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7/30/2019 It d Present

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International Technology Diusion: Theory andMeasurement

By Jonathan Eaton and Samuel Kortum

Presented by: Anna Wong and Louis Serranito

Eaton and Kortum

March 10, 2008

(Eaton and Kortum) International Technology Diusion M arch 10, 2008 1 / 47
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Motivation

Countries that were slow to adopt or imitate outside ideas experienced

slower growth. Example: Britain vs. Germany, US, JapanWhy does research occur in dierent countries?

How does research give rise to innovations?

Where do these innovations generate increase in productivity?

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Model Features: Data

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Overview: What will this paper do?

Present a model of world growth driven by technological diusion

Characterize steady state as balanced growth path

Fit model to data after estimating some key parameters. It willpredict for 5 countries:

-Number of researchers-Productivity relative to US-Direction of patents for protection in each of the 5

countries (5 x 5 matrix)

Counterfactual experiments - patterns of diusion (autarky vs.borderless) and rigor of patent protection



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Model: Production

Final goodFinal goods Ynt produced in country n = 1, ..N, at time t producedwith Cobb-Douglas technology, from intermediate goods Xnt(j) ofdierent quality Znt(j)

ln(Ynt

J) = J1 Z

J

0

ln [Znt (j)Xnt (j)] dj

Intermediate goods

X(j) = K(j)L(j)1

where 2 [0, 1] =capital elasticity

Assumptions:Output is homogeneous and tradable across countriesInputs are nontradedRange of inputs, J, is xed over time

capital elasticity same across inputs, countries, and time(Eaton and Kortum) International Technology Diusion M arch 10, 2008 5 / 47
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Model: Ideas

Idea: a unit of research output

research input: sti (share of labor force in research)

ideas production/arrival rate: itsitLit

it =overall productivity of research eort in country i at time t = rate at which research productivity declines as less talentedworkers become researchersLit =labor force in country i at time t

3 dimensions Quality, Adoption, Diusion Lag



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Quality of Idea

Q F(Q)

Assume Pareto distribution. So F(Q) =Prob(x< Q)= 1Q

An idea of quality q is adopted if its quality is higher than currentstate of the art z, thus:

Prob of adopting idea = P(q> z) = z

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Diusion Lag of Idea

Ideas diuse from country i to country n at rate in

in = speed of diusion from country i to country n

Assume that diusion lags, in , follows exponetial distribution

in exponential (in)

This means that the probability that an idea invented at country itake less than periods x to diuse to country n is

Pr(in x) = 1 einx

Mean diusion time is

average time it takes to diuse from i to n =1

in



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Idea Adoption

An idea is diused doesnt mean it is adopted by the recipient country

An idea of quality q is adopted/used only if:

q> Z(j)

The ideas quality is higher than the current state of the art forproducing that intermedate good j

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Technological Frontier

Dene the highest quality for each intermediate good j in country nat time t as, Znt(j)the "State of the Art"

"The State of the Art" across all intermediate goods in that country

form that technological frontierThe technological frontier in country n at time t is summarized by thecumulative distribution of the state of the arts

Fraction of inputs whose state of the art is below z:

Znt(j) Hn(z; t)

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Obtaining the Technological FrontierStep (1): Dynamics of diusion of ideas into country n

Dene the stock of diused ideas at country n nt =Rt

nsds

is the stochastic rate at which ideas diuse to country n from

research done all over the world and domestically:

nt = J1

N

i=1

Zt

inein (ts)

| {z }fraction diused tocountry n in remaining time iss

isLis

| {z }# of ideas producedat country i at time s

ds

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Obtaining the Technological FrontierStep (2): Adoption of some of the diused ideas

The rate of adopting diused ideas:

Prob(q> z) = z

Now we can solve for H(z; t)

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Obtaining the Technological FrontierStep (3): Solving for H

Let x =time adopting new ideas

By the memoryless property of the exponential distribution

P(x< t+ s) = P(x< t) P(x< s)

Hn(z; t+ dt) = Hn(z; t) Hn(z; dt)

Hn(z; dt) can be interpreted as the probability of having no newadoption within the period dt

Hn(z; dt) = P(no adoption in dt)

= P(x> dt)

= ezdt

Rewrite, giving us a dierential equation.

Hn(z; t+ dt) = Hn(z; t) ezdt



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Obtaining the Technological FrontierStep (3): Solving for H

Solve the dierential equation, with two boundary conditions

lims!

Hn(z; s) = 1 8z 1

lims!

ns = 0

GivesHn(z; t) = e

tnz

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Production

Now we can rewrite the production technology

Ynt = AntKnt [Lnt(1 snt)]

1

where the TFP is the geometric mean of the technological frontier

Ant = exp

Z1

ln(z)dHn (z; t)

EK shows that as nt becomes large, TFP is proportional to growth

in the stock of ideas diused to the country

Ant = e/1/nt

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Market Structure

All producers of intermediates in a country face the same w and costof capital r0. So they have the same unit cost

c = r0

w1

1

Bertrand Competition - new idea compete against the previous stateof the art

Owner of the invention charges the highest price at which it remainsthe only seller of that input


I li i f M k S f I P i


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Implication of Market Structure for Input Prices

Think about cost per quality. With Bertrand Competition, pricesdriven down to perfect competition.

Equating the cost per quality of the previous state of the art and thecounter part with the new quality

c

z =pq

q

Thus prices for inputs dier across inputs, depending on the "step ofinvention"

p(j) =

q(j)

z(j)

c


V l f Id


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Value of an Idea

An idea has positive value only ifq z

ideas face a hazard rate of of being imitated, in which case it losesall of its value

The expected discounted value of the right to use an idea fromcountry i of quality q in country n, given that the previous state ofthe art z

Vint(z, q) = Z

0n,t+s(z, q)e

rses 1 eins

e(nt+snt)qds


V l f Id
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Value of an Idea

Prots are

n,t+s(z, q) =Y

J

1

z

q

because

X(j) =P Y

J P(j) =Y

J P(j)

and = P(j)X(j) cX(j)

=Y

J

Yz

Jq

= YJ

1 z

q


V l f Id
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Value of an Idea

Assumption: at the time of invention research knows the quality ofhis idea, but not the quality of the competing input in any country

The expected value of an idea of quality q from country i in country

n,

Vint(q) =Zq

1Vint(z, q)dhn(z; t)


D i i t P t t
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Decision to Patent

Having a patent decreases the hazard rate of imitation

pat < not

The cost of the patent for inventor in country i in country n shouldequal to

Vpatint (q) Vnotint (q) = fint

The equation above determines the threshold qint above whichinventors in country i patent in country n

The rate inventors in country i patent in country n is

Pint = itsitLit| {z }

ideas produced in i

(qint)| {z }

probability ofq >q


Value of an Idea: Return to R&D
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Value of an Idea: Return to R&D

Value of an idea: max Vpatint (q) fint,Vnotint (q)Before the quality is known, the expected value of an idea for countryi in country n is

Vint = Zqint

1

Vnot

int

(q) dF(q) + Z

qint

Vpat

int

(q) dF(q) fint(qint

)

Summing across countries n, the expected return to an idea ofunknown quality is

Vit =

N

n=1Vint


Equilibrium Number of Researchers
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Equilibrium Number of Researchers

Equalization of wages between the research and production sector incountry i gives the equilibrium sit, the share of labor force who are

researchersitVits

1it = wit


Technology and Income
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Technology and Income

Aggregate output in country i at time t is

Yit =1 ()

2 ()Aitk

itLit(1 sit)

Cobb Douglas assumption implies that the capital to labor ratio k is

kit =

1

wit

r0

Rewrite the aggregate output in terms of wage and cost of capital

Yit =1

2 ()

"1 ()Ait

r0

# 11Lit(1 sit)


Wages


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Wages

Wage for production workers is

wit = (1 )1 ()Aitkit

Rewrite wages in terms of cost of capital

wit = (1 )

"1 ()Ait

r0

# 11


Constant Growth Path


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Constant Growth Path

We want nt to grow at a constant rate - g.

Additional Assumptions

Workforce grows at rate gL.The relative productivity of researchers is proportional to the relativelevel of technology in their country and to the world stock of ideas:

it =

itt

t

Patenting costs are a constant proportion of output ) fint = finYitInterest rate (r) and cost of capital (r0) are constant.


Two Scenarios


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Two Scenarios

Full endogenous growth

gL = 0 and = 1 as in Romer(1990)

Y = K (ALY)1

A = LAA

Semi-endogenous growth

gL > 0 and < 1 as in Jones(1995)

Y = K (ALY)1A = LAA

, < 1

Note that ifgL > 0 and 1 then we have explosive behaviour.


Features of Growth Path (i)
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Features of Growth Path (i)

Fraction of researchers (si) is constant in each country.

Patenting is constant in each country.

TFP grows at rate g .

Wage rate grows at rate g(1) .


Features of Growth Path (ii)


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Features of Growth Path (ii)

Output grows at rate gy =g

(1)+ gL.

Mean lag between invention in country i and adoption in country n is1

ni+g(conditional on it being adapted).

Country n adopts fraction nini+g of the ideas from country i that itwould have immediately accepted if they arrived immediately.

Li Lit1t is constant in either the full endogenous or

semi-endogenous case (g = gL1).


Steady State Relative Productivities and Growth
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With a constant si the stock of ideas in each country grows at rate g:

g =ii

=

J

N

n=1

inin + g

ni

sn Ln

Three eects on growth:

1 Generation of ideas in n: ntsn Ln

2 Fraction of ideas useful in country i when invented: 1it

3 Fraction of ideas adopted which where useful when invented:in

in+g




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To solve for g we must solve a system of N equations for g:

Dene h1tNt

,2tNt

, ...,N1tNt

, 1i

System can be represented as:

g = (g)

Where:

(g) =

2664

111+g

Js1 L1

1N1N+g

JsNLN

.... . .

...N1

N1 +gJs1 L1

NNNN+g

JsNLN

3775

Recover g and nt.




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y

Using solution to it calculate ratio of TFPs:

Ait

ANt=

itNt

1


Steady State Patenting
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y g

We have already seen that qint denes the threshold from which it is worth

patenting.

To ensure a steady state we require that the ratio of patented ideas toadpoted ideas be constant and given by:

bin = it (qint)

Patenting threshold is only aected by:

adoption lag - it

patent protection - patin and notin

cost of patenting fin


Steady State Patenting
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y g

Using rate of patented ideas, the patenting of ideas from country i incountry n is given by:

Pin = sn Ln nibin


Steady State Labor Market Equilibrium
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y q

Using the model we can derive the following equation:

s1n

N

i=1

vin Li (1 si) in1+(1)

= (1 ) 2 ()

Where vin itVintYit

, which is constant.


Data
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Data for the ve leading research nations in the OECD ! France,Germany, Japan, UK and US

Researchers employed in 1988 and R&D expenditure - OECD (1991)

Workforce - Summer and Heston (1991)

Labor productivity in 1990 - van Ark (1996)

Patent applications (1988-1990 average) - WIPO (1990)

Patent costs - Helfgott (1993)


Estimation


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Model

Assume that the countries are in steady-state at the end of 1980s

Model is:Y = G(,X)

Where

Y =

2664Productivity GrowthRelative Productivity

ResearchPatents

3775 ,X = Workforces

Patenting Costs relative to GDP

=(, ,, patin , notin , in , r, gL, , )


Estimation


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Fix parameters (i)

Imitation rates - patin , notin

Assume all patent systems (and imitation rates) are the same )patD ,

patF ,

notD and

notF

notF 0.25 Manseld and Romeo (1980)

patD 0.23 Manseld, Schwartz and Wagner (1981)

patD 0.415 Manseld, Schwartz and Wagner (1981)

Diusion rates - niDene:

in = i..nD

if i 6= n N then D = 1 and N. = 0.1.

Adoption rate in US is from 1.2 to 2.5 years ) 2.5 = 1US..USD+g


Estimation
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Fix parameters (ii)

Other Restrictions

r 0.07 Long run real return in US stock market 0.3 Capital elasticity from Lysko (1995)

chosen so that model gives gA = 0.018 from Lysko (1995) - averagefrom 1979-1990 of the mean of TFP growth in France Germany andUS.

Endogenous case: gL = 0 and = 1

Semiendogenous case: set so that gA = gL(1) = 0.018 withgL = 0.02.


Estimation


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Model - revised

With parameter restrictions and after applying logs the model is:

y = g(,X) + u

Where

y =

264 Relative Productivity - ln AiAN

Research - ln (siLi)

Patents - Pij

375 ,

X = Workforces - LiPatenting Costs relative to GDP - fij Estimator:

y g

,X

0y g

,X


Results
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Results
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Speed of Diusion
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From our calculations g' 3.35% in the endogenous case

Speed of DiusionResearch Performed in

Diusion to Germany France UK Japan USGermany 3.1280 0.0532 0.1102 0.2223 0.0399

France 0.2046 1.0903 0.1276 0.2574 0.0462

UK 0.0651 0.0196 0.7186 0.0819 0.0147Japan 0.1023 0.0308 0.0638 2.2780 0.0231

US 0.0930 0.0280 0.0580 0.1170 0.0399

Ideas diuse quickly in Germany and Japan but slowly in the US (?)

Japanese and German ideas diuse more rapidly while US ideasdiuse more slowly

Ideas diuse more rapidly to France


Results
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Percentage of adopted ideas that would have been initially adopted:in

in+g

High adoption percentage of domestic ideas in each country

High adoption percentage of German and Japanese ideas and loweradoption percentage of US ideas.


Growth Decomposition
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Using equation that separated growth into several sources we can nd the

importance of each country in aecting growth

US and Japanese research contribute signicantly to the growth in allcountries.


Counterfactuals
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Counterfactuals
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