Business cycles, innovation and growth: welfare analysis EEA Marcin Bielecki

1. Business cycles, innovation and growth:
welfare analysis
Marcin Bielecki
University of Warsaw
National Bank of Poland
24th August 2017
EEA - ESEM 2017 Lisbon
1 / 41

2. Presentation outline
1 Introduction
2 Model
3 Results
4 Conclusions
5 Appendix
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3. Presentation outline
1 Introduction
2 Model
3 Results
4 Conclusions
5 Appendix
3 / 41

4. Motivation
Modern business cycle theory starts with the view that
growth and fluctuations are not distinct phenomena
to be studied with separate data and different analytical tools.
– Cooley and Prescott (1995) Economic Growth and Business Cycles
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5. Cyclical behavior of US R&D expenditures
1950 1960 1970 1980 1990 2000 2010
Date
−10
−5
0
5
10
DeviationfromHPtrend
Total R&D
Industrial R&D
Sources:
Total R&D: Bureau of Economic Analysis, 1947q1-2016q4
Industrial R&D: National Science Foundation, 1953-2014
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6. Cyclical behavior of US establishments
1995 2000 2005 2010 2015
Date
−15
−10
−5
0
5
10
15
DeviationfromHPtrend
Expansions
Contractions
Source: BLS Business Employment Dynamics, 1992q3-2016q2
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7. Cyclical behavior of US establishments
1995 2000 2005 2010 2015
Date
−15
−10
−5
0
5
10
15
DeviationfromHPtrend
Births
Deaths
Source: BLS Business Employment Dynamics, 1992q3-2016q2
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8. Literature review
Endogenous business cycles: cyclical consequences of “uneven”
endogenous growth or granularities / networks / complementarities
Ozlu (1996), Maliar & Maliar (2004), Jones et al. (2005),
Walde (2005), Phillips & Wrase (2006)
Gabaix (2011), Acemoglu et al. (2012), Rozsypal (2015)
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9. Literature review
Endogenous business cycles: cyclical consequences of “uneven”
endogenous growth or granularities / networks / complementarities
Ozlu (1996), Maliar & Maliar (2004), Jones et al. (2005),
Walde (2005), Phillips & Wrase (2006)
Gabaix (2011), Acemoglu et al. (2012), Rozsypal (2015)
Medium-term business cycles:
long-term impact of transitory shocks (not microfounded)
Comin & Gertler (2006), Anzoategui et al. (2016)
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10. Literature review
Endogenous business cycles: cyclical consequences of “uneven”
endogenous growth or granularities / networks / complementarities
Ozlu (1996), Maliar & Maliar (2004), Jones et al. (2005),
Walde (2005), Phillips & Wrase (2006)
Gabaix (2011), Acemoglu et al. (2012), Rozsypal (2015)
Medium-term business cycles:
long-term impact of transitory shocks (not microfounded)
Comin & Gertler (2006), Anzoategui et al. (2016)
Optimal monetary policy in New Keynesian models
with growth via learning-by-doing
Annicchiarico et al. (2011), Annicchiarico & Rossi (2015),
Annicchiarico & Pelloni (2016)
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11. Literature review
Endogenous business cycles: cyclical consequences of “uneven”
endogenous growth or granularities / networks / complementarities
Ozlu (1996), Maliar & Maliar (2004), Jones et al. (2005),
Walde (2005), Phillips & Wrase (2006)
Gabaix (2011), Acemoglu et al. (2012), Rozsypal (2015)
Medium-term business cycles:
long-term impact of transitory shocks (not microfounded)
Comin & Gertler (2006), Anzoategui et al. (2016)
Optimal monetary policy in New Keynesian models
with growth via learning-by-doing
Annicchiarico et al. (2011), Annicchiarico & Rossi (2015),
Annicchiarico & Pelloni (2016)
“Missing generations of firms”:
macroeconomic impact of depressed firm entry rates
Siemer (2014), Pugsley et al. (2015), Messer et al. (2016),
Gourio et al. (2016)
8 / 41

12. Literature review
Endogenous business cycles: cyclical consequences of “uneven”
endogenous growth or granularities / networks / complementarities
Ozlu (1996), Maliar & Maliar (2004), Jones et al. (2005),
Walde (2005), Phillips & Wrase (2006)
Gabaix (2011), Acemoglu et al. (2012), Rozsypal (2015)
Medium-term business cycles:
long-term impact of transitory shocks (not microfounded)
Comin & Gertler (2006), Anzoategui et al. (2016)
Optimal monetary policy in New Keynesian models
with growth via learning-by-doing
Annicchiarico et al. (2011), Annicchiarico & Rossi (2015),
Annicchiarico & Pelloni (2016)
“Missing generations of firms”:
macroeconomic impact of depressed firm entry rates
Siemer (2014), Pugsley et al. (2015), Messer et al. (2016),
Gourio et al. (2016)
Close in spirit are recent works by Clementi & Palazzo (2016) and
Cozzi et al. (2017), but only entry-exit channel is present 8 / 41

13. Contribution to literature
Business cycle model with endogenous growth
Endogenous growth fully microfounded,
contrary to Comin & Gertler (2006) or Annicchiarico et al. (2011)
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14. Contribution to literature
Business cycle model with endogenous growth
Endogenous growth fully microfounded,
contrary to Comin & Gertler (2006) or Annicchiarico et al. (2011)
Link between R&D expenditures and establishment dynamics
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15. Contribution to literature
Business cycle model with endogenous growth
Endogenous growth fully microfounded,
contrary to Comin & Gertler (2006) or Annicchiarico et al. (2011)
Link between R&D expenditures and establishment dynamics
Assessment of the influence of transitory shocks
on endogenous growth rate and resulting shifts in the BGP level
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16. Contribution to literature
Business cycle model with endogenous growth
Endogenous growth fully microfounded,
contrary to Comin & Gertler (2006) or Annicchiarico et al. (2011)
Link between R&D expenditures and establishment dynamics
Assessment of the influence of transitory shocks
on endogenous growth rate and resulting shifts in the BGP level
Assessment of the welfare cost of business cycles
with endogenous growth rates
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17. Contribution to literature
Business cycle model with endogenous growth
Endogenous growth fully microfounded,
contrary to Comin & Gertler (2006) or Annicchiarico et al. (2011)
Link between R&D expenditures and establishment dynamics
Assessment of the influence of transitory shocks
on endogenous growth rate and resulting shifts in the BGP level
Assessment of the welfare cost of business cycles
with endogenous growth rates
Assessment of the welfare effects of
static and countercyclical subsidies
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18. Presentation outline
1 Introduction
2 Model
3 Results
4 Conclusions
5 Appendix
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19. Key model features
Inspirations: Acemoglu et al. (2013) and Melitz & Redding (2014)
No capital, two types of labor
Skilled: “managers” and R&D
Unskilled: production
Fixed proportion s ∈ (0, 1) of skilled workers graphs
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20. Key model features
Inspirations: Acemoglu et al. (2013) and Melitz & Redding (2014)
No capital, two types of labor
Skilled: “managers” and R&D
Unskilled: production
Fixed proportion s ∈ (0, 1) of skilled workers graphs
Perfectly competitive final goods sector
Monopolistic competition in the intermediate goods sector
Elasticity of substitution between varieties σ ∈ (1, ∞)
Increasing returns to scale (due to fixed costs)
Establishments produce goods heterogeneous w.r.t. quality
Establishments spend on R&D to improve their varieties’ quality
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21. Key model features
Inspirations: Acemoglu et al. (2013) and Melitz & Redding (2014)
No capital, two types of labor
Skilled: “managers” and R&D
Unskilled: production
Fixed proportion s ∈ (0, 1) of skilled workers graphs
Perfectly competitive final goods sector
Monopolistic competition in the intermediate goods sector
Elasticity of substitution between varieties σ ∈ (1, ∞)
Increasing returns to scale (due to fixed costs)
Establishments produce goods heterogeneous w.r.t. quality
Establishments spend on R&D to improve their varieties’ quality
Vertical and horizontal (outside BGP) innovations
Creative destruction
Endogenous entry & exit and R&D intensity
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22. Incumbents: environment
An active establishment has to employ mass f of skilled labor
to gain access to the production function linear in quality and labor
yi,t = Ztqi,tni,t
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23. Incumbents: environment
An active establishment has to employ mass f of skilled labor
to gain access to the production function linear in quality and labor
yi,t = Ztqi,tni,t
Aggregate (“average”) quality index Qt
Qt =
1
Mt
Mt
0
qσ−1
i,t di
1/(σ−1)
Increase in Q over time is responsible for sustained long-run growth
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24. Incumbents: environment
An active establishment has to employ mass f of skilled labor
to gain access to the production function linear in quality and labor
yi,t = Ztqi,tni,t
Aggregate (“average”) quality index Qt
Qt =
1
Mt
Mt
0
qσ−1
i,t di
1/(σ−1)
Increase in Q over time is responsible for sustained long-run growth
Define relative quality of i-th variety φi,t
φi,t = (qi,t/Qt)
σ−1
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25. Incumbents: environment
An active establishment has to employ mass f of skilled labor
to gain access to the production function linear in quality and labor
yi,t = Ztqi,tni,t
Aggregate (“average”) quality index Qt
Qt =
1
Mt
Mt
0
qσ−1
i,t di
1/(σ−1)
Increase in Q over time is responsible for sustained long-run growth
Define relative quality of i-th variety φi,t
φi,t = (qi,t/Qt)
σ−1
Real operating profit πo
i,t (excluding R&D expenditures)
πo
i,t (φi,t) =
Yt
σMt
φi,t
revenue - variable cost
− ws
t f
fixed cost
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26. Incumbents: innovation
Successful innovation raises product quality by ι
Aggregate quality index grows at rate ηt
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27. Incumbents: innovation
Successful innovation raises product quality by ι
Aggregate quality index grows at rate ηt
Next period’s relative quality φi,t+1 evolves as follows
φi,t+1 =
ι · φi,t/ηt with probability αi,t
φi,t/ηt with probability 1 − αi,t
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28. Incumbents: innovation
Successful innovation raises product quality by ι
Aggregate quality index grows at rate ηt
Next period’s relative quality φi,t+1 evolves as follows
φi,t+1 =
ι · φi,t/ηt with probability αi,t
φi,t/ηt with probability 1 − αi,t
Employing R&D labor nx
i,t raises innovative success probability αi,t
(cf. Pakes & McGuire (1994) and Ericson & Pakes (1995))
αi,t =
anx
i,t/φi,t
1 + anx
i,t/φi,t
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29. Incumbents: innovation
Successful innovation raises product quality by ι
Aggregate quality index grows at rate ηt
Next period’s relative quality φi,t+1 evolves as follows
φi,t+1 =
ι · φi,t/ηt with probability αi,t
φi,t/ηt with probability 1 − αi,t
Employing R&D labor nx
i,t raises innovative success probability αi,t
(cf. Pakes & McGuire (1994) and Ericson & Pakes (1995))
αi,t =
anx
i,t/φi,t
1 + anx
i,t/φi,t
Real profit πi,t is affine in φi,t
πi,t (φi,t, αi,t) =
Yt
σMt
−
ws
t
a
αi,t
1 − αi,t
R&D cost
φi,t − ws
t f
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30. Incumbents: value function
Key tradeoff: spending on R&D is costly today,
but raises the expected future establishment value
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31. Incumbents: value function
Key tradeoff: spending on R&D is costly today,
but raises the expected future establishment value
Establishments choose αt to maximize their value Vt
Vt (φt) = max
αt ∈[0,1)
πt (φt, αt) +
max {0, Et [Λt,t+1 (1 − δt) Vt+1 (φt+1|φt, αt)]}
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32. Incumbents: value function
Key tradeoff: spending on R&D is costly today,
but raises the expected future establishment value
Establishments choose αt to maximize their value Vt
Vt (φt) = max
αt ∈[0,1)
πt (φt, αt) +
max {0, Et [Λt,t+1 (1 − δt) Vt+1 (φt+1|φt, αt)]}
System reduces to functions of two state variables
Exogenous shock Zt and endogenous establishment mass Mt
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33. Incumbents: value function
Key tradeoff: spending on R&D is costly today,
but raises the expected future establishment value
Establishments choose αt to maximize their value Vt
Vt (φt) = max
αt ∈[0,1)
πt (φt, αt) +
max {0, Et [Λt,t+1 (1 − δt) Vt+1 (φt+1|φt, αt)]}
System reduces to functions of two state variables
Exogenous shock Zt and endogenous establishment mass Mt
For high enough φ the value function is affine in φ
Incumbents choose the same level of α – Gibrat’s law
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34. Incumbents: value function
Key tradeoff: spending on R&D is costly today,
but raises the expected future establishment value
Establishments choose αt to maximize their value Vt
Vt (φt) = max
αt ∈[0,1)
πt (φt, αt) +
max {0, Et [Λt,t+1 (1 − δt) Vt+1 (φt+1|φt, αt)]}
System reduces to functions of two state variables
Exogenous shock Zt and endogenous establishment mass Mt
For high enough φ the value function is affine in φ
Incumbents choose the same level of α – Gibrat’s law
Piecewise linear approximation makes problem tractable
No need to track distribution over time!
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35. Incumbents: value function approximation
Piecewise linear function changes slope at φ∗Valuefunctionv
accurate
approximation
φ∗
Relative quality level φ
Policyfunctionα
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36. Incumbents: policy function
Innovative success probability (%)
0.94 0.96 0.98 1.00 1.02 1.04 1.06
Productivity shock Z
0.90
0.95
1.00
1.05
1.10
EstablishmentmassM
47
48
49
50
51
52
53
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37. Entrants: policy function
Desired entry rate (%)
0.94 0.96 0.98 1.00 1.02 1.04 1.06
Productivity shock Z
0.90
0.95
1.00
1.05
1.10
EstablishmentmassM
0
2
4
6
8
10
12
14
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38. Presentation outline
1 Introduction
2 Model
3 Results
4 Conclusions
5 Appendix
18 / 41

39. Long-run moments
Comparison of model outcomes with long-run US data averages
Description Model Data
Annual GDP p. c. growth 2.02% 2.08%
Rel. share of exp. estabs. 1.00 1.01
Exit rate 3.07% 3.07%
Share of R&D employment 0.98% 0.98%
Share of R&D in GDP 2.07% 2.23%
“Skilled wage premium” 2.55 2.07
Share of profits in GDP 4.65% 6.53%
parameters
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40. Model vs data over the business cycle I
1995 2000 2005 2010 2015
Date
−2.0
−1.5
−1.0
−0.5
0.0
0.5
1.0
1.5
2.0
DeviationfromHPtrend
Data
Model
1995 2000 2005 2010 2015
Date
−15
−10
−5
0
5
10
DeviationfromHPtrend
Data (left)
Model (right)
−3
−2
−1
0
1
2
Establishments Expansions
1995 2000 2005 2010 2015
Date
−1.0
−0.5
0.0
0.5
1.0
1.5
DeviationfromHPtrend
Data
Model
1995 2000 2005 2010 2015
Date
−10
−5
0
5
10
15
DeviationfromHPtrend
Data (left)
Model (right)
−1.0
−0.5
0.0
0.5
1.0
1.5
Net Entry Contractions
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41. Model vs data over the business cycle II
1995 2000 2005 2010 2015
Date
−8
−6
−4
−2
0
2
4
6
8
DeviationfromHPtrend
Data (NSF)
Model
1995 2000 2005 2010 2015
Date
−6
−4
−2
0
2
4
6
DeviationfromHPtrend
Data (left)
Model (right)
−2.0
−1.5
−1.0
−0.5
0.0
0.5
1.0
1.5
2.0
Research & Development Hours
business cycle moments
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42. Key impulse response function
0 20 40 60 80 100
Quarter
0.0
0.2
0.4
0.6
0.8
1.0
0 20 40 60 80 100
Quarter
0.00
0.01
0.02
0.03
0.04
0.05
0.06
Productivity Quality
Shock hysteresis on BGP
almost 6% of shock becomes “permanent”
more irfs
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43. Long shadows of shocks: Great Recession
2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
Date
0.97
0.98
0.99
1.00
1.01
1.02
Deviationfromthelong-runtrend
Establishments (left)
Quality (right)
0.9997
0.9998
0.9999
1.0000
1.0001
1.0002
Establishments return to trend by 2012
Quality index is permanently depressed
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44. Welfare
Is the hysteresis effect meaningful?
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45. Welfare
Is the hysteresis effect meaningful?
µ is the extent an agent’s consumption has to increase
for the agent to be indifferent across two “worlds”
“World type” Welfare
Consumption
equivalent (µ)
Balanced
-122.26 –
Growth Path
Stochastic
-122.37 0.06%
(exogenous growth)
Stochastic
-129.89 4.54%
(endogenous growth)
24 / 41

46. Welfare
Is the hysteresis effect meaningful?
µ is the extent an agent’s consumption has to increase
for the agent to be indifferent across two “worlds”
“World type” Welfare
Consumption
equivalent (µ)
Balanced
-122.26 –
Growth Path
Stochastic
-122.37 0.06%
(exogenous growth)
Stochastic
-129.89 4.54%
(endogenous growth)
The influence of transitory shocks on endogenous growth rate
changes the assessment of welfare costs
of business cycles considerably
Estimated to be two orders of magnitude higher
relative to exogenous growth models
24 / 41

47. Effects of subsidies (static)
Static subsidies
Subsidy type Growth rate ∆Q20 −µ
Baseline 2.04 2.25 –
Incumbents’ R&D 2.09 2.17 1.06%
Entrants’ R&D 2.04 2.26 0.45%
Inc. operating cost 2.00 2.29 -1.70%
Ent. operating cost 2.04 2.28 0.22%
25 / 41

48. Effects of subsidies (static)
Static subsidies
Subsidy type Growth rate ∆Q20 −µ
Baseline 2.04 2.25 –
Incumbents’ R&D 2.09 2.17 1.06%
Entrants’ R&D 2.04 2.26 0.45%
Inc. operating cost 2.00 2.29 -1.70%
Ent. operating cost 2.04 2.28 0.22%
In line with endogenous growth literature:
R&D subsidies welfare improving
Direct subsidies to incumbents welfare deteriorating
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49. Effects of subsidies (countercyclical)
Countercyclical subsidies
Subsidy type ∆Q20 −µ
Baseline 2.25 –
0.5% subsidy if Y is 1% below trend
Incumbents’ R&D 3.03 -1.86%
Entrants’ R&D 2.22 0.04%
Inc. operating cost 0.91 0.60%
Ent. operating cost 2.14 0.13%
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50. Effects of subsidies (countercyclical)
Countercyclical subsidies
Subsidy type ∆Q20 −µ
Baseline 2.25 –
0.5% subsidy if Y is 1% below trend
Incumbents’ R&D 3.03 -1.86%
Entrants’ R&D 2.22 0.04%
Inc. operating cost 0.91 0.60%
Ent. operating cost 2.14 0.13%
0.5% subsidy if M is 1% below trend
Incumbents’ R&D 2.58 -0.62%
Entrants’ R&D 2.25 0.03%
Inc. operating cost 1.69 0.14%
Ent. operating cost 2.24 0.09%
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51. Effects of subsidies (countercyclical)
Countercyclical subsidies
Subsidy type ∆Q20 −µ
Baseline 2.25 –
0.5% subsidy if Y is 1% below trend
Incumbents’ R&D 3.03 -1.86%
Entrants’ R&D 2.22 0.04%
Inc. operating cost 0.91 0.60%
Ent. operating cost 2.14 0.13%
0.5% subsidy if M is 1% below trend
Incumbents’ R&D 2.58 -0.62%
Entrants’ R&D 2.25 0.03%
Inc. operating cost 1.69 0.14%
Ent. operating cost 2.24 0.09%
Over the business cycle:
R&D subsidies to incumbents welfare deteriorating
Direct subsidies to incumbents welfare improving
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52. Presentation outline
1 Introduction
2 Model
3 Results
4 Conclusions
5 Appendix
28 / 41

53. Conclusions
Able to replicate business cycle features
of establishment dynamics and R&D expenditures
29 / 41

54. Conclusions
Able to replicate business cycle features
of establishment dynamics and R&D expenditures
Found long-run effects of short-run fluctuations
6% of shock becomes “permanent”
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55. Conclusions
Able to replicate business cycle features
of establishment dynamics and R&D expenditures
Found long-run effects of short-run fluctuations
6% of shock becomes “permanent”
Effect economically significant
welfare cost of business cycles two orders of magnitude higher
than for exogenous growth models
29 / 41

56. Conclusions
Able to replicate business cycle features
of establishment dynamics and R&D expenditures
Found long-run effects of short-run fluctuations
6% of shock becomes “permanent”
Effect economically significant
welfare cost of business cycles two orders of magnitude higher
than for exogenous growth models
Over the business cycle
R&D subsidies to incumbents welfare deteriorating
Direct subsidies to incumbents welfare improving
Justification for policies supporting existing firms
during severe downturns
29 / 41

57. Thank you for your attention
mbielecki@wne.uw.edu.pl
30 / 41

58. References I
Acemoglu, D., Akcigit, U., Bloom, N., & Kerr, W. R. (2013). Innovation,
Reallocation and Growth. Working Paper 18993, National Bureau of
Economic Research.
Acemoglu, D., Carvalho, V. M., Ozdaglar, A., & Tahbaz-Salehi, A.
(2012). The Network Origins of Aggregate Fluctuations.
Econometrica, 80(5), 1977–2016.
Annicchiarico, B. & Pelloni, A. (2016). Innovation, Growth and Optimal
Monetary Policy. Technical Report 376, Tor Vergata University, CEIS.
Annicchiarico, B., Pelloni, A., & Rossi, L. (2011). Endogenous growth,
monetary shocks and nominal rigidities. Economics Letters, 113(2),
103–107.
Annicchiarico, B. & Rossi, L. (2015). Taylor rules, long-run growth and
real uncertainty. Economics Letters, 133(C), 31–34.
Anzoategui, D., Comin, D., Gertler, M., & Martinez, J. (2016).
Endogenous Technology Adoption and R&D as Sources of Business
Cycle Persistence. Working Paper 22005, National Bureau of
Economic Research.
31 / 41

59. References II
Christopoulou, R. & Vermeulen, P. (2010). Markups in the Euro area and
the US over the period 1981-2004: a comparison of 50 sectors.
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Clementi, G. L. & Palazzo, B. (2016). Entry, Exit, Firm Dynamics, and
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Comin, D. & Gertler, M. (2006). Medium-Term Business Cycles.
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Cooley, T. F. & Prescott, E. C. (1995). Economic growth and business
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Keynes and how much Schumpeter? An Estimated Macromodel of the
US Economy. Technical Report 77771, University Library of Munich,
Germany.
32 / 41

60. References III
Ericson, R. & Pakes, A. (1995). Markov-Perfect Industry Dynamics: A
Framework for Empirical Work. The Review of Economic Studies,
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Gabaix, X. (2011). The Granular Origins of Aggregate Fluctuations.
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Gourio, F., Messer, T., & Siemer, M. (2016). Firm Entry and
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Jones, L. E., Manuelli, R. E., & Siu, H. E. (2005). Fluctuations in convex
models of endogenous growth, II: Business cycle properties. Review of
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Laincz, C. A. & Peretto, P. F. (2006). Scale effects in endogenous
growth theory: an error of aggregation not specification. Journal of
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Maliar, L. & Maliar, S. (2004). ENDOGENOUS GROWTH AND
ENDOGENOUS BUSINESS CYCLES. Macroeconomic Dynamics,
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61. References IV
Melitz, M. J. & Redding, S. J. (2014). Chapter 1 - Heterogeneous Firms
and Trade. In E. H. a. K. R. Gita Gopinath (Ed.), Handbook of
International Economics, volume 4 of Handbook of International
Economics (pp. 1–54). Elsevier.
Messer, T., Siemer, M., & Gourio, F. (2016). A Missing Generation of
Firms? Aggregate Effects of the Decline in New Business Formation.
2016 Meeting Paper 752, Society for Economic Dynamics.
Ozlu, E. (1996). Aggregate economic fluctuations in endogenous growth
models. Journal of Macroeconomics, 18(1), 27–47.
Pakes, A. & McGuire, P. (1994). Computing Markov-Perfect Nash
Equilibria: Numerical Implications of a Dynamic Differentiated Product
Model. The RAND Journal of Economics, 25(4), 555–589.
Phillips, K. L. & Wrase, J. (2006). Is Schumpeterian ’creative
destruction’ a plausible source of endogenous real business cycle
shocks? Journal of Economic Dynamics and Control, 30(11),
1885–1913.
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62. References V
Pugsley, B., Sahin, A., & Karahan, F. (2015). Understanding the 30 year
Decline in Business Dynamism: a General Equilibrium Approach. 2015
Meeting Paper 1333, Society for Economic Dynamics.
Rozsypal, F. (2015). Schumpeterian business cycles. 2015 Meeting Paper
320, Society for Economic Dynamics.
Siemer, M. (2014). Firm Entry and Employment Dynamics in the Great
Recession. Finance and Economics Discussion Series 2014-56, Board of
Governors of the Federal Reserve System (U.S.).
Walde, K. (2005). Endogenous Growth Cycles. International Economic
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63. Presentation outline
1 Introduction
2 Model
3 Results
4 Conclusions
5 Appendix
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64. Relatively stable share of employees performing R&D
Source: Laincz & Peretto (2006)
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65. Stable share of production and nonsupervisory employees
1970 1980 1990 2000 2010
Date
70
75
80
85
90
95
Percent
Share of production and nonsupervisory employees
in total private employment
Source: BLS Current Employment Statistics, 1964-2016
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66. Parameters
Par. Description Value Justification
β Discount factor 0.99 Standard (quarterly)
θ Inverse of IES 2 Standard
κ Inverse of Frisch elasticity 1 − 2θ Volatility of hours worked
σ Elasticity of substitution 4 Average markup ≈ 1.331
ρZ Autocorr. of TFP process 0.95 Cooley & Prescott (1995)
σZ Std. dev. of TFP shock 0.0055 Match std. dev. of output
s Share of skilled labor 10% Ballpark estimate2
ι Innovative step size 1.015 Annual GDP p. c. growth
a Incumbent R&D eff. 10 Expansions ≈ contractions
ae
Entrant R&D eff. 10 a = ae
f Incumbent labor req. 1 Share of R&D employment
f e
Entrant labor req. 1 Share of R&D in GDP
δexo
Exog. exit shock prob. 0.02 Exit rate
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1Christopoulou & Vermeulen (2010)
2Acemoglu et al. (2013)
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67. Business cycle moments
Std. dev. Corr. with Y Autocorr.
Variable Data Model Data Model Data Model
Output 1.58 1.58 1.00 1.00 0.82 0.77
Hours 1.36 0.73 0.86 0.99 0.89 0.72
R&D 2.36 2.95 0.32 0.98 0.89 0.68
Establishments 0.62 0.64 0.71 0.70 0.87 0.88
Expansions 2.84 1.22 0.82 0.89 0.75 0.91
Contractions 2.38 0.42 -0.11 -0.46 0.69 0.39
Net Entry 0.31 0.31 0.31 0.49 0.24 0.40
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68. Impulse response functions
0 20 40 60 80 100
Quarter
0.0
0.2
0.4
0.6
0.8
1.0
0 20 40 60 80 100
Quarter
0.0
0.5
1.0
1.5
2.0
2.5
0 20 40 60 80 100
Quarter
0
0.25
0.5
0.75
1
1.25
(a) Productivity (b) Output (c) Hours
0 20 40 60 80 100
Quarter
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0 20 40 60 80 100
Quarter
0
1
2
3
4
5
0 20 40 60 80 100
Quarter
0.0
0.2
0.4
0.6
0.8
1.0
(d) Quality (e) R&D (f) Establishments
0 20 40 60 80 100
Quarter
0.0
0.5
1.0
1.5
2.0
0 20 40 60 80 100
Quarter
−0.8
−0.6
−0.4
−0.2
0.0
0.2
0 20 40 60 80 100
Quarter
−0.2
0.0
0.2
0.4
0.6
(g) Expansions (h) Contractions (i) Net Entry
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