Endogenous Technological GrowthPaul Romer 1990

Seyed Ali Madanizadeh

November 2013

Introduction

Output per hour worked in the United States today is 10times as valuable as output per hour worked 100 years ago

The raw materials that we use have not changed, but as aresult of trial and error, experimentation, refinement, andscientific investigation, the instructions that we follow forcombining raw materials have become vastly moresophisticated

This paper

Solow model with technological change.

Technological change provides the incentive for continuedcapital accumulationCapital accumulation and technological change account formuch of the increase in output per hour worked.

Technological change arises in large part because of intentionalactions taken by people who respond to market incentives.

Not all but some: Our initial understanding ofelectromagnetism arose from research conducted in academicinstitutions, but magnetic tape and home videocassetterecorders resulted from attempts by private firms to earn aprofitThus endogenous and not exogenous growth model

This paper

Instructions for working with raw materials are inherentlydifferent from other economic goods

Once the cost of creating a new set of instructions has beenincurred, the instructions can be used over and over again atno additional cost.Developing new and better instructions is equivalent toincurring a fixed cost.Thus no price taking behavior

A firm incurs fixed design or research and development costswhen it creates a new good.

It recovers those costs by selling the new good for a price thatis higher than its constant cost of production.

Since there is free entry into this activity, firms earn zeroprofit in a present value sense.

Findings

Increases in the size of the market have effects not only on thelevel of income and welfare but also on the rate of growth.

Larger markets induce more research and faster growth.

Population is not the right measure of market size but humancapital

The growth rate is increasing in the stock of human capital

If the stock of human capital is too low, growth may not takeplace at all.

The Model

Labor

Human Capital: wHNew Designs pAIntermediate goods:p (i)

Final goods: pY = 1

Capital: pK = 1, rental rate r

The Model

Consumers :

Labor, Human CapitalY = K + C

Research sector:

Uses human capital and current stock of knowledge(A)Produces designs for new producer durables

Intermediate good sector: x (i)

Uses the designs from the research sector and capitalProduces the large number of producer durablesto be used in final goods production

Final good sector

Uses labor, human capital, and the set of producer durables

Research Sector

New designsA = δHAA

pay wages wh and receive PA

wh = PAδA

Linearity in A makes unbounded growth possibleThere is little doubt that much of the value to society of anygiven innovation or discovery is not captured by the inventor,and any model that missed these spillover would missimportant elements of the growth process

Final Good

Uses human capital, labor and intermediate goods

Y = HαY L

β

(∫ A

0x (i)1−α−β di

)wh = wages for human capital, Output price = 1

Final Good

Demand for x (i)

maxxi

∫ ∞

0

[HαY L

βx (i)1−α−β − p (i) x (i)]di

p (i) = (1− α− β)HαY L

βx (i)−α−β

x (i) =((1− α− β)Hα

Y Lβp (i)

) 1α+β

Intermediate durable producers

They buy a research product by initial investment to get thenew design

The owner of a design has property rights over its use in theproduction of a new producer durable but not over its use inresearch.

Uses only capital: ηx

Each producer of specialized durables must rent its output toa large number of final-goods producers that can operate atany scale.

Intermediate durable producers

Producers of x (i) has monopoly over its good :(Monopolistic Competition)

π = maxxp (x) x − rηx

Constant markup

p =rη

1− α− β

π = (α+ β) px

Intermediate durable producers

Free Entry ∫ ∞

te−R (τ)π (τ) dτ = PA (t)

R (t) =∫ τt r (s) ds

PA constant:π (t) = r (t)PA

Consumers

Constant L

Constant H = HA +HYConsume C

Saves K

max∫ ∞

0

C 1−σ − 11− σ

e−ρtdt

s.t Y = K + C

FOC:CC=r − ρ

σ

Equilibrium

1 Consumers make savings and consumption decisions takinginterest rates as given.

2 Holders of human capital decide whether to work in theresearch sector or the manufacturing sector taking as giventhe stock of total knowledge A, the price of designs PA, andthe wage rate in the manufacturing sector wA

3 Final-goods producers choose labor, human capital, and a listof differentiated durables taking prices as given

4 Each firm that owns a design and manufactures a producerdurable maximizes profit taking as given the interest rate andthe downward-sloping demand curve it faces, and settingprices to maximize profits

5 Firms contemplating entry into the business of producing adurable take prices for designs as given

6 The supply of each good is equal to the demand

Equilibrium allocation and prices

Variable PriceC 1K rY 1HY ,HA wAA PAx (i) p (i)

Solution

x : Production of every intermediate producer

K = ηAx

Y = HαY L

βAx1−α−β

= (HY A)α (LA)β K 1−α−βηα+β−1

It’s like the neoclassical growth model

BGP

A,K ,Y ,C grows at constant rates

HA is constant

It implies: x : constant

BGP

BGP Equations

Consumers

CC

=r − ρ

σH = HA +HY

Final good sector

wH = αHYα−1LβAx1−α−β

Intermediate sector

p =rη

1− α− β

x =((1− α− β)Hα

Y Lβp) 1

α+β

π = (α+ β) px

PA =π

r

BGP Equations

Research sector

wH = δAPAAA

= δHA

Market clearing

K = ηAx

g ≡ AA=KK=CC=YY

BGP Equations

1 wH = αHY α−1LβAx1−α−β = δAPA

PA =α

δHY

α−1Lβx1−α−β

2 PA = πr =

(α+β)pxr

PA =(α+ β) (1− α− β)Hα

Y Lβx1−α−β

r

3 Equating:

HY =α

δ ((α+ β) (1− α− β))r =

Λrδ

4 g = AA = δHA = δ (H −HY )

g = δH −Λr

BGP Solutions

g =δH −Λρ

Λσ+ 1

r =δHσ+ ρ

Λσ+ 1

HA = H − Λrδ=H −Λρ/δ

Λσ+ 1

Results

Interpretation of g = δH −ΛrNeither L nor the parameter η is present.

Increase in L increases the demand for the monopolyA reduction in η reduces the costs of the monopolist andincreases output x .The net revenue should increase with the rise in L and fall in η.But they have no effect on HA.

Results

In a partial equilibrium analysis, one would always expect anychange that increases the return to an activity to increase theallocation of resources to that activity.

A general equilibrium analysis emphasizes that anyintervention that increases the return to one activity can verywell increase the return to some other activity that competeswith the first activity for resources.

An increase in L or a reduction in η (which increases x) raisesthe return to human capital employed in manufacturing at thesame time that it raises the return to human capital inresearch.With this functional form, these two effects cancel out.It’s not always. But it means that the net effect is ambiguous.

Results

Anything that reduces r increases growth. (like more patienceand higher IES)

Policy: reducing η is different from reducing r .

Subsidy to investment financed by lump-sum taxes isequivalent to reduction in η. So it is not growth enhancing.

The model presented here shows that when the decision toinvest in physical capital is uncoupled from the decision toinvest in research, the effects of a subsidy to physical capitalare quite different from the effects of a reduction in themarket interest rate.

If the fundamental policy problem is that we have too manylawyers and MBAs and not enough engineers, a subsidy tophysical capital accumulation is a weak, and possiblycounterproductive, policy response

Results

The research sector in this model exhibits increasingreturns.⇒ a doubling of the human capital and the stock ofknowledge leads to an increase in the marginal product ofhuman capital in research. ⇒ a permanent increase in thetotal stock of human capital in the population leads to anincrease in the ratio of A to K and a more than proportionalincrease in the amount of human capital that is devoted tothe research sector

Empirics: the total level of human capital and the fraction ofhuman capital devoted to research are higher now than theywere at any time in the past & fraction of human capitaldevoted to research is apparently highest in the mostdeveloped countries of the world.

Results

Lower H results in lower growth rates.

Small H results in zero growth rate.

Thus, the model can explain the large variety of growth ratesacross countries.

A subsidy to employment in the research sector that isfinanced through lump-sum taxes has the same effects ongrowth as an increase in the productivity parameter δ.

In the long run, the subsidy will cause an increase in thegrowth rate, a fall in PA, and a reduction in x and in the ratioof K to A.

Results

Two reasons to expect that too little human capital is devotedto research.

Research has positive external effects.Research produces an input that is purchased by a sector thatengages in monopoly pricing.

Any intervention designed to move an economy from onebalanced growth path to another must consider the transitiondynamics along the way.

Role of Trade: H → 2H

Social Planner

max∫ ∞

0

C 1−σt − 11− σ

e−ρtdt

subject to

K = ηα+β−1HαY L

βAα+βK 1−α−β − CA = δHAA

H ≥ HA +HY

Social Planner

g ∗ =δH −Θρ

Θσ+ (1−Θ)

Θ = αα+β = Λ.markup: Monopoly power ineffi ciency

1−Θ : Reflects the effect of correcting for the external effectsassociated with the production of new ideas

Conclusion

A one-sector neoclassical model to explain sources ofendogenous technological changewelfare conclusion: the rate of technological change issensitive to the rate of interest

since research projects exchange current costs for a stream ofbenefits in the future.a subsidy to physical capital accumulation may be a very poorsubstitute for direct subsidies that increase the incentive toundertake researcha second-best policy would be to subsidize the accumulation oftotal human capital

Positive implication: an economy with a larger total stock ofhuman capital will experience faster growth

Why high growth rates in developed economies in the 20thcenturyWhy stagnation in underdeveloped economies.Why integration with the world economy help less developedeconomies