Bank Of Greece Sa · ATHEX:TELL
Bank Of Greece Sa — Technical Presentation (November 2012)
48 slides from Bank Of Greece Sa's technical presentation, Nov 27, 2012
Slide 1: Fiscal and monetary policy actions under wage rigidity
Fiscal and monetary policy actions under wage rigidity Natasha Miaouli Apostolis Philippopoulos Petros Varthalitis Vanghelis Vassilatos November 27, 2012 Philippopoulos et al. () Fiscal and monetary policy actions November 27, 2012 1 / 48
Slide 2: Motivation
Motivation Policymakers use policy instruments to stabilize the economy. See e.g. the Taylor rule. Question asked here: What is the optimal (…scal and monetary) policy reaction to the business cycle under labor market frictions? In particular, does optimal (…scal and monetary) policy depend on wheth
Slide 3: Use of fiscal policy for stabilization has been controversial
Recall that the use of …scal policy for stabilization has always been more controversial (Leeper, 2010). Before the 2008-9 world …nancial and economic crisis, there was a widespread consensus in academia that …scal policy should not be used actively for output stabilization. In particular, the so-ca
Slide 4: This changed during the 2008-2009 crisis
This changed during the 2008-2009 crisis. Most governments used active …scal policy to counter the economic downturn. Also several academics argued that the consensus assignment needs to be modi…ed in the sense that, if the economy is hit by an adverse shock, …scal reaction to the output gap is prod
Slide 5: A clarification
A clari…cation Since it might be optimal to respond to more than one indicators at the same time, the central issue is what is the dominant response. It is this that will shape the net change in a particular policy instrument. Philippopoulos et al. (AUEB) Fiscal and monetary policy actions November
Slide 6: Description of the model
Description of the model Standard New Keynesian (imperfect competition and Calvo-type price …xities). Wage rigidity as in Blanchard and Gali (2005) and many others. Thus, wages respond sluggishly to labor market conditions as a result of some (unmodeled) friction. See Blanchard and Gali (2010) and G
Slide 7: Model: Household's problem
Model Household’s problem There are i = 1, 2, ..., .N households. Each i solves: ∞ E0 ∑ βt U (ci ,t , ni ,t , mi ,t , gt ) (1) t =0 1 +η 1 µ ci1,t σ n m g 1 ζ ui ,t (ci ,t , ni ,t , mi ,t , gt ) = χn i ,t + χm i ,t + χg t (2) 1 σ 1+η 1 µ 1 ζ (1 + τ ct ) ci ,t + xi ,t + bi ,t + mi ,t = 1 τ kt (rtk ki
Slide 8: Model: Household's problem
Model Household’s problem Household i’s consumption bundle at t, ci ,t , is a composite of h = 1, 2, ..., N varieties of goods, ci ,t (h), where each variety h is produced monopolistically by one …rm h. Using a Dixit-Stiglitz aggregator, we de…ne: φ N φ 1 φ 1 ci ,t = ∑ λ[ci ,t (h)] φ (5) h =1 where
Slide 9: Model: Household's optimality conditions
Model Household’s optimality conditions Each household i acts competitively taking prices and policy as given. ci ,tσ ci ,tσ+1 h i = βE t 1 τ kt+1 rtk+1 + (1 δ) (7) (1 + τ ct ) 1 + τ ct+1 σ ci .tσ ci ,t +1 Pt c = βEt c Rt (8) (1 + τ t ) 1 + τ t +1 Pt +1 µ ci ,tσ ci ,tσ+1 Pt χm mi ,t + βEt =0 (9) (1
Slide 10: Model: Wage setting
Model Wage setting In nominal terms: Wt (Wt 1 )γ (Pt mrst )1 γ (12) or in real terms: γ Pt 1 wt wt 1 (mrst )1 γ (13) Pt where 0 γ 1 is the degree of wage sluggishness. If γ = 0, the labor market is Walrasian. Philippopoulos et al. (AUEB) Fiscal and monetary policy actions November 27, 2012 10 / 48
Slide 11: Model: Firm's problem
Model Firm’s problem There are h = 1, 2, ..., .N …rms. Each …rm h produces a di¤erentiated good of variety h under monopolistic competition facing Calvo-type nominal …xities. Each …rm h maximizes nominal pro…ts, Dt (h), de…ned as: Dt (h) = Pt (h)yt (h) rtk Pt (h)kt 1 (h) Wt nt (h) (14) yt (h) = At [
Slide 12: Model: Firm's optimality condition
Model Firm’s optimality condition wt = mct (1 a)At [kt 1 (h)]α [nt (h)] α (16) rtk = mct aAt [kt 1 (h)]α 1 [nt (h)]1 α (17) " # φ ( ) ∞ Pt# (h) Pt# (h) φ Pt +k ∑ (θ )k Et [Ξt,t +k Pt +k yt +k Pt φ 1 mct +k Pt ]=0 k =0 (18) The evolution of the aggregate price level is given by: 1 φ (Pt )1 φ = θ (Pt
Slide 13: Model: Government Budget Constraint
Model Government Budget Constraint bt + mt = Rt 1 PPt t 1 bt 1 + PPt t 1 mt 1 + gt (20) τ ct ct τ kt (rtk kt 1 + dt ) τ nt wt nt τ lt Philippopoulos et al. (AUEB) Fiscal and monetary policy actions November 27, 2012 13 / 48
Slide 14: Decentralized Equilibrium (for any feasible policy)
Decentralized Equilibrium (for any feasible policy) ct σ ct + 1 σ h i = βE t 1 τ kt+1 rtk+1 + (1 δ) (21) (1 + τ ct ) 1 + τ ct+1 1 ct +σ1 Pt ct σ c = βE t Rt c (22) (1 + τ t ) 1 + τ t +1 Pt +1 µ ct σ ct +σ1 Pt χ m mt + βE t =0 (23) (1 + τ ct ) 1 + τ ct+1 Pt +1 η 1 γ Pt 1 γ χn (1 + τ ct ) nt wt = wt 1
Slide 15: Decentralized Equilibrium (for any feasible policy)
Decentralized Equilibrium (for any feasible policy) kt = (1 δ) kt 1 + xt (25) ( " # ε !) ∞ Pt# Pt# ε Pt +k ∑ θ k Et Ξt,t +k Pt +k yt +k Pt ε 1 mct +k Pt =0 k =0 (26) yt wt = mct (1 a) (27) nt yt rtk = mct a (28) kt Philippopoulos et al. (AUEB) Fiscal and monetary policy actions November 27, 2012 15
Slide 16: Decentralized Equilibrium (for any feasible policy)
Decentralized Equilibrium (for any feasible policy) dt = yt wt nt rtk kt 1 (29) 1 a 1 a yt = φ At kt 1 nt (30) et P Pt bt + mt = Rt 1 bt 1 PPt t 1 +mt 1 PPt t 1 + (31) +gt τ ct ct τ nt wt nt τ kt rtk kt 1 + dt τ lt yt = ct + xt + gt (32) Philippopoulos et al. (AUEB) Fiscal and monetary policy action
Slide 17: Decentralized Equilibrium (for any feasible policy)
Decentralized Equilibrium (for any feasible policy) 1 φ (Pt )1 φ = θ (Pt 1 )1 φ + (1 θ ) Pt# (33) φ et ) φ = θ (P (P et 1 ) φ +(1 θ ) Pt# (34) 1 e φ where Pet ∑Nh =1 [Pt (h )] φ and PPtt φ is a measure of price dispersion. We thus have 14 equilibrium conditions for the DE. Philippopoulos et al. (AUE
Slide 18: Decentralized Equilibrium (for any feasible policy)
Decentralized Equilibrium (for any feasible policy) To solve the model, we need to specify the policy regime and thus classify variables into endogenous and exogenous. Regarding monetary policy, we assume that the nominal interest rate, Rt , is used as a policy instrument. Regarding …scal policy, we
Slide 19: Decentralized Equilibrium transformed
Decentralized Equilibrium transformed (for any feasible policy) Variables expressed in ratios # Pt We use the gross in‡ation rate Πt Pt , the auxiliary variable Θt Pt , h Pt i1 φ et and the price dispersion index ∆t P Pt . We also use stg gt yt and τ lt stl yt . Thus, from now on, we use Πt , Θt , ∆
Slide 20: Decentralized Equilibrium transformed
Decentralized Equilibrium transformed (for any feasible policy) Equation (26) expressed in recursive form We replace the recursive equation: " # φ ( ) ∞ Pt# Pt# φ Pt +k ∑ (θ ) Et Ξt,t +k k Pt +k yt +k Pt (φ 1) mct +k Pt =0 k =0 (35) with: φ zt1 = z2 (36) (φ 1) t Philippopoulos et al. (AUEB) Fiscal a
Slide 21: Decentralized Equilibrium transformed
Decentralized Equilibrium transformed (for any feasible policy) Equation (26) expressed in recursive form where: φ 1 φ 1 c σ 1 + τ ct Θt 1 φ zt1 = Θt yt + βθEt t +σ1 zt1+1 ct 1 + τ ct+1 Θ t +1 Π t +1 (37) 1 φ c σ 1 + τ ct Θt φ 1 zt2 = Θt yt mct + βθEt t +σ1 zt2+1 φ ct 1 + τ ct+1 Θ t +1 Π t +1 (38) P
Slide 22: Decentralized Equilibrium transformed
Decentralized Equilibrium transformed (for any feasible policy) Lifetime utility written as a …rst-order dynamic equation 1 +φ 1 µ 1 ζ c1 σ n m (s g yt ) Vt = t χn t + χm t + χg t + βEt Vt +1 (39) 1 σ 1+φ 1 µ 1 ζ Thus, from now on, we add equation (39) to the equilibrium system. Philippopoulos et al
Slide 23: Policy rules
Policy rules Rt Πt yt log = φπ log + φy log + νRt (40) R Π y stg sg = γgl (lt 1 l) γgy (yt y ) + νgt (41) τ ct τ c = γcl (lt 1 l ) + γcy (yt y ) + νct (42) τ kt τ k = γkl (lt 1 l ) + γky (yt y ) + νkt (43) τ nt τ n = γnl (lt 1 l ) + γny (yt y ) + νnt (44) Rt bt lt (45) yt where νjt N 0, σ2j . Philip
Slide 24: Exogenous stochastic variables
Exogenous stochastic variables log At = 1 ρA log (A) + ρA log At 1 + εAt (46) log νRt = 1 ρR log νR + ρR log νRt 1 + εRt (47) log νgt = (1 ρg ) log (νg ) + ρg log νgt 1 + εgt (48) log νct = (1 c ρ ) log (ν ) + ρc c log νct 1 + εct (49) log νkt = 1 ρk log νk + ρk log νkt 1 + εkt (50) log νnt = (1 ρn
Slide 25: Final Equilibrium system
Final Equilibrium system ct σ ct + 1 σ h i = βE t 1 τ kt+1 rtk+1 + (1 δ) (52) (1 + τ ct ) 1 + τ ct+1 ct σ 1 ct + 1 σ 1 = βE t (53) c Rt (1 + τ t ) 1 + τ t +1 Π t +1 c µ ct σ ct +σ1 1 χ m mt + βE t =0 (54) c (1 + τ t ) 1 + τ t +1 Π t +1 c η 1 γ 1 γ χn (1 + τ ct ) nt wt = wt 1 (55) Πt (1 τ nt ) ct σ P
Slide 26: Final Equilibrium system
Final Equilibrium system kt = (1 δ) kt 1 + xt (56) φ 1 2 zt1 = zt (57) φ yt wt = mct (1 a) (58) nt yt rtk = mct a (59) kt 1 Philippopoulos et al. (AUEB) Fiscal and monetary policy actions November 27, 2012 26 / 48
Slide 27: Final Equilibrium system
Final Equilibrium system dt = yt wt nt rtk kt 1 (60) 1 At kta 1 nt1 a yt = (61) ∆t 1 1 h bt + mt = Rt 1 bt 1 + mt 1 + stg yt τ ct ct τ nt wt nt τ kt rtk kt 1 + dt Πt Πt (62) yt = ct + xt + stg yt (63) 1 φ Πt = θ + (1 θ ) [ Θt Πt ]1 φ (64) ∆t = (1 θ ) Θt + θΠt ∆t 1 φ φ (65) Philippopoulos et al. (AUE
Slide 28: Final Equilibrium system
Final Equilibrium system φ 1 φ 1 c σ 1 + τ ct Θt zt1 = yt mct Θt + βθEt t +σ1 Πt +1 zt1+1 φ (66) ct 1 + τ ct+1 Θ t +1 c σ 1 + τ ct Θt φ φ 1 zt2 = Θt yt + βθEt t +σ1 Πt +1 zt2+1 φ (67) ct 1 + τ ct+1 Θ t +1 1 µ 1 +φ 1 ζ ct1 σ m nt (s g yt ) Vt = + χm t χn + χg t + βEt Vt +1 (68) 1 σ 1 µ 1+φ 1 ζ Philip
Slide 29: Final Equilibrium system
Final Equilibrium system Rt Πt yt log = φπ log + φy log + νRt (69) R Π y stg sg = γgl (lt 1 l) γgy (yt y ) + νgt (70) τ ct τ c = γcl (lt 1 l ) + γcy (yt y ) + νct (71) τ kt τ k = γkl (lt 1 l ) + γky (yt y ) + νkt (72) τ nt τ n = γnl (lt 1 l ) + γny (yt y ) + νnt (73) Rt bt lt (74) yt Philippopoulos
Slide 30: Final Equilibrium system
Final Equilibrium system There are therefore 23 equations in 23 endogenous variables, fyt , ct , nt , xt , kt , mt , bt , Πt , Θt , ∆t , wt , mct , dt , rtk , zt1 , zt2 , Vt , Rt , stg , τ ct , τ kt , τ nt , lt gt∞=0 . Among them, there are 16 non-predetermined or jump variables, fyt , ct , nt , xt
Slide 31: Data, calibration and long-run solution
Data, calibration and long-run solution Table 1: Parameter values Parameter Value Description a 0.33 share of capital β 0.9926 discount factor µ 3.42 real money balances elasticity δ 0.021 capital depreciation rate (quarterly) φ 6 price elasticity of demand η 1 Frisch labour supply elasticity σ 1 el
Slide 32: Data, calibration and long-run solution
Data, calibration and long-run solution Table 1(continued) ρA 0.8 serial correlation of TFP shock ρR 0.85 serial correlation of monetary shock ρg 0.87 serial correlation of spending shock ρc 0.96 serial correlation of consumption tax shock ρk 0.97 serial correlation of capital tax shock ρn 0.94 seri
Slide 33: Data, calibration and long-run solution
Data, calibration and long-run solution Table 2: Long-run values of policy instruments τl R τc τk τn sg sl yH 1.0075 0.19 0.28 0.38 0.23 -0.20 Philippopoulos et al. (AUEB) Fiscal and monetary policy actions November 27, 2012 33 / 48
Slide 34: Status quo long-run solution
Status quo long-run solution Table 3: Long-run solution and some data Long-run Long-run Variables Variables Data solution solution y 0.74 mc 0.83 - c 0.46 d 0.12 - n 0.28 r k 0.04 - x 0.11 z1 1.82 - k 5.19 z 2 2.18 - m 1.46 V -161.62 - b 2.52 l 3.43 - Π 1 c y 0.62 0.57 Θ 1 b y 3.4 3.4 ∆ 1 x y 0.15 0
Slide 35: How we work
How we work We take a second-order approximation of expected discounted lifetime utility, V0 , subject to a second-order approximation of the equilibrium conditions. See Schmitt-Grohé and Uribe (2004). This is given policy and in particular feedback policy coe¢ cients. We compute the feedback policy
Slide 36: Results without wage rigidity: Optimized policy rules
Results without wage rigidity Optimized policy rules Table 4: Optimal monetary reaction to in‡ation and output and optimal …scal reaction to debt and output Optimal interest-rate Optimal …scal Policy reaction to reaction to ξ instruments in‡ation and output debt and output φπ = 3 γgl = 0.1 Rt stg 0.
Slide 37: Results without wage rigidity: Impulse Response Functions
Results without wage rigidity Impulse Responce Functions Figure 1: Impulse responce functions to a negative TFP shock under the best possible policy mix y -3 c -3 n x 10 x 10 0 0 5 -0.005 -1 0 -0.01 -2 -5 0 50 100 0 50 100 0 50 100 g x 10 -4 R x 10 -4 Π s 5 2 0.01 0 0 0 -5 -2 -0.01 0 50 100 0 50 100
Slide 38: Results without wage rigidity: Impulse Response Functions
Results without wage rigidity Impulse Responce Functions Figure 2: Impulse responce functions to a negative TFP shock when the …scal instrument is the consumption tax rate y -3 c -3 n x 10 x 10 0 5 5 -0.005 0 0 -0.01 -5 -5 0 50 100 0 50 100 0 50 100 c x 10 -4 R x 10 -4 Π τ 2 4 0.02 1 2 0 0 0 -0.02 0
Slide 39: Results without wage rigidity: Impulse Response Functions
Results without wage rigidity Impulse Responce Functions Figure 3: Impulse responce functions to a negative TFP shock when the …scal instrument is the capital tax rate y -3 c -3 n x 10 x 10 0.01 5 5 0 0 0 -0.01 -5 -5 0 50 100 0 50 100 0 50 100 k x 10 -4 R x 10 -3 Π τ 5 2 0.1 0 0 0 -5 -2 -0.1 0 50 10
Slide 40: Results without wage rigidity: Impulse Response Functions
Results without wage rigidity Impulse Responce Functions Figure 4: Impulse responce functions to a negative TFP shock when the …scal instrument is the labour tax rate -3 y -3 c -3 n x 10 x 10 x 10 0 0 5 -2 -0.5 0 -4 -1 -5 0 50 100 0 50 100 0 50 100 n x 10 -5 R x 10 -5 Π τ 5 4 0.02 0 2 0 -5 0 -0.02 0
Slide 41: Results with wage rigidity: Optimized policy rules
Results with wage rigidity Optimized policy rules Table 5: Optimal monetary reaction to in‡ation and output and optimal …scal reaction to debt and output Optimal interest-rate Optimal …scal Policy reaction to reaction to ξ instruments in‡ation and output debt and output φπ = 3 γgl = 0.1 Rt stg 0.031
Slide 42: Results with wage rigidity: Impulse responce functions
Results with wage rigidity Impulse responce functions Figure 5: Impulse responce functions to a negative TFP shock under the best possible policy mix y -3 c -3 n x 10 x 10 0.01 0 4 0 -0.5 2 -0.01 -1 0 0 50 100 0 50 100 0 50 100 g x 10 -3 R x 10 -3 Π s 2 2 0.05 0 0 0 -2 -2 -0.05 0 50 100 0 50 100 0 5
Slide 43: Results with wage rigidity: Impulse responce functions
Results with wage rigidity Impulse responce functions Figure 6: Impulse responce functions to a negative TFP shock when the …scal instrument is the consumption tax rate y c -3 n x 10 0.01 0.01 5 0 0 0 -0.01 -0.01 -5 0 50 100 0 50 100 0 50 100 c x 10 -3 R x 10 -3 Π τ 2 2 0.05 0 0 0 -2 -2 -0.05 0 50 1
Slide 44: Results with wage rigidity: Impulse responce functions
Results with wage rigidity Impulse responce functions Figure 7: Impulse responce functions to a negative TFP shock when the …scal instrument is the capital tax rate y -3 c -3 n x 10 x 10 0.01 5 5 0 0 0 -0.01 -5 -5 0 50 100 0 50 100 0 50 100 k x 10 -4 R x 10 -3 Π τ 5 2 0.2 0 0 0 -5 -2 -0.2 0 50 100 0
Slide 45: Results with wage rigidity: Impulse responce functions
Results with wage rigidity Impulse responce functions Figure 8: Impulse responce functions to a negative TFP shock when the …scal instrument is the labour tax rate -3 y -4 c n x 10 x 10 5 0 0.01 -2 0 0 -4 -5 -0.01 0 50 100 0 50 100 0 50 100 n x 10 -3 R x 10 -3 Π τ 2 5 0.05 0 0 0 -2 -5 -0.05 0 50 100
Slide 46: Results
Results Among …scal instruments, public spending is the best, or the least distorting, instrument to use in all cases. It is optimal to use the nominal interest rate to react aggresively to in‡ation and a …scal policy instrument (as said, preferably, public spending) to react to the debt cycle in al
Slide 47: Results (continued)
Results (continued) Under wage rigidity, if the economy is hit by an adverse supply shock, which causes a fall in output and a rise in the debt burden as share of output, public spending should rise, and all tax rates should fall, at impact. Only in turn the …scal authorities should use their tax-sp
Slide 48: Extensions
Extensions Other labor market frictions Open economy (semi-small open economy or 2-country model) Heterogeneity across agents (e.g. workers versus capitalists) and distributional implications of stabilization policy Philippopoulos et al. (AUEB) Fiscal and monetary policy actions November 27, 2012 48
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