The Global Diffusion of Ideas - Frontier Research, Global Impact. | … · 2018. 8. 13. · The...

The Global Diffusion of Ideas

Francisco Buera Ezra Oberfield

FRB Chicago Princeton

Conference in honor of Robert E. LucasBFI, University of Chicago

October 7-8, 2016

Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 1 / 38

By the problem of economic development I mean simply the problemof accounting for the observed pattern, across countries and across time,in levels and rates of growth of per capita income. This may seem toonarrow a definition, and perhaps it is, but thinking about incomepatterns will necessarily involve us in thinking about many other aspectsof societies too. so I would suggest that we withhold judgment on thescope of this definition until we have a clearer idea of where it leads us.

Lucas (1988), “On the Mechanics...”


RE Lucas - Journal of monetary economics, 1988 - ElsevierAbstract This paper considers the prospects for constructing a neoclassical theory of growth and international trade that is consistent with some of the main features of economic development. Three models are considered and compared to evidence: a model ...Cited by 25514 Related articles All 45 versions Cite Save More

RE Lucas - Carnegie-Rochester conference series on public policy, 1976 - North-HollandCited by 7188 Related articles All 24 versions Cite Save

RE Lucas Jr - Econometrica: Journal of the Econometric Society, 1978 - JSTORThis paper is a theoretical examination of the stochastic behavior of equilibrium asset prices in a one-good, pure exchange economy with identical consumers. A general method of constructing equilibrium prices is developed and applied to a series of examples.Cited by 5294 Related articles All 32 versions Cite Save

RE Lucas - Journal of economic theory, 1972 - ElsevierThis paper provides a simple example of an economy in which equilibrium prices and quantities exhibit what may be the central feature of the modern business cycle: a systematic relation between the rate of change in nominal prices and the level of real output. The ...Cited by 5118 Related articles All 21 versions Cite Save

RE Lucas - The American Economic Review, 1973 - JSTORThis paper reports the results of an empirical study of real output-inflation tradeoffs, based on annual time-series from eighteen countries over the years 1951-67. These data are examined from the point of view of the hypothesis that average real output levels are ...Cited by 3176 Related articles All 13 versions Cite Save More

RE Lucas, NL Stokey - Journal of monetary Economics, 1983 - ElsevierAbstract This paper is concerned with the structure and time-consistency of optimal fiscal and monetary policy in an economy without capital. In a dynamic context, optimal taxation means distributing tax distortions over time in a welfare-maximizing way. For a barter ...Cited by 1951 Related articles All 8 versions Cite Saved

RE Lucas - The American Economic Review, 1990 - JSTORThe egalitarian predictions of the simplest neoclassical models of trade and growth are well known and easy to explain, as they follow from entirely standard assumptions on technology alone. Consider two countries producing the same good with the same constant returns to ...Cited by 2876 Related articles All 22 versions Cite Saved More

RE Lucas Jr - The Bell Journal of Economics, 1978 - JSTORThis paper proposes a new theory of the size distribution of business firms. It postulates an underlying distribution of persons by managerial" talent" and then studies the division of persons into managers and employees and the allocation of productive factors across ...Cited by 3031 Related articles All 11 versions Cite Saved

RE Lucas - Journal of Monetary Economics, 1982 - ElsevierAbstract This paper is a theoretical study of the determination of prices, interest rates and currency exchange rates, set in an infinitely-lived two-country world which is subject both to stochastic endowment shocks and to monetary instability. Formulas are obtained for ...Cited by 1397 Related articles All 5 versions Cite Saved

On the mechanics of economic development

Econometric policy evaluation: A critique

Asset prices in an exchange economy

Expectations and the Neutrality of Money

Some international evidence on output-inflation tradeoffs

Optimal fiscal and monetary policy in an economy without capital

Why doesn't capital flow from rich to poor countries?

On the size distribution of business firms

Interest rates and currency prices in a two-country world


“But we know from ordinary experience that there are groupinteractions that are central to individual productivity and that involvegroups larger than the immediate family and smaller than the humanrace as a whole. Most of what we know we learn from other people. Wepay tuition to a few of these teachers, either directly or indirectly byaccepting lower pay so we can hang around them, but most of it we getfor free, and often in ways that are mutual - without a distinctionbetween student and teacher.”

Lucas (1988), “On the Mechanics...”, Section 6



Long held belief that openness affects the diffusion of technologies/ideas

“The progress of a society is all the more rapid in proportion as it ismore completely subjected to external influences.” Pirenne (1936)

Empirical debateI Sachs & Warner (95), Coe & Helpman (95), Frankel & Romer (99), Rodriguez

& Rodrik (00), Keller (09), Feyrer (09a,b), Pascali (2014)

Growth Miracles: Openness and protracted periods of growth

But standard mechanisms imply relatively small effectsI e.g., Connolly & Yi (14), Atkeson & Burstein (10)



Provide explicit model of diffusion process based on local interactionsI Kortum (1997), Eaton & Kortum (1999), Alvarez, Buera, & Lucas (2008), Lucas (2009), Lucas &

Moll (2014), Perla & Tonetti (2014) Luttmer (2012, 2014), Jovanovic & Rob (1989)

How does openness shape ideas to which individuals are exposed?I Alvarez, Buera, & Lucas (2014), Perla, Tonetti & Waugh (2014), Sampson (2014),

Monge-Naranjo (2012)

Combine new ideas with insights from others ⇒ “general” Frechet limitI related to model of random networks in Oberfield (2013)

Interface with static models of tradeI Eaton & Kortum (2002), Bernard, Eaton, Jensen, & Kortum (2003), Alvarez & Lucas (2007)

Country’s “stock of knowledge” depends only on trade shares, trade partners’knowledge

⇒ Use observed trade flows to quantify role of trade in facilitating idea flows



Which interactions facilitate exchange of ideas? Does it matter?I Learning from Sellers, Learning from ProducersI Determines how gains spill over across countries, Speed of convergence

Static and Dynamic Gains from Trade?I (Potentially) Large dynamic gains, protracted transition after opennessI Learning from Sellers: Dynamic gains especially large close to autarkyI Learning from Producers: Dynamic gains amplify static gains

Nest workhorse models of innovation, diffusionI Learning from Sellers: at either extreme, small dynamic gainsI Intermediate case: dynamic gains more important

Quantitative exploration: Rich enough to take to cross-country dataI Accounting for cross-sectional TFP-trade relationship...I Accounting for changes in TFP, growth miracles...



Two potential questions

1 What is role of cross-country idea flows in growth?F Many channels, e.g., trade, FDI,...

2 What is the role of trade in facilitating idea flows?F “Productivity spillover” from trade

Today’s focus second question

For most of talk: research effort is exogenousI Endogenize research intensity at endI Generalize result from Eaton & Kortum (1999)

F Across BGPs, research intensity does not depend on trade costs


Learning from an Arbitrary Source


Innovation and Diffusion

Continuum of goods s ∈ [0, 1]I For each good m managers (m is large)I Bertrand Competition

Manager with productivity qI Ideas arrive stochastically at rate αtI New idea has productivity zq′β

F Insight from someone with productivity q′ ∼ Gt(q′)F Original component z ∼ H(z)

I Adopts if zq′β > q

β measures strength of diffusionI Pure innovation: β = 0 (Kortum, 1997)I Pure diffusion: β = 1, H degenerate (ABL, 2008, 2014; with Poisson arrivals)


Productivity Distribution

Frontier of knowledge Ft(q)

I m managers for each good

I Probability best manager’s productivity is ≤ q

d

dtlog Ft(q) = −mαt Pr(zq′β > q)

= −mαt∫ ∞0

[1− Gt

((q/z)

1/β)]dH(z)


Frechet LimitAssumptions

Distr. of original component of ideas has Pareto tail: limz→∞1−H(z)z−θ

= 1

For now: Gt has sufficiently thin right tail: limq→∞ qβθ[1− Gt(q)] = 0

I Later: initial frontier F0(q) has sufficiently thin tail, (e.g., bounded)

β < 1

mαt = αeγt

Convenient to study productivity scaled by an exponential growth factor

Ft(q) = Ft(eνtq

)Gt(q) = Gt

(eνtq

)Proposition

As t→∞, Ft(q) = e−λtq−θ, λt = α

∫∞0xβθdGt(x)− νθλt

λt: stock of knowledge , ν = γ(1−β)θ : growth rate of productivity


Simple Example

Individuals learn from managers at frontier

Gt(q) = Ft(q)

Then stock of knowledge evolves as

λt = Γ(1− β)αλβt − νθλt

The detrended stock of knowledge in a balance growth path

λ ∝ α1

1−β

Compounding: New ideas lead to even better insights


Trade


World Economy (BEJK, 2003)

n countries, defined byI Labor, LiI Stock of knowledge, λiI Iceberg trade costs, κij

Household in i has Dixit-Stiglitz preferences Ci =[∫ 1

0ci(s)

ε−1ε ds

] εε−1

Production is linear, uses only labor

For manager in j, unit cost of providing good to country i is

wjκijq

Bertrand Competition:

pi(s) = min

ε

ε− 1

lowestunit cost

,second lowest

unit cost


Static Trade Equilibrium

Price indexP−θi ∝

∑j

λj(wjκij)−θ

Trade Shares

πij =λj(wjκij)

−θ∑k λk(wkκik)−θ

Labor market clearing (under balanced trade)

wiLi =∑j

πjiwjLj


Source distributions

1 Learn from Sellers (Alvarez-Buera-Lucas)I in proportion to expenditure on good

GSi (q) ≡∑j

∫s∈Sij |qj(s)<q

pi(s)ci(s)

PiCids

2 Learn from Producers (Perla-Tonetti-Waugh, Sampson)I Equal exposure to active domestic producers (uniformly)

GPi (q) ≡∑j

∫s∈Sji|qi(s)≤q

ds

Sij be set of goods for which j is lowest-cost provider for i


The Global Diffusion of ideas1 Learn from Sellers (Alvarez-Buera-Lucas)

λi ∝ αi∑j

πij

(λjπij

)β

I Expenditure-weighted average

I Selection: hold fixed λj , lower πij ⇒ import goods with higher q

2 Learn from Producers (Perla-Tonetti-Waugh, Sampson)

λi ∝ αi

(λiπii

)βI Impact of trade: Selection

F High productivity producers likely to expandF Low productivity producers likely to drop out


The Global Diffusion of ideas1 Learn from Sellers (Alvarez-Buera-Lucas)

λi ∝ αi∑j

πij

(λjπij

)βI To maximize growth:

λjλj′

=πijπij′

(=

λj (wjκij)−θ

λj′ (wj′κij′)−θ

)

2 Learn from Producers (Perla-Tonetti-Waugh, Sampson)

λi ∝ αi

(λiπii

)βI Growth is maximized with the highest trade exposure (lowest πii)


Gains from Trade


Gains from Trade

Real income is

yi ∝wiPi∝(λiπii

)1/θ

Static gains from trade: hold λ fixed

Dynamic gains from trade: operate through idea flows

Symmetric world (independent of the specification of learning)

yFT

yAUT= n

1θ︸︷︷︸

static

nβ

(1−β)θ︸︷︷︸dynamic

= n1θ

11−β


Gains from Trade

Real income is

yi ∝wiPi∝(λiπii

)1/θ

Static gains from trade: hold λ fixed

Dynamic gains from trade: operate through idea flows

What is the fate of a single country that is isolated?

I Consider world with n symmetric countries

I Trade among n− 1 countries is costless

I Trade to and from “deviant” economy incurs iceberg cost κn


Long-Run Gains from Trade: Single Deviant

0.01 0.1 0.5 10

0.2

0.4

0.6

0.8

1

1.2Learning from Sellers, 6

n1/3

- = 0- = 0.5- = 0.9

deviant openness, 1-:nn

0.01 0.1 0.5 10

0.2

0.4

0.6

0.8

1y

n

0.01 0.1 0.5 10

0.2

0.4

0.6

0.8

1

1.2Learning from Producers, 6

n1/3

deviant openness, 1-:nn

0.01 0.1 0.5 10

0.2

0.4

0.6

0.8

1y

n


Trade Liberalization

years0 20 40

0

0.2

0.4

0.6

0.8

1Autarky to Costless Trade

from sellersfrom producers

years0 20 40

0.8

0.85

0.9

0.95

11-:

n = 0.05 ! 0.20

- = 0.20- = 0.50- = 0.80

β = 0.5, θ = 4, TFP Growth rate on BGP = 0.01


Gains from Trade: Takeaways

Learning from sellers

I Static gains relevant when economy relatively openDynamic gains relevant when economy relatively closed

I For moderately open economy: Dynamic gains from reducing trade barriersF Small if β ≈ 0 or β ≈ 1F Larger when β in intermediate range

Learning from producers (uniformly)

I Simple amplification of static gains

I Slower transitional dynamics


Quantitative Exploration



Questions:

I Can openness account for a significant part of evolution of TFP?

I Can model account for the cross-section relationship between TFP and trade?

−0.2 −0.1 0 0.1−1.5

−1

−0.5

0

0.5

1

1.5

∆ log πii

∆ lo

g T

FP

slope = −2.26 (0.69)

−0.04−0.02 0 0.02 0.04−1.5

−1

−0.5

0

0.5

1

1.5

(∆ Π) TFP0

slope = 11.99 (2.87)

0.2 0.4 0.6−1.5

−1

−0.5

0

0.5

1

1.5

Π0 ∆ log TFP

slope = 0.30 (0.67)



Generalized trade model: intermediate inputs, capital, non-traded goods(Alvarez & Lucas, 2007)

Let Lit be equipped labor (= K1/3it (empit · hit)2/3, from the PWT)

Parameter ValueTrade Elasticity, θ 4Share of Non-Traded Goods 0.5Intermediate Good Share of Cost 0.5

Diffusion parameter, β:

I Agnostic: Explore the effects for various β (recalibrating γ)

I Heroic: d log TFP = 0.008 = γθ

11−β ⇒ β ≈ 0.7 (γ = pop. growth)

Focus on the case of learning from sellers to a country


Calibration

Two sets of residuals to exactly match trade and TFP

Calibrate the evolution of trade costs, κijt, to match bilateral trade flows

Arrival rate of ideas, αit: residual TFP level/growth

Two counterfactuals to measure contribution of trade

lnTFPi(αt, κt)

TFPi(α0, κ0)= ln

TFPi(α0, κt)

TFPi(α0, κ0)︸︷︷︸cont. from trade

+ lnTFPi(αt, κt)

TFPi(α0, κt)︸︷︷︸cont. from arrival rates

lnTFPi(αt, κt)

TFPi(α0, κ0)= ln

TFPi(αt, κ0)

TFPi(α0, κ0)︸︷︷︸cont. from arrival rates

+ lnTFPi(αt, κt)

TFPi(αt, κ0)︸︷︷︸cont. from trade


Development Dynamics, South Korea (vs. US)

Hold research intensities (α0) fixed at 1962 levels

1960 1980 20000.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6Korea

1960 1980 20000.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6US

data- = 0- = 0.6- = 0.9


Development Dynamics, Growth Miracles

1960 1970 1980 1990 2000

1

1.5

2

China

Data5

t, ,

0, -=0

5t, ,

0, -=0.7

data - 50, ,

t, -=0.7

1960 1970 1980 1990 2000

1

1.5

2

Korea

1960 1970 1980 1990 2000

1

1.5

2

Taiwan

1960 1970 1980 1990 2000

1

1.5

2

Thailand


Contribution of Trade: Transitions

-0 0.5 1

Fra

ctio

n ex

plai

ned

by tr

ade

0

0.1

0.2

0.3

0.4

0.5World Growth

, varying, constant

-0 0.5 1

0

0.1

0.2

0.3

0.4

0.5Cross-Sectional Variance

, varying, incl. cov., constant, incl. cov., varying, excl. cov., constant, excl. cov.


Distribution of TFP in Cross-section

Two counterfactuals to measure contribution of trade

lnTFPi(αi, κij)

TFPi(α, κ)= ln

TFPi(α, κij)

TFPi(α, κ)︸︷︷︸cont. from trade

+ lnTFPi(αi, κij)

TFPi(α, κij)︸︷︷︸cont. from arrival rates

lnTFPi(αi, κij)

TFPi(α, κ)= ln

TFPi(αi, κ)

TFPi(α, κ)︸︷︷︸cont. from arrival rates

+ lnTFPi(αi, κij)

TFPi(αi, κij)︸︷︷︸cont. from trade


Distribution of TFP in Cross-Section

-0 0.5 1

0

0.1

0.2

0.3

0.4

0.5

0.6Cross-Sectional Variance, 1962

-0 0.5 1

0

0.1

0.2

0.3

0.4

0.5

0.6Cross-Sectional Variance, 2000

, varying, incl. cov., constant, incl. cov., varying, excl. cov., constant, excl. cov.


Effect of Moving Niger to ...

years2000 2050 21000

0.1

0.2

0.3

0.4

0.5TFP, Niger

in Belgiumin Switzerland

years2000 2050 21000

0.1

0.2

0.3

0.4

0.51-:

ii, Niger


Incentives to Innovate

Labor used for production or R&D

Lit = LProductionit + LR&Dit

I Arrival of ideas: α = α× lI Tax Ti on profit (Parente & Prescott, 1994)

Result:I Across BGPs,

LR&DitLit

independent of trade barriers

F Market size ↑, but competition ↑F Like Eaton & Kortum (2001), Atkeson & Burstein (2010)

I But, openness ⇒ same R&D effort leads to better insights

F Related to Baldwin & Robert-Nicoud (2008)


Conclusions/Future Research

Present tractable model that incorporates large class of diffusion mechanisms,based on local interactions

Leading Example:

I Large dynamics gains from trade, specially for intermediate values of β

I able to account for the cross-sectional TFP-trade relationship

I ... generate growth miracles with a significant role for trade

Future research:

I Infer value for β: aggregate TFP-trade dynamics, e.g., Feyrer (2009a,b),Hanson & Muendler (2013), Levchenko & Zhang(2014), Pascali (2014); microevidence, e.g., Aitken & Harrison (1999), Javorcik (2004)

I Multinational Production/FDI: Ramondo & Rodriguez-Clare (2014)


Frechet Limit

PropositionGiven assumptions, the frontier of knowledge evolves as:

limm→∞

d lnFt(q)

dt= −αtq−θ

∫ ∞0

xβθdGt(x)

Define λt =∫ t−∞ ατ

∫∞0xβθdGτ (x)

Corollary

Suppose that limt→∞ λt =∞. Then limt→∞ Ft(λ1/θt q) = e−q

−θ.

Back

Learning from Producers

in proportion to employment

Gi(q) =

n∑j=1

∫ q

0

LjwjLiwi

(wiκjiPj

)1−ε

xε−1︸︷︷︸fraction of employment in x

∏k 6=j

Fk

(wkκikwiκii

x

)︸︷︷︸prob. j buys x from i

dFi(x)

back


uniformly

Gi(q) =

n∑j=1

∫ q

0

1

πii

∏k 6=j

Fk

(wkκjkwiκji

x

)dFi(x)

The evolution of the stock of knowledge

λi ∝(λiπii

)βback

Multivariate Pareto

H(z1, ..., zn) = max

1−

∑j

(ziz0

)− Θ1−ρ

1−ρ

, 0

Each marginal is distribution is Pareto

ρ ∈ [0, 1] like a correlation

Back

Endogenous Growth Case, β = 1Alvarez, Buera & Lucas (2013)

Learning from sellers

Trade only

Evolution of the distribution of productivities

∂ log(Fit(q))

∂t= −α

1−n∑j=1

∫ q

0

∏k 6=j

Fkt

(wkκikwjκij

x

)dFjt(x)

Endogenous Growth Case, β = 1Alvarez, Buera & Lucas (2013)

Growth rate in a BGP, ν = nα/θ

Tails converge if κij <∞

limq→∞

limt→∞

1− Fit (qeνt)

λq−θ= 1

Distribution not Frechet (log-logistic if κij = wi = 1)

Single Deviant: Stock of Knowledge

0 5 10 15 20 25 30 35 40 45 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Per−capita Income, y

n

years

Generalized Trade Model

Technology requiring an intermediate aggregate and labor

yi(q) =1

ηηζζ(1− η − ζ)1−η−ζqixi(q)ηki(q)ζ li(q)1−η−ζ

Intermediate (investment) aggregate technology

Xi =

[∫cxi(q)1−1/εdFi(q)

]ε/(ε−1)Fraction µ of the goods are tradable, i.e.,

p1−εi = (1− µ)

∫ ∞0

(pηiR

ζiw

1−η−ζi

q

)1−ε

dFj(q)

+ µ

n∑j=1

∫ ∞0

(pηjR

ζiw

1−ηj κij

q

)1−ε∏k 6=j

Fk

(pηkR

ζiw

1−η−ζk κik

pηjRζiw

1−η−ζj κij

q

)dFj(q)

Back

Speed of Convergence: Small Open Economy

For small open economy, speed of convergence is

If agents learn from sellers

γ

1− ΩSii − πii

1 + θ (1 + πii)+

β

1− β(1− ΩSii

)

If agents learn from producers

γ

1− ΩPii − πii

1 + θ (1 + πii)+

β

1− β

(1− ΩPii

)(1 + πii)

1 + θ (1 + πii)

where ΩSii ≡πii(λi/πii)

β∑j πij(λj/πij)

β and ΩPii ≡rii(λi/πii)

β∑j rji(λi/πji)

β .

Back

Calibrating Trade Costs

Use trade data from Feenstra et al. (2005), GDP from PWT 8.0 and theequilibrium relations

κijt = κjit =

[1− πiitπijt

1− πjjtπjit

(Zit

1− Zit

)(1− ZjtZjt

)] 12θ

where Zit solves

πiit =(1− µ) + µZ

1− ε−1θ

it

(1− µ) + µZ− ε−1

θit

.

Back

Distribution of TFP in 2000Calibration of homogeneous arrival rates α

I αi = αLΥi , calibrate Υ to match TFP ∝ L0.15 Back

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.7

0.75

0.8

0.85

0.9

0.95

1

Diffusion Parameter, β

Mea

n S

quar

ed E

rror

/std

(TF

P)

Learning from SellersLearning from Sellers, λ

−i data


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