Fiscal Activism and the Zero Nominal Interest Rate Bound Sebastian Schmidt European Central Bank
September 2016
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Disclaimer: The views expressed on the slides are those of the author and do not necessarily represent those of the European Central Bank.
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Macroeconomic stabilization at the zero lower bound
In the absence of policy commitment, the ZLB can be a severe drag on conventional monetary stabilization policy (e.g. Adam and Billi 2007; Nakov 2008)
Using fiscal policy as an additional stabilization tool can mitigate the welfare costs associated with the presence of the ZLB (e.g. Eggertsson 2001; Nakata 2013; Schmidt 2013)
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This paper
Existing normative studies of optimal discretionary fiscal policy at the ZLB assume that the policymaker has the same preferences as society as a whole.
Can the discretionary equilibrium be improved by the appointment of a policymaker whose preferences differ from those of society?
Focus on policymaker’s preferences towards government consumption.
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Outline
Analytical results for a simple two state New Keynesian model
Numerical results for a bigger continuous state NK model
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An illustrative model Identical, infinitely-living households maximize expected lifetime utility. Utility is separable in private consumption, consumption of public goods and leisure Goods-producing firms act under monopolistic competition and maximize profits s.t. staggered price setting A benevolent, discretionary policymaker decides each period about nominal interest rate and government spending (financed by lump-sum taxes) Uncertainty arises from a stochastic natural real rate of interest 6 / 28
Aggregate private sector behavior Log-linearized behavioral constraints πt = κ (Yt − ΓGt ) + βEt πt+1 Yt = Gt + Et Yt+1 − Et Gt+1 −
1 (it − Et πt+1 − rtn ) , σ
where rtn follows a two state Markov process n rH > 0 (normal state) n < 0 (crisis state) rL
n n n n ) = pL = rL |rt = rL Prob(rt+1 n n n n Prob(rt+1 = rL |rt = rH ) = 0. 7 / 28
Social welfare
Society’s preferences are represented by a linear-quadratic approximation to household welfare
−Et
∞ X
βj
j=0
i 1h 2 πt+j + λ (Yt+j − ΓGt+j )2 + λG G2t+j 2
where λ=
κ , θ
ν λG = λΓ 1 − Γ + , σ
ν>0
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The policymaker The policymaker’s preferences are given by
−Et
∞ X j=0
βj
i 1h 2 ˜ G G2 πt+j + λ (Yt+j − ΓGt+j )2 + λ t+j 2
where ˜G ≥ 0 λ Details on preferences
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The policymaker The policymaker’s preferences are given by
−Et
∞ X j=0
βj
i 1h 2 ˜ G G2 πt+j + λ (Yt+j − ΓGt+j )2 + λ t+j 2
where ˜G ≥ 0 λ Details on preferences
˜ G maximizes society’s welfare? Main question: Which value of λ
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The optimization problem of a generic policymaker Each period t, the generic discretionary policymaker solves i 1h 2 ˜ G G2 πt + λ (Yt − ΓGt )2 + λ t {πt ,Yt ,Gt ,it } 2 min
subject to it ≥ 0 NKPC, Euler equation rtn given {πt+j , Yt+j , Gt+j , it+j ≥ 0} given for j ≥ 1
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Optimality conditions
˜ G Gt = 0 (1 − Γ) [κπt + λ (Yt − ΓGt )] + λ
(1)
it (κπt + λ (Yt − ΓGt )) = 0
(2)
it ≥ 0
(3)
κπt + λ (Yt − ΓGt ) ≤ 0,
(4)
as well as the NKPC and the consumption Euler equation. Reformulated policy problem
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Bounded rational expectations equilibrium n , and denote the stochastic period in which the natural real Let r0n = rL n to r n by T . rate jumps from rL H
If (1 − pL ) (1 − βpL ) > σκ pL , then there exists a bounded rational expectations equilibrium where n for all t ≥ T i. πt , Yt , Gt = 0 and it = rH n < 0, Y = ω r n , G = ω r n > 0, ii. πt = ωπ rL t t Y L G L n < 0 and i = 0 for all 0 ≤ t < T . Yt − ΓGt = (ωY − ΓωG )rL t Policy function parameters
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Appointing a policymaker
˜G Given the assumptions about the shock process, the optimal value for λ minimizes h i 1 1 2 n 2 ωπ2 + λ (ωY − ΓωG )2 + λG ωG (rL ) 2 1 − βpL
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The desirability of fiscal activism
Proposition Under discretionary policy, welfare can be enhanced by the appointment of a policymaker who puts less weight on the stabilization of public spending than society as a whole. The best-performing policymaker exhibits (1 − pL ) (1 − βpL ) − σκ pL κ2 + (1 − βpL ) λ ∗ ˜ λG < λG . λG = κ2 (1 − pL ) (1 − βpL ) 1−βp + (1 − βp ) λ L L ˜ ∗ → λG as pL → 0. Note that λ G
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The desirability of fiscal activism c’td Proposition In a liquidity trap, the best-performing policymaker raises government spending by more than a policymaker whose preferences are identical to those of society as a whole ˜ ∗ > GL λG . GL λ G
Furthermore, the analytical expressions for (ωπ , ωY , ωG ) imply that ˜∗ < 0 πL λG < πL λ G ˜ ∗ − ΓGL λ ˜∗ < 0 YL λG − ΓGL λG < YL λ G G
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Intuition
Fiscal policy is transmitted through two interrelated channels: i. A transitory government spending stimulus at the ZLB raises current aggregate demand and thereby reduces contemporaneous deflationary pressures ii. Forward-looking agents anticipate that government spending will be expanded in future crisis states, which increases inflation and output gap expectations.
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Intuition c’td At the ZLB, the generic policymaker would like the private sector to expect a larger fiscal expansion, and, therefore, higher inflation, in future crisis states. However, such an announcement is not time-consistent and therefore not credible. The appointment of a fiscally activist policymaker makes government spending more elastic, allowing the government to better exploit the expectations channel of fiscal policy transmission. 17 / 28
The role of the crisis state persistence
Proposition The optimal degree of fiscal activism is increasing in the persistence pL of the low natural real rate shock ˜ ∗ /λG ∂ λ G < 0. ∂pL
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Comparison to an optimized fiscal rule
Consider a simple class of feedback rules that relates government spending to the natural real rate Gt =
n τ rn if t < T t
(5)
0 if t ≥ T
Proposition Suppose, the policymaker could commit to fiscal policy rule (5). Monetary policy is conducted under discretion. Then it is optimal to ˜∗ . set τ = ωG λ G
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A continuous state model
Model’s state variables are allowed to assume a continuum of values Price and nominal wage rigidities Economy is buffeted by discount factor shock, price mark-up shock, wage mark-up shock, technology shock
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Aggregate private sector behavior and shock processes 1 Yt = Gt + Et Yt+1 − Et Gt+1 − (it − Et πt+1 − rtn ) σ γ πt = κ p Yt + wt + βEt πt+1 + ut 1−γ η W W πt = κ w σ+ (Yt − ΓGt ) − wt + βEt πt+1 + et 1−γ πtW = wt − wt−1 + πt − ∆wtn n rtn = ρr rt−1 + (1 − ρr ) rn + rt
ut = ρu ut−1 + ut et = ρe et−1 + et " # 1 γ (1 + η) n A 1− ∆wt = −1 t . 1−γ η + γ + (1 − γ) σν (σ + ν) 21 / 28
Society’s welfare
A linear quadratic approximation to household welfare: Et
∞ X j=0
βj
i 1h 2 W 2 πt+j + λ (Yt+j − ΓGt+j )2 + λG G2t+j + λW (πt+j ) , 2
where λ = κp σ +
η+γ 1−γ
1 θ,
λG = λΓ 1 − Γ +
ν σ
,
(1−γ)θW λW = λ κw (σ+(η+γ)/(1−γ)) .
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Calibration and model solution
The model is calibrated to the U.S. economy. The period length is one quarter.
β
0.9938
η
1.69
α
0.72
αW
0.72
ρu
0
σe
0.05
σ
1.22
G/Y
0.2
γ
0.3
ρr
0.8
σu
0.17
σA
0.62
ν
4.88
θ
9
θW
9
σr
0.363
ρe
0
The model is solved using global methods.
details
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Welfare losses (normalized) 1.3 Preference & technology shocks Preference & price mark-up shocks Preference & wage mark-up shocks
1.2
1.1
1
0.9
0.8
0.7 0.002 0.004 0.006 0.008
0.01
0.012 0.014 0.016 0.018
0.02
˜G λ Note: All losses are normalized by the welfare loss under the benchmark regime, respectively.
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Results
Additional shock
Technology
Price mark-up
Wage mark-up
Preference
shock
shock
shock
shock only
λG
0.0161
0.0161
0.0161
0.0161
˜ ∗G λ
0.0035
0.0040
0.0040
0.0040
0.22
0.25
0.25
0.25
˜ ∗G ) in % Welfare gain (λ
15
12
30
38
ZLB frequency (λG ) in %
25
26
27
26
˜ ∗G ) in % ZLB frequency (λ
22
23
22
23
˜ ∗G /λG λ
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Equilibrium responses to the natural real rate Output gap
Price inflation
Wage inflation
0
0
0 −0.5
−2
−0.5
−4
−1
−1
−5
0
5
10
−5
Government spending
0
5
10
−1.5
−5
Output
0
5
10
Real wage rate 0
0
4
−1
2
−0.1
−2 0
−5
0
5
10
−5
Nominal interest rate
0
5
−0.2
Real interest rate
−5
0
5
10
Excerpt of nominal rate 1.5
10
10
5
5
0
0
1
−5
0 5 10 Natural real rate
0.5
−5
0 5 10 Natural real rate
˜G = Model with preference and price mark-up shocks. Solid lines: λ
˜∗ . λ G
0
0
1 Natural real rate
2
˜ G = λG . Dashed lines: λ 26 / 28
Equilibrium responses to price mark-up shock Output gap
Price inflation
Wage inflation 0
2 0.5
−0.05 0
0
−0.1 −2
−0.5 −0.5
0
0.5
−0.5
Government spending 0.5
0
0.5
−0.5
Output
0
0.5
Real wage rate
1
0.5
0.5 0
0
0 −0.5
−0.5
−0.5
0
0.5
Nominal interest rate 4
0
0.5
−0.5
Real interest rate
0
0.5
0.05
0
2
−0.5 0 0.5 Price mark−up shock
0
Lagrange multiplier
4
2
0
−0.5 −0.5
−0.5 0 0.5 Price mark−up shock
˜G = Model with preference and price mark-up shocks. Solid lines: λ
˜∗ . λ G
−0.05
−0.5 0 0.5 Price mark−up shock
˜ G = λG . Dashed lines: λ 27 / 28
Conclusion The credibility problem of discretionary monetary policy at the ZLB also persists under the jointly optimal discretionary monetary-fiscal policy The appointment of a policymaker who is less concerned with the stabilization of government spending than society makes government spending more elastic This mitigates the credibility problem of discretionary policymaking and improves society’s welfare 28 / 28
Appendix
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Society’s preferences
The period utility function reads Ct1−ˆσ − 1 G1−ˆν − 1 + ξG t − ξN 1−σ ˆ 1 − νˆ
Z 0
1
Nt (i)1+η di 1+η
In the efficient equilibrium Ct−ˆσ = ξG Gt−ˆν
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The policymaker’s preferences
ν −1 Ct1−ˆσ − 1 ˜ G1−˜ + ξG t − ξN 1−σ ˆ 1 − ν˜
Z 0
1
Nt (i)1+η di 1+η
In the flexible price equilibrium, the policymaker implements Ct−ˆσ = ξ˜G Gt−˜ν ˜−ˆ ν Choose ξ˜G = ξG Gνsociety to replicate the efficient equilibrium steady state. back
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Reformulated policy problem Let Xt ≡ Yt − ΓGt . Then i 1h 2 ˜ G G2 min πt + λXt2 + λ t {πt ,Xt ,Gt ,it } 2 subject to it ≥ 0 πt = κXt + βEt πt+1 Xt = Et Xt+1 + (1 − Γ)(Gt − Et Gt+1 ) −
1 (it − Et πt+1 − rt ) σ
rtn given {πt+j , Xt+j , Gt+j , it+j ≥ 0} given for j ≥ 1 back 32 / 28
Policy function parameters
˜G κλ
1 ˜ G (1 − pL ) (1 − βpL ) − λ + (1 − pL ) (1 − Γ) ((1 − βpL ) λ + κ2 ) σ ˜ G − λΓ (1 − Γ) − κ2 Γ (1 − Γ) (1 − βpL ) λ 1 ωY = 2 κ 2 ˜ σ λG (1 − pL ) (1 − βpL ) − σ pL + (1 − pL ) (1 − Γ) ((1 − βpL ) λ + κ ) (1 − Γ) (1 − βpL ) λ + κ2 1 ωG = − 2 κ 2 ˜ σ λG (1 − pL ) (1 − βpL ) − pL + (1 − pL ) (1 − Γ) ((1 − βpL ) λ + κ ) ωπ =
κ σ pL
2
σ
back
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Numerical procedure Equilibrium conditions H (z, s), where z are the free endogenous variables. Want to approximate unknown policy functions z = f (s). Use a weighted sum of known basis functions ψ1 , ..., ψn : f (s) ≈ CΨ (s) Choose coefficients in C such that H (CΨ (s) , s) is close to zero for s ∈ S. I
cubic splines (finite elements)
I
collocation method
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