Is Government Spending: at the Zero Lower Bound Desirable?

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1 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

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

3 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.

4 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.

5 I Yet what about welfare?

6 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)

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

8 A Sticky Price Economy

9 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 <

10 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

11 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

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

13 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)

14 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.

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

16 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

17 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

18 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)

19 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

20 E ect of G on welfare 2 du L = W L L U C (C L, N L ) dg L 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

21 E ect of G on welfare 2 du L = W L L U C (C L, N L ) dg L 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 I Welfare e ect of G: three channels. Multiplier channel 2. Income e ect 3. In ation distortion

22 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

23 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 p (persistence of shock) p (persistence of shock)

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

25 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 φ π Taylor rule coe cient.5

26 U L tilda U L tilda Government spending and welfare Welfare Gap: Useful Spending Welfare Gap: Wasteful Spending first order (CER) second order *(G G)/Y L *(G G)/Y L!Optimal G is 0.5% of steady state output (baseline calibration) in useful case

27 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 Approximation method: first order (CER) Useful spending Wasteful spending Implied fall in GD P p (shock persistence)!large values of optimal G occur when decline in GDP is exceptionally high

28 00*(G L G)/Y 00* dlog GDP Optimal government spending and slope of PC Optimal Govt. Spending at the ZLB: Wasteful 7 rho = L rho = 0.0 L Implied Fall in GDP slope of Phillips curve: κ slope of Phillips curve: κ

29 Holding constant the decline in GDP

30 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

31 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 Approximation method: first order (CER) Useful spending Wasteful spending Imp lie d s h o c k s.t. G D P fa lls b y 4 % p (shock persistence)!optimal increase in G about 0.6% of steady-state GDP

32 Alternative solution methods

33 Optimal G: Alternative Solution Methods

34 Great Depression

35 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 = ! about 20 qrt) and higher shock persistence p = 0.903)

36 Optimal Government Spending: Great Depression Calibration

37 Consumption at ZLB C L /C Why Larger Values of Optimal G in the Great Depression? consumption multiplier M C Consumption multiplier Consumption level at ZLB p (shock persistence) 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

38 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