Optimal Redistributive Taxation

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Optimal Redistributive Taxation

• Louis Kaplow

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Book Overview

• Scope Conceptual Framework
• Focus on major structural features
• Emphasizing relationships among the pieces
• contrast existing Public Economics Handbook (4
  vols.) and surveys of specific subjects
• Not
• Empirical
• Political economy
• Macroeconomics (stabilization, ...)

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Contents

1. Framework
2. Optimal Income Taxation
3. Optimal Commodity Taxation
4. Applications
5. Tax Equity

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Contents

1. Framework
2. Optimal Income Taxation
3. Optimal Commodity Taxation
4. Applications
5. Tax Equity

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Framework

• Purposes of taxation
• Redistribution
• Revenue-raising
• identical individuals trivial result that
  uniform (lump-sum) levy optimal no distortion
• distortionary income tax (etc.) because
  distribution matters
• equity-efficiency tradeoff thus central
• Corrective (Pigouvian)

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Integrated view (ch. 2)

• Optimal use of instrument A depends on whether
  instrument B available
• Notably, income tax (and transfers) are core
  instrument for revenue/redistribution
• Other tools (commodity taxes, estate/gift tax,
  ...) viewed as special-purpose supplements
• assessed on efficiency grounds income tax
  adjustments can hold distribution constant
• Likewise for public goods, regulation,

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Approach

• Distribution-neutral adjustment to the income tax
• Isolates distinctive effects of policies
  (estate/gift taxation, public goods, Pigouvian
  taxation)
• Developed in detail, below, with commodity
  taxation

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Social objective (ch. 3)

• Explicit reference to social welfare function
• surprisingly high use of fuzzy proxies (ability
  to pay) and often unspecified notions of fairness
• inappropriate, and often indeterminate in any
  event
• value of tracing all to welfare is large (e.g.,
  family unit, estate/gift tax, administration/error
  )
• Welfarism notion that all of social relevance
  can be traced to effects on individuals welfare
• some defense in chapters 13-15
• see generally Fairness versus Welfare (2002) (w/
  Shavell)

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SWF

• Ex. Utilitarianism sum of utilities
• Decreasing marginal utility in u
• Ex u ln y
• MU 1/y
• Utilitarian SWF marginal worth 10 times to
  those with 1/10 the income

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Common formulation

• e inequality aversion parameter
• Also decreasing MU, in the u function
• Weight on redistribution depends on both
• But arguably mainly the latter

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Contents

1. Framework
2. Optimal Income Taxation
3. Optimal Commodity Taxation
4. Applications
5. Tax Equity

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Optimal taxation setup

• Income taxation
• Really a labor income tax (one-period model)
• Roughly equivalent to a wage tax or a cash-flow
  consumption tax in this one-period setting
• Commodity taxation
• Think of as incorporating all manner of
  differential taxation (including of savings)
• Tax expenditures (and penalties) can be analyzed
  as differential commodity taxation

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Optimal income taxation (ch. 4)

• Problem statement Choose tax system to max SWF,
  subject to
• Individuals choose labor supply to max U
• Exogenous revenue requirement
• Source of equality/efficiency tradeoff
• Type (earning ability w) assumed unobservable
• Tax income, a signal of ability
• Hence distortion because not taxing ability
  directly

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Illustration of tax/transfer fn
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Linear income tax
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Linear income tax F.O.C.

• Stern (1976) t54, g34 of ave. inc.

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Two-bracket income taxSlemrod et al. (1994)

• Upper bracket w/ lower marginal rate
• More so as weight on equality increases

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Nonlinear income tax concept

• Problem
• Determine marginal tax rate at all levels of
  income
• Determine intercept i.e., grant to individual
  earning zero
• Perturbation thought experiment
• Suppose we raise the proposed marginal tax rate
  on all income in the range (50,000, 50,100) by 1
  (one percentage point)
• Two effects
• Inframarginal all individuals with y (wl) above
  50,100 pay 1 more in tax
• They all face same marginal tax rate as before
  no substitution effect
• (Income effect all work a tiny bit more)
• Sum obtain significant revenue, and from
  higher-income individuals (where high is relative
  to 50,100 in this case)
• Marginal all individuals with y in the interval
  (50,000, 50,100)
• Pay 0 to 1 more if behavior unchanged
• They face higher marginal tax rate, so
  substitution effect induces to work less (is also
  an income effect)
• Questions how large is each effect, what does it
  depend on, and how does it relate to social
  welfare?

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Nonlinear income tax F.O.C.

• Perturbation thought experiment
• marginal folks (with income wl)
• inframarginal folks (income gt wl)
• (1-F)/f
• 1-F is fraction of population above marginal
  rate in question collect more revenue
  inframarginally from them as raise marginal rate
  at a given point
• f is density at margin, those who are distorted
• ?, w
• Second term average welfare cost to the group
  that pays the increase (for case with no income
  effects)
• Many simulations have high marginal rates that
  trail downward at top

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Ability taxation (ch. 5.C)

• Ideal tax is ability tax
• Explanation of Pareto improvement
• Could have full equalization
• Income taxed as observable signal of ability
• Source of incentive tradeoff
• Ability tax surrogates possible?
• Height? Age?

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Transfer payments (ch. 7)

• Optimal transfers optimal income tax
• I.e., if have figured out optimal income tax,
  including (plausibly negative) taxes on the poor,
  why arent we done?
• Categorical assistance
• Model as type-specific income tax (ability
  taxation, above)
• Results phase-outs
• Work inducements
• Hard to justify
• Informational assumptions
• Cash versus in-kind (raises different types of
  questions)

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Contents

1. Framework
2. Optimal Income Taxation
3. Optimal Commodity Taxation
4. Applications
5. Tax Equity

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Commodity taxation (ch. 6)

• Problem choose relative tax rates on different
  commodities, given an income tax that can be
  adjusted
• Result no differentiation optimal in basic case
• Atkinson Stiglitz (1976) showed true with
  optimal income tax Kaplow (2006) extends to when
  income tax nonoptimal
• Intuition adds additional distortion without
  helping on the redistribution/distortion tradeoff
• Example inefficiency of luxury taxes, exemptions
  for necessities (e.g., for food in a VAT)
• Assumptions and qualifications

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Proof sketch

• Step 1 begin with differential commodity tax
• Step 2 abolish tax differentials and adjust
  income tax to hold utility level constant for
  each taxpayer (at each level of prior income)
• Step 3 this combined reform has no effect on
  labor supply
• intuition utility return to every level of labor
  effort same (for everyone) hence labor same
  (see diagram)
• Step 4 a surplus is produced (due to reducing
  the distortion of consumption choices)
• Step 5 pro rata rebate of surplus Pareto
  improvement

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Summary of intuition

• Distribution can be ignored
• Because by construction is distribution-neutral
• Labor supply effects can be ignored
• Because are none (qualifications coming)
• Whats left? the distinctive efficiency
  consequences of the reform

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Two-step decomposition

• What if a reform is not distribution-neutral?
• Decompose as follows
• (1) Construct distribution-neutral reform
• (2) Move from that to actual reform
• Note latter is purely redistributive
• Comments
• Clarifies analysis
• Facilitates specialization

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Qualifications

• Commodities that interact with utility of
  labor-leisure choice
• higher tax rate on books, which are leisure
  complements, because discouraging leisure reduces
  labor supply distortion
• subsidize central city amenities
• Other qualifications
• Goods that signal ability (as distinct from
  income) opera?
• Externalities e.g., pollution, gifts, (more
  below)
• Still, it provides general way to assimilate many
  fiscal issues into a common framework

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Contents

1. Framework
2. Optimal Income Taxation
3. Optimal Commodity Taxation
4. Applications
5. Tax Equity

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General implications

• Ramsey taxation principles (inverse elasticity
  rule) essentially wrong in this setting
• All analysis based thereon (e.g., of capital
  income taxation) not right when is an income tax
  that may be adjusted
• Examples
• Exemption of food from VAT (groceries vs.
  restaurant meals)
• Taxation of gifts viewed as one sort of
  consumption expenditure
• Public goods can compare price to marginal WTP
• Taxation of savings (income versus consumption
  tax, etc.) standard income tax is equivalent to
  pure labor income tax plus differential taxation
  on commodities consumed in different periods . . .

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Income vs. consumption Tax and taxation of
capital (ch. 9)

• Earn in period 1, consume in periods 1 and 2
  model difference in terms of budget constraints
  (illustration with flat-rate tax, no grant)

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Analysis

• Interpret as differential commodity taxation
• Consumption in different periods consumption of
  two different commodities
• Atkinson-Stiglitz result applies
• Note not pro-rich because doing it
  distribution-neutral (income tax adjusts)

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Discussion

• Capital taxation generally
• Including wealth taxation
• Corporate income tax
• As a form of differential capital taxation
• Recent dynamic Mirrlees literature
• Intertemporal wedge
• Intuition multi-period, future labor income
  uncertainty, induces precautionary savings, but
  that dampens future labor supply (wealth effect)
• Administrative arguments bearing on income tax
  vs. consumption tax

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Corrective taxation (ch. 8.G)

• Pigouvian taxes and subsidies
• Similar features for much of regulation
• Including liability through the legal system
• Qualifications?
• Distributive weights
• Labor supply distortion (double dividend, etc.)
• Neither again
• Analogy to differential commodity taxation
• Distribution-neutral income tax adjustment

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Transfer (estate/gift) taxation (ch. 10)

• Description/model differential commodity
  taxation based on own- versus other-consumption
• Analysis
• again, presumptively inefficient
• Gift externalities
• Positive, to donee
• Negative, income effect on donee
• Note again, integrating w/ income tax (which can
  tax rich however would like) transforms question
  and produces qualitatively different analysis
  results
• Extension charitable giving

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Unit of taxation (ch. 12)

• Marrieds vs. singles number of children
• Controversial
• Qualitative changes over time
• Differences across countries
• Huge common denominator problem need link to
  objective function (social welfare function)
• Approach
• Positive model of family (e.g., models of
  sharing, as in Becker 1974)
• SWF with each individual counting once

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Analysis distribution

• Does unequal sharing clearly favor
  individualized treatment? (no)
• Do scale economies clearly favor less generous
  treatment of marrieds? (no)
• Should child benefits be fixed amounts /
  declining with income? (no)
• Note form of SWF and degree of risk-aversion
  (rate of declining MU of consumption) have
  qualitative effect here

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Analysis incentives

• Work
• Marriage
• Child-bearing

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Contents

1. Framework
2. Optimal Income Taxation
3. Optimal Commodity Taxation
4. Applications
5. Tax Equity

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Framework (ch. 13 14)

• Welfarism
• Restate definition
• Other norms can lead to Pareto conflicts
• Proxy rationales
• Choice of social welfare function
• Original position
• Sufficiently egalitarian?
• Whose welfare included?

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Other tax equity norms (ch. 15)

• E.g.,
• Ability to pay
• Horizontal equity
• Benefit principle
• Sacrifice principle
• Definitions as norms (e.g., use of Haig-Simons
  definition of income)
• Criticism
• Need root in social welfare
• Vague, incoherent
• Conflict with Pareto principle
• Possible value as proxy principles