Redistributive Taxation in a Partial Insurance Economy Jonathan Heathcote Federal Reserve Bank of Minneapolis Kjetil Storesletten Federal Reserve Bank of Minneapolis, and Oslo University Gianluca Violante New York University University of Delaware, November 26th, 2012 Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Redistributive Taxation • How progressive should earnings taxation be? Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Redistributive Taxation • How progressive should earnings taxation be? • Arguments in favor of progressivity: 1. Social insurance of privately-uninsurable shocks 2. Redistribution from high to low innate ability Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Redistributive Taxation • How progressive should earnings taxation be? • Arguments in favor of progressivity: 1. Social insurance of privately-uninsurable shocks 2. Redistribution from high to low innate ability • Arguments against progressivity: 1. Distortion to distribution of labor supply 2. Distortion to human capital investment 3. Redistribution from low to high taste for leisure 4. Inefficient financing of G expenditures Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Ramsey Approach Government/Planner takes policy instruments and market structure as given, and chooses the CE that yields the largest social welfare • CE of an heterogeneous-agent, incomplete-market economy • Nonlinear tax/transfer system • Valued public expenditures also chosen by the government • Various social welfare functions Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Ramsey Approach Government/Planner takes policy instruments and market structure as given, and chooses the CE that yields the largest social welfare • CE of an heterogeneous-agent, incomplete-market economy • Nonlinear tax/transfer system • Valued public expenditures also chosen by the government • Various social welfare functions Tractable equilibrium framework clarifies economic forces shaping the optimal degree of progressivity Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Overview of the model • Huggett (1994) economy: ∞ -lived agents, idiosyncratic productivity risk, and a risk-free bond in zero net-supply, plus: Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Overview of the model • Huggett (1994) economy: ∞ -lived agents, idiosyncratic productivity risk, and a risk-free bond in zero net-supply, plus: 1. differential “innate” (learning) ability 2. endogenous skill investment + multiple-skill technology Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Overview of the model • Huggett (1994) economy: ∞ -lived agents, idiosyncratic productivity risk, and a risk-free bond in zero net-supply, plus: 1. differential “innate” (learning) ability 2. endogenous skill investment + multiple-skill technology 3. endogenous labor supply 4. heterogeneity in preferences for leisure 5. valued government expenditures Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Overview of the model • Huggett (1994) economy: ∞ -lived agents, idiosyncratic productivity risk, and a risk-free bond in zero net-supply, plus: 1. differential “innate” (learning) ability 2. endogenous skill investment + multiple-skill technology 3. endogenous labor supply 4. heterogeneity in preferences for leisure 5. valued government expenditures 6. additional partial private insurance (other assets, family, etc) Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Overview of the model • Huggett (1994) economy: ∞ -lived agents, idiosyncratic productivity risk, and a risk-free bond in zero net-supply, plus: 1. differential “innate” (learning) ability 2. endogenous skill investment + multiple-skill technology 3. endogenous labor supply 4. heterogeneity in preferences for leisure 5. valued government expenditures 6. additional partial private insurance (other assets, family, etc) • Steady-state analysis Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Demographics and preferences • Perpetual youth demographics with constant survival probability δ • Preferences over consumption ( c ) , hours ( h ) , publicly-provided goods ( G ) , and skill-investment effort ( s ) : ∞ � ( βδ ) t u i ( c it , h it , G ) U i = v i ( s i ) + E 0 t =0 s 2 − 1 i v i ( s i ) = κ i 2 µ log c it − exp( ϕ i ) h 1+ σ it u i ( c it , h it , G ) = 1 + σ + χ log G κ i ∼ Exp ( η ) � v ϕ � ϕ i ∼ N 2 , v ϕ Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Technology • Output is CES aggregator over continuum of skill types: �� ∞ � θ θ − 1 θ − 1 Y = N ( s ) ds , θ ∈ (1 , ∞ ) θ 0 • Aggregate effective hours by skill type: � 1 N ( s ) = I { s i = s } z i h i di 0 • Aggregate resource constraint: � 1 Y = c i di + G 0 Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Individual efficiency units of labor log z it = α it + ε it � � • α it = α i,t − 1 + ω it − v ω with ω it ∼ N 2 , v ω α i 0 = 0 ∀ i � � • ε it − v ε i.i.d. over time with ε it ∼ N 2 , v ε • ϕ ⊥ κ ⊥ ω ⊥ ε cross-sectionally and longitudinally Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Individual efficiency units of labor log z it = α it + ε it � � • α it = α i,t − 1 + ω it − v ω with ω it ∼ N 2 , v ω α i 0 = 0 ∀ i � � • ε it − v ε i.i.d. over time with ε it ∼ N 2 , v ε • ϕ ⊥ κ ⊥ ω ⊥ ε cross-sectionally and longitudinally • Pre-government earnings: y it = p ( s i ) × exp( α it + ε it ) × h it ���� ���� � �� � hours skill price efficiency determined by skill, fortune, and diligence Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Government • Runs a two-parameter tax/transfer function to redistribute and finance publicly-provided goods G • Disposable (post-government) earnings: y i = λy 1 − τ ˜ i • Government budget constraint (no government debt): � 1 � � y i − λy 1 − τ G = di i 0 Government chooses ( G, τ ) , and λ balances the budget residually Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Our model of fiscal redistribution T ( y i ) = y i − λy 1 − τ i • The parameter τ measures the rate of progressivity: ◮ τ = 1 : full redistribution → ˜ y i = λ T ′ ( y ) ◮ 0 < τ < 1 : progressivity → T ( y ) /y > 1 ◮ τ = 0 : no redistribution → flat tax 1 − λ T ′ ( y ) ◮ τ < 0 : regressivity → T ( y ) /y < 1 Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Our model of fiscal redistribution T ( y i ) = y i − λy 1 − τ i • The parameter τ measures the rate of progressivity: ◮ τ = 1 : full redistribution → ˜ y i = λ T ′ ( y ) ◮ 0 < τ < 1 : progressivity → T ( y ) /y > 1 ◮ τ = 0 : no redistribution → flat tax 1 − λ T ′ ( y ) ◮ τ < 0 : regressivity → T ( y ) /y < 1 • Marginal tax rate monotone in earnings • Negative average tax rates below y 0 = λ 1 τ Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Our model of fiscal redistribution 12 11.5 Log of Diisposable Income 11 10.5 10 9.5 9 9 9.5 10 10.5 11 11.5 12 Log of Pre Government Income • CPS 2005, Nobs = 52 , 539 : R 2 = 0 . 92 and τ = 0 . 18 Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Our model of fiscal redistribution 0.6 0.5 Marginal and average tax rates 0.4 0.3 0.2 0.1 US Marginal ( τ US = 0.18) 0 US Average ( τ US = 0.18) −0.1 −0.2 −0.3 −0.4 1 2 3 4 5 6 7 8 9 10 Labor Income (1 = Average Earnings) Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Representative Agent Warm Up log C − H 1+ σ max U = 1 + σ + χ log G C,H s.t. C + G = Y = H Y − λY 1 − τ G = Equilibrium allocations: log λ ∗ ( G, τ ) + (1 − τ ) log C RA ( G, τ ) = (1 + σ ) log(1 − τ ) 1 log H RA ( G, τ ) = (1 + σ ) log(1 − τ ) Heathcote -Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Representative Agent Optimal Policy • Welfare: W RA ( g, τ ) = log(1 + g ) + χ log g + (1 + χ )log(1 − τ ) − 1 − τ (1 + σ ) (1 + σ ) • Welfare maximizing ( g, τ ) pair: χ g ∗ = 1 + χ τ ∗ = − χ • Allocations are first best W RA ( τ ) = χ log χ − (1+ χ ) log(1+ χ )+(1+ χ )log(1 − τ ) − 1 − τ (1 + σ ) (1 + σ ) Heathcote -Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
Markets • Competitive good and labor markets • Competitive asset markets (all assets in zero net supply) ◮ Non state -contingent bond Heathcote-Storesletten-Violante, ”Redistributive Taxation in a Partial Insurance Economy”
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