Lecture 3. Equality of opportunity

1. Lecture 3. Equality of opportunity Erik Schokkaert (KULeuven, Department of Economics)

2. Structure • Roemer's model of "equality of opportunity" • An application to optimal income taxation • An alternative: Van de gaer's approach • Comparing different approaches

3. 1. Roemer's model of "equality of opportunity" • Make a distinction between characteristics for which persons are responsible ("effort") and for which they are not ("circumstances") • Persons who are identical wrt the “compensation characteristics” are of the same “type” • Persons who are identical wrt the “responsibility characterics” have exerted the same “effort” level

4. Relation between effort and output for various types instruments

5. "Effort" dependent on type high SES low SES 5 8 cigarettes smoked

6. Equality of opportunity-criterion • "equalize" outcomes at a given level of π (remember EWEP or EIER!)

7. "sum" over all the possible π-levels

8. Special cases • if everybody has the same π: • if there is only one type: MAXIMIN UTILITARIANISM this is very different from the responsibility axioms in Fleurbaey!

9. 2. Application: optimal income taxation • circumstance (type): level of education of parents • outcome function - instruments φ: post-tax income = (1 – a) x + c therefore: φ=(a,c) • effort is the residual: π in income distribution per type

10. => OUTCOME AS A FUNCTION OF π

11. "Final" objective function: (in the monotonic case) maximize the average income of the worst-off type

12. Modelling behavioural reactions • individuals have utility function • hence,

13. Government budget constraint B

14. Objective function: "maximize the average post-fisc income of the worst-off type": post-tax income = (1-a)x +c

15. The optimal tax rate • interpretation 1: η • interpretation 2: (B – A)

18. value of the objective function at the observed policy value of the objective function at the (proportional) benchmark value of the objective function at the EOP-policy

20. Refining the definition of "type"

21. 3. An alternative: Van de gaer-approach

22. Roemer: Van de gaer: Comparing the rules

23. both rules coincide: • in the extreme cases (one type OR everybody the same effort) • if there is a dominance relation between the different outcome functions

24. In general: different intuitions • Compensation of results (Roemer): try to equalize outcomes for different types at the same effort level • Compensation at the level of opportunity sets (Van de gaer): try to equalize the value of opportunity sets of different types • axiomatic analysis in Ooghe, Schokkaert, Van de gaer (Social Choice and Welfare, February 2007)

25. Illustration

26. 4. Comparing both approachesSchokkaert, Van de gaer, Vandenbroucke, Luttens (Mathematical Social Sciences, 2004) • Individuals differ in two dimensions • Independently distributed with density functions fw(w) and fe(e) • Quasi-linear utility function (cfr Roemer et al., 2003) • Budget constraint Y=B+(1-t)wL • Labor supply L=(e(1-t)w)εL0

28. SUBJECTIVE OUTCOME EGALITARIANISM OBJECTIVE OUTCOME EGALITARIANISM SUBJECTIVE OPPORTUNITY EGALITARIANISM OBJECTIVE OPPORTUNITY EGALITARIANISM

29. Optimal subjective outcome egalitarian tax rate NOTE: worst-off individual has characteristics (eL,,wL) • Smaller than tBI • If eLdecreases (the laziest person in society gets lazier), the optimal marginal tax rate will increase

30. SUBJECTIVE OUTCOME EGALITARIANISM OBJECTIVE OUTCOME EGALITARIANISM SUBJECTIVE OPPORTUNITY EGALITARIANISM OBJECTIVE OPPORTUNITY EGALITARIANISM

31. Optimal subjective opportunity egalitarian tax rate • Smaller than optimal subjective outcome egalitarian tax rate • Independent of the distribution of e

32. SUBJECTIVE OUTCOME EGALITARIANISM OBJECTIVE OUTCOME EGALITARIANISM SUBJECTIVE OPPORTUNITY EGALITARIANISM OBJECTIVE OPPORTUNITY EGALITARIANISM

34. tE(A) tBI tE(W) g (eL, wL) (1,1) (1,wL)

35. Objective egalitarianism and subjective Pareto-efficiency 1 • Individuals with larger values of (larger labor income) prefer a lower tax rate • Tax rates are not Pareto-efficient if • smaller than tax rate preferred by (1,1) - easily possible for large values of g (e.g. income as advantage); • larger than tax rate preferred by (eL, wL) - definitely true for low values of g.

36. Objective egalitarianism and subjective Pareto-efficiency 2 • Political feasibility? (but then why not go for the option of the median voter?) • Ethical trade-offs: • Pareto-efficiency as a side-constraint • reject subjectivism altogether (extreme case of laundering subjective preferences?)

37. SUBJECTIVE OUTCOME EGALITARIANISM OBJECTIVE OUTCOME EGALITARIANISM SUBJECTIVE OPPORTUNITY EGALITARIANISM OBJECTIVE OPPORTUNITY EGALITARIANISM

38. tI(A) tS(A) tBI tE(W) g

39. tE(A) tI(A) tS(A) tBI tE(W) g

40. Application: description of the sample

41. Optimal tax rates (subjective cases) introducing opportunity considerations has a minor influence important effects of ε

42. Results for ε=0.30 introducing “advantage” matters for low values of g Introducing opportunity considerations has a minor influence

43. ε = 0.06 versus ε=1 Effects of ε: (a) level of optimal tax; (b) breakpoint

44. Conclusion • It is possible to derive operational tax rules from rather complex objective functions • Real debate is about the choice of the objective function • How to interpret equality of opportunity? • How to trade off compensation versus responsibility? • Where do “reference preferences” come from? • What about (subjective) Pareto-efficiency? How to correct "happiness" measures?