Sticky Wages and Financial Frictions Alex Clymo 1 1 University of Essex EEA-ESEM, August 2017 1 / 18
Introduction Recent work highlights that new wages more flexible than old: Pissarides (2009), Haefke, Sonntag and Van Rens (2013) New wages respond close to (but less) than one-for-one with productivity, existing wages much stickier Casts doubt on ability of S&M model to generate volatility in unemployment: Flexibility of new wages is crucial for job creation (average discounted wage over life of job vs productivity) Financial frictions offer potential solution: Schoefer (2015): financial channel of wage rigidity Rigidity of existing wages squeezes cashflow, reducing firm s ability to fund vacancies 2 / 18
Two opposing views Simple two period model No financial frictions: Tightness determined by free entry: κ q(θ 0 ) = β(z 1 w 1 ) θ 0 = Only new wages matter Financial frictions: ( βψ0 (z 1 w 1 ) Firm has available cash from profits: (z 0 w 0 )l 0 Suppose borrowing fixed: d0 κ ) 1 ψ 1 Then total spend on vacancies entirely determined by old wages: v 0 = (z 0 w 0 )l 0 + d 0 θ 0 = (z 0 w 0 )l 0 + d 0 u 0 3 / 18
This paper Blend and extend these two polar theories. Financial channel of wage rigidity plus: 1. Firm borrowing against future profits: ( firm-value channel ) Reactivates role for future wages Can either amplify or dampen FCWR results 2. Capital: ( capital substitution channel ) Effect of cashflow on vacancy posting no longer immediate Firms allocate scarce cash between investment/vacancy costs New wages allocative for K/L tradeoff both existing and new wage stickiness matters, and play distinct roles. 4 / 18
Related literature Flexibility of new wages: Pissarides (2009), Haefke, Sonntag and Van Rens (2013), Kudlyak (2014), Carneiro et al. (2012), Martins et al. (2012) Matching and financial frictions: Schoefer (2015): financial channel of wage rigidity Petrosky-Nadeau (2009), Petrosky-Nadeau and Wasmer (2013), Christiano, Trabandt and Walentin (2011), Quadrini and Sun (2015) Firm financing over the cycle: Covas and Den Haan (2011), Jermann and Quadrini (2012), Azariadis, Kaas and Wen (2015) Firm value over the cycle: Belo, Gala, Pokomy, and Salomao (2017) Value of labour force most procyclical component of firm value 5 / 18
Section 1: Model 5 / 18
Model Standard S&M (Pissarides, 2000) model enhanced with: Financial frictions (Gertler and Karadi, 2011) Infra-marginal wage rigidity (Schoefer, 2015) Capital (today, only in theory part) Technology: Production function: y t = z t k α t 1l 1 α t 1 Matching: vacancy filling probability q t = q(θ t ), where θ t = v t /u t Flows: l t = q t v t + (1 ρ)l t 1 k t = i t + (1 δ)k t 1 Capital adjustment costs p i t = f(i t, k t 1 ). 6 / 18
Wage rigidity Simple wage rules: New-hire wages: w n t = wz γn t Wage fixed until receive shock which resets you to new going wage Shock is i.i.d over matches and time, occurring w.p γ o Firm payroll: Suppose currently employing l t 1 workers at average wage w t. Total payroll Φ t = w t l t 1. Payroll tomorrow: Φ t+1 = wt+1(l n t (1 γ o )(1 ρ)l t 1 ) + (1 γ o )(1 ρ)φ t 7 / 18
Firm problem Cashflow: e t + p i ti t + κ(z t )v t = z t k α t 1l 1 α t 1 w tl t 1 r t 1 d t 1 + d t Define price of a match: p v t κ(z t) q t Plug in the flows and we get balance sheet: And net worth definition: e t + p i tk t + p v t l t = n t + d t n t z t k α t 1l 1 α t 1 w tl t 1 + p i t(1 δ)k t 1 + p v t (1 ρ)l t 1 r t 1 d t 1 Stickiness of existing wages w t amplifies response of cashflow to shocks Schoefer s (2015) financial channel of wage rigidity 8 / 18
Firm-value channel Firm maximises discounted sum of dividends: details Maximised value: V (n t, Φ t, l t 1, s t) contains matching rents Simple limit on borrowing a la Gertler and Karadi (2011) After raising funds, firm can run away with fraction λ k of capital and λ l of matches, at cost of losing firm Lenders only willing to lend if value of theft less than cost: λ k p i tk t + λ l p v t l t V (n t, Φ t, l t 1, s t ) Two key ideas: (following positive TFP shock) 1. Stickiness of old wages means matching rents elevated for longer, increasing firm value and borrowing amplifies cashflow channel 2. Flexibility of new wages reduces future matching rents, reducing firm value and borrowing dampens cashflow channel Why? Unsecured debt especially cyclical, and firm value cyclicality driven by labour. 9 / 18
FOCs and capital-labour ratio Capital FOC: Labour FOC: E t [ Ωt,t+1 ( αz t+1k α 1 t l 1 α t + p i t+1(1 δ) p i t )] = λ kµ tp i t 1 + µ t E t [ Ωt,t+1 ( (1 α)zt+1k α t l α t w n t+1 + p v t+1(1 ρ) p v t ) +...... + Ω t,t+1 (V 2,t+1w n t+1 + V 3,t+1)] = λ lµ tp v t 1 + µ t µ t: multiplier on borrowing constraint. Ω t,t+1: SDF. Implications: If equally collateralisable (λ k = λ l ) and old wages flexible (γ o = 1) firm equalises one period ahead return on k vs l If old wages sticky, then new wage determines K/L choice: even if old wages are sticky, sufficiently flexible new wages can insulate L from cashflow channel by twisting K/L choice 10 / 18
Summary New/existing wage stickiness influences three key margins: 1. Current cashflow: n t z t k α t 1l 1 α t 1 w tl t 1 +... existing wages active here (Schoefer, 2015) 2. Current ability to raise debt: p i tk t + p v t l t = n t + d t, λ k p i tk t + λ l p v t l t V (n t, Φ t, l t 1, s t ) future value reactivates role for new wages both new/existing wages active here 3. Capital labour tradeoff: Er k t+1 Er l t+1 + Γ new wages active here 11 / 18
Section 2: Numerical results 11 / 18
A very simple thought experiment Calibration to stock market volatility has strong implications for ability to match movements in unemployment: p v t stock price of single-worker firm Arbitrage between old/new matches: p v t κzt q t = κzt ψ 0 θ ψ1 t Total stock market value is S t = p v t l t 1, output is y t = z t l t 1, giving S t = κ y t q(θ t ) var (θ) = 1 var ψ 1 ( St any calibration which matches volatility of stock market matches 82% of volatility in tightness (for ψ 1 = 0.5) This paper uses financial frictions to generate stock market volatility. But: firm value also contains debt, capital, financial rents... more work to be done. y t ) 12 / 18
Results Today: results in model without capital model Focus will be on role of debt and firm value. calibration All experiments: 1 s.d. (persistent) productivity shock: 1. Can debt smooth timing of wage rigidity? Firm can borrow against future wage changes to smooth timing of wage rigidity 2. Does volatility of matching rents, (z t w t ), amplify borrowing ability and hence unemployment? Comparison to Schoefer (2015), who assumes Dt = D. Endogenous debt can either amplify or dampen shocks depending on form of wage rigidity. For sensible calibration, FCMR survives. 13 / 18
Experiment 1: Debt and the timing of wage rigidity Despite financial friction, firms can use debt to smooth timing of wage rigidity 4.5 10-3 0 0.03 4 3.5-0.01 0.025 3-0.02 0.02 w (average) 2.5 2 1.5 1 0.5 0 0 20 40 60 u -0.03-0.04-0.05-0.06-0.07 0 20 40 60 Debt 0.015 0.01 0.005 stickier old w stickier new w 0 0 20 40 60 Blue: γ n = 0.52, γ o = 0.1. Red dash: γ n = 0.45, γ o = 0.5. Black dot: TFP Key channel: firm borrows against future lower wages in red line 14 / 18
Experiment 2: Does firm-value channel amplify u? Yes, if old wages are flexible and new sticky (γ n = 0.7, γ o = 1) 4.5 10-3 0 0.016 w (average) 4 3.5 3 2.5 2 1.5 0 20 40 60 u -0.005-0.01-0.015-0.02-0.025-0.03-0.035 0 20 40 60 Debt 0.014 0.012 0.01 0.008 0.006 0.004 0.002 endog Debt fix Debt 0 0 20 40 60 Blue: λd t = V t. Red dash: D t = D ss. Black dot: TFP Key channel: firm borrows against future lower wages, can t in exog D model and has no cashflow boost since wages flex 15 / 18
Experiment 2: Does firm-value channel amplify u? No, if old wages are sticky and new flexible (γ n = 1, γ o = 0.1) 4.5 10-3 0.005 0 4 0-0.002 w (average) 3.5 3 2.5 2 1.5 1 0.5 0 20 40 60 u -0.005-0.01-0.015-0.02-0.025-0.03-0.035-0.04-0.045 0 20 40 60 Debt -0.004-0.006-0.008-0.01-0.012-0.014-0.016-0.018 endog Debt fix Debt -0.02 0 20 40 60 Blue: λd t = V t. Red dash: D t = D ss. Black dot: TFP Key channel: Sticky old wages so both get cashflow boost. But high wages in the future, reduce borrowing ability 16 / 18
Experiment 2: Does firm-value channel amplify u? In sensible calibration (γ n = 0.7, γ o = 0.04) effects wash out 4.5 10-3 0 7 10-3 4 3.5-0.01 6 5 endog Debt fix Debt 3-0.02 4 w (average) 2.5 2 u -0.03 Debt 3 2 1.5-0.04 1 1 0.5-0.05 0-1 0 0 20 40 60-0.06 0 20 40 60-2 0 20 40 60 Blue: λd t = V t. Red dash: D t = D ss. Black dot: TFP But: counterfactual acyclicality of debt 17 / 18
Summary Many things affect unemployment: Firm cashflow Future firm profits ( debt) Capital/labour decisions Each distinctly affected by the flexibility of old and new wages. Challenge is to build a calibrated model which can replicate the joint behaviour of stock markets, debt, labour, and capital. Going forward: Add capital Better debt/equity microfoundations Heterogeneous firms? 18 / 18
Appendix 18 / 18
Firm problem return V (n t, Φ t, l t 1, s t) = max E t [Ω t,t+1 ((1 σ)n t+1 + V (σn t+1 + n e, Φ t+1, l t, s t+1))] s.t. Φ t+1 = w n t+1(l t (1 γ o)(1 ρ)l t 1) + (1 γ o)(1 ρ)φ t and ( ) n t+1 = z t+1kt α l 1 α t + p i t+1(1 δ) p i t k t +(p v t+1(1 ρ) wt+1 n p v t ) l t...... w n t+1(1 ρ)l t 1 + (1 ρ)φ t + r tn t and λ k p i tk t + λ l p v t l t V (n t, Φ t, l t 1, s t) 19 / 18
Model (identical except no capital) return Firm: n c t = z t l t 1 Φ t + p v t (1 ρ)l t 1 rd t 1, n t = σn c t + n e t p v t l t = n t + d t, p v t κ(z t) q t λq v t l t = V t, V t = E t [ Ωt,t+1 ( (1 σ)n c t+1 + σv t+1 )] Matching: q t = ψ 0 θ ψ1 t, θ t = v t /u t l t = q t v t + (1 ρ)l t 1, u t = 1 l t 1 Wages: w n t = wz γn t Φ t = w n t (l t 1 (1 γ o )(1 ρ)l t 2 ) + (1 γ o )(1 ρ)φ t 1 Note σ: extra discount as if exits w.p σ, needed for λ < 1. 20 / 18
Calibration return Table: Calibration Interpretation Value Source β Discount factor 0.9966 4.17% annual interest rate σ c Risk aversion 0 ρ x Job destruction 0.0274 Steady state transition probabilities ψ 0 Match efficiency 0.3917 Steady state transition probabilities ψ 1 Matching elasticity 0.5 Petrongolo & Pissarides (2001) κ Recruiting cost 0.3107 0.32 steady state wage w Steady state real wage 0.9709 Steady state unemployment 5.7% γ n new wage flexibility Various values used γ o old wage flexibility Various values used σ Expert exit prob. 0.9770 Asset price moments w e New expert equity 0.3026 Asset price moments Λ Frac. of divertable capital 0.4854 Asset price moments z Steady state productivity 1 Normalisation ρ Autocorr. of productivity 0.98975 Quarterly (log HP-filtered) autocorr. σ e Standard deviation of ε 0.0043 Quarterly (log HP-filtered) std. 21 / 18