High Discounts and High Unemployment By Robert E. Hall, American Economic Review (forthcoming) Peter K. Kruse-Andersen
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Introduction Main idea: • Fluctuations in financial discounts affect unemployment
fluctuations • There should be a correlation between the stock market
value and the unemployment rate Previous studies: • Productivity drops depress the payoff to job creation in
recessions • There should be a correlation between the productivity
and the unemployment rate
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Unemployment and Productivity
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Unemployment and Stock Market Value
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Introduction Connecting unemployment and discount rates: • The financial literature: • Discount rates rise dramatically in recessions • High volatility of discount rates
• Mechanism: • Some event creates a financial crisis • Risk premiums rise, discount rates increase, and asset values fall • All types of investment fall • Hiring (investment) has financial risk comparable to corporate earnings • Hiring falls and unemployment rises
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The Model Driving forces: • The states of the economy: s • The states follow a Markov process: πs,s 0 • Driving force 1: productivity growth • Productivity: x 0 • Productivity growth: gs,s 0 = xx • Driving force 2: Stochastic discounter s0 • Stochastic discount factor: Ms,s 0 = β m ms • ms is the state-contingent valuation
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The Model Value of flow payoff ys (in productivity units): xYs =
X s0
Ys =
X
πs,s 0 β
ms 0 ys 0 x 0 ms
ωs,s 0 ys 0 ,
s0
⇔
ωs,s 0 ≡ πs,s 0 β
ms 0 gs,s 0 ms
• Ys x is the capital value • ωs,s 0 is the Arrow state price adjusted for productivity
growth
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The Model Diamond-Mortensen-Pissarides framework: • Fixed workforce and a fraction searching for jobs • Employers recruit by posting vacancies • Number of vacancies: V • Number of unemployed: UE V • Index of tightness in labor market: θ ≡ UE • Large value of θ means low labor market tightness
• Job finding rate: φ(θs ),
φ0 > 0
s) • Recruiting rate: q(θs ) = φ(θ θs ⇔ Vq(θs ) = UE φ(θs )
• Probability that a job ends: ψ • If there is a match, the worker receives the wage: Ws
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The Model Value for an unemployed: X ωs,s 0 [φ(θs ) (Ws 0 + Cs 0 ) + (1 − φ(θs )) Us 0 ] Us = z + s0
where z is flow value received while searching, and C is the carrier value. X Cs = ωs,s 0 [ψUs 0 + (1 − ψ)Cs 0 ] s0
Job-seeker’s reservation wage, W , mounts to: W s = Us − Cs
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The Model Value of output created over the course of a job: X ωs,s 0 Xs 0 Xs = 1 + (1 − ψ) s0
The employer’s net value of a match: Xs − Ws In this setup, the return to holding a firm’s stock equals the return to hiring a worker (see working paper version) Zero profit condition: q(θ ) | {zs }
Recruiting rate
×
(X − W ) | s {z s }
Net value from hiring
=
κ |{z}
Cost of vacancy
where κ is recruiting cost per vacancy per period. 13.10.2016 Slide 10/32
The Model Observed tightness and inferred wage: • One can find Ws given an observed tightness, θs • This is used later
Why look at labor market tightness? The labor market tightness is intimately related to the unemployment rate: ut = (1 − φ(θs ))ut−1 + ψ(1 − ut−1 ) Over time with constant θ: u ∗ =
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ψ ψ+φ(θ)
The Model Credible bargaining: • Canonical DMP model employed Nash bargaining • Shimer (2005) showed that Nash bargaining made the
wage too responsive to driving forces • Labor market tightness hardly responds to driving forces • Solution: Alternating-offer bargaining • Counter offers can be made, but with a probability δ,
some event prevents a match
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The Model Indifference condition - worker: #
" WsE + Cs = δUs + (1 − δ) z +
X
ωs,s 0 (WsK0 + Cs 0 )
s0
|
{z
}
PV of job with counter offer wage
Indifference condition - employer: #
" Xs − WsK = (1 − δ) −γ +
X
ωs,s 0 (Xs 0 − WsE0 )
s0
where γ reflects the flow cost for delay in bargaining (see page 10) 13.10.2016 Slide 13/32
The Model Finally, it is assumed that the resulting wage is: 1 Ws = (WsE + WsK ) 2 Equilibrium: 7 equations and 7 unknowns (θs , Us , Cs , Xs , WsE , WsK , Ws ) Stock market: Ps =
X
ωs,s 0 (Ps 0 + ds 0 )
s0
But really, the point is that: Ps = Xs − Ws = Js where Js is the job value 13.10.2016 Slide 14/32
Specifications and Parameters State space: • Data can be used to calculate: • Labor market tightness: θ ≡ • Price/dividend ratio: P/d
V UE
(P/d)t θt • Compute index: indext = std. + std. θ P/d • Divide index into quintiles (5 quantiles) • These are the five states
• Compute average value of quintiles • Compute transition probabilities between states
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Specifications and Parameters
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Specifications and Parameters
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Specifications and Parameters
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Specifications and Parameters
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Specifications and Parameters Parameters and functions: • Use common values for κ, ψ, and z • Job finding rate: φ(θ) = µθ 0.5 • Job recruiting rate: q(θ) = µθ −0.5 • Hiring flow = Vq(θ) = µθ −0.5 V
Solving the model: • The model is solved with two additional restrictions to infer values of δ and γ • θ3 = 0.59 (actual value) • θ5 − θ1 = 0.63 (actual value)
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Specifications and Parameters Stochastic discount factor: X ωs,s 0 (Ps 0 + ds 0 ), Ps =
ωs,s 0 ≡ πs,s 0 β
s0
• Solving for m2 , ..., m5 with m1 = 1
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ms 0 gs,s 0 ms
Specifications and Parameters Stochastic discount rate: X X ms 0 1 πs,s 0 β ωs,s 0 = = gs,s 0 1 + rs ms 0 0 s
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s
Model without Credible Bargaining Solving the model in three steps: 1
Xs is computed from the stochastic discount factor
2
The actual value of θ is used to compute Ws
3
Verify that Ws lies in the bargaining set
Computing job value (stock value): κ = q(θs ) (Xs − Ws ) | {z }
and q(θs ) = µθs−0.5
Js
µ 2 θs = Js κ 13.10.2016 Slide 23/32
⇔
Js =
θs0.5
κ µ
Model without Credible Bargaining
• The job value decreases when θ decreases • Productivity falls more than the wage • In that sense the wage is sticky • Note that state 1 has the highest discount rate 13.10.2016 Slide 24/32
Model with Credible Bargaining
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Model with Credible Bargaining
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Job value and stock value From model κ = Jq From data (JOLTS): 1
Hires = qV
2
Vacancies = V
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⇔
J = κ/q
Job value and stock value
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Job value and stock value
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Concluding remarks • The stock market value and the unemployment rate
move together due to common role of the discount rate • Yet, studies continue to focus on the
productivity-unemployment relationship • Novelty: connects labor and stock market outcomes
through stochastic discount rate • Forces affecting the discount rate affects both
unemployment and asset prices
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What have we learned? • The paper links movements in the stock and labor
market in an intuitive way • It seems like a stochastic discount rate could drive movements in unemployment • Consistent with co-movements in unemployment rate
and stock prices • Might be a better driving force than productivity shocks
• But, we do not know what drives discount rate
movements • Hence we do not really know what the actual policy
implications are
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Thank you
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