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...”
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 2 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 3 / 38
“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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 4 / 38
The Global Diffusion of Ideas
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)
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 5 / 38
The Global Diffusion of Ideas
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)
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 5 / 38
The Global Diffusion of Ideas
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 6 / 38
The Global Diffusion of Ideas
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 6 / 38
The Global Diffusion of Ideas
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...
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 7 / 38
The Global Diffusion of Ideas
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 8 / 38
Learning from an Arbitrary Source
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 9 / 38
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)
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 10 / 38
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)
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 11 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 12 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 12 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 13 / 38
Trade
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 14 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 15 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 16 / 38
The Global Diffusion of Ideas
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 17 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 18 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 19 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 19 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 19 / 38
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)
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 20 / 38
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)
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 20 / 38
Gains from Trade
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 21 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 22 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 22 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 23 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 23 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 24 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 25 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 26 / 38
Quantitative Exploration
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 27 / 38
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)
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 28 / 38
Quantitative Exploration
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 29 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 30 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 31 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 32 / 38
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.
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 33 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 34 / 38
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.
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 35 / 38
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
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 36 / 38
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)
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 37 / 38
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)
Buera & Oberfield (FRB Chicago, Princeton) β: Strength of Diffusion, λ: Stock of Knowledge October 2016 38 / 38
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
Learning from Producers
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
Learning from Producers