A Motivating Example Economic Model Calibration and Counterfactuals Trade, Inequality and Costly Redistribution Pol Antr` as Harvard University Alonso de Gortari Harvard University Oleg Itskhoki Princeton University London School of Economics May 8, 2015 Antr` as, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 1 / 46
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A Motivating ExampleEconomic Model
Calibration and Counterfactuals
Trade, Inequality and Costly Redistribution
Pol AntrasHarvard University
Alonso de GortariHarvard University
Oleg ItskhokiPrinceton University
London School of EconomicsMay 8, 2015
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 1 / 46
A Motivating ExampleEconomic Model
Calibration and Counterfactuals
Introduction
I Empirical evidence suggests that increased trade integration raises realincome but also increases inequality and makes some worse off
I Standard approach to demonstrating and quantifying the gains from tradelargely ignores trade-induced inequality
I Kaldor-Hicks compensation principle:
1. Compute compensation variation or equivalent variation at the individuallevel of a move to free trade
2. Aggregate these monetary transfers across agents and show that everybodycan be compensated
I Two issues with this approach:
I How much compensation/redistribution actually takes place?
I Is this redistribution costless, as the Kaldor-Hicks approach assumes?
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 2 / 46
A Motivating ExampleEconomic Model
Calibration and Counterfactuals
This Paper
I We study the welfare implications of trade opening in a world in whichtrade affects the income distribution...
I ... and in which redistribution policies are constrained by informationfrictions (Mirrlees, 1971)
I In the model, trade increases inequality and redistribution needs to occurvia a distortionary income tax/transfer system
I Consistent with very limited role of trade adjustment assistance programs
I Despite the fact that the tax system is progressive, trade still leads to anincrease in inequality in the after-tax distribution of income
I We propose two types of adjustments to standard welfare measures:
1. A ‘welfarist’ correction reflecting the preferences of an inequality-aversesocial planner (risk-adjustment under the veil of ignorance)
2. A ‘costly-redistribution’ correction capturing behavioral responses totrade-induced shifts across marginal tax rates
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 3 / 46
Openness and Inequality in the United States (1979‐2007)
Trade Share Gini of Market Income
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 4 / 46
A Motivating ExampleEconomic Model
Calibration and Counterfactuals
A Motivating Quote
“If, as will often happen, the best methods of compensation feasibleinvolve some loss in productive efficiency, this loss will have to betaken into account.”
Hicks (1939, p. 712)
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 5 / 46
A Motivating ExampleEconomic Model
Calibration and Counterfactuals
Building Blocks
I Skeleton of Trade Model: Itskhoki (2008)
I Melitz (2003) with heterogeneous workers/entrepeneurs and a labor supplydecision
I Costly Redistribution: Nonlinear tax system as in Heathcote et al. (2014)
I After-tax income is log-linear function of pre-tax income (great fit)
I Welfarist correction: constant degree of inequality- (or risk-) aversion
I widely used in Public Finance; veil of ignorance rationale, Vickers (1945)
I Model calibrated to fit 2007 U.S. data:
I distribution of skills calibrated to match U.S. distribution of (adjustedgross) income from IRS public records
I trade costs calibrated to match U.S. trade share
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 6 / 46
A Motivating ExampleEconomic Model
Calibration and Counterfactuals
Related Literature (see paper for full list)
I Trade models with heterogeneous workers: Itskhoki (2008) but also
I matching/sorting models (see Grossman, 2013, and Costinot and Vogel,2015, for surveys)
I models with imperfect labor markets (Helpman, Itskhoki, Redding..., andearlier Davidson and Matusz)
I Gains from trade and costly redistribution: Dixit and Norman (1986),Rodrik (1992), Spector (2001), Naito (2006)
I Old literature on Kaldor-Hicks: Kaldor (1939), Hicks (1939), Scitovszky(1941)
I Welfarist approach: Bergson (1938), Samuelson (1947), Diamond &Mirlees (1971), Saez more recently
I Costly-redistribution: Kaplow (2008), Hendren (2014)
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 7 / 46
A Motivating ExampleEconomic Model
Calibration and Counterfactuals
Road Map
1. A Motivating Example
2. Economic Model
3. Calibration
4. Counterfactuals: Inequality and the Gains from Trade
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 8 / 46
I Principle does not rely on interpersonal comparisons of utility
I indirect utility can be heterogeneous across agentsI result relies on ordinal rather than cardinal preferencesI notion of efficiency argued to be free of value judgments
I What if redistribution does not take place and the losers are notcompensated?
I under the veil of ignorance, agents will see a probability distribution overpotential outcomes
I VN-M preferences over these lotteries are necessarily cardinalI risk aversion ≈ inequality aversion
I Even if some redistribution takes place, whenever it is costly, shouldn’t∆W /W reflect those costs?
I Dixit and Norman (1986) showed that ∆W /W > 0 using a course set oftax policies - but by how much is ∆W /W diminished?
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 11 / 46
I Suppose now that lump-sum transfers are not feasible (i.e., T (ϕ) = 0 forall ϕ) and redistribution has to happen through the income tax/transfersystem
I Focus on the particular case (as in Heathcoate et al., 2014) in which
1− τ (r (ϕ)) = k (r (ϕ))−φ , (4)
for some constant k which can be set to ensure that the governmentbudget is balanced
I Average net-of-tax rates decrease in reported income at a constant rate φ,which captures the degree of progressivity of the tax system
I Behavioral response to taxation: positive, constant elasticity of reportedincome to the net-of-tax rate, or
ε ≡ ∂r (ϕ)
∂ (1− τ (r (ϕ)))
1− τ (r (ϕ))
r (ϕ)> 0 (5)
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 16 / 46
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 21 / 46
A Motivating ExampleEconomic Model
Calibration and Counterfactuals
Closed EconomyOpen EconomyTrade and Inequality
Closed Economy: Environment
I Unit measure of heterogeneous households with ability ϕ ∼ H(ϕ)
I Each household provides its own differentiated good or task
I Linear production technology y = ϕ`
I All tasks are imperfectly substitutable and are combined into a final goodaccording to CES aggregator with elasticity of substitution 1/(1− β) > 1
I Real market revenue of household ϕ is
raut(ϕ) = Q1−βy(ϕ)β , (6)
where Q is the quantity of final output in the economy
I Households have utility over consumption and labor:
u(ϕ) = c(ϕ)− 1
γ`(ϕ)γ , γ > 1 (7)
where 1/(γ − 1) is the Frish elasticity of labor supply (no income effects)
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 22 / 46
A Motivating ExampleEconomic Model
Calibration and Counterfactuals
Closed EconomyOpen EconomyTrade and Inequality
Closed Economy: Taxation
I Informational constraint: Only household income (not household ability)is observable to the government
I Market revenue of households are taxed according to a tax schedule T (r)
I Households consume disposable income net of tax payments:
c(ϕ) = r(ϕ)− T(r(ϕ)
)(8)
I The household chooses labor input `(ϕ) to maximize utility in (7) giveny (ϕ) = ϕ`(ϕ), the revenue function (6) and the budget constraint (8)
I We adopt the same tax schedule as in (4), so that the disposable incomeis given by
r(ϕ)− T(r(ϕ)
)= kr(ϕ)1−φ,
where k is chosen to ensure balanced government budget∫T (r (ϕ))dH(ϕ) = 0
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 23 / 46
A Motivating ExampleEconomic Model
Calibration and Counterfactuals
Closed EconomyOpen EconomyTrade and Inequality
Equilibrium
I Distribution of disposable income (and utility) is shaped by underlyingdistribution of ability and by parameters β, γ and φ:
c(ϕ) ∝ ϕγβ(1−φ)
γ−β(1−φ)
I Higher after-tax income inequality when
I tasks are more substitutable (higher β)
I labor supply is more elastic (lower γ)
I taxes are less progressive (higher φ)
I For distributions closed under power transformations (Pareto, Lognormal,Pareto-lognormal), the distribution of disposable income will inherit thatof ϕ, i.e., H ((ϕ))
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 24 / 46
A Motivating ExampleEconomic Model
Calibration and Counterfactuals
Closed EconomyOpen EconomyTrade and Inequality
Social Welfare
I Individual utility levels are proportional to ϕγβ(1−φ)
γ−β(1−φ)
I Suppose social preferences feature a constant degree of inequalityaversion, then in the Pareto and Lognormal cases, we can write
W = δ (G) · R
where R is aggregate income (both market and disposable) and G is theGini coefficient of disposable income
I In those cases, we can also write
R = θ (G) · R
where θ (G) < 1 decreases in G , and R is aggregate income with zero taxprogressivity (i.e., φ = 0)
I Optimal degree of tax progressivity trades off reducing inequality versustax distortions
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 25 / 46
A Motivating ExampleEconomic Model
Calibration and Counterfactuals
Closed EconomyOpen EconomyTrade and Inequality
Open Economy: Environment
I Consider a world economy with N + 1 symmetric countries
I Households can market their output locally or in any of the other Ncountries
I Trade/Offshoring involves two types of additional costs
1. Symmetric iceberg cost τ (reduces revenue per unit shipped)
2. Fixed cost of exporting f (n) increasing in the number n of foreign marketsserved f (n) = fxn
α (in terms of final output)
I enhances potential inequality effects from trade
I Household sale revenue is now
r(ϕ) = Υ1−βn(ϕ)Q
1−βy(ϕ)β , (9)
whereΥn(ϕ) = 1 + n (ϕ) τ−
β1−β
and y(ϕ) is total household output, i.e., y(ϕ) = ϕ` (ϕ)
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 26 / 46
A Motivating ExampleEconomic Model
Calibration and Counterfactuals
Closed EconomyOpen EconomyTrade and Inequality
Open Economy: Taxation
I Assume again that the government only observes market revenue ofhouseholds and taxes according to the tax schedule T (r) in (4)
I government does not observe exporting decisions and f (n (ϕ)) is not taxdeductible
I Disposable income or consumption is thus
c(ϕ) = r(ϕ)− T(r(ϕ)
)− fxn (ϕ)α . (10)
I Households now choose labor input `(ϕ) and market access investmentn(ϕ) to maximize utility (7) given the revenue function (6) and budgetconstraint (10)
I Given symmetry, goods market clearing imposes
Q =
(∫ 1
0
Υ1−βn(ϕ)y(ϕ)β
)1/β
(11)
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 27 / 46
A Motivating ExampleEconomic Model
Calibration and Counterfactuals
Closed EconomyOpen EconomyTrade and Inequality
Trade and Inequality
I Result: Trade increases inequality of revenues and utilities
c (ϕ)
Q∝
ϕγβ(1−φ)
γ−β(1−φ) , ϕ < ϕx1 ,
Υγ(1−β)(1−φ)γ−β(1−φ)
1 ϕγβ(1−φ)
γ−β(1−φ) , ϕ < ϕx2,
......
Υγ(1−β)(1−φ)γ−β(1−φ)
N ϕγβ(1−φ)
γ−β(1−φ) ϕ ≥ ϕxN
Υn = 1 + nτ−β
1−β
I Two limiting cases:
I no agent exports (ϕx1 →∞)I all agents export (ϕxN → ϕmin)
c (ϕ)
Q=
caut (ϕ)
Qaut∝ ϕ
γβ(1−φ)γ−β(1−φ)
Antras, de Gortari and Itskhoki Trade, Inequality and Costly Redistribution 28 / 46
A Motivating ExampleEconomic Model
Calibration and Counterfactuals
Closed EconomyOpen EconomyTrade and Inequality
Trade and Inequality (cont.)
I Trade increases sale revenue of high-ability households but reduces that oflow-ability households