Knowledge, Di¤usion and Reallocation
Hugo A. Hopenhayn
UCLA

May 28, 2012

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 2012

1 / 42

Introduction
Reallocation

Quantitatively important
Contributes to productivity and di¤usion of new ideas
Recent contributions: barriers to reallocation very costly
Results are very sensitive to assumptions about returns to scale or
demand elasticity.

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 2012

2 / 42

Introduction
Returns to scale and knowledge transmission

Fixed factors.vs. replication
Links to knowledge transmission – in general costly to replicate.
What is …xed or not may depend on incentives for knowledgetransmission
Develop a deeper theory of replication/knowledge transmission

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 2012

3 / 42

Roadmap

1

Background: example on reallocation and returns to scale

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 20124 / 42

Roadmap

1
2

Background: example on reallocation and returns to scale
Theory of learning and replication of knowledge

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 20124 / 42

Roadmap

1
2
3

Background: example on reallocation and returns to scale
Theory of learning and replication of knowledge
Policy experiment - sensitive to incentives for knowledge accumulation

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 20124 / 42

Roadmap

1
2
3
4

Background: example on reallocation and returns to scale
Theory of learning and replication of knowledge
Policy experiment - sensitive to incentives for knowledge accumulation
Links to …rm dynamics.

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 20124 / 42

Example: gains to reallocation and returns to scale…rm i has technology qi = zi niα

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 20125 / 42

Example: gains to reallocation and returns to scale…rm i has technology qi = zi niα
z1 = 1, z2 = z > 1
Total labor endowment = 2

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 20125 / 42

Example: gains to reallocation and returns to scale…rm i has technology qi = zi niα
z1 = 1, z2 = z > 1
Total labor endowment = 2
Initial situation: n1 = n2 = 1, q = 1 + z
after reallocation marginal products equalized.

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 20125 / 42

Example: gains to reallocation and returns to scale…rm i has technology qi = zi niα
z1 = 1, z2 = z > 1
Total labor endowment = 2
Initial situation: n1 = n2 = 1, q = 1 + z
after reallocation marginal products equalized.
Upper bound for gains: α = 1
n1 = 0, n2 = 2 and q = 2z.

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 20125 / 42

Example: gains to reallocation and returns to scale…rm i has technology qi = zi niα
z1 = 1, z2 = z > 1
Total labor endowment = 2
Initial situation: n1 = n2 = 1, q = 1 + z
after reallocation marginal products equalized.
Upper bound for gains: α = 1
n1 = 0, n2 = 2 and q = 2z.
α < 1, then smaller gains.

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 20125 / 42

Example: productivity gains

α = 0.5
α = 0.8
α=1

z = 1.52%
7%
20%

Hugo A. Hopenhayn (UCLA)

z =2
5%
17%
33%

z =4
17%
39%
60%

Knowledge, Di¤usion and Reallocation

May 28, 2012

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Gains depend on returns to scale and speed of reallocation.
Maximum with CRS (case α = 1)
Models explicitly or implicitly make assumptions about this.

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 20127 / 42Predicted gains from lowered barriers:

Hopenhayn and Rogerson
Eaton and Kortum

5%
3.5%

eliminate layo¤ costs
loss going to autharky

Burstein Monge
RamondoMcGrattan and Prescott

8% to 15%
50%
30%

zero cost to FDI
zero costs to FDIform union 20 countries

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 20128 / 42

A model of learning and di¤usion

GE economy, …xed labor endowment L, representative agent –preferences: balanced growth
Z

e rt

U

=

r

= ρ + θgc (t )1 θ
dt
1 θTechnology: Solow (vintage model) meets Lucas (adjustment cost)
Basic component: knowledge capital pair (z, k ) : z is knowledge
embodied in this kproduction technology zf (k, n) , CRS
f (k, n) = min (k, n) and θ = 1 for this talk.

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 2012

9 / 42

Technology for replicationk̇ (z ) has cost Ck̇kzk, depreciation δk.

C ( ) increasing, convex.
CRS in k, k̇
More costly to replicate better knowledge

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201210 / 42

Optimal Accumulationv (z, t ) value of one unit of k (z ) at time t

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201211 / 42

Optimal Accumulationv (z, t ) value of one unit of k (z ) at time t
Bellman equation:(r + δ) v (z, t ) =z w (t ) + maxk̇ v (z, t ) k̇ C k̇ z + v2 (z, t )Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201211 / 42

Optimal Accumulationv (z, t ) value of one unit of k (z ) at time t
Bellman equation:(r + δ) v (z, t ) =z w (t ) + maxk̇ v (z, t ) k̇ C k̇ z + v2 (z, t )Optimal replication:

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201211 / 42

Optimal Accumulationv (z, t ) value of one unit of k (z ) at time t
Bellman equation:(r + δ) v (z, t ) =z w (t ) + maxk̇ v (z, t ) k̇ C k̇ z + v2 (z, t )Optimal replication:v (z, t ) = C 0 k̇ z

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201211 / 42

Optimal Accumulationv (z, t ) value of one unit of k (z ) at time t
Bellman equation:(r + δ) v (z, t ) =z w (t ) + maxk̇ v (z, t ) k̇ C k̇ z + v2 (z, t )Optimal replication:v (z, t ) = C 0 k̇ z
k̇ (z ) /k (z ) increasing in z

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201211 / 42

Rates of replication
Knowledge replication

55.0%

growth rate of k(z)

45.0%

35.0%

25.0%

15.0%

5.0%

-5.0%
1.00

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

0.55

0.50

z

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201212 / 42Entry of new vintages

Technological frontier γ (t ) = e gt
Technology for entry: one worker ! k0 units of knowledge capital oftype x γ (t )x 2 [0, 1]

F (dx )

Heterogeneity in productivity within a cohort
Coexistence of several cohorts

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201213 / 42Equilibrium with no new arrivals of z

g =0
Fixed labor endowment L
Initial distribution k (z ) with highest z̄
Converge to steady state: k (z̄ ) = L (if C 0 (0) = 0)Complete reallocation: all resources ‡ow to most productive

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201214 / 42Balanced growth pathw ( t ) = w0 γ ( t )Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201215 / 42Balanced growth pathw ( t ) = w0 γ ( t )knowledge capital z is discontinued when w (t ) > z

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201215 / 42Balanced growth pathw ( t ) = w0 γ ( t )knowledge capital z is discontinued when w (t ) > z

Can normalize all to frontier γ (t )Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201215 / 42Balanced growth pathw ( t ) = w0 γ ( t )knowledge capital z is discontinued when w (t ) > z

Can normalize all to frontier γ (t )Normalized z (t ) value falls at the rate of technological progress g .

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201215 / 42Balanced growth pathw ( t ) = w0 γ ( t )knowledge capital z is discontinued when w (t ) > z

Can normalize all to frontier γ (t )Normalized z (t ) value falls at the rate of technological progress g .
Vintage is active and producing while z (t ) > w0 . When z (t ) = w0 it
is discontinued and the stock k (t ) lost.
Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201215 / 42Life cycle of new innovation

Innovator starts with k0 units of knowledge capitalz0 2 [0, 1] , γ(t ) = 1
Active only if z0 > w (t ) .

Replicates at declining rate
Shut down after s periods when z0 = e gs w (t )Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201216 / 42Life cycle of innovation

Technologies and Knowledge Capital(path when all mass of F is at 1)
16

14

12

measure of z's

10

8

6

4

2

0
1

42

83

124 165 206 247 288 329 370 411 452 493 534 575 616 657 698 739 780 821 862 903 944 985zHugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201217 / 42Stationary distribution of knowledge capital
Normalize γ(t ) = 1
constant ‡ow of entry m
Steady state – stationary distribution k (z )Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201218 / 42Equilibrium

Invariant measure linear in m

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201219 / 42Equilibrium

Invariant measure linear in m
Labor demand for production LP linear in m.

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201219 / 42Equilibrium

Invariant measure linear in m
Labor demand for production LP linear in m.
w (t ) = w0 e gt = w0 γ (t )Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201219 / 42Equilibrium

Invariant measure linear in m
Labor demand for production LP linear in m.
w (t ) = w0 e gt = w0 γ (t )w0 determined by new research technology:
w0 = k0

Hugo A. Hopenhayn (UCLA)Z

v (z, w0 ) F (dz )Knowledge, Di¤usion and Reallocation

May 28, 201219 / 42Equilibrium

Invariant measure linear in m
Labor demand for production LP linear in m.
w (t ) = w0 e gt = w0 γ (t )w0 determined by new research technology:
w0 = k0Zv (z, w0 ) F (dz )LR + LP = L

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201219 / 42Equilibrium

Invariant measure linear in m
Labor demand for production LP linear in m.
w (t ) = w0 e gt = w0 γ (t )w0 determined by new research technology:
w0 = k0Zv (z, w0 ) F (dz )LR + LP = L‡ow of entry m = k0 LR

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201219 / 42Equilibrium

Invariant measure linear in m
Labor demand for production LP linear in m.
w (t ) = w0 e gt = w0 γ (t )w0 determined by new research technology:
w0 = k0Zv (z, w0 ) F (dz )LR + LP = L‡ow of entry m = k0 LR
Total labor demand linear in LR .

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201219 / 42Reallocation and the incentives for replication
Productivity of R&D

An increase in k0 (productivity of frontier research)
Increases w0
Lowers v (z, w0 ) and thus k̇ (z ) /k for all z
Decreases lifetime of vintages and slows down di¤usion

Similar e¤ect for improvement in F

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201220 / 42Reallocation and the incentives for replication
Higher rate of technological advanceincrease in rate of obsolescence
Decreases w0 (ratio w (t ) /γ (t ))Increases v (z, w0 ) for low z 0s but reduces it for high z 0 s.

Intuition: Low z discounts more the future (when wage will be higher)
Flattens replication pro…le and lowers gain of drawing better z 0 s
Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201221 / 42Reallocation and the incentives for replication
Higher cost of replication

γC k̇ , increase in γ
Bigger direct impact on higher z 0 s (envelope argument)
w0 decreases
Again, ‡atten v (z, w0 ) pro…le.
Lower replication.

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201222 / 42Connection to decreasing returns

Static allocation: ln n = A + 1 1 α ln z
Higher elasticity of n with respect to z i¤ higher αConsider n (z, a) = k (z, a) employment of one original unit of type z
after a periodsk̇ (z ) k̇ (zeg∂ ln k (z, a) /∂ ln z =ga )For case C k̇ = c k̇ 2 /2 equals
Elasticity falls with c.

Hugo A. Hopenhayn (UCLA)hv (z )zv (ze ga )ze ga

Knowledge, Di¤usion and Reallocationi/gc

May 28, 201223 / 42Policy experimentTax on investment tC k̇ (z ) z
Tax decreases investment and reallocation from less to moreproductive
Impact: depends on importance of reallocation
3 scenarios: baseline, high adjustment cost, high g

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201224 / 42

Scenarios

Baseline, high adjustment cost, high g
C k̇ quadratic;r = 5%, δ = 5%, g = 3%; baseline w0 = 0.5 (Bartelsman andDomes)
1 exp ( λz )F (z ) = 1 exp ( λ) , λ = 2

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201225 / 42

Impact of tax

Higher taxes reduce the incentive to invest.
lowers equilibrium wage
Less turnover of knowledge chains
Lower average productivity

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201226 / 42

Impact of tax

t=0
t = 0.5
t = 1.0

Base case
w0
prod
100
100
6.5%
2.1%
9.8%
4.1%

Hugo A. Hopenhayn (UCLA)

high adj. cost
w0
prod
93.7
93.7
3.5%
0.9%
6.1%
2%

Knowledge, Di¤usion and Reallocationhigh g
w0
83.9
3.9%
6.4%

prod
80.7
0.8%
1.7%

May 28, 201227 / 42Firms and Knowledge Capital

Above considers only allocations. Data is based on …rms/plants.
Quantitative discipline
Help explain some facts?
Recent paper Luttmer - motivation: explaining the rapid growth oflarge …rms.
How can we take this model to the data?

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201228 / 42

Some motivating facts

Large degree of reallocation: 10% yearly job creation and destruction(Davis, Haltiwanger, Schuh)
Fairly large changes in …rm size over 10 year horizon period.
Growth rate independent of sizes ( Gibrat’s law)
Growth rate decreasing in age
Productivity di¤erences are persistent (Bartelsman and Doms)
Low productivity helps predict exit.
Entry and exit play an important role (15% of yearly job creation and
20% of job destruction.)

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201229 / 42Size distribution - Zipf’s law

Firm Size Distribution
1

0.9

us 2003

0.8

0.7

tail

0.6

0.5

0.4

0.3

0.2

0.1

1

10

100

1,000

10,000Size (employment)

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201230 / 42Firm as one Knowledge chain and no obsolescence (g=0)

Counterfactual implications:1Firms grow at di¤erent rates

2

No heterogeneity in the long run

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201231 / 42Obsolescence - g>0

If …rms homogeneous (standard vintage model)
strong …rm life-cycle
death increases with age

Sources of heterogeneity:12

Initial draws
random success in staying at the frontier/upgrading

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201232 / 42Heterogeneity in initial draws

Distribution F (s )Depreciates relative to the frontier at rate g
Exit rates and age: more ‡exibility but increases at some point
Older …rms tend to be larger
Productivity decreases with age in some range.
Still some strong life cycle e¤ects

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201233 / 42

2. Random success in staying at the frontier

Potential way of getting …rms to grow fast for longer time
Indivisibility? What is a …rm?
A …rm as specialized knowledge capital.
Frontier could move randomly, perhaps drastic
Or smoother: pieces of knowledge capital may fail to learn

Promising road

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201234 / 42Firms as portfolios of knowledge capital.

Lots of R&D done in existing …rms
State of the …rm (z1 , k1 , z2 , k2 ..., zn , kn ) , new draws arrival rate m.
Firm grows or contracts. When number of z 0 s in operation goes tozero, consider an exit. Substituted by a draw from an outsider.
Simple aggregation procedure - no change in behavior.

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201235 / 42Firm’s life-cycle

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201236 / 42

Special case: all draws from frontier

F point mass (standard vintage model)

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201237 / 42

Special case: all draws from frontier

F point mass (standard vintage model)
Problem: too little turnover

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201237 / 42

Special case: all draws from frontier

F point mass (standard vintage model)
Problem: too little turnover
Productivity of lower end = 0.5

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201237 / 42

Special case: all draws from frontier

F point mass (standard vintage model)
Problem: too little turnover
Productivity of lower end = 0.5
Growth rate g = 0.03

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201237 / 42

Special case: all draws from frontier

F point mass (standard vintage model)
Problem: too little turnover
Productivity of lower end = 0.5
Growth rate g = 0.03=) 24 years to go from frontier to 0.5

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201237 / 42

Special case: all draws from frontier

F point mass (standard vintage model)
Problem: too little turnover
Productivity of lower end = 0.5
Growth rate g = 0.03=) 24 years to go from frontier to 0.5
Expected turnover = 1/24=4% is too small even without resampling.

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201237 / 42

Stochastic draws (distribution F )Very few free parameters: λ, w0 , g , m where w0 and g are pinned
down.
Growth and size: Gibrat’s law (sort of)

Growth declines with age
Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201238 / 42

Stochastic draws (distribution F )Very few free parameters: λ, w0 , g , m where w0 and g are pinned
down.
Growth and size: Gibrat’s law (sort of)

Growth declines with age
Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201238 / 42

Stochastic draws (distribution F )Very few free parameters: λ, w0 , g , m where w0 and g are pinned
down.
Growth and size: Gibrat’s law (sort of)

Growth declines with age
Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201238 / 42

Survival: Firms running more vintages are less likely to exit - also
tend to be larger.
model USsize of entrants/incumbents 45%
35%
Rate of entry/exit (annual)
5%
7%
job creation/destruction rate 7%
10%
Share of entry/exit
30%
20%

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201239 / 42Age, size, productivity and growthage

size/avg

average z growthless than 5
5 to 1010 to 15
15 to 25
25 to 50
more than 50

0.3
0.6
0.9
1.1
1.0
1.1

0.71
0.69
0.65
0.60
0.61
0.60

8.6%
5.7%
2.6%
0.1%
0.4%
-0.2%

total

1.0

0.61

2.0%

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

B&D
7.7%
3.7%
2.9%

May 28, 201240 / 42Size distribution
Zipf’s law: (1F (size )) = size 1
Firm Size Distribution

1.1

1

us 2003
Benchmark
c=4

0.9

0.8

tail

0.7

0.6

0.5

0.4

0.3

0.2

0.1

1

10

100

1,000

10,000100,000

Size (employment)

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201241 / 42Size distribution
Zipf’s law: (1F (size )) = size 1
Firm Size Distribution

1.1

1

us 2003
Benchmark
c=4

0.9

0.8

tail

0.7

0.6

0.5

0.4

0.3

0.2

0.1

1

10

100

1,000

10,000100,000

Size (employment)

Fails in our benchmark (too few large …rms)
Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201241 / 42Size distribution
Zipf’s law: (1F (size )) = size 1
Firm Size Distribution

1.1

1

us 2003
Benchmark
c=4

0.9

0.8

tail

0.7

0.6

0.5

0.4

0.3

0.2

0.1

1

10

100

1,000

10,000100,000

Size (employment)

Fails in our benchmark (too few large …rms)
With lower C 0, "missing middle".
Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201241 / 42Final Remarks

The study of di¤usion through replication of knowledge importantarea.
Important to understand the gains from reallocation and overall
productivity.
Reduced-form returns to scale have implicit assumptions about
replication.
Incentives to replicate may vary signi…cantly across economies, timeand space
Need for deeper models to understand overall process and incentives
for knowledge transmission across time and space.

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201242 / 42Final Remarks

The study of di¤usion through replication of knowledge importantarea.
Important to understand the gains from reallocation and overall
productivity.
Reduced-form returns to scale have implicit assumptions about
replication.
Incentives to replicate may vary signi…cantly across economies, timeand space
Need for deeper models to understand overall process and incentives
for knowledge transmission across time and space.

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201242 / 42Final Remarks

The study of di¤usion through replication of knowledge importantarea.
Important to understand the gains from reallocation and overall
productivity.
Reduced-form returns to scale have implicit assumptions about
replication.
Incentives to replicate may vary signi…cantly across economies, timeand space
Need for deeper models to understand overall process and incentives
for knowledge transmission across time and space.

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201242 / 42Final Remarks

The study of di¤usion through replication of knowledge importantarea.
Important to understand the gains from reallocation and overall
productivity.
Reduced-form returns to scale have implicit assumptions about
replication.
Incentives to replicate may vary signi…cantly across economies, timeand space
Need for deeper models to understand overall process and incentives
for knowledge transmission across time and space.

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201242 / 42Final Remarks

The study of di¤usion through replication of knowledge importantarea.
Important to understand the gains from reallocation and overall
productivity.
Reduced-form returns to scale have implicit assumptions about
replication.
Incentives to replicate may vary signi…cantly across economies, timeand space
Need for deeper models to understand overall process and incentives
for knowledge transmission across time and space.

Hugo A. Hopenhayn (UCLA)

Knowledge, Di¤usion and Reallocation

May 28, 201242 / 42