Firm and Worker Dynamics in a rictionalF Labor...
Transcript of Firm and Worker Dynamics in a rictionalF Labor...
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Firm and Worker Dynamics
in a Frictional Labor Market
Adrien Bilal - Niklas Engbom - Simon Mongey - Gianluca Violante
EUI
December 12th, 2019
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Labor reallocation
Reallocation of labor in the economy is key to understand:
dynamics of aggregate productivity
adjustment after sectoral/occupational shocks
impact of labor and product market policies
1. Jobs move across rms: job turnover (JD = 4%)
2. Workers move across jobs: worker turnover (SEP = 10%)
⇓
Two approaches to the analysis of labor reallocation
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Labor reallocation
Reallocation of labor in the economy is key to understand:
dynamics of aggregate productivity
adjustment after sectoral/occupational shocks
impact of labor and product market policies
1. Jobs move across rms: job turnover (JD = 4%)
2. Workers move across jobs: worker turnover (SEP = 10%)
⇓
Two approaches to the analysis of labor reallocation
![Page 5: Firm and Worker Dynamics in a rictionalF Labor Marketviolante.mycpanel.princeton.edu/Slides/Presentation_EUI.pdf · impact of labor and product market policies 1.Jobs move across](https://reader033.fdocuments.us/reader033/viewer/2022050107/5f4536f4d754165b92234f34/html5/thumbnails/5.jpg)
Labor reallocation
Reallocation of labor in the economy is key to understand:
dynamics of aggregate productivity
adjustment after sectoral/occupational shocks
impact of labor and product market policies
1. Jobs move across rms: job turnover (JD = 4%)
2. Workers move across jobs: worker turnover (SEP = 10%)
⇓
Two approaches to the analysis of labor reallocation
![Page 6: Firm and Worker Dynamics in a rictionalF Labor Marketviolante.mycpanel.princeton.edu/Slides/Presentation_EUI.pdf · impact of labor and product market policies 1.Jobs move across](https://reader033.fdocuments.us/reader033/viewer/2022050107/5f4536f4d754165b92234f34/html5/thumbnails/6.jpg)
Two approaches
1. Firm dynamics with competitive labor market
Span of control or taste for variety: DRS
Lucas (1978), Hopenhayn (1992), Melitz (2003)
Firm size distribution and job turnover: determined
Worker ows: indeterminate
2. Worker dynamics with frictional labor market
Job ladder: OJS with 1w-1f / CRS
Postel-Vinay & Robin (2002), Burdett & Mortensen (1998)
Worker ows: determined
Firm size distribution indeterminate/pinned down by frictions
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Two approaches
1. Firm dynamics with competitive labor market
Span of control or taste for variety: DRS
Lucas (1978), Hopenhayn (1992), Melitz (2003)
Firm size distribution and job turnover: determined
Worker ows: indeterminate
2. Worker dynamics with frictional labor market
Job ladder: OJS with 1w-1f / CRS
Postel-Vinay & Robin (2002), Burdett & Mortensen (1998)
Worker ows: determined
Firm size distribution indeterminate/pinned down by frictions
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This paper
A theory of joint rm & worker dynamics in a frictional LM
Hopenhayn-type rms: DRS, enter, receive shocks, hire/re, exit
PVR-type workers: search at random o and on the job
Challenge: value sharing btw workers and rm with DRS + OJS
1. Propose a contractual environment s.t.
Allocation characterized by joint value of rm + all employees
Parsimonious: joint value depends only on productivity + size
Privately ecient
Endogenous job ladder in marginal surplus
2. Characterization of rm dynamics, job and worker ows
3. Parameterization + Questions
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This paper
A theory of joint rm & worker dynamics in a frictional LM
Hopenhayn-type rms: DRS, enter, receive shocks, hire/re, exit
PVR-type workers: search at random o and on the job
Challenge: value sharing btw workers and rm with DRS + OJS
1. Propose a contractual environment s.t.
Allocation characterized by joint value of rm + all employees
Parsimonious: joint value depends only on productivity + size
Privately ecient
Endogenous job ladder in marginal surplus
2. Characterization of rm dynamics, job and worker ows
3. Parameterization + Questions
![Page 10: Firm and Worker Dynamics in a rictionalF Labor Marketviolante.mycpanel.princeton.edu/Slides/Presentation_EUI.pdf · impact of labor and product market policies 1.Jobs move across](https://reader033.fdocuments.us/reader033/viewer/2022050107/5f4536f4d754165b92234f34/html5/thumbnails/10.jpg)
This paper
A theory of joint rm & worker dynamics in a frictional LM
Hopenhayn-type rms: DRS, enter, receive shocks, hire/re, exit
PVR-type workers: search at random o and on the job
Challenge: value sharing btw workers and rm with DRS + OJS
1. Propose a contractual environment s.t.
Allocation characterized by joint value of rm + all employees
Parsimonious: joint value depends only on productivity + size
Privately ecient
Endogenous job ladder in marginal surplus
2. Characterization of rm dynamics, job and worker ows
3. Parameterization + Questions
![Page 11: Firm and Worker Dynamics in a rictionalF Labor Marketviolante.mycpanel.princeton.edu/Slides/Presentation_EUI.pdf · impact of labor and product market policies 1.Jobs move across](https://reader033.fdocuments.us/reader033/viewer/2022050107/5f4536f4d754165b92234f34/html5/thumbnails/11.jpg)
Questions for an environment with DRS + OJS
1. What is the misallocation cost of labor market frictions?
Can't do this counterfactual with CRS, nor w/o OJS
2. Which rm characteristics determine its rank on the job ladder?
Speak to new micro data on poaching ows by rm type
3. Why the failure of the job ladder in Great Recession?
Conjecture: related to the sharp drop in rm entry
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Environment
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Demographics and preferences
Continuous time
Unit continuum of ∞-lived workers
Ex-ante homogeneous
Risk neutral with discount rate ρ
Supply inelastically one unit of labor
Endogenous wage payment w as employed
Exogenous ow value of leisure b as unemployed
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Technology
Endogenous mass m of rms produce the nal good (numeraire)
Production function:
y(z, n)
z is idiosyncratic productivity:
dzt = µdt+ σdWt
n is the number of workers
Properties: yz > 0, yn > 0, ynn ≤ 0, yzn ≥ 0
Workers recruited by posting vacancies v at cost c(v;n)
Firm entry cost c0 and scrap value ϑ
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Random search in a single labor market
Unemployed: meet vacancies at rate λU
Employed:
Search with relative intensity ξ → λE = ξλU
Lose job endogenously, or exogenously at rate δ
Vacancies v: meet workers at rate λF
CRS matching function (v, s) → θ = v/s
s = u + ξ(1− u) is the mass of eective job seekers
φ = u/s is the share of unemployed job seekers
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Desired representation
Allocative decisions (entry, exit, vacancy, mobility) are obtainedfrom the joint value Ω of the rm (owner of the technology) andits incumbent workers
Appealing properties of such representation:
1. All decisions within `coalitions' are privately ecient
2. Parsimonious state space: (z, n)
3. Endogenous job ladder in marginal value Ωn (or Sn = Ωn − U)
With complete information & contracts: Coase Theorem
What if we impose plausible restrictions on contracts?
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Desired representation
Allocative decisions (entry, exit, vacancy, mobility) are obtainedfrom the joint value Ω of the rm (owner of the technology) andits incumbent workers
Appealing properties of such representation:
1. All decisions within `coalitions' are privately ecient
2. Parsimonious state space: (z, n)
3. Endogenous job ladder in marginal value Ωn (or Sn = Ωn − U)
With complete information & contracts: Coase Theorem
What if we impose plausible restrictions on contracts?
![Page 18: Firm and Worker Dynamics in a rictionalF Labor Marketviolante.mycpanel.princeton.edu/Slides/Presentation_EUI.pdf · impact of labor and product market policies 1.Jobs move across](https://reader033.fdocuments.us/reader033/viewer/2022050107/5f4536f4d754165b92234f34/html5/thumbnails/18.jpg)
Contractual environment I
Contract: a constant wage in exchange for labor services
[A-LC] Two-sided limited commitment
Quits: Workers can always quit the rm
Layos / Exit: Firms can always re workers / exit
[A-MC] Self-enforcing labor contracts
Contracts can be renegotiated only under mutual consent
Both parties agree to renegotiate when one has a credible threat
Credible threat: when one party is better o dissolving the match
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Contractual environment I
Contract: a constant wage in exchange for labor services
[A-LC] Two-sided limited commitment
Quits: Workers can always quit the rm
Layos / Exit: Firms can always re workers / exit
[A-MC] Self-enforcing labor contracts
Contracts can be renegotiated only under mutual consent
Both parties agree to renegotiate when one has a credible threat
Credible threat: when one party is better o dissolving the match
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Contractual environment II
Negotiation protocol between rm and workers
[A-EN] External negotiation between rm and jobseekers
Meeting with unemployed: rm makes TOL oer
Meeting with employed: sequential auction with TOL oers
[A-IN] Internal negotiation between rm and its incumbents
Zero sum game
With additional assumptions: can determine wage payments
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Contractual environment II
Negotiation protocol between rm and workers
[A-EN] External negotiation between rm and jobseekers
Meeting with unemployed: rm makes TOL oer
Meeting with employed: sequential auction with TOL oers
[A-IN] Internal negotiation between rm and its incumbents
Zero sum game
With additional assumptions: can determine wage payments
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Contractual environment II
Negotiation protocol between rm and workers
[A-EN] External negotiation between rm and jobseekers
Meeting with unemployed: rm makes TOL oer
Meeting with employed: sequential auction with TOL oers
[A-IN] Internal negotiation between rm and its incumbents
Zero sum game
With additional assumptions: can determine wage payments
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Contractual environment III
DRS + OJS: prot maximizing vacancies are privately inecient
1. Fire and swap incentives, even if hiring is not protable
CRS + OJS: absent because hiring is always protable
DRS w/o OJS: absent because all workers paid same wage
2. Over-hiring incentives to push down MPL and keep wages low
CRS + OJS: absent
DRS w/o OJS: present, but tractable (Elsby-Michaels, 2013)
DRS + OJS: Private eciency yields tractability
[A-VP] Ecient vacancy posting
After rm chooses vacancies, incumbents make TOL counteroer
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Contractual environment III
DRS + OJS: prot maximizing vacancies are privately inecient
1. Fire and swap incentives, even if hiring is not protable
CRS + OJS: absent because hiring is always protable
DRS w/o OJS: absent because all workers paid same wage
2. Over-hiring incentives to push down MPL and keep wages low
CRS + OJS: absent
DRS w/o OJS: present, but tractable (Elsby-Michaels, 2013)
DRS + OJS: Private eciency yields tractability
[A-VP] Ecient vacancy posting
After rm chooses vacancies, incumbents make TOL counteroer
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Contractual environment III
DRS + OJS: prot maximizing vacancies are privately inecient
1. Fire and swap incentives, even if hiring is not protable
CRS + OJS: absent because hiring is always protable
DRS w/o OJS: absent because all workers paid same wage
2. Over-hiring incentives to push down MPL and keep wages low
CRS + OJS: absent
DRS w/o OJS: present, but tractable (Elsby-Michaels, 2013)
DRS + OJS: Private eciency yields tractability
[A-VP] Ecient vacancy posting
After rm chooses vacancies, incumbents make TOL counteroer
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Joint value representation
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The maximized joint value
ρΩ(z, n) =
maxv≥0
y (z, n)− c (v;n)︸ ︷︷ ︸net output ow
+(vλFφ− δn
)·[Ωn(z, n)− U
]︸ ︷︷ ︸
net hires from unemployment
+ vλF (1− φ) ·Ωn(z,n)
U
[Ωn(z, n)− Ω′n
]dG(Ω′n)
︸ ︷︷ ︸hires from rms ranked lower in the job ladder
− nλE
Ωn(z,n)
[Ωn(z, n)− Ωn(z, n)
]dF(Ω′n)
︸ ︷︷ ︸quits to other rms ranked higher in the job ladder
+ µ(z)Ωz(z, n) +σ2(z)
2Ωzz(z, n)︸ ︷︷ ︸
productivity shocks
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The maximized joint value
ρΩ(z, n) =
maxv≥0
y (z, n)− c (v;n)︸ ︷︷ ︸net output ow
+(vλFφ− δn
)·[Ωn(z, n)− U
]︸ ︷︷ ︸
net hires from unemployment
+ vλF (1− φ) ·Ωn(z,n)
U
[Ωn(z, n)− Ω′n
]dG(Ω′n)
︸ ︷︷ ︸hires from rms ranked lower in the job ladder
− nλE
Ωn(z,n)
[Ωn(z, n)− Ωn(z, n)
]dF(Ω′n)
︸ ︷︷ ︸quits to other rms ranked higher in the job ladder
+ µ(z)Ωz(z, n) +σ2(z)
2Ωzz(z, n)︸ ︷︷ ︸
productivity shocks
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The maximized joint value
ρΩ(z, n) =
maxv≥0
y (z, n)− c (v;n)︸ ︷︷ ︸net output ow
+(vλFφ− δn
)·[Ωn(z, n)− U
]︸ ︷︷ ︸
net hires from unemployment
+ vλF (1− φ) ·Ωn(z,n)
U
[Ωn(z, n)− Ω′n
]dG(Ω′n)
︸ ︷︷ ︸hires from rms ranked lower in the job ladder
− nλE
Ωn(z,n)
[Ωn(z, n)− Ωn(z, n)
]dF(Ω′n)
︸ ︷︷ ︸quits to other rms ranked higher in the job ladder
+ µ(z)Ωz(z, n) +σ2(z)
2Ωzz(z, n)︸ ︷︷ ︸
productivity shocks
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The maximized joint value
ρΩ(z, n) =
maxv≥0
y (z, n)− c (v;n)︸ ︷︷ ︸net output ow
+(vλFφ− δn
)·[Ωn(z, n)− U
]︸ ︷︷ ︸
net hires from unemployment
+ vλF (1− φ) ·Ωn(z,n)
U
[Ωn(z, n)− Ω′n
]dG(Ω′n)
︸ ︷︷ ︸hires from rms ranked lower in the job ladder
− nλE
Ωn(z,n)
[Ωn(z, n)− Ωn(z, n)
]dF(Ω′n)
︸ ︷︷ ︸quits to other rms ranked higher in the job ladder
+ µ(z)Ωz(z, n) +σ2(z)
2Ωzz(z, n)︸ ︷︷ ︸
productivity shocks
![Page 31: Firm and Worker Dynamics in a rictionalF Labor Marketviolante.mycpanel.princeton.edu/Slides/Presentation_EUI.pdf · impact of labor and product market policies 1.Jobs move across](https://reader033.fdocuments.us/reader033/viewer/2022050107/5f4536f4d754165b92234f34/html5/thumbnails/31.jpg)
The maximized joint value
ρΩ(z, n) =
maxv≥0
y (z, n)− c (v;n)︸ ︷︷ ︸net output ow
+(vλFφ− δn
)·[Ωn(z, n)− U
]︸ ︷︷ ︸
net hires from unemployment
+ vλF (1− φ) ·Ωn(z,n)
U
[Ωn(z, n)− Ω′n
]dG(Ω′n)
︸ ︷︷ ︸hires from rms ranked lower in the job ladder
− nλE
Ωn(z,n)
[Ωn(z, n)− Ωn(z, n)
]dF(Ω′n)
︸ ︷︷ ︸quits to other rms ranked higher in the job ladder
+ µ(z)Ωz(z, n) +σ2(z)
2Ωzz(z, n)︸ ︷︷ ︸
productivity shocks
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The maximized joint value
ρΩ(z, n) = maxv≥0
y (z, n)− c (v;n)︸ ︷︷ ︸net output ow
+(vλFφ− δn
)·[Ωn(z, n)− U
]︸ ︷︷ ︸
net hires from U
+ vλF (1− φ) ·Ωn(z,n)
U
[Ωn(z, n)− Ω′n
]dG(
Ω′n
)︸ ︷︷ ︸
hires from below in job ladder
− 0
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The maximized joint value
ρΩ(z, n) = maxv≥0
y (z, n)− c (v;n)︸ ︷︷ ︸net output ow
+(vλFφ− δn
)·[Ωn(z, n)− U
]︸ ︷︷ ︸
net hires from U
+ vλF (1− φ) ·Ωn(z,n)
U
[Ωn(z, n)− Ω′n
]dG(
Ω′n
)︸ ︷︷ ︸
hires from below in job ladder
+ µ(z)Ωz(z, n) +σ2(z)
2Ωzz(z, n)︸ ︷︷ ︸
productivity shocks
![Page 34: Firm and Worker Dynamics in a rictionalF Labor Marketviolante.mycpanel.princeton.edu/Slides/Presentation_EUI.pdf · impact of labor and product market policies 1.Jobs move across](https://reader033.fdocuments.us/reader033/viewer/2022050107/5f4536f4d754165b92234f34/html5/thumbnails/34.jpg)
The maximized joint value
ρΩ(z, n) = maxv≥0
y (z, n)− c (v;n)︸ ︷︷ ︸net output ow
+(vλFφ− δn
)·[Ωn(z, n)− U
]︸ ︷︷ ︸
net hires from U
+ vλF (1− φ) ·Ωn(z,n)
U
[Ωn(z, n)− Ω′n
]dG(
Ω′n
)︸ ︷︷ ︸
hires from below in job ladder
+ µ(z)Ωz(z, n) +σ2(z)
2Ωzz(z, n)︸ ︷︷ ︸
productivity shocks
subject to:
Ωn(z, n) ≥≥≥ U︸ ︷︷ ︸endogenous separations if ===
; Ω(z, n) ≥≥≥ nU + ϑ︸ ︷︷ ︸exit if ===
; E[Ω(z, n0)
]≤≤≤ n0U + c0︸ ︷︷ ︸
entry if ===
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Static example
Static Example
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Equilibrium
and limiting economies
Equilibrium
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Stationary equilibrium
(i) Ω(z, n) satises the HJB equation and its boundary conditions
(ii) The vacancy policy v(z, n) satises the rst order condition:
cv(v(·)) = λF (θ)
[φ (Ωn(z, n)− U) + (1− φ)
Ωn(z,n)
0
(Ωn(z, n)− Ω′n
)dG(Ω′n)
]
(iii) Law of motion for rm-level employment satises:
dn
dt(z, n) = λF (θ)v(z, n)
[φ+(1−φ)G(Ωn(z, n))
]−n[δ+λE(θ)F (Ωn(z, n))
](iv) Free-entry determines m0
(v) F (Ωn) and G(Ωn) are stationary and solve KFE(dndt , m0
)(vi) u, v, θ are consistent with vacancy policy and distributions
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Two limiting economies
1. If y(z, n) and c(v, n) are linear in n =⇒ PVR (2012)
ρΩ(z) = maxv≥0
y(z) − c(v) +(vλFφ− δ
)[Ω(z) − U
]
+ vλF (1 − φ)
Ω(z)
U
[Ω(z) − Ω′
]dG(Ω′)
Exogenous job ladder in productivity z
2. If matching eciency →∞ =⇒ Hopenhayn (1992)
Non degenerate rm size distribution
No dispersion in marginal product of labor across rms
Perfect correlation between size and productivity
Zero unemployment
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Two limiting economies
1. If y(z, n) and c(v, n) are linear in n =⇒ PVR (2012)
ρΩ(z) = maxv≥0
y(z) − c(v) +(vλFφ− δ
)[Ω(z) − U
]
+ vλF (1 − φ)
Ω(z)
U
[Ω(z) − Ω′
]dG(Ω′)
Exogenous job ladder in productivity z
2. If matching eciency →∞ =⇒ Hopenhayn (1992)
Non degenerate rm size distribution
No dispersion in marginal product of labor across rms
Perfect correlation between size and productivity
Zero unemployment
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Characterization
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Firm dynamics and job reallocation in (n, z) space
z
0 n
dn = 0
Job Creation
Entry
Job Destruction
Exit
Ω(z, n) = nU + ϑ
n0
dn = 0
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Firm dynamics and job reallocation in (n, z) space
z
0 n
dn = 0
Job Creation
Entry
Job Destruction
Exit
Ω(z, n) = nU + ϑ
n0
dn = 0
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Firm dynamics and job reallocation in (n, z) space
z
0 n
dn = 0
Job Creation
EntryJob Destruction
Exit
Ω(z, n) = nU + ϑ
n0
dn = 0
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Worker reallocation in (n, z) space
z
0 n
Hire
Fire
Ωn(z, n) = U
dn = 0dn = 0
Hire & JC
Hire & JD
Fire
Exit
Ω(z, n) = nU + ϑ
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Worker reallocation in (n, z) space
z
0 n
Hire
Fire
Ωn(z, n) = U
dn = 0dn = 0
Hire & JC
Hire & JD
Fire & JD
Exit
Ω(z, n) = nU + ϑ
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Worker reallocation in (n, z) space
z
0 n
Hire
Fire
Ωn(z, n) = U
dn = 0dn = 0
Hire & JC
Hire & JD
Fire & JD
Exit
Ω(z, n) = nU + ϑ
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Worker reallocation in (n, z) space
z
0 n
Hire
Fire
Ωn(z, n) = U
dn = 0dn = 0
Hire & JC
Hire & JD
Fire & JD
Exit
Ω(z, n) = nU + ϑ
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Worker reallocation in (n, z) space
z
0 n
Hire
Fire
Ωn(z, n) = U
dn = 0dn = 0
Hire & JC
Hire & JD
Fire & JD
Exit
Ω(z, n) = nU + ϑ
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Worker reallocation in (n, z) space
z
0 n
Hire
Fire
Ωn(z, n) = U
dn = 0dn = 0
Hire & JC
Hire & JD
Fire & JD
Exit
Ω(z, n) = nU + ϑ
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Worker reallocation in (n, z) space
z
0 n
Hire
Fire
Ωn(z, n) = U
dn = 0dn = 0
Hire & JC
Hire & JD
Fire & JD
Exit
Ω(z, n) = nU + ϑ
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Worker reallocation in (n, z) space
z
0 n
Hire
Fire
Ωn(z, n) = U
dn = 0dn = 0
Hire & JC
Hire & JD
Fire & JD
Exit
Ω(z, n) = nU + ϑ
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Worker reallocation in (n, z) space
z
0 n
Hire
Fire
Ωn(z, n) = U
dn = 0dn = 0
Hire & JC
Hire & JD
Fire & JD
Exit
Ω(z, n) = nU + ϑ
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Worker reallocation in (n, z) space
z
0 n
Hire
Fire
Ωn(z, n) = U
dn = 0dn = 0
Hire & JC
Hire & JD
Fire & JD
Exit
Ω(z, n) = nU + ϑ
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Worker reallocation in (n, z) space
z
0 n
Hire
Fire
Ωn(z, n) = U
dn = 0dn = 0
Hire & JC
Hire & JD
Fire & JD
Exit
Ω(z, n) = nU + ϑ
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Worker reallocation in (n, z) space
z
0 n
Hire
Fire
Ωn(z, n) = U
dn = 0dn = 0
Hire & JC
Hire & JD
Fire & JD
Exit
Ω(z, n) = nU + ϑ
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Worker reallocation in (n, z) space
z
0 n
Hire
Fire
Ωn(z, n) = U
dn = 0dn = 0
Hire & JC
Hire & JD
Fire & JD
Exit
Ω(z, n) = nU + ϑ
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Worker reallocation in (n, z) space
z
0 n
Hire
Fire
Ωn(z, n) = U
dn = 0dn = 0
Hire & JC
Hire & JD
Fire & JD
Exit
Ω(z, n) = nU + ϑ
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Worker reallocation in (n, z) space
z
0 n
Hire
Fire
Ωn(z, n) = U
dn = 0dn = 0
Hire & JC
Hire & JD
Fire & JD
Exit
Ω(z, n) = nU + ϑ
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Composition of worker ows
dn
n= λF v
∗(Ωn)
n
φ︸︷︷︸UE
+ (1− φ)G(
Ωn
)︸ ︷︷ ︸
EE+
− δ︸︷︷︸
EU
+ λEF(
Ωn
)︸ ︷︷ ︸
EE−
Gross ows
n
Ω = nU + ϑ
n∗E(z)
dnn = 0 Ωn = U
n∗S(z)
δ
λE
qv∗(z, n)φ
qv∗(z, n)(1− φ)G(Ωn)
EE+
UE
EE−
EU
Net poaching
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Composition of worker ows
dn
n= λF v
∗(Ωn)
n
φ︸︷︷︸UE
+ (1− φ)G(
Ωn
)︸ ︷︷ ︸
EE+
− δ︸︷︷︸
EU
+ λEF(
Ωn
)︸ ︷︷ ︸
EE−
Gross ows
n
Ω = nU + ϑ
n∗E(z)
dnn = 0 Ωn = U
n∗S(z)
δ
λE
qv∗(z, n)φ
qv∗(z, n)(1− φ)G(Ωn)
EE+
UE
EE−
EU
Net poaching
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Quantitative Analysis
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Parameters - SMM Estimation
Productivity distribution
- Dispersion of rm-level TFP
Firm dynamics
- Average rm size
- Employment share of large rms
- Exit rate
Job reallocation
- Job reallocation rate (JC + JD)
- Job creation by entrants
Worker reallocation
- UE rate, EU rate, EE rate
Parameters Local Global
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Firm and employment distributions by size and age
Group A. Firms B. Employment
Model Data Model Data
A. By rm size
0-9 0.792 0.761 0.116 0.10710-49 0.169 0.195 0.135 0.16750-249 0.032 0.036 0.133 0.153250-999 0.005 0.006 0.096 0.1111000-4999 0.001 0.002 0.116 0.1285000+ 0.000 0.001 0.404 0.335
B. By rm age
1-5 0.350 0.242 0.058 0.0876-10 0.218 0.176 0.072 0.07911+ 0.432 0.499 0.871 0.813
Data: Census BDS
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Job and worker reallocation by size and age
Job reallocation Worker reallocation
Creation Destruction Hire Separate
Model Data Model Data Model Data Model Data
A. By rm size
0-19 0.045 0.049 0.038 0.038 0.116 0.122 0.109 0.11020-49 0.029 0.033 0.029 0.029 0.104 0.106 0.105 0.10250-249 0.031 0.031 0.031 0.027 0.105 0.102 0.105 0.097250-499 0.032 0.031 0.033 0.025 0.105 0.101 0.107 0.096500+ 0.029 0.029 0.031 0.024 0.103 0.087 0.106 0.084
A. By rm age
0-1 0.161 0.161 0.024 0.038 0.233 0.212 0.096 0.1402-3 0.049 0.049 0.030 0.051 0.121 0.150 0.102 0.1444-5 0.042 0.040 0.032 0.044 0.115 0.134 0.104 0.1306-10 0.035 0.035 0.032 0.037 0.109 0.125 0.106 0.12111+ 0.028 0.026 0.033 0.024 0.102 0.086 0.107 0.084
Data: Census BDS and J2J (quarterly rates) Vacancies
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Questions
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Life-cycle dynamics of rm distribution over (z, n)
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Misallocation costs of labor market frictions
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Who poaches from whom?
EE+ − EE−
n= λF
v∗(Ωn)
n(1− φ)G
(Ωn
)− λEF
(Ωn
)
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Net poaching by size and age
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Net poaching by size and age: model and data
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Net poaching by labor productivity & growth rate
Growth
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Three key facts about the Great Recession
Fact I: Firm entry dropped by 30%
Fact II: EE rate declined by 30%
Fact III: Net poaching of high-wage rms fell → failure of job ladder
Conjecture: causal link from I ⇒ II & III
Need a model with rm dynamics + OJS
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What explains the failure of the job ladder?
Shock to the discount rate: ρ ↑ (proxy for nancial shock)
Path for the shock calibrated to match dynamics of unemployment
Transmission mechanism:
Firm continuation value ↓ ⇒ rm entry ↓
Vacancy creation at the top of job ladder ↓
Fewer workers move up the job ladder
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IRFs for a discount factor shock
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Why do we care about the failure of the job ladder?
Yt = TFPt ×Nαt , TFPt =
z
(n
Nt
)αdGt (n, z)
Slower labor reallocation ⇒ persistent decline in TFP
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Conclusion
Framework to study rm and worker dynamics with frictions
Low-dimensional state space (z, n): tractable
Endogenous job ladder in marginal surplus
Can be applied to a number of macro/labor/trade questions
`MIT' shock → aggregate uncertainty
Next step:
Document rm-level wage dynamics from admin data
Model wage determination protocol that matches those facts
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Thanks!
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Static example: hires from unemployment
Technology y(z, n) = z · nα, n = 1
Firm has met unemployed worker → TOL oer b [A-EN]
Let w∗ < w1 be the renegotiated wage of the incumbent
Credible threat: z − b > z2α − w1 − b [A-LC+A-MC]
Hire with ren. : z2α − w∗ − b > z − w∗ [A-IN]
Hire w/o ren. : z2α − w1 − b > z − w1
Firm hires if and only if the coalition is better o:
z · (2α − 1) > b ⇒ Ωn > U
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Static example: hires from unemployment
Technology y(z, n) = z · nα, n = 1
Firm has met unemployed worker → TOL oer b [A-EN]
Let w∗ < w1 be the renegotiated wage of the incumbent
Credible threat: z − b > z2α − w1 − b [A-LC+A-MC]
Hire with ren. : z2α − w∗ − b > z − w∗ [A-IN]
Hire w/o ren. : z2α − w1 − b > z − w1
Firm hires if and only if the coalition is better o:
z · (2α − 1) > b ⇒ Ωn > U
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Static example: hires from unemployment
Technology y(z, n) = z · nα, n = 1
Firm has met unemployed worker → TOL oer b [A-EN]
Let w∗ < w1 be the renegotiated wage of the incumbent
Credible threat: z − b > z2α − w1 − b [A-LC+A-MC]
Hire with ren. : z2α − w∗ − b > z − w∗ [A-IN]
Hire w/o ren. : z2α − w1 − b > z − w1
Firm hires if and only if the coalition is better o:
z · (2α − 1) > b ⇒ Ωn > U
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Static example: hires from unemployment
Technology y(z, n) = z · nα, n = 1
Firm has met unemployed worker → TOL oer b [A-EN]
Let w∗ < w1 be the renegotiated wage of the incumbent
Credible threat: z − b > z2α − w1 − b [A-LC+A-MC]
Hire with ren. : z2α − w∗ − b > z − w∗ [A-IN]
Hire w/o ren. : z2α − w1 − b > z − w1
Firm hires if and only if the coalition is better o:
z · (2α − 1) > b ⇒ Ωn > U
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Static example: hires from unemployment
Technology y(z, n) = z · nα, n = 1
Firm has met unemployed worker → TOL oer b [A-EN]
Let w∗ < w1 be the renegotiated wage of the incumbent
Credible threat: z − b > z2α − w1 − b [A-LC+A-MC]
Hire with ren. : z2α − w∗ − b > z − w∗ [A-IN]
Hire w/o ren. : z2α − w1 − b > z − w1
Even if hiring not protable, rm may gain through wage cut:
[A-VP] ensures vacancy posted only if hiring protable
Back to Equilibrium
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Static example: hires from employment
Firm z attempts to poach a worker in rm z′ (both n = 1)
Let w∗∗ < w1 the wage oer to the external worker
Let w∗ < w1 be the renegotiated wage of the incumbent
Credible threat: z − w∗∗ > z2α − w1 − w∗∗
Hire with ren. : z2α − w∗ − w∗∗ > z − w∗
Hire w/o ren. : z2α − w1 − w∗∗ > z − w1
Firm hires if and only if coalition better o:
z · (2α − 1) > w∗∗ = z′ · (1α − 0) = z′
Back to Equilibrium
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Static example: hires from employment
Firm z attempts to poach a worker in rm z′ (both n = 1)
Let w∗∗ < w1 the wage oer to the external worker
Let w∗ < w1 be the renegotiated wage of the incumbent
Credible threat: z − w∗∗ > z2α − w1 − w∗∗
Hire with ren. : z2α − w∗ − w∗∗ > z − w∗
Hire w/o ren. : z2α − w1 − w∗∗ > z − w1
Firm hires if and only if coalition better o:
z · (2α − 1) > w∗∗
= z′ · (1α − 0) = z′
Back to Equilibrium
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Static example: hires from employment
Firm z attempts to poach a worker in rm z′ (both n = 1)
Let w∗∗ < w1 the wage oer to the external worker
Let w∗ < w1 be the renegotiated wage of the incumbent
Credible threat: z − w∗∗ > z2α − w1 − w∗∗
Hire with ren. : z2α − w∗ − w∗∗ > z − w∗
Hire w/o ren. : z2α − w1 − w∗∗ > z − w1
Firm hires if and only if coalition better o:
z · (2α − 1) > w∗∗ = z′ · (1α − 0) = z′
Back to Equilibrium
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Static example: separation after drop in z
Consider a rm with productivity z and two incumbents paidw2, w1, with w2 > w1
Technology y(z, n) = z · nα
Assume z > w1, so the rst worker is never under threat
Credible threat: z − w1 > z2α − w1 − w2
Separation : z − w1 > z2α − w1 − b
Firm res worker 1 if and only if the coalition is better o:
z · (2α − 1) < b
Back to Equilibrium
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Static example: separation after drop in z
Consider a rm with productivity z and two incumbents paidw2, w1, with w2 > w1
Technology y(z, n) = z · nα
Assume z > w1, so the rst worker is never under threat
Credible threat: z − w1 > z2α − w1 − w2
Separation : z − w1 > z2α − w1 − b
Firm res worker 1 if and only if the coalition is better o:
z · (2α − 1) < b
Back to Equilibrium
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Static example: vacancy creation
Now rm must pay vacancy cost ccc to meet unemployed worker
Conditional on paying ccc, all decisions unchanged
Threat to post vacancy and swap is credible if w1 > b+ ccc
But this vacancy would be jointly inecient
Worker makes counteroer: no vacancy + wage cut to w∗ = b+ c
Firm indierent, worker better o, threat removed
Firm posts vacancy and hires if and only if:
z · (2α − 1)︸ ︷︷ ︸marginal hiring gain
> b+ c︸ ︷︷ ︸marginal hiring cost
Back to Equilibrium
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Static example: vacancy creation
Now rm must pay vacancy cost ccc to meet unemployed worker
Conditional on paying ccc, all decisions unchanged
Threat to post vacancy and swap is credible if w1 > b+ ccc
But this vacancy would be jointly inecient
Worker makes counteroer: no vacancy + wage cut to w∗ = b+ c
Firm indierent, worker better o, threat removed
Firm posts vacancy and hires if and only if:
z · (2α − 1)︸ ︷︷ ︸marginal hiring gain
> b+ c︸ ︷︷ ︸marginal hiring cost
Back to Equilibrium
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Static example: vacancy creation
Now rm must pay vacancy cost ccc to meet unemployed worker
Conditional on paying ccc, all decisions unchanged
Threat to post vacancy and swap is credible if w1 > b+ ccc
But this vacancy would be jointly inecient
Worker makes counteroer: no vacancy + wage cut to w∗ = b+ c
Firm indierent, worker better o, threat removed
Firm posts vacancy and hires if and only if:
z · (2α − 1)︸ ︷︷ ︸marginal hiring gain
> b+ c︸ ︷︷ ︸marginal hiring cost
Back to Equilibrium
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Parameters
Parameter Value Target
ρ Discount rate 0.004 5% annual real interest rateβ Elast. of matches w.r.t. v 0.5 Petrongolo and Pissarides (2001)ϑ Firm scrap value 1/ρ Normalizationκ Shifter in vacancy cost 100 Normalization
Parameter Value
µ Mean of productivity shocks -0.004σ Std. of productivity shocks 0.054ζ Shape of entry distribution 2.955ce Entry cost 379n0 Size of entrants 2.058α Curvature in production 0.587γ Curvature of vacancy cost 6.023A Matching eciency 0.157ξ Search eciency of employed 0.142δ Exogenous separation rate 0.017b Flow value of leisure 0.295
Target Model Data
Exit rate (unweighted) 0.084 0.076Std. dev. of log TFP 0.484 0.500Std. dev. of log TFP (age 1-5) 0.362 0.400Average rm size 22 22JC rate at age 1 0.237 0.244Employment share 500+ 0.551 0.518Std. dev. emp. growth 0.337 0.420UE rate 0.243 0.242EE rate / UE rate 0.068 0.076EU rate 0.018 0.016Leisure to output 0.367 0.400
Back to SMM
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Parameters
Parameter Value Target
ρ Discount rate 0.004 5% annual real interest rateβ Elast. of matches w.r.t. v 0.5 Petrongolo and Pissarides (2001)ϑ Firm scrap value 1/ρ Normalizationκ Shifter in vacancy cost 100 Normalization
Parameter Value
µ Mean of productivity shocks -0.004σ Std. of productivity shocks 0.054ζ Shape of entry distribution 2.955ce Entry cost 379n0 Size of entrants 2.058α Curvature in production 0.587γ Curvature of vacancy cost 6.023A Matching eciency 0.157ξ Search eciency of employed 0.142δ Exogenous separation rate 0.017b Flow value of leisure 0.295
Target Model Data
Exit rate (unweighted) 0.084 0.076Std. dev. of log TFP 0.484 0.500Std. dev. of log TFP (age 1-5) 0.362 0.400Average rm size 22 22JC rate at age 1 0.237 0.244Employment share 500+ 0.551 0.518Std. dev. emp. growth 0.337 0.420UE rate 0.243 0.242EE rate / UE rate 0.068 0.076EU rate 0.018 0.016Leisure to output 0.367 0.400
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Are the targeted moments informative?
-10 -8 -6 -4 -2
10-3
-50
050
0.2 0.4 0.6 0.8
-50
050
5 10 15 20
-50
050
0.02 0.04 0.06 0.08
-50
050
0.1 0.2 0.3 0.4
-50
050
0.01 0.02 0.03
-50
050
0.2 0.4 0.6 0.8
-50
050
1 2 3
10-3
-50
050
0.1 0.2 0.3
-50
050
2 4 6 8
-50
050
2 4 6 8
-50
050
Back to SMM
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Global identication: a graphical approach
-8 -6 -410-3
0.10.20.30.4
Min
imum
dis
tanc
e
0.1 0.2 0.3 0.4
0.10.20.30.4
Min
imum
dis
tanc
e
2 4 6 8 10 12
0.10.20.30.4
Min
imum
dis
tanc
e
0.02 0.04 0.06 0.08
0.10.20.30.4
Min
imum
dis
tanc
e
0.1 0.15 0.2 0.25
0.10.20.30.4
Min
imum
dis
tanc
e
0.01 0.02
0.10.20.30.4
Min
imum
dis
tanc
e
0.5 0.6 0.7 0.8
0.10.20.30.4
Min
imum
dis
tanc
e
1 2 310-3
0.10.20.30.4
Min
imum
dis
tanc
e
0.05 0.1 0.15 0.2 0.25
0.10.20.30.4
Min
imum
dis
tanc
e
2 4 6 8
0.10.20.30.4
Min
imum
dis
tanc
e
1 2 3 4 5
0.10.20.30.4
Min
imum
dis
tanc
e
Minimum Distance plotted in each dimension of the parameter space
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Vacancy rates and vacancy yields
Missing: endogenous recruiting intensity
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