What Can Benefit Cost Analysis Tell Us?

1. What Can Benefit Cost Analysis Tell Us? Ted Bergstrom UCSB

2. New Welfare Economics • Kaldor and Hicks, 1939. • Compensation Principle. • Change is an improvement if gainers could compensate losers.

3. A Dollar is a Dollar? “When evaluating net benefits and costs of a given action the costs and benefits accruing to each individual should normally be added without regard to the individual(s) to whom they accrue.”---Harberger

4. A Sound Chain of reasoning? 1) If a project passes the Compensation test, it is Potentially Pareto improving 2) If a project is potentially Pareto improving, it should be adopted.

5. Message of this paper • Though both links are broken, Benefit cost analysis remains a useful tool.

6. Link 2 of the chain: Hicks on Compensation “Every simple economic reform inflicts a loss on some people. Yet when such reforms have been carried through…compensation has not been given, and economic progress has accumulated a roll of victims, sufficient to give all sound policy a bad name. “

7. Link 1 of the chain • A reallocation in a pure exchange private goods economy need not be potentially Pareto improving even if the sum of compensating variations over all individuals is positive. • Money values are a rubbery measuring rod—Samuelson (1950) • Boadway paradox.

8. A public goods economy • Consider an economy with 1 private good, and n public goods. • Each consumer has utility Ui(xi,y) • Cost of private goods vector y is given by a function C(y). • Sum of individual private consumptions plus C(y) is a constant.

9. Salvaging Link 1: • In public goods economy there is only 1 private good. • This can be used as measuring rod, avoiding index number problems, Boadway paradox, etc. • Reasonable if policy change does not substantially affect relative prices of private goods. (Ng-Mishan defense)

10. Compensation test in a public goods economy • Define consumer j’s willingness to pay for a change in public goods from y to y’ as wj where: • Ui(xj- wj,y) = Ui(xj,y’) • Compensation test: Compare . Sum of wj’s to C(y’)-C(y).

11. Repairs on Link 1 • Theorem: For a public goods economy, a project passes the compensation test if and only if it is potentially Pareto improving. • Trivial proof.

12. What to choose? • Disadvantage of compensation test: It doesn’t order alternatives relative to each other, only a single alternative relative to status quo. • You could proceed sequentially, but you would need a separate study for each conceivable alternative.

13. Samuelson condition • Samuelson condition brings calculus to aid in search. • With smoothness, a necessary condition for an increase in y to be potentially Pareto improving is (sum of mrs)> mc • Also sufficient for small changes.

14. Potential Pareto Improvement in a public goods model

15. Scitovsky-style paradoxes remain • An “ordering” on allocations that respects the compensation principle will have still have cycles, even with a single public good.

16. Got Paradoxes?

17. Orderly Nesting

18. Three Repair Crews • Rotten-Kid Defense –Becker, Parish, Ng • Fair Gamble Defense • Search Tool Defense Hicks, et al

19. Rotten-Kid Defense • Income distribution is controlled by forces beyond control of benefit cost analysts. • A project that passes the benefit cost test will ultimately result in a better outcome for (almost) everybody • Therefore the dollar-is-a-dollar rule is a good one for benefit cost.

20. Probing the Rotten Kid Defense? • Like Becker’s family example, this argument has some appeal if utility possibility frontiers are nested and “parallel.” • Supported by bargaining theory only if “threat points” are not altered. (Pollack and Lundberg examples) • Projects may change shape of UPF. If so, potential Pareto improvement need not result in actual Pareto improvement.

21. The Fair Gamble Defense • Government should have a policy of accepting projects if and only if they the benefit-cost test, while paying for them using the existing tax structure. • Although individuals win some and lose some, they will on average be best off with this policy.

22. Weakness of the Fair Gamble Defense • It does not offer a complete ordering among multiple projects • Some projects, though passing the fair gamble test have clearly identifiable winners and losers.

23. When Fair Gamble Defense Applies. • Incomplete information about individual preference types, but good statistical information about distribution. • Projects (though possibly large) have small enough impacts on individual wealth so that risk neutrality is a good assumption.

24. The Search Tool Defense Benefit Cost can tell Where to look and Where not to look for Pareto improvements

25. Two-Stage Procedure . • If policy fails the BC test, drop it. If policy passes, look for Pareto improving ways to apply it. • If policy passes and benefits are unevenly distributed in known ways, allocate costs accordingly. If specific beneficiaries unidentifiable, consider whether fair gamble argument justifies.