Firm Entry and Exit and Growth
Jose Asturias (Georgetown University, Qatar)
Sewon Hur (University of Pittsburgh)
Timothy Kehoe (UMN, Mpls Fed, NBER)
Kim Ruhl (NYU Stern)
Minnesota Workshop in Macroeconomic Theory
August 2015
What drives aggregate productivity growth?
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Is productivity growth due to
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continuing firms?
entry and exit of firms?
What drives aggregate productivity growth?
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Is productivity growth due to
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continuing firms?
entry and exit of firms?
Foster, Haltiwanger, and Krizan (2001)
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net entry accounts for 25% of U.S. productivity growth
What drives aggregate productivity growth?
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Is productivity growth due to
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Foster, Haltiwanger, and Krizan (2001)
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continuing firms?
entry and exit of firms?
net entry accounts for 25% of U.S. productivity growth
Brandt, Van Biesebroeck, and Zhang (2012)
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net entry accounts for 72% of Chinese productivity growth
What drives aggregate productivity growth?
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Is productivity growth due to
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Foster, Haltiwanger, and Krizan (2001)
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net entry accounts for 25% of U.S. productivity growth
Brandt, Van Biesebroeck, and Zhang (2012)
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continuing firms?
entry and exit of firms?
net entry accounts for 72% of Chinese productivity growth
These studies are widely cited to justify assumptions that net
entry (creative destruction) is unimportant/important.
Firm entry and aggregate growth: empirics
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How does firm entry and exit contribute to aggregate
productivity growth?
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During periods of rapid GDP growth
During periods of slow GDP growth
Firm entry and aggregate growth: empirics
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How does firm entry and exit contribute to aggregate
productivity growth?
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During periods of rapid GDP growth
During periods of slow GDP growth
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Plant-level data from Chile and Korea
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Review literature that uses identical decomposition
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Net entry is more important in periods of rapid growth
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Average contribution, rapid growth: 54 percent
Average contribution, slow growth: 26 percent
Firm entry and aggregate growth: model
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Construct a model of firm entry and exit
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Calibrate to the United States
Firm entry and aggregate growth: model
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Construct a model of firm entry and exit
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Calibrate to the United States
Use the calibrated model for policy analysis
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Reduce entry barriers
Reduce barriers to technology adoption
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Quantitatively accounts for Chile and Korea data
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Entry and exit are crucial to understanding reform
data
Plan
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Decompose aggregate productivity growth
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Use manufacturing plant data from Chile and Korea
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Terms related to entry and exit of firms
Terms related to growth in continuing firms
Follow Foster, Haltiwanger, and Krizan (2001)
Periods of rapid growth
Periods of slow growth
Review comparable studies in the literature
Defining industry productivity
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Productivity of industry i:
log Zit =
X
set log zet
e∈Eit
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set : gross output share of plant e in time t in industry i
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zet : TFP of plant e in time t in industry i
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Change in productivity (window defined by t − 1, t ):
∆ log Zit = log Zit − log Zi,t−1
Estimating plant productivity
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Plant e in industry i production function
i
log yeit = log zeit + βki log keit + β`i log `eit + βm
log meit
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Following Foster et al. (2001)
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βji : average cost shares of input j in industry i
Consider alternative methods to estimate z
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Woolridge-Levinsohn-Petrin methods (Chile)
Generate similar productivity decompositions
Productivity decomposition of industry growth
∆ log Zit = ∆ log ZitNE + ∆ log ZitC
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∆ log ZitNE : change due to entering/exiting plants
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∆ log ZitC : change due to continuing plants
Net entry
∆ZitNE =
X
set (log zet − log Zi,t−1 )
e∈Nit
|
−
{z
entering plants
X
}
se,t−1 (log ze,t−1 − log Zi,t−1 )
e∈Xit
|
{z
exiting plants
}
Nit and Xit are sets of entering and exiting plants
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“entering plants” is positive if entrants have high productivity
(compared to initial aggregate productivity)
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“exiting plants” is negative if exiting plants have low
productivity
Continuing plants
∆ZitC =
X
se,t−1 ∆ log zet +
+
(log ze,t−1 − log Zi,t−1 ) ∆set
e∈Cit
e∈Cit
{z
|
X
within plant
X
}
|
{z
between plant
∆ log ze,t ∆set
e∈Cit
|
{z
covariance
}
Cit is the set of continuing plants
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“within plant” is average within-plant productivity growth
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“between plant” is positive if relatively productive plants
expand market share
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“covariance” is positive if plants that expand also increase
their productivity
}
Productivity growth and aggregation
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At the industry-level we determine
1. Productivity change
2. Productivity change from entry/exit
3. Productivity change from continuing plants
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To aggregate, weight each of these three components by
gross output of industry (using average of beginning and end
of window)
Decomposing productivity growth: Chile and Korea
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How does the net entry term change in Chile and Korea?
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Look within the same country at two windows
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Avoids cross-country differences
Uses consistent datasets
Real GDP per working-age person
400
Index (1985=100)
slow growth (4.0%)
2002-2007
Korea
fast growth (5.9%)
1992-1997
200
Chile
slow growth (2.4%)
2001-2006
fast growth (6.8%)
1990-1995
100
1985
1990
1995
2000
2005
2010
Plant-level manufacturing data
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Chile
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Encuesta Nacional Industrial Anual
Collected by the Chilean national statistical agency
Covers all plants with more than 10 employees
127 industries and 5,500 plants (2005)
Two panels: 1986-1996 and 1995-2006
Korea
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Survey of Mining and Manufacturing
Collected by the Korean national statistical agency
Covers all plants with more than 10 employees
104 industries and 8,300 plants
Panel: 1992, 1997, 2002, and 2007
The relative importance of net entry
Country
Period
Chile
Chile
Korea
Korea
1990-1995
2001-2006
1992-1997
2002-2007
GDP WAP
growth
(percent)
6.8
2.4
5.9
4.0
Window
5
5
5
5
years
years
years
years
Effect of
net entry
(percent)
85
35
44
39
Other empirical studies
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Existing studies with identical methodology
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Slow growth: Portugal, U.K., U.S.
Rapid growth: China, Korea, Chile
Other empirical studies
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Existing studies with identical methodology
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Problem: Studies use different length time windows
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Slow growth: Portugal, U.K., U.S.
Rapid growth: China, Korea, Chile
Makes comparisons difficult
Solution: Use calibrated model to make adjustments
Use model to make window adjustments
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Solve the baseline equilibrium for the U.S.
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Decompose model output using 5, 10, 15 year windows
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Fit a quadratic to contribution of net entry to productivity
growth for the 3 windows
Contribution of net entry to aggregate productivity
Net entry under various windows in the model
40
30
20
10
0
1
2
3
4
5
6
7
8
9 10
Window length (years)
11
12
13
14
15
Use model to make window adjustments
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Portugal: 3-year window, 15 percent net entry contribution
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In the calibrated model
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5 year window generates 25 percent contribution
3 year window generates 20 percent contribution
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Adjust proportionally
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Adjustment: 15 × 25/20 = 19 (5-year window equivalent)
Contribution of net entry
Net entry more important during periods of fast growth
Country
Period
US
UK
Portugal
Chile
Korea
Average
China
Chile
Korea
Chile
Korea
Average
1977–1992
1982–1987
1991–1997
2001–2006
2002–2007
1998–2007
1990–1997
1990–1998
1990–1995
1992–1997
GDP growth
15–64
1.9
3.3
1.4
2.4
4.0
2.6
8.3
6.4
4.3
6.8
5.9
6.3
Window
5 years∗
5 years
3 years∗
5 years
5 years
9
7
8
5
5
years
years
years
years
years
Effect of
net entry
25
12
15
35
39
72
49
57
85
44
5 year
equiv.
25
12
19
35
39
26
54
42
45
85
44
54
Sources: U.S.: Foster et al. (2002); U.K.: Disney et al. (2005); Portugal: Carreira and Teixeira (2008); China:
Brandt et al. (2012); Chile (1990–97): Bergoeing and Repetto (2006); Korea (1990–98) Ahn et al. (2005)
∗ Average
over multiple windows
Net entry important for fast-growth economies
90
Contribution of net entry (percent)
CHL 1990-95
80
70
60
CHN 1998-07*
50
KOR 1990-98*KOR 1992-97
CHL 1990-97*
KOR 2002-07
40
CHL 2001-06
30
USA 1977-92
20
PRT 1991-97*
GBR 1982-87
10
0
0
∗
1
2
3
4
5
6
7
8
GDP (per 15-64) growth rate (percent)
9
adjusted to 5 year windows using elasticities generated by model
10
model
Model
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We develop a model in which
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Potential entrants draw from frontier efficiency distribution,
which improves by growth factor ge
Efficiency of continuing firms grows, by gc < ge
Endogenous entry/exit of firms
Easy to characterize balanced growth path
Model
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We develop a model in which
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Potential entrants draw from frontier efficiency distribution,
which improves by growth factor ge
Efficiency of continuing firms grows, by gc < ge
Endogenous entry/exit of firms
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Easy to characterize balanced growth path
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Implications:
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BGP growth factor ge
Level is determined by barriers to entry, technology adoption
Purpose of model: Investigate policy reforms
Household problem
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Representative household solves
max
Ct ,Bt+1
∞
P
β t log Ct
t=0
subject to
Pt Ct + qt+1 Bt+1 = wt + Dt + Bt
Ct ≥ 0, No Ponzi condition, B0 given
Dt : aggregate dividends
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Normalize Pt = 1, ∀t
Firm dynamics
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Based on Hopenhayn (1992)
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Continuum of perfectly competitive firms
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A firm in the model is a plant in the data
Heterogenous in efficiency x
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Productivity depends on efficiency
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Pay κ to draw initial efficiency, f to operate
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Exogenous exit probability δ and endogenous exit
Fixed costs paid by firms
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Potential entrants pay κt = κYt to draw efficiency x
κ = κT + κP
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Paid in consumption/investment good
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κT is the technological cost, common across countries
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κP is the policy induced cost
Fixed costs paid by firms
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Potential entrants pay κt = κYt to draw efficiency x
κ = κT + κP
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Paid in consumption/investment good
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κT is the technological cost, common across countries
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κP is the policy induced cost
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Firms pay fixed cost of operating, ft = fYt , or exit
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κt + ft is the capital of a firm in t
Firms face two decisions
1. Entry/exit decision
2. Conditional on operating: maximize profits
Firm’s static problem
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Conditional on operating, firm with efficiency x solves
πt (x) = max x`t (x)α − wt `t (x) − ft
`t (x)
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Solution is
`t (x) =
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More efficient firms are larger
1
w α−1
t
αx
Firm’s dynamic problem
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Firms with efficiency x choose to exit or continue to solve
Vt (x) = max {πt (x) + qt+1 (1 − δ)Vt+1 (gc,t+1 x), 0}
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Efficiency grows at gc
Operating firm efficiency growth
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Efficiency of existing firms grow by
gct = ḡgtε
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ḡ is constant
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gt is average efficiency growth
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ε measures the degree of spillovers
Operating firm efficiency growth
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Efficiency of existing firms grow by
gct = ḡgtε
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ḡ is constant
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gt is average efficiency growth
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ε measures the degree of spillovers
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Quantitatively, but not qualitatively important
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Further discussion in calibration
New entrant’s problem
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Potential entrants draw efficiency from
Ft (x) = 1 −
ϕx
get
−γ
,x≥
get
ϕ
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Mean grows by growth factor ge
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Barrier to technology adoption, ϕ (Parente-Prescott 1994)
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Mass of potential entrants, µt , from costly entry condition:
Ex [Vt (x)] = κt
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Firm enters if and only if x ≥ x̂t
Measure of firms
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Measure of firms of age j in operation
"
ηjt = µt−j+1 (1 − δ)j−1 1 − Ft−j+1
x̂t
Qj−1
s=1
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Convert age-j efficiency to initial efficiency
j−1
Y
gc,t−s+1
s=1
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Total measure of operating firms
ηt =
∞
X
i=1
ηit
gc,t−s+1
!#
Equilibrium definition
Given initial conditions, an equilibrium is
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Household consumption and bond plans
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Allocations and entry/exit thresholds for firms
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Measure of potential entrants for firms
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Prices and aggregate dividends
Equilibrium definition
such that
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Household maximizes lifetime utility
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Firms maximize discounted dividends
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Costly entry condition binds
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Goods, labor, and bond markets clear
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Dividends satisfy
Dt = Πt − µt κt
Existence of balanced growth path
Economy converges to a balanced growth path in which
1. Entry and exit thresholds grow by ge
2. Real consumption, output, wages, and dividends grow by ge
3. Masses of potential entrants and operating firms are constant
Characterizing BGP: growth
x̂t =
wt =
Yt =
µ =
η =
Economy grows by ge
γ1
get ω
µ
ϕ η
1−α
1−α
α
x̂t
f
1−α
1−α
x̂t
f
ξ
γκω
γ(1 − α) − 1
γf
Characterizing BGP: levels
µ =
x̂t =
wt =
Yt =
η =
I
ξ
γκω
γ1
get ω
µ
ϕ η
1−α
1−α
x̂t
α
f
1−α
1−α
x̂t
f
γ(1 − α) − 1
γf
As κ decreases
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More potential entrants pay to draw efficiency
More-efficient firms enter and aggregate income increases
quantitative exercise
Entry cost reform
1. Calibrate model to U.S. (high BGP)
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No policy distortions in entry costs
κus = κT
2. Model a distorted country on a lower balanced growth path
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Income level is 15 percent lower than U.S.
κD = κT + κP
κD = 5 × κus
3. Reform entry costs in distorted country to U.S. level
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Solve for transition to higher balanced growth path
Measuring capital
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Fixed costs (κ, f ) are investments (new approach)
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How are they accounted for
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In the firm’s accounts?
In the national accounts?
Measuring capital
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Fixed costs (κ, f ) are investments (new approach)
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How are they accounted for
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In the firm’s accounts?
In the national accounts?
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Aggregate investment = µt κt + ηt ft
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Depreciation is the sum of
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Capital of firms that die or exit
κt of potential entrants that do not enter
ft minus costs of upgrading capital for continuing firms
Measuring capital
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Fixed costs (κ, f ) are investments (new approach)
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How are they accounted for
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In the firm’s accounts?
In the national accounts?
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Aggregate investment = µt κt + ηt ft
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Depreciation is the sum of
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Capital of firms that die or exit
κt of potential entrants that do not enter
ft minus costs of upgrading capital for continuing firms
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Aggregate capital stock = ηt (κt + ft )
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Depreciation rate constant on BGP, not in transition
Measuring capital
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Alternatives we are considering
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In the model
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κt , ft scale with get rather than Yt
Policy distortions are ad valorem, κT + κP = τ κT
In the accounting
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Some parts of κ and f are intermediate inputs
Expensed, rather than counted as investment
Measuring productivity
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Need model measurement consistent with data measurement
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Productivity z of firm with efficiency x
log(zt (x)) = log(yt (x)) − α log(`t (x)) − αkt log(kt )
= log(x) − αkt log(kt )
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Capital share is given by
αkt =
where Rt =
1
− 1 + δkt
qt
Rt Kt
Yt
Calibration
Calibrate model to match size distribution of plants as well as
effect of net entry on aggregate productivity growth.
Calibrated parameters
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Model period is 5 years
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Data from United States
Parameter
Operating cost f
Entry cost κ
Pareto parameter γ
Firm growth ḡ 1/(1−ε)
Death rate δ
Entrant productivity ge
Discount factor β
Returns to scale α
∗
Value
0.32 × 5
0.26
10.08
(1.017)5
1 − (0.97)5
(1.02)5
(0.98)5
0.8
Target
average establishment size = 16.0
entry cost / fixed cost∗ = 0.82
establishment size s.d. = 91.2
effect of net entry on growth† = 25%
exiting plant employment share‡ =17.7%
BGP growth factor = 1.02
4 percent real interest rate
Atkeson and Kehoe (2005)
Survey in Barseghyan and DiCecio (2011); † Foster et al. (2001); ‡ Dunne et al. (1989)
Technological spillovers
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Take logs of equation that characterizes spillovers
log gct = log ḡ + ε log gt
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We estimate this equation as follows
log gct,i = β0 + ε log git + υit
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gct,i is weighted productivity growth of continuing plants in i
git is weighted productivity growth of entire industry i
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Estimate using Chile and Korea data (would like U.S. data)
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Average estimate: ε = 0.52
Solving for transition path
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Unanticipated reform at t = t0 : κD = κus
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System of 2T equations and 2T unknowns for large T
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Labor market clearing
x̂tγ
N
i−1
Y
geγt X −γ
γ
i−1 γ(1−i)
ϕt−i+1 µt−i+1 (1 − δ) ge
gc,t−s+1
=
η
s=1
i=1
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Costly entry condition
N
geγt −γ X
ϕ
(1 − δ)i−1
κt =
γη t
i=1
i−1
Y
s=1
!
γ
qt+s gc,t+s
wt+i−1 −γ
x̂t+i−1
α
Output per worker
300
250
200
150
100
0
2
4
6
model periods
8
10
Transition: more potential entrants
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More potential entrants increases efficiency thresholds
Detrended efficiency thresholds
Mass of potential entrants
0.8
120
0.6
115
0.4
110
0.2
105
0.0
100
0
2
4
6
model periods
8
10
0
2
4
6
model periods
8
10
Transition: more entry and exit
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Efficient firms enter, inefficient firms exit
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Total mass of firms is constant
Mass of entering firms
Mass of exiting firms
0.04
0.04
0.03
0.03
0.02
0.02
0.01
0.01
0
2
4
6
model periods
8
10
0
2
4
6
model periods
8
10
Transition: wages and output
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Higher wages increase efficiency thresholds
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More efficient firms increase output
Detrended output
Detrended wage
120
120
115
115
110
110
105
105
100
100
0
2
4
6
model periods
8
10
0
2
4
6
model periods
8
10
Transition: consumption and interest rates
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More attractive investment opportunities
Detrended consumption
Interest rate
120
7
115
6
110
5
105
100
4
0
2
4
6
model periods
8
10
0
2
4
6
model periods
8
10
Productivity growth decompositions
Model periods
(5 years)
0-2
3 (reform)
4
5
6+
Entry Cost
1.32
0.26
0.26
0.26
0.26
Output growth
(%, annualized)
2.0
5.0
2.3
2.0
2.0
Contribution of
net entry (%)
25.0
78.3
33.5
26.3
25.0
Net entry and productivity in model and data
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Model generates quantitatively reasonable numbers
GDP/WAP growth (%)
Contribution of net entry (%)
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Model
reform
5.0
78.3
Data
rapid
6.3
54.0
Calibration and experiment need further work
Model
BGP
2.0
25.0
Data
slow
2.6
26.0
Reforming barriers to technology adoption
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A reform that does not involve entry costs
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Potential entrants draw efficiency from
Ft (x) = 1 −
ϕx
get
−γ
,x≥
get
ϕ
ϕ ≥ 1: policy-induced barriers to technology adoption
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Set ϕ so that distorted BGP is 15 percent lower than U.S.
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Reform ϕ to generate a transition to higher BGP
Transition: more potential entrants
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More potential entrants only in the transition
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Efficiency thresholds increase
Detrended efficiency thresholds
Mass of potential entrants
0.7
120
0.6
115
0.5
110
0.4
105
0.3
100
0
2
4
6
model periods
8
10
0
2
4
6
model periods
8
10
Transition: more entry and exit
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Efficient firms enter, inefficient firms exit
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Total mass of firms is constant
Mass of entering firms
Mass of exiting firms
0.04
0.04
0.03
0.03
0.02
0.02
0.01
0.01
0
2
4
6
model periods
8
10
0
2
4
6
model periods
8
10
Transition: wages and output
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Higher wages increase efficiency thresholds
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More efficient firms increase output
Detrended output
Detrended wage
120
120
115
115
110
110
105
105
100
100
0
2
4
6
model periods
8
10
0
2
4
6
model periods
8
10
Transition: consumption and interest rates
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More attractive investment opportunities
Detrended consumption
Interest rate
120
7
115
6
110
5
105
100
4
0
2
4
6
model periods
8
10
0
2
4
6
model periods
8
10
Productivity growth decompositions
Model periods
(5 years)
0-2
3 (reform)
4
5
6+
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Barrier to
tech. adoption
1.17
1.00
1.00
1.00
1.00
Productivity growth
(%, annualized)
2.0
5.0
2.3
2.0
2.0
Almost identical to reform in entry cost
Contribution of
net entry (%)
25.0
78.2
33.5
26.2
25.0
Reform and growth
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Reforms that increase aggregate productivity
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Increase entry and exit in the transition
Increase the contribution of net entry
Need models of entry and exit to understand productivity