1. No category

The Global Diffusion of Ideas
Francisco Buera
Ezra Oberfield
FRB Chicago
Princeton
April 2015
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
1 / 44
The Global Diffusion of Ideas
Long held belief that openness affects the diffusion of technologies/ideas
Empirical debate
I
Sachs & Warner (95), Coe & Helpman (95), Frankel & Romer (99), Rodriguez
& Rodrik (00), Keller (09), Feyrer (09a,b)
Growth Miracles: Openness and protracted periods of growth
But standard mechanisms imply relatively small effects
I
e.g., Connolly & Yi (14)
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
2 / 44
The Global Diffusion of Ideas
Long held belief that openness affects the diffusion of technologies/ideas
Empirical debate
I
Sachs & Warner (95), Coe & Helpman (95), Frankel & Romer (99), Rodriguez
& Rodrik (00), Keller (09), Feyrer (09a,b)
Growth Miracles: Openness and protracted periods of growth
But standard mechanisms imply relatively small effects
I
e.g., Connolly & Yi (14)
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
2 / 44
The Global Diffusion of Ideas
Provide explicit model of diffusion process based on local interactions
I
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
I
⇒
“general” Frechet limit
related to model of random networks in Oberfield (2013)
Interface with static models of trade, multinational production (MP)
I
Eaton & Kortum (2002), Bernard, Eaton, Jensen, & Kortum (2003), Alvarez & Lucas (2007),
Ramondo & Rodriguez-Clare (2014)
Comparative advantage: Asymmetric countries, transition dynamics
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
3 / 44
The Global Diffusion of Ideas
How does openness affect development? Potential for growth miracles?
Which interactions facilitate exchange of ideas? Does it matter?
Role of policy, international barriers in shaping interactions?
Rich and tractable enough to take to cross-country data
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
4 / 44
The Global Diffusion of Ideas
How does openness affect development? Potential for growth miracles?
I
I
(Potentially) Large dynamic gains, protracted transition after openness
Especially for countries close to autarky
Which interactions facilitate exchange of ideas? Does it matter?
Role of policy, international barriers in shaping interactions?
Rich and tractable enough to take to cross-country data
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
4 / 44
The Global Diffusion of Ideas
How does openness affect development? Potential for growth miracles?
I
I
(Potentially) Large dynamic gains, protracted transition after openness
Especially for countries close to autarky
Which interactions facilitate exchange of ideas? Does it matter?
I
I
Determines how gains spillover across countries
Speed of convergence
Role of policy, international barriers in shaping interactions?
Rich and tractable enough to take to cross-country data
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
4 / 44
The Global Diffusion of Ideas
How does openness affect development? Potential for growth miracles?
I
I
(Potentially) Large dynamic gains, protracted transition after openness
Especially for countries close to autarky
Which interactions facilitate exchange of ideas? Does it matter?
I
I
Determines how gains spillover across countries
Speed of convergence
Role of policy, international barriers in shaping interactions?
I
Free-trade not necessarily best policy
Rich and tractable enough to take to cross-country data
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
4 / 44
The Global Diffusion of Ideas
How does openness affect development? Potential for growth miracles?
I
I
(Potentially) Large dynamic gains, protracted transition after openness
Especially for countries close to autarky
Which interactions facilitate exchange of ideas? Does it matter?
I
I
Determines how gains spillover across countries
Speed of convergence
Role of policy, international barriers in shaping interactions?
I
Free-trade not necessarily best policy
Rich and tractable enough to take to cross-country data
I
I
Can we explain growth miracles?
Work in progress, some preliminary results today...
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
4 / 44
Roadmap
Learning from an arbitrary source distribution, Frechet Limit
Trade
I
I
I
Illustrate implications of alternative learning mechanisms
Static and dynamic gains from trade
Long-run and short-run (liberalization)
Incentives for Innovation
Quantitative exploration
I
South Korea: trade and development in the postwar period
(probably not today) Trade and Multinational Production
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
5 / 44
Learning from an Arbitrary Source
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
6 / 44
Innovation and Diffusion
Continuum of goods s ∈ [0, 1]
I
I
For each good m managers (m is large)
Bertrand Competition
Manager with productivity q
I
Ideas arrive stochastically at rate αt
I
New idea has productivity
F
F
I
zq 0β
˜ t (q 0 )
Insight from someone with productivity q 0 ∼ G
Original component z ∼ H(z)
Adopts if
zq 0β > q
β measures strength of diffusion
I
I
Pure innovation: β = 0 (Kortum (1997))
Pure diffusion: β = 1, H degenerate (ABL (2008, 2014), with Poisson arrivals)
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
7 / 44
Productivity Distribution
Distribution of productivity among managers Mt (q)
Frontier of knowledge F˜t (q) = Mt (q)m
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
8 / 44
Productivity Distribution
Distribution of productivity among managers Mt (q)
Frontier of knowledge F˜t (q) = Mt (q)m
The distribution of productivities at time t + ∆
i
h
Mt+∆ (q) = Mt (q) (1 − αt ∆) + αt ∆ Pr(zq 0β ≤ q)
|
{z
}
| {z }
no new idea
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
new idea ≤ q
April 2015
8 / 44
Productivity Distribution
Distribution of productivity among managers Mt (q)
Frontier of knowledge F˜t (q) = Mt (q)m
The distribution of productivities at time t + ∆
i
h
Mt+∆ (q) = Mt (q) (1 − αt ∆) + αt ∆ Pr(zq 0β ≤ q)
|
{z
}
| {z }
no new idea
new idea ≤ q
Taking the limit as ∆ → 0
d
log Mt (q) = −αt Pr(zq 0β > q)
dt
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
8 / 44
Productivity Distribution
Distribution of productivity among managers Mt (q)
Frontier of knowledge F˜t (q) = Mt (q)m
The distribution of productivities at time t + ∆
i
h
Mt+∆ (q) = Mt (q) (1 − αt ∆) + αt ∆ Pr(zq 0β ≤ q)
|
{z
}
| {z }
no new idea
new idea ≤ q
Taking the limit as ∆ → 0
1 d
d
log F˜t (q) =
log Mt (q) = −αt Pr(zq 0β > q)
m dt
dt
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
8 / 44
Productivity Distribution
Distribution of productivity among managers Mt (q)
Frontier of knowledge F˜t (q) = Mt (q)m
The distribution of productivities at time t + ∆
i
h
Mt+∆ (q) = Mt (q) (1 − αt ∆) + αt ∆ Pr(zq 0β ≤ q)
|
{z
}
| {z }
new idea ≤ q
no new idea
Taking the limit as ∆ → 0
1 d
d
log F˜t (q) =
log Mt (q) = −αt Pr(zq 0β > q)
m dt
dt
Z ∞h
i
˜ t (q/z)1/β dH(z)
= −αt
1−G
0
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
8 / 44
Frechet Limit
Assumptions
Distr. of original component of ideas has Pareto tail: limz→∞
1−H(z)
z −θ
=1
˜ t has sufficiently thin right tail: limq→∞ q βθ [1 − G
˜ t (q)] = 0
For now: G
I
Later: initial distribution M0 (q) has sufficiently thin tail
β<1
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
9 / 44
Frechet Limit
Assumptions
1−H(z)
z −θ
Distr. of original component of ideas has Pareto tail: limz→∞
=1
˜ t has sufficiently thin right tail: limq→∞ q βθ [1 − G
˜ t (q)] = 0
For now: G
I
Later: initial distribution M0 (q) has sufficiently thin tail
β<1
Convenient to study productivity scaled by number of managers
1
1
˜ t m (1−β)θ
Gt (q) = G
Ft (q) = F˜t m (1−β)θ q
q
Proposition
Formal Statement
As m → ∞, t → ∞,
Ft (q) = e−λt q
−θ
,
λ˙ t = αt
R∞
0
xβθ dGt (x)
λt : stock of knowledge
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
9 / 44
Simple Example
Individuals learn from managers at frontier
Gt (q) = Ft (q)
Then stock of knowledge evolves as
λ˙ t = Γ(1 − β)αt λβt
Long-run growth requires the arrival rate grows,
α
˙t
αt
=γ
Implies growth in stock of knowledge at rate
λ˙
γ
=
λ
1−β
Compounding: New ideas lead to even better insights
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
10 / 44
Trade
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
11 / 44
World Economy (BEJK, 2003)
n countries, defined by
I
I
I
Labor, Li
Stock of knowledge, λi
Iceberg trade costs, κij
Household in i has Dixit-Stiglitz preferences Ci =
ε
i ε−1
hR
ε−1
1
c (s) ε ds
0 i
Production is linear, uses only labor
For manager in j, unit cost of providing good to country i is
wj κij
q
Bertrand Competition:
pi (s) = min
Buera & Oberfield (FRB Chicago, Princeton)
ε
lowest
second lowest
,
unit cost
ε − 1 unit cost
The Global Diffusion of Ideas
April 2015
12 / 44
Static Trade Equilibrium
Price index
Pi−θ ∝
X
λj (wj κij )−θ
j
Trade Shares
λj (wj κij )−θ
πij = P
−θ
k λk (wk κik )
Labor market clearing (under balanced trade)
X
wi Li =
πji wj Lj
j
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
13 / 44
The Global Diffusion of Ideas
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
14 / 44
Diffusion of ideas
1
2
Learn from Sellers
I
Equally exposed to goods consumed (Alvarez-Buera-Lucas)
I
Learn in proportion to quantity consumed (or expenditure)
Learn from Producers
I
Equal exposure to active domestic producers (Perla-Tonetti-Waugh, Sampson)
I
Exposed in proportion to labor used (Monge-Naranjo)
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
15 / 44
Source distributions
Let Sij be set of goods for which j is lowest-cost provider for i
Learning from sellers
I
in proportion to expenditure on good
GSi (q)
≡
XZ
s∈Sij |qj (s)<q
j
pi (s)ci (s)
ds
Pi Ci
Learning from producers
I
in proportion to labor used to produce good
GP
i (q)
≡
XZ
j
Buera & Oberfield (FRB Chicago, Princeton)
s∈Sji |qi (s)≤q
The Global Diffusion of Ideas
1 κji
cj (s)ds
Li qi (s)
April 2015
16 / 44
Learning From Sellers
λ˙ i = αi
Z
∞
βθ
q dGi (q)
∝
0
αi
X
j
πij
λj
πij
β
Expenditure-weighted average
Selection: hold fixed λj
I
lower πij
⇒
import goods with higher q
To maximize growth:
λj
πij
=
λj 0
πij 0
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
17 / 44
Learning From Sellers
λ˙ i = αi
Z
∞
βθ
∝
q dGi (q)
0
αi
X
πij
j
λj
πij
β
Expenditure-weighted average
Selection: hold fixed λj
I
lower πij
⇒
import goods with higher q
To maximize growth:
λj
πij
=
λj 0
πij 0
I
I
−θ
=
λj (wj κij )
!
−θ
λj 0 (wj 0 κij 0 )
Import more from high wage countries
Conflicts with maximizing current welfare
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
17 / 44
Learning from Producers
Stock of knowledge
λ˙ i = αi
Z
∞
βθ
q dGi (q)
∝
αi
0
Revenue-weighted average:
X
j
rji =
Pπji Pj Cj
k πki Pk Ck
rji
λi
πji
β
is i’s revenue share
Impact of trade: Selection
I
I
High productivity producers likely to expand
Low productivity producers likely to drop out
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
18 / 44
Gains from Trade
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
19 / 44
Static and Dynamic Gains from Trade
Real income is
wi
∝
yi ∝
Pi
λi
πii
1/θ
Static gains from trade: hold λ fixed
Dynamic gains from trade: operate through idea flows
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
20 / 44
A Symmetric World
Consider world with n symmetric countries
Long-run gains from trade
yF T
=
y AU T
1
nθ
|{z}
static
β
1
1
(1−β)θ
θ 1−β
n
| {z } = n
dynamic
Dynamic gains from trade
I
I
Increase with β
Similar to input-output multiplier
Note: For special case of symmetric world, specifications of learning are identical
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
21 / 44
Long-Run Gains from Trade: Reduction in common κ
1/θ
Stock of Ideas, λ
per−capita income
1
1
0.8
0.8
0.6
0.6
0.4
0.4
β = 0.1
β = 0.5
β = 0.9
0.2
0
0
0.5
openness, 1/κ
Buera & Oberfield (FRB Chicago, Princeton)
0.2
1
0
0
The Global Diffusion of Ideas
0.5
openness, 1/κ
April 2015
1
22 / 44
Long-Run Gains from Trade: Single Deviant
What is the fate of a single country that is isolated?
Trade among n − 1 countries is costless
Trade to and from “deviant” economy incurs iceberg cost κn
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
23 / 44
Long-Run Gains from Trade: Single Deviant
1/θ
Learning from Sellers, λn
1/θ
Learning from Producers, λn
1
1
0.8
0.8
0.6
0.6
β=0
β = 0.5
β = 0.9
0.4
0.2
0
0
0.5
0.4
0.2
1
0
0
0.5
yn
yn
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0.5
1
deviant openness, 1/κn
Buera & Oberfield (FRB Chicago, Princeton)
1
0
0
0.5
1
deviant openness, 1/κn
The Global Diffusion of Ideas
April 2015
24 / 44
Single Deviant: Arrival Rate
Learning from Sellers
Learning from Producers
1/θ
(λ /λ (κ =1))1/θ
(λ /λ (κ =1))
n
1
n
n
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0.5
1
0
0
1
1
0.8
0.6
α1/(1+θ)
= 0.5
n
0.4
α1/(1+θ)
= 0.9
n
0.4
0.2
α1/(1+θ)
=1
n
0.2
Buera & Oberfield (FRB Chicago, Princeton)
1
(λn/λn(κn=1))1/θ
0.8
0.5
1
deviant openness, 1/κn
n
0.5
(λn/λn(κn=1))1/θ
0
0
1
0.6
0
0
0.5
1
deviant openness, 1/κn
The Global Diffusion of Ideas
April 2015
25 / 44
Long-Run Gains: Takeaways
Static gains relevant when economy relatively open
Dynamic gains relevant when economy relatively closed
For moderately open economy, dynamic gains non-monotonic in β
Learning from producers: open economy can get better insights if more
isolated
Low arrival rate compounded when
I
I
Learning from producers
Close to autarky
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
26 / 44
Speed of Convergence: Small Open Economy
For small open economy, (relatively) simple expressions for speed of
convergence expressions
Lessons:
I
Faster with high β
I
α plays no role
I
Slower with learning from domestic producers
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
27 / 44
Trade Liberalization, κn = 100 → κ0n = 1
1/θ
n
stock of ideas, λ
per−capita income, y
n
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0
0
from sellers
from producers
20
years
40
0.2
0
0
20
years
40
β = 0.5, θ = 5, TFP Growth rate on BGP = 0.01, κ1 = 1
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
28 / 44
Trade Liberalization, κn = 100 → κ0n = 1
1/θ
n
stock of ideas, λ
per−capita income, y
n
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0
0
from sellers
from producers
20
years
40
0.2
0
0
20
years
40
β = 0.6, θ = 5, TFP Growth rate on BGP = 0.01, κ1 = 1
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
29 / 44
Incentives to Innovate
roduction
Ljt = LP
+ LR&D
jt
jt
Across BGPs,
LR&D
jt
Ljt
independent of trade barriers
I
Market size ↑, but competition ↑
I
Like Eaton & Kortum (2001), Atkeson & Burstein (2010)
But, openness
I
⇒
same R&D effort leads to better insights
Related to Baldwin & Robert-Nicoud (2008)
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
30 / 44
Quantitative Exploration
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
31 / 44
Quantitative Exploration
Generalized trade model: intermediate inputs, capital, non-traded goods
1/3
2/3
Let Lit be equipped labor (= Kit (popit · hit )
, from the PWT)
Question: Can openness account for a significant part of the evolution of
TFP of growth miracles?
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
32 / 44
Calibration
Calibrate the evolution of trade costs, κijt , to match bilateral trade flows
Parameter
θ
Share of Non-Traded Goods
Intermediate Good Share of Cost
Capital Share of VA
TFP Growth on BGP
Value
5
0.5
0.5
1/3
1% per year
αit , β?
I
I
Homogenous α. How much does diffusion contribute for various β?
Heterogenous αit . Match TFP in 1960. Allow αi to change?
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
33 / 44
Distribution of TFP, 1962
TFP/TFP(US), model
β=0
β = 0.25
1.4
1.4
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0
0.5
1
1.5
0.4
0
0.5
TFP/TFP(US), model
β = 0.75
1.4
1.2
1.2
1
1
0.8
0.8
0.6
0.6
Buera & Oberfield (FRB Chicago, Princeton)
0.5
1
TFP/TFP(US), data
1.5
β = 0.9
1.4
0.4
0
1
1.5
0.4
0
0.5
1
TFP/TFP(US), data
The Global Diffusion of Ideas
1.5
April 2015
34 / 44
Development Dynamics, South Korea (vs. US)
Learning From Sellers
Korean TFP
Learning From Producers
Korean TFP
2
2
1.8
1.8
1.6
1.6
1.4
1.4
1.2
1.2
1
1960
1
1980
2000
1960
US TFP
1.6
1.4
1.4
1.2
1.2
1
1
Buera & Oberfield (FRB Chicago, Princeton)
2000
US TFP
1.6
1960
1980
1980
2000
1960
The Global Diffusion of Ideas
data
β=0
β = 0.25
β = 0.75
β = 0.9
1980
2000
April 2015
35 / 44
Development Dynamics, South Korea (vs. US)
TFP, Korea
TFP, US
2
2
1.8
1.8
data
β = 0.0, κt, α0
1.6
1.6
β = 0.9, κt, α0
1.4
1.4
1.2
1.2
1
1
1960
1980
Buera & Oberfield (FRB Chicago, Princeton)
2000
1960
The Global Diffusion of Ideas
β = 0.9, κ0, αt
β = 0.9, κt, αt
1980
2000
April 2015
36 / 44
Other Applications/Extensions
Trade and Multinational Production
Incentives for Innovation: endogenizing α
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
37 / 44
Multinational Production (MP)
Multinational Production (build on Ramondo & Rodriguez-Clare (2013))
Manager associated with
I
I
Home country i
Profile of productivities, {q1 , ..., qn }
Iceberg MP costs δij
Trade equilibrium: Eaton-Kortum
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
38 / 44
Multinationals and Learning
Manager with {q1 , ..., qn } draws insight from good with q 0
Location-specific {z1 , ..., zn }, drawn from H(z1 , ..., zn )
New Profile
o
n
q 0β }, ..., max{qn , z 1−β
q 0β }
max{q1 , z 1−β
n
1
{z1 , ..., zn } drawn from multivariate Pareto, correlation ρ
Details
Fit (q1 , ..., qn ) is multivariate Frechet
−λit
Fit = e
P
−
j
qj
θ
1−ρ
!1−ρ
and λ˙ it = α
Z
∞
q βθ dGit (q)
0
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
39 / 44
Multinational Production
Learning from Sellers & Producers
Sellers:
λ˙ i
∝
α
XX
j
Producers:
λ˙ i
∝
α
XX
j
where rjik =
πijk
k
rjik
k
1−ρ
πijk
[
1−ρ
πjik
[
λk
P
l
λk
P
l
!β
ρ
πilk ]
!β
ρ
πjlk ]
wj πjik
wi
Autarky vs Free Trade, Free MP
(2−ρ)β
2−ρ
yF T
1−β
θ
=n
×n
AU
T
|
{z
}
|
{z }
y
static
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
dynamic
April 2015
40 / 44
Trade and FDI
Are trade and FDI complements or substitutes?
Let y(κ, δ) be real income for symmetric world with
I
I
trade costs κ
FDI costs δ
Depends on ρ. Two polar cases:
y(κ, δ)
lim
=
ρ→0 y(1, 1)
1 + (n − 1)κ−θ(1−β)
n
1 + (n − 1)δ −θ(1−β)
n
1
θ(1−β)
and
y(κ, δ)
= max
lim
ρ→1 y(1, 1)
1 + (n − 1)κ−θ(1−β)
n
Buera & Oberfield (FRB Chicago, Princeton)
1
θ(1−β)
1 + (n − 1)δ −θ(1−β)
,
n
The Global Diffusion of Ideas
April 2015
41 / 44
Opening to Trade and/or MP, ρ = 0.5
1/θ
n
Stock of Ideas, λ
per−capita income, y
n
1
1
0.8
0.8
0.6
0.6
trade+MP
only trade
only MP
0.4
0
20
years
β = 0.5,
αS
40
0.4
0
20
years
40
αS
= 0.1, ρ = 0.5, κ = 100 → 2.15, δ = 100 → 3
+ αP
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
42 / 44
Opening to Trade and/or MP, ρ = 0.1
1/θ
n
Stock of Ideas, λ
per−capita income, y
n
1
1
0.8
0.8
0.6
0.6
trade+MP
only trade
only MP
0.4
0
20
years
β = 0.5,
αS
40
0.4
0
20
years
40
αS
= 0.1, ρ = 0.1, κ = 100 → 2.15, δ = 100 → 3
+ αP
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
43 / 44
Ongoing/Future Work
Full quantitative exploration
I
Calibrate β to match the effect of trade on GDP estimated by Feyrer (09) (?)
I
Quantify the dynamic gains from trade/ impact of trade on growth miracles,
e.g., Korea development experience
Buera & Oberfield (FRB Chicago, Princeton)
The Global Diffusion of Ideas
April 2015
44 / 44
Frechet Limit
Proposition
Given assumptions, the frontier of knowledge evolves as:
Z ∞
d ln Ft (q)
= −αt q −θ
xβθ dGt (x)
lim
m→∞
dt
0
Define λt =
Rt
−∞
ατ
R∞
0
xβθ dGτ (x)
Corollary
−θ
1/θ
Suppose that limt→∞ λt = ∞. Then limt→∞ Ft (λt q) = e−q .
Back
Learning from Producers
in proportion to employment
Gi (q) =
n Z
X
j=1
0
q
Lj wj
Li wi
|
f raction of
back
1−ε
Y
wk κik
xε−1
Fk
x dFi (x)
wi κii
} |k6=j
{z
}
employment in x
wi κji
Pj
{z
prob. j buys x f rom i
Learning from Producers
uniformly
Gi (q) =
n Z
X
j=1
0
q
1 Y
wk κjk
Fk
x dFi (x)
πii
wi κji
k6=j
The evolution of the stock of knowledge
λ˙ i ∝
back
λi
πii
β
Multivariate Pareto




1−ρ 
Θ


X zi − 1−ρ

H(z1 , ..., zn ) = max 1 − 
,0


z0


j
Each marginal is distribution is Pareto
ρ ∈ [0, 1] like a correlation
Back
Endogenous Growth Case, β = 1
Alvarez, Buera & Lucas (2013)
Learning from sellers
Trade only
Evolution of the distribution of productivities


n Z q Y
X
∂ log(Fit (q))
wk κik
= −α 1 −
Fkt
x dFjt (x)
∂t
wj κij
j=1 0
k6=j
Endogenous Growth Case, β = 1
Alvarez, Buera & Lucas (2013)
Growth rate in a BGP, ν = nα/θ
Tails converge if κij < ∞
1 − Fit (qeνt )
=1
q→∞ t→∞
λq −θ
lim lim
Distribution not Frechet (log-logistic if κij = wi = 1)
Single Deviant: Stock of Knowledge
Per−capita Income, yn
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
5
10
15
20
25
years
30
35
40
45
50
Generalized Trade Model
Technology requiring an intermediate aggregate and labor
yi (q) =
1
qi xi (q)η ki (q)ζ li (q)1−η−ζ
η η ζ ζ (1 − η − ζ)1−η−ζ
Intermediate (investment) aggregate technology
Z
Xi =
/(−1)
cxi (q)1−1/ dFi (q)
Fraction µ of the goods are tradable, i.e.,
p1−ε
i
∞
Z
= (1 − µ)
0
+µ
n Z
X
j=1
Back
0
∞
pηi Riζ wi1−η−ζ
q
!1−ε
pηj Riζ wj1−η κij
q
dFj (q)
!1−ε
Y
k6=j
Fk
pηk Riζ wk1−η−ζ κik
pηj Riζ wj1−η−ζ κij
!
q dFj (q)
Speed of Convergence: Small Open Economy
For small open economy, speed of convergence is
If agents learn from sellers
ΩSii − πii
β
S
γ 1−
+
1 − Ωii
1 + θ (1 + πii ) 1 − β
If agents learn from producers
)
(
1 − ΩP
β
ΩP
ii (1 + πii )
ii − πii
γ 1−
+
1 + θ (1 + πii ) 1 − β 1 + θ (1 + πii )
where ΩSii ≡
Back
β
Pπii (λi /πii ) β
π
(λ
/π
)
ij
j
ij
j
and ΩP
ii ≡
β
Prii (λi /πii ) β .
r
(λ
/π
)
ji
i
ji
j