from population growth to firm demographics, slides · concentration average firm size exit rate...

From Population Growth to Firm Demographics:Implications for Concentration, Entrepreneurship and the

Labor Share

Hugo Hopenhayn Julian Neira Rish SinghaniaUCLA University of Exeter University of Exeter

May 17, 2019

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Motivation

I Puzzling aggregate trends in the US since 1980s

I Decline in the firm entry rate (14% to 8%)

I Decline in firm exit rate (9.7% to 7.7%)

I Increase in average firm size (20 to 24 employees)

I Increase in (employment) concentration (51% to 58%)

I Decline in the (corporate) labor share (66% to 60%)

I What explains this?I We look at population growth + firm demographics

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Outline

I Why population growth + firm demographics?I Document new factsI Feedback effects

I Theory

I Accounting

I Calibration

I Results

3 / 43

Overview of Results

I Reallocation across firm-age groups accounts forI ConcentrationI Average firm sizeI Exit ratesI Labor share

I Declining entry rates generate the reallocation

I Declining population growth lowers entry rate

I Feedback from firm demographics to entry is 2/3 of the effect

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Motivating Evidence

5 / 43

52%

54%

56%

58%

20

21

22

23

7%

8%

9%

10%

1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010

Concentration Average Firm Size Exit Rate

Source: BDS

0%

10%

20%

30%

40%

50%

1980 1990 2000 2010

Concentration

2.0

2.5

3.0

3.5

1980 1990 2000 2010

Log Average Firm Size

5%

10%

15%

20%

25%

1980 1990 2000 2010

Exit Rate

Firm agea) 0 b) 1 c) 2 d) 3 e) 4

f) 5 g) 6 to 10 h) 11 to 15 i) 16 to 20 j) 21 to 25

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52%

54%

56%

58%

20

21

22

23

7%

8%

9%

10%

1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010

Concentration Average Firm Size Exit Rate

Source: BDS

0%

10%

20%

30%

40%

50%

1980 1990 2000 2010

Concentration

2.0

2.5

3.0

3.5

1980 1990 2000 2010


5%

10%

15%

20%

25%

1980 1990 2000 2010

Exit Rate

Firm agea) 0 b) 1 c) 2 d) 3 e) 4

f) 5 g) 6 to 10 h) 11 to 15 i) 16 to 20 j) 21 to 256 / 43

Firms are Aging

1990 1995 2000 2005 2010 201530%

35%

40%

45%

50%

55%

1975 1980 1985 1990 1995 2000 2005 2010 20157%

8%

9%

10%

11%

12%

13%

14%

15%

7 / 43

Firms are Aging

1990 1995 2000 2005 2010 201530%

35%

40%

45%

50%

55%

1975 1980 1985 1990 1995 2000 2005 2010 20157%

8%

9%

10%

11%

12%

13%

14%

15%

8 / 43

∆Population Growth → ∆Entry Rates

I Average firm size:et ≡ Nt/Mt

I Growth Decomposition:

M = N − e (1)

I Growth in the number of firms is entry rate minus exit rate

M = λ− ξ (2)

I Combining (1) and (2):

λ = N − e+ ξ

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The Rise and Fall of Population Growth

1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010s0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

10 / 43

Is This Driving Force Enough?

λ = N − e︸︷︷︸0

+ ξ︸︷︷︸12%

1940 1950 1960 1970 1980 1990 2000 2010 20202%

4%

6%

8%

10%

12%

14%

16%

18%

20%

11 / 43

Is This Driving Force Enough?

I Qualitatively yes, quantitatively no.

I Cannot explain movements in exit rate

I Cannot explain increase in average size

I In the data

∆λ︸︷︷︸6%

= ∆N︸︷︷︸2%

− ∆e︸︷︷︸2%

+ ∆ξ︸︷︷︸2%

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Firm Demographics

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∆Population Growth + Firm Demographics

I Need to account for firm demographics

I Important feedback effects

λ = N − e+ ξ

I ∆ entry rates → ∆ age distributionI This affects average firm sizeI Also affects average exit rates

I Decrease in population growth implies:I Decline in entry rateI Aging of firms

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Theory

15 / 43

Environment

I Common discount factor β

I Fixed endowment of a resource (labor) Nt inelasticallysupplied. Numeraire.

I Firm’s idiosyncratic state s

I st ∼ F (st+1|st). Persistence.

I Revenue function R (s, n, Z)

I Aggregate summary state Z

I Employment function n (s, Z)

I Profit function π (s, Z)

I Both strictly increasing

I Accomodates perfect competition and variable markups

16 / 43

Equilibrium: Definition

An equilibrium for a given sequence {Nt} and given initial measureµ0 are sequences {s∗t ,mt, µt, Zt}

1. Exit: Optimal exit condition.

2. Entry: No rents for entrants

3. Resource constraint holds

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Equilibrium: Analysis

I Guess Zt = Z∗ for all t, where ve (Z∗) = 0

I Exit rates, average firm size, and size distributions by cohortsare time invariant.

18 / 43

Resource Constraint

I Define firm demographic variables:I Sa : Probability an entrant survives at least a periodsI ea : Average size of cohort of age a

I Resource constraint

Nt = mte0 + EIt

I Mass of entrants:

mt =Nt − EIt

e0

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Dynamic Entry Equation

mt =Nt − EIt

e0

I Employment by incumbents depends on firm demographics

EIt =

∞∑a=1

mt−aSaea

I History dependence: Current entry depends on past entry

mt =Nt −

∑∞a=1mt−aSaeae0

I Feedback of firm demographics on entry

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From Population Growth to Entry

1. Long run effects

I e = 0I Population growth g affects share of age cohorts:

Lower growth implies lower exit rates

2. Adjustment Path

I Change in g implies changes in average size

I e 6= 0 in the transition

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Accounting

22 / 43

Accounting Exercise

I Composition effect due to changes in Nt

I Take firm demographics Sa and ea from data

I Feed Nt into dynamic entry equation

mt =Nt −

∑∞a=1mt−aSaeae0

I Remain agnostic about the underlying model

23 / 43

1980 1985 1990 1995 2000 2005 20100%

2%

4%

6%

8%

10%

12%

14%

16%

18%

1980 1985 1990 1995 2000 2005 201018

20

22

24

26

28

30

1980 1985 1990 1995 2000 2005 20106%

7%

8%

9%

10%

11%

12%

1980 1985 1990 1995 2000 2005 201050%

51%

52%

53%

54%

55%

56%

57%

58%

24 / 43

I Extrapolation necessary due to data limitations Extrapolation

I Do not observe ea and Sa for older firms (age > 25)

I Match time-series of average firm size and exit rates ofleft-censored firms Match

I Do not observe µ0 (age distribution in 1940)

I Match time-series of employment weight of left-censoredfirms Match

I Alternative to extrapolation: calibrate a structural model

25 / 43

Calibration

26 / 43

Calibration strategy

I Pick a model: perfect competitionI Homogeneous goodI Aggregate state Z equals market price p

I Assume economy in balanced growth path in 1939

I Feed labor force growth rate from 1940 to 2014

I Calibrate to (mostly) 1978 moments

I Look at non-targeted moments

27 / 43

Functional Forms

I Production function

f(s, n) = snα; α < 1

I Log-productivity follows AR(1)

log(st+1) = µs + ρ log(st) + εt+1; εt+1 ∼ N (0, σ2ε)

I Startups draw productivity from

G ∼ logN(s0, σ

20

)I Overhead labor is increasing in firm size

cf = cfa + cfb × h(s)

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Parameter Values

Non-targeted moments on Firm Dynamics?

29 / 43

Parameter Values

Non-targeted moments on Firm Dynamics?29 / 43

Exit, Size, and Concentration by Firm Age

30 / 43

Entry Rate

1940 1950 1960 1970 1980 1990 2000 2010 20202%

4%

6%

8%

10%

12%

14%

16%

18%

20%

31 / 43

Non-targeted moments

1980 2000 202018

20

22

24

26

28

30

1980 2000 20207.0%

7.5%

8.0%

8.5%

9.0%

9.5%

10.0%

10.5%

1980 2000 202050%

51%

52%

53%

54%

55%

56%

57%

58%

59%

32 / 43

Counterfactuals

1940 1950 1960 1970 1980 1990 2000 2010 20204%

6%

8%

10%

12%

14%

16%

33 / 43

Counterfactuals

1940 1950 1960 1970 1980 1990 2000 2010 2020-10%

-8%

-6%

-4%

-2%

0%

2%

34 / 43

Projections

1940 1960 1980 2000 2020 2040 2060

0%

2%

4%

6%

8%

10%

12%

14%

16%

35 / 43

Labor share: Autor et al / Kehrig (2019) + Aging

Labor sharei︸︷︷︸Declining in firm size

=Comp. to production labori

Value addedi︸︷︷︸Same across firms

+Comp. to overhead labori

Value addedi︸︷︷︸Declining in firm size

1940 1950 1960 1970 1980 1990 2000 2010 2020-9%

-8%

-7%

-6%

-5%

-4%

-3%

-2%

-1%

0%

1%

Karabarbounis and Neiman (2014)Koh, Santaeulalia-Llopis and Zheng (2018)Model

36 / 43


Labor sharei

︸︷︷︸Declining in firm size


Value addedi

︸︷︷︸Same across firms


Value addedi


1940 1950 1960 1970 1980 1990 2000 2010 2020-9%

-8%

-7%

-6%

-5%

-4%

-3%

-2%

-1%

0%

1%


36 / 43


Labor sharei





Value addedi


1940 1950 1960 1970 1980 1990 2000 2010 2020-9%

-8%

-7%

-6%

-5%

-4%

-3%

-2%

-1%

0%

1%


36 / 43


Labor sharei






1940 1950 1960 1970 1980 1990 2000 2010 2020-9%

-8%

-7%

-6%

-5%

-4%

-3%

-2%

-1%

0%

1%


36 / 43


Labor sharei︸︷︷︸Declining in firm size





1940 1950 1960 1970 1980 1990 2000 2010 2020-9%

-8%

-7%

-6%

-5%

-4%

-3%

-2%

-1%

0%

1%


36 / 43

Discussion

Labor force and labor supply

Job Creation and Destruction

TFP

CONCLUSION

37 / 43

Alternative Measures of Labor Supply Back

1947-54 1955-64 1965-74 1975-84 1985-94 1995-04 2005-140.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%Labor ForceTotal EmploymentPrivate Sector EmploymentNon-Manufacturing Employment

38 / 43

Labor Force Growth Decomposition Back

LFt = Civilian Noninstitutional Population Age 16 And Overt× Participation Ratet

LF Growth Ratet = CNP16 Growth Ratet + PR Growth Ratet

CNP16 Growth Ratet = Birth Ratet−16 + Other(Migration, Death, Instit)t

39 / 43

Participation Rate By Gender Back

1940 1950 1960 1970 1980 1990 2000 2010 202030%

40%

50%

60%

70%

80%

90%

40 / 43

Job Reallocation: Accounting Approach Back

1980 2000 202022%

24%

26%

28%

30%

32%

34%

36%DataComposition

1980 2000 202011%

12%

13%

14%

15%

16%

17%

18%

19%

20%

21%DataComposition

1980 2000 202011%

12%

13%

14%

15%

16%

17%

18%

19%DataComposition

41 / 43

TFP Growth by Decade Back

I Aggregate production function is Y = AM1−αNα.

I TFP is A =[∫s1/(1−α)dµ(s)

]1−αI Measured TFP is AM1−α.

42 / 43

Conclusions

I Unified quantitative explanation for long-term changes inI Entry rateI Exit ratesI Average firm sizeI ConcentrationI Labor Share

I Population growth as driving force

I Importance of firm demographics

I Interplay of population and firm demographics explains a largepart of these facts

43 / 43

25%

30%

35%

12.5%

15%

17.5%

20%

11%

13%

15%

17%

1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010

Reallocation Rate Job Creation Rate Job Destruction Rate

20%

30%

40%

50%

60%

1980 1990 2000 2010

Reallocation Rate

10%

20%

30%

1980 1990 2000 2010

Job Creation Rate

10%

20%

30%

1980 1990 2000 2010

Job Destruction Rate

Firm ageb) 1 c) 2 d) 3 e) 4 f) 5

g) 6 to 10 h) 11 to 15 i) 16 to 20 j) 21 to 25

Back

Implied interest rate with log utility Back

1980 1985 1990 1995 2000 2005 20103.0%

3.5%

4.0%

4.5%

5.0%

5.5%

6.0%

Regression of reallocation rate on firm age Back

Regression of job creation rate on firm age Back

Regression of job destruction rate on firm age Back

Regression of log average firm size on firm age Back

Regression of exit rate on firm age Back

Regression of concentration on firm age Back

Extrapolation Back

0 10 20 30 40 50 600

50

100

150

0 10 20 30 40 50 600%

5%

10%

15%

20%

25%

0 10 20 30 40 50 600%

20%

40%

60%

80%

0 20 40 60 80 1000%

20%

40%

60%

80%

100%

Accounting Exercise: Left-Censored Match Back

1975 1980 1985 1990 1995 2000 2005 2010 201520

40

60

80

100

120

140DataAccounting

1975 1980 1985 1990 1995 2000 2005 2010 20150.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13DataAccounting

1975 1980 1985 1990 1995 2000 2005 2010 201555%

60%

65%

70%

75%

80%

85%DataAccounting

1975 1980 1985 1990 1995 2000 2005 2010 201540%

50%

60%

70%

80%

90%

100%DataAccounting

Accounting Exercise: Robustness checks Back

0 50 1000%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

BGPFitted

0 50 1000%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

BGPFitted

1980 1990 2000 20100.75

0.8

0.85

0.9

0.95

1

1.05DataAccounting

Distributional Moments Match: Competitive Model

1990 2000 2010 202030%

35%

40%

45%

50%

55%

1990 2000 2010 202066%

68%

70%

72%

74%

76%

78%

80%

82%

84%

86%

1980 2000 20201.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

Age-Size Distribution Match: Competitive Model

1990 1995 2000 2005 2010 20150

0.05

0.1

0.15

0.2

0.25

0.3

1990 1995 2000 2005 2010 20150.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

I Model: Dashed Line

I Data: Solid Line

Establishments

1980 1990 2000 20107%

8%

9%

10%

11%

12%

13%

14%

1990 1995 2000 2005 2010 201530%

32%

34%

36%

38%

40%

42%

44%

46%

48%

Establishments

16.0

16.5

17.0

17.5

18.0

8%

10%

12%

14%

1980 1990 2000 2010 1980 1990 2000 2010

Average establishment size Exit rate

2.0

2.4

2.8

1980 1990 2000 2010

Log Avg. Estab. Size

5%

10%

15%

20%

25%

1980 1990 2000 2010

Exit Rate

Establishment agea) 0 b) 1 c) 2 d) 3 e) 4

f) 5 g) 6 to 10 h) 11 to 15 i) 16 to 20 j) 21 to 25

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

b) 1 c) 2 d) 3 e) 4 f) 5 g) 6-10 h) 11-15 i) 16-20 j) 21-25

Employment Destroyed by Exit(adjusted per year)

Statistics including firms age > 25

0%

10%

20%

30%

40%

50%

60%

70%

80%

1980 1990 2000 2010

Concentration

2.0

2.5

3.0

3.5

4.0

4.5

1980 1990 2000 2010


5%

10%

15%

20%

25%

1980 1990 2000 2010

Exit Rate

Firm agea) 0 b) 1 c) 2 d) 3 e) 4 f) 5

g) 6 to 10 h) 11 to 15 i) 16 to 20 j) 21 to 25 k) Above 25

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