Trade, Inequality and Costly Redistribution

Trade, Inequality and Costly Redistribution Pol Antràs Alonso de Gortari Oleg Itskhoki Harvard Harvard Princeton ILO Symposium September 2015 1 / 30

Introduction International trade raises real income but also increases inequality and makes some worse off Standard approach to demonstrating and quantifying the gains from trade largely ignore trade-induced inequality Kaldor-Hicks compensation principle Two issues with this approach: 1 How much compensation/redistribution actually takes place? 2 Is this redistribution costless, as the Kaldor-Hicks approach assumes? These issue are relevant not just for trade, but also for technology adoption etc. 2 / 30

This Paper We study quantitatively welfare implications of trade in a model where: 1 trade leads to an increase in inequality 2 redistribution requires distortionary taxation (e.g., due to informational constraints, as in Mirrlees) 3 despite progressive tax system, trade still increases inequality in after-tax incomes We propose two types of adjustment to standard welfare measures: 1 Welfarist correction: taking into account inequality-aversion of society (or risk-adjustment under the veil of ignorance) 2 Costly-redistribution correction: capturing behavioral responses to trade-induced shifts across marginal tax rates 3 / 30

Motivating Figure 1.7 1.6 Mean Income Median Income Real Income in the United States (1979-2007) 1.5 1.4 1.3 1.2 1.1 1 0.9 1975 1980 1985 1990 1995 2000 2005 2010 1.74% versus 0.47% annualized annual growth 4 / 30

Motivating Figure 14% Openness and Inequality in the United States (1979 2007) 0.60 13% 0.58 12% 0.56 11% 0.54 10% 0.52 9% 0.50 8% 0.48 7% 0.46 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 Trade Share Gini of Market Income 4 / 30

Building Blocks and Related Literature Trade models with heterogeneous workers Itskhoki (2008) matching/sorting models (see Grossman, and Costinot and Vogel for surveys) models with imperfect labor markets (Helpman, Itskhoki, Redding, and others) Gains from trade and costly redistribution: Dixit and Norman (1986), Rodrik (1992), Spector (2001), Naito (2006) Welfarist approach: Bergson (1938), Samuelson (1947), Diamond & Mirlees (1971), Saez more recently Costly-redistribution: Kaplow (2008), Hendren (2014) Nonlinear tax system as in Heathcote, Storesletten and Violante (2014) Model calibrated to fit 2007 U.S. data on income distribution from IRS public records 5 / 30

Road Map 1 A Motivating Example 2 Open Economy Model 3 Calibration 4 Counterfactuals: Inequality and the Gains from Trade 6 / 30

MOTIVATING EXAMPLE 7 / 30

The Kaldor-Hicks Principle Consider an economy with a unit measure of individuals with ability ϕ H ϕ earning market income r ϕ F r We want to evaluate a shift of income distribution F r F r 7 / 30

The Kaldor-Hicks Principle Consider an economy with a unit measure of individuals with ability ϕ H ϕ earning market income r ϕ F r We want to evaluate a shift of income distribution F r F r The compensating variation v ϕ for each individual: Hence: u(r ϕ ) = u(r ϕ + v ϕ ) v ϕ = r ϕ r ϕ v ϕ dh ϕ = = r ϕdh ϕ r ϕ dh ϕ rdf r rdf r = R R Kaldor-Hicks Gains = Aggregate Real Income Growth G KH = R R R µ 7 / 30

The Kaldor-Hicks Principle Pros and Cons Principle does not rely on interpersonal comparisons of utility: indirect utility can be heterogeneous across agents result relies on ordinal rather than cardinal preferences notion of efficiency argued to be free of value judgements What if redistribution does not take place? under the veil of ignorance, agents see a probability distribution over potential outcomes (need cardinal preferences) risk aversion inequality aversion Even if some redistribution takes place, whenever it is costly, shouldn t W /W reflect those costs? Dixit and Norman (1986) showed that W /W > 0 using a course set of taxes, but by how much is W /W diminished? 8 / 30

A Constant-Elasticity Model Closed Economy A unit measure of individuals with CRRA-GHH utility: U(c, l) = 1 (c 1 1 + ρ γ lγ) Each individual produces a task according to y = ϕl, ϕ H ϕ This translates into market income r = Q 1 β y β, Q = r ϕ dh ϕ Consumption equals after-tax income: show data c = r T (r) = kr 1 φ Government runs balanced budget g = G r 1 φ Q = 1 k ϕ dh ϕ rϕ dh ϕ 9 / 30

Welfare: W 0 = 1 1 + ε (1 g) Q, Welfare Corrections W ρ = 1 + εφ 1 + ε (1 g)q = W 0 Θ, 10 / 30

Welfare: W 0 = 1 1 + ε (1 g) Q, Welfare Corrections W ρ = 1 + εφ 1 + ε (1 g)q = W 0 Θ, Welfarist Correction (Atkison, 1970): ( ) 1 (1 φ)(1 ρ) 1 ρ r ϕ dh ϕ r 1 φ ϕ dh ϕ 10 / 30

Welfare: W 0 = 1 1 + ε (1 g) Q, Welfare Corrections W ρ = 1 + εφ 1 + ε (1 g)q = W 0 Θ, Welfarist Correction (Atkison, 1970): ( ) 1 (1 φ)(1 ρ) 1 ρ r ϕ dh ϕ r 1 φ ϕ dh ϕ Costly Redistribution Correction: [ ( ) 1+ε rϕ dh ϕ Θ (1+εφ) Q Q = (1 + εφ)(1 φ) }{{} Θ κε ( r 1 φ ) ε ϕ dh ϕ r 1+εφ ϕ dh ϕ }{{} Θ ] κ 10 / 30

Properties of the Correction Terms General properties: 1, Θ [0, 1] and independent of µ. 2 = 1 if either ρ = 0 or F r is degenerate. < 1 otherwise, and monotonically decreasing in ρ 3 Θ = 1 iff φ = 0. If F r is degenerate, Θ = 1 and Θ = Θ 1. Θ is monotonically decreasing in φ and ε. Special-case: log-normal ability distribution { } = exp ρ(1 φ) 2 σ2 r, 2 { Θ = exp κε(1 + ε)φ 2 σ2 r 2 }. both and Θ decrease in dispersion of income (σ r, Gini, etc.) yet, increases and Θ decreases in φ policy tradeoff 11 / 30

GDP growth rates: Welfarist correction: Corrections for Welfare Gains µ = Q Q Q, µ = Q Q Q = G G W W ρ W ρ = (1 + µ) 1 Costly redistribution correction: µ = (1 + µ) Θ Θ 1 12 / 30

Look at the data Growth corrections for US, 1979 2007 Welfare correction: G W /µ / ρ = 0.5 1 2 Non-parametric 0.89 0.80 0.08 Log-normal 0.90 0.80 0.60 CR correction: µ/ µ Θ /Θ ε = 0.5 1 2 Non-parametric 1.04 1.14 1.98 Log-normal 1.06 1.27 ( µ < 0) Recall that annualized µ = 1.74% over 1979 2007, inequality increased but progressively (φ) decreased 13 / 30

3 Contribution (Taxation) 3 Contribution (Taxation) Policy Tradeoff for US, 1979 2007 θ δ {}}{{}}{ In logs: log W ρ = log W 0 + log Θ + log 0.12 (/,3) Phase Diagram, rho=0.5, eps=0.5 0.11 0.1 0.09 0.08 0.07 0.06 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 / Contribution (Inequality) 0.12 (/,3) Phase Diagram, rho=0.7, eps=0.5 0.11 0.1 0.09 0.08 0.07 0.06 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 / Contribution (Inequality) 14 / 30

Trade and Welfarist Correction A Preliminary Quantitative Assessment How large is the negative correction to social welfare associated with trade-induced inequality? Consider U.S. during the period 1979 2007: Two crucial questions: 1979 2007 Trade Share 0.092 0.140 Gini Coefficient 0.367 0.489 1 How much did the rise in the trade share increase aggregate disposable income? 2 Which share s of the 0.122 increase in the Gini is caused by that trade opening? Trade model will answer these questions, but suppose µ = 3% and s = 5%, 10%, and 20% 15 / 30

Welfarist Correction A Preliminary Quantitative Assessment It does not take an awful lot of inequality aversion to generate significant downward corrections to gains from trade Table 1. Social Welfarist Inequality Correction to Welfare Effects of Trade Integration Pareto Correction Lognormal Correction Contribution of Trade to Inequality Contribution of Trade to Inequality s = 5% s = 10% s = 20% s = 5% s = 10% s = 20% Inequality Aversion (1) (2) (3) (4) (5) (6) ρ = 0 3.00% 3.00% 3.00% 3.00% 3.00% 3.00% ρ = 0.1 2.85% 2.69% 2.36% 2.91% 2.83% 2.65% ρ = 0.25 2.67% 2.33% 1.64% 2.79% 2.57% 2.12% ρ = 0.5 2.46% 1.92% 0.80% 2.57% 2.14% 1.25% ρ = 0.75 2.32% 1.63% 0.23% 2.36% 1.72% 0.39% ρ = 1 2.22% 1.43% -0.18% 2.15% 1.29% -0.46% ρ = 2 1.98% 0.96% -1.08% 1.31% -0.39% -3.81% 16 / 30

ECONOMIC MODEL 17 / 30

Open Economy Environment Consider a world economy with N + 1 symmetric regions Households can market their output locally or in any of the other N regions Trade/Offshoring involves two types of additional costs 1 Variable iceberg trade cost τ 2 Fixed cost of market access f (n) increasing in the number n of foreign markets served. We adopt f (n) = fn α Household income r ϕ = Υ 1 β n ϕ Q 1 β y β ϕ, where Υ nϕ = 1 + n ϕ τ β 1 β Taxation: the government does not observe export decisions and f (n) is not tax deductible: c ϕ = krϕ 1 φ fnϕ α 17 / 30

Relative Revenues, r/r Trade and Inequality Trade increases relative revenues of high-ability households (due to market access), but reduces that of low-ability households (due to foreign competition) 6 5 Autarky Open Economy 4 3 2 1 0 0 100 200 300 400 500 600 700 800 900 1000 Productivity 18 / 30

Trade and Inequality 1.035 Gini Ratio, N=1 1.07 Variance(R/mean(R)) Ratio, N=1 1.03 1.025 1.02 1.015 1.01 Pre-Tax Post-Tax 1.06 1.05 1.04 1.03 1.005 1.02 1 1 1.5 2 2.5 Variable Trade Cost = 1.01 1 1.5 2 2.5 Variable Trade Cost = 1.12 1.1 1.08 1.06 1.04 1.02 Gini Ratio, N=10 Variance(R/mean(R)) Ratio, N=10 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1 1 1.5 2 2.5 Variable Trade Cost = 1.2 1 1.5 2 2.5 Variable Trade Cost = 19 / 30

CALIBRATION AND COUNTERFACTUALS 20 / 30

Calibration and Counterfactuals Road Map We first calibrate the model to 2007 U.S. data (trade share, income distribution, tax progressivity) We then explore the implication of a move to autarky on 1 Aggregate Income 2 Income Inequality We use the model to gauge the quantitative importance of the two corrections developed above 1 How large are the gains from trade for different degrees of inequality aversion? 2 How large would the gains from trade be in the absence of costly redistribution (i.e., φ = 0)? 20 / 30

Hold the following parameters fixed Calibration 1 Elasticity of substitution = 4 (β = 3/4) BEJK (2003), Broda and Weinstein (2006), Antràs, Fort and Tintelnot (2014) 2 Iceberg trade costs (τ = 1.83) Anderson and Van Wincoop (2004), Melitz and Redding (2014) 3 Number of countries (N = 10) U.S. roughly 10-15% of world manufacturing; results not too sensitive to N above 5 Set baseline fixed cost f to match a U.S. trade share of 0.14 Set convexity of fixed costs to either α = 1 or α = 3 (consistent with preliminary estimates using U.S. exports) Labor supply elasticity: experiment with various values for γ between γ = 10000 (or ε 0) and γ = 5/3 (or ε = 1.5) 21 / 30

Calibration: Progressivity We set φ = 0.147, consistent with 2007 income data: 14.5 Log Income After Taxes and Transfers, 2007 13.5 12.5 11.5 10.5 y = 0.853x + 1.661 R² = 0.995 9.5 9.5 10.5 11.5 12.5 13.5 14.5 Log Market Income, 2007 22 / 30

Calibration: Distribution of Ability Use 2007 U.S. Individual Income Tax Public Use Sample approximately 2.5 million anonymized tax returns use NBER weights to ensure this is a representative sample we map market income to adjusted gross income in line 37 of IRS Form 1040 We follow two types of approaches: 1 Nonparametric approach: given other parameter values, one can recover the ϕ s from the observed distribution of adjusted gross income 2 Parametric approach: assume that ϕ LogNormal(µ, σ) and calibrate µ and σ to match the mean and the Gini coefficient of adjusted gross income 23 / 30

Parametric vs. Non-Parametric Approach Lognormal provides a reasonably good approximation, but it does a poor fit for the right-tail of the distribution, which looks Pareto 1 Income Distribution 2.6 Empirical Pareto Coefficient 0.9 0.8 0.7 Nonparametric Lognormal Data 2.4 2.2 0.6 2 0.5 1.8 0.4 1.6 0.3 0.2 1.4 0.1 1.2 0 6 8 10 12 log(r) 1 0 2 4 6 8 10 R #10 5 24 / 30

Gains from Trade and Inequality Calibrated welfare gains from trade are higher, the higher is the labor supply elasticity ε But relative to autarky trade induces more inequality when ε is high Gains from Trade Increase in Gini Coefficient Labor supply elasticity α = 1 α = 3 α = 1 α = 3 ε = 0 4.86% 4.02% 2.31% 1.70% ε = 0.1 5.52% 4.54% 2.44% 1.81% ε = 0.25 6.54% 5.36% 2.64% 1.95% ε = 0.5 8.31% 6.77% 2.92% 2.17% ε = 0.75 10.40% 8.32% 3.16% 2.35% ε = 1 12.41% 9.89% 3.36% 2.51% ε = 1.5 16.72% 13.21% 3.72% 2.78% 25 / 30

Welfarist Correction Welfarist correction is higher, the higher is risk/inequality aversion ρ and the lower is the labor supply elasticity ε With log utility (ρ = 1) and a labor supply elasticity of ε = 0.5, welfare gains are 20 25% lower 1.00 Welfarist Correction ( ) 1.00 Welfarist Correction ( ) 0.95 0.95 0.90 0.90 0.85 0.85 0.80 0.80 0.75 0.75 0.70 0.70 0.65 0.65 0.60 0 0.1 0.25 0.5 0.75 1 2 Degree of Risk/Inequality Aversion ( ) 0.60 0 0.1 0.25 0.5 0.75 1 2 Degree of Risk/Inequality Aversion ( ) 26 / 30

Costly Redistribution Correction Costly redistribution correction is higher, the higher is the labor supply elasticity ε When ε = 0.5, welfare gains are 15 20% lower 1.00 Costly Redistribution Correction ( =0) 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 Elasticity of Labor Supply 27 / 30

Welfare gains from trade 1.25 1.2 Undistorted Mean Income growth 1.15 1.1 Mean Welfare Median 1.05 1 0 0.05 0.1 0.15 0.2 0.25 Export share of revenues 28 / 30

OPTIMAL PROGRESSIVITY 29 / 30

Progressivity and Inequality Aversion Optimal progressively is lower in open economy greater inequality increase if φ is adjusted 1.25 1.2 Trade Equilibrium Social welfare, W 1.15 1.1 1.05 Autarky φ T φ A 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Progressivity of taxation, φ 29 / 30

Progressivity and Inequality Aversion Observed progressivity φ 0.15 in 2007 is optimal if ρ 0.7 0.25 0.2 Progressivity of taxation, φ 0.15 0.1 0.05 Autarky Trade Equilibrium 0 0 0.2 0.4 0.6 0.8 1 Inequality aversion, ρ 29 / 30

Progressivity and Inequality Aversion Optimal progressively is lower in open economy greater inequality increase if φ is adjusted 0.66 1.2 0.64 1.1 0.62 1 Gini of revenues 0.6 0.58 Trade Equilibrium Mean revenues 0.9 0.8 Trade Equilibrium 0.56 0.7 0.54 Autarky 0.6 Autarky φ T φ A 0.52 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Progressivity of taxation, φ φ 0.5 T φ A 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Progressivity of taxation, φ 29 / 30

Conclusions Trade-induced inequality is partly mitigated via a progressive income tax system Still, compensation is not full so trade induces an increase in the inequality of disposable income should we measure gains using average income or adjust for inequality? Income taxation induces behavioral responses that affect the aggregate income response to trade integration should we adjust for this leaky bucket effect? We developed welfarist and costly redistribution corrections to standard measures of the gains from trade Under plausible parameter values, these corrections are nonneglible and eliminate about one-fifth of the gains 30 / 30

APPENDIX 31 / 30

On the Shape of the Tax Schedule The tax schedule might seem ad hoc, but it fits U.S. data remarkably well: log r d ϕ = log k + (1 φ) log r ϕ 14 Log Income After Taxes and Transfers 13 12 11 10 y = 0.818x + 2.002 R² = 0.988 9 9 10 11 12 13 14 Log Market Income CBO data, percentiles of income distribution 1979 2010 (similar fit with PSID) back to slides 32 / 30

On the Shape of the Tax Schedule Over Time Degree of Progressivity φ φ 0.1.2.3.4.5 1980 1990 2000 2010 Year back to slides 33 / 30