than the fixed cost of innovation, ζI .

I

Innovations are drastic.

Limit prices Northern firms facing Northern competition choose a limit price slightly below q times the lowest price at which the previous innovator could sell, since their product is q times more productive than its predecessor. I Northern firms facing Northern competition, nNN : I I

I

Northern firms facing Southern competition, nNS : I I

I

PNN = qMCN = q for domestic sales (N), ∗ PNN = q(1 + τxS ) for exports to South. PNS = qMCS (1 + τxS ) domestically (N), ∗ PNS = qMCS abroad (S).

Southern firms, nS , always face Northern competition: I I

PS∗ = 1 domestically (S), PS = 1 + τxS abroad (N).

Intermediate goods demand

In either country i, for a given limit price, Px , and final goods price, Pi , implied demand for intermediate goods in sector j is  1 α kij (1−α) Pi xij = Li Ai (1 − α)q . Px

(7)

Aggregate production

  α−1 α−1 1−α α α α MCS + nS q , (8) YN = QN ΛN nNN + nNS (1 + τxN ) "   1−α  1−α #  α α 1−α MCS MCS YS = QN ΛS nNN + nNS + nS q α , 1 + τxS 1 + τxS

where

QN =

J X

q

kNj (1−α) α

1/α

and ΛS = LS AS

j=1

QN represents the Northern aggregate quality index.



1−α q

(9)  1−α α

.

Transitional dynamics

The cost of imitation, and hence the probability of imitation for the average sector, depends on the average South/North technology ratio, which equals the aggregate South/North ˆ = QS . The interest rates and growth rates will technology ratio, Q QN change during the transition to steady state: ·

 1−α  ˆ Q Q˙ S Q˙ N = − = q α − 1 (pCkNa − pIkNa ) . ˆ QS QN Q

(10)

Free entry conditions Interest rates, rN and rS , will be determined by two free-entry conditions: pIkNa E(vIkNa +1 ) = ZIkNa

(11)

pCkNa E(vCkNa ) = ZCkNa ,

(12)

where E(vIkNa +1 ) = πIkNa +1 × Z t

∞

Rs

e − t [rN (v)+pCkNa +1 (v)+pIkNa +1 (v)−pCkNa +1 (v)pIkNa +1 (v)]dv ds, Z ∞ R s E(vCkNa ) = πCkNa e − t [rS (v)+pIkNa (v)]dv ds. t

Expressions for the interest rates in both countries: rN =

pIkNa πIkNa +1 Z˙ IkNa p˙ IkNa π˙ IkNa +1 + − − ZIkNa ZIkNa pIkNa πIkNa +1

− pCkNa +1 − pIkNa +1 + pCkNa +1 pIkNa +1 Z˙ CkNa p˙ CkNa π˙ CkNa pCkNa πCkNa + − − − pIkNa . rS = ZCkNa ZCkNa pCkNa πCkNa

(13)

Industrial dynamics

Entry and exit into intermediate goods production depends on pI and pC : n˙ NN = pI (1 − pC )nNS − [pI pC + (1 − pI )pC ]nNN

(14)

n˙ NS = pI (pC nNN + nS ) − [(1 − pI )pC + pI (1 − pC )]nNS

(15)

n˙ S = (1 −

∗ pI )pC (nNN

+

∗ nNS )

− pI n S .

(16)

Consumption growth

We find expressions for consumption demand growth for each type of good. For example, the demand growth for domestically produced goods is given by: ! P˙ S∗ P˙ S∗ 1 C˙ N = (1 − κ) ∗ + rN − ρ − (1 − κ) ∗ CN PS θ PS ! (17) C˙ S P˙ S 1 P˙ S = −κ + rS − ρ − (1 − κ) . CS PS θ PS

Solutions

Solutions are found using: 1. Free-Entry Conditions 2. Sector Entry-Exit Conditions 3. 2 World Resource Constraints 4. Balanced Trade Condition 5. 2 Consumer Demand Conditions 6. 2 Consumption Growth Paths 7. Functional Forms for pC and pI

Experiments

1. Southern trade liberalization alone I I I

Steady-state welfare gains for both regions Transitional welfare loss for North Overall welfare loss for N., gain for S.

2. Southern trade liberalization and rapid technological diffusion I

I

Increasing rate of technological diffusion speeds up convergence, reducing cost to North, and increasing benefit to South. Rate of transition should be important empirically.

3. Southern trade liberalization with licensing I I

Overall welfare gain for both N. and S. S. gains by more than with trade liberalization alone

Southern trade liberalization

Table: Steady-State Values Innovation Rate (pI ) Interest Rate Growth Rate ˆ Q nS nNS nNN

S. Tariffs = .05 0.2124 0.1410 0.0403 0.1644 0.4406 0.3130 0.2465

S. Tariffs=.01 0.2148 0.1423 0.0408 0.2682 0.4398 0.3138 0.2464

Figure: Experiment: Southern Trade Liberalization

Compensating variations

Table: Compensating variations of aggregate consumption (%) Steady State (North & South) North (with transition) South (with transition)

S. Trade Liberalization 0.0040 -0.0031 0.0224

Southern trade liberalization, high technical diffusion

Table: Steady-State Values Innovation Rate (pI ) Interest rate Growth rate ˆ Q nS nNS nNN

S trade liberalization 0.2125 0.2148 0.1410 0.1423 0.0403 0.0408 0.1920 0.3224 0.4406 0.4398 0.3130 0.3138 0.2465 0.2464

high tech. diff. 0.2125 0.2148 0.1410 0.1423 0.0403 0.0408 0.1665 0.2720 0.4406 0.4398 0.3130 0.3138 0.2465 0.2464

Figure: Experiment: Southern Trade Liberalization, High Rate of Technical Diffusion

Compensating variations

Table: Compensating variations of aggregate consumption (%) Steady State (North & South) North (with transition) South (with transition)

S. Trade Liberalization 0.0040 -0.0031 0.0224

with high tech. diff. 0.0040 -0.0027 0.0228

Southern trade liberalization with licensing

Table: Steady-State Values

Innovation Rate (pI ) Interest Rate Growth Rate ˆ Q nS nNS nNN

S. Tariffs = .05

S. Tariffs=.01

0.2124 0.1410 0.0403 0.1644 0.4406 0.3130 0.2465

0.2148 0.1423 0.0408 0.2682 0.4398 0.3138 0.2464

S. Tariffs=.01 Licensing Fee =.15 0.2205 0.1455 0.0418 0.2910 0.4381 0.3158 0.2462

Figure: Experiment: Southern Trade Liberalization with Licensing

Compensating variations

Table: Compensating variations of aggregate consumption (%)

SS Only North and South Transition Plus SS North Transition Plus SS South

S. Trade Liberalization

S. Trade Liberalization with Licensing Fee

0.4

1.4

-0.3

0.9

2.2

3.2

Conclusions I

Must consider transition paths to see full welfare implications, not only steady-state.

I

In a model of technological diffusion, both regions ultimately care about the same world growth rate.

I

Optimal policy depends on whether technological diffusion is occurring and whether there are feedback effects between innovating and imitating firms.

I

Feedback effects imply that there may not be a direct conflict from the perspective of DCs and LDCs.

I

Empirically, as integration increases, feedback effects, and learning-to-learn should become more important.

I

Hence, policies (trade, IPR) that maximize this world growth rate will be in the interest of both regions.

I

In this model, despite Southern specialization in an activity with less spillovers, S gains from trade liberalization, and even more from trade liberalization with IPRs.