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The Distributional Consequences of Government Spending Santanu Chatterjee University of Georgia Stephen J. Turnovsky University of Washington Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 1 / 26 Background Government

  1. The Analytical Framework Source of heterogeneity: initial distribution of private capital (wealth) (Atkinson 2003, Checchi and Garcia-Penalosa 2010) Labor-leisure choice is endogenous Initial distribution of private capital = ) equilibrium distribution of labor supply = ) distribution of income and welfare Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 6 / 26

  2. The Analytical Framework Source of heterogeneity: initial distribution of private capital (wealth) (Atkinson 2003, Checchi and Garcia-Penalosa 2010) Labor-leisure choice is endogenous Initial distribution of private capital = ) equilibrium distribution of labor supply = ) distribution of income and welfare Government-provided public capital: Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 6 / 26

  3. The Analytical Framework Source of heterogeneity: initial distribution of private capital (wealth) (Atkinson 2003, Checchi and Garcia-Penalosa 2010) Labor-leisure choice is endogenous Initial distribution of private capital = ) equilibrium distribution of labor supply = ) distribution of income and welfare Government-provided public capital: non-rival and non-excludable ( pure public good) Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 6 / 26

  4. The Analytical Framework Source of heterogeneity: initial distribution of private capital (wealth) (Atkinson 2003, Checchi and Garcia-Penalosa 2010) Labor-leisure choice is endogenous Initial distribution of private capital = ) equilibrium distribution of labor supply = ) distribution of income and welfare Government-provided public capital: non-rival and non-excludable ( pure public good) Interacts with private capital to generate composite externalities for both labor (in production) and leisure (in utility) Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 6 / 26

  5. The Analytical Framework Source of heterogeneity: initial distribution of private capital (wealth) (Atkinson 2003, Checchi and Garcia-Penalosa 2010) Labor-leisure choice is endogenous Initial distribution of private capital = ) equilibrium distribution of labor supply = ) distribution of income and welfare Government-provided public capital: non-rival and non-excludable ( pure public good) Interacts with private capital to generate composite externalities for both labor (in production) and leisure (in utility) …nanced by a range of distortionary taxes (on capital, labor, or consumption) or debt/lumpsum taxes Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 6 / 26

  6. The Analytical Framework Source of heterogeneity: initial distribution of private capital (wealth) (Atkinson 2003, Checchi and Garcia-Penalosa 2010) Labor-leisure choice is endogenous Initial distribution of private capital = ) equilibrium distribution of labor supply = ) distribution of income and welfare Government-provided public capital: non-rival and non-excludable ( pure public good) Interacts with private capital to generate composite externalities for both labor (in production) and leisure (in utility) …nanced by a range of distortionary taxes (on capital, labor, or consumption) or debt/lumpsum taxes a determinant of growth and distributional dynamics: a¤ects relative factor returns Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 6 / 26

  7. The Model Firms and Technology Firms (indexed by j ) are all identical and use the following CES production technology h i � 1 / ρ α ( X P L j ) � ρ + ( 1 � α ) K � ρ Y j = A j Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 7 / 26

  8. The Model Firms and Technology Firms (indexed by j ) are all identical and use the following CES production technology h i � 1 / ρ α ( X P L j ) � ρ + ( 1 � α ) K � ρ Y j = A j L j : employment of labor by …rm j Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 7 / 26

  9. The Model Firms and Technology Firms (indexed by j ) are all identical and use the following CES production technology h i � 1 / ρ α ( X P L j ) � ρ + ( 1 � α ) K � ρ Y j = A j L j : employment of labor by …rm j K j : employment of private capital by …rm j Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 7 / 26

  10. The Model Firms and Technology Firms (indexed by j ) are all identical and use the following CES production technology h i � 1 / ρ α ( X P L j ) � ρ + ( 1 � α ) K � ρ Y j = A j L j : employment of labor by …rm j K j : employment of private capital by …rm j X P = K ε K 1 � ε : composite "public-private" externality ( 0 � ε � 1 ) G Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 7 / 26

  11. The Model Firms and Technology Firms (indexed by j ) are all identical and use the following CES production technology h i � 1 / ρ α ( X P L j ) � ρ + ( 1 � α ) K � ρ Y j = A j L j : employment of labor by …rm j K j : employment of private capital by …rm j X P = K ε K 1 � ε : composite "public-private" externality ( 0 � ε � 1 ) G K : aggregate stock of private capital-amalgam of physical and human capital, as in Romer (1986) Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 7 / 26

  12. The Model Firms and Technology Firms (indexed by j ) are all identical and use the following CES production technology h i � 1 / ρ α ( X P L j ) � ρ + ( 1 � α ) K � ρ Y j = A j L j : employment of labor by …rm j K j : employment of private capital by …rm j X P = K ε K 1 � ε : composite "public-private" externality ( 0 � ε � 1 ) G K : aggregate stock of private capital-amalgam of physical and human capital, as in Romer (1986) K G : aggregate stock of public capital (infrastructure), provided by the government Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 7 / 26

  13. The Model Firms and Technology Firms (indexed by j ) are all identical and use the following CES production technology h i � 1 / ρ α ( X P L j ) � ρ + ( 1 � α ) K � ρ Y j = A j L j : employment of labor by …rm j K j : employment of private capital by …rm j X P = K ε K 1 � ε : composite "public-private" externality ( 0 � ε � 1 ) G K : aggregate stock of private capital-amalgam of physical and human capital, as in Romer (1986) K G : aggregate stock of public capital (infrastructure), provided by the government s = 1 / ( 1 + ρ ) : elasticity of substitution between private capital and "e¤ective" labor in production Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 7 / 26

  14. The Model Firms and Technology Since all …rms are identical, the production function pins down the economy-wide average real wage and return on capital: � y ( z , l ) � 1 + ρ ω ( z , l ) = α A � ρ z � ρ ( 1 � ε ) w = ω ( z , l ) K , 1 � l r = r ( z , l ) � ( 1 � α ) A � ρ y ( z , l ) 1 + ρ Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 8 / 26

  15. The Model Firms and Technology Since all …rms are identical, the production function pins down the economy-wide average real wage and return on capital: � y ( z , l ) � 1 + ρ ω ( z , l ) = α A � ρ z � ρ ( 1 � ε ) w = ω ( z , l ) K , 1 � l r = r ( z , l ) � ( 1 � α ) A � ρ y ( z , l ) 1 + ρ z = K G / K : economy-wide ratio of public to private capital Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 8 / 26

  16. The Model Firms and Technology Since all …rms are identical, the production function pins down the economy-wide average real wage and return on capital: � y ( z , l ) � 1 + ρ ω ( z , l ) = α A � ρ z � ρ ( 1 � ε ) w = ω ( z , l ) K , 1 � l r = r ( z , l ) � ( 1 � α ) A � ρ y ( z , l ) 1 + ρ z = K G / K : economy-wide ratio of public to private capital L = 1 � l : average employment of labor Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 8 / 26

  17. The Model Firms and Technology Since all …rms are identical, the production function pins down the economy-wide average real wage and return on capital: � y ( z , l ) � 1 + ρ ω ( z , l ) = α A � ρ z � ρ ( 1 � ε ) w = ω ( z , l ) K , 1 � l r = r ( z , l ) � ( 1 � α ) A � ρ y ( z , l ) 1 + ρ z = K G / K : economy-wide ratio of public to private capital L = 1 � l : average employment of labor h i � 1 / ρ � ( 1 � l ) z 1 � ε � � ρ + ( 1 � α ) y ( z , l ) = A α : average product of private capital (output-capital ratio) Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 8 / 26

  18. The Model Consumers Continuum of in…nitely-lived consumers, indexed by i Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 9 / 26

  19. The Model Consumers Continuum of in…nitely-lived consumers, indexed by i Identical in all respects, except for initial endowment of private capital (wealth), K i , 0 Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 9 / 26

  20. The Model Consumers Continuum of in…nitely-lived consumers, indexed by i Identical in all respects, except for initial endowment of private capital (wealth), K i , 0 The i -th consumer’s (cross section’s) resource allocation problem: Z ∞ h + θ ( X U l i ) � υ i � γ / υ 1 C � υ e � β t dt Maximize U i = i γ 0 subject to ˙ K i = ( 1 � τ k ) rK i + ( 1 � τ w ) w ( 1 � l i ) � ( 1 + τ c ) C i � T K i ( 0 ) = K i , 0 , K i , 0 6 = K m , 0 Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 9 / 26

  21. The Model Consumers Continuum of in…nitely-lived consumers, indexed by i Identical in all respects, except for initial endowment of private capital (wealth), K i , 0 The i -th consumer’s (cross section’s) resource allocation problem: Z ∞ h + θ ( X U l i ) � υ i � γ / υ 1 C � υ e � β t dt Maximize U i = i γ 0 subject to ˙ K i = ( 1 � τ k ) rK i + ( 1 � τ w ) w ( 1 � l i ) � ( 1 + τ c ) C i � T K i ( 0 ) = K i , 0 , K i , 0 6 = K m , 0 X U = K ϕ K 1 � ϕ : composite "public-private" externality (creates units G of "e¤ective" leisure), 0 � ϕ � 1 Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 9 / 26

  22. The Model Consumers Continuum of in…nitely-lived consumers, indexed by i Identical in all respects, except for initial endowment of private capital (wealth), K i , 0 The i -th consumer’s (cross section’s) resource allocation problem: Z ∞ h + θ ( X U l i ) � υ i � γ / υ 1 C � υ e � β t dt Maximize U i = i γ 0 subject to ˙ K i = ( 1 � τ k ) rK i + ( 1 � τ w ) w ( 1 � l i ) � ( 1 + τ c ) C i � T K i ( 0 ) = K i , 0 , K i , 0 6 = K m , 0 X U = K ϕ K 1 � ϕ : composite "public-private" externality (creates units G of "e¤ective" leisure), 0 � ϕ � 1 q = 1 / ( 1 + υ ) : intratemporal elasticity of susbstitution between consumption and e¤ective leisure Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 9 / 26

  23. Government Provides the aggregate stock of public capital (e.g. infrastructure), whose evolution is given by ˙ K g = G = gY , 0 < g < 1 Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 10 / 26

  24. Government Provides the aggregate stock of public capital (e.g. infrastructure), whose evolution is given by ˙ K g = G = gY , 0 < g < 1 Maintains a balanced budget G = τ k rK + τ w w ( 1 � l ) + τ c C + T Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 10 / 26

  25. Government Provides the aggregate stock of public capital (e.g. infrastructure), whose evolution is given by ˙ K g = G = gY , 0 < g < 1 Maintains a balanced budget G = τ k rK + τ w w ( 1 � l ) + τ c C + T Lumsum tax revenues, T , is a fraction of aggregate GDP: T = τ Y , 0 < τ < 1 Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 10 / 26

  26. Aggregate Equilibrium Dynamics Due to the Gorman (1953) properties, the aggregate equilibrium is independent of distributional characterisitcs: z z = g y ( z , l ) ˙ � [( 1 � g ) y ( z , l ) � Ω ( z , l ) l ] z ˙ l l = H ( z , l ) J ( z , l ) Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 11 / 26

  27. Aggregate Equilibrium Dynamics Due to the Gorman (1953) properties, the aggregate equilibrium is independent of distributional characterisitcs: z z = g y ( z , l ) ˙ � [( 1 � g ) y ( z , l ) � Ω ( z , l ) l ] z ˙ l l = H ( z , l ) J ( z , l ) Evolution of the aggregate economy represents the behavior of averages : z ) e µ t z ( t ) = ˜ z + ( z 0 � ˜ l + ( µ � a 11 ) l ( t ) = ˜ [ z ( t ) � ˜ z ] a 12 Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 11 / 26

  28. Aggregate Equilibrium Dynamics Due to the Gorman (1953) properties, the aggregate equilibrium is independent of distributional characterisitcs: z z = g y ( z , l ) ˙ � [( 1 � g ) y ( z , l ) � Ω ( z , l ) l ] z ˙ l l = H ( z , l ) J ( z , l ) Evolution of the aggregate economy represents the behavior of averages : z ) e µ t z ( t ) = ˜ z + ( z 0 � ˜ l + ( µ � a 11 ) l ( t ) = ˜ [ z ( t ) � ˜ z ] a 12 µ is the stable eigenvalue of the dynamic system, and a ij are linearized coe¢cients Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 11 / 26

  29. Aggregate Equilibrium Dynamics Due to the Gorman (1953) properties, the aggregate equilibrium is independent of distributional characterisitcs: z z = g y ( z , l ) ˙ � [( 1 � g ) y ( z , l ) � Ω ( z , l ) l ] z ˙ l l = H ( z , l ) J ( z , l ) Evolution of the aggregate economy represents the behavior of averages : z ) e µ t z ( t ) = ˜ z + ( z 0 � ˜ l + ( µ � a 11 ) l ( t ) = ˜ [ z ( t ) � ˜ z ] a 12 µ is the stable eigenvalue of the dynamic system, and a ij are linearized coe¢cients Convergence to a balanced growth path in the steady-state Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 11 / 26

  30. Distributional Dynamics: Wealth Relative capital/wealth is de…ned as k i = K i / K Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 12 / 26

  31. Distributional Dynamics: Wealth Relative capital/wealth is de…ned as k i = K i / K Evolution of relative wealth: � � � ˜ z , ˜ � δ 1 ( ˜ l ) z ) e µ t k i ( t ) � 1 = 1 + l ) ( z 0 � ˜ k i � 1 z , ˜ µ � δ 2 ( ˜ Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 12 / 26

  32. Distributional Dynamics: Wealth Relative capital/wealth is de…ned as k i = K i / K Evolution of relative wealth: � � � ˜ z , ˜ � δ 1 ( ˜ l ) z ) e µ t k i ( t ) � 1 = 1 + l ) ( z 0 � ˜ k i � 1 z , ˜ µ � δ 2 ( ˜ Steady-state relationship between relative wealth and leisure: � � z , ˜ � ˜ � l � ∆ ( ˜ l ) ˜ l i � ˜ ˜ l = k i � 1 z , ˜ Γ ( ˜ l ) | {z } + Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 12 / 26

  33. Distributional Dynamics: Wealth Relative capital/wealth is de…ned as k i = K i / K Evolution of relative wealth: � � � ˜ z , ˜ � δ 1 ( ˜ l ) z ) e µ t k i ( t ) � 1 = 1 + l ) ( z 0 � ˜ k i � 1 z , ˜ µ � δ 2 ( ˜ Steady-state relationship between relative wealth and leisure: � � z , ˜ � ˜ � l � ∆ ( ˜ l ) l i � ˜ ˜ ˜ l = k i � 1 z , ˜ Γ ( ˜ l ) | {z } + Agents with above average wealth consume above average leisure (Holtz-Eakin et al., 1993, Algan et al., 2003) Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 12 / 26

  34. Distributional Dynamics: Wealth Relative capital/wealth is de…ned as k i = K i / K Evolution of relative wealth: � � � ˜ z , ˜ � δ 1 ( ˜ l ) z ) e µ t k i ( t ) � 1 = 1 + l ) ( z 0 � ˜ k i � 1 z , ˜ µ � δ 2 ( ˜ Steady-state relationship between relative wealth and leisure: � � z , ˜ � ˜ � l � ∆ ( ˜ l ) l i � ˜ ˜ ˜ l = k i � 1 z , ˜ Γ ( ˜ l ) | {z } + Agents with above average wealth consume above average leisure (Holtz-Eakin et al., 1993, Algan et al., 2003) Dispersion of relative wealth: h i z , ˜ δ 1 ( ˜ l ) 1 + l ) f z ( t ) � ˜ z g z , ˜ µ � δ 2 ( ˜ h i σ k , 0 σ k ( t ) = z , ˜ δ 1 ( ˜ l ) 1 + l ) f z 0 � ˜ z g z , ˜ µ � δ 2 ( ˜ Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 12 / 26

  35. Distributional Dynamics: Income Relative income: y i = Y i / Y Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 13 / 26

  36. Distributional Dynamics: Income Relative income: y i = Y i / Y Dispersion of pre-tax relative income: σ y ( t ) = ζ ( t ) σ k ( t ) Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 13 / 26

  37. Distributional Dynamics: Income Relative income: y i = Y i / Y Dispersion of pre-tax relative income: σ y ( t ) = ζ ( t ) σ k ( t ) Dispersion of post-tax relative income: � � s k ( t )( τ w � τ k )( 1 � ζ ( t )) σ N y ( t ) = ζ ( t ) + σ k ( t ) ( 1 � τ w ) ( 1 � s k ( t )) + ( 1 � τ k ) s k ( t ) Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 13 / 26

  38. Distributional Dynamics: Income Relative income: y i = Y i / Y Dispersion of pre-tax relative income: σ y ( t ) = ζ ( t ) σ k ( t ) Dispersion of post-tax relative income: � � s k ( t )( τ w � τ k )( 1 � ζ ( t )) σ N y ( t ) = ζ ( t ) + σ k ( t ) ( 1 � τ w ) ( 1 � s k ( t )) + ( 1 � τ k ) s k ( t ) s k ( t ) : share of capital in total income Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 13 / 26

  39. Distributional Dynamics: Income Relative income: y i = Y i / Y Dispersion of pre-tax relative income: σ y ( t ) = ζ ( t ) σ k ( t ) Dispersion of post-tax relative income: � � s k ( t )( τ w � τ k )( 1 � ζ ( t )) σ N y ( t ) = ζ ( t ) + σ k ( t ) ( 1 � τ w ) ( 1 � s k ( t )) + ( 1 � τ k ) s k ( t ) s k ( t ) : share of capital in total income ζ ( t ) = h i h i � 1 z , ˜ z , ˜ l ( t ) 1 � ∆ ( ˜ l ) δ 1 ( ˜ l ) s k ( t ) � [ 1 � s k ( t )] 1 + l ) f z ( t ) � ˜ z g z , ˜ l ) ˜ z , ˜ 1 � l ( t ) Γ ( ˜ l µ � δ 2 ( ˜ Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 13 / 26

  40. Distributional Dynamics: Welfare Relative welfare: � � � � ˜ �� γ z , ˜ U i 1 � ∆ ( ˜ l ) U = 1 + k i � 1 z , ˜ l ) ˜ Γ ( ˜ l Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 14 / 26

  41. Distributional Dynamics: Welfare Relative welfare: � � � � ˜ �� γ z , ˜ U i 1 � ∆ ( ˜ l ) U = 1 + k i � 1 z , ˜ l ) ˜ Γ ( ˜ l Dispersion of relative welfare � � z , ˜ 1 � ∆ ( ˜ l ) σ u = ˜ σ k z , ˜ l ) ˜ Γ ( ˜ l Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 14 / 26

  42. Fiscal Policy, Growth, and Inequality: A Numerical Analysis Increase in government spending on public capital , …nanced by an increase in Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 15 / 26

  43. Fiscal Policy, Growth, and Inequality: A Numerical Analysis Increase in government spending on public capital , …nanced by an increase in lumpsum tax (or debt) Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 15 / 26

  44. Fiscal Policy, Growth, and Inequality: A Numerical Analysis Increase in government spending on public capital , …nanced by an increase in lumpsum tax (or debt) capital income tax Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 15 / 26

  45. Fiscal Policy, Growth, and Inequality: A Numerical Analysis Increase in government spending on public capital , …nanced by an increase in lumpsum tax (or debt) capital income tax labor income tax Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 15 / 26

  46. Fiscal Policy, Growth, and Inequality: A Numerical Analysis Increase in government spending on public capital , …nanced by an increase in lumpsum tax (or debt) capital income tax labor income tax consumption tax Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 15 / 26

  47. Fiscal Policy, Growth, and Inequality: A Numerical Analysis Increase in government spending on public capital , …nanced by an increase in lumpsum tax (or debt) capital income tax labor income tax consumption tax E¤ects on the distributional dynamics of wealth and income Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 15 / 26

  48. Fiscal Policy, Growth, and Inequality: A Numerical Analysis Increase in government spending on public capital , …nanced by an increase in lumpsum tax (or debt) capital income tax labor income tax consumption tax E¤ects on the distributional dynamics of wealth and income Nature of the growth-income inequality relationship along the transition path Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 15 / 26

  49. Fiscal Policy, Growth, and Inequality: A Numerical Analysis Increase in government spending on public capital , …nanced by an increase in lumpsum tax (or debt) capital income tax labor income tax consumption tax E¤ects on the distributional dynamics of wealth and income Nature of the growth-income inequality relationship along the transition path Relationship between average welfare and its dispersion Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 15 / 26

  50. Fiscal Policy, Growth, and Inequality: A Numerical Analysis Increase in government spending on public capital , …nanced by an increase in lumpsum tax (or debt) capital income tax labor income tax consumption tax E¤ects on the distributional dynamics of wealth and income Nature of the growth-income inequality relationship along the transition path Relationship between average welfare and its dispersion Robustness check: Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 15 / 26

  51. Fiscal Policy, Growth, and Inequality: A Numerical Analysis Increase in government spending on public capital , …nanced by an increase in lumpsum tax (or debt) capital income tax labor income tax consumption tax E¤ects on the distributional dynamics of wealth and income Nature of the growth-income inequality relationship along the transition path Relationship between average welfare and its dispersion Robustness check: spillover e¤ect (externality) of government spending Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 15 / 26

  52. Fiscal Policy, Growth, and Inequality: A Numerical Analysis Increase in government spending on public capital , …nanced by an increase in lumpsum tax (or debt) capital income tax labor income tax consumption tax E¤ects on the distributional dynamics of wealth and income Nature of the growth-income inequality relationship along the transition path Relationship between average welfare and its dispersion Robustness check: spillover e¤ect (externality) of government spending intratemporal elasticity of substitution between Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 15 / 26

  53. Fiscal Policy, Growth, and Inequality: A Numerical Analysis Increase in government spending on public capital , …nanced by an increase in lumpsum tax (or debt) capital income tax labor income tax consumption tax E¤ects on the distributional dynamics of wealth and income Nature of the growth-income inequality relationship along the transition path Relationship between average welfare and its dispersion Robustness check: spillover e¤ect (externality) of government spending intratemporal elasticity of substitution between private capital and labor in production Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 15 / 26

  54. Fiscal Policy, Growth, and Inequality: A Numerical Analysis Increase in government spending on public capital , …nanced by an increase in lumpsum tax (or debt) capital income tax labor income tax consumption tax E¤ects on the distributional dynamics of wealth and income Nature of the growth-income inequality relationship along the transition path Relationship between average welfare and its dispersion Robustness check: spillover e¤ect (externality) of government spending intratemporal elasticity of substitution between private capital and labor in production consumption and leisure in utility Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 15 / 26

  55. Benchmark Speci…cation of Structural Parameters Preferences β = 0 . 04 , γ = � 1 . 5 , θ = 1 . 75 , υ = 0 Production A = 0 . 6 , α = 0 . 6 , ρ = 0 Externalities ε = ϕ = 0 . 6 Fiscal g = 0 . 05 , τ = 0 . 05 , τ k = τ w = τ c = 0 Benchmark: Cobb-Douglas production and utility functions Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 16 / 26

  56. Benchmark Equilibrium and Aggregate Steady-State E¤ects Benchmark equilibrium: Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 17 / 26

  57. Benchmark Equilibrium and Aggregate Steady-State E¤ects Benchmark equilibrium: ˜ ˜ ψ ( % ) Financing Policy z ˜ l y ˜ Lump-sum tax …nancing, τ = 0 . 05 0 . 531 0 . 714 0 . 243 2 . 29 Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 17 / 26

  58. Benchmark Equilibrium and Aggregate Steady-State E¤ects Benchmark equilibrium: ˜ ˜ ψ ( % ) Financing Policy z ˜ l y ˜ Lump-sum tax …nancing, τ = 0 . 05 0 . 531 0 . 714 0 . 243 2 . 29 An increase in government spending from 5 % to 8 % of GDP ( dg = 0 . 03 ) Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 17 / 26

  59. Benchmark Equilibrium and Aggregate Steady-State E¤ects Benchmark equilibrium: ˜ ˜ ψ ( % ) Financing Policy z ˜ l y ˜ Lump-sum tax …nancing, τ = 0 . 05 0 . 531 0 . 714 0 . 243 2 . 29 An increase in government spending from 5 % to 8 % of GDP ( dg = 0 . 03 ) d ˜ d ˜ Policy Change ( dg = 0 . 03 ) d ˜ z l ψ Lump-sum tax-…nancing ( d τ = 0 . 03 ) 0 . 259 � 0 . 01 0 . 206 Capital income tax-…naning ( d τ k = 0 . 075 ) 0 . 353 � 0 . 006 0 . 101 Labor income tax-…nancing ( d τ w = 0 . 05 ) 0 . 268 0 . 002 0 . 168 Consumption tax-…nancing ( d τ c = 0 . 096 ) 0 . 265 � 0 . 001 0 . 179 Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 17 / 26

  60. Wealth Inequality E¤ects of an Increase in Government Spending: Lumpsum Tax-…nancing Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 18 / 26

  61. Wealth Inequality E¤ects of an Increase in Government Spending: Distortionary Tax-…nancing Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 19 / 26

  62. Income Inequality E¤ects of an Increase in Government Spending: Lumpsum Tax-…nancing Pre- and Post-tax Income Inequality Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 20 / 26

  63. Income Inequality E¤ects of an Increase in Government Spending: Distortionary Tax-…nancing Pre-tax income inequality Post-tax income inequality Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 21 / 26

  64. Robustness to Structural Parameters The distributional e¤ects of an increase in government spending are robust to Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 22 / 26

  65. Robustness to Structural Parameters The distributional e¤ects of an increase in government spending are robust to the intratemporal elasticity of substitution between private capital and labor in the production function, s = 1 / ( 1 + ρ ) (Figure 3) Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 22 / 26

  66. Robustness to Structural Parameters The distributional e¤ects of an increase in government spending are robust to the intratemporal elasticity of substitution between private capital and labor in the production function, s = 1 / ( 1 + ρ ) (Figure 3) the intratemporal elasticity of substitution between consumption and leisure in the utility function, q = 1 / ( 1 + υ ) (Figure 4) Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 22 / 26

  67. Robustness to Structural Parameters The distributional e¤ects of an increase in government spending are robust to the intratemporal elasticity of substitution between private capital and labor in the production function, s = 1 / ( 1 + ρ ) (Figure 3) the intratemporal elasticity of substitution between consumption and leisure in the utility function, q = 1 / ( 1 + υ ) (Figure 4) relative magnitude of the composite public-private externality in the utility and production functions, ϕ and ε (Table 4) Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 22 / 26

  68. The Growth-Inequality Relationship Generated by an Increase in Government Spending Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 23 / 26

  69. Trade-o¤ between Average Welfare and its Dispersion Generated by an Increase in Government Spending Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 24 / 26

  70. Conclusions Three issues: Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 25 / 26

  71. Conclusions Three issues: E¤ects of pro-growth …scal policies on inequality Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 25 / 26

  72. Conclusions Three issues: E¤ects of pro-growth …scal policies on inequality Nature of the growth-inequality relationship generated by public investment and …nancing policies Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 25 / 26

  73. Conclusions Three issues: E¤ects of pro-growth …scal policies on inequality Nature of the growth-inequality relationship generated by public investment and …nancing policies Trade-o¤s between average welfare and its dispersion due to government spending policies Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 25 / 26

  74. Conclusions Three issues: E¤ects of pro-growth …scal policies on inequality Nature of the growth-inequality relationship generated by public investment and …nancing policies Trade-o¤s between average welfare and its dispersion due to government spending policies Summary of results: Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 25 / 26

  75. Conclusions Three issues: E¤ects of pro-growth …scal policies on inequality Nature of the growth-inequality relationship generated by public investment and …nancing policies Trade-o¤s between average welfare and its dispersion due to government spending policies Summary of results: Government spending increases wealth inequality in transition, but income inequality may be subject to intertemporal trade-o¤s Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 25 / 26

  76. Conclusions Three issues: E¤ects of pro-growth …scal policies on inequality Nature of the growth-inequality relationship generated by public investment and …nancing policies Trade-o¤s between average welfare and its dispersion due to government spending policies Summary of results: Government spending increases wealth inequality in transition, but income inequality may be subject to intertemporal trade-o¤s The growth-inequality relationship depends on (a) magnitude of externalities (b) …nancing policies (c) time period of consideration Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 25 / 26

  77. Conclusions Three issues: E¤ects of pro-growth …scal policies on inequality Nature of the growth-inequality relationship generated by public investment and …nancing policies Trade-o¤s between average welfare and its dispersion due to government spending policies Summary of results: Government spending increases wealth inequality in transition, but income inequality may be subject to intertemporal trade-o¤s The growth-inequality relationship depends on (a) magnitude of externalities (b) …nancing policies (c) time period of consideration Government spending increases average welfare but also its dispersion Chatterjee & Turnovsky (UGA, UW) Govt Spending and Inequality 25 / 26

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