aggregate recruiting intensity - princeton university

yl

Aggregate Recruiting Intensity

Alessandro Gavazza

London School of Economics

Simon Mongey

New York University

Gianluca Violante

New York University

Macroeconomics Lunch

Princeton, November 8th 2016

Aggregate recruiting intensityyyl

Ht = AtVαt U1−α

t

Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.1/28hello


Ht = AtVαt U1−α

t

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



Ht = AtVαt U1−α

t


Macro data

• Large and persistent decline in A in the last recession

• Q1: How much of the decline in A is accounted for by ARI?



Ht = AtVαt U1−α

t


Macro data

• Large and persistent decline in A in the last recession

• Q1: How much of the decline in A is accounted for by ARI?

Micro data (Davis-Faberman-Haltiwanger, 2013)

• 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 active

recruiting 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 active

recruiting 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 productivity shocks

• Endogenous entry and exit


Model yyl

Firm dynamics




Financial frictions

• Borrowing secured by collateral

• Limits to equity issuance


Model yyl

Firm dynamics




Financial frictions

• Borrowing secured by collateral

• Limits to equity issuance

Labor market frictions

• Random matching with homogeneous workers

• 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


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


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}

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 aggregate economy


Parameter values estimated internallyyl

Parameter Value Target Model Data

Flow of home production ω 1.000 Monthly separ. 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: 0-49 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: 0-49 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 75.161 76.000

Mean z0 ∼ Exp(z̄−10 ) 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: <50/>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 Survive ≥ 5 years 0.497 0.500Entry cost χ0 9.354 Annual entry rate 0.099 0.110Operating cost χ 0.035 Fraction of JD 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-Net worth 0.280 0.350


Non-targeted momentsyl

Moment Model Data Source

Aggregate dividend / profits 0.411 0.400 NIPA

1Employment 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 0.020 BDSEmployment share: Age ∈ (1, 10) 0.309 0.230 BDSEmployment share: Age ≥ 10 0.678 0.750 BDS

(1.) Firm growth rates are annual and are interior to [−2, 2] so do not include entering andexiting firms

Fig. Average �rm life y le (i) size, (ii) job reation, (iii) fra tion onstrained, (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: true 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

Ma ro TD


Transition dynamics yl

0 1 2 3 4 5 6Years

-1

-0.5

0

0.5

1

Logdeviationfrom

date

0

A. US Data 2008:01 - 2014:01

0 1 2 3 4 5 6Years

-1

-0.5

0

0.5

1

Logdeviationfrom

date

0

B. Model - Finance ϕ-shock

Vacancies Vacancy yield Unemployment Job finding rate Agg. recruiting intensity

Fig. Ma ro variables (i) output, (ii) debt/output, (iii) labor produ tivity


Impulse response for Φyl

0 1 2 3 4 5 6Years

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0Logdeviationfrom

date

0

Aggregate recruiting intensity Φt

Data - Aggregate match efficiency

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

0 1 2 3 4 5 6Years

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05Logdeviationfrom

date

0


Slackness effectComposition effect

Result II:

• Slackness effect is dominant


Decomposing Φtyl

0 1 2 3 4 5 6Years

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05Logdeviationfrom

date

0


Slackness effectComposition effect

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 - Data 2008:01-2010:12

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 - Model

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

• Slackness and composition explains 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. Slackness and composition explains 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. Slackness and composition explains vacancy yields by size

Extensions

1. Effect of changes in sectoral composition of firms over recession

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 3% 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)

Ba k


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

Ba k


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

Ba k


aggregate recruiting intensity - princeton university

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