Monetary Economics Lecture 11: monetary/fiscal interactions in the new Keynesian model, part one Chris Edmond 2nd Semester 2014 1 This class Monetary/fiscal interactions in the new Keynesian model, part one • Fiscal policy and multipliers • Reading • Woodford “Simple analytics of the government expenditure ⇧ multiplier” AEJ: Macroeconomics,2011 Available from the LMS 2 This class 1- Benchmark fiscal multipliers – long-run multiplier (neoclassical case) – short-run multiplier (for constant real rate) 2- Detailed new Keynesian example – illustrates how multiplier depends on monetary policy reaction, price stickiness, etc 3 Neoclassical benchmark Household utility function • U(C) V (N) − Goods market • C + G = Y = F (N) Standard optimality conditions • V 0(N) W = = F 0(N) U 0(C) P Utility cost of producing Y output • 1 V 0(N) V˜ (Y ) V (F − (Y )), V˜ 0(Y )= ⌘ F 0(N) 4 Neoclassical benchmark (cont) Key optimality condition can then be written • U 0(Y G)=V˜ 0(Y ) − Implicitly differentiating and using U (C)=V˜ (Y ) gives • 0 0 U 00(C) dY U (C) U (C) Y = 00 = − 0 ˜ U (C) V˜ (Y ) dG U 00(C) V 00(Y ) 00 00 U (C) Y + ˜ Y − − 0 V 0(Y ) ⌘ = u (0, 1) ⌘u + ⌘v 2 where ⌘u > 0 and ⌘v > 0 are elasticities of U 0(C) and V˜ 0(Y ) with respect to Y 5 Imperfect competition Not much changes with constant markup • W " P = , MF (N) M⌘" 1 0 − Key condition can then be written • U 0(Y G)= V˜ 0(Y ) − M Again, implicitly differentiating and using U (C)= V˜ (Y ) gives • 0 M 0 dY ⌘ = u (0, 1) dG ⌘u + ⌘v 2 Constant markup reduces level of Y , but does not affect multiplier • 6 Aside: countercyclical markups? Suppose markup depends on output, (Y ). Multiplier formula • M then generalises to dY ⌘ = u dG ⌘u + ⌘m + ⌘v where ⌘m is elasticity of markup with respect to output Multiplier > 1 if markups sufficiently countercyclical, ⌘ < ⌘ • m − v Large literature provides microfoundations for countercyclical • markups. More generally, key is for endogenous decline in gap between real wage and household MRS 7 Short-run vs. long-run effects This neoclassical benchmark determines long-run multiplier • dY¯ ⌘ = u Γ (0, 1) dG¯ ⌘u + ⌘v ⌘ 2 [i.e., effects of permanent changes in government purchases] Consider government purchases G with permanent value G¯ • { t} What are the effects of transitory or short-run changes in G ? • t 8 Transitory change in Gt Multiplier effects depends on assumed monetary policy response.If • we want to “keep monetary policy unchanged”, what should we hold constant? Suppose monetary policy seeks to maintain a constant real interest • rate r = ⇢ = log β>0. Household consumption Euler equation t − then implies Ct = Ct+1 = C¯ for some level of consumption determined by the permanent level G¯ Hence for a purely transitory change • dYt Yt = C¯ + Gt, =1 dGt independent of details of wage or price stickiness! 9 Summary Long-run/neoclassical multiplier • dY¯ ⌘ = u Γ (0, 1) dG¯ ⌘u + ⌘v ⌘ 2 Short-run multiplier, holding real interest rate constant • dY t =1 dGt What if policy cannot maintain constant real rate? • – depends on details of monetary policy reaction, price stickiness etc – next, a simple new Keynesian example 10 Simple new Keynesian example Intertemporal consumption Euler equation • 1 ct = (it Et[⇡t+1] ⇢)+Et[ct+1] −σ − − Goods market, constant productivity • c + g = y = a +(1 ↵)n t t t − t Labor supply • w p = σc + 'n t − t t t Static markup (with flexible prices) • p = µ + w + n y log(1 ↵) t t t − t − − 11 Flexible price equilibrium Natural output, in log deviations • n yˆt =Γgˆt If measure G relative to Y¯ ,thatisgˆ (G G¯)/Y¯ , then this • t t ⌘ t − elasticity is the long-run multiplier, as above ⌘ σ Γ= u = ⌘u + ⌘v '+↵ σ + 1 ↵ − ⇣ ⌘ 12 Flexible price equilibrium (cont). Output gap • y˜ yˆ yˆn =ˆy Γgˆ =ˆc +(1 Γ)ˆg t ⌘ t − t t − t t − t Plug back into intertemporal consumption Euler equation to get dynamic IS curve 1 n y˜t = (it Et[⇡t+1] r )+Et[˜yt+1] −σ − − t Natural real rate [assuming gˆ process is AR(1)] • { t} rn = ⇢ + σ(1 Γ)(1 ⇢ )ˆg t − − g t 13 Simple new Keynesian example Dynamic IS curve • 1 n y˜t = (it Et[⇡t+1] r )+Et[˜yt+1] −σ − − t New Keynesian Phillips curve • ⇡t = βEt[⇡t+1]+y˜t Interest rate rule • it = ⇢ + φ⇡⇡t + φyy˜t Natural real rate • rn = ⇢ + σ(1 Γ)(1 ⇢ )ˆg t − − g t 14 Method of undetermined coefficients Guess • ⇡t = '⇡ggˆt, and y˜t = 'yggˆt for some coefficients '⇡g,'yg to be determined As usual, new Keynesian Phillips curve immediately implies • proportional relationship ' = ' ⇡g 1 ⇢ yg − g And from dynamic IS curve • (1 Γ)(1 ⇢ ) 1 ' = − − g , φ + (φ ⇢ ) > 0 yg +1 ⇢ ⌘ σ y 1 ⇢ ⇡ − g − g − g 15 Effects of increases in government purchases Output gap increases • @y˜t = 'yg > 0 @gˆt Inflation increases • @⇡t = '⇡g > 0 @gˆt Monetary policy tightens • @it = φ⇡'⇡g + φy'yg > 0 @gˆt 16 Multipliers redux Output then given by • 1 ⇢ + Γ yˆ =˜y +ˆyn =(' +Γ)g ˆ = − g gˆ t t t gy t 1 ⇢ + t − g (hence output [and employment] also increase) Since G is measured relative to Y¯ , this elasticity is also the new • t Keynesian multiplier Observe that • 1 ⇢ + Γ Γ < − g < 1 1 ⇢ + − g 17 Discussion Sticky prices imply a larger multiplier than classical benchmark • But multiplier still less than one • [interest rate rule here allows rt to vary] Size of multiplier increasing in degree of price stickiness • [high ✓ reduces which reduces and increases multiplier] Size of multiplier decreasing in monetary policy reactiveness • [high policy coefficients φ⇡,φy increase and reduce multiplier] Size of multiplier decreasing in persistence of gˆ shock • t 18 Discussion Larger multipliers obtain when monetary policy accommodates • fiscal expansion Important special case is when monetary policy is constrained by • the zero-lower-bound (ZLB) on it Can then have multipliers (substantially) larger than one • 19 Next class Monetary/fiscal interactions in the new Keynesian model, part two • The zero lower bound. Implications for multipliers. • Main reading: • Woodford “Simple analytics of the government expenditure ⇧ multiplier” AEJ: Macroeconomics,2011 Further reading • Christiano, Eichenbaum and Rebelo “When is the government ⇧ spending multiplier large?” Journal of Political Economy,2011 Available from the LMS 20.