Uninsured Unemployment Risk and Optimal Monetary Policy

Transcription

1 Uninsured Unemployment Risk and Optimal Monetary Policy Edouard Challe CREST & Ecole Polytechnique ASSA 2018

2 Strong precautionary motive Low consumption Bad aggregate shock High unemployment Low output Auclert and Rognlie (2017), Beaudry et al. (2017), Challe et al. (2017), Chamley (2014), Den Haan et al. (2017), Heathcote and Perri (2017), Kekre (2017), McKay and Reis (2017), Ravn and Sterk (2017a, 2017b), Werning (2015)

3 Basic questions I how should the central bank respond to this feedback loop? I how much does this response di er from that under full insurance? I how well does the optimal policy stabilise welfare-relevant aggregates (relative to full-insurance benchmark)?

4 Framework and main results I tractable HANK model with endogenous unemployment I focus on (transitory, persistent) productivity & cost-push shocks I monetary policy should be (much) more accomodative in recessions (and less in expansions) than under full insurance I policy rate should typically be lowered after productivity or cost-push driven recessions (opposite as in RANK) I This is because monetary policy should counter the rise in desired savings due to the precautionary motive I optimal policy almost fully neutralises feedback loop between aggregate demand and unemployment risk

5 Model overview I 2 household types: workers, rm owners I 3 rm types ( nal, wholesale, intermediate goods) I government: I sets (lump sum, constant) taxes and transfers I balanced budget I central bank: sets policy rate Firms Frictions Taxes household labour ) intermediate goods costly search τ I, T, ζ t + di erentiated monopolistic comp. τ W consumption & vacancy costs wholesale goods & Calvo pricing + (pt, π t, t ) ( nal goods

6 Households I discount factor β, nonnegative asset wealth I workers: period utility u (c) (u 0 > 0, u 00 < 0) and constraints: a i,t + c i,t = e i,t w t + (1 e i,t ) δ + R t a i,t 1 and a i,t 0 I rm owers: period utility ũ (c) (ũ 0 > 0, ũ 00 0) and constraints: a F t + c F t = D t + ϖ + τ t ν + R t a F t 1 and af t 0 I only workers have a precautionary motive I a = real value of nominal bond holdings; hence R t = 1+i t 1 1+π t

7 Intermediate goods rms and labor market ows I job creation/destruction a la DMP, with matching technology M t = m (1 (1 ρ) n t 1 ) γ v 1 γ t I free-entry c = λ t J t, where J t = (1 τ I )(z t ϕ t w t + T ζ t ) + (1 ρ) E t Mt+1 F J t+1 ow pro t from employ. relationship I equivalently: γ 1 γ ft = (1 τ I ) m 1 c 1 γ (z t ϕ t w t + T ζ t ) + (1 ρ) E t Mt+1 F f 1 γ t+1 γ

8 Equilibrium I optimal choices consistent with market-clearing + free entry I zero debt limit ) equilibrium wo. asset trades I with common β, eq m such that I I I employed workers precautionary-save, hence take down Rt at that rate, the other households would like to borrow, but cannot thus all households consume their current income I preserves precautionary motive whilst maintaining tractability I allows aggregation of ind. welfares into social welfare function

9 Constrained e ciency Social welfare function I constrained-e cient allocation solves: W t (n t 1, t 1, z t ) = max p t,w t,n t 0 fu t + βe t W t+1 (n t, t, z t+1 )g, where U t = n t u (w t ) + (1 n t ) u (δ) workers I 5 potential ine ciencies: 1 + Λνũ ν 1. monopolistic competition () τ W > 0) 2. relative price distortions () π t = 0) 3. congestion externalities () τ I > 0) 4. imperfect insurance () T > 0) zt ϖ + n t t w t cv t rm owners 5. income-redistributive wage ) u 0 (wt ) = Λũ 0 ν 1 [nt (z t wt ) cvt + ϖ]

10 Constrained e ciency Details constrained-e cient f t vs decentralised-eq m f t : f γ 1 γ t = (1 γ) m 1 1 γ c z t w + u (w t ) u (δ) u 0 (w t ) + (1 ρ) E t M F t+1 1 γft+1 t+1 f γ 1 γ γ 1 γ ft = (1 τi )m 1 c 1 γ h z t ϕ t w t + T ζ t i + (1 ρ) E t M F t+1 f γ 1 γ t+1 I u(w ) u(δ) u 0 (w ) re ects insurance externality and calls for T > 0 I 1 γ & 1 γf t+1 re ect congestion externalities and call for τi > 0 I ϕ t ( 1) re ects monopolistic distortions and calls for τ W > 0 I assume taxes decentralise constr.-e cient allocation in steady state

11 Full worker reallocation + risk-neutral rm owners Linear-quadratic problem I ρ = 1 and ũ (c) = c; then, to 2nd order max W t is equivalent to: s.t. min L t = 1 2 E t β k (ñt+k 2 + Ωπ2 t+k ), ñ t ˆn t ˆn t k =0 employment gap π t = βe t π t+1 + κ Φ ñt + κ ˆζ t (NKPC) ΨE t ñ t+1 = î t E t π t+1 r t (EC) where r t = ΨΦµ z ẑ t I EC re ects precautionary motive, with strength Ψ 2 (0, + ) I e cient rate r t is a ected by precautionary motive

12 Full worker reallocation + risk-neutral rm owners Optimal Ramsey policy and i 0 (ẑ 0, ˆζ 0 ) = Υ(α + µ ζ 1)ˆζ 0 perfect-insurance response i t1 (ẑ 0, ˆζ 0 ) = Υ[µ t ζ (1 α) t k =0 αk µ t ζ k ]ˆζ 0 perfect-insurance response ΨΥθn(α + µ ζ )ˆζ 0 + ΨΦµ z ẑ 0, imperfect-insurance correction ΨΥθn[ t k =0 αk µ t ζ k ]ˆζ 0 + ΨΦµ z t+1 ẑ 0 imperfect-insurance correction I imperfect insurance mutes down / reverts interest-rate response I implied fñ t, π t gt=0 is the same as under perfect insurance

13 Full worker reallocation + risk-neutral rm owners Optimal discretionary policy î t (ẑ 0, ˆζ 0 ) = κφµ t+1! ζ ˆζ (1 βµ ζ )Φ + κθn 0 perfect-insurance response Ψ κφθnµ t+1! ζ ˆζ (1 βµ ζ )Φ + θnκ 0 + ΨΦµ z t+1 z 0 imperfect-insurance correction I more accomodation + replication of perfect-insurance dynamics

14 Partial worker reallocation + risk-averse rm owners I solve Ramsey problem numerically for calibrated economy I baseline: e cient wage with σ = 1, σ = 0.38 () d log w d log z = 1/3) Calibration. Parameters Targets Description Value Eq. Description Value β Discount factor i Annual interest rate 2% θ Elasticity of subst θ 1 Markup rate 20% ω % unchanged price ω Mean price duration 1 year c Vacancy cost c w Labor cost of vacancy 4.5% w Real wage f Job- nding rate 80% m matching e ciency λ Vacancy- lling rate 70% ρ Job-destruction rate s Job-loss rate 5% δ Home production δ w Opp. cost of empl. 90%

15 Figure: Contractionary productivity shock (imperfect vs. perfect insurance).

16 Figure: Contractionary cost-push shock (imperfect vs perfect insurance).

17 Figure: Contractionary productivity shock (alternative wage settings).

18 Figure: Contractionary cost-push shock (alternative wage settings).

19 Summary I optimal monetary policy in NK model with endogenous unemployment risk () ampli cation through feedback loop) I replicates RANK predictions under perfect insurance I but policy should be much more accomodative under imperfect insurance hence RANK predictions may be overturned I optimal policy (almost) replicates perfect-insurance dynamics I incomplete markets do not matter when monetary policy is unconstrained and optimised I robust to various model variants I I I plausible iwage responses distorted steady state degree of insurance