Negative Income Taxes, Inequality and Poverty

Transcription

1 Negative Income Taxes, Inequality and Poverty Constantine Angyridis Brennan S. Thompson Department of Economics Ryerson University July 8, 2011

2 Overview We use a dynamic heterogeneous agents general equilibrium model to analyze the redistributive effects of a negative income tax (NIT) This issue has been previously considered primarily in the context of static partial equilibrium models

3 Pre-Tax Gini Index, U.S., Source: U.S. Census Bureau, September 2010

4 Share of Total Pre-Tax Income Earned by Top 1%, U.S., Source: Piketty and Saez (2003), Data updated July 2010

5 Post-Tax Income Growth by Quintile, U.S., Source: Congressional Budget Office, June 2010

6 Poverty, U.S., Source: U.S. Census Bureau, September 2010

7 Inequality and Poverty Measurement Inequality: Poverty: Lorenz dominance Lower value for any inequality measure satisfying Pigou-Dalton principle of transfers (e.g., Gini) We use a relative poverty line (e.g., 50% of median) We focus on the FGT measure: z ( ) γ z x P(γ) = dx, z where: z: poverty line γ: poverty aversion parameter 0

8 Negative Income Taxes Advocated by Friedman, Rawls, Tobin, etc. Post-tax income is m = m(1 τ) + D, where: m: pre-tax income (from wages and interest) τ: flat tax rate D: demogrant

9 Related Literature Effect of tax reforms on inequality/poverty primarily studied with static partial equilibrium models Typically,the wage distribution is given exogenously, and agents choose how much labour to supply Lambert (1985): Flat tax and inequality Kanbur, Keen & Tuomala (1994): Progressive tax and poverty Creedy (1997): Flat tax and inequality/poverty Thompson (forthcoming): Flat/negative tax and relative poverty

10 More recently, effect of tax reform on equality have been studied with heterogeneous agents models Castaneda, Diaz-Gimenez & Rios-Rull (1999): Flat tax Benabou (2003): Progressive tax and education financing Heathcote (2005): Temporary changes in flat tax rate Conesa and Krueger (2006): Flat tax with allowance All of these papers focus exclusively on changes to the Gini index, none consider poverty

11 Key results for NIT: Inequality: Davies & Hoy (2002) find that increasing demogrant leads to a new post-tax distribution that Lorenz dominates the old one Pre-tax income is given exogenously (Relative) poverty: Thompson (forthcoming) finds that increasing demogrant will reduce P(γ) for all γ Wages given exogenously; agents choose labour supply

12 The Model Based on Aiyagari and McGrattan (1998) Closed economy with large number of infinitely lived agents that face idiosyncratic shocks to their labour productivity Agents try to smooth their consumption over time by trades in two risk-free assets: capital and government bonds

13 Production Production function exhibits CRS and is given by Y t = F (K t, z t N t ), where: Y t : output per capita K t : capital stock per capita N t : labor input per capita zt : exogenous labor-augmenting measure of technical progress We assume z t = z 0 (1 + g) t Along the BGP: K t grows at rate g and N t = N for all t

14 Assuming competitive product and factor markets: w t = z t F 2 (K t, z t N t ) r t = F 1 (K t, z t N t ) δ, where δ is the depreciation rate of capital Let w t = (1 τ)w t r t = (1 τ)r t Along the BGP: r t = r and w t /Y t = w for all t

15 Agents Objective function: subject to where: max E {c t,l t,a t+1 } t=0 β t ( c η t l 1 η t 1 µ ) 1 µ a 0, e 0, c t + a t+1 w t e t (1 l t ) + (1 + r)a t + D t, c t 0, 0 l t 1, a t 0 ct : consumption l t : leisure a t : asset holdings (note no borrowing condition)

16 Government Budget constraint: G t + D t + rb t = B t+1 B t + τ (w t N + ra t ), where: Gt : government consumption per capita Bt : government debt per capita

17 Market Clearing Conditions Asset market: Labour market: A t = K t + B t N = E [e t (1 l t )] Along the BGP, B t and A t (along with K t ) will be growing at rate g

18 Stationary Transformation Assume that G t /Y t = γ and D t /Y t = χ for all t Divide all variables that grow at rate g by Y t : k = K t Y t, b = B t Y t, a t = A t Y t, ã t = a t Y t, c t = c t Y t

19 Agents problem becomes: max E Y η(1 µ) 0 [β (1 + g) η(1 µ)] t { c t,l t,ã t+1 } t=0 ( c η t l 1 η t 1 µ ) 1 µ ã0, e 0, subject to c t + (1 + g) ã t+1 (1 + r)ã t + w t e t (1 l t ) + χ, Government s budget constraint becomes: γ + χ + [(1 τ)r g] b = τ (1 δk) Asset market equilibrium condition becomes: a = k + b

20 Parameterization Follow approach of Aiyagari and McGrattan (1998) Production function is Cobb-Douglas with capital share θ Process for productivity shocks is ln(e t ) = ρ ln (e t 1 ) + v t, where E(v t ) = 0 and Var(v t ) = σ 2. Approximated using the method of Tauchen (1986), with a first-order Markov chain that has seven states Parameters are calibrated from post-wwii U.S. data: θ = 0.3, g = , δ = ρ = 0.6, σ = 0.3 β = 0.991, µ = 1.5, η = γ = 0.217, b = 0.666

21 Results: Macro Variables Demogrant-to-GDP ratio (D t /Y t ) Demogrant GDP Tax rate Aggregate hours Wage rate Pre-tax Post-tax Capital stock Interest rate Pre-tax Post-tax

22 Results: Wage Income

23 Results: Interest Income

24 Results: Total Income

25 Results: Lorenz Curves

26 Results: Inequality and Poverty

27 Results: Summary Inequality: Increasing χ always leads to a new post-tax distribution that Lorenz dominates the old one As in Davies & Hoy (2002) (Relative) poverty: Increasing χ monotonically decreases P(γ) for all γ As in Thompson (forthcoming) (Utilitarian) Welfare : Increasing χ monotonically decreases W = u(c, l)dcdl With χ = 0.27, welfare loss in terms of consumption is is 13.4% than with χ = 0

28 Extensions Multidimensional measures of inequality and poverty (consumption and labour) Endogenizing the growth rate