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

5. 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

6. 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

7. 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

8. 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

9. Define a tax package • dp=δ.d • where δ = 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

10. Substitute for dp in the private budget constraint and solve • Solve for the impact of dG on welfare (1-MCF(p-p*)'χI). eudu = [ - MCF{cG-(p-p*)'epG}]dG or eudu = FXM. [ - MCF{cG-(p-p*)'epG}]dG

11. What is the MCF? • MCF= ep'δ/[ep'δ + (p-p*)'eppδ] • For a single tax economy • MCF = 1/(1+t.) 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

12. What is FXM? • FXM =1/(1-MCF(p-p*)'χI)) • 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), • FXM<1 if a transfer reduces the volume of taxed good/service (eg labour tax) • Depends on initial taxes, not tax change

13. Welfare evaluation eudu = FXM. [ - MCF{cG-(p-p*)'epG}]dG • 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

14. Money-Metric Approach eudu = [π – MMCF.{cG-(p - p*)'(epG+χIπ')}]dG • where • MMCF = ep'δ/[ep'δ+(p-p*)'(epp- χIep')δ] • For a single-tax economy, this is • MMCF = 1/(1+t.U) • Note the χIπ'dG term. • This is the income effect of the provision of public goods. Must be added if MMCF used

15. 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 MCF*fiscal cost • With MMCF, an analyst must adjust the assessed value for income effects of public good change on taxed items

16. 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

17. When is MMCF sufficient? • In the case of “ordinary independents” • eudu = [π – MMCF.cG]dG • This arises when (epG+χIπ‘)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– doesn’t rule out substitution effects (nor Y effects)

18. 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 Feldstein’s 1995 paper has been to move from labor supply elasticities (eg 0.2) to much higher elasticities of income

19. Impacts on MWC

20. 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