Financial Markets and Unemployment
Tommaso Monacelli
Bocconi University

Vincenzo Quadrini
University of Southern California
Antonella Trigari
Bocconi University
May 27, 2012

WHY FINANCIAL MARKETS?
Strong comovement unemployment and debt flows
Recessions more severe and long-lasting with banking crisis.

POSSIBLE LINKS?

• As a consequence of a credit contraction, employers lack the liquidity forinvestment and hiring:– Credit Channel.

• As a consequence of a credit contraction, employers face weakerbargaining conditions with workers.
– Bargaining channel.

2

THEORETICAL INTUITION• Suppose that there are only two periods. No discounting.
– Period 1: The firm issues debt b and hires a worker.
– Period 2: The firm produces z and splits the net surplus:
Wage = 12 (z − b),

Dividend = 12 (z − b)

• The value of hiring a worker in period 1 (Value of a Match) is:
1b + (z − b)
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MODEL• Agents have utility E0

P∞tβct.
t=0– They could be employed or unemployed.
– They are the owners of firms. The interest rate is r = 1/β − 1.
• A firm is created when a vacancy is filled with an unemployed worker.
– The cost of posting a vacancy is κ.
– A vacancy is filled with probability qt = m(vt, ut)/vt.
– An unemployed worker finds a job with probability pt = m(vt, ut)/ut.
– The match is separated with probability λ.
• Wages are determined through bargaining (η=Workers’ Power).

4

MODEL• Agents have utility E0

P∞tβct.
t=0– They could be employed or unemployed.
– They are the owners of firms. The interest rate is r = 1/β − 1.
• A firm is created when a vacancy is filled with an unemployed worker.
– The cost of posting a vacancy is κ.
– A vacancy is filled with probability qt = m(vt, ut)/vt.
– An unemployed worker finds a job with probability pt = m(vt, ut)/ut.
– The match is separated with probability λ.
• Wages are determined through bargaining (η=Workers’ Power).
• Added features:b

1. Firms can issue debt bt and pay dividends dt = zt − wt + t+1
R − bt .
2. There are credit shocks (φt) that affect the borrowing limit.
5TIMING FOR INCUMBENTS
Standard model

Separation withprobability λzt+1zt?
66Wagebargaining, wt

Payment of dividends, dt .

-TIMING FOR INCUMBENTS
Standard model with added features

Separation withprobability λzt+1 , φt+1 , bt+1

zt , φt , bt?

-66

6

Wage
bargaining, wt

Payment of dividends, dt .
Choice of new debt, bt+1

Choice todefault

BORROWING LIMIT

Firm’s value:Jt(bt) = dt + β(1 − λ)EtJt+1(bt+1)

Enforcement constraint:
φtEtJt+1(bt+1) ≥ bt+18

WAGE BARGAINING
Bargaining problem:
hmax Jˆt(bt, wt)1−η Ŵt(bt, wt) − Utiη wt

Wage equation:
wt = η · (zt − bt) + η ·[pt + (1 − λ)φt]κ
qt(1 + φt)(1 − λ)

9

CHOICE OF DEBT
Jt = max zt − wt − bt +bt+1bt+1+ β(1 − λ)(1 − η)EtSt+1(bt+1)
R

subject to(1 − η)φtEtSt+1(bt+1) ≥ bt+110

First order condition

11 1−ηµt =−×.
1 + (1 − η)φtRR{z} |{z}|Total changein debt

Marginal gainfrom borrowing

RESULT: Borrowing constraint binding if η > 0.

11

TIMING FOR NEW FIRMS
AND JOB CREATIONVacancies are filledwith probability qt

zt+1 , φt+1 , bt+1zt , φt?

-66Job posting(vacancy)

Payment of dividends, dt .
Choice of new debt, bt+1

FREE ENTRY AND JOB CREATION

qtQt = κ• qt = Probability of finding a worker.
• Qt = Value of a filled vacancy.
• κ = Cost of posting a vacancy.

13

SENSITIVITY OF Qt TO CREDIT SHOCK

∂Qt
βEtJt+1(bt+1)=η·∂φt1 + φt(1 − η)

14

NUMERICAL IMPULSE RESPONSES

Description

Discount factor for entrepreneurs, βMatching parameter, ξ̄Matching parameter, αRelative bargaining power, ηProbability of separation, λCost of posting vacancy, κUtility flow unemployed, aEnforcement parameter, φ̄Value

0.990
0.773
0.649
0.672
0.049
0.711
0.468
3.637

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Response credit shockEXTENSION: Monopolistic competition• Each firm is a monopolistic producer of differentiated goods, yi.
Z N• Aggregate production: Y =! 1εyiεdi0• Demand function: Pi = Y 1−εyiε−11+ϕ• Production: yi = zli;

Cost:

Ali1+ϕ .

IN REDUCED FORM: Replace zt with z̃tNtν .
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PARAMETERS• Price mark-up, 1ε − 1 = 0.33.

• Elasticity of intensive margin ϕ1 = 1.

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Response credit shock

STRUCTURAL ESTIMATION• Three AR(1) shocks:
1. Productivity, zt
2. Credit, φt
3. Matching, ξt• Three empirical variables in first differences:
1. Log-GDP, Yt
2. Log-employment, Nt+1B−B3. New debt over GDP in business sector, t+1Yt t• Three parameters are pre-determined: β, λ, κ.

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PARAMETERS

Estimated parameter

Productivity shock persistence, ρz
Productivity shock volatility, σz
Credit shock persistence, ρφCredit shock volatility, σφMatching shock persistence, ρξMatching shock volatility, σξMatching share parameter, αBargaining power workers, ηUtility flow unemployed, aMean enforcement parameter, φ̄Mark-up parameter, εElasticity of effort, ϕPrior[mean,std]

Mode

Beta[0.5,0.20]
IGamma[0.001,0.05]
Beta[0.5,0.20]
IGamma[0.001,0.05]
Beta[0.5,0.20]
IGamma[0.001,0.05]
Beta[0.5,0.1]
Beta[0.5,0.1]
Beta[0.4,0.1]
IGamma[8,5]Beta[0.8,0.05]
Beta[1,0.2]

0.944
0.005
0.965
0.143
0.983
0.056
0.650
0.674
0.470
3.621
0.937
1.033

Posterior thresholds
Below 5%
Below 95%

0.937
0.004
0.954
0.135
0.977
0.052
0.638
0.676
0.433
3.607
0.932
1.002

0.968
0.006
0.970
0.155
0.987
0.062
0.656
0.696
0.463
3.654
0.954
1.035

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VARIANCE DECOMPOSITION

OutputEmployment
New debt/output
Hourly wage

TFPshockzCreditshock
φMatchingshock
ξ

46.2
0.4
0.1
12.0

29.2
54.1
66.7
57.0

24.6
45.5
33.1
31.0

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Quarter-by-quarter decomposition

TESTING THE BARGAINING CHANNEL
Quadrini & Sun (2012)• We start from an industry dynamics model.
• Model is an extension of the previous model:– Multi-workers firms.
– Firm-level idiosyncratic shocks to productivity and credit.
– Collectively bargaining of wages.
– The bargaining power of workers η differ across firms.
– Partial equilibrium analysis.

24Optimality condition for hiringβBηgt+1bt
0N(1 − η)Ets̄t+1 + N= Υ gt+1 − 1 + λgt+125

LINEARIZED OPTIMALITY CONDITIONNB
gt+1= αc + αs · Ets̄t+1 + αb · bt + αg (η) · gt+1whereαs =(1 − η)γ(g N − 1 + λ)g N,NNB[ηγ(g − 1 + λ)/g + η(1 − γ) + (1 − η)(1 − γ)(1 + ξ)/ξ]bgαb =ηγ(g N − 1 + λ),[ηγ(g N − 1 + λ)/g N + η(1 − γ) + (1 − η)(1 − γ)(1 + ξ)/ξ]bαg (η) =ηγ(g N − 1 + λ)[ηγ(g N − 1 + λ)/g N + η(1 − γ) + (1 − η)(1 − γ)(1 + ξ)/ξ]g B

26

TESTING HYPOTHESISThe sensitivity of employment to credit increases
with the bargaining power of workers.

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EMPIRICAL EQUATION∆employit = β1 · unioncic,t · ∆debtit +β2 · unioncic,t +β3 · ∆debtit +β4 · leverageit−1 +β5 · log(employit−1) +β6 · Qit +β7 · cashf lowit + νi + τt + εit28

Unionization RateHighLow

unioncic,t · ∆debtit
unioncic,t∆debtit
leverageit−1log(employt−1 )Qitcashf lowit

Firm Fixed Effects
Year Dummies
Adjusted R2
Observations

0.252∗∗∗(0.087)-0.009(0.111)
0.051∗∗∗(0.010)-0.038(0.025)-0.314∗∗∗(0.022)0.018∗∗∗(0.007)0.118∗∗∗(0.025)0.092∗∗∗(0.011)
0.003(0.031)-0.352∗∗∗(0.047)0.034∗∗∗(0.013)0.138∗∗∗(0.048)0.051∗∗∗(0.009)-0.088∗∗(0.038)-0.292∗∗∗(0.028)0.011(0.009)0.117∗∗∗(0.029)

Yes
Yes
0.40
9,148

Yes
Yes
0.41
4,441

Yes
Yes
0.39
4,707

CONCLUSION• We have proposed a mechanism through which leverage affects the hiring
decision of employers.
• The mechanism is not based on the typical credit channel but on thewage determination process.
• This may explain why in a tight credit market firms do not invest andhire even if they are not short of cash.
• The mechanism finds empirical support at the micro level.

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