The impact of business cycle fluctuations on aggregate endogenous growth rates SMYE Marcin Bielecki

1. The impact of business cycle fluctuations
on aggregate endogenous growth rates
Marcin Bielecki
University of Warsaw
National Bank of Poland
23 March 2017
22nd Spring Meeting of Young Economists 2017

2. Presentation outline
1 Motivation
2 Model
3 Results
4 Conclusions
5 Appendix

3. Presentation outline
1 Motivation
2 Model
3 Results
4 Conclusions
5 Appendix

4. 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

5. 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

6. 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

7. Motivation
Business cycles research typically employs
the neoclassical growth model with exogenous technological progress
(with either deterministic or stochastic trend)
Endogenous growth research typically abstracts
from cyclical fluctuations, focusing on the (balanced) growth path
and transition dynamics
My research aims to fill the gap in the literature
by employing a single framework to analyze both business cycle
and growth phenomena and examine links between the two

8. Literature review
Endogenous business cycles literature is interested
in the cyclical consequences of “uneven” endogenous growth:
Ozlu (1996), Maliar and Maliar (2004), Jones et al. (2005),
Walde (2005), Phillips and Wrase (2006)
Gabaix (2011), Acemoglu et al. (2012), Rozsypal (2015)
Medium-term business cycles literature is interested
in the long-term impact of transitory shocks:
Comin and Gertler (2006), Anzoategui et al. (2016)
“Missing generations of firms” literature is interested
in the macroeconomic impact of depressed firm entry rates:
Siemer (2014), Pugsley et al. (2015), Messer et al. (2016),
Gourio et al. (2016)

9. Contribution to literature
Business cycle model with endogenous growth
Endogenous growth fully microfounded,
contrary to Comin and Gertler (2006)
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

10. Presentation outline
1 Motivation
2 Model
3 Results
4 Conclusions
5 Appendix

11. Key model ingredients
Inspirations: Acemoglu et al. (2013) and Melitz and Redding (2014)
Constant household population (measure 1)
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 invest in R&D to improve their varieties’ quality
Vertical and horizontal (outside BGP) innovations
Creative destruction
Endogenous entry & exit and R&D intensity

12. Production functions
Intermediates are aggregated into final goods via CES function:
Yt =
ˆ Mt
0
y
(σ−1)/σ
i,t di
σ/(σ−1)
(1)
Yt : final good output
Mt ∈ (0, 1): measure of active establishments, stable along the BGP
yi,t : demand for intermediate good of i-th variety
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,t
u
i,t (2)
Zt : stochastic aggregate productivity level with mean of 1
qi,t : idiosyncratic quality of i-th variety
u
i,t : mass of unskilled labor producing i-th variety

13. Aggregate quality, relative quality and profits
Aggregate (“average”) quality index:
Qt =
1
Mt
ˆ Mt
0
qσ−1
i,t di
1/(σ−1)
(3)
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
(4)
Real “operating profit” of i-th establishment πo
i,t
is an affine function of relative quality φi,t:
πo
i,t (φi,t) =
Yt
σMt
φi,t − ws
t f (5)
ws
t : skilled labor real wage

14. Incumbents: quality evolution
Next period’s quality qi,t+1 of i-th variety is a result of a lottery:
qi,t+1 =
ι · qi,t with probability αi,t
qi,t with probability 1 − αi,t
(6)
ι: size of innovative step
αi,t : endogenous innovative success probability
Other establishments also try to innovate and some succeed,
so the (scaled) 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
(7)

15. Incumbents: R&D intensity and profits
Employing R&D labor x
i,t raises innovative success probability αi,t
(Pakes and McGuire (1994) i Ericson and Pakes (1995)):
αi,t
x
i,t, φi,t =
a x
i,t/φi,t
1 + a rd
i,t/φi,t
(8)
a: R&D input efficacy
Real profit of i-th establishment πi,t is affine in φi,t:
πi,t (φi,t, αi,t) =
Yt
σMt
−
ws
t
a
αi,t
1 − αi,t
φi,t − ws
t f (9)
Establishments with same φ will behave identically, dropping i

16. Incumbents: key tradeoff
Investing in R&D is costly today,
but raises the expected future establishment value
Implication: invest more in R&D
when future productivity is expected to be higher than average

17. Incumbents: value function
Establishments choose αt to maximize the value function:
Vt (φt) = max
αt ∈[0,1)
πt (φt, αt) +
max {0, Et [Λt,t+1 (1 − δt) Vt+1 (φt+1|φt, αt)]}
(10)
Λt,t+1: stochastic discount factor
δt : state-dependent endogenous exit probability
For high enough φ value function is affine in φ
– incumbents choose the same level of α – Gibrat’s law
Piecewise linear approximation makes problem tractable
System reduces to functions of two state variables:
exogenous shock Zt and endogenous establishment mass Mt

18. Piecewise linear approximation of the value function
Piecewise linear function changes slope at φ∗
No need to track full distribution over time!
Policyfunctionα
true
approx.
φ∗
Relative quality level φ
Valuefunctionv

19. Incumbents’ policy function
0.95 1.00 1.05
Productivity shock Z
0.90
0.95
1.00
1.05
1.10
EstablishmentmassM
Success probability α (%)
47
48
49
50
51
52
53

20. Incumbents’ policy function
Productivity shock Z
0.90
0.95
1.00
1.05
1.10 Establishm
ent m
ass M
0.90
0.95
1.00
1.05
1.10
Successprobabilityα(%)
47
48
49
50
51
52
53

21. Entrants
Entry success function mirrors incumbents’ R&D function
Choose entry probability αe
t maximizing value function:
V e
t = max
αe
t ∈[0,1]
−ws
t f e
+ 1
ae
αe
t
1−αe
t
+αe
t · Et [Λt,t+1Vt (φe
)]
(11)
f e
: skilled labor required to attempt entry
ae
: entrant R&D input efficacy
Entrant establishments draw their quality from incumbents’
quality distribution upscaled by σ
σ−1 (no limit pricing)
Free entry condition allows for no entry at all:
V e
t ≤ 0 (12)

22. Entrants’ policy function
0.95 1.00 1.05
Productivity shock Z
0.90
0.95
1.00
1.05
1.10
EstablishmentmassM
Entry rate Me
/M (%)
0
2
4
6
8
10
12
14
16

23. Entrants’ policy function
Establishment mass M
0.90
0.95
1.00
1.05
1.10 Productivity shock
Z
0.90
0.95
1.00
1.05
1.10
EntryrateMe
/M(%)
−2
0
2
4
6
8
10
12
14
16

24. Aggregate growth
Aggregate quality index improves at the following rate:
ηt = (1 + αt (ι − 1)) 1 +
Me
t
Mt+1
1
σ − 1
(13)
Growth rate positively depends on αt and Me
t , ceteris paribus
Along the BGP entries are responsible for around 1/3
of aggregate quality increases (cf. Acemoglu and Cao (2015))

25. Presentation outline
1 Motivation
2 Model
3 Results
4 Conclusions
5 Appendix

26. Parameters
Par. Description Value Justification
s Share of skilled labor 0.1 Ballpark estimate1
β Discount factor 0.99 Standard (quarterly)
θ Inverse of IES 2 Standard
κ Inverse of Frisch elasticity 2 Standard
σ Elasticity of substitution 4 Average markup ≈ 1.332
ρ Autocorr. of TFP process 0.95 Cooley and Prescott (1995)
σε Std. dev. of TFP shock 0.007 Cooley and Prescott (1995)
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 profits in GDP
δexo
Exog. exit shock prob. 0.02 Exit rate
1Acemoglu et al. (2013)
2Christopoulou and Vermeulen (2010)

27. Long-run moments
Comparison of model outcomes with long-run US data averages
Description Model Data Source
Annual GDP p. c. growth 2.02% 2.08% BEA, 1947q1-2016q2
Rel. share of exp. estabs. 1.005 1.01 BDM, 1992q3-2015q4
Share of R&D employment 0.98% 0.98% NSF & CBP, 1975-2008
Share of profits in GDP 4.65% 6.53% BEA, 1947q1-2016q2
Exit rate3
3.07% 3.07% BDM, 1992q3-2015q4
Share of R&D in GDP 2.07% 2.23% BEA, 1947q1-2016q2
Skilled wage premium4
2.55 2.07 CPS, 2000-2016
3Calculated from the data as the average between death and birth rates.
4Ratio of median wages of advanced degree holders vs high school graduates

28. Business cycle moments
Variable
Std. dev. Rel. s. d. Corr. w. Y Autocorr.
Data Model Data Model Data Model Data Model
Output 1.52 1.09 1.00 1.00 1.00 1.00 0.89 0.80
Establishments 0.73 0.76 0.48 0.71 0.72 0.74 0.94 0.89
Expansions 2.76 1.26 1.82 1.16 0.82 0.86 0.77 0.92
Contractions 2.49 0.40 1.64 0.37 0.01 0.13 0.79 0.60
Births 3.43 12.13 2.26 12.08 0.62 0.53 0.46 0.45
Deaths 4.47 2.12 2.94 0.67 -0.10 -0.04 0.66 0.08
Net entry 0.33 0.35 0.22 0.36 0.34 0.50 0.58 0.43
Data moments based on the 1992q3-2015q4 sample (95 quarters).
Model moments are based on 10000 simulated quarters.

29. Cross-correlations with output
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Output, Establishments (+i)
Data
Model
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Output, Net entry (+i)
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Output, Contractions (+i)
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Output, Expansions (+i)
Good qualitative fit to the data
Excellent match for expansions
Slightly worse for contractions and net entry

30. Key impulse response function
Shock hysteresis on BGP: 3.5% of shock remains
0 20 40 60 80 100
Quarter
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Productivityshock(%)
0 20 40 60 80 100
Quarter
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
Qualitylevel(%)

31. Impulse response function
Shock hysteresis on BGP: 3.5% of shock remains
0 20 40 60 80 100
Quarter
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Productivityshock(%)
0 20 40 60 80 100
Quarter
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Output(%)
0 20 40 60 80 100
Quarter
−0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Netentry(%)
0 20 40 60 80 100
Quarter
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Establishments(%)
0 20 40 60 80 100
Quarter
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Expansions(%)
0 20 40 60 80 100
Quarter
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035Qualitylevel(%)

32. 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” Utility
Consumption
equivalent (µ)
Balanced
-249.00 –
Growth Path
Stochastic
-249.12 0.05%
(exogenous growth)
Stochastic
-257.85 3.56%
(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

33. Presentation outline
1 Motivation
2 Model
3 Results
4 Conclusions
5 Appendix

34. Conclusions
Able to replicate business cycle features
of establishment dynamics
Found long-run effects of short-run fluctuations:
3.5% of shock becomes “permanent”
Effect economically significant: welfare cost
of business cycles two orders of magnitude higher
than for exogenous growth models
Lack of salient frictions generates smaller volatility than in the data
Frictions expected to be amplifiers
– obtained lower bound estimate on hysteresis

35. Thank you for your attention
mbielecki@wne.uw.edu.pl

36. References I
Acemoglu, D., Akcigit, U., Bloom, N., and Kerr, W. R. (2013).
Innovation, Reallocation and Growth. Working Paper 18993, National
Bureau of Economic Research.
Acemoglu, D. and Cao, D. (2015). Innovation by entrants and
incumbents. Journal of Economic Theory, 157:255–294.
Acemoglu, D., Carvalho, V. M., Ozdaglar, A., and Tahbaz-Salehi, A.
(2012). The Network Origins of Aggregate Fluctuations.
Econometrica, 80(5):1977–2016.
Anzoategui, D., Comin, D., Gertler, M., and Martinez, J. (2016).
Endogenous Technology Adoption and R&D as Sources of Business
Cycle Persistence. Working Paper 22005, National Bureau of
Economic Research.
Christopoulou, R. and Vermeulen, P. (2010). Markups in the Euro area
and the US over the period 1981-2004: a comparison of 50 sectors.
Empirical Economics, 42(1):53–77.
Comin, D. and Gertler, M. (2006). Medium-Term Business Cycles.
American Economic Review, 96(3):523–551.

37. References II
Cooley, T. F. and Prescott, E. C. (1995). Economic growth and business
cycles. In Cooley, T. F., editor, Frontiers of Business Cycle Research,
chapter 1, pages 1–38. Princeton University Press.
Ericson, R. and Pakes, A. (1995). Markov-Perfect Industry Dynamics: A
Framework for Empirical Work. The Review of Economic Studies,
62(1):53–82.
Gabaix, X. (2011). The Granular Origins of Aggregate Fluctuations.
Econometrica, 79(3):733–772.
Gourio, F., Messer, T., and Siemer, M. (2016). Firm Entry and
Macroeconomic Dynamics: A State-Level Analysis. American
Economic Review, 106(5):214–218.
Greenwood, J., Hercowitz, Z., and Huffman, G. W. (1988). Investment,
Capacity Utilization, and the Real Business Cycle. The American
Economic Review, 78(3):402–417.
Jones, L. E., Manuelli, R. E., and Siu, H. E. (2005). Fluctuations in
convex models of endogenous growth, II: Business cycle properties.
Review of Economic Dynamics, 8(4):805–828.

38. References III
Laincz, C. A. and Peretto, P. F. (2006). Scale effects in endogenous
growth theory: an error of aggregation not specification. Journal of
Economic Growth, 11(3):263–288.
Maliar, L. and Maliar, S. (2004). ENDOGENOUS GROWTH AND
ENDOGENOUS BUSINESS CYCLES. Macroeconomic Dynamics,
8(5):559–581.
Melitz, M. J. and Redding, S. J. (2014). Chapter 1 - Heterogeneous
Firms and Trade. In Gita Gopinath, E. H. a. K. R., editor, Handbook
of International Economics, volume 4 of Handbook of International
Economics, pages 1–54. Elsevier.
Messer, T., Siemer, M., and 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. and 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.

39. References IV
Phillips, K. L. and 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.
Pugsley, B., Sahin, A., and Karahan, F. (2015). Understanding the 30
year Decline in Business Dynamism: a General Equilibrium Approach.
2015 Meeting Paper 1333, Society for Economic Dynamics.
Rossi-Hansberg, E. and Wright, M. L. J. (2007). Establishment Size
Dynamics in the Aggregate Economy. American Economic Review,
97(5):1639–1666.
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
Review, 46(3):867–894.

40. Presentation outline
1 Motivation
2 Model
3 Results
4 Conclusions
5 Appendix

41. US establishment size distribution is stable over time
1975 1980 1985 1990 1995 2000 2005 2010
Date
10−3
10−2
10−1
100
Counter-cumulativedistribution
5
10
20
50
100
250
500
1000
Establishmentsize(employees)
Source: County Business Patterns (CBP), 1975-2014
Note: Break in the data in 1983 (change in definition of establishment)

42. US establishment size distribution is stable over time
100
101
102
103
104
Establishment size (employees)
10−5
10−4
10−3
10−2
10−1
100
Counter-cumulativedistribution
fitted
1990
1995
2000
Source: Data from Rossi-Hansberg and Wright (2007), 1990-2000

43. Relatively stable share of employees performing R&D
Source: Laincz and Peretto (2006)
back

44. 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
Źródło: BLS Current Employment Statistics, 1964-2016
back

45. Households: utility
Each household is a large family with share s of skilled workers
and share (1 − s) of unskilled workers
Maximize expected lifetime utility;
Greenwood et al. (1988) (GHH)-like felicity function:
U0 = E0
∞
t=0
βt



1
1 − θ




ct
− (1 − s) ψu
t ( u
t )
1+κ
/ (1 + κ) − 1
−sψs
t ( s
t )
1+κ
/ (1 + κ) − 1




1−θ


(14)
ct : per capita consumption
u
t , s
t : unskilled and skilled labor supply
β: discount factor
θ: inverse of the elasticity of intertemporal substitution
κ: inverse of Frisch elasticity of labor supply
ψu
t , ψs
t : unskilled and skilled labor disutility parameters,
trend over time such that u
BGP = s
BGP = 1
Utility function reduces to CRRA along the BGP,
behaves like GHH over the business cycle

46. Households: optimality conditions
As is standard for GHH, labor supply depends on real wage only:
u
t =
wu
t
(1 − s) ψu
t
1/κ
(15)
s
t =
ws
t
sψs
t
1/κ
(16)
wu
t , ws
t : unskilled and skilled real wage
Marginal utility from consumption:
λt = ct − (1 − s) ψu
t
( u
t )
1+κ
1 + κ
− 1 − sψs
t
( s
t )
1+κ
1 + κ
− 1
−θ
(17)
Stochastic discount factor:
Λt,t+1 = βEt
λt+1
λt
(18)