Optimal Redistribution in an Open Economy

Optimal Redistribution in an Open Economy Oleg Itskhoki Harvard University Princeton University January 8, 2008 1 / 29

How should society respond to increasing inequality? 2 / 29

How should society respond to increasing inequality? Conventional view: more redistribution 2 / 29

How should society respond to increasing inequality? Conventional view: more redistribution My answer: depends on the source of inequality 1 Skill (increasing dispersion of ability): increase redistribution 2 Globalization (falling trade costs): increase less or even reduce 2 / 29

Model of Trade and Inequality Melitz-based model: 1 Heterogeneity in productivity 2 Selection into exporting (fixed costs) 3 / 29

Model of Trade and Inequality Melitz-based model: 1 Heterogeneity in productivity 2 Selection into exporting (fixed costs) Stylized model of labor market: One type of heterogeneous agents: worker-entrepreneurs Data: more productive firms... hire more productive workers... are larger and pay higher wages... are more likely to export 3 / 29

Why this model? Conventional framework: Stolper-Samuelson (HO model) Challenges: Inequality in developing countries Within-sector reallocation Residual inequality 4 / 29

Why this model? Conventional framework: Stolper-Samuelson (HO model) Challenges: Inequality in developing countries Within-sector reallocation Residual inequality Alternative framework: Helpman-Itskhoki-Redding (2008a,b) Heterogeneous firms and workers Positive assortative matching Rent-sharing 4 / 29

Results Trade increases inequality Participation: only most productive agents export Gains from trade: disproportionately at the top 5 / 29

Results Trade increases inequality Participation: only most productive agents export Gains from trade: disproportionately at the top Taxation is more distortive in an open economy Marginal taxes distort intensive margin Distorted scale of production discourages entry Extensive margin of trade: greater income inequality (inequality margin) greater efficiency loss from taxation (efficiency margin) 5 / 29

Related Literature Recent work on trade and inequality: Verhoogen (2008), Amiti and Davis (2008) Helpman, Itskhoki and Redding (2008a,b) Public Finance models with extensive margin: Diamond (1980), Saez (2002) Compensation of losers from trade: Dixit and Norman (1980,1986) Spector (2001), Davidson and Matusz (2006), Egger and Kreickemeier (2008) 6 / 29

Outline 1 Economic Environment 2 Closed Economy 3 Open Economy Optimal Linear Tax Additional Tax Instruments 4 Summary and Discussion 7 / 29

Standard Public Finance Setup: Economic Environment Heterogeneous agents with productivity n H(n) Linear production technology y = nl 8 / 29

Standard Public Finance Setup: Economic Environment Heterogeneous agents with productivity n H(n) Linear production technology y = nl Each worker-entrepreneur produces distinct variety: Q = [ ] β 1/β yn dh(n), 0 β 1 8 / 29

Agent s problem: Agents and Government ( U n max U c, c,y 0 subject to budget constraint: c = r T (r), where r = Q 1 β y β y n ) 9 / 29

Agent s problem: Agents and Government ( U n max U c, c,y 0 subject to budget constraint: c = r T (r), where r = Q 1 β y β y n ) Government maximizes a Social Welfare Function: G ( ) U n dh(n) max T ( ) subject to individual optimality and GBC: T (rn )dh(n) 0 9 / 29

Assumptions No income effects in labor supply: U(c, l) = c v(l) Constant labor supply elasticity: v(l) = 1 γ lγ ε v (l) l v (l) = 1 γ 1 Constant relative inequality aversion: G ( U ) = 1 1 ρ U 1 ρ, ρ 0 Restricted set of tax instruments: Linear tax rate: T (r) = + tr, = tr Additional tax instruments 10 / 29

Proposition Closed Economy i. Income inequality is determined uniquely by the ability distribution ii. Optimal linear tax rate increases in income inequality 11 / 29

Proposition Closed Economy i. Income inequality is determined uniquely by the ability distribution ii. Optimal linear tax rate increases in income inequality Sketch of the Proof: Lemma: Distribution of relative revenues: Lemma: r n n βγ γ β Efficiency Margin = Intensive Margin of Labor Supply = ε Lemma: Inequality Margin increases in income inequality (variance of relative revenues) 11 / 29

Open Economy Setup Source of trade: love-of-variety (β < 1) Krugman (1980); Helpman and Krugman (1985) Broda and Weinstein (2006) Two symmetric countries No tariffs and efficient bargaining about national tax policies Variable iceberg trade cost τ > 1 Fixed costs of trade f x (Melitz, 2003) selection Evidence: Bernard-Jensen (2004); Das-Roberts-Tybout (2007) Alternatives: BEJK (2003); Melitz-Ottaviano (2008) 12 / 29

Open Economy Agent s Problem Revenues: Q 1 β yn β, non-exporter, r n = Υ 1 β x Q 1 β yn β, exporter Υ x 1 + τ β 1 β Consumption: Utility: c n = + (1 t)r n I n f x { } U n = max c v(y/n) c,y,i n Selection: n x is exporting cutoff 13 / 29

Trade and Inequality Result: Trade increases inequality of revenues and utilities 14 / 29

Trade and Inequality Result: Trade increases inequality of revenues and utilities Relative revenues: r n R Υ γ 1 β γ β x n βγ γ β, n < n x, n βγ γ β, n n x, Υ x = 1 + τ β 1 β 14 / 29

Trade and Inequality Result: Trade increases inequality of revenues and utilities Relative revenues: r n R Υ γ 1 β γ β x n βγ γ β, n < n x, n βγ γ β, n n x, Υ x = 1 + τ β 1 β Two limiting cases: no agent exports (n x n max ) all agents export (n x n min ) r n R = r a n R a n βγ γ β 14 / 29

Relative Revenues Illustration 2 Relative Revenues, r n / R 1.5 1 0.5 Autarky Open Economy 0 n min n x 1 1.5 2 2.5 3 Productivity, n 15 / 29

Utilities Illustration 3 Individual Utility, U n 2.5 2 1.5 1 Autarky Open Economy 0.5 n min n x 1 1.5 2 2.5 3 Productivity, n 15 / 29

Proposition Holding the tax rate constant: Open Economy Equilibrium Properties i. All agents gain from trade, although these gains are not proportionally distributed; ii. Inequality of relative revenues and utilities is higher in an open economy than in autarky given that some agents do not export; iii. Falling trade costs first increase and then decrease inequality. Replicates Helpman, Itskhoki and Redding (2008): inequality is higher in open economy inequality is non-monotonic with the fraction of exporting agents 16 / 29

Inequality in Open Economy Illustration 1.3 var(r/r) / var(r a /R a ) 1.2 1.1 1 0.9 1 1.5 2 2.5 Variable Trade Cost, τ 17 / 29

Optimal Redistribution Proposition In response to the same increase in inequality, optimal linear tax rate increases by less (or even falls) in the open economy relative to closed economy. 18 / 29

Optimal Redistribution Proposition In response to the same increase in inequality, optimal linear tax rate increases by less (or even falls) in the open economy relative to closed economy. Intuition: Inequality Margin still increases in income inequality (variance of relative revenues) Efficiency Margin = Intensive Margin + Extensive Margin > ε 18 / 29

General optimality condition: t 1 t Optimal Linear Tax Rate = 1 ε α (1 β)(1 α), 0 α 1 1 β 1 t β }{{}} 1 {{ + } ε efficiency max revenue 19 / 29

General optimality condition: t 1 t Optimal Linear Tax Rate = 1 ε α (1 β)(1 α), 0 α 1 Efficiency Margin: ε d ln Q d ln(1 t) = ε Inequality Margin: G ( ) U n α λ { 1, no trade/no selection, 1 + κ x, trade with selection ( r n R G ( U ) dh(n) = cov R λ ( r ) R = β U var, r R ) 19 / 29

Policy Response to Inequality Open Economy 0.2 Autarky Marginal Tax Rate, t 0.15 0.1 0.05 0 1 1.5 2 2.5 Variable Trade Cost, τ 20 / 29

Policy Response to Inequality Open Economy 0.2 Deductible f x Autarky Marginal Tax Rate, t 0.15 0.1 0.05 Non deductible f x 0 1 1.5 2 2.5 Variable Trade Cost, τ 20 / 29

Policy Response to Inequality Open versus Closed Economy 0.25 Linear Tax Rate, t 0.2 0.15 Closed Economy Open Economy with extensive margin 0.1 α a α max 0.2 0.21 0.22 0.23 0.24 0.25 Inequality Margin, α 20 / 29

Additional Tax Instruments 1 Can government target entry directly? 2 Marginal vs Average tax rates 21 / 29

Additional Tax Instruments 1 Can government target entry directly? 2 Marginal vs Average tax rates Natural candidates for additional tax instruments: export market entry subsidy (s) differential tax rates on exporters and non-exporters (t d, t x ) A type of a two-bracket tax system 21 / 29

Utilitarian Welfare (ρ = 0): W = Q π x f x v Optimal Entry ( yn ) dh(n) n 22 / 29

Utilitarian Welfare (ρ = 0): W = Q π x f x v Optimal Entry ( yn ) dh(n) n Proposition i. Entry is efficient when intensive margin is undistorted: t = 1 β β s = 0 ii. There is too little entry when intensive margin is distorted: t > 1 β β 0 < s /f x < 1 iii. ds /t d < 0 and ds /t x > 0 iv. Optimal entry subsidy for ρ > 0, s < s 22 / 29

Numerical Analysis Parameter Calibration Pareto ability distribution with shape parameter 2.2 upper end of the empirical ability distribution in Saez (2001) Elasticity of substitution = 4 (β = 3/4) BEJK (2003) and Broda and Weinstein (2006) Labor supply elasticity ε = 1/2 Tuomala (1990) and Saez (2002) Inequality aversion ρ = 2 Saez (2002) Fixed trade cost f x such that 35% of output is produced by exporting agents and exports accounts for 18% of consumption Bernard and Jensen (1999) 23 / 29

Average and Marginal Tax Rates Three Instruments 0.3 0.2 t d MTR t x Tax Rates 0.1 0 ATR 0.1 r + min r x r x 0.2 1 1.5 2 2.5 3 3.5 Revenue, r n Figure: Average and Marginal Tax Rates for Different Skill Levels (τ = 1.3) 24 / 29

Optimal Entry Additional Tax Instruments 15 Export Productivity Cutoff, n x 10 5 Linear Tax Rate Three Instruments Efficient n min =1 0 1 1.2 1.4 1.6 1.8 2 Variable Trade Cost, τ Figure: Optimal Entry, n x 25 / 29

Marginal Tax Rates Additional Tax Instruments 0.35 Marginal Tax Rate 0.3 0.25 0.2 Autarky t t d t x 0.15 1 1.2 1.4 1.6 1.8 2 Variable Trade Cost, τ Figure: Optimal Marginal Tax Rates, t d and t x 26 / 29

Marginal Tax Rates Additional Tax Instruments 0.35 Marginal Tax Rate 0.3 0.25 0.2 t x with (t d,t x,s) t d with (t d,t x ) Autarky: t a =0.257 t with (t,t,s) d d x t x with (t d,t x ) 0.15 1 1.2 1.4 1.6 1.8 2 Variable Trade Cost, τ Figure: Optimal Marginal Tax Rates, t d and t x 26 / 29

Inequality Outcome Additional Tax Instruments 1.4 1.3 Linear t No policy response var(r/r) 1.2 1.1 Three Instruments 1 Autarky: var(r/r)=1.05 1 1.2 1.4 1.6 1.8 2 Variable Trade Cost, τ Figure: Inequality of Relative Revenues, var ( r/r ) 27 / 29

Summary Trade intensifies both inequality and efficiency margins through selection into exporting (extensive margin of trade) An optimal tax system should balance equity, efficiency and, in particular, entry decisions Negative marginal tax rates for agents at the threshold Greater inequality may be a necessary outcome to reap the most gains from trade 28 / 29

Discussion Second dimension of heterogeneity: fixed costs General non-linear taxes in the open economy 29 / 29

Discussion Second dimension of heterogeneity: fixed costs General non-linear taxes in the open economy Other activities with extensive margin: technology adoption The role of free entry condition Losers from trade Optimal unemployment insurance 29 / 29