Is Government Spending: at the Zero Lower Bound Desirable?

Is Government Spending: at the Zero Lower Bound Desirable? Florin Bilbiie (Paris School of Economics and CEPR) Tommaso Monacelli (Università Bocconi, IGIER and CEPR), Roberto Perotti (Università Bocconi, IGIER, CEPR and NBER), May 205

Government spending at the ZLB I Recent papers (Christiano, Eichenbaum, Rebelo 20, Eggertson and Krugman 20): government spending particularly powerful at ZLB.

Government spending at the ZLB I Recent papers (Christiano, Eichenbaum, Rebelo 20, Eggertson and Krugman 20): government spending particularly powerful at ZLB. I Basic intuition. In neoclassical model, government spending increases output via a wealth e ect on labor supply.

Government spending at the ZLB I Recent papers (Christiano, Eichenbaum, Rebelo 20, Eggertson and Krugman 20): government spending particularly powerful at ZLB. I Basic intuition. In neoclassical model, government spending increases output via a wealth e ect on labor supply. 2. At ZLB with sticky prices, further kick: " G! "demand facing rms =) "marginal cost =) " expected in ation =) # real interest rate (since i = 0) =) private consumption increases further, etc.

I Yet what about welfare?

I Yet what about welfare? I Negative income e ect of taxation makes agents want to work more to produce extra output I Consumption can increase only by working more (in these models)

This paper I Multipliers extremely large at ZLB I Government spending is generally welfare detrimental at the ZLB

A Sticky Price Economy

Economy I Utility U(C t, N t, G t ) = hc ζ t ( N t ) ζi σ σ + χ G G σ t σ σ > 0 0 < ζ <

Economy I Utility U(C t, N t, G t ) = hc ζ t ( N t ) ζi σ σ + χ G G σ t σ σ > 0 0 < ζ < I Convex price adjustment costs I Weight of G in utility χ G computed optimally

Utility Weight of Government Spending I In the steady state U C (Y G ) = U G (G )!Derive optimal weight χ G = ζ G σ Y G Y ζ( σ) ( ζ)( σ) N N

Cyclical vs. Structural Spending I Structural spending:"steady state" spending G t = G I Cyclical G is "extra spending" at the ZLB

Wasteful vs Useful Spending I Useful spending: cyclical G t has weight χ G in utility I Wasteful spending: cyclical spending has zero utility weight, "structural" spending enters utility: G σ χ G ( σ)

Markovian Shock Process Prfρ t+ = ρ L jρ t = ρ L g = p Prfρ t+ = ρjρ t = ρ L g = p Prfρ t+ = ρ L jρ t = ρg = 0.

Monetary Policy i t = max (ρ + φ π π t, 0)

Solution c L = π L = κ + βp Ω ρ L + M c N N Ω Y G Y G Y G g L where Ω ( βp) ( p) κp + N N ρ L + M π G Y g L, Y G Y

Solution c L = π L = κ + βp Ω ρ L + M c N N Ω Y G Y G Y G g L where Ω ( βp) ( p) κp + N N I Consumption and in ation multipliers M c ρ L + M π G Y g L, Y G Y ( βp) ( p) ζ (σ ) + κp N N Ω M π ( p) κ Y Y G + N N Ω I Impose restriction Ω > 0 Y G Y ζ (σ ) + N N

Welfare gap Ũ L (g L ) = 00 with extra G z } { U L (g L ) ju L (0)j with G kept at ss z } { U L (0)

Understanding the Welfare E ect of Government Spending t C t + G t = N t t {z} in ation distortion ν 2 π2 t I Second order approximation to resource constraint y L = n L = Y Y G c L + G Y g L + 2 νπ2 L {z } in ation distortion

E ect of G on welfare 2 du L = W L L U C (C L, N L ) dg L 6 4 + v 0 (G L ) {z } contribution of G in utility dcl MRS t /MRT t dg {z L } multiplier channel: L wedge {z} income e ect C L d L L dg {z L } in ation distortion 3 7 5

E ect of G on welfare 2 du L = W L L U C (C L, N L ) dg L 6 4 + v 0 (G L ) {z } contribution of G in utility dcl MRS t /MRT t dg {z L } multiplier channel: L wedge {z} income e ect C L d L L dg {z L } in ation distortion 3 7 5 I Welfare e ect of G: three channels. Multiplier channel 2. Income e ect 3. In ation distortion

Multiplier channel multiplier channel: dcl MRS t /MRT t dg L I Requires positive consumption multiplier at the ZLB I High when MRS t /MRT t is low, ie, labor wedge is high I In NK jargon: when markup is high

consumption at ZLB C L /C Multiplier: extreme non-linearity in transition probability p 35 Consumption Multiplier Consumption Level at ZLB consumption multiplier M C 30 25 20 5 0 5 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0 0.6 0.8 p (persistence of shock) 0. 0.6 0.8 p (persistence of shock)

Baseline experiment I Natural real interest rate falls to -% per annum!at baseline calibration: GDP falls 4% per annum

Table. Baseline calibration Parameter Description Value p transition probability 0.8 ρ L quarterly discount rate.0025 β discount factor in steady state 0.99 σ relative risk aversion 2 ϕ inverse labor elasticity N/( N) κ slope of the Phillips curve 0.028 φ π Taylor rule coe cient.5

U L tilda U L tilda Government spending and welfare Welfare Gap: Useful Spending 50 45 40 35 Welfare Gap: Wasteful Spending 50 0 50 30 00 25 20 50 5 200 0 5 first order (CER) second order 0 0 0.2 0.4 0.6 00*(G G)/Y L 250 300 0 0.2 0.4 0.6 00*(G G)/Y L!Optimal G is 0.5% of steady state output (baseline calibration) in useful case

00* dloggdp 00*(G L G)/Y 00*(G L G)/Y Optimal government spending and shock persistence 2 Approximation method: second order Useful spending Wasteful spending 0 0.79 0.795 0.8 0.805 0.8 0.85 0.82 0.825 0.83 2 Approximation method: first order (CER) Useful spending Wasteful spending 0 0.79 0.795 0.8 0.805 0.8 0.85 0.82 0.825 0.83 00 Implied fall in GD P 50 0 0.79 0.795 0.8 0.805 0.8 0.85 0.82 0.825 0.83 p (shock persistence)!large values of optimal G occur when decline in GDP is exceptionally high

00*(G L G)/Y 00* dlog GDP Optimal government spending and slope of PC Optimal Govt. Spending at the ZLB: Wasteful 7 rho = 0.0025 L rho = 0.0 L 6 70 60 Implied Fall in GDP 5 50 4 40 3 30 2 20 0 0 0.025 0.03 0.035 0.04 slope of Phillips curve: κ 0 0.025 0.03 0.035 0.04 slope of Phillips curve: κ

Holding constant the decline in GDP

I So far: when p is at its maximum admissible level optimal increase in G is about.9 percent of steady state GDP I GDP declines by 70 percent from its steady state I Now: hold size of recession constant by changing value of the shock

rho L 00*(G L G)/Y 00*(G L G)/Y Optimal government spending and shock persistence Decline in GDP constant at 4 percent. 0.5 Approximation method: second order Useful spending Wasteful spending 0 0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.5 Approximation method: first order (CER) Useful spending Wasteful spending 0 0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.0 Imp lie d s h o c k s.t. G D P fa lls b y 4 % 0.005 0 0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 p (shock persistence)!optimal increase in G about 0.6% of steady-state GDP

Alternative solution methods

Optimal G: Alternative Solution Methods

Great Depression

Reproducing the Great Depression I Woodford (20), Eggertsson (200) I GDP collapse of 28.8 percent (annualized) I De ation of 0 percent (annualized)! Need much higher price stickiness (κ = 0.00347! about 20 qrt) and higher shock persistence p = 0.903)

Optimal Government Spending: Great Depression Calibration

Consumption at ZLB C L /C Why Larger Values of Optimal G in the Great Depression? consumption multiplier M C Consumption multiplier 4 3.5 3 2.5 2.5 0.5 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0. Consumption level at ZLB 0 0.7 0.8 0.9 p (shock persistence) 0 0.7 0.8 0.9 p (shock persistence) I GD calibration very close to asymptote and starvation points I Price stickiness 20 qrts! very high cost of negative output gap

Conclusions I Standard NK model supports notion of extremely high multiplier of G at the ZLB I Optimal increase in G is however generally small or zero I Need setups in which welfare cost of negative output gap at the ZLB is signi cantly higher