Stabilization versus Sustainability: Macroeconomic Tradeoffs Huixin - - PowerPoint PPT Presentation

Stabilization versus Sustainability: Macroeconomic Tradeoffs

Huixin Bi, Eric Leeper & Campbell Leith

Bank of Canada, Indiana University & University of Glasgow

March 2011 (Preliminary)

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

This Paper

Motivation:

◮ Sovereign debt crisis in Europe

Question:

◮ Do routine monetary & fiscal policy actions taken to achieve

stabilization goals. . .

◮ . . . have different macroeconomic effects in economies facing

sustainability issues than in economies not facing such issues? This is an interim report on progress toward answering this increasingly relevant question.

◮ Closed economy with nominal debt ◮ Allow the possibility of sovereign debt default & risk premia

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Paper’s Findings

◮ Specification of monetary policy rule is central to link between

default and inflation

◮ If sustainability an issue, monetary policy may lose control of

inflation even if it always obeys Taylor principle

◮ If sustainability an issue, expansionary fiscal consolidations are

possible over the long run, but not in the short run

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

This Talk

◮ Simple analytics in an endowment economy with exogenous

default

◮ New-Keynesian model with state-dependent default

(nonlinear)

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Simple Analytics: Endowment Economy

◮ Exogenous sovereign default rate ∆t ∈ [0, 1] ◮ Active monetary policy & passive fiscal policy ◮ Household problem: max E0 ∞

t=0

βtu (ct) s.t. Ptct + Bt Rt + PtTt = (1 − ∆t)Bt−1 + Ptyt Risky rate: 1 Rt = βEt 1 − ∆t+1 πt+1 Risk-free rate: 1 Rf

t

= βEt 1 πt+1 ◮ Government: Bt Rt + PtTt = (1 − ∆t)Bt−1 Tt − T = γ

• (1 − ∆t)Bt−1

Pt−1 − b

• (γ >

β−1 − 1 1 − Et∆t+1 )

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Simple Analytics: Risk-Free Instrument

◮ Monetary instrument risk-free rate 1 Rf

t

= 1 R + α 1 πt − 1 π

• α/β > 1

◮ Yields dynamic equation for inflation 1 πt − 1 π = β αEt

• 1

πt+1 − 1 π

• ◮ Unique bounded solution: inflation always on target

πt = π ◮ With passive fiscal policy, default causes no problems for

monetary policy’s control of inflation (Ricardian)

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Simple Analytics: Risky Instrument

◮ Monetary instrument risky rate 1 Rt = 1 R + α 1 πt − 1 π

• ◮ Yields dynamic equation for inflation

1 πt − 1 π = β αEt 1 − ∆t+1 πt+1 − 1 π

• ◮ Unique bounded solution: inflation always away from target

1 πt = 1 π

• 1 − β

α   1 + Et

∞

• i=1

β α i

i

• j=1

(1 − ∆t+j)    ◮ With passive fiscal policy, inflation rises with expected default

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Risky Instrument

◮ Monetary policy accommodates default even without

changing policy rate

◮ Risky rate rule implies (with fixed default rate) 1 Rt = 1 R + α 1 πt − 1 π

• −

→ 1 Rf

t

= 1 R + α 1 − δ 1 πt − 1 π − δ αR

• ◮ Higher δ: raises the effective inflation target from π to

π 1−δβ/α

◮ bonds lose value, raises aggregate demand & inflation Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

So Far...

◮ Simple analytics in an endowment economy with exogenous

default

◮ New-Keynesian model with state-dependent default

(nonlinear)

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Numerical Model

◮ Off-the-shelf new Keynesian model

◮ elastic labor, fixed capital, costly price adjustment ◮ tax on labor income, nominal debt, exogenous spending &

transfers

◮ interest rate rule for monetary policy ◮ tax rule for fiscal policy ◮ default rule: model-based “fiscal limit” (Bi (2010))

◮ Solve full non-linear model

◮ find fixed point in decision rules over discretized state space ◮ calibrate—loosely—to Greek fiscal data Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Numerical Model: Household

Household problem:

max E0

∞

• t=0

βtu (ct, nt) s.t. Ptct + Bt Rt + Bf

t

Rf

t

= (1 − ∆t)Bt−1 + Bf

t−1 + (1 − τt) (Wtnt + PtΥt) + Ptz

◮ FOC: − un(t) uc(t) = wt (1 − τt) 1 Rt = βEt 1 − ∆t+1 πt+1 uc(t + 1) uc(t)

• 1

Rf

t

= βEt

• 1

πt+1 uc(t + 1) uc(t)

• Huixin Bi, Eric Leeper & Campbell Leith

Stabilization versus Sustainability: Macroeconomic Tradeoffs

Numerical Model: Firm

◮ Final goods firm: competitive firm with CES production form ◮ Intermediate goods firm: Rotemberg adjustment cost max

∞

• t=0

R0,t

• pt(i)yt(i) − mctPtyt(i) − φ

2 pt(i) pt−1(i) 1 π − 1 2 PtYt

• s.t.

yt(i) = pt(i) Pt −θ Yt FOC: (1 − θ) + θmct − φ πt π − 1 πt π + βφEt uc(t + 1) uc(t) πt+1 π − 1 πt+1 π Yt+1 Yt = 0.

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Numerical Model: Government

Government budget:

Bt Rt + τt (Wtnt + Υt)

• PtTt

= (1 − ∆t)Bt−1 + Ptgt + Ptz − → bt Rt + Tt = 1 − ∆t πt bt−1 + gt + z ◮ Unenforceable bond contract: ∆t =      if bt−1 < b∗

t with

b∗

t ∼ N (b∗, σ2 b)

• Model-based fiscal limit

δ if bt−1 ≥ b∗

t Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Numerical Model

◮ Fiscal rule: τt − τ = γ

• (1 − ∆t)bt−1
• bd

t

−b

• ◮ Monetary rule:

Rt − R = α(πt − π) + εR

t

εR

t ∼ N (0, σ2 R)

◮ Stochastic government spending: ln gt g = ρe ln gt−1 g + εg

t

εg

t ∼ N (0, σ2 g)

◮ Stochastic technology: ln At A = ρu ln At−1 A + εA

t

εA

t ∼ N (0, σ2 A) Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Fiscal Limit

Following Bi (2010),

◮ Peak of Laffer curve a natural fiscal limit, given spending

◮ A function of exogenous state & model parameters

τ max

t

= τ max(At, gt, Θ) T max

t

= T max(At, gt, Θ) ◮ Fiscal limit ≡ expected present value of future maximum

surpluses (inflation & transfers at steady state)

B∗ = E

∞

• t=0

βt umax

c

(At, gt) umax

c

(A0, g0) βp

t

• political factor

(T max(At, gt) − gt − z)

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Fiscal Limit

B∗ = E

∞

• t=0

βt umax

c

(At, gt) umax

c

(A0, g0) βp

t

• political factor

(T max(At, gt) − gt − z) ◮ Political risk: βp

t ∈ {βp L, βp H} ∼ Markov chain ◮ uncertainty about whether maximum surpluses will be

forthcoming

◮ βp < 1 necessary to generate risk premia at plausible

debt-GDP levels

◮ Compute unconditional distribution of fiscal limit, f (B∗)

1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1 2 3 4 5 6

Debt over steady−state GDP Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Default Rule

◮ Literature of optimal, strategic default: generates default at

implausibly low debt levels

◮ Effective fiscal limit is b∗ t drawn from N(b∗, σ2 b)

◮ choice of effective fiscal limit is random ◮ determined by political considerations: willingness to meet

• bligations

◮ fiscal limit f (B∗): ability to meet obligations

◮ Default rule: ∆t =

• δ

if bt−1 > b∗

t (Above Effective Fiscal Limit)

if bt−1 ≤ b∗

t (Below Effective Fiscal Limit)

◮ With partial default, debt outstanding at beginning of period

t is

bd

t = (1 − ∆t)bt−1 Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Nonlinear solution

Monotone mapping method (Coleman(1991), Davig(2004)):

◮ Grid points the state space, ψt = (bd

t , At, gt, εR t ), using Tauchen

(1991);

◮ Initial guess of the decision rule

• bt = f b

0 (ψt), πt = f π 0 (ψt), wt = f w 0 (ψt)

• ;

◮ Update the decision rule

• bt = f b

j (ψt), πt = f π j (ψt), wt = f w j (ψt)

• by

iterating over the equilibrium conditions until converge

(ǫ = 1e − 6).

Numerical integration: Newton-Cotes formulas.

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Calibration

Calibrated to quarterly data:

β θ φ π n 0.99 11 100 1.03 0.25 g/y z/y b/y τ γ 0.167 0.134 0.3526 0.315 0.5/4 α A ρA σA σR 1.5 1 0.85 0.01 0.005 ρg σg 0.85 0.015 ◮ Default rate: 4 or 20 percent at annual rate ◮ Political risk (ICRG index): βp

L = 0.4, βp H = 0.6, pLL = pHH = 0.9 Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Decision Rules

◮ Important non-linearities (ψt = (bd

t , At, gt, εR t )) 0.8 1 1.2 1.4 1.6 −10 10 20 30 40 Net Nominal Interest Rate Bond−GDP 0.8 1 1.2 1.4 1.6 5 10 15 Net Real Interest Rate Bond−GDP 0.8 1 1.2 1.4 1.6 0.2 0.22 0.24 0.26 Output Bond−GDP 0.8 1 1.2 1.4 1.6 5 10 15 Risk Premium Bond−GDP 0.8 1 1.2 1.4 1.6 −5 5 10 15 20 Net Inflation Rate Bond−GDP 0.8 1 1.2 1.4 1.6 0.2 0.4 0.6 0.8 1 Default Probability Bond−GDP Low A ss A High A Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Policy Disturbances

◮ Exogenous monetary contraction or fiscal expansion when

◮ debt-GDP at steady state ◮ debt-GDP near fiscal limit

◮ Distinct sources of dynamics

• 1. initial policy disturbance
• 2. intrinsic dynamics when debt away from steady state
• 3. dynamics stemming from possibility of default & risk premia

◮ Report differences in time paths with and without policy

shock, contrasting far from and near to fiscal limit

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Monetary Contraction: Away from Fiscal Limit

Conventional effects of i.i.d. monetary contraction

10 20 30 40 0.247 0.248 0.249 0.25 0.251

Labor (nt)

10 20 30 40 0.204 0.206 0.208 0.21

Consumption (ct)

10 20 30 40 0.89 0.9 0.91 0.92

Wage (wt)

10 20 30 40 0.35 0.355 0.36 0.365

Bond (bt−1)

10 20 30 40 0.315 0.3155 0.316 0.3165 0.317

Tax Rate (τt)

10 20 30 40 6 8 10 12

Nominal risky Rate

10 20 30 40 2.2 2.4 2.6 2.8 3

Inflation (πt)

10 20 30 40 −1 −0.5 0.5 1

Default Probability

10 20 30 40 4 6 8 10

Real risky rate

No shock (SS) R shock (SS)

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Monetary Contraction: No Default

Difference in paths with vs. without i.i.d. monetary contraction in model that rules out default

5 10 15 20 25 30 35 40 2 4 6 Percentage

Bond

5 10 15 20 25 30 35 40 −0.15 −0.1 −0.05

Difference of Real Risky Rate

Percentage Point 5 10 15 20 25 30 35 40 −0.8 −0.6 −0.4 −0.2 0.2

Inflation

Percentage Point 5 10 15 20 25 30 35 40 −1 −0.5 Percentage

Output

∆ rt (B*) − ∆ rt (SS)

Close to Steady State

Close to Fiscal Limit Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Monetary Contraction: Effect of Default

Difference in paths from solving with default rule and with ∆t ≡ 0, conditional on debt being near the fiscal limit

10 20 30 40 −0.2 0.2 0.4 0.6 Percentage

Labor Difference(Nt)

10 20 30 40 1 2 3 4 Percentage

Bond (bt−1)

10 20 30 40 −4 −2 2 Percentage Point

Expected tax rate (Et τt+1)

10 20 30 40 0.05 0.1 0.15 0.2 Percentage Point

Tax rate (tau

L t ) 10 20 30 40 −0.2 0.2 0.4 0.6 Percentage

Consumption (ct)

10 20 30 40 0.5 1 1.5

Inflation (πt)

Percentage Point (Annual) 10 20 30 40 0.5 1 1.5 2 Percentage Point (Annual)

Nominal Risk Premia

rd

t − rnd t

10 20 30 40 0.05 0.1 0.15 0.2

Default Probability

10 20 30 40 −0.5 0.5 1 Percentage Point (Annual)

Real Risk Premia

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Monetary Contraction: Effect of Default

Difference in paths with vs. without i.i.d. monetary contraction in model where default is possible

5 10 15 20 25 30 35 40 5 10 Percentage

Bonds

5 10 15 20 25 30 35 40 0.1 0.2

Difference in Risky Real Rate

Percentage Points 5 10 15 20 25 30 35 40 −0.5 0.5

Inflation

Percentage Points 5 10 15 20 25 30 35 40 −1 −0.5 Percentage

Output

Close to fiscal limit Close to steady state

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Monetary Contraction: Synopsis

◮ Monetary contraction in economy close to fiscal limit

◮ raises debt service through ◮ more debt in hands of public ◮ higher real interest rates ◮ lower output reduces revenues, reinforcing rise in debt ◮ higher debt raises Pr(bt−1 > b∗

t ), raising risk premia

◮ monetary policy accommodate ◮ inflation falls initially, then rises ◮ tax policy passively raises tax rates with debt

◮ Output decline larger ◮ Inflation higher, despite active monetary/passive fiscal policies

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Monetary Contraction: Effect of Default

Difference in paths with vs. without an i.i.d. monetary contraction in model where default is possible

5 10 15 20 25 30 35 40 5 10

Percentage

Bonds

5 10 15 20 25 30 35 40 0.2 0.4

Difference in Risky Real Rate

Percentage Points

5 10 15 20 25 30 35 40 −0.5 0.5

Inflation

Percentage Points

5 10 15 20 25 30 35 40 −1 −0.5

Percentage

Output ∆ rt(B*) − ∆ rt(SS) (Risk−free) ∆ rt(B*) − ∆ rt(SS) (Risky) Close to steady state Close to fiscal limit (Risk−free) Close to fiscal limit (Risky) Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Fiscal Expansion

◮ No Default: usual effects

◮ negative wealth effect raises employment & output ◮ higher demand for goods raises inflation & interest rates ◮ output multiplier < 1; consumption multiplier < 0 ◮ longer run: labor taxes rise, employment & output fall

◮ Effect of default:

◮ Monetary policy partially accommodates default risk ◮ Debt, inflation, and risky real rate rise more ◮ Important long-run differences to emerge near the limit:

reduce output more

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Fiscal Multiplier

Present-value fiscal multiplier, following Uhlig (AER 2010):

Present-value multiplier Γy

t+k =

k

j=0

j

i=0 r−1 t+i−1

y s

t+j − y ns t+j

• k

j=0

j

i=0 r−1 t+i−1

gs

t+j − gns t+j

• ◮ If the government spending increases by 1 unit in terms of

present value, how much does the present value of output increase over a k-period horizon.

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Fiscal Expansion: Long-Run Output Effects

50 100 150 200 250 300 350 400 −0.4 −0.2 0.2 0.4 0.6 0.8 1

Output Multiplier

Quarters

Debt close to steady state

At steady state

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Fiscal Expansion: Long-Run Output Effects

50 100 150 200 250 300 350 400 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1

Output Multiplier

Quarters

Debt close to fiscal limit, δ = 0

Near fiscal limit: No default

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Fiscal Expansion: Long-Run Output Effects

50 100 150 200 250 300 350 400 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1

Output Multiplier

Quarters

Debt close to fiscal limit, δ = 0.01

Near fiscal limit: Small default rate

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Fiscal Expansion: Long-Run Output Effects

50 100 150 200 250 300 350 400 −1.5 −1 −0.5 0.5 1

Output Multiplier

Quarters

Debt close to fiscal limit, δ = 0.05

Near fiscal limit: Higher default rate

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Fiscal Expansion: Long-Run Debt Dynamics

50 100 150 200 250 300 350 400 1 2 3 4 5 6 7 8 9 10 Debt Difference Percentage Quarters

Close to Steady State Close to Fiscal Limit (δ = 0) Close to Fiscal Limit (δ = 0.01) Close to Fiscal Limit (δ = 0.05)

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs

Conclusion

Main finding so far:

◮ If sustainability an issue, monetary policy may lose control of

inflation even if it always obeys Taylor principle

◮ Sovereign default risk can substantially lower the fiscal

multiplier over the long run, but not in the short run. Extension:

◮ To model working capital ◮ To model the spill-over effect of sovereign risk premium to

private sector (through the interbank market)

◮ To consider sovereign risk premium and monetary policy in a

monetary union

Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs