The Zero Bound and Fiscal Policy Based on work by: Eggertsson and Woodford, 2003, The Zero Interest Rate Bound and Optimal Monetary Policy, Brookings Panel on Economic Activity. Christiano, Eichenbaum, Rebelo, When is the Government Spending Multiplier Big? (JPE, 20)
Introduction The New Keynesian model suggests that an economy may be vulnerable to deep recession when the zero lower bound on the nominal interest rate is binding. Fiscal policy could be very effective and desirable in the zero lower bound, though it is relatively less effective in normal times. 2
The ZLB Analysis (Over) Simplified Identity: expenditures GDP If one group reduces spending, then GDP must fall unless another group increases. Another group increases if real rate drops: R e If R is at lower bound and e cannot rise, have a problem.
The ZLB Analysis, cnt d Two reasons people may be reluctant to raise e Ex post, monetary authority would not deliver high inflation (Eggertsson). Real world monetary authorities spent years persuading people they would not use inflation to stabilize economy. Fears consequences of loss of credibility in case they now raise e for stabilization purposes.
The ZLB Analysis (Over) Simplified Recession likely to follow, as real rate fails to drop. The recession could be very severe if a deflation spiral occurs. R e The decrease in spending leads to a fall in marginal cost, which makes firms cut prices. When there are price frictions, downward pressure on prices is manifest as a reduction in inflation. 5
Deflation Cycle in Zero Bound Low spending High real interest rate Low marginal cost Low expected inflation
The Whole Analysis, cnt d The preceding indicates that the drop in output might be substantial. Options for solving zlb problem Direct: by interrupting destructive deflation spiral, increase government spending may have a very large effect on output. Tax credits Investment tax credit cash for clunkers Increase anticipated inflation Convert to a VAT tax in the future (Feldstein, Correia Fahri Nicolini Teles). Don t: cut labor tax rate or subsidize employment (Eggertsson)
Outline Analysis in normal times when zlb constraint on interest rate can be ignored. Show that the government spending multiplier is fairly small. Analysis when zlb is binding. Government spending can have a big, welfareimproving impact on output. 20
Derivation of Model Equilibrium Conditions Households First order conditions Firms: final goods and intermediate goods marginal cost of intermediate good firms Aggregate resources Monetary policy Three linearized equilibrium conditions: Intertemporal, Pricing, Monetary policy Results 2
Model Household preferences and constraints: E 0 t0 t C t Nt King Plosser Rebelo (KPR) preferences. vg t P t C t B t W t N t R t B t T t, T t ~lump sum taxes and profits Optimality conditions marginal benefit tomorrow from saving more today marginal cost of giving up one unit of consumption to save uc,t E t u c,t extra goods tomorrow from saving more today R t t, marginal cost (in units of goods) of labor effort u N,t u c,t marginal benefit of labor effort Wt P t 23
Linearized Intertemporal Equation Inter temporal Euler equation E t In zero inflation no growth steady state: Totally differentiate: u c,t u c,t R t t 0 R du c,t Rdu c,t u c dr t u c Rd t 0 Log differentiation: u c û c,t Ru c û c,t dr R t d t 0 Finally: û c,t û c,t dr t d t 0 24
Linearized intertemporal, cnt d Repeat: û c,t û c,t dr t d t 0 u C t Nt u c,t C t N t û c,t Ĉ t N N N t 25
Firms Final, homogeneous good Y t Yt i 0 di, Efficiency condition: P t i P t i th intermediate good Y t Y t i Y t i N t i Optimize price with probability θ, otherwise P t i P t i 26
Intermediate Good Firm Marginal Cost Marginal cost: MC t dcost t dwor ker t doutput t dwor ker t W t Wt P t subsidy to undo effects of monopoly power / MP L,t household first order condition un,t u c,t Real marginal cost s t MC t P t u N,t u c,t in steady state marginal cost to household of providing one more unit of labor un,t u c,t in steady state marginal benefit of one extra unit of labor 27
Resource relation: p t Aggregate Resources is Tak Yun distortion recall, distortion = to first order: Ŷ t N t Log linear expansion: Consumption: C t G t Y t p t N t gĉ t gĝ t Ŷ t, g G Y Ĉ t g Ŷ t g g Ĝ t 28
Simplifying Marginal Utility of C u N,t u c,t in steady state N C û c,t Ĉ t N N Ĉ t N C Ĉ t g N t N t N t g Ŷ t g g Ĝ t g Ŷ t g Ŷ t g g Ĝ t 29
Simplify Intertemporal Equation Intertemporal Euler equation: Substitute out marginal utility of consumption: g Ŷ t Rearranging: û c,t û c,t dr t d t g Ŷ t g g Ĝ t g g Ĝ t dr t d t Ŷ t gĝ t Ŷ t gĝ t gdr t d t 30
Phillips Curve Equilibrium condition associated with price setting just like before: t t s t, Marginal cost: s t C t N t Ĉ t N t Ĉ t N N N t Ĉ t g Ŷ t g g Ĝ t, N tŷ t g N N Ŷ t g g Ĝ t 3
Monetary Policy Monetary policy rule (after linearization) dr t R dr t R tk 2 Ŷ tl dr t R t R, R Ŷ t Y t Y Y k,l 0,. 32
Pulling All the Equations Together IS equation: Ŷ t gĝ t Ŷ t gĝ t gdr t d t Phillips curve: t t g N N Ŷ t g g Ĝ t Monetary policy rule: dr t R dr t R tk 2 Ŷ tl 33
The Equations in Matrix Form g 0 0 0 l R 2 k R 0 Ŷ t t dr t2 0 g Ŷ t 0 0 0 Ŷ t g N N 0 t 0 0 0 t l R 2 k R dr t 0 0 R dr t g g 0 0 Ĝ t g g g g 0 Ĝ t, or, 0 z t z t 2 z t 0 s t s t 0. s t Ps t t, s t Ĝ t, P 34
Solution: Undetermined coefficients, A and B: z t Az t Bs t A and B must satisfy: 0 A 2 A 2 0 0 AB BP B 0 P 0. When R 0, 2 0 A 0 works. 35
Results Fiscal spending multiplier small, but can easily be bigger than unity (i.e., C rises in response to G shock) Contrasts with standard results in which multiplier is less than unity Typical preferences in estimated models: E 0 t0 t C t N t vg t,,, 0. Marginal utility of C independent of N for CGG Marginal utility of C increases in N for KPR. 36
APR % of gdp %deviation from ss APR Simulation Results Benchmark parameter values: 0. 035, 0. 99,. 5, 2 0, N 0.23, g 0. 2, 2, 0. 8, R 0 output inflation 4 3.5 3.2 2.5 2.5 0.5 0.6 0.4 0.2 Multiplier =.05, constant. 2 5 0 5 20 interest rate 4 3.5 5 0 5 20 Ghat G t G Y G t G G G Y Ĝ tg.5 3 2.5 2.5 0.5 0.5 5 0 5 20 5 0 5 20 38
Multiplier for Alternative Parameter Values =.5, = 0, = 0, =, = 0.03, 2 R = 0.99, = 0.2857, N = 0.33333, g = 0.2, = 2.2.5.2...05 0.95 0.9 2 3 0.9 0 2 0.6 0.4 0.2 0.2.4.6.8.2.2 0.9..5 0.7 0.6 0.5.05 0 0.2 0.4 0 0.2 0.4 0.6 2 R. 0.9 0 0.2 0.4 0.6 Results: multiplier bigger the less monetary policy allows R to rise. the more complementary are consumption and labor (i.e., the bigger is ). the smaller the negative income effect on consumption (i.e., the smaller is ). smaller values of κ (i.e., more sticky prices) 39
Multiplier for Alternative Parameter Values =.5, = 0, = 0, =, = 0.03, 2 R = 0.99, = 0.2857, N = 0.33333, g = 0.2, = 2.2.5..05 dr t R dr t R 0.95 0.9 2 3.2. t 2 0.9 Ŷ t 0 2 0.6 0.4 0.2 0.2.4.6.8.2.2 0.9..5 0.7 0.6 0.5.05 0 0.2 0.4 0 0.2 0.4 0.6 2 R. 0.9 0 0.2 0.4 0.6 Results: multiplier bigger the less monetary policy allows R to rise. the more complementary are consumption and labor (i.e., the bigger is ). the smaller the negative income effect on consumption (i.e., the smaller is ). smaller values of κ (i.e., more sticky prices) 40
Multiplier for Alternative Parameter Values =.5, = 0, = 0, =, = 0.03, 2 R = 0.99, = 0.2857, N = 0.33333, g = 0.2, = 2.2.5..05 0.95 0.9 0.9 2 3.2. 0.9.2 uc t,n t.5 0 2 0.6 0.4 0.2.2. 0.2.4.6.8 C t N t 0.7. 0.9 0.6 0.5.05 0 0.2 0.4 0 0.2 0.4 0.6 0 0.2 0.4 0.6 2 u c,t C t R N t Results: multiplier bigger the less monetary policy allows R to rise. the more complementary are consumption and labor (i.e., the bigger is ). the smaller the negative income effect on consumption (i.e., the smaller is ). smaller values of κ (i.e., more sticky prices) 4
Multiplier for Alternative Parameter Values =.5, = 0, = 0, =, = 0.03, 2 R = 0.99, = 0.2857, N = 0.33333, g = 0.2, = 2.2.5.2...05 0.95 0.9 0.9 Ĝ t Ĝ 2 3 t 0 t 2 0.6 0.4 0.2 0.2.4.6.8.2.2 0.9..5 0.7 0.6 0.5.05 0 0.2 0.4 0 0.2 0.4 0.6 2 R. 0.9 0 0.2 0.4 0.6 Results: multiplier bigger the less monetary policy allows R to rise. the more complementary are consumption and labor (i.e., the bigger is ). the smaller the negative income effect on consumption (i.e., the smaller is ). smaller values of κ (i.e., more sticky prices) 42
Multiplier for Alternative Parameter Values =.5, = 0, = 0, =, = 0.03, 2 R = 0.99, = 0.2857, N = 0.33333, g = 0.2, = 2.2.5.2...05 0.95 0.9 2 3 0.9 0 2 0.6 0.4 0.2 0.2.4.6.8.2.2 0.9..5 0.7 0.6 0.5.05 0 0.2 0.4 0 0.2 0.4 0.6 2 R. 0.9 0 0.2 0.4 0.6 Results: multiplier bigger the less monetary policy allows R to rise. the more complementary are consumption and labor (i.e., the bigger is ). the smaller the negative income effect on consumption (i.e., the smaller is ). smaller values of κ (i.e., more sticky prices) 43
Analysis of Case when the Nonnegativity Constraint on the Nominal Interest Rate is Binding Need a shock that puts us into the lower bound. One possibility: increased desire to save. Seems particularly relevant at the current time. Other shocks will do it too... Discount rate shock. 44
Monetary Policy Monetary policy rule (after linearization) Z t R R R t R R t 2 Ŷ t Ŷ t Y t Y Y, R R t Z t if Z t 0 0 ifz t 0. nonlinearity 45
Eggertsson Woodford Saving Shock Preferences: uc 0,N 0, G 0 r E 0 uc, N,G r 2 uc 2, N 2,G r 2 r 3 uc 3, N 3,G 3... Before t=0 System was in non stochastic, zero inflation steady state, r t R R t R Ĝ t 0, for all t 46
At time t=0, Saving Shock, cnt d r r l 0 Probr t r r t r l p Probr t r l r t r l p Probr t r l r t r 0 Discount rate drops in t=0 and is expected to return permanently to its normal level with constant probability, p. 47
Zero Bound Equilibrium simple characterization: l,ŷ l,r 0, Z l 0 while discount rate is low t Ŷ t 0, R r as soon as discount rate snaps back up 48
Fiscal Policy Government spending is set to a constant deviation from steady state, during the zero bound. That is, Ĝ t may be nonzero while r t r l, Ĝ t 0 when r t r 49
Equations With Discount Shock IS equation: Ŷ t g Ĝ t gr t r t E t t E t Ŷ t g E t Ĝ t Ŷ l g Ĝ l g0 r l p l pŷ l g pĝ Phillips curve: t E t t g Monetary Policy: R t 0 N Ŷ N t g Ĝ g t l p l g N N Ŷ l g g Ĝl Z t R R R t R R t 2 Ŷ t 0 50
Solving for the Zero Bound Allocations Is equation: Ŷ l g Ĝ l g0 r l p l pŷ l g pĝ Phillips curve: l p l g N Ŷ l g N g Ĝl Two equations in two unknowns! Solve for and verify that Ŷ l, l Z l 0 5
Solution Inflation: l g N N g Ĝ l g p rl p g N N p g p g g Ĝl Output: Ŷ l g Ĝ l g p rl p l 52
Zl Yhatl Numerical Simulations 40 20 00 80 60 40 20 0.028 0.03 0.032 0.034 0.036 kappa -2-4 -6-8 -0 0.028 0.03 0.032 0.034 0.036 kappa - -2 =.5, = 0, = 0, =, 2 R = 0.03, = 0.99, = 0.2857, N = 0.33333, g = 0.2, Ghat = 0, s -3-4 Problem is worse with more flexible prices! 0.028 0.03 0.032 0.034 0.036 kappa Results: multiplier 3.7 at benchmark parameter values and may be gigantic. 53
Zl inflation Yhatl benchmark parameter values: =.5, = 0, = 0, =, = 0.03, 2 R = 0.99, = 0.2857, N = 0.33333, g = 0.2, k = 0, l = 0, Ghat = 0, sig = 2, p =, r l = -0.0 70 60 50 40 30 20 0 at baseline: 3.6857 - -2-3 -4-5 0.72 0.74 0.76 0.78 p 0.72 0.74 0.76 0.78 p -0.5 - -.5-0.5 - -2 0.72 0.74 0.76 0.78 p -.5 0.72 0.74 0.76 0.78 p As p increases, zero bound becomes more severe this is because with higher p, fall in output is more persistent and resulting negative wealth effect further depresses consumption. 54
Fiscal Expansion in Zero Bound Highly Effective, But is it Desirable? Intuition: Yes. the vicious cycle produces a huge, inefficient fall in output in the first best equilibrium, output, consumption and employment are invariant to discount rate shocks If G helps to partially undo this inefficiency, then surely it s a good thing 55
Fiscal Expansion in Zero Bound Highly Effective, But is it Desirable? Preferences t0 p r l t C l N l vg l p r l C l N l vg l p r l Compute optimal (i) vg l = 0, (ii) N Ŷ l Ng Ĝ l N Ŷl Ĝ l v Ng Ĝ l vg g G, g chosen to rationalize g 0.2 as optimal in steady state 56
C over C steady state nominal rate of interest inflation Utility Y over Y steady state Zl Case Where G is not Valued phi =.5, phi2 = 0, rhor = 0, rho =, kap = 0.03, bet = 0.99, gam = 0.2857, N = 0.33333, g = 0.2, k = 0, l = 0, Ghat = 0, sig = 2, p Optimal G is substantial, around 5%. -0.96-0.97-0.98-0.99 - -.0 -.02 0 0.2 0.4 Ghat.05 0.95 0.9 5 0 0.5 Ghat 0.04 0.02 0-0.02-0.04-0.06 0 0.5 Ghat 0.75 x 0-3 5 4 3-0.0-0.02 0.7 2-0.03 0.65 0.6 0 0.2 0.4 Ghat 0-0 0.2 0.4 Ghat -0.04-0.05 0 0.5 Ghat 58
C over C steady state nominal rate of interest inflation Utility Y over Y steady state Zl Case Where Gov t Spending is Desirable Optimal Y higher than before crisis phi =.5, phi2 = 0, rhor = 0, rho =, kap = 0.03, bet = 0.99 gam = 0.2857, N = 0.33333, g = 0.2, k = 0, l = 0, Ghat = 0, sig = 2, psig -.6 -.7 -.8 -.9 -.2 0 0.2 0.4 Ghat.05 0.95 0.9 5 0 0.5 Ghat 0.04 0.02 0-0.02-0.04-0.06 0 0.5 Ghat Ĝ t Ĝ t Ĝ t Ĝ t psig=0.05226 The high level of output is necessary to get partial recovery in consumption 0.75 0.7 0.65 0.6 0 0.2 0.4 Ghat x 0-3 5 4 3 2 0-0 0.2 0.4 Ghat -0.0-0.02-0.03-0.04-0.05 0 0.5 Ghat 60
Introducing Investment Inclusion of investment does not have a large, qualitative effect. Financial frictions could make things much worse. Deflation hurts net worth of investors with nominal debt, and this forces those agents to cut spending by more. 6
Conclusion of G Multiplier Analysis Government spending multiplier in a neighborhood of unity in normal times. Multiplier can be large when the zero bound is binding (because R constant then). Increase in G is welfare improving during lower bound crisis. Caveat: focused exclusively on multiplier Increasing G may be bad idea because hard to reverse. May be other ways of accomplishing similar thing (e.g., transition to VAT tax over time). 62