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Aggregate Recruiting Intensity
Alessandro GavazzaLondon School of Economics
Simon MongeyFRB of Minneapolis & University of Chicago
Gianluca ViolantePrinceton University
FRB of Minneapolis
Aggregate recruiting intensityyyl
Ht = AtVαt U1−α
t
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.1/29hello
Aggregate recruiting intensityyyl
Ht = AtVαt U1−α
t
The component of At accounted for by firms’ effort to fill vacancies
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.1/29hello
Aggregate recruiting intensityyyl
Ht = AtVαt U1−α
t
The component of At accounted for by firms’ effort to fill vacancies
Macro data
• Large and persistent decline in At in the last recession
• Q1: How much of the decline in At is accounted for by ARI?
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.1/29hello
Aggregate recruiting intensityyyl
Ht = AtVαt U1−α
t
The component of At accounted for by firms’ effort to fill vacancies
Macro data
• Large and persistent decline in At in the last recession
• Q1: How much of the decline in At is accounted for by ARI?
Micro data (Davis-Faberman-Haltiwanger, 2013)
• In the cross-section, fast growing firms fill vacancies more quickly
• Q2: What is the transmission mechanism from macro shocks to ARI?
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.1/29hello
Firm-level hiring technologyyl
Random-matching model hit = qtvit
+ recruiting intensity hit = qteitvit
• JOLTS vacancies - vit
• BLS: “Specific position that exists... for start within 30-days... with activerecruiting from outside the establishment”
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.2/29hello
Firm-level hiring technologyyl
Random-matching model hit = qtvit
+ recruiting intensity hit = qteitvit
• JOLTS vacancies - vit
• BLS: “Specific position that exists... for start within 30-days... with activerecruiting from outside the establishment”
• Recruitment intensity - eit
1. Shifts the filling rate (or yield) of an open position
2. Costly on a per vacancy basis
• An outcome of expenditures on recruiting activities
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.2/29hello
Recruiting cost by activityy
Tools 1%
Employment branding services
2%
Professional networking sites
3% Print / newspapers /
billboards 4%
University recruiting 5%
Applicant tracking system
5% Travel 8%
Contractors 8%
Employee referrals 9%
Other 12%
Job boards 14%
Agencies / third-party recruiters
29%
Bersin and Associates, Talent Acquisition Factbook (2011)
- Average cost per hire (at 100+ employee firms): $3,500
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.3/29hello
From firm-level to aggregate recruiting intensityyl
• Aggregation
Ht = qt
∫
eitvit dλht = qtV
∗t
• Aggregate matching function
Ht = V∗t
αU1−αt = ΦtVt
αU1−αt
• Aggregate recruiting intensity
Φt =
[V∗
t
Vt
]α
=
[∫
eit
(vit
Vt
)
dλht
]α
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.4/29hello
Transmission mechanism: two channelsyyl
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.5/29hello
Transmission mechanism: two channelsyyl
1. Composition: macro shock → shift in hiring rate distribution
y
h
n= q̄
ye
y
v
n
• Slow-growing firms recruit less intensively
• Great Recession - large decline in firm entry
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.5/29hello
Transmission mechanism: two channelsyyl
1. Composition: macro shock → shift in hiring rate distribution
y
h
n= q̄
ye
y
v
n
• Slow-growing firms recruit less intensively
• Great Recession - large decline in firm entry
2. Slackness: macro shock → slacker labor market
h̄
n=
xq
ye
y
v
n
• Firms substitute away from costly hiring measures
• Great Recession - large decline in market tightness
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.5/29hello
Model yyl
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.6/29hello
Model yyl
Firm dynamics
• Operate DRS technology
• Idiosyncratic persistent productivity shocks
• Endogenous entry and exit
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.6/29hello
Model yyl
Firm dynamics
• Operate DRS technology
• Idiosyncratic persistent productivity shocks
• Endogenous entry and exit
Financial frictions
• Borrowing secured by collateral (macro shock)
• Limits to equity issuance
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.6/29hello
Model yyl
Firm dynamics
• Operate DRS technology
• Idiosyncratic persistent productivity shocks
• Endogenous entry and exit
Financial frictions
• Borrowing secured by collateral (macro shock)
• Limits to equity issuance
Labor market frictions
• Random matching with homogeneous workers (no OJS)
• Recruiting effort e and vacancies v are costly
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.6/29hello
Valueyfunctionsyl
Let V(n, a, z) be the present discounted value of dividends of a firm withemployment n, net-worth a, and productivity z
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.7/29hello
Valueyfunctionsyl
Let V(n, a, z) be the present discounted value of dividends of a firm withemployment n, net-worth a, and productivity z
• Exit exogenously or endogenously
V(n, a, z) = ζa + (1 − ζ)max{
a , Vi(n, a, z)
}
• Fire or hire
Vi(n, a, z) = max
{
Vf (n, a, z) , V
h(n, a, z)}
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.7/29hello
Value functions - Firingyl
Vf (n, a, z) = max
n′≤n,k,dd + β
∫
ZV(n′, a′, z′)Γ(z, dz′)
s.t.
d + a′ =(
zn′νk1−ν)σ
+ (1 + r)a − ωn′ − (r + δ)k − χ
k ≤ ϕa
d ≥ 0
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.8/29hello
Value functions - Firingyl
Vf (n, a, z) = max
n′≤n,k,dd + β
∫
ZV(n′, a′, z′)Γ(z, dz′)
s.t.
d + a′ =(
zn′νk1−ν)σ
+ (1 + r)a − ωn′ − (r + δ)k − χ
k ≤ ϕa
d ≥ 0
• Define debt: b := k − a
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.8/29hello
Value functions - Firingyl
Vf (n, a, z) = max
n′≤n,k,dd + β
∫
ZV(n′, a′, z′)Γ(z, dz′)
s.t.
d + a′ =(
zn′νk1−ν)σ
+ (1 + r)a − ωn′ − (r + δ)k − χ
k ≤ ϕa
d ≥ 0
• Define debt: b := k − a
• Firms make take-leave offers: ω = flow value of leisure
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.8/29hello
Value functions - Hiringyl
Vh(n, a, z) = max
v>0,e>0,k,dd + β
∫
ZV(n′, a′, z′)Γ(z, dz′)
s.t.
d + a′ =(
zn′νk1−ν)σ
+ (1 + r)a − ωn′ − (r + δ)k − χ − C(e, v, n)
n′ − n = q(θ∗)ev
k ≤ ϕa
d ≥ 0
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.9/29hello
Reverse engineering the hiring-cost functionyl
0 0.5 1.0 1.5 2.0 2.5 3.0Log hiring rate log
(
hn
)
0
0.5
1.0
1.5
2.0
2.5
3.0Log vacancy yield - log
(
hv
)
= log (qe)Log vacancy rate - log
(
vn
)
Slope = 0.82
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.10/29hello
Reverse engineering the hiring-cost functionyl
0 0.5 1.0 1.5 2.0 2.5 3.0Log hiring rate log
(
hn
)
0
0.5
1.0
1.5
2.0
2.5
3.0Log vacancy yield - log
(
hv
)
= log (qe)Log vacancy rate - log
(
vn
)
Slope = 0.82
C(e, v, n) =
[κ1
γ1eγ1 +
κ2
γ2 + 1
(v
n
)γ2]
︸ ︷︷ ︸
Cost per vacancy
v, γ1 ≥ 1, γ2 ≥ 0
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.10/29hello
Reverse engineering the hiring-cost functionyl
0 0.5 1.0 1.5 2.0 2.5 3.0Log hiring rate log
(
hn
)
0
0.5
1.0
1.5
2.0
2.5
3.0Log vacancy yield - log
(
hv
)
= log (qe)Log vacancy rate - log
(
vn
)
Slope = 0.82
log e = Const. −γ2
γ1 + γ2log q (θ∗)+
γ2
γ1 + γ2log
(h
n
)
log( v
n
)
= Const. −γ1
γ1 + γ2log q (θ∗)+
γ1
γ1 + γ2log
(h
n
)
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.10/29hello
Reverse engineering the hiring-cost functionyl
0 0.5 1.0 1.5 2.0 2.5 3.0Log hiring rate log
(
hn
)
0
0.5
1.0
1.5
2.0
2.5
3.0Log vacancy yield - log
(
hv
)
= log (qe)Log vacancy rate - log
(
vn
)
Slope = 0.82Slope = 0.82
log e = Const. −γ2
γ1 + γ2log q (θ∗)+
γ2
γ1 + γ2log
(h
n
)
log( v
n
)
= Const. −γ1
γ1 + γ2log q (θ∗)+
γ1
γ1 + γ2log
(h
n
)
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.10/29hello
Value functions - Entryyl
• Initial wealth: Household allocates a0 to λ0 potential entrants
• Productivity: Potential entrants draw z ∼ Γ0(z)
• Entry: Choice to become incumbent and pay χ0 start-up costs
Ve(a0, z) = max
{
a0 , Vi (n0, a0 − χ0, z)
}
Selection at entry based only on productivity z
Life cycle: slow growth b/c of fin. constraints and convex hiring costs
Equilibrium
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.11/29hello
Parameter values set externallyyl
Parameter Value Target
Discount factor (monthly) β 0.9967 Ann. risk-free rate = 4%Mass of potential entrants λ0 0.02 Meas. of incumbents = 1Size of labor force L̄ 24.6 Average firm size = 23Elasticity of matching function wrt Vt α 0.5 JOLTS
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.12/29hello
Parameter values set externallyyl
Parameter Value Target
Discount factor (monthly) β 0.9967 Ann. risk-free rate = 4%Mass of potential entrants λ0 0.02 Meas. of incumbents = 1Size of labor force L̄ 24.6 Average firm size = 23Elasticity of matching function wrt Vt α 0.5 JOLTS
Add to the model• Heterogeneity in DRS σ ∈ {σL, σM, σH}
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.12/29hello
Parameter values set externallyyl
Parameter Value Target
Discount factor (monthly) β 0.9967 Ann. risk-free rate = 4%Mass of potential entrants λ0 0.02 Meas. of incumbents = 1Size of labor force L̄ 24.6 Average firm size = 23Elasticity of matching function wrt Vt α 0.5 JOLTS
Add to the model• Heterogeneity in DRS σ ∈ {σL, σM, σH}
Calibration strategy
1. Worker flows and labor share
2. Distribution of firm size and firm growth rates
3. Micro-evidence on job-filling and vacancy-posting
4. Entry and exit
5. Leverage for young firms and for aggregate economy
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.12/29hello
Parameter values estimated internallyyl
Parameter Value Target Model Data
Flow of home production ω 1.000 Monthly separation rate 0.033 0.030Scaling of match. funct. Φ̄ 0.208 Monthly job-finding rate 0.411 0.400Prod. weight on labor ν 0.804 Labor share 0.627 0.640
Midpoint DRS in prod. σM 0.800 Employment share n < 50 0.294 0.306High-Low spread in DRS ∆σ 0.094 Employment share n ≥ 500 0.430 0.470Mass - Low DRS µL 0.826 Firm share n < 50 0.955 0.956Mass - High DRS µH 0.032 Firm share n ≥ 500 0.004 0.004
Std. dev. of z shocks ϑz 0.052 Std. dev. ann. emp. growth 0.440 0.420Persistence of z shocks ρz 0.992 Mean Q4 emp. / Mean Q1 emp. 75.16 76.00Mean z0 ∼ Exp(z̄−1
0 ) z̄0 0.390 ∆ log z: Young vs. Mature -0.246 -0.353
Cost elasticity wrt e γ1 1.114 Elasticity of vac. yield wrt g 0.814 0.820Cost elasticity wrt v γ2 4.599 Ratio vac. yield: n < 50/n ≥ 50 1.136 1.440Cost shifter wrt e κ1 0.101 Hiring cost (100+) / wage 0.935 0.927Cost shifter wrt v κ2 5.000 Vacancy share n < 50 0.350 0.370
Exogenous exit probability ζ 0.006 Five year survival rate 0.497 0.500Entry cost χ0 9.354 Annual entry rate 0.099 0.102Operating cost χ 0.035 Share of job destruction by exit 0.210 0.340
Initial wealth a0 10.000 Start-up Debt to Output 1.361 1.280Collateral constraint ϕ 10.210 Aggregate Debt to Assets 0.280 0.350
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.13/29hello
Non-targeted momentsyl
Moment Model Data Source
Aggregate dividend / profits 0.411 0.400 NIPA
Employment share: growth ∈ (−2.00,−0.20) 0.070 0.076 Davis et al. (2010)Employment share: growth ∈ (−0.20, 0.20] 0.828 0.848 Davis et al. (2010)Employment share: growth ∈ (0.20, 2.00) 0.102 0.076 Davis et al. (2010)
Employment share: Age ≤ 1 0.013 0.028 BDSEmployment share: Age ∈ (1, 10) 0.309 0.212 BDSEmployment share: Age ≥ 10 0.678 0.760 BDS
Fig. Average firm lifecycle (i) size, (ii) job creation, (iii) fraction constrained, (iv) leverage
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.14/29hello
Hire and vacancy shares by size classyl
1-9 10-49 50-249 250-999 1000+0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
A. Hires
1-9 10-49 50-249 250-999 1000+0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
B. Vacancies
Model Data - JOLTS 2002-2007
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.15/29hello
Vacancy and recruitment intensity by ageyl
0 2 4 6 8 10
Age (years)
0
0.2
0.4
0.6
0.8
1
Logdifferen
cefrom
10yearold
A. Cohort average growth and recruitment
Growth rateRecruiting intensityVacancy rate
0 5 10 15
Age (years)
0
0.01
0.02
0.03
0.04
Fractionoffirm
sbyage(m
onthly)
B. Age distributions
Hiring firmsRecruiting intensityVacant positions
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.16/29hello
Vacancy and recruitment intensity by ageyl
0 2 4 6 8 10
Age (years)
0
0.2
0.4
0.6
0.8
1
Logdifferen
cefrom
10yearold
A. Cohort average growth and recruitment
Growth rateRecruiting intensityVacancy rate
0 5 10 15
Age (years)
0
0.01
0.02
0.03
0.04
Fractionoffirm
sbyage(m
onthly)
B. Age distributions
Hiring firmsRecruiting intensityVacant positions
• Young firms exert more recruiting effort in the model
• US? No firm-age in JOLTS. But true, e.g., in Austrian micro-data
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.16/29hello
Transition dynamics experimentsyl
Trace transitional dynamics of the economy in response to:
• Tightening of financial constraint ↓ ϕ
• Size of shock: match max drop in output (Fernald, 2015)
- Requires 75% drop in ϕ
• Persistence of shock: match half-life of output decline of 3 years
- Monthly persistence of ϕ shock of 0.97
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.17/29hello
Transition dynamics experimentsyl
Trace transitional dynamics of the economy in response to:
• Tightening of financial constraint ↓ ϕ
• Size of shock: match max drop in output (Fernald, 2015)
- Requires 75% drop in ϕ
• Persistence of shock: match half-life of output decline of 3 years
- Monthly persistence of ϕ shock of 0.97
In the paper: examine also productivity shock
Fig. Macro variables (i) output, (ii) debt/output, (iii) labor productivity, (iv) entry
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.17/29hello
Transition dynamics in labor marketyl
Fig. Labor wedge
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.18/29hello
Impulse response for Φyl
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.19/29hello
Impulse response for Φyl
Result I:
• Recruiting intensity accounts for ≈ 1/3 of decline in match efficiency
• Less persistence than empirical match efficiency
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.19/29hello
Decomposing Φtyl
Recruiting effort policy
e = Const. × q (θ∗)−
γ2γ1+γ2 ×
(h
n
) γ2γ1+γ2
Aggregate recruiting intensity
Φ =
[∫
e( v
V
)
dλh
]α
Decomposition
∆ log Φ = −αγ2
γ1 + γ2∆ log q(θ∗)
︸ ︷︷ ︸
Slackness effect
+ α∆ log
[∫ (
h
n
) γ2γ1+γ2
( v
V
)
dλh
]
︸ ︷︷ ︸
Composition effect
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.20/29hello
Decomposing Φtyl
Result II:
• Slackness effect is dominant
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.21/29hello
Decomposing Φtyl
Result III:
• Composition effect is roughly zero
• Why? Constrained vs. unconstrained firms
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.21/29hello
Understanding vacancy yields by sizeyl
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.22/29hello
Understanding vacancy yields by sizeyl
0 6 12 18 24
Month
-0.2
0
0.2
0.4
0.6
Logdev.from
date
0
C. Vacancy yield - Model
Size 1-9Size 1000+
0 6 12 18 24
Month
-0.2
0
0.2
0.4
0.6
Logdev.from
date
0
D. Vacancy yield - Data 2008:01-2010:12
Size 1-9Size 1000+
0 6 12 18 24-1.5
-1
-0.5
0
0.5
1
Log
dev.from
date0
A. Recruiting intensity per vacancy
UnconstrainedConstrained
0 6 12 18 240
0.1
0.2
0.3
0.4
0.5
Level
B. Fraction constrained
Size 1-9Size 1000+
Result IV
• Constrained high-scale firms explain flat vacancy yields of large firms
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.22/29hello
Summaryyl
Results
I. Recruiting intensity explains 1/3 of decline in match efficiency
II. Dominant: Slack labor markets reduce need for costly recruiting
III. Strong GE forces limit the role of the composition effect
IV. Constrained high-scale firms explain vacancy yields by size
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.23/29hello
Summaryyl
Results
I. Recruiting intensity explains 1/3 of decline in match efficiency
II. Dominant: Slack labor markets reduce need for costly recruiting
III. Strong GE forces limit the role of the composition effect
IV. Constrained high-scale firms explain vacancy yields by size
Extensions
1. Sectoral composition plays sizable role
2. Construct an easy-to-measure index of aggregate recruiting intensity
3. Relationship to Kaas & Kircher (2015)
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.23/29hello
1. Sectoral compositionyl
2007 2008 2009 2010 2011 20120
0.05
0.10
0.15
0.20
0.25
Level
A. Sector component: φ̂γ1
γ1+γ2s
vstVt
ConManTradeProf servEd/HthHospGov
2007 2008 2009 2010 2011 2012-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
Logdeviationfrom
Jan2001
B. Sectoral composition effect
Result
- Sectoral composition effect adds 15% to decline in Φt (0.20 → 0.23)
- It adds some persistence too
- Driven by (i) Hospitality, (ii) Construction, (iii) Manufacturing
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.24/29hello
2. Approximate index of aggregate recruiting intensityyl
DFH provide an easy-to-compute index of aggregate recruiting intensity
log Φt = log(Ht/Vt)− log qt
d log Φt
d log(Ht/Nt)=
d log(Ht/Vt)
d log(Ht/Nt)−
d log qt
d log(Ht/Nt)
(a) Use firm-level elasticity for first term, ξ = 0.82
(b) Assume second term is small
d log Φt
d log(Ht/Nt)≈ ξ
d log ΦDFHt = ξ × d log(Ht/Nt)
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.25/29hello
2. Approximate index of aggregate recruiting intensityyl
Return to model based decomposition
log Φt = −αγ2
γ1 + γ2log q(θ∗t )
︸ ︷︷ ︸
slackness effect
+ α log
[∫ (
hit
nit
) γ2γ1+γ2
(vit
Vt
)
dλht
]
︸ ︷︷ ︸
composition effect
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.26/29hello
2. Approximate index of aggregate recruiting intensityyl
Return to model based decomposition
log Φt = −αγ2
γ1 + γ2log q(θ∗t )
︸ ︷︷ ︸
slackness effect
+ α log
[∫ (
hit
nit
) γ2γ1+γ2
(vit
Vt
)
dλht
]
︸ ︷︷ ︸
composition effect
GMV
(a) Model tells us the composition effect is approximately zero
d log ΦGMVt = α
γ2
γ1 + γ2× (1 − α)× d log θ∗t
(b) Elasticity of θ∗t to θt from transition dynamics
d log ΦGMVt = α
γ2
γ1 + γ2× (1 − α) εθ∗,θ
︸︷︷︸
≈1.5
×d log θt
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.26/29hello
2. Approximate index of aggregate recruiting intensityyl
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
LogAggregate
RecruitingIntensity
Aggregate match efficiencyDFH measure of recruiting intensityGMV measure of recruiting intensityGMV + Sectoral component
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.27/29hello
3. Relation to Kaas Kircher (2015)yl
KK model
ΦKKt =
∫q(θmt)
q̄(θt)
vmt
Vtdm
The reason why [recruiting intensity] is pro-cyclical in our model is that q isconcave, and the cross-sectional dispersion in θmt is counter-cyclical
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.28/29hello
3. Relation to Kaas Kircher (2015)yl
KK model
ΦKKt =
∫q(θmt)
q̄(θt)
vmt
Vtdm
The reason why [recruiting intensity] is pro-cyclical in our model is that q isconcave, and the cross-sectional dispersion in θmt is counter-cyclical
Our model
∆ log Φt = −αγ2
γ1 + γ2∆ log q(θ∗t )
︸ ︷︷ ︸
slackness effect
+ α∆ log
[∫ (
hit
nit
) γ2γ1+γ2
(vit
Vt
)
dλht
]
︸ ︷︷ ︸
Composition effect
Dispersion effect is present but small
• ϕt shock delivers 45% increase in SD of growth rates, as in data
↓ Φt, since γ2γ1+γ2
< 1 but close to 1
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.28/29hello
Equilibriumyl
• Aggregate state St = (λt, Ut, Zt, ϕt)
1. Measure of firms evolves via decision rules and z process
2. Labor market flows are equalized at θ∗t : Uflowst+1 = Udemand
t+1
Uflowst+1 = Ut − H(θ∗t , St) + F(θ∗t , St)− λe,tn0
Udemandt+1 = L̄ −
∫
n′ (n, a, z, St) dλt
• Stationary equilibrium: measure is stationary, and S = (λ, U, Z, ϕ)
Back
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.28/29hello
Average life cycle of firms in the modelyl
0 1 2 3 4 5
Age (years)
0
0.05
0.10
0.15
0.20
0.25B. Job creation and destruction
Job creation rateJob destruction rate
0 5 10 15
Age (years)
0
100
200
300
400A. Average size
High σH
Med σM
Low σL
0 1 2 3 4 5
Age (years)
0
0.2
0.4
0.6
0.8
1C. Fraction of firms constrained
0 5 10 15 20
Age (years)
0
5
10
15D. Average leverage
Back
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.28/29hello
Labor wedge - Financial shockyl
1 − τt = N1+ϕt
Ct
Yt
Back
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.29/29hello
Transition dynamics - Macroyl
0 1 2 3 4 5 6Years
-0.25
-0.2
-0.15
-0.1
-0.05
0
Logdeviationfrom
date
0
A. Productivity Z-shock
0 1 2 3 4 5 6Years
-0.25
-0.2
-0.15
-0.1
-0.05
0
Logdeviationfrom
date
0
B. Finance ϕ-shock
Debt/Output (B+t /Yt) Labor Productivity (Yt/Nt) Entry
Back
Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.29/29hello