Costs of Taxation and the Benefits of Public Goods

1
Costs of Taxation and the Benefits of Public
Goods

• Will Martin
• World Bank
• 12 July 2005

2
Outline

• How should costs of public good provision be
  measured?
• Develop a simple yet general model
• Does it matter with the new estimates of income
  response?

3
Debate on this Central Issue

• Traditional Harberger-Browning analysis uses
  compensated measures of the marginal cost of
  funds (MCF)
• Recent consensus in the public finance literature
  uses compensated measures of impacts on
  consumers-producers, but allows for income
  effects on tax revenues
• Kaplow says income effects wash out

4
Implications of Consensus

• Two measures needed- thought experiments
• Compensated measures for differential incidence
• Uncompensated measures for public goods
• Huge differences in results.
• Fullerton estimates compensated MCF of 1.25 vs
  1.07 for the uncompensated measure
• Marginal excess burden said to be 0.25 under
  consensus approach vs 0.07 under compensated

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Modeling Approach

• Need a framework that incorporates both public
  good provision and taxation
• Want multiple public goods, taxes
• Single, representative household faces a vector
  of prices, p
• Market prices, p exogenous
• Government cost function c(G, p,?)
• cG Direct cost to govt of public good

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Modeling approach (contd)

• Household behavior e(p,G,u)
• including taxes on consumption supply of
  factors such as labor
• Producer behaviour g(p,G)
• Private sector behavior captured by
• E e(p,G,u) - g(p,G)
• Vector of valuations of public goods
• -EG ? ?MRS gG

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Budget Constraints

• Government budget constraint
• c(G,p,?) - p - p'ep(p,G,u) ?
• Private budget constraint.
• E(p,p,G,u) ?
• Gives us a complete model

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Public good provision financed by taxes

• Consider a change in G financed by tax changes
  that change p.
• Totally differentiate in p, G, u to get

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Define a tax package

• dpd.d?
• where d W.p if the tax as specified relative
  to market prices, eg 1c on a consumption tax or
  1 on an income tax
• and d? is the size of the tax change needed to
  restore balance
• Note the marginal tax change may be quite
  different from the initial tax structure

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Substitute for dp in the private budget
constraint and solve

• Solve for the impact of dG on welfare
• (1-MCF(p-p)'?I). eudu
• ? - MCFcG-(p-p)'epGdG
• or
• eudu FXM. ? - MCFcG-(p-p)'epGdG

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What is the MCF?

• MCF ep'd/ep'd (p-p)'eppd
• For a single tax economy
• MCF 1/(1t.?) where t is a proportional tax
  and ? the compensated elasticity of supply/demand
• Compensation to the private sector needed to
  maintain utility when the government reduces its
  transfer from the rest of the world, and balances
  its budget by raising taxes

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What is FXM?

• FXM 1/(1-MCF(p-p)'?I))
• eudu FXM.d?
• The value to the private sector of a transfer
  from outside the system
• FXM ?1 if a transfer increases demand for taxed
  goods (eg consumption tax),
• FXMlt1 if a transfer reduces the volume of taxed
  good/service (eg labour tax)
• Depends on initial taxes, not tax change

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Welfare evaluation

• eudu FXM. ? - MCFcG-(p-p)'epGdG
• As long as FXM is positive, we can use the term
  in square brackets to determine the sign of
  welfare effects
• Have included income effects from both taxation
  and public good provision, but gathered them
  together-- the Hatta (1977) multiplier

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Money-Metric Approach

• eudu p MMCF.cG-(p - p)'(epG?Ip')dG
• where
• MMCF ep'd/ep'd(p-p)'(epp- ?Iep')d
• For a single-tax economy, this is
• MMCF 1/(1t. ?U)
• Note the ?Ip'dG term.
• This is the income effect of the provision of
  public goods. Must be added if MMCF used

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Policy implications

• Either the MCF or MMCF can be used for policy
  analysis
• MCF facilitates decentralization. Analyst must
  compare the assessed value of the public good
  with MCFfiscal cost
• With MMCF, an analyst must adjust the assessed
  value for income effects of public good change on
  taxed items

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Question of numeraire

• MCF experiment focuses on compensation to the
  private sector from outside the system
• MMCF experiment focuses on value to the private
  sector
• Could also ask the Little-Mirrlees question of
  compensation to the govt. from outside the system

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When is MMCF sufficient?

• In the case of ordinary independents
• eudu p MMCF.cGdG
• This arises when (epG?Ip)dG 0
• but this relies on pure coincidence
• and is infeasible when substitution and income
  effects operate in the same direction
• Also, makes the MCF depend on use of funds
• Separability also insufficient doesnt rule out
  substitution effects (nor Y effects)

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Does it still matter?

• With traditional parameter values eg
  uncompensated labour supply zero, compensated
  supply 0.2, the differences were huge
• A focus of the literature since Feldsteins 1995
  paper has been to move from labor supply
  elasticities (eg 0.2) to much higher elasticities
  of income

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Impacts on MWC
MWCC MWCU Redn using MWCU
Ballard 90 0.20 0.03 85
Fullerton 91 0.25 0.07 72
Feldstein 99 0.57 0.27 53
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Conclusions

• Either MCF or MMCF can be used to evaluate costs
  of public good
• But use of MMCF requires an adjustment to the
  perceived value of the public good
• Done right, no policy significance
• Difference is choice of numeraire
• Empirically, MCF MMCF very different even with
  new substitution effects
• Higher effic. cost raises hurdle for use of
  public funds