sssipart1: thesocialcostofinequality · 2016. 7. 19. · sssipart1: thesocialcostofinequality...
TRANSCRIPT
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SSSI Part 1: The Social Cost of Inequality
Nathaniel Hendren
Harvard
July, 2016
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Motivation
Inequality generates need for interpersonal comparisonsDecisions about economic policies (R&D, free trade, mergers, safetynet, health, education, taxation, etc.)General measurement of societal well-being
Two common economic methods for resolving interpersonalcomparisons
1 Kaldor Hicks Compensation Principle (Kaldor (1939), Hicks (1939,1940))
Motivates aggregate surplus, or “efficiency”, as normative criteriaIgnores issues of “equity”
2 Social welfare function (Bergson (1938), Samuelson (1947), Diamondand Mirrlees (1971), Saez and Stantcheva (2015))
Allows preference for equitySubjective choice of researcher or policy-maker
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This Lecture
Follow Hendren (2014) “The Inequality Deflator: InterpersonalComparisons without a Social Welfare Function”Revisit Kaldor-HicksModify so that transfers are incentive compatible (Mirrlees (1971))Kaldor and Hicks envisioned feasible transfers:
“If, as will often happen, the best methods of compensation feasibleinvolve some loss in productive efficiency, this loss will have to be takeninto account. (Hicks, 1939)
Existing literature: Hylland and Zeckhauser (1979), Coate (2000),Kaplow (1996, 2004, 2006, 2008)
Provide simple (yet general) empirical method of accounting for thesedistortions
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 3 / 49
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This Lecture
Key idea: Envelope theorem allows for empirical method to accountfor distortions
Corresponds to weighting surplus by the “inequality deflator”Turns unequal surplus into equal surplus using modifications to the taxschedule
Inequality deflator is the marginal cost to government of providing $1of welfare to an income level
Differs from $1 because of how behavioral response affects governmentbudget (basic PF logic)
Suppose we want to provide transfers to those earning near y ∗
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(c) y-‐T(y)
Consum
p/on
Earnings (y)
Modifications to Income Tax Schedule
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(c)
y*
y-‐T(y)
Consum
p/on
Earnings (y)
Modifications to Income Tax Schedule
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(c)
y*
ε
y-‐T(y)
Consum
p/on
Earnings (y)
Modifications to Income Tax Schedule
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(c)
η
ε
y-‐T(y)
Consum
p/on
Earnings (y) y*
Modifications to Income Tax Schedule
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(c)
η
ε
y-‐T(y)
Consum
p/on
Earnings (y)
Marginal welfare impact per η: =$1 per mechanical beneficiary
y*
Modifications to Income Tax Schedule
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(c)
η
ε
y-‐T(y)
Consum
p/on
Earnings (y)
Mechanical cost per η: =F(y*+ε/2)-‐F(y*-‐ε/2) =$1 per mechanical beneficiary
y*
Modifications to Income Tax Schedule
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(c)
η
ε
y-‐T(y)
Consum
p/on
Earnings (y)
Behavioral responses affect tax revenue But don’t affect u/lity (Envelope Theorem)
y*
Modifications to Income Tax Schedule
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(c)
η
ε
y-‐T(y)
Consum
p/on
Earnings (y)
Total cost per η per beneficiary: =1+FE(y*), FE = “fiscal externality”
y*
Modifications to Income Tax Schedule
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(c)
η
ε
y-‐T(y)
Consum
p/on
Earnings (y)
Total cost per η per beneficiary: =1+FE(y*), FE = “fiscal externality”
y*
g(y) = 1+FE(y)
E[1+FE(y)]
Inequality Deflator:
Modifications to Income Tax Schedule
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Formal Model
Inequality deflator: Formal Model
g (y) = 1+ FE (y)E [1+ FE (y)]
To first order: $1 surplus to those earning y can be turned into$g (y) /n surplus to everyone through modifications to tax schedule
Fiscal externality logic does not rely on functional form assumptions
Allows for each person to have her own utility function and arbitrarybehavioral responsesExtends to multiple policy dimensionsNests a lot of optimal tax expressions as special case (e.g. Mirrlees)
Key assumption: “partial equilibrium” / “local incidence”
Behavioral response only induces a fiscal externalityOther incidence/externalities would need to be accounted for
Inequality Deflator can turn unequal surplus into equal surplus
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 14 / 49
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Formal Model
Inequality deflator: Formal Model
g (y) = 1+ FE (y)E [1+ FE (y)]
To first order: $1 surplus to those earning y can be turned into$g (y) /n surplus to everyone through modifications to tax scheduleFiscal externality logic does not rely on functional form assumptions
Allows for each person to have her own utility function and arbitrarybehavioral responsesExtends to multiple policy dimensionsNests a lot of optimal tax expressions as special case (e.g. Mirrlees)
Key assumption: “partial equilibrium” / “local incidence”
Behavioral response only induces a fiscal externalityOther incidence/externalities would need to be accounted for
Inequality Deflator can turn unequal surplus into equal surplus
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 14 / 49
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Formal Model
Inequality deflator: Formal Model
g (y) = 1+ FE (y)E [1+ FE (y)]
To first order: $1 surplus to those earning y can be turned into$g (y) /n surplus to everyone through modifications to tax scheduleFiscal externality logic does not rely on functional form assumptions
Allows for each person to have her own utility function and arbitrarybehavioral responsesExtends to multiple policy dimensionsNests a lot of optimal tax expressions as special case (e.g. Mirrlees)
Key assumption: “partial equilibrium” / “local incidence”Behavioral response only induces a fiscal externalityOther incidence/externalities would need to be accounted for
Inequality Deflator can turn unequal surplus into equal surplus
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 14 / 49
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Formal Model
Inequality deflator: Formal Model
g (y) = 1+ FE (y)E [1+ FE (y)]
To first order: $1 surplus to those earning y can be turned into$g (y) /n surplus to everyone through modifications to tax scheduleFiscal externality logic does not rely on functional form assumptions
Allows for each person to have her own utility function and arbitrarybehavioral responsesExtends to multiple policy dimensionsNests a lot of optimal tax expressions as special case (e.g. Mirrlees)
Key assumption: “partial equilibrium” / “local incidence”Behavioral response only induces a fiscal externalityOther incidence/externalities would need to be accounted for
Inequality Deflator can turn unequal surplus into equal surplusNathaniel Hendren (Harvard) Cost of Inequality July, 2016 14 / 49
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(s)
Surplus
Earnings (y)
0
s(y)
Example: Alterna/ve environment benefits the poor and harms the rich
Example: Alternative Environment Benefits Poor
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EV and CV
Given s (y), two ways of neutralizing distributional comparisons
“EV”: modify status quo tax schedule
By how much can everyone be made better off in modified status quoworld relative alternative environment?
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 16 / 49
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EV and CV
Given s (y), two ways of neutralizing distributional comparisons“EV”: modify status quo tax schedule
By how much can everyone be made better off in modified status quoworld relative alternative environment?
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 16 / 49
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EV and CV
Given s (y), two ways of neutralizing distributional comparisons“EV”: modify status quo tax schedule
By how much can everyone be made better off in modified status quoworld relative alternative environment?
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 16 / 49
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(c) y-‐T(y)
Consum
p/on
Earnings (y)
Replicate surplus in status quo environment
“EV” Example
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(c) y-‐T(y)
Consum
p/on
Earnings (y)
Replicate surplus in status quo environment
s(y) ∧ y-‐T(y)
y-‐T(y)+s(y)
=
“EV” Example
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(c) y-‐T(y)
Consum
p/on
Earnings (y)
Replicate surplus in status quo environment
Is T budget feasible?
s(y) y-‐T(y) ∧
∧
y-‐T(y)+s(y)
=
“EV” Example
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(c) y-‐T(y)
Consum
p/on
Earnings (y)
s(y) y-‐T(y) ∧
Is T budget feasible? Case 1: YES
∧
“EV” Example
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(c) y-‐T(y)
Consum
p/on
Earnings (y)
s(y) y-‐T(y) ∧
Is T budget feasible? Case 2: NO
∧
“EV” Example
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(c) y-‐T(y)
Consum
p/on
Earnings (y)
SID > 0 s(y)
Inequality Deflated Surplus: SID=E[s(y)g(y)] How much be+er off is everyone in the alterna6ve environment rela6ve to a modified status quo?
y-‐T(y) ∧
“EV” Example
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(c) y-‐T(y)
Consum
p/on
Earnings (y)
SID > 0 s(y)
Inequality Deflated Surplus: SID=E[s(y)g(y)] How much be+er off is everyone in the alterna6ve environment rela6ve to a modified status quo?
y-‐T(y) ∧
SID < 0 Modified status quo delivers Pareto improvement
“EV” Example
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EV and CV
Given s (y), two ways of neutralizing distributional comparisons“EV”: modify status quo tax schedule
By how much can everyone be made better off in modified status quoworld relative alternative environment? Formal "First Order" Statement
“CV”: modify alternative environment tax scheduleBy how much can everyone be made better off in modified alternativeenvironment relative to status quo?
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 24 / 49
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(c) y-‐Ta(y)
Consum
p/on
Earnings (y)
Compensate Lost Surplus in Alterna/ve environment
“CV” Example
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(c) y-‐Ta(y)
Consum
p/on
Earnings (y)
Compensate Lost Surplus in Alterna/ve environment
-‐s(y)
y-‐Ta(y) ∧
“CV” Example
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(c)
Consum
p/on
Earnings (y)
-‐s(y) y-‐Ta(y)
y-‐Ta(y) ∧
SID > 0
Compensate Lost Surplus in Alterna/ve environment
“CV” Example
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(c)
Consum
p/on
Earnings (y)
-‐s(y) y-‐Ta(y)
y-‐Ta(y) ∧
SID < 0
Compensate Lost Surplus in Alterna/ve environment
“CV” Example
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(c)
Consum
p/on
Earnings (y)
-‐s(y) y-‐Ta(y)
y-‐Ta(y) ∧
SID > 0
Inequality Deflated Surplus: SID=E[s(y)g(y)] How much be+er off is everyone in the modified alterna6ve environment rela6ve to the status quo?
“CV” Example
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(c)
Consum
p/on
Earnings (y)
-‐s(y) y-‐Ta(y)
y-‐Ta(y) ∧
SID > 0
Inequality Deflated Surplus: SID=E[s(y)g(y)] How much be+er off is everyone in the modified alterna6ve environment rela6ve to the status quo?
SID > 0 Modified alterna/ve environment delivers Pareto improvement
“CV” Example
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Inequality Deflated Surplus <-> Pareto Comparisons
If g (y) is similar in status quo and alternative environment, thesethese two interpretations of inequality deflated surplus are first-orderequivalent Formal Assumptions and Proposition
Similar to first order equivalence of CV and EV
When surplus is homogeneous conditional on income:S ID provides first-order characterization of potential ParetocomparisonsS ID quantifies difference between environments without makinginter-personal comparisons
By how much is everyone better off?
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 31 / 49
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Heterogeneous Surplus
Redistribution based on income, not individual-specificTwo people with same income, y (θ), can have different surplus, s (θ)Income tax is a “blunt instrument”∫s (θ) g (y (θ)) = how much on average is each income level better off
Search for potential Pareto comparisons more difficult
But inequality deflator can still be used to characterize Paretocomparisons Proposition
DefineS ID = E [min {s (θ) |y (θ) = y} g (y)] > 0
S ID= E [max {s (θ) |y (θ) = y} g (y)] < 0
Modified alternative environment delivers Pareto improvement iffS ID > 0Modified status quo offers Pareto improvement iff S ID
< 0
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 32 / 49
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Heterogeneous Surplus
No potential Pareto ranking when S ID < 0 < S ID
Potential solution: Add more status quo policiesMarginal cost 1+ FE (X) as opposed to 1+ FE (y)
Augment both tax schedule and Medicaid
Inequality deflator well-suited for comparisons in which surplus doesnot vary conditional on income, so that S ID = S ID = S ID
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 33 / 49
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Rough Bound from Behavioral Responses to Tax Changes
Existing evidence on behavioral responses to taxation providesguidance on 1+ FE (y)
EITC causes people to:
Enter the labor force (summary in Hotz and Scholz (2003))Distort earnings (Chetty et al 2013).1+ FE (y) ≈ 1.14 for low-earners (calculation in Hendren 2013)
Taxing top incomes causes:
Reduction in taxable income (review in Saez et al 2012)Implies 1+ FE (y) ≈ 0.50− 0.75Disagreement about amount, but general agreement on the sign:FE (y) < 0
Reduced form empirical evidence suggests deflator values poormore so than the rich
Despite evidence that taxable income elasticities may be quite stableacross the income distribution (e.g. Chetty 2012)
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 34 / 49
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Rough Bound from Behavioral Responses to Tax Changes
Existing evidence on behavioral responses to taxation providesguidance on 1+ FE (y)
EITC causes people to:Enter the labor force (summary in Hotz and Scholz (2003))Distort earnings (Chetty et al 2013).1+ FE (y) ≈ 1.14 for low-earners (calculation in Hendren 2013)
Taxing top incomes causes:
Reduction in taxable income (review in Saez et al 2012)Implies 1+ FE (y) ≈ 0.50− 0.75Disagreement about amount, but general agreement on the sign:FE (y) < 0
Reduced form empirical evidence suggests deflator values poormore so than the rich
Despite evidence that taxable income elasticities may be quite stableacross the income distribution (e.g. Chetty 2012)
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 34 / 49
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Rough Bound from Behavioral Responses to Tax Changes
Existing evidence on behavioral responses to taxation providesguidance on 1+ FE (y)
EITC causes people to:Enter the labor force (summary in Hotz and Scholz (2003))Distort earnings (Chetty et al 2013).1+ FE (y) ≈ 1.14 for low-earners (calculation in Hendren 2013)
Taxing top incomes causes:Reduction in taxable income (review in Saez et al 2012)Implies 1+ FE (y) ≈ 0.50− 0.75Disagreement about amount, but general agreement on the sign:FE (y) < 0
Reduced form empirical evidence suggests deflator values poormore so than the rich
Despite evidence that taxable income elasticities may be quite stableacross the income distribution (e.g. Chetty 2012)
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 34 / 49
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Rough Bound from Behavioral Responses to Tax Changes
Existing evidence on behavioral responses to taxation providesguidance on 1+ FE (y)
EITC causes people to:Enter the labor force (summary in Hotz and Scholz (2003))Distort earnings (Chetty et al 2013).1+ FE (y) ≈ 1.14 for low-earners (calculation in Hendren 2013)
Taxing top incomes causes:Reduction in taxable income (review in Saez et al 2012)Implies 1+ FE (y) ≈ 0.50− 0.75Disagreement about amount, but general agreement on the sign:FE (y) < 0
Reduced form empirical evidence suggests deflator values poormore so than the rich
Despite evidence that taxable income elasticities may be quite stableacross the income distribution (e.g. Chetty 2012)
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 34 / 49
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Rough Bound from Behavioral Responses to Tax Changes
Existing evidence on behavioral responses to taxation providesguidance on 1+ FE (y)
EITC causes people to:Enter the labor force (summary in Hotz and Scholz (2003))Distort earnings (Chetty et al 2013).1+ FE (y) ≈ 1.14 for low-earners (calculation in Hendren 2013)
Taxing top incomes causes:Reduction in taxable income (review in Saez et al 2012)Implies 1+ FE (y) ≈ 0.50− 0.75Disagreement about amount, but general agreement on the sign:FE (y) < 0
Reduced form empirical evidence suggests deflator values poormore so than the rich
Despite evidence that taxable income elasticities may be quite stableacross the income distribution (e.g. Chetty 2012)
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 34 / 49
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A More Precise Representation
Use optimal tax approach to write FE (y) as function of taxableincome elasticities
Letεc (y) = avg comp. elasticity for those earning y
ζ (y) = avg inc. effect for those earning y
εP (y) = avg LFP rate elasticity for those earning yFormal Definitions
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 35 / 49
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A More Precise Representation
Use optimal tax approach to write FE (y) as function of taxableincome elasticitiesLet
εc (y) = avg comp. elasticity for those earning y
ζ (y) = avg inc. effect for those earning y
εP (y) = avg LFP rate elasticity for those earning yFormal Definitions
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 35 / 49
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Optimal Tax Expression
For every point, y ∗, such that T ′ (y) and εc (y ∗) are locally constant andthe distribution of income is continuous:
FE (y∗) = − εP (y∗) T (y)−T (0)y −T (y)︸ ︷︷ ︸
Participation Effect
− ζ (y∗) τ (y∗)1− T (y∗)
y∗︸ ︷︷ ︸Income Effect
− εc (y∗) τ (y∗)1− τ (y∗)
α (y∗)︸ ︷︷ ︸Substitution Effect
where α (y) = −(1+ yf ′(y)
f (y)
)is the local Pareto parameter of the income
distribution General Formula
Heterogeneity in FE (y) depends on:1 Shape of income distribution, α (y)2 Shape and size of behavioral elasticities3 Shape of tax rates
Generalized version of “uni-dimensional” formulas (e.g. Bourguignonand Spadaro (2012), Zoutman (2013a, 2013b))
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 36 / 49
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Optimal Tax Expression
For every point, y ∗, such that T ′ (y) and εc (y ∗) are locally constant andthe distribution of income is continuous:
FE (y∗) = − εP (y∗) T (y)−T (0)y −T (y)︸ ︷︷ ︸
Participation Effect
− ζ (y∗) τ (y∗)1− T (y∗)
y∗︸ ︷︷ ︸Income Effect
− εc (y∗) τ (y∗)1− τ (y∗)
α (y∗)︸ ︷︷ ︸Substitution Effect
where α (y) = −(1+ yf ′(y)
f (y)
)is the local Pareto parameter of the income
distribution General Formula
Heterogeneity in FE (y) depends on:1 Shape of income distribution, α (y)2 Shape and size of behavioral elasticities3 Shape of tax rates
Generalized version of “uni-dimensional” formulas (e.g. Bourguignonand Spadaro (2012), Zoutman (2013a, 2013b))
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 36 / 49
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Estimation Approach
Calibrate behavioral elasticities from existing literature on taxableincome elasticities
Assess robustness to range of estimates (e.g. compensated elasticity of0.1, 0.3, and 0.5) Calibration Details
Estimate shape of income distribution and marginal income tax rateusing universe of US income tax returns
Account for covariance between elasticity of income distribution andmarginal tax rate Estimation Details
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 37 / 49
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Estimation Approach
Calibrate behavioral elasticities from existing literature on taxableincome elasticities
Assess robustness to range of estimates (e.g. compensated elasticity of0.1, 0.3, and 0.5) Calibration Details
Estimate shape of income distribution and marginal income tax rateusing universe of US income tax returns
Account for covariance between elasticity of income distribution andmarginal tax rate Estimation Details
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 37 / 49
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Estimation Approach
Calibrate behavioral elasticities from existing literature on taxableincome elasticities
Assess robustness to range of estimates (e.g. compensated elasticity of0.1, 0.3, and 0.5) Calibration Details
Estimate shape of income distribution and marginal income tax rateusing universe of US income tax returns
Account for covariance between elasticity of income distribution andmarginal tax rate Estimation Details
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 37 / 49
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Estimation Approach
Calibrate behavioral elasticities from existing literature on taxableincome elasticities
Assess robustness to range of estimates (e.g. compensated elasticity of0.1, 0.3, and 0.5) Calibration Details
Estimate shape of income distribution and marginal income tax rateusing universe of US income tax returns
Account for covariance between elasticity of income distribution andmarginal tax rate Estimation Details
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 37 / 49
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Average Alpha
-10
12
3Al
pha
0 20 40 60 80 100Ordinary Income Quantile
Average Alpha by Income Quantile
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Inequality Deflator
.6.8
11.
2In
equa
lity D
eflat
or
0 20 40 60 80 100Ordinary Income (Quantile Scale)
Inequality Deflator
Estimation Details / Components Income Scale
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Inequality Deflator
0.5
11.
5In
equa
lity D
eflat
or
0 20 40 60 80 100Ordinary Income (Quantile Scale)
Baseline Specification Low Elasticity (e=0.1)High Elasticity (e=0.5)
Alternative Elasticity SpecificationsInequality Deflator
Household Income
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Application #1: Income Inequality
400
600
800
1000
1200
1400
Top
1% (K
)
050
000
1000
0015
0000
2000
00In
com
e ($
)
1980 1990 2000 2010year
Bottom Quintile 2nd Quintile3rd Quintile 4th Quintile5th Quintile Top 1% (K)
Source: CBO; Supplamental Tables 43373, Table 7
After-Tax Household Income Distribuition by Quintile
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 41 / 49
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1. Income Distributions
Define surplus function
s (θ) = Qa (α (θ))−Q0 (α (θ))
How much growth if tax schedule distributed it equally?
Could do other counterfactual experiments...
Search for Pareto comparisons using particular counterfactuals (e.g.SBTC vs no SBTC)
Quantile stability implements Kaldor (1939)’s idea of holdingdistribution constant + Hicks (1939) idea of doing it in cheapestmanner possible
More costly to make the rich poor and the poor rich than to keepeveryone rich and poor
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 42 / 49
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1. Income Distributions
Define surplus function
s (θ) = Qa (α (θ))−Q0 (α (θ))
How much growth if tax schedule distributed it equally?
Could do other counterfactual experiments...
Search for Pareto comparisons using particular counterfactuals (e.g.SBTC vs no SBTC)
Quantile stability implements Kaldor (1939)’s idea of holdingdistribution constant + Hicks (1939) idea of doing it in cheapestmanner possible
More costly to make the rich poor and the poor rich than to keepeveryone rich and poor
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 42 / 49
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1. Income Distributions
Define surplus function
s (θ) = Qa (α (θ))−Q0 (α (θ))
How much growth if tax schedule distributed it equally?Could do other counterfactual experiments...
Search for Pareto comparisons using particular counterfactuals (e.g.SBTC vs no SBTC)
Quantile stability implements Kaldor (1939)’s idea of holdingdistribution constant + Hicks (1939) idea of doing it in cheapestmanner possible
More costly to make the rich poor and the poor rich than to keepeveryone rich and poor
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 42 / 49
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1. Income Distributions
Define surplus function
s (θ) = Qa (α (θ))−Q0 (α (θ))
How much growth if tax schedule distributed it equally?Could do other counterfactual experiments...
Search for Pareto comparisons using particular counterfactuals (e.g.SBTC vs no SBTC)
Quantile stability implements Kaldor (1939)’s idea of holdingdistribution constant + Hicks (1939) idea of doing it in cheapestmanner possible
More costly to make the rich poor and the poor rich than to keepeveryone rich and poor
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 42 / 49
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1. Income Distributions
Define surplus function
s (θ) = Qa (α (θ))−Q0 (α (θ))
How much growth if tax schedule distributed it equally?Could do other counterfactual experiments...
Search for Pareto comparisons using particular counterfactuals (e.g.SBTC vs no SBTC)
Quantile stability implements Kaldor (1939)’s idea of holdingdistribution constant + Hicks (1939) idea of doing it in cheapestmanner possible
More costly to make the rich poor and the poor rich than to keepeveryone rich and poor
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 42 / 49
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1. Income Distributions
Define surplus function
s (θ) = Qa (α (θ))−Q0 (α (θ))
How much growth if tax schedule distributed it equally?Could do other counterfactual experiments...
Search for Pareto comparisons using particular counterfactuals (e.g.SBTC vs no SBTC)
Quantile stability implements Kaldor (1939)’s idea of holdingdistribution constant + Hicks (1939) idea of doing it in cheapestmanner possible
More costly to make the rich poor and the poor rich than to keepeveryone rich and poor
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 42 / 49
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Deflated Growth
-200
00-1
0000
010
000
2000
0D
iffer
ence
Rel
ativ
e to
201
2
1980199020002010Year
Mean HH Inc (CPI Deflated) Inequality Deflated HH IncLow Elasticity Specification High Elasticity Specification
Difference Relative to 2012Raw and Deflated Household Income Change
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Social Cost of Increased Income Inequality
-400
-200
020
040
060
0So
cial
Cos
t of I
ncom
e In
equa
lity
1980199020002010Year
Baseline Low Elasticity (e = 0.1)High Elasticity (e = 0.5)
119K * (Mean - Deflated Change in HH Income)Social Cost of Increased Income Inequality
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Country Comparison to US
AUS
AUT
BEL
CAN
DEU
DNK
FIN
FRA
NLD
SWE
USA
-100
00-5
000
050
0010
000
Ineq
ualit
y D
eflat
ed S
urpl
us
40000 45000 50000 55000 60000GNI Per Capita
Inequality Deflated Surplus Low/HighGNI PC Comparison
Inequality Deflated Surplus vs. 2012 GNI Per Capita
Other Country Orderings
Preference for “pro poor” policies?Two conceptualizations of policy experiments:
Non-Budget Neutral (“should the government spend money on G”)Budget Neutral
Budget neutral policies: weight surplus by inequality deflator
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 45 / 49
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Example: Producer versus Consumer Surplus
Suppose budget neutral policy with benefits to producers SP andconsumers SC
Extreme assumption: producer surplus falls to top 1%Consumer surplus falls evenly across income distribution
Optimal weighting:S ID = 0.77SP + SC
“Consumer surplus standard” requires top tax rate near Laffer curveFrance should have tighter merger regulations?
Key assumption: policy is budget neutral (inclusive of fiscalexternalities)What about non-budget neutral policies?
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 46 / 49
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Targeted Policies
Suppose G affects those with income yConstruct
MVPFG =s (y)
1+ FEG
WTP per unit gov’t revenue (Mayshar 1990; Slemrod and Yitzhaki2001; Hendren 2013)Depends on causal effects (FEG) and WTP for non-market good
Additional spending on G desirable iff
MVPFG︸ ︷︷ ︸Value of G
≥ 11+ FE (y)︸ ︷︷ ︸
Value of T (y)
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Welfare Impact
Section 8Food Stamps
JTPA
Income Tax / EITC
0.5
11.
52
MVP
F
0 18K 33K 53K 90K 696KHousehold Income (Quantile Scale)
Source: MVPFs compiled in Hendren (2013) drawing on existing estimates from Bloom et al (1997), Hoynes and Schanzenbach (2012), and Jacob and Ludwig (2012) Income is average income of policy beneficiaries normalized to 2012 income using CPI-U
MVPF of Targeted Policies
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 48 / 49
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Conclusion
Inequality isn’t just a transfer!Policy implications
Compare policies to the efficiency of the tax scheduleWeighting individual WTP by inequality deflator provides method to dothis
General idea: use marginal costs of feasible redistribution +envelope theorem + Pareto principle instead of a SWFKey question: what policies are more efficient than the income taxschedule at redistribution?
Nathaniel Hendren (Harvard) Cost of Inequality July, 2016 49 / 49