Aggregate Recruiting Intensity - Simon Mongey - Home · Introductiony yl What is aggregate...

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Aggregate Recruiting Intensity

Alessandro GavazzaLondon School of Economics

Simon MongeyNew York University

Gianluca ViolanteNew York University

NBER Summer Institute EFMPL - July 18, 2016

Introductionyyl

What is aggregate recruiting intensity?

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

Aggregate match efficiency

Ht = AtVαt U1−α

t

Gavazza-Mongey-Violante, "Aggregate Recruiting Intensity" p.1/33hello

Introductionyyl

What is aggregate recruiting intensity?

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

Aggregate match efficiency

Ht = AtVαt U1−α

t

Why study aggregate recruiting intensity?

• Micro data (Davis-Faberman-Haltiwanger, 2013)

Firms fill vacancies at different rates, depending on how fast they grow

Distribution of firm growth rates important for match efficiency

• Macro data

Large and persistent decline in At in ‘08 recession

Existing studies focus on mismatch, composition, job-search effort


Introductionyyl

Questions

1. What fraction of decline in At is accounted for by Φt?

2. How do macro shocks transmit to aggregate recruiting intensity Φt?

Model

• Equilibrium random matching model with firm dynamicsCooper-Haltiwanger-Willis (2007), Elsby-Michaels (2013), Acemoglu-Hawkins (2014)

+ Choice of recruiting intensity per vacancy

+ Entry and exit

+ Financial frictions

Approach

1. Examine transition dynamics to financial & productivity shocks

2. Decomposition of Φt and cross-section of firms along the transition


Firm-level hiring technologyyl

Random-matching model hit = qtvit

+ recruiting effort hit = qteitvit

• JOLTS vacancies - vit

• BLS: “Specific position that exists...for start within 30-days...activerecruiting from outside the establishment”


Firm-level hiring technologyyl

Random-matching model hit = qtvit

+ recruiting effort hit = qteitvit

• JOLTS vacancies - vit

• BLS: “Specific position that exists...for start within 30-days...activerecruiting from outside the establishment”

• Recruitment intensity - eit

1. Shifts the filling rate of an open position

2. Costly on a per vacancy basis

• An outcome of expenditures on recruiting activities


Recruiting costsy

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 hiring cost at 100+ employee firms $3,479


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 =

[∫

eit

(vit

Vt

)

dλht

]α


Macro shocks and aggregate recruiting intensityyl

1. Composition effectyhit = qt

yeit

yvit

- Shift in growth rate distribution

∗ Moderated by selection

- Better entrants and hiring firms

2. Slackness effect

hit =xqt

yeit

yvit

- Firms substitute away from costly hiring measures


Value functionsyyl


Value functionsyyl

Firms are heterogeneous in n, a, z and age

Let V(n, a, z) be the present discounted value of dividends

• 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 - 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 engineer C(e, v, n) toymatch micro-evidencey

Log-linear relation between the vacancy-yield and hiring rate

-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-5.0 -4.0 -3.0 -2.0 -1.0

Log Daily Fill Rate

Log Hires Rate

Hires-Weighted Least Squares

Slope (s.e.) = 0.820 (0.006)R-squared = 0.993

Data points correspond to

growth rate bins

Davis, Faberman and Haltiwanger (2013)


Reverse engineer C(e, v, n) toymatch micro-evidencey

Cost function

C(e, v, n) =

[κ1

γ1eγ1 +

κ2

γ2 + 1

(v

n

)γ2]

v, γ1 ≥ 1, γ2 ≥ 0

First-order conditions give the DFH specification

log

(hi,t

vi,t

)

= Ω (θ∗t ) +γ2

γ1 + γ2log

(hi,t

ni,t

)


Optimal job filling and vacancy ratesyl

-0.3 -0.2 -0.1 0 0.1 0.2

Growth rate

0

0.01

0.02

0.03

0.04

0.05

0.06

Vacancy

rate

A. Vacancy rate

ModelData

-0.3 -0.2 -0.1 0 0.1 0.2

Growth rate

0

1

2

3

4

5

6

7

8

Jobfillingrate

B. Job filling rate

ModelData

v

n= const. · q (θ∗)

−γ1

γ1+γ2 ·

(n′ − n

n

) γ1γ1+γ2

= 0.18

e = const. · q (θ∗)−

γ2γ1+γ2 ·

(n′ − n

n

) γ2γ1+γ2

= 0.82


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

Given z, growth determined by financial constraints and hiring costs


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 = V∗t /Ut

Uflowst+1 = Ut − H (θ∗t , St) + F(θ∗t , St)− λe,tn0

Udemandt+1 = L −

∫

n′ (n, a, z, θ∗t , St) dλt

3. Hires are given by the matching function Ht = ΦV∗αt U1−α

t

• Stationary equilibrium Measure is stationary, and S = (λ, U)


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 L 24.6 Average firm size = 23Elasticity of matching function wrt Vt α 0.5 JOLTS

Add to the model• Heterogeneity in returns to scale σ ∈ σL, σM, σH

Calibration strategy

1. Worker flows and labor share

2. Distribution of firm size, growth rates

3. Micro-evidence on job-filling and vacancy-posting

4. Entry and exit

5. Young firms’ and aggregate leverage


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. Φ 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

Persistence of z shocks ρz 0.992 Std. dev ann emp growth 0.440 0.420Std. dev. of z shocks ϑz 0.052 Mean Q1 emp / Mean Q4 emp 75.161 76.000Mean z0 ∼ Exp(z−1

0 ) z0 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 One year old Debt to Output 1.394 1.250Collateral constraint ϕ 10.210 Aggregate debt-to-assets 0.276 0.330


Non-targeted momentsyl

Moment Model Data Source

Aggregate dividend / profits 0.411 0.400 NIPA1Aggregate capital / output 1.100 1.370 Flow of funds

2Employment 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

Note (1.) Capital measured from Flow of Funds B.103 non-financial business corporations: real-estate plus equipment (2.) Firm growth rates areannual.

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

0.35A. Hires

1-9 10-49 50-249 250-999 1000+0

0.05

0.1

0.15

0.2

0.25

0.3

0.35B. 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. Growth and Recruitment

Recruitment intensityVacancy rateGrowth rate

0 5 10 15

Age (years)

0

0.01

0.02

0.03

0.04

Den

sity

B. Distributions

Recruitment intensityVacant positionsHiring firms

y

(n′ − n

n

)

= q (θ∗) ×

(ye

)

×

(

↓v

n

)


Transition dynamics experimentsyl


Transition dynamics experimentsyl

Trace transitional dynamics of the economy in response to:

• Tightening of financial constraint ↓ ϕ

• Decline in aggregate productivity ↓ Z

• Size of shocks to match 10% decline in output (Fernald, 2015)

• Geometric decay with half-life of six years

Shocks: (i) 4% drop in Z, (ii) 75% drop in ϕ


US data 2008:01 - 2013:12yyl

0 1 2 3 4 5 6

Years

-1

-0.5

0

0.5

1

Logdeviatioonfrom

date

0

Vacancies Vacancy yield Unemployment Job finding rate Agg. Matching Efficiency Entry


Transition dynamics - Modelyl

0 1 2 3 4 5 6Years

-1

-0.5

0

0.5

1

Log

deviatioon

from

date0

A. Productivity A-shock

0 1 2 3 4 5 6Years

-1

-0.5

0

0.5

1

Log

deviatioon

from

date0

B. Finance ϕ-shock

Vacancies Vacancy yield Unemployment Job finding rate Agg. Recruitment Intensity Entry

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


Decomposing aggregate recruiting intensityyl

Aggregate recruiting intensity

Φt =

(V∗

t

Vt

)α

=

[∫

ei,t

(vi,t

Vt

)

dλht

]α




Φt =

(V∗

t

Vt

)α

=

[∫

ei,t

(vi,t

Vt

)

dλht

]α

Substituting in the policy function for effort ei,t

∆ log Φt = −αγ2

γ1 + γ2∆ log q(θ∗t )

︸︷︷︸

1. Slackness effect

+ α∆ log

[∫

g

γ2γ1+γ2i,t

(vi,t

Vt

)

dλht

]

︸︷︷︸

2. Composition effect

1. Slackness effect

g =xq (θ∗) ×

(ye

)

×

(

↓v

n

)




Φt =

(V∗

t

Vt

)α

=

[∫

ei,t

(vi,t

Vt

)

dλht

]α

Substituting in the policy function for effort ei,t



︸︷︷︸

1. Slackness effect

+ α∆ log

[∫

g

γ2γ1+γ2i,t

(vi,t

Vt

)

dλht

]

︸︷︷︸



↓ g = q (θ∗) ×

(ye

)

×

(

↓v

n

)



0 1 2 3 4 5 6Years

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05Logdeviatioonfrom

date

0

Aggregate recruiting intensity Φt

Slackness effectComposition effect

• Slackness effect dominates

• Composition effect roughly zero


Why is the composition effect zero?yl

Composition effect

∆ΦCompt = α∆ log

[∫

g

γ2γ1+γ2i,t

(vi,t

Vt

)

dλht

]

1. Two off-setting forces of the shock

↓ PE Composition effect under shock to ϕt, keeping θ∗ fixed

↑ GE Composition effect under θ∗t , keeping ϕ fixed



Composition effect

∆ΦCompt = α∆ log

[∫

g

γ2γ1+γ2i,t

(vi,t

Vt

)

dλht

]

1. Two off-setting forces of the shock

↓ PE Composition effect under shock to ϕt, keeping θ∗ fixed

↑ GE Composition effect under θ∗t , keeping ϕ fixed

2. Both moderated by selection

↑ PE More productive entrants and hiring firms

↓ GE Less productive entrants and hiring firms



0 1 2 3 4 5 6Years

-0.15

-0.1

-0.05

0

0.05

0.1Logdeviatioonfrom

date

0

Composition effectPE component (ϕt)GE component (θ∗t )

• At impact large negative PE component, offset by GE effect

• Followed by offsetting selection effects


Hiring by returns to scale parameter (σ)yl

0 6 12 18 240

0.2

0.4

0.6A. Fraction constrained

High σ

Low σ

0 6 12 18 24

-0.02

0

0.02

B. Hiring rate

0 6 12 18 24

Month

-1

-0.5

0

0.5

1C. Average effort

0 6 12 18 24

Month

-0.2

-0.1

0

0.1

0.2D. Vacancy yield


Vacancy yields by firm sizeyl

0 6 12 18 24

Month

-0.2

0

0.2

0.4

0.6

Log

deviation

from

date0

A. Data 2008:01 - 2010:12

0 6 12 18 24

Month

-0.2

0

0.2

0.4

0.6B. Model

Size 1-9Size 1000+


Taking stock and going forwardyl

Answers

1. Recruiting intensity explains approx. 1/3 of decline in match eff.

2a. Dominant effect: Slack markets reduce need for costly recruiting

2b. Strong selection effects limit role of compositional changes

2 . Slackness and composition explain vacancy yields by size


Taking stock and going forwardyl

Answers

1. Recruiting intensity explains approx. 1/3 of decline in match eff.

2a. Dominant effect: Slack markets reduce need for costly recruiting

2b. Strong selection effects limit role of compositional changes

2 . Slackness and composition explain vacancy yields by size

Extensions

1. Relationship to Kaas & Kircher (2015)

2. Construct an easy-to-measure index of aggregate recruiting intensity

3. How would Φt respond to hiring / job-search subsidies?


1. Relation to Kaas Kircher (2015)yl

KK model

ΦKKt =

∫q(θmt)

q(θt)

vmt

Vtdm

“The reason why [recruiting intensity] is pro-cyclical in our model is that q is concave,

and the cross-sectional dispersion in θmt is counter-cyclical”



KK model

ΦKKt =

∫q(θmt)

q(θt)

vmt

Vtdm



Our model



︸︷︷︸

1. Slackness effect

+ α∆ log

[∫

g

γ2γ1+γ2it

(vit

Vt

)

dλht

]

︸︷︷︸


Dispersion effect is present

1.

γ2γ1+γ2

< 1

2. ϕt shock delivers 45% increase in SD of git, as in data



KK model

ΦKKt =

∫q(θmt)

q(θt)

vmt

Vtdm



Our model



︸︷︷︸

1. Slackness effect

+ α∆ log

[∫

g

γ2γ1+γ2it

(vit

Vt

)

dλht

]

︸︷︷︸


Quantitatively, this effect is small

1.

γ2γ1+γ2

= 0.82 ≈ 1

2. Strong offsetting selection


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 zero

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 )

︸︷︷︸

Substitution effect

+ α log

[∫

g

γ2γ1+γ2i,t

(vi,t

Vt

)

dλht

]

︸︷︷︸

Composition effect



Return to model based decomposition

log Φt = −αγ2

γ1 + γ2log q(θ∗t )

︸︷︷︸

Substitution effect

+ α log

[∫

g

γ2γ1+γ2i,t

(vi,t

Vt

)

dλht

]

︸︷︷︸

Composition effect

GMV

(a) Model tells us that the composition effect is approximately zero

d log ΦGMVt = α

γ2

γ1 + γ2× (1 − α)× d log θ∗t

(b) Take elasticity of θ∗t to θt from transition dynamics

d log ΦGMVt = α

γ2

γ1 + γ2× (1 − α)× εθ∗,θ

≈1.45

d log θt



2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

Log

Aggregate

RecruitingIntensity

Aggregate match efficiencyDFH measure of recruiting intensityGMV measure of recruiting intensity



2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

Log

Aggregate

RecruitingIntensity

Aggregate match efficiencyDFH measure of recruiting intensityGMV measure of recruiting intensity

• DFH proxy Persistently low Φt explains persistently low At

• Our proxy Persistence due to other sources


3. Subsidies and aggregate recruiting intensityyl

1. Hiring subsidy paid to firms

• e.g. Hiring Incentives to Restore Employment Act, 2010

• Increases hiring• Increase in hiring achieved by ↑ et

• Increase in aggregate recruiting intensity ↑ Φt


3. Subsidies and aggregate recruiting intensityyl

1. Hiring subsidy paid to firms

• e.g. Hiring Incentives to Restore Employment Act, 2010

• Increases hiring• Increase in hiring achieved by ↑ et

• Increase in aggregate recruiting intensity ↑ Φt

2. Search-effort subsidy to workers

Ht = V∗αt S1−α

t , St = stUt, Ht =(

Φtst1−α

)

Vαt U1−α

t

• Increases unemployed search intensity ↑ st

• Increases labor market slackness ↑ qt

• For constant hiring-rates ↓ et

• Reduction in aggregate recruiting intensity ↓ Φt


yl

THANK YOU!


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 - Non-targetted moments


Transition dynamics - Macroyl

0 1 2 3 4 5 6Years

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

Log

deviatioon

from

date0

A. Productivity A-shock

0 1 2 3 4 5 6Years

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

Log

deviatioon

from

date0

B. Finance ϕ-shock

Output Yt Employment Nt Capital Kt Labor Productivity Yt/Nt

Ba k - Transition dynami s - Labor


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