yl Aggregate Recruiting Intensity - Simon Mongey

yl

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


Ht = AtVαt U1−α

t

The component of At accounted for by firms’ effort to fill vacancies



Ht = AtVαt U1−α

t


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?



Ht = AtVαt U1−α

t


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?


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”


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


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


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


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



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


Model yyl


Model yyl

Firm dynamics

• Operate DRS technology

• Idiosyncratic persistent productivity shocks

• Endogenous entry and exit


Model yyl

Firm dynamics




Financial frictions

• Borrowing secured by collateral (macro shock)

• Limits to equity issuance


Model yyl

Firm dynamics




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


Valueyfunctionsyl

Let V(n, a, z) be the present discounted value of dividends of a firm withemployment n, net-worth a, and productivity z


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)}


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



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



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


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


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




(

hn

)

0

0.5

1.0

1.5

2.0

2.5


(

hv

)


(

vn

)

Slope = 0.82

C(e, v, n) =

[κ1

γ1eγ1 +

κ2

γ2 + 1

(v

n

)γ2]

︸︷︷︸

Cost per vacancy

v, γ1 ≥ 1, γ2 ≥ 0




(

hn

)

0

0.5

1.0

1.5

2.0

2.5


(

hv

)


(

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

)




(

hn

)

0

0.5

1.0

1.5

2.0

2.5


(

hv

)


(

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

)


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


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}





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


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


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


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


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


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


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


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


Transition dynamics in labor marketyl

Fig. Labor wedge


Impulse response for Φyl


Impulse response for Φyl

Result I:

• Recruiting intensity accounts for ≈ 1/3 of decline in match efficiency

• Less persistence than empirical match efficiency


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


Decomposing Φtyl

Result II:

• Slackness effect is dominant


Decomposing Φtyl

Result III:

• Composition effect is roughly zero

• Why? Constrained vs. unconstrained firms


Understanding vacancy yields by sizeyl


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


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


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)


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


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)



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



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



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


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


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


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


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


Labor wedge - Financial shockyl

1 − τt = N1+ϕt

Ct

Yt

Back


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


yl Aggregate Recruiting Intensity - Simon Mongey

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Transcript of yl Aggregate Recruiting Intensity - Simon Mongey