Responsibility, well-being, information, and the design of distributive policies

Download fulltext

1 RESPONSIBILITY WELL-BEING INFORMATION AND THE DESIGN OF DISTRIBUTIVE POLICIES Frank Vandenbroucke‡ ABSTRACT The model developed in this paper admits a systematic discussion of the normative rationale behind use two distributive instruments: negative income taxation creating an unconditional basic on one hand and wage subsidies other integrates opposite conceptions personal responsibility (whether or not we are responsible for our propensity to work labour market) into single framework Thus can compare these systematically define conditions practical convergence between policies they indicate This also illustrates how optimal theory may proceed when utilities considered ordinal interpersonally comparable requires definition objective notion individual well-being I incorporate “time nonmarket activity” shows alternative choices with regard inclusion weighing non-market Rawlsian basket primary goods affect prescription More generally it posttransfer reward scheme government proposes is used illustrate idea defended by Fleurbaey et al that responsibility-sensitive egalitarian justice imposes principle natural Given simplifying assumptions will establish second-best regimes excluding corner solutions each conception set instruments one-to-one correspondence principles Hence given there unique which yields neutral i e “neutral” official then study “egalitarian earnings subsidy scheme” proposed White (1999) assess related (1997) Van Parijs reciprocity According implies rejection be complementary However under certain demands earned only fund so has funded (possibly together expenditures) capital tax available “personal dividends” ‡ based Chapter 3 my D Phil thesis (Vandenbroucke 1999) am grateful Anthony Atkinson Marc Erik Schokkaert Frans Spinnewyn Tom Puyenbroeck Philippe comments earlier versions INTRODUCTION With employment policy welfare reform large degree consensus among makers scholars taxes benefits must lead situation poor individuals (or their families) face very high marginal rates take up job hours increase Benefit systems too selective beset “inactivity traps” discouraging market participation low-skilled workers In academic research various proposals “basic income” “negative taxation” put forward remedy such inactivity traps Obviously approaches incentive problem low earners possible as (i) topping skilled workers’ purchasing power credits (ii) increasing net pay lowering social security contributions (iii) supporting sufficiently minimum wages selectively subsidizing employers These reflect technical differences but more fundamental approach Therefore useful first from vantage point examining underpinning without reference particular problems created benefit economies involuntary unemployment present (which mutually exclusive): mathematical objective1 call “advantage”) except special case what follows “objective” “interpersonally comparable” interchangeably advantage defined purely way violations Pareto (a judged better whereas every agent worse-off his view) justification cannot pursue here Note propose depends upon judgement sense “subjective” 2 view improves Rawls’s nonRawlsian “incentive policy”) allows comparison qua information availability redistributive efficiency: (1) taxation; (2) form thus universal responsibilitysensitive (see references footnote 5) look allocation rules fully compensate influence differentials non-responsible characteristics over agents’ let operate argument owes its appeal neutrality vis-à-vis preferences akin liberal ideal “neutrality fact do think respect Vandenbroucke 1999 pp 40-41) Yet provides benchmark versus (Sections 14 15) presents simple world action completely determined answering three questions: 1) responsibility? 2) citizens? 3) (hence feasible)? simplicity review due both concerning economic environment government’s Within specific strictest One specify axioms specifying See Rawls 1993 p 193 aim” (advantage) citizens’ (ESS) prove White’s ESS result optimisation exercise specification solution equality On basis demonstrates trade-off level rate moves holds people shift ASSUMPTIONS CONCERNING ECONOMIC ENVIRONMENT Each population P characterized vector ( ) [ 1] ] L w Î ´ ¥ ³ 0 Individuals have range skills levels associated A citizen’s productivity he earn per unit paid 4 marketplace putting best rewarded assume citizens always choose kind rewards So neither nor citizen (w whose working time earns wL We metric = most productive An individual’s human “internal endowment” external endowments houses land invested economy value assets represent him expressed equivalent flow average yield need reinvested order maintain redistributed any side-effect “per capita dividend” construe individually owned unequally distributed dividends assumption highly abstract no doubt unreal adjudicate philosophical debate divide activity outside (e g eating organizing household caring children sleeping resting leisure factor characterizes preference ordering Individual utility functions noncomparable e) represented strictly monotonically transformation f(Ue) o eL U Y – whereby disposable parameter Lo sets standard maximal might chosen Since maximum crazy workaholic would if were maximize (Maximizing expression (ÞY L) postulate humanly leaves indifferent (i substitution indifference curve by: 5 ¶ If small values highly: she prepared forgo much buy factors independently variance s Concerning distribution dividend data relevant assume: “(w )Î : Þ implying partitioned “productivity types” “preference Tw* having same w* “type”: {(w } * Pe* e* “tranche”: continuously infinite number 6 GOVERNMENT’S POLICY STANCE Recall aim focus dimensions stance: responsibility; well-being; simplify defining gives absolute priority position worst-off dimension want distinguish branches justice: “RAWLS” activity; “RESPO” ultra-simple (RAWLS RESPO short) consider people’s possession circumstance (say because results history gifts bequests could influence) second postulated Section incomparable RAWLS hold although does reflects John thinks happiness mainstream exposition out “work effort”4 some “advantage” Below continuum depending “burden work” significant simplification obtains “impartial” aggregation method utilitarian flavour explain following sections Finally about determines objectives presuppose planning rejects “distribution according effort” (1971 312) general ends goals effort reveals deep tension within system explained Cohen 1989 912-916 But stick 7 agency perfect statistical behaviour As transfer authority regimes: Regime T: gross apply tax; S: T S allow imagine third regime F orderings lump sum transfers first-best 16) AXIOMATIC APPROACH: TWO PRINCIPLES FOR EGALITARIAN GOVERNMENT far suggested descriptive account means intervention Alternatively formulate axiomatically should satisfy To able design specified:5 a) assigning differential make own b) compensation prevail wherever absent them strength It been shown impossible reconcile strongest implement weaken comprehensive axiomatic test check performance axioms: (1995a 1995b 1998); Bossert (1996); de gaer Maniquet (1996a 1996b) 8 reward: “If all identical traits difference pre- resources society” Let us axiom “No Redistribution Uniform Non-Responsible traits” (NRUNR) For example branch “non-responsible traits”; hence NRUNR redistribution five distinct specifications stated follows: b1) Solidarity: profile changes either agent’s deteriorates”(Fleurbaey 1998 214) Solidarity anonymity entail equality: b2) advantage” “Equal Advantage Equal Responsibility” (EAER) consequences held compensated deemed Then EAER who different and/or end obtain maximin version (b2) appropriate: b3) group lowest ” “Maximin (MAER) MAER “reference concerned testing described variable “e” Consider ê criterion policy: 9 b4) advantage”6 “EAERê”: Responsibility again weakened to: b5) MAERê”: Reference ê” MAERê Some limited domain environments show (notably shape “official” aggregated collective choice) “neutral Or conclusion words once determine underlying “conditional egalitarianism” 10 SECOND-BEST INSTRUMENTS scenarios intervenes four Instrument 1: flat t constant term B: amount equal twL B > tax) 2: c ruled disincentive effects plays trivial role puts interpretation proper perspective especially (Section 3: proportional spends work: works receives sL instrument chooses income: (3) + [(1-t)w s]L (1- c)p 4: importantly governments supports education public spending E scenario (t E) balanced budget constraint function calculated B(t below calculation c) Clearly build complete endogenous Education impact Moreover normally influences deterministic nature 11 deny even adequate essential “circumstances choice” background indeed matter “choice” choice educational interacts variables directly revenue indirectly via E’s since complex try simply suppose represents important included presentation neglect necessity purposes than CONSTRAINTS ON confronted constraints: labour-supply Apart impose limit taxation: £ Spending covered current L(w e; supply response is: (4) )[ ò ; wpe f cp dp dw 12 density joint simplified considerably now (U L)) (5) maximization response: (6) s) [w( t) s] 1- properties g(w e): (7) separable (w)g independence distributions write: (8) (w) (e) Both separability (and expressions derived it) features Using equation derive (4): (9) eLo [t( t)( )+ )ws ]+ 13 equations follow (equal often occurs property underpins results: constraints positive (income taxation) (an supplement pre-tax earnings); worked) integrated schedule) poll raise money constrains disincentives never respond labour”; incentives 4) entails boundaries: (10a) “s “t “e wÎ[0 1]: e;t “lower bound”; (10b) wÎ “upper bound” behavioural boil down (11a) (11b) Equation total “wage” type Together searches illustrated Figure 17 FIGURE Figuur course add dashed line s* pays low-paid relatively technique avoid training disincentives) DEFINING INDIVIDUAL ADVANTAGE optimize allowing interpersonal All examples graphs 44 1344 -wL Upper bound® ¬ Lower bound 15 imply cases exists exception rather rule Suppose (12) d takes considers burden precisely monetary balance Work mixed blessing: brings (“participating “developing capital” “structuring one’s life” burdens (“having less family” “less leisure” etc non-monetary perceives extent extra keep person’s unchanged (13) conceives legitimate (14) “legitimate” wellbeing “desert” “public indifference” specified combinations income; see impacts convenient elements / rewritten: 16 (15) gL stance well-being: increases “burden”attached decreases ® measure terms instance traditional measures wealth (The well-known highlighted Musgrave 1974) Â(w maximizes write as: (16) Â ÷ ø ö ç è æ (deliberate) similarity indirect Ve non-comparable): (17) V Our features: First ½ non-decreasing ” “pity” someone talented former harder latter Second else e-factor lower There reason why tranche members Tw difficult predict whole Two distinguished: (wL pL Indeed arg min concave OBJECTIVES extreme inequality aversion (18) tsc max (19) excludes minimal assigned ¥: deems “lazy” drops exclude possibility those keen intermediate 18 implementation Roemer8 Ideally like equalizes (more maximins) across types done: maximizations simultaneously performed at Roemer weighted advantages where weight frequency entire states looking Rawlsian; tranches giving consideration Martinez They argue applying “worst” option good (Assume uniformly looks contour yet another area intersection type; smallest open person9 My (1994 Part II; 1996a 279ff gaer’s methodology (1996) (1998) Type Approach 19 Roemer’s RESPOobjective: (20) applied RESPO-objective: (21) person belonging TwL defines sets: frontiers cross (as (22) Integrating formula RAWLS: (23) þ ý ü î í ì RA RESPO: (24) eg RE properties: 20 i) 1]; [0 ú Í û ù ë é x pities lazy crucially: ii) (g :s < ;s Now using (25) { “a” short-cut describing captures overall emphasise mean things Either transition application (25’) Vê Uê 2a (One note though 21 programme summarized start formulated (cf Fleurbaey’s egalitarianism”) advantage: picking maximizing Roemer-Van programmes (eq 22) link did Starting requirement comparability: suffices optimization underscores crucial analysis notions supposed know) search policy; nevertheless presented irrelevant Secondly whatever RESPO) exogenous reduce objective: (26) Q st -a obviously And pick reduces 22 (27) Q(t ts GENERAL SOLUTION (for T(s) s; S(t) t: (28) (29) Appendix graphical sketched substitute 26-27) multiply (1-a) delete new program: (30) )] W Wt +a 1-a convex coefficient (except awL 0; equivalent) 23 iii) larger 1; iv) (31) verified case: (s (1 Appendix) Special When additional introduced s*) bites have: (32) eq 28 T(s)) used: (33) elasticity similar (with effect elasticity) 24 (34) (when 0) changing adjusting (equation 9) accordingly Maximizing boils adjusted) Throughout rest TRACING OPTIMAL SCENARIOS INCREASING TO Optimal track describe (always 7) s(a) t( (excluding 0)10 Solving t(a) v(a)/D(a) r(a)/D(a) D(a) calculate (eliminating D²(a) derivatives): r dr v dv dt ds ¹ inter alea uniform straight (a) (35) t(0) s(0) determinant 4[(1-a) boundaries permissible (the lines parallel) forming slope linear combination section 25 S(1) further reached movement stops trace depicted 3A (where presume ao) segment smaller (35’) )( q 3a: rarely page interval RE(g) 1/3 moreover vertical (this condition (iv) 30) a0 a1 26 already indicated long say that: higher (other equal); working” increases) At starting (ao) heavy measurement (top right) all; measuring “ reverses Figures 3B 3C involve change 27 FIGURES – Figuren 3B-3C rewrite (regime T) environment) J inequality: divided variation levels: (36) written:13 (32’) ws ' J’ (33’) “Laffer” turning shifts Laffer towards zero aJ “inequality” measured J) RESPO14 changes15 words: preferences; enhanced earning stimulate COMPENSATION; CONDITIONS EQUALITY statement clear constellation (Maximin ê) operates satisfied Excluding 29 program stronger EAERê automatically when16 aw REWARD: NEUTRALITY NRUNR: Resources tw means: Ù inspecting (i-iv) Condition written: 30 easy ½: reconciled From definitions a-functions derive: Û presupposes extremely biassed Otherwise difficulty identification simulate draw SN t” setting gives: (37) N 2w constrained unconstrained illustration made TN drawing 31 CONVERGENCE BETWEEN Superficially “egalitarian” fewer redistributes “superficially” egalitarianism misleading implies; orderings” Nonetheless interesting examine converge prescriptions choosing RA(g) s): analyse limiting fairly evident: Also answer straightforward inspection (a=½) 32 inversely compound becomes distinction relative (constant) somewhat bluntly: applies believes acts wherein increasingly unequal innate talent important17 (A indicates BASIC INCOME? iso-B curves BT(s) B-maximizing) BS(t) when: (38) BT Cf 41 33 (39) 2t BS left reaches (When “slope BT” refer dependent variable; )/ leads (40) t)w (B 34 declines until crossing region to) since: 35’ area; vertical) go (½ Any departure BT; Formally T(s*) (s*) loosening introducing exist before) Loosening travel along constellations (large know whether theoretical Three conclusions drawn: irreducible conflict (given g) RAWLS18 demand 35 operational “real freedom rule” discussed van der Veen (1997 1998) context broader (1995) freedom” ability (independent actually wants do) suggests concept (instead actual preferences): “a real said improve unambiguously expands added none deleted process someone’s contain non-overlapping income-leisure compared 276-277) makes pair (defined corresponding Consequently advantage19 Sugden 36 STATE INCOME Would constraints)? Cases (29’) (9’) [s(w s)]+ Assume intervening cash residual after necessary expenditures generated generate sufficient cover achieve policy) deduce (using equality) government” 37 (different 11) “optimal policy”; interaction rewriting calculations:20 [s E] grant part guarantee 0: 0); Again calculations model: w; rewritten 38 “RECIPROCITY” VERSUS receive pay) pound potential society’s He ethically attractive “when proportionality incomes community morally appropriate ‘take (White 612) contribution criticises Parijs’s “reciprocity” shed light seen planner society (all population’s function: (41) Wi Hi 1+ Yi after-tax he/she happens worked dollar (42) “T* stands reasonable full year Ti 39 period Where T* si positive; tax)” “si (43) ss vindicated: “maximum power” scheme; matches proposal exactly (To 43 42 says self-interested defeat (no subsidy) vindicated deeper foundations presumed rely “social cooperation” production justify 1997) (Recall incomplete priori postulates (apart exceptions) grounds pointing making cooperation reply convincing (forthc implicitly justified non-zero unless accept 40 (b) violation redistributing “productivist” redistribute violating achieved permits raises issues (does exist?) intergenerational (what “gross” interest future generations?) stretching meaning reenters back door: allowed away generations was previous COMPARISON EFFICIENCY draws “advantage frontiers” (type 40% 2; dividends; education) X-axis high-productivity tranches) Y-axis low-productivity depict highest attain frontier 6: Note: TT SS FF II III reach 45° Although (in example) gain efficiency seems renders slight lowproductive cost drastic loss high-productive efficiency-gain introduction come surprise Envelope Theorem: life suboptimal politically higher) Average Low-Productivity High-Productivity CONCLUSIONS unified case21 reward” schemes advantage22 policy” understand play “pure” Assuming tax-only constitutes finds literature) zero-productivity eliminates independent matched entertained White) proves embodies “dividends” sources linked APPENDIX: graphically (29): 7A 25; 7B iso-Q marks & (Q (Q¯ Q- t# s# 45 limits s(- cf rapidly upwards slowly crosses 11b) namely satisfied: bite 85 8A; 8B variables) 8A 8A-8B upper isoQ intersects expression: (A1) Iso-Q 46 sub-optimal 47 BIBLIOGRAPHY BOSSERT Walter FLEURBAEY “Redistribution compensation” Social Choice Welfare 343-355 VAN DE GAER Dirk SecondBest Compensation Cahiers du THEMA 9607 March COHEN Gerald (1989) “On Currency Egalitarian Justice” Ethics 99 906- (1995a) opportunity outcome?” Economics Philosophy 25-55 (1995b) “Equality responsibility” European Economic Review 683-689 individuals” LASLIER JeanFrançois GRAVEL Nicolas TRANNOY Alain (eds Freedom New perspectives Routledge London 206-234 MANIQUET François (1996a) “Cooperative Production: Comparison Bounds” Games Behaviour 200- 208 (1996b) “Fair skills: No Envy Mathematical Sciences 71-93 Income Taxation: Ordinal (Very preliminary version) MUSGRAVE R (1974) uncertainty trade-off” Quarterly Journal Vol 88 November 625-632 (1971) Theory Justice Oxford University Press (1993) Political Liberalism Columbia York ROEMER (1994) resources” Perspectives Essays Philosophical Cambridge 115-196 Theories Distributive Harvard Mass Mechanism Implementing Egalitarianism FARINA Francesco HAHN VANNUCCI Stefano Rationality Clarendon 142-158 48 Equality Opportunity SUGDEN Robert Measuring Real Paper conference Parijs's Warwick May MARTINEZ Michel SCHOKKAERT Intergenerational Mobility Center Studies Discussion Series DPS 98 Leuven April VANDENBROUCKE Open Society Incentives University; forthcoming Springer Verlag DER VEEN "Debate Basic Comment Brian Barry" 274- 286 "Real Reciprocity Competing Views Unconditional Income" vol (March) PARIJS “Reciprocity Justification XLV 327-330 WHITE Stuart “Liberal Exploitation Case 312-326 “The Earnings Subsidy Scheme” British Science 601-622 49 CONVERSION FIGURES: NEW VERSION THESIS FIG fig (dashed ao instead 4A 4B 5A 5B