Fiscal Policy and the Distribution of Consumption Risk M. Max Croce - - PowerPoint PPT Presentation

Fiscal Policy and the Distribution of Consumption Risk

• M. Max Croce

Thien T. Nguyen Lukas Schmid

UNC AT CHAPEL HILL

KENAN‐FLAGLER BUSINESS SCHOOL

Question

Given the current debate on fiscal interventions, we ask the following question:

◮ What are the long-term effects of government policies aimed at

short-run stabilization?

Question

Given the current debate on fiscal interventions, we ask the following question:

◮ What are the long-term effects of government policies aimed at

short-run stabilization?

• Budget deficits imply future financing needs
• Uncertainty about future fiscal policies and taxation
• How does this uncertainty affect long-term growth?

Question

Given the current debate on fiscal interventions, we ask the following question:

◮ What are the long-term effects of government policies aimed at

short-run stabilization?

• Budget deficits imply future financing needs
• Uncertainty about future fiscal policies and taxation
• How does this uncertainty affect long-term growth?

◮ What is the trade-off between short-run stabilization and long-run

welfare prospects?

Question

Given the current debate on fiscal interventions, we ask the following question:

◮ What are the long-term effects of government policies aimed at

short-run stabilization?

• Budget deficits imply future financing needs
• Uncertainty about future fiscal policies and taxation
• How does this uncertainty affect long-term growth?

◮ What is the trade-off between short-run stabilization and long-run

welfare prospects? We address this question in a version of the Lucas and Stokey (1983) economy with 2 twists

Question

Given the current debate on fiscal interventions, we ask the following question:

◮ What are the long-term effects of government policies aimed at

short-run stabilization?

• Budget deficits imply future financing needs
• Uncertainty about future fiscal policies and taxation
• How does this uncertainty affect long-term growth?

◮ What is the trade-off between short-run stabilization and long-run

welfare prospects? We address this question in a version of the Lucas and Stokey (1983) economy with 2 twists

◮ Endogenous growth

• Fiscal policy affects long-term growth prospects

◮ Recursive Epstein-Zin (EZ) preferences

• Agents care about long-run uncertainty

◮ Asset market data suggest a high price of long-run uncertainty

Step 1: Model

◮ Accumulation of product varieties (Romer 1990) ◮ EZ preferences

Notation and Feasibility

◮ Yt: total production ◮ Ct: aggregate consumption ◮ Gt: government expenditure

Notation and Feasibility

◮ Yt: total production ◮ Ct: aggregate consumption ◮ Gt: government expenditure ◮ St: aggregate investment in R&D ◮ At: total mass of intermediate products (.i.e, patents/blueprints) ◮ Xt: quantity of intermediate good produced

GDPt = Yt − AtXt = Ct + St + Gt

Government

◮ We assume exogenous government expenditures

Gt Yt = 1 1 + e−gyt ∈ (0, 1), where gyt = (1 − ρ)gy + ρggyt−1 + ǫG,t, ǫG,t ∼ N(0, σgy).

Government

◮ We assume exogenous government expenditures

Gt Yt = 1 1 + e−gyt ∈ (0, 1), where gyt = (1 − ρ)gy + ρggyt−1 + ǫG,t, ǫG,t ∼ N(0, σgy).

◮ A government policy finances expenditures Gt using a mix of

• labor income tax

Tt = τtWtLt

• public debt

Bt = Bt−1(1 + rf

t−1) + Gt − Tt

Consumers

◮ Agent has Epstein-Zin preferences defined over consumption and leisure:

Ut =

• (1 − β)u

1− 1

ψ

t

+ β(EtU 1−γ

t+1 )

1− 1 ψ 1−γ

• 1

1−1/ψ

ut =

• κC1−1/ν

t

+ (1 − κ)[At(1 − Lt)]1−1/ν

• 1

1−1/ν

Consumers

◮ Agent has Epstein-Zin preferences defined over consumption and leisure:

Ut =

• (1 − β)u

1− 1

ψ

t

+ β(EtU 1−γ

t+1 )

1− 1 ψ 1−γ

• 1

1−1/ψ

◮ Ordinally equivalent transformation:

Ut =

U

1− 1 ψ t

1− 1

ψ

• Ut ≈ (1 − δ) u

1− 1

ψ

t

1 − 1

ψ

+ δEt[ Ut+1]

• CRRA Preferences

− (γ − 1 ψ )V art[ Ut+1]κt

• Utility

Variance

Consumers

◮ Agent has Epstein-Zin preferences defined over consumption and leisure:

Ut =

• (1 − β)u

1− 1

ψ

t

+ β(EtU 1−γ

t+1 )

1− 1 ψ 1−γ

• 1

1−1/ψ

◮ Ordinally equivalent transformation:

Ut =

U

1− 1 ψ t

1− 1

ψ

• Ut ≈ (1 − δ) u

1− 1

ψ

t

1 − 1

ψ

+ δEt[ Ut+1]

• CRRA Preferences

− (γ − 1 ψ )V art[ Ut+1]κt

• Utility

Variance

◮ Stochastic Discount Factor:

Mt+1 = β

• U 1−γ

t+1

Et[U 1−γ

t+1 ]

1/ψ−γ

1−γ ut+1

ut 1

ν − 1 ψ Ct+1

Ct − 1

ν

Consumers

◮ Agent has Epstein-Zin preferences defined over consumption and leisure:

Ut =

• (1 − β)u

1− 1

ψ

t

+ β(EtU 1−γ

t+1 )

1− 1 ψ 1−γ

• 1

1−1/ψ

◮ Ordinally equivalent transformation:

Ut =

U

1− 1 ψ t

1− 1

ψ

• Ut ≈ (1 − δ) u

1− 1

ψ

t

1 − 1

ψ

+ δEt[ Ut+1]

• CRRA Preferences

− (γ − 1 ψ )V art[ Ut+1]κt

• Utility

Variance

◮ Stochastic Discount Factor:

Mt+1 = β

• U 1−γ

t+1

Et[U 1−γ

t+1 ]

1/ψ−γ

1−γ ut+1

ut 1

ν − 1 ψ Ct+1

Ct − 1

ν

◮ The intratemporal optimality condition on labor

MRSc,L

t

= (1 − τt) Tax Distortion Wt

Competitive Final Goods Sector

◮ Firm uses labor and a bundle of intermediate goods as inputs:

Yt = ΩtL1−α

t

At Xα

it di

• ◮ Growth comes from increasing measure of intermediate goods At.

◮ Ωt is the stationary productivity process in this economy:

log(Ωt) = ρ log(Ωt−1) + ǫt, ǫt ∼ N(0, σ2)

Competitive Final Goods Sector

◮ Firm uses labor and a bundle of intermediate goods as inputs:

Yt = ΩtL1−α

t

At Xα

it di

• ◮ Growth comes from increasing measure of intermediate goods At.

◮ Ωt is the stationary productivity process in this economy:

log(Ωt) = ρ log(Ωt−1) + ǫt, ǫt ∼ N(0, σ2)

◮ Intermediate goods are purchased at price Pit. Optimality implies:

Xit = Lt Atα Pit

• 1

1−α

Wt = (1 − α) Yt Lt

Intermediate Goods Sector

◮ The monopolist producing patent i ∈ [0, At] sets prices in order to

maximize profits: Πit ≡ max

Pit

PitXit Revenues − Xit

• Costs

= ( 1 α − 1)

• Markup

(Ωtα2)

1 1−α Lt ≡ ΘtLt

Intermediate Goods Sector

◮ The monopolist producing patent i ∈ [0, At] sets prices in order to

maximize profits: Πit ≡ max

Pit

PitXit Revenues − Xit

• Costs

= ( 1 α − 1)

• Markup

(Ωtα2)

1 1−α Lt ≡ ΘtLt

◮ Assume in each period intermediate goods become obsolete at rate δ. ◮ The value of a new patent is the PV of future profits

Vt = Et ∞

• j=0

(1 − δ)jMt+jΘt+jLt+j

R&D Sector

◮ Recall St denotes R&D investments, the measure of input variety At

evolves as: At+1 = ϑtSt + (1 − δ)At

• ϑt measures R&D productivity: ϑt = χ( St

At )η−1

R&D Sector

◮ Recall St denotes R&D investments, the measure of input variety At

evolves as: At+1 = ϑtSt + (1 − δ)At

• ϑt measures R&D productivity: ϑt = χ( St

At )η−1

◮ Free-entry condition:

1 ϑt

• Cost

= Et

• Mt+1Vt+1
• Benefit

Equilibrium Growth

◮ The equilibrium growth rate is given by

At+1 At = 1 − δ + χ

1 1−η Et [Mt+1Vt+1] η 1−η

Equilibrium Growth

◮ The equilibrium growth rate is given by

At+1 At = 1 − δ + χ

1 1−η Et [Mt+1Vt+1] η 1−η

Mt+1 = β

• U 1−γ

t+1

Et[U 1−γ

t+1 ]

1/ψ−γ

1−γ ut+1

ut 2− 1

ψ − 1 ν Ct+1

Ct − 1

ν

◮ Discount rate channel: Growth rate is negatively related to discount rate

and hence risk

• With recursive preferences, long-run uncertainty affects growth rate

Equilibrium Growth

◮ The equilibrium growth rate is given by

At+1 At = 1 − δ + χ

1 1−η Et [Mt+1Vt+1] η 1−η

= 1 − δ + χ

1 1−η Et

  

∞

• j=1

Mt+j|t(1 − δ)j−1Θt+jLt+j

• Profits

  

η 1−η

.

◮ Labor channel: Long-term movements in taxes affect future labor supply,

and hence profits and growth

• Short-run tax stabilization may come at the cost of slowdown in

growth

Step 2: Exogenous Fiscal Policy

◮ Goal: quantitatively characterize the trade-off between current vs

future taxation distortions risk

Step 2: Exogenous Fiscal Policy

◮ Goal: quantitatively characterize the trade-off between current vs

future taxation distortions risk

◮ Financing policy → consumption risk reallocated toward long-run

Step 2: Exogenous Fiscal Policy

◮ Goal: quantitatively characterize the trade-off between current vs

future taxation distortions risk

◮ Financing policy → consumption risk reallocated toward long-run ◮ Preference for early resolution of uncertainty → short-run

countercyclical fiscal policies lead to long-run distortions and sizeable welfare losses

Exogenous Policy Rule

◮ Government implements (uncontingent) debt policies of the form

Bt Yt = ρB Bt−1 Yt−1 + ǫB,t (1) ǫB,t = φG

1 · (log Lss − log Lt)

• Lss steady state level of labor
• φG

1 = 0: Zero deficit policy

⊲ Bt = 0 and ⊲ Gt = Tt

• φG

1 > 0: Countercyclical policy (tax smoothing)

Exogenous Policy Rule

◮ Government implements (uncontingent) debt policies of the form

Bt Yt = ρB Bt−1 Yt−1 + ǫB,t (1) ǫB,t = φG

1 · (log Lss − log Lt)

• Lss steady state level of labor
• φG

1 = 0: Zero deficit policy

⊲ Bt = 0 and ⊲ Gt = Tt

• φG

1 > 0: Countercyclical policy (tax smoothing)

◮ Combine (2) with Bt = (1 + rf,t−1)Bt−1 + Gt − Tt to recover the implied

tax-rate policy.

Fiscal variables after a negative productivity shock

50 100 150 200 250 300 −0.05 −0.04 −0.03 −0.02 −0.01 0.01

τStrong

t

− τZD

t

Quarters

100 200 300 400 500 0.01 0.02 0.03 0.04 0.05 0.06

BG/Y (%) Quarters

100 200 300 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1

Productivity, log(Ω) Quarters

Deficit Surplus

Calibration

Description Symbol Value Preference Parameters Consumption-Labor Elasticity ν 0.7 Utility Share of Consumption κ 0.095 Discount Factor β 0.996 Intertemporal Elasticity of Substitution ψ 1.7 Risk Aversion γ 7 Technology Parameters Elasticity of Substitution Between Intermediate Goods α 0.7 Autocorrelation of Productivity ρ 0.96 Scale Parameter χ 0.45 Survival rate of intermediate goods φ 0.97 Elasticity of New Intermediate Goods wrt R&D η 0.8 Standard of Deviation of Technology Shock σ 0.006 Government Expenditure Parameters Level of Expenditure-Output Ratio (G/Y ) gy −2.2 Autocorrelation of G/Y ρg 0.98 Standard deviation of G/Y shocks σg 0.008

Main Statistics

◮ Quarterly calibration; time aggregated annual statistics. Data Zero deficit φB = 0 E(∆c) 2.03 2.04 σ(∆c) 2.34 2.14 ACF1(∆c) 0.44 0.58 E(L) 33.0 35.63 E(τ) (%) 33.5 33.50 σ(τ) (%) 3.10 1.80 σ(m) (%) 43.24 E(rf ) 0.93 1.48 E(rC − rf ) 1.89 ◮ We use asset prices to discipline the calibration (Lustig et al 2008).

Welfare costs (WCs)

◮ Benchmark: the zero-deficit consumption process

E [U({Czd})]

◮ The welfare costs (benefits) of an alternative consumption process

C∗ is: log E [U({C∗})] − log E [U({Czd})]

Welfare costs (WCs)

◮ Benchmark: the zero-deficit consumption process

E [U({Czd})]

◮ The welfare costs (benefits) of an alternative consumption process

C∗ is: log E [U({C∗})] − log E [U({Czd})]

◮ Welfare reflects the present value of consumption, PC:

Ut = [(1 − δ) · (Pc,t + Ct)]

1 1−1/Ψ

Welfare costs (WCs) and consumption distribution

◮ Pc/C in the BY(2004) log-linear case:

∆ct+1 = µ + xt + σcǫc,t+1 xt = ρxxt−1 + σxǫx,t

◮ For explanation purposes, we map:

µ → E[∆ct] σc → StDt[∆ct+1] StD[xt] =

σx

√

1−ρ2

x

→ StD[Et[∆ct]] ρx → ACF1[Et[∆ct]]

Welfare costs (WCs) and consumption distribution

◮ Pc/C in the BY(2004) log-linear case:

∆ct+1 = µ + xt + σcǫc,t+1 xt = ρxxt−1 + σxǫx,t

◮ For explanation purposes, we map:

µ → E[∆ct] σc → StDt[∆ct+1] StD[xt] =

σx

√

1−ρ2

x

→ StD[Et[∆ct]] ρx → ACF1[Et[∆ct]]

◮ Debt policy {φB, ρB}: a device altering the distribution of

consumption risk. ∆ct+1 ≈ µ(φB, ρB) + xt + σc(φB, ρB)ǫc,t+1 xt ≡ Et[∆ct+1] = ρx(φB, ρB)xt−1 + σx(φB, ρB)ǫx,t

WCs when 1/IES=RRA=7 (CRRA)

◮ Small welfare benefits of tax smoothing

0.9 0.92 0.94 0.96 0.98 −5 −4 −3 −2 −1 x 10

−3

Welfare Costs (%) Faster ← Repayment → Slower Weak Strong 0.9 0.92 0.94 0.96 0.98 3.045 3.05 3.055 3.06 3.065 3.07 3.075 StDt(∆ct+1) (%) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 0.98 0.8 0.85 0.9 0.95 ACF1(Et[∆ct+1]) Annualized ACF1(BG/Y ), ρ4

B

0.9 0.92 0.94 0.96 0.98 0.1 0.15 0.2 0.25 0.3 0.35 0.4 StD(Et[∆ct+1]) (%) Annualized ACF1(BG/Y ), ρ4

B

WCs when 1/IES=RRA=7 (CRRA)

◮ Small welfare benefits of tax smoothing

0.9 0.92 0.94 0.96 0.98 −5 −4 −3 −2 −1 x 10

−3

Welfare Costs (%) Faster ← Repayment → Slower Weak Strong 0.9 0.92 0.94 0.96 0.98 3.045 3.05 3.055 3.06 3.065 3.07 3.075 StDt(∆ct+1) (%) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 0.98 0.8 0.85 0.9 0.95 ACF1(Et[∆ct+1]) Annualized ACF1(BG/Y ), ρ4

B

0.9 0.92 0.94 0.96 0.98 0.1 0.15 0.2 0.25 0.3 0.35 0.4 StD(Et[∆ct+1]) (%) Annualized ACF1(BG/Y ), ρ4

B

WCs when 1/IES=RRA=7 (CRRA)

◮ Small welfare benefits of tax smoothing

0.9 0.92 0.94 0.96 0.98 −5 −4 −3 −2 −1 x 10

−3

Welfare Costs (%) Faster ← Repayment → Slower Weak Strong 0.9 0.92 0.94 0.96 0.98 3.045 3.05 3.055 3.06 3.065 3.07 3.075 StDt(∆ct+1) (%) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 0.98 0.8 0.85 0.9 0.95 ACF1(Et[∆ct+1]) Annualized ACF1(BG/Y ), ρ4

B

0.9 0.92 0.94 0.96 0.98 0.1 0.15 0.2 0.25 0.3 0.35 0.4 StD(Et[∆ct+1]) (%) Annualized ACF1(BG/Y ), ρ4

B

WCs when IES=1.7 & RRA=7

◮ Substantial welfare costs of tax smoothing

0.9 0.92 0.94 0.96 0.98 0.5 1 1.5 Welfare Costs (%) Faster ← Repayment → Slower Weak Strong 0.9 0.92 0.94 0.96 0.98 0.7 0.8 0.9 1 1.1 1.2 StDt(∆ct+1) (%) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 0.98 0.86 0.88 0.9 0.92 0.94 0.96 ACF1(Et[∆ct+1]) Annualized ACF1(BG/Y ), ρ4

B

0.9 0.92 0.94 0.96 0.98 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 StD(Et[∆ct+1]) (%) Annualized ACF1(BG/Y ), ρ4

B

WCs when IES=1.7 & RRA=7

◮ Substantial welfare costs of tax smoothing

0.9 0.92 0.94 0.96 0.98 0.5 1 1.5 Welfare Costs (%) Faster ← Repayment → Slower Weak Strong 0.9 0.92 0.94 0.96 0.98 0.7 0.8 0.9 1 1.1 1.2 StDt(∆ct+1) (%) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 0.98 0.86 0.88 0.9 0.92 0.94 0.96 ACF1(Et[∆ct+1]) Annualized ACF1(BG/Y ), ρ4

B

0.9 0.92 0.94 0.96 0.98 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 StD(Et[∆ct+1]) (%) Annualized ACF1(BG/Y ), ρ4

B

WCs when IES=1.7 & RRA=7

◮ Substantial welfare costs of tax smoothing

0.9 0.92 0.94 0.96 0.98 0.5 1 1.5 Welfare Costs (%) Faster ← Repayment → Slower Weak Strong 0.9 0.92 0.94 0.96 0.98 0.7 0.8 0.9 1 1.1 1.2 StDt(∆ct+1) (%) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 0.98 0.86 0.88 0.9 0.92 0.94 0.96 ACF1(Et[∆ct+1]) Annualized ACF1(BG/Y ), ρ4

B

0.9 0.92 0.94 0.96 0.98 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 StD(Et[∆ct+1]) (%) Annualized ACF1(BG/Y ), ρ4

B

Patent value (V), profits (π) distribution, and growth

E [At+1/At] = 1 − δ + χ

1 1−η Et [Mt+1Vt+1] η 1−η 0.9 0.92 0.94 0.96 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 log(V ) − log(V ZD) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 4.4 4.6 4.8 5 5.2 5.4 StDt(∆πt+1) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 0.87 0.875 0.88 0.885 0.89 0.895 0.9 0.905 ACF1(Et[∆πt+1]) ACF1(BG/Y ), ρ4

B

0.9 0.92 0.94 0.96 0.4 0.5 0.6 0.7 0.8 StD(Et[∆πt+1]) ACF1(BG/Y ), ρ4

B

Weak Strong

Patent value (V), profits (π) distribution, and growth

E [At+1/At] = 1 − δ + χ

1 1−η Et [Mt+1Vt+1] η 1−η 0.9 0.92 0.94 0.96 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 log(V ) − log(V ZD) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 4.4 4.6 4.8 5 5.2 5.4 StDt(∆πt+1) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 0.87 0.875 0.88 0.885 0.89 0.895 0.9 0.905 ACF1(Et[∆πt+1]) ACF1(BG/Y ), ρ4

B

0.9 0.92 0.94 0.96 0.4 0.5 0.6 0.7 0.8 StD(Et[∆πt+1]) ACF1(BG/Y ), ρ4

B

Weak Strong

Patent value (V), profits (π) distribution, and growth

E [At+1/At] = 1 − δ + χ

1 1−η Et [Mt+1Vt+1] η 1−η 0.9 0.92 0.94 0.96 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 log(V ) − log(V ZD) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 4.4 4.6 4.8 5 5.2 5.4 StDt(∆πt+1) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 0.87 0.875 0.88 0.885 0.89 0.895 0.9 0.905 ACF1(Et[∆πt+1]) ACF1(BG/Y ), ρ4

B

0.9 0.92 0.94 0.96 0.4 0.5 0.6 0.7 0.8 StD(Et[∆πt+1]) ACF1(BG/Y ), ρ4

B

Weak Strong

The Term Structure of Profits Risk

10 20 30 40 50 60 −1 −0.5 0.5

Maturity (quarters)

EZ: Rπ,Active

n,t

− Rπ,ZD

n,t

(%)

10 20 30 40 50 60 −1 −0.5 0.5

CRRA: Rπ,Active

n,t

− Rπ,ZD

n,t

(%)

Maturity (quarters)

Less risk More risk

Long-Run Stabilization (I): stabilize Vt.

◮ The government now adopts the following rule:

Bt Yt = ρB Bt−1 Yt−1 + ǫB,t (2) ǫB,t = φG

1 · (V − Vt)

• V unconditional average
• φG

1 = 0: Zero deficit policy

⊲ Bt = 0 and ⊲ Gt = Tt

• φG

1 > 0: long-term oriented tax smoothing

Long-Run Stabilization: Results

0.9 0.92 0.94 0.96 0.98 1 −0.8 −0.6 −0.4 −0.2 Welfare Costs (%) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 0.98 1 1.3 1.4 1.5 1.6 1.7 StDt(∆ct+1) (%) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 0.98 1 0.8 0.82 0.84 0.86 0.88 0.9 ACF1(Et[∆ct+1]) Annualized ACF1(BG/Y ), ρ4

B

0.9 0.92 0.94 0.96 0.98 1 0.45 0.5 0.55 0.6 0.65 0.7 0.75 StD(Et[∆ct+1]) (%) Annualized ACF1(BG/Y ), ρ4

B

Weak Strong

Long-Run Stabilization: Results

0.9 0.92 0.94 0.96 2 4 6 8 10 12 14 16 x 10

−3

log(V ) − log(V ZD) Faster ← Repayment → Slower Weak Strong 0.9 0.92 0.94 0.96 5.8 5.85 5.9 5.95 StDt(∆πt+1) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 0.845 0.85 0.855 ACF1(Et[∆πt+1]) ACF1(BG/Y ), ρ4

B

0.9 0.92 0.94 0.96 0.12 0.13 0.14 0.15 0.16 0.17 0.18 StD(Et[∆πt+1]) ACF1(BG/Y ), ρ4

B

Conclusions

◮ Results:

• Endogenous growth: short-run stabilization can come at the cost of

lower long-run stability

• EZ preferences: ‘standard’ tax smoothing may not be as good as

you think

Conclusions

◮ Results:

• Endogenous growth: short-run stabilization can come at the cost of

lower long-run stability

• EZ preferences: ‘standard’ tax smoothing may not be as good as

you think

◮ Asset Pricing Perspective:

• Fiscal policy alters long-run growth risk and wealth

Conclusions

◮ Results:

• Endogenous growth: short-run stabilization can come at the cost of

lower long-run stability

• EZ preferences: ‘standard’ tax smoothing may not be as good as

you think

◮ Asset Pricing Perspective:

• Fiscal policy alters long-run growth risk and wealth

◮ Fiscal Policy Perspective:

• Financial markets dynamics are essential to design optimal fiscal

policy

Conclusions

◮ Results:

• Endogenous growth: short-run stabilization can come at the cost of

lower long-run stability

• EZ preferences: ‘standard’ tax smoothing may not be as good as

you think

◮ Asset Pricing Perspective:

• Fiscal policy alters long-run growth risk and wealth

◮ Fiscal Policy Perspective:

• Financial markets dynamics are essential to design optimal fiscal

policy

◮ Broader Point:

• Conveying the need of introducing risk considerations in the current

fiscal debate

Step 4: Link to Ramsey’s Problem

◮ Write Ramsey FOCs determining optimal policy ◮ Goal: qualitative analysis of relevance of the intertemporal

distribution of tax distortions with EZ

◮ Optimal policy: Croce-Karantounias-Nguyen-Schmid (2013)

Ramsey Problem

max

{Ct,Lt,St,At+1}∞

t=0,ht

U0 = W(u0, U1) subject to Yt = Ct + AtXt + St + Gt (3) Υ0 =

∞

• t=0
• ht
• t
• j=1

W2(uj−1, Uj)

• W1(ut, Ut+1)[uCtCt + uLtLt]

(4) where

◮ Υ0 = W1(u0, U1)uC0(Q0 + D0)

Ramsey Problem

max

{Ct,Lt,St,At+1}∞

t=0,ht

U0 = W(u0, U1) subject to Yt = Ct + AtXt + St + Gt (3) Υ0 =

∞

• t=0
• ht
• t
• j=1

W2(uj−1, Uj)

• W1(ut, Ut+1)[uCtCt + uLtLt]

(4) where

◮ Υ0 = W1(u0, U1)uC0(Q0 + D0)

and subject to At+1 = ϑtSt + (1 − δ)At (5) 1 ϑt = Et [Mt+1Vt+1] (6) Ut = W(ut, Ut+1) (7)

Optimal Tax policy (I): FOC Ct

◮ Let:

• uRam,EZ

C,t

and uRam,SL

C,t

be the multiplier attached to the resource constraint in benchmark model, and Lucas and Stokey (1983)

• ξ and Ot be multipliers on the implementability & free-entry

constraints

• ΞC,t =

∂Mt+1/∂Ct Mt+1

uRam,EZ

Ct

= W1tuRam,SL

Ct

− OtΞC,tVt

• Incentives

+ ξW1tuCtFDt

• Distortions

Optimal Tax policy (I): FOC Ct

◮ Let:

• uRam,EZ

C,t

and uRam,SL

C,t

be the multiplier attached to the resource constraint in benchmark model, and Lucas and Stokey (1983)

• ξ and Ot be multipliers on the implementability & free-entry

constraints

• ΞC,t =

∂Mt+1/∂Ct Mt+1

uRam,EZ

Ct

= W1tuRam,SL

Ct

− OtΞC,tVt

• Incentives

+ ξW1tuCtFDt

• Distortions

◮ Endogenous growth: incentives for growth depend on asset prices, Vt

Optimal Tax policy (I): FOC Ct

◮ Let:

• uRam,EZ

C,t

and uRam,SL

C,t

be the multiplier attached to the resource constraint in benchmark model, and Lucas and Stokey (1983)

• ξ and Ot be multipliers on the implementability & free-entry

constraints

• ΞC,t =

∂Mt+1/∂Ct Mt+1

uRam,EZ

Ct

= W1tuRam,SL

Ct

− OtΞC,tVt

• Incentives

+ ξW1tuCtFDt

• Distortions

◮ Endogenous growth: incentives for growth depend on asset prices, Vt ◮ EZ: Ramsey cares about future distortions, i.e., Ut+1 smoothing

FDt = (uCtCt + uLtLt) W11t W1t + W1tW22t−1 W2t−1

Optimal Tax policy (II): FOC Lt

◮ Let ΞL,t =

∂Mt+1/∂Lt Mt+1

.

◮ Let MPL denote the marginal product of labor:

MPLt = MRSRam,EZ

Ct,Lt

= uRam,SL

Lt

+ ξuLtFDt − OC,tΞC,tVt uRam,SL

Ct

+ ξuCtFDt − OL,tΞL,tVt

◮ Intuition: Ramsey planner aims at smoothing consumption and

continuation utilities

Optimal Tax policy (II): FOC Lt

◮ Let ΞL,t =

∂Mt+1/∂Lt Mt+1

.

◮ Let MPL denote the marginal product of labor:

MPLt = MRSRam,EZ

Ct,Lt

= uRam,SL

Lt

+ ξuLtFDt − OC,tΞC,tVt uRam,SL

Ct

+ ξuCtFDt − OL,tΞL,tVt

◮ Intuition: Ramsey planner aims at smoothing consumption and

continuation utilities

• Continuation utilites reflect future tax distortions (FD)
• Continuation utilites reflect future growth prospects (incentives)

◮ Intertemporal distribution of consumption reflects policy

∆ct+1 ≈ xt + σc(Ψ)ǫc,t+1 xt ≡ Et[∆ct+1] = ρx(Ψ)xt−1 + σx(Ψ)ǫx,t

Optimal Tax policy (III): FOC At+1

◮ Let:

• V Ram

t

denote the shadow value of one extra patent

• M Ram

t+1

be the adjusted SDF embodying uRam,EZ

Ct

: Mt+1 = W2tW1t+1uCt+1 W1tuCt M Ram

t+1

= W2tW1t+1uRam,EZ

Ct+1

W1tuRam,EZ

Ct

• MPAt be the marginal product of a new patent

Optimal Tax policy (III): FOC At+1

◮ Let:

• V Ram

t

denote the shadow value of one extra patent

• M Ram

t+1

be the adjusted SDF embodying uRam,EZ

Ct

: Mt+1 = W2tW1t+1uCt+1 W1tuCt M Ram

t+1

= W2tW1t+1uRam,EZ

Ct+1

W1tuRam,EZ

Ct

• MPAt be the marginal product of a new patent

◮ The accumulation of varieties under the optimal tax policy satisfies:

V Ram

t

= Et

• M Ram

t+1

• MPAt+1 + (1 − δ)V Ram

t+1

+ (ηV Ram

t+1 ϑt+1 − 1) St+1

At+1

Price of Long-Run Uncertainty

◮ Bansal and Yaron (2004): high premia on long-run uncertainty

rationalize asset price puzzles

◮ Alvarez and Jermann (2004) compute marginal costs of fluctuations

from asset prices. They find

• costs of business cycles (SRR) to be small
• costs of low-frequency movements in consumption (LRR) to be

substantial

We examine fiscal policy design in the presence of high costs of endogenous long-run consumption uncertainty

The Role of IES (I)

0.5 1 1.5 0.1 0.2 0.3 0.4 0.5

Welfare Costs (%) IES, ψ ← CRRA

ρ4

B = 0.9

ρ4

B = 0.97

The Role of IES (II): IES = 1

◮ Smooth taxes, but not too much...

0.9 0.92 0.94 0.96 0.98 1 −0.025 −0.02 −0.015 −0.01 −0.005 0.005 Welfare Costs (%) Faster ← Repayment → Slower Weak Medium Strong 0.9 0.92 0.94 0.96 0.98 1 3 3.05 3.1 3.15 3.2 3.25 StDt(∆ ct+1) (%) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 0.98 1 0.884 0.886 0.888 0.89 0.892 0.894 0.896 0.898 ACF1(Et[∆ ct+1]) Annualized ACF1(BG/Y), ρB

4

0.9 0.92 0.94 0.96 0.98 1 0.15 0.16 0.17 0.18 0.19 0.2 0.21 StD(Et[∆ ct+1]) (%) Annualized ACF1(BG/Y), ρB

4

96 .96

Utility Mean-Variance Frontier

1.023 1.0235 1.024 1.0245 5.7 5.702 5.704 5.706 5.708 5.71 5.712 5.714 5.716

Std[Ut/ct] (%) E[Ut/ct] low ρB → ← low ρB

Weak Strong

Impulse responses: G ↑

At+1 At = 1 − δ + χ

1 1−η Et [Mt+1Vt+1] η 1−η

Impulse responses: G ↑ and IES = 1/RRA (CRRA)

At+1 At = 1 − δ + χ

1 1−η Et [Mt+1Vt+1] η 1−η

Income effects?

◮ Crowding out

MRS = (1 − τ)W C = Y − S − AX − G

Income effects?

◮ Crowding out

MRS = (1 − τ)W C = Y − S − AX − G

◮ A possible way to isolate the distortionary effect

MRS = (1 − τ)W C = Y − S − AX

• Tax is transfered back to household in lump-sum.

WCs and consumption distribution with transfer

◮ Substantial welfare costs even with lump-sum transfer

0.9 0.92 0.94 0.96 0.98 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Welfare Costs (%) Faster ← Repayment → Slower Weak Strong 0.9 0.92 0.94 0.96 0.98 1.4 1.5 1.6 1.7 1.8 StDt(∆ct+1) (%) Faster ← Repayment → Slower 0.9 0.92 0.94 0.96 0.98 0.86 0.88 0.9 0.92 0.94 0.96 ACF1(Et[∆ct+1]) Annualized ACF1(BG/Y ), ρ4

B

0.9 0.92 0.94 0.96 0.98 0.55 0.6 0.65 0.7 0.75 StD(Et[∆ct+1]) (%) Annualized ACF1(BG/Y ), ρ4

B

Agenda

Where we are coming from:

◮ Croce, Kung, Nguyen, Schmid (RFS 2012): ”Fiscal Policies and

Asset Prices” AP implications of corporate tax smoothing in an RBC model with financial leverage.

Agenda

Where we are coming from:

◮ Croce, Kung, Nguyen, Schmid (RFS 2012): ”Fiscal Policies and

Asset Prices” AP implications of corporate tax smoothing in an RBC model with financial leverage.

◮ Croce, Nguyen, Schmid (JME 2012):“Market Price of Fiscal

Uncertainty”, robustness concerns about public debt policy with endogenous growth;

Agenda

Where we are coming from:

◮ Croce, Kung, Nguyen, Schmid (RFS 2012): ”Fiscal Policies and

Asset Prices” AP implications of corporate tax smoothing in an RBC model with financial leverage.

◮ Croce, Nguyen, Schmid (JME 2012):“Market Price of Fiscal

Uncertainty”, robustness concerns about public debt policy with endogenous growth; What’s next?

◮ Nguyen (2013)“Bank Capital Requirements: A Quantitative

Analysis”, financial intermediaries: stabilization versus growth.

Agenda

Where we are coming from:

◮ Croce, Kung, Nguyen, Schmid (RFS 2012): ”Fiscal Policies and

Asset Prices” AP implications of corporate tax smoothing in an RBC model with financial leverage.

◮ Croce, Nguyen, Schmid (JME 2012):“Market Price of Fiscal

Uncertainty”, robustness concerns about public debt policy with endogenous growth; What’s next?

◮ Nguyen (2013)“Bank Capital Requirements: A Quantitative

Analysis”, financial intermediaries: stabilization versus growth.

◮ Diercks (2013)“Inflating Debt Away: Trading Off Inflation and

Taxation Risk”, fiscal policy first order also in neo-keynesian models.

Agenda

Where we are coming from:

◮ Croce, Kung, Nguyen, Schmid (RFS 2012): ”Fiscal Policies and

Asset Prices” AP implications of corporate tax smoothing in an RBC model with financial leverage.

◮ Croce, Nguyen, Schmid (JME 2012):“Market Price of Fiscal

Uncertainty”, robustness concerns about public debt policy with endogenous growth; What’s next?

◮ Nguyen (2013)“Bank Capital Requirements: A Quantitative

Analysis”, financial intermediaries: stabilization versus growth.

◮ Diercks (2013)“Inflating Debt Away: Trading Off Inflation and

Taxation Risk”, fiscal policy first order also in neo-keynesian models.