Economic Policy and Equality of Opportunity

Transcription

1 Economic Policy and Equality of Opportunity Sang Yoon (Tim) Lee 1 Ananth Seshdari 2 1 University of Mannheim 2 University of Wisconsin October 25, 2014 Normative Ethics and Welfare Economics

2 Redistributive Justice in Quantitative Economics Operationalize equality of opportunity (EOP) concepts in quantitative macro 1. Current state-of-the-art is dominated by utilitarian social welfare criteria; occasionally Rawlsian, the other extreme 2. We show equality of outcomes EOP Using an intergenerational model as a testbed, we argue 1. outcome variables of the child should be chosen differently according to which parental background variables a social planner wishes to compensate for, 2. which is not apparent in a static, 2-generational framework

3 Measuring EOP 1. Map the state space and choices of a recursive decision problem into background" and outcome" variables 2. Ordinal EOP measure follow Lefranc et al. (2008) s pair-wise stochastic dominance tests between distributions conditioned on background variables : an empirical operationalization of EOP concepts pioneered by Arneson (1989); Roemer (1993) 3. Theil index of outcomes decomposed by background used for cardinal comparison of counterfactual policies against utilitarian social welfare and equality of outcomes (IGE lifetime earnings, Gini s of lifetime earnings/wealth)

4 Model Features Intergenerational aspect (Becker and Tomes, 1986): 3 channels of transmission 1. childhood investments: parental time and goods 2. transmission of genetics: smart parents have smart kids 3. bequest constraints: some parents unable to invest enough in child Lifecycle aspect captures: 1. college education costs tuition and time 2. life-cycle earnings (Ben-Porath, 1967) 3. splits the timing of investment in children and bequests

5 Beyond 2 Generations Infinite dynastic structure reveals issues not revealed in 2 generations framework Suppose we choose Y : child earnings as the outcome 1. then the background we compensate for should be B: parental luck, not earnings 2. everything else is itself an outcome of previous generation efforts

6 Beyond 2 Generations Infinite dynastic structure reveals issues not revealed in 2 generations framework Suppose we choose Y : child earnings as the outcome 1. then the background we compensate for should be B: parental luck, not earnings 2. everything else is itself an outcome of previous generation efforts But we probably want to maintain B: parental earnings as the background 1. but then, the outcome we look at should be Y : child s net wealth at later age, not earnings 2. a lot of child s earnings are used in grandchild investments

7 Main Findings 1. Compared to B: parent earnings and Y : child earnings, if B: parent s genetic luck and Y : child earnings EOP is much higher if B: parent s earnings and Y : child s net wealth EOP is lower 2. This pairing is confirmed by cross-checking with child s continuation utilities, which is unobserved in the data 3. Education subsidies help equality of outcomes but not so much EOP

8 Why? Our previous work shows that investment in children that happens much more in advance of bequests helps explain previously puzzling lifecycle and intergenerational facts Parental human capital, through investment in children, is main determinant of intergenerational persistence little room for ability persistence Bequest constraints matter early on in the lifecycle poor parents unable to invest efficiently in children, who in turn are unable to invest efficiently in grandchildren,...

9 EOP as a Derivative Norm Arneson (2014) argues lack of EOP may not be a wrong in itself, but an indication of something wrong Our model has two inherent market imperfections 1. imperfect insurance against descendant s luck shocks 2. no borrowing against unrealized descendant s incomes Interpretation: 1. imperfect insurance against descendant s luck shocks less of a problem, but 2. inefficient investment in children due to constraints manifested as less EOP

10 Quick Description of Model: Young Parent W y (S, a ; x; z y ) = } max {q y u(c y ) + β 4 V o (a ; x ; z o )df (a, ɛ a ) e a,ɛ subject to a long budget constraint that includes z h. x = [S, a, ɛ, h] : state of parent e : parent s choices include investment in children (m p, n p ) and self (n y ) x : state of child depends on x and e z y : bequests from grandparent z h : lifetime earnings z o : middle-age wealth

11 Quick Description of Model: Old Parent V o (a ; x { ; z o ) = max qo u(c o ) + θv y (a ; x ; z y) } C o,z y C o + z y = z o z y 0, In the simplified model old parents only eat and leave bequests, subject to a non-negativity constraint Dynastic preferences generated by θ (0, 1) Lack of EOP can be viewed as a manifestation of this constraint

12 Closing the Model: Environment and Empirics The model includes government policies, including education and lump-sum transfers Decisions are aggregated to be consistent in a general equilibrium wt goods, labor and asset markets Parameters calibrated to empirical data, simulated model reconciles previous empirical puzzles

13 Effort and Luck We view the choices made by individuals in the model as efforts," that should be equally rewarded (relatively, Roemer (1993)) (a, ɛ) depends on a 1 (stochastically) a : should be rewarded by self-ownership principle ɛ : should be rewarded as later brute luck (Dworkin, 1981; Vallentyne, 2002) * but only the part uncorrelated with a 1

14 Effort and Luck We view the choices made by individuals in the model as efforts," that should be equally rewarded (relatively, Roemer (1993)) (a, ɛ) depends on a 1 (stochastically) a : should be rewarded by self-ownership principle ɛ : should be rewarded as later brute luck (Dworkin, 1981; Vallentyne, 2002) * but only the part uncorrelated with a 1 All other variables can be viewed as outcomes from efforts of previous generations This is manifested as human capital, the main determinant of lifetime earnings z h EOP: z h distributions conditional on a 1 should be equal

15 Parental Background But if the planner decides to ignore ancestral efforts, should also ignore the child s efforts directed to descendants Hence to analyze EOP, we should first purge z h of investment in children and bequests:

16 Parental Background But if the planner decides to ignore ancestral efforts, should also ignore the child s efforts directed to descendants Hence to analyze EOP, we should first purge z h of investment in children and bequests: Define net wealth z w = z }{{} o z y }{{} free of hc transfers financial transfers EOP: z w distributions conditional on z h, 1 should be equal

17 Intergenerational Transmission of Background, Luck and Effort z h, 1 E 1 n y, 1 p e B z h E n y k e B z h n p, 1 m p, 1 p b S 1 h y, 1 n p m p k b S h y L b ɛ 1 a 1 L e ɛ a a

18 Visual Inspections, Conditional c.d.f. z h by z h, 1 z w by z h, 1 z h by a 1

19 The Pairing Reflects Continuation Utilities c v by z h, 1 c v by a 1 z w by z h, 1 z h by a 1

20 Visual Inspections, Lorenz Curves z h by z h, 1 z w by z h, 1 z h by a 1

21 The Pairing Reflects Continuation Utilities c v by z h, 1 c v by a 1 z w by z h, 1 z h by a 1

22 T = = J j=1 J j=1 = T b + µ j µ Theil Index ( y ȳ log ȳ ) df j(y) y [ ( ) ȳj s j ȳ log ȳj + ȳ 4 s jt j j=1 ) ] y (log ȳyj df j(y) ȳ j s j = type j s share of of total y in the population, ȳ = mean of y in the population, ȳ j = conditional mean of y in type j, T b = Theil index across the means of each type T j = Theil index within each type

23 T = = J j=1 J j=1 = T b + µ j µ Theil Index ( y ȳ log ȳ ) df j(y) y [ ( ) ȳj s j ȳ log ȳj + ȳ 4 s jt j j=1 ) ] y (log ȳyj df j(y) ȳ j s j = type j s share of of total y in the population, ȳ = mean of y in the population, ȳ j = conditional mean of y in type j, T b = Theil index across the means of each type T j = Theil index within each type EOP: T b = 0 and T j = T j, j j

24 Equity and Efficiency Effects of Subsidies B E G IGE Gini z h Theil z h Retirement Wealth Gini log z h - 34% -1% log z w - 29% -1% log c v - 28% -1% B: Benchmark E: shift all subsidies to education, has large impact G: shift all subsidies to lumpsum, has minimal impact

25 Shifting Subsidies and EOP: Parental Abilities B E G TOTAL Between 8% 8% 8% Within 92% 92% 92% Q z h by a 1 Q Q Q Between 46% 43% 47% Within 54% 57% 53% Q z h by z h, 1 Q Q Q

26 Shifting Subsidies and EOP: Parental Abilities B E G TOTAL Between 8% 8% 8% Within 92% 92% 92% Q z h by a 1 Q Q Q Between 46% 43% 47% Within 54% 57% 53% Q z h by z h, 1 Q Q Q

27 Shifting Subsidies and EOP: Parental Human Capital B E G TOTAL Between 52% 49% 53% Within 48% 51% 47% Q z w by z h, 1 Q Q Q TOTAL Between 46% 43% 47% Within 54% 57% 53% Q z h by z h, 1 Q Q Q

28 Shifting Subsidies and EOP: Parental Human Capital B E G TOTAL Between 52% 49% 53% Within 48% 51% 47% Q z w by z h, 1 Q Q Q TOTAL Between 46% 43% 47% Within 54% 57% 53% Q z h by z h, 1 Q Q Q

29 Conclusion Operationalize EOP concepts in a quantitative integenerational model Outcome variables should differ depending on planner s choice of background variables: Parental luck is more compensated for than parental lifetime earnings Parental human capital is less compensated for Equality of outcomes EOP

30 Arneson, RichardJ., Equality and equal opportunity for welfare, Philosophical Studies, 1989, 56 (1), Becker, Gary S and Nigel Tomes, Human Capital and the Rise and Fall of Families, Journal of Labor Economics, July 1986, 4 (3), S1 39. Ben-Porath, Yoram, The Production of Human Capital and the Life Cycle of Earnings, Journal of Political Economy, 1967, 75, 352. Dworkin, Ronald, What is Equality? Part 2: Equality of Resources, Philosophy & Public Affairs, 1981, 10 (4), pp Lefranc, Arnaud, Nicolas Pistolesi, and Alain Trannoy, Inequality Of Opportunities Vs. Inequality Of Outcomes: Are Western Societies All Alike?, Review of Income and Wealth, December 2008, 54 (4), Roemer, John E., A Pragmatic Theory of Responsibility for the Egalitarian Planner, Philosophy and Public Affairs, 1993, 22 (2), pp

31 Vallentyne, Peter, Brute Luck, Option Luck, and Equality of Initial Opportunities, Ethics, 2002, 112 (3), pp