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 ◮ Y t : total production ◮ C t : aggregate consumption ◮ G t : government expenditure

Notation and Feasibility ◮ Y t : total production ◮ C t : aggregate consumption ◮ G t : government expenditure ◮ S t : aggregate investment in R&D ◮ A t : total mass of intermediate products (.i.e, patents/blueprints) ◮ X t : quantity of intermediate good produced GDP t = Y t − A t X t = C t + S t + G t

Government ◮ We assume exogenous government expenditures G t 1 = 1 + e − gy t ∈ (0 , 1) , Y t where gy t = (1 − ρ ) gy + ρ g gy t − 1 + ǫ G,t , ǫ G,t ∼ N (0 , σ gy ) .

Government ◮ We assume exogenous government expenditures G t 1 = 1 + e − gy t ∈ (0 , 1) , Y t where gy t = (1 − ρ ) gy + ρ g gy t − 1 + ǫ G,t , ǫ G,t ∼ N (0 , σ gy ) . ◮ A government policy finances expenditures G t using a mix of ◦ labor income tax T t = τ t W t L t ◦ public debt B t = B t − 1 (1 + r f t − 1 ) + G t − T t

Consumers ◮ Agent has Epstein-Zin preferences defined over consumption and leisure: � � 1 1 − 1 1 − 1 1 − 1 /ψ ψ + β ( E t U 1 − γ ψ = (1 − β ) u t +1 ) U t 1 − γ t � � 1 1 − 1 /ν κC 1 − 1 /ν + (1 − κ )[ A t (1 − L t )] 1 − 1 /ν u t = t

Consumers ◮ Agent has Epstein-Zin preferences defined over consumption and leisure: � � 1 1 − 1 1 − 1 ψ 1 − 1 /ψ + β ( E t U 1 − γ ψ = (1 − β ) u t +1 ) U t 1 − γ t 1 − 1 ψ ◮ Ordinally equivalent transformation: � U U t = t 1 − 1 ψ 1 − 1 ψ − ( γ − 1 U t ≈ (1 − δ ) u � + δE t [ � ψ ) V ar t [ � t U t +1 ] U t +1 ] κ t 1 − 1 ψ � �� � � �� � Utility CRRA Preferences Variance

Consumers ◮ Agent has Epstein-Zin preferences defined over consumption and leisure: � � 1 1 − 1 1 − 1 ψ 1 − 1 /ψ + β ( E t U 1 − γ ψ = (1 − β ) u t +1 ) U t 1 − γ t 1 − 1 ψ ◮ Ordinally equivalent transformation: � U U t = t 1 − 1 ψ 1 − 1 ψ − ( γ − 1 U t ≈ (1 − δ ) u � + δE t [ � ψ ) V ar t [ � t U t +1 ] U t +1 ] κ t 1 − 1 ψ � �� � � �� � Utility CRRA Preferences Variance ◮ Stochastic Discount Factor: � � 1 /ψ − γ 1 − γ � u t +1 � 1 ψ � C t +1 � − 1 ν − 1 U 1 − γ ν t +1 M t +1 = β E t [ U 1 − γ t +1 ] u t C t

Consumers ◮ Agent has Epstein-Zin preferences defined over consumption and leisure: � � 1 1 − 1 1 − 1 ψ 1 − 1 /ψ + β ( E t U 1 − γ ψ = (1 − β ) u t +1 ) U t 1 − γ t 1 − 1 ψ ◮ Ordinally equivalent transformation: � U U t = t 1 − 1 ψ 1 − 1 ψ − ( γ − 1 U t ≈ (1 − δ ) u � + δE t [ � ψ ) V ar t [ � t U t +1 ] U t +1 ] κ t 1 − 1 ψ � �� � � �� � Utility CRRA Preferences Variance ◮ Stochastic Discount Factor: � � 1 /ψ − γ 1 − γ � u t +1 � 1 ψ � C t +1 � − 1 ν − 1 U 1 − γ ν t +1 M t +1 = β E t [ U 1 − γ t +1 ] u t C t ◮ The intratemporal optimality condition on labor MRS c,L = (1 − τ t ) W t t � �� � Tax Distortion

Competitive Final Goods Sector ◮ Firm uses labor and a bundle of intermediate goods as inputs: �� A t � Y t = Ω t L 1 − α X α it di t 0 ◮ Growth comes from increasing measure of intermediate goods A t . ◮ Ω t is the stationary productivity process in this economy: ǫ t ∼ N (0 , σ 2 ) log(Ω t ) = ρ log(Ω t − 1 ) + ǫ t ,

Competitive Final Goods Sector ◮ Firm uses labor and a bundle of intermediate goods as inputs: �� A t � Y t = Ω t L 1 − α X α it di t 0 ◮ Growth comes from increasing measure of intermediate goods A t . ◮ Ω t is the stationary productivity process in this economy: ǫ t ∼ N (0 , σ 2 ) log(Ω t ) = ρ log(Ω t − 1 ) + ǫ t , ◮ Intermediate goods are purchased at price P it . Optimality implies: � A t α � 1 1 − α = X it L t P it (1 − α ) Y t W t = L t

Intermediate Goods Sector ◮ The monopolist producing patent i ∈ [0 , A t ] sets prices in order to maximize profits: Π it max ≡ P it X it − X it � �� � ���� P it Revenues Costs ( 1 1 (Ω t α 2 ) 1 − α L t ≡ Θ t L t = α − 1) � �� � Markup

Intermediate Goods Sector ◮ The monopolist producing patent i ∈ [0 , A t ] sets prices in order to maximize profits: Π it max ≡ P it X it − X it � �� � ���� P it Revenues Costs ( 1 1 (Ω t α 2 ) 1 − α L t ≡ Θ t L t = α − 1) � �� � Markup ◮ Assume in each period intermediate goods become obsolete at rate δ . ◮ The value of a new patent is the PV of future profits � ∞ � � (1 − δ ) j M t + j Θ t + j L t + j V t = E t j =0

R&D Sector ◮ Recall S t denotes R&D investments, the measure of input variety A t evolves as: A t +1 = ϑ t S t + (1 − δ ) A t ◦ ϑ t measures R&D productivity: ϑ t = χ ( S t A t ) η − 1

R&D Sector ◮ Recall S t denotes R&D investments, the measure of input variety A t evolves as: A t +1 = ϑ t S t + (1 − δ ) A t ◦ ϑ t measures R&D productivity: ϑ t = χ ( S t A t ) η − 1 ◮ Free-entry condition: � � 1 = E t M t +1 V t +1 ϑ t ���� � �� � Cost Benefit

Equilibrium Growth ◮ The equilibrium growth rate is given by A t +1 η 1 1 − η E t [ M t +1 V t +1 ] = 1 − δ + χ 1 − η A t

Equilibrium Growth ◮ The equilibrium growth rate is given by A t +1 η 1 1 − η E t [ M t +1 V t +1 ] = 1 − δ + χ 1 − η A t � � 1 /ψ − γ 1 − γ � u t +1 � 2 − 1 ν � C t +1 � − 1 ψ − 1 U 1 − γ ν t +1 M t +1 = β E t [ U 1 − γ u t C t t +1 ] ◮ 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 A t +1 η 1 1 − η E t [ M t +1 V t +1 ] = 1 − δ + χ 1 − η A t   η 1 − η ∞ �   1 1 − η E t M t + j | t (1 − δ ) j − 1 Θ t + j L t + j = 1 − δ + χ .   � �� � j =1 Profits ◮ 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