Optimal Fiscal Consolidation under Frictional Financial Markets - - PowerPoint PPT Presentation

Optimal Fiscal Consolidation under Frictional Financial Markets

Dejanir Silva UIUC ADEMU 2020

0 / 20

Stabilization versus Consolidation

After sharp rise in spreads, European countries faced a key trade-off

2004 2007 2010 2013 2016 2 4 6 8 10

Sovereign spreads

year %

Portugal Ireland Italy Spain 2004 2007 2010 2013 2016 10 20 30

Unemployment

year %

2004 2007 2010 2013 2016 20 40 60 80 100 120 140

Debt- to- GDP ratio

year %

1 / 20

Stabilization versus Consolidation

Use fiscal policy to achieve macroeconomic stabilization

2004 2007 2010 2013 2016 2 4 6 8 10

Sovereign spreads

%

2004 2007 2010 2013 2016 10 20 30

Unemployment

year %

2004 2007 2010 2013 2016 20 40 60 80 100 120 140

Debt- to- GDP ratio

%

1 / 20

Stabilization versus Consolidation

Or engage in fiscal consolidation and reduce debt

2004 2007 2010 2013 2016 2 4 6 8 10

Sovereign spreads

%

2004 2007 2010 2013 2016 10 20 30

Unemployment

%

2004 2007 2010 2013 2016 20 40 60 80 100 120 140

Debt- to- GDP ratio

year %

1 / 20

Optimal Fiscal Consolidation in a Currency Union

This paper: study optimal resolution of this trade-off

• Optimal fiscal policy in a currency union with frictional financial markets
• Rich choice of instruments: spending vs. tax choices

2 / 20

Optimal Fiscal Consolidation in a Currency Union

This paper: study optimal resolution of this trade-off

• Optimal fiscal policy in a currency union with frictional financial markets
• Rich choice of instruments: spending vs. tax choices

Two key ingredients:

1 Sticky prices ⇒ macroeconomic-stabilization motive

• Open economy NK model as in Gali and Monacelli (2005)

2 Endogenous spreads ⇒ debt-management motive

• Frictional financial markets as in Gabaix and Maggiori (2015)

2 / 20

Optimal Fiscal Consolidation in a Currency Union

This paper: study optimal resolution of this trade-off

• Optimal fiscal policy in a currency union with frictional financial markets
• Rich choice of instruments: spending vs. tax choices

Two key ingredients:

1 Sticky prices ⇒ macroeconomic-stabilization motive

• Open economy NK model as in Gali and Monacelli (2005)

2 Endogenous spreads ⇒ debt-management motive

• Frictional financial markets as in Gabaix and Maggiori (2015)

Main results:

• It is not optimal to engage in stimulus spending
• VAT should be increasing over time
• It is optimal to raise and front-load taxes: a fiscal consolidation

2 / 20

Outline

1

Currency union with imperfect financial markets

2

Capital Flow Reversals and Boom/Bust Cycle

3

The Optimal Policy Problem

4

Optimal VAT Dynamics

5

Optimal Fiscal Consolidation

2 / 20

Preferences

Preferences: ∞ e−ρt

• C 1−σ

t

1 − σ + χ log Gt − N1+φ

t

1 + φ

• dt

3 / 20

Preferences

Preferences: ∞ e−ρt

• C 1−σ

t

1 − σ + χ log Gt − N1+φ

t

1 + φ

• dt

Consumption: aggregate of domestic and foreign goods Ct = CH,t 1 − α 1−α CF,t α α

where H ∈ [0, 1].

3 / 20

Preferences

Preferences: ∞ e−ρt

• C 1−σ

t

1 − σ + χ log Gt − N1+φ

t

1 + φ

• dt

Consumption: aggregate of domestic and foreign goods Ct = CH,t 1 − α 1−α CF,t α α

where H ∈ [0, 1].

Composite of country i ∈ [0, 1]: Ci,t = 1 Ci,t(j)

ǫ−1 ǫ dj

• ǫ

ǫ−1

Composite of foreign goods: CF,t = 1 C

γ−1 γ

i,t

di

• γ

γ−1

where ǫ > γ.

3 / 20

Preferences

Preferences: ∞ e−ρt

• C 1−σ

t

1 − σ + χ log Gt − N1+φ

t

1 + φ

• dt

Consumption: aggregate of domestic and foreign goods Ct = CH,t 1 − α 1−α CF,t α α

where H ∈ [0, 1].

Composite of country i ∈ [0, 1]: Ci,t = 1 Ci,t(j)

ǫ−1 ǫ dj

• ǫ

ǫ−1

Composite of foreign goods: CF,t = 1 C

γ−1 γ

i,t

di

• γ

γ−1

where ǫ > γ.

3 / 20

Technology, profits, and pricing

Technology:

Yt(j) = AtNt(j).

4 / 20

Technology, profits, and pricing

Technology:

Yt(j) = AtNt(j).

Profits:

Πt = (1 − τ v

t )Pc H,t(CH,t + Gt) + (1 − τ x t )P∗,c H,tC ∗ H,t − (1 + τ p t )WtNt.

4 / 20

Technology, profits, and pricing

Technology:

Yt(j) = AtNt(j).

Profits:

Πt = (1 − τ v

t )Pc H,t(CH,t + Gt) + (1 − τ x t )P∗,c H,tC ∗ H,t − (1 + τ p t )WtNt.

4 / 20

Technology, profits, and pricing

Technology:

Yt(j) = AtNt(j).

Profits:

Πt = (1 − τ v

t )Pc H,t(CH,t + Gt) + (1 − τ x t )P∗,c H,tC ∗ H,t − (1 + τ p t )WtNt.

4 / 20

Technology, profits, and pricing

Technology:

Yt(j) = AtNt(j).

Profits:

Πt = (1 − τ v

t )Pc H,t(CH,t + Gt) + (1 − τ x t )P∗,c H,tC ∗ H,t − (1 + τ p t )WtNt.

4 / 20

Technology, profits, and pricing

Technology:

Yt(j) = AtNt(j).

Profits:

Πt = (1 − τ v

t )Pc H,t(CH,t + Gt) + (1 − τ x t )P∗,c H,tC ∗ H,t − (1 + τ p t )WtNt.

Sticky producer prices

• Producer prices PH,t(j) are subject to Calvo pricing
• Full pass through: consumer prices are given by

Pc

H,s(j) = PH,t(j)

1 − τ v

s

, P∗,c

H,s(j) = PH,t(j)

1 − τ x

s

.

4 / 20

Technology, profits, and pricing

Technology:

Yt(j) = AtNt(j).

Profits:

Πt = (1 − τ v

t )Pc H,t(CH,t + Gt) + (1 − τ x t )P∗,c H,tC ∗ H,t − (1 + τ p t )WtNt.

Sticky producer prices

• Producer prices PH,t(j) are subject to Calvo pricing
• Full pass through: consumer prices are given by

Pc

H,s(j) = PH,t(j)

1 − τ v

s

, P∗,c

H,s(j) = PH,t(j)

1 − τ x

s

.

Terms of trade:

St = P∗

t

PH,t , ˜ St = (1 − τ x

t ) P∗ t

PH,t .

4 / 20

International financial intermediaries

Important: households cannot invest in foreign bonds

• Arbitrage is done by international financial intermediaries
• Friction as in Gabaix and Maggiori (2015): diversion of fraction ΓBI

t

5 / 20

International financial intermediaries

Important: households cannot invest in foreign bonds

• Arbitrage is done by international financial intermediaries
• Friction as in Gabaix and Maggiori (2015): diversion of fraction ΓBI

t

Intermediaries’ problem: V I

t = max BI

t

(it − i∗

t )BI t

s.t. V I

t ≥ Γ(BI t )2

5 / 20

International financial intermediaries

Important: households cannot invest in foreign bonds

• Arbitrage is done by international financial intermediaries
• Friction as in Gabaix and Maggiori (2015): diversion of fraction ΓBI

t

Intermediaries’ problem: V I

t = max BI

t

(it − i∗

t )BI t

s.t. V I

t ≥ Γ(BI t )2

Demand for domestic bonds: BI

t = 1

Γ(it − i∗

t )

5 / 20

International financial intermediaries

Important: households cannot invest in foreign bonds

• Arbitrage is done by international financial intermediaries
• Friction as in Gabaix and Maggiori (2015): diversion of fraction ΓBI

t

Intermediaries’ problem: V I

t = max BI

t

(it − i∗

t )BI t

s.t. V I

t ≥ Γ(BI t )2

Demand for domestic bonds: BI

t = 1

Γ(it − i∗

t )

Country is also subject to exogenous capital flows BN

t :

it = ρ + i∗

t − ρ − ΓBN t

• exogenous component≡ψt

+ ΓEt

• endogenous component

using BI

t + BN t = Et, where Et is net external debt.

5 / 20

Outline

1

Currency union with imperfect financial markets

2

Capital Flow Reversals and Boom/Bust Cycle

3

The Optimal Policy Problem

4

Optimal VAT Dynamics

5

Optimal Fiscal Consolidation

5 / 20

Capital inflows compressed interest rates...

2000 2002 2004 2006 2008 3.5 4.0 4.5 5.0 5.5

10 year yield

%

Portugal Italy Greece Spain Germany 2000 2002 2004 2006 2008 5 10 15 20 25 30 35

Gross Capital Inflows

% (Trend GDP)

2000 2002 2004 2006 2008 2010 40 60 80 100

Net External Debt

% GDP Output, terms of trade, and net exports. 6 / 20

...inducing a boom financed by external debt

1 2 3 4 5 6

time

0.01 0.00 0.01 0.02 0.03 0.04

Output

1 2 3 4 5 6

time

0.100 0.075 0.050 0.025 0.000

Terms of trade

1 2 3 4 5 6

time

0.08 0.06 0.04 0.02

Net exports

1 2 3 4 5 6

time

0.00 0.05 0.10 0.15 0.20 0.25

External debt

Sticky prices Flex prices

7 / 20

Capital outflows generate a rise in spreads and a bust

1 2 3 4 5 6

time

0.05 0.04 0.03 0.02 0.01 0.00 0.01

Output

1 2 3 4 5 6

time

0.000 0.025 0.050 0.075

Terms of trade

1 2 3 4 5 6

time

0.02 0.03 0.04 0.05 0.06 0.07

Net exports

1 2 3 4 5 6

time

0.10 0.15 0.20 0.25

External debt

Sticky prices Flex prices

8 / 20

Outline

1

Currency union with imperfect financial markets

2

Capital Flow Reversals and Boom/Bust Cycle

3

The Optimal Policy Problem

4

Optimal VAT Dynamics

5

Optimal Fiscal Consolidation

8 / 20

Implementability

Equilibrium conditions

Intratemporal: C σ

t Nφ t = (1 − τ v t )Wt

Pt Intertemporal: ˙ Ct Ct = σ−1(it − πt − ˙ τ v

t − ρ)

Pricing (flexible prices): S−α

t

= ǫ ǫ − 1 1 + τ p

t

1 − τ v

t

C σ

t Y φ t

9 / 20

Implementability

Equilibrium conditions

Intratemporal: C σ

t Nφ t = (1 − τ v t )Wt

Pt Intertemporal: ˙ Ct Ct = σ−1(it − πt − ˙ τ v

t − ρ)

Pricing (flexible prices): S−α

t

= ǫ ǫ − 1 1 + τ p

t

1 − τ v

t

C σ

t Y φ t

Implementability conditions:

Market clearing: Yt = (1 − α)Sα

t Ct + Gt + α ˜

Sγ

t C ∗ t

9 / 20

Implementability

Equilibrium conditions

Intratemporal: C σ

t Nφ t = (1 − τ v t )Wt

Pt Intertemporal: ˙ Ct Ct = σ−1(it − πt − ˙ τ v

t − ρ)

Pricing (flexible prices): S−α

t

= ǫ ǫ − 1 1 + τ p

t

1 − τ v

t

C σ

t Y φ t

Implementability conditions:

Market clearing: Yt = (1 − α)Sα

t Ct + Gt + α ˜

Sγ

t C ∗ t

External debt: ˙ Et = ρEt + ΓE 2

t + αSα−1 t

Ct − α ˜ Sγ−1

t

C ∗

t

9 / 20

The optimal policy problem

The Ramsey problem can be written as

max

{Ct,St, ˜ St,Yt,Gt,Et}

∞ e−ρt

• C 1−σ

t

1 − σ + χ log Gt − 1 1 + φ Yt At 1+φ dt subject to implementability conditions and St = S if prices are fully rigid.

10 / 20

The optimal policy problem

The Ramsey problem can be written as

max

{Ct,St, ˜ St,Yt,Gt,Et}

∞ e−ρt

• C 1−σ

t

1 − σ + χ log Gt − 1 1 + φ Yt At 1+φ dt subject to implementability conditions and St = S if prices are fully rigid.

Proposition (Optimal Fiscal Policy in Benchmark Economy)

Suppose prices are flexible and Γ = 0. Then, taxes are constant and 1 + τ p 1 − τ v ǫ ǫ − 1

• labor wedge

= 1; 1 + τ x

external wedge

= γ γ − 1; Gt = χ Y φ

t

• ptimal provision
• f public goods

Passive policy benchmark: keep taxes at level of stationary solution.

10 / 20

Suboptimality of stimulus spending

Proposition (Pecking order of fiscal instruments)

Suppose Γ ≥ 0, ρδ ≥ 0, and let gS

t ≡ gt + φyt denote stimulus spending.

1 Full set of instruments:

gS

t = 0.

2 No tax instruments:

gS

t = κφγt

where γt is the Lagrange multiplier on the pricing condition.

11 / 20

Suboptimality of stimulus spending

Proposition (Pecking order of fiscal instruments)

Suppose Γ ≥ 0, ρδ ≥ 0, and let gS

t ≡ gt + φyt denote stimulus spending.

1 Full set of instruments:

gS

t = 0.

2 No tax instruments:

gS

t = κφγt

where γt is the Lagrange multiplier on the pricing condition.

It is suboptimal to use spending to achieve stimulus

• The reason is that spending is a dominated instrument
• Recession creates a labor wedge:

”...when involuntary unemployment exists, the marginal disutility of labour is necessarily less than the utility of the marginal product,” Keynes (1936)

• Principle of Targeting: you should act directly in this margin

11 / 20

Outline

1

Currency union with imperfect financial markets

2

Capital Flow Reversals and Boom/Bust Cycle

3

The Optimal Policy Problem

4

Optimal VAT Dynamics

5

Optimal Fiscal Consolidation

11 / 20

Proposition (The debt-management motive)

Suppose prices are flexible, then

• Optimal taxes satisfy

ˆ τ v

t + ˆ

τ p

t = 0;

˙ ˆ τ v

t = −Γet

• External debt satisfy

et = e−νote0

12 / 20

Proposition (The debt-management motive)

Suppose prices are flexible, then

• Optimal taxes satisfy

ˆ τ v

t + ˆ

τ p

t = 0;

˙ ˆ τ v

t = −Γet

• External debt satisfy

et = e−νote0 Under flexible prices, it is optimal to set a declining VAT over time

• This shifts demand to the future
• Country then pays off external debt at a faster pace

Households do not internalize their impact on interest rate

• Intervention corrects this pecuniary externality

12 / 20

Proposition (Optimal VAT Dynamics)

Suppose prices are fully rigid, E0 > 0, and ψt = 0 for t ≥ 0. Then,

1 Optimal VAT dynamics:

˙ ˆ τ v

t =

−1 − α α ˙ ˆ ωL

t

• macro-stabilization

− Γet

• debt-management

.

2 Role of openness:

˙ ˆ τ v

t = χv r Γet,

where χv

r ∈ [−1, 1],

and χv

r > 0 iff α < α∗, for a threshold α∗ satisfying 0.5 < α∗ < 1.

13 / 20

Proposition (Optimal VAT Dynamics)

Suppose prices are fully rigid, E0 > 0, and ψt = 0 for t ≥ 0. Then,

1 Optimal VAT dynamics:

˙ ˆ τ v

t =

−1 − α α ˙ ˆ ωL

t

• macro-stabilization

− Γet

• debt-management

.

2 Role of openness:

˙ ˆ τ v

t = χv r Γet,

where χv

r ∈ [−1, 1],

and χv

r > 0 iff α < α∗, for a threshold α∗ satisfying 0.5 < α∗ < 1.

Two forces pushing in opposite directions:

• Debt-management: declining VAT to payoff debt at a faster pace
• Macro-stabilization: increasing VAT to stimulate the economy

13 / 20

Role of openness

Degree of openness plays important role

• If α → 1, planner aligns private and social cost of foreign goods
• Debt-management motive dominates

14 / 20

Role of openness

Degree of openness plays important role

• If α → 1, planner aligns private and social cost of foreign goods
• Debt-management motive dominates
• If α → 0, planner aligns private and social cost of domestic goods
• Macro-stabilization motive dominates

14 / 20

Role of openness

Degree of openness plays important role

• If α → 1, planner aligns private and social cost of foreign goods
• Debt-management motive dominates
• If α → 0, planner aligns private and social cost of domestic goods
• Macro-stabilization motive dominates

Macro-stabilization dominates if α < 0.5

Table: Share of foreign demand in private absorption

Portugal Italy Greece Spain PIGS

ςx ςc+ςx

35.7% 31.1% 26.5% 31.8% 31.3%

Source: Eurostat. Average value for the period 1998 through 2008.

Then, it is optimal to have an increasing path of VATs.

14 / 20

Outline

1

Currency union with imperfect financial markets

2

Capital Flow Reversals and Boom/Bust Cycle

3

The Optimal Policy Problem

4

Optimal VAT Dynamics

5

Optimal Fiscal Consolidation

14 / 20

Ramsey problem under sticky prices

Linear-quadratic problem:

min

[ct,st,gt,yt,et,πH,t]

∞ e−ρt σ(ςc + ςm)c2

t + ςgg 2 t + ǫ

κπ2

H,t + φy 2 t + ηss2 t + 2Γe2 t

• dt,

subject to

yt = ςcct + ςggt + ηsst, ˙ et = ρet − [ηsst − ςmct] , ˙ st = −πH,t, where ηs ≡ γςx + αςc, given s0 = 0 and e0 > 0.

15 / 20

Ramsey problem under sticky prices

Linear-quadratic problem:

min

[ct,st,gt,yt,et,πH,t]

∞ e−ρt σ(ςc + ςm)c2

t + ςgg 2 t + ǫ

κπ2

H,t + φy 2 t + ηss2 t + 2Γe2 t

• dt,

subject to

yt = ςcct + ςggt + ηsst, ˙ et = ρet − [ηsst − ςmct] , ˙ st = −πH,t, where ηs ≡ γςx + αςc, given s0 = 0 and e0 > 0.

15 / 20

Ramsey problem under sticky prices

Linear-quadratic problem:

min

[ct,st,gt,yt,et,πH,t]

∞ e−ρt σ(ςc + ςm)c2

t + ςgg 2 t + ǫ

κπ2

H,t + φy 2 t + ηss2 t + 2Γe2 t

• dt,

subject to

yt = ςcct + ςggt + ηsst, ˙ et = ρet − [ηsst − ςmct] , ˙ st = −πH,t, where ηs ≡ γςx + αςc, given s0 = 0 and e0 > 0.

15 / 20

Ramsey problem under sticky prices

Linear-quadratic problem:

min

[ct,st,gt,yt,et,πH,t]

∞ e−ρt σ(ςc + ςm)c2

t + ςgg 2 t + ǫ

κπ2

H,t + φy 2 t + ηss2 t + 2Γe2 t

• dt,

subject to

yt = ςcct + ςggt + ηsst, ˙ et = ρet − [ηsst − ςmct] , ˙ st = −πH,t, where ηs ≡ γςx + αςc, given s0 = 0 and e0 > 0.

Lemma (Labor wedge)

Suppose e0 > 0. Under the optimal policy, the labor wedge satisfies ˆ ωL

0 > 0,

lim

t→0 ˆ

ωL

t = 0,

∞ e−ρt ˆ ωL

t dt > 0.

15 / 20

Dynamics under optimal and passive fiscal policy

2 4 6 8

time

0.04 0.03 0.02 0.01 0.00 0.01

Output

2 4 6 8

time

0.00 0.02 0.04 0.06

Terms of trade

2 4 6 8

time

0.02 0.03 0.04 0.05

Net exports

2 4 6 8

time

0.05 0.10 0.15 0.20 0.25

External debt

Passive policy Optimal policy

16 / 20

Proposition (Optimal taxes: sticky prices)

Suppose e0 > 0. The optimal policy satisfies

1 Optimal VAT dynamics:

˙ ˆ τ v

t =

−1 − α α ˙ ˆ ωL

t

• macro stabilization

− Γet

• debt-management

.

2 Optimal payroll tax:

ˆ τ p

t + ˆ

τ v

t =

• 1 − ηs

ǫα

• ˆ

ωL

t .

A sufficient condition for the term in brackets to be positive is ǫ > γ. Optimality condition for VAT and payroll tax

• Condition for VAT is the same as for rigid prices
• Overall tax level depends on the labor wedge with an ambiguous sign

17 / 20

The determination of the tax level

Depending on parameters, it may be optimal to raise taxes

• One could expect the opposite: cut taxes to depreciate terms of trade
• Mimicking the flexible price allocation

This logic ignores the cost of inflation

• If ǫ is relatively low, it is optimal to cut taxes
• The planner depreciates the terms of trade to stimulate the economy
• If ǫ is relatively high, it is optimal to raise taxes
• This way the planner limits the (costly) deflation

A sufficient condition to be optimal raise taxes is ǫ > γ

• ǫ is an elasticity of substitution for disaggregated goods
• γ is an elasticity of substitution for bundles of goods
• Empirical estimates systematically point to ǫ >> γ

18 / 20

Taxes and debt under optimal and passive fiscal policy

1 2 3 4 5 6

• 0.02

0.00 0.02 0.04 0.06

Value- added tax

time

1 2 3 4 5 6

• 0.06
• 0.03

0.00 0.03 0.06

Payroll tax

time

Passive policy Optimal policy 1 2 3 4 5 6 0.00 0.05 0.10 0.15 0.20 0.25

Labor wedge

time

1 2 3 4 5 6 0.00 0.05 0.10 0.15

Government debt

time 19 / 20

Conclusion

In this paper, I study optimal fiscal policy in a currency union with a

• Macroeconomic stabilization motive
• Debt management motive

Lessons for fiscal policy

1 It is not optimal to use stimulus spending 2 VAT should increase over time 3 It is optimal to raise and front-load taxes, leading to a fiscal consolidation 20 / 20

Thanks!

20 / 20

Calibration

Calibration follows closely Gali and Monacelli (2008) φ ǫ ρ σ γ α ςg d 3.0 6.0 0.04 1.5 1.2 0.35 0.19 0.77 Price setting and spread shock

• Average price duration is set to three quarters
• Initial shock is 4% with half-life three years
• Value in line with experience of Italy and Spain

back 20 / 20

Net exports, growth, and real exchange rate

2002 2004 2006 2008 2010 2012 2014 2016

• 12
• 10
• 8
• 6
• 4
• 2

2

Net exports

% GDP

2002 2004 2006 2008 2010 2012 2014 2016 0.00 0.05 0.10 0.15 0.20 0.25

Cumulative growth differential

%

2002 2004 2006 2008 2010 2012 2014 2016 85 90 95 100

Real exchange rate

Portugal Italy Greece Spain

back 20 / 20