lecture 3. equality of opportunity

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Lecture 3. Equality of opportunity. Erik Schokkaert (KULeuven, Department of Economics). Structure. Roemer's model of "equality of opportunity" An application to optimal income taxation An alternative: Van de gaer's approach Comparing different approaches. - PowerPoint PPT Presentation


  • Lecture 3. Equality of opportunityErik Schokkaert (KULeuven, Department of Economics)

  • Structure

    Roemer's model of "equality of opportunity"An application to optimal income taxationAn alternative: Van de gaer's approachComparing different approaches

  • 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 typePersons who are identical wrt the responsibility characterics have exerted the same effort level

  • Relation between effort and output for various typesinstruments

  • "Effort" dependent on typecigarettes smokedlow SEShigh SES58

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

  • "sum" over all the possible -levels

  • Special casesif everybody has the same :

    if there is only one type: MAXIMINUTILITARIANISMthis is very different from the responsibilityaxioms in Fleurbaey!

  • 2. Application: optimal income taxationcircumstance (type): level of education of parentsoutcome function - instruments :post-tax income = (1 a) x + ctherefore: =(a,c)effort is the residual: in income distribution per type


  • "Final" objective function:

    (in the monotonic case) maximize the average income of the worst-off type

  • Modelling behavioural reactionsindividuals have utility function


  • Government budget constraint


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

  • The optimal tax rate

    interpretation 1: interpretation 2: (B A)

  • value of the objective functionat the (proportional) benchmark

    value of the objective function at the observed policyvalue of the objective function at the EOP-policy

  • Refining the definition of "type"

  • 3. An alternative: Van de gaer-approach

  • Comparing the rulesRoemer:Van de gaer:

  • 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

  • In general: different intuitionsCompensation 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 typesaxiomatic analysis in Ooghe, Schokkaert, Van de gaer (Social Choice and Welfare, February 2007)

  • Illustration

  • 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)wLLabor supply L=(e(1-t)w)L0



    For later reference:

    EMBED Equation.3




  • Optimal subjective outcome egalitarian tax rate

    NOTE: worst-off individual has characteristics (eL,,wL)

    Smaller than tBIIf eL decreases (the laziest person in society gets lazier), the optimal marginal tax rate will increase

  • Optimal subjective opportunity egalitarian tax rate

    Smaller than optimal subjective outcome egalitarian tax rateIndependent of the distribution of e


    compare with utility function:

    as g increases, the burden of market work, as perceived by the social planner decreases

    if g goes to infinity, only income matters (cf Roemer et al.)



  • gtE(A)tBItE(W)(1,1)(1,wL)(eL, wL)

  • Objective egalitarianism and subjective Pareto-efficiency 1Individuals with larger values of (larger labor income) prefer a lower tax rate

    Tax rates are not Pareto-efficient ifsmaller 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.

  • Objective egalitarianism and subjective Pareto-efficiency 2Political feasibility? (but then why not go for the option of the median voter?)

    Ethical trade-offs:Pareto-efficiency as a side-constraintreject subjectivism altogether (extreme case of laundering subjective preferences?)

  • gtS(A)tI(A)tBItE(W)

  • gtE(A)tS(A)tI(A)tBItE(W)

    PROPOSITION: for a given value of g,


  • Application: description of the sample

  • Optimal tax rates (subjective cases)introducing opportunity considerations has a minor influenceimportant effects of

  • Results for =0.30introducing advantage matters for low values of gIntroducing opportunity considerations has a minor influence

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

  • ConclusionIt is possible to derive operational tax rules from rather complex objective functions

    Real debate is about the choice of the objective functionHow 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?


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