The Normative Analysis of Tagging Revisited: Dealing with Stigmatization

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1 The Normative Anaysis of Tagging Revisited: Deaing with Stigmatization Laurence Jacquet and Bruno Van der Linden February 20, 2006 Abstract Shoud income transfers be conditiona upon persona characteristics of the potentia recipients (so-caed tagging or shoud they ony be tied to reported incomes? A sti widespread socia norm consists in requiring that individuas (of working age support themseves and their famiies. Being a wefare recipient is then sociay disapproved because it reveas to others that one is unabe to fend for onesef and one s famiy. In this context, tagging is aways suboptima under a maxi-min criterion. With a utiitarian criterion, tagging can ony be recommended if the distribution of the intensity of stigmatization reative to earnings has sma mean and variance and if the mean and variance of the distribution of abiities among the high-abiity peope are neither too arge nor too sma. Key words : tagging, optima taxation, wefare programs, stigmatization. JEL Cassification : H2, I3 1 Introduction It is typicay argued that a combination of income taxation and testing ( tagging of socia security payments, as with a targeted minimum income guarantee, eads to a better trade-off between the incentive costs of distortionary income taxes and the socia wefare gains of redistribution. If tagging does not invove any monetary cost and can prevent uneigibe peope from benefiting from the targeted transfers, society is necessariy better off by its use since it enabes a redistribution from the untagged to the tagged group without creating mimicking effects or work disincentives among the former group. This view is chaenged in this paper which introduces the demeaning or stigmatizing effect of tagging. The editor, Wofram Richter and the comments of two anonymous referees are gratefuy acknowedeged. We aso deepy thank Maurice Marchand and Linda Andersson, Robin Boadway, Bart Cockx, Kate Cuff, Jean-Yves Ducos, Ginette Herman, Jean Hindriks, Etienne Lehmann and Phiippe Van Parijs for very usefu discussions and comments. Any remaining error coud ony be attributed to the authors. The authors acknowedge financia support from the Begian Federa Government (Grant PAI P5/21, Equiibrium theory and optimization for pubic poicy and industry reguation Begian Nationa Scientific Fund (FNRS, Department of economics, Université Cathoique de Louvain. Department of economics, Université Cathoique de Louvain, FNRS and IZA. 1

2 The iterature on optima income taxation (see the semina papers by Mirrees, 1971; and Stigitz, 1987 characterizes the optima shape of margina tax rates under imperfect information about the earning abiity of the tax payers. This approach has been used to recommend a form of non inear negative income tax (Boadway and Keen, A negative income tax is a refundabe tax credit with an expicit tax schedue which can be, but need not by definition be, inear (Cournot, 1838; Friedman, 1962; Tobin, 1966; Another strand of the iterature is concerned with optima wefare programs (Akerof, 1978; Diamond and Sheshinski, 1995; Parsons, 1996; Boadway, Marceau and Sato, 1999; Saanié, In this iterature, the wefare agencies are assumed to observe more than ony reported income eves and the aggregate distribution of abiities. The agencies condition (tag transfers on persona characteristics (such as disabiity or empoyabiity of potentia recipients, that provide some imperfect information about the earning abiity. Akerof (1978 deas with errors of type I (some of those who are entited to the benefits are rejected and Parsons (1996 adds errors of type II (individuas not entited are accepted. Both argue that tagging increases aggregate wefare. Moreover, as ong as the disutiity of work is not too arge, Parsons (1996 shows that the optima system shoud et tagged peope work. In Akerof (1978, Diamond and Sheshinski (1995, Parsons (1996, and Saanié (2002, tagging is costess. The accuracy of the tag and therefore the probabiities of errors are taken as given. Boadway, Marceau and Sato (1999 emphasize the roe of socia workers whose (imperfecty observabe effort affects the magnitude of these errors and induces administrative costs. They show that the choice between transferring income to the poor through tagging or excusivey via a non inear negative income tax system depends on the magnitude of administrative costs reative to the benefits of targeting. The use of tagging can be questioned due to the evidence that non-take-up is important. Many reasons can be invoked to expain this phenomenon: imperfect information among the eigibe popuation, ack of iteracy or numeracy, transaction costs reated in particuar to the time spent queuing and fiing out forms, the oss of privacy of caiming benefits that require an assessment of persona characteristics (socia workers evauate the eigibiity of caimants through enquiries and tests of a searching and detaied kind, the demeaning or stigmatizing effect of appying and receiving such benefits. Moffitt (1983 provides an econometric test for stigma in the Aid to Famiies with Dependent Chidren program. His resuts show definite evidence of a stigma-reated disutiity of participation (p in wefare programs. Aong these ines, an empirica iterature has studied the non-take-up of various types of wefare or means-tested benefits. Stigma is mentioned among the nonpecuniary participation costs (see, e.g., Ashenfeter, 1983; Moffitt, 1983; Bunde, Fry and Waker, 1988; Bank and Rugges, 1996; Ducos, 1995; 1997; Hancock, Pudney, Barker, 2

3 Hernandez and Sutherand, 2004; and Currie, In this paper, we emphasize stigma as an expanation to the non-take-up phenomenon. This focus is motivated by the growing evidence that stigma is important and by the reative ack of interest for this expanation in the economic iterature. Those who appy and receive assistance benefit suffer from a oss of utiity due to stigmatization. Stigmatized individuas possess (or are beieved to possess some attribute, or characteristic, that conveys a socia identity that is devauated in some particuar socia context (Crocker, Major and Steee, Rues (or norms about who is a member of the devauated category are defined by society. A sti widespread socia norm consists in requiring that individuas (of working age support themseves and their famiies. Being a wefare recipient is then sociay disapproved because it reveas to others that one is unabe to fend for onesef and one s famiy. This phenomenon has been stressed by Sen (1995 who writes: Any system of subsidy that requires peope to be identified as poor and that is seen as specia benefaction for those who cannot fend for themseves woud tend to have some effects on their sef-respect as we as on the respect accorded them by others (... there are (aso direct costs and osses invoved in feeing and being stigmatized. In a simiar perspective, Yaniv (1997 writes: The shame, embarrassment, and socia disapprova afficting a caimant whose participation in a wefare program is observed by others or becomes known to significant others (i.e., famiy, friends neighbors, empoyers, etc have been strongy stressed by socioogists addressing the issue of wefare stigma (e.g., Goffman, 1963; Waxman, 1983; Spicker, It is important to notice that stigmatization woud not occur if redistribution was ony based on income reported to the tax authority. For, the handing of income reports by tax authority can be considered as fairy anonymous: Receiving a transfer from the tax authority (e.g., a refundabe tax credit does not require to revea to other peope that one is unabe to fend for onesef. Our theoretica setting is cose to the one presented in Akerof (1978. There are two types of workers, the ow-abiity workers (whose productivity, at the imit, can be zero - the disabiity case and the high-abiity ones. As in the standard optima taxation iterature, each productive individua has access to a job which remunerates him according to his productivity. As in Akerof (1978, the targeted transfer, if any, is added to the abor earnings of tagged peope. This contrasts with Parsons (1996 and Boadway, Marceau and Sato (1999. In their modes, the popuation is subdivided between (nonworking disabe and abe peope and ony the atter are abe to work. We deiberatey negect errors of type II and administrative costs inked to imperfect monitoring of socia workers. By assumption, the atter do costessy observe the abiity of workers and 3

4 can prevent high-abiity workers from benefiting from the assistance scheme. Under these rather extreme assumptions, it is expected that the combination of income taxation designed by the tax authority and an assistance scheme targeted on the ess abe is superior to using ony (non inear negative income tax. This paper shows that the introduction of stigmatization chaenges the we-known superiority of costess tagging. As Besey and Coate (1992 notice, there is no reason to beieve that caiming wefare benefits wi affect a individuas in the same way. Therefore, in our mode, ow-abiity workers are endowed with an individua-specific parameter that measures the impact of stigma on we-being. This parameter is exogenousy distributed in the popuation. Low-abiity peope are aware of their eigibiity, but part of them, possiby, do not caim assistance benefits because they prefer not to be stigmatized. To the best of our knowedge, stigmatization has never been considered in an optima income taxation framework. Some economists have modeed the decision to appy for wefare when the appication process entais a disutiity that can be attributed to one of the above reasons (see Bishop, 1982; or Moffitt, Besey and Coate (1992 mode stigmatization which resuts from peope s disapprova of and resentment against those who choose to go on wefare (and are considered either as responsibe for their recipient status or as frauduent recipients and whose benefits are financed by mandatory taxation. Yaniv (1997 studies how the decision of taking up wefare benefits is affected by stigmatization (generated through observed participation in wefare programs and/or by the expected penaty for underreporting income to quaify for wefare benefits. Redistribution mechanisms based on tagging aso raise issues of horizonta equity (which requires that those with equa status, whether measured by abiity or some other appropriate scae, shoud be treated the same and of poitica feasibiity (Sen, The more targeted the transfers towards the truy needy, the ower the support from the excuded midde income cass. This can have detrimenta effects on the actua eve of redistribution (Gebach and Pritchett, 1996; De Donder and Hindriks, The paper is organized as foows. Section 2 introduces assumptions and notations. Anaytica resuts are presented in Section 3. Since this normative anaysis does not ead to cear-cut concusions in the utiitarian case, a numerica anaysis is summarized in Section 5. Section 6 concudes the paper. 2 Assumptions and notations By assumption, workers suppy one unit of abor. Let us consider two types of individuas who differ in terms of their abiities indexed by j. Moreover, there are two types of jobs and pretax earnings are specific to the job. The ow-abiity workers (j = are characterized 4

5 by exogenous gross or pretax earnings, w 0. 1 If w = 0, these individuas are by assumption unabe to work (say, because of a disabiity. A high-abiity worker (j = h can either occupy a job designed for his abiity (abeed a skied job or he can have an occupation requiring ow abiities (abeed an unskied job. Because of their ow abiity, type- workers cannot perform skied jobs. Gross earnings in skied jobs are given and denoted by w h, with w h > w. Compared to unskied jobs, we assume that performing skied work requires more effort. In this respect, high-abiity workers are assumed to be heterogeneous. If they occupy a skied job, their consumption eve is c h and their eve of utiity is u(c h δ, where δ is the disutiity of working in a skied job rather than an unskied one. By assumption, δ is distributed on the interva [0, + [ 2 according to the cumuative distribution F (δ and the density function f (δ. Whie δ is an individua attribute that no other agent can observe, F (δ is common knowedge. By assumption, f(δ > 0 δ [0, + [ with im δ + f(δ = 0. u(c is a continuous, differentiabe, stricty increasing and stricty concave function with im c 0 u (c = +. If instead a high-abiity worker chooses an unskied job, his consumption eve is c and his utiity eve u(c. As is usuay assumed, the tax authority knows the proportion of individuas with ow abiity γ (0 γ 1 but it does not observe the abiity of a given individua. It perfecty and costessy observes reported income. As is standard in the optima taxation iterature, the occupationa choice of the high-abiity workers wi imit the extent of redistribution which the tax authority can impement. To reax this sef-seection constraint, et us introduce wefare agencies. They occupy socia workers who have access to more information than the tax authority. To adopt a simpe setting where tagging woud be advocated in the absence of stigmatization, et us assume ideaized wefare agencies which costessy and perfecty can assess the abiity of caimants. In this ideaized setting, wefare agencies can separate ow-abiity caimants from high-abiity individuas with high disutiity δ. Wefare agencies ony provide a targeted transfer to ow-abiity individuas. Not a of these individuas wi however caim the targeted benefit. This is not because of a ack of information or iteracy. They are instead deterred by the osses invoved in feeing and being stigmatized. The eve of utiity of ow-abiity individuas who choose to 1 As it is standard in the optima tax iterature, empoyers perfecty and costessy observe the abiity of the worker. This is however not the source of stigmatization. As we expain above, the atter is due to the participation to a wefare program. 2 The assumption that δ is non negative coud be criticized if δ is interpreted in a broader sense. The occupation requiring ow abiities coud be interpreted as poor jobs because they are the ony type of occupation accessibe to ow-abiity workers. The support of δ woud then probaby incude negative vaues in order to dea with individuas for whom the negative status of these unskied jobs outweighs the penibiity of effort required to perform a skied job. This interpretation woud however not change the nature of our resuts as ong as the support of δ is not restricted to negative vaues. So, we stick to the case where δ ies in [0,+ [. 5

6 caim assistance benefits is written as: u(c T σ (1 where c T equas w pus the targeted transfer net of tax iabiities, if any (superscript T denotes the tagged status. Here, σ is an individua parameter that represents the intensity of stigma. There is no reason to beieve that caiming wefare benefit wi affect a individuas in the same way. So, σ is by assumption distributed on the interva [0, + [, according to the cumuative distribution G(σ and its associated density function g(σ. It is assumed that g(σ > 0 σ [0, + [ with im σ + g(σ = 0. It is aso assumed that the individua vaue of σ is unknown by a except the person hersef, whie G(σ is common knowedge. The utiity eve of the ow-abiity individuas who do not caim assistance benefit is equa to u(c (2 where c denotes their consumption eve. The choice of taxes and transfers is equivaent to the determination of consumption bundes c T, c and c h. Since the unobservabe parameters δ and σ are distributed on a wide (formay of infinite size support, it simpy becomes too costy to induce a highabiity individuas to work in skied jobs 3 and to induce a type individuas to caim the targeted transfer. So, whatever the aocation of consumption eves, there wi be some finite cut-off eves δ and σ such that ony those high-abiity individuas with δ < δ are occupied in skied jobs and ony those with σ < σ and a ow abiity opt for the targeted transfer. Therefore, in the subpopuation with net income c, one necessariy finds some ow-abiity peope and the high-abiity ones with a sufficienty arge disutiity of effort. These cut-off vaues or threshod eves satisfy the foowing equaities: u(c h δ = u(c (3 u(c T σ = u(c (4 Tabe 1 dispays the proportions of individuas in each position and Figure 1 summarizes the mode. TABLE 1 ABOUT HERE FIGURE 1 ABOUT HERE 3 This eement distinguishes our mode from standard modes of redistribution which rey on the reveation principe to induce a individuas to report their true types in an optimum. 6

7 Let us now turn to the normative criteria used in this paper. This paper compares outcomes under a utiitarian criterion and a maxi-min criterion. The resuts are ater extended to a more genera socia wefare function where the degree of aversion to inequaity can take vaues in a broader range. The utiitarian criterion is as usua a sum of the individuas utiity functions weighted by their share in the popuation: W (c T, c, c h, σ, δ γ { { u(c T G( σ σ δ +(1 γ u(c h F ( δ 0 0 σg(σdσ + u(c (1 G( σ } δf (δdδ + u(c (1 F ( δ } (5 The maxi-min (or Rawsian 4 criterion wi pace a the weight on the most needy (in terms of utiity. In our mode, by definition of σ, those who caim a targeted transfer are at east as we-off as those who do not. The atter benefit from a eve of utiity u(c which is equa to the eve that high-abiity workers get if they opt for an unskied job. So the appropriate criterion which shoud be maximized under the maxi-min (or Rawsian objective is: u(c (6 The utiitarian and maxi-min criteria are standard in the iterature. However, some authors have criticized this approach when individuas differ in severa dimensions. Appendix 7.1 deas with an aternative wefare criterion for which no compensation is given for individua characteristics faing within the responsibiity of individuas. In this context, Appendix 7.1 considers criterion (5 where σ and δ are ignored. 3 Normative anaysis: Anaytica resuts This section focuses on first-order necessary conditions for an optimum under asymmetric information. As wi become cear, these are not in genera sufficient conditions for a goba maximum. This section is organized as foows. First, using the utiitarian criterion (5, we expain why the case with and without tagging can fufi the first-order conditions with a utiitarian criterion. Second, anaytica properties are derived with the maxi-min objective (6. 4 Foowing Okun s (1975 interpretation of Raws, when a the weight is paced on the most needy, the optima tax iterature uses the term Rawsian objective. Obviousy, this interpretation does not adequatey refect the richness of the Theory of Justice of Raws (1971 but it is common practice in economics. 7

8 3.1 The utiitarian criterion The abiity characteristics (j, the disutiity parameter in skied job (δ and the stigma parameter (σ cannot be observed by the tax authority. The atter perfecty observes reported incomes. When a ow-abiity worker appies for the targeted transfer, his abiity eve is observed by socia workers. The threshod vaues δ and σ resut from decisions taken by the individuas conditiona on the tax and transfer systems (see Equations (3 and (4. The government chooses the tax-transfer schedue that maximizes the utiitarian socia wefare function (5 subject to Equations (3 and (4 and its budget constraint: φ(c T, c, c h, σ, δ π T (w c T + π (w c + π h (w h c h = 0 (7 where π T = γg( σ, i.e. the share of the popuation which is ow-abe and targeted, π = γ(1 G( σ + (1 γ(1 F( δ, i.e. the share of the popuation (high-abiity persons as we as ow-abiity ones which is occupied in unskied jobs and π h = (1 γf ( δ, i.e. the share of the popuation which is high-abe and in a skied job. Without tagging (π T = 0, ony two consumption eves can be optimay chosen. It is expected that high-abiity workers pay taxes (w h c h > 0 and ow-abiity workers receive transfers (w c < 0. It is aso expected that tagged individuas wi receive a higher transfer than in the absence of tagging. Whether a ow-abiity individuas receive a transfer or ony the tagged ones is an open question. Let λ1, λ 2, λ 3 be the mutipiers associated respectivey with the budget constraint (7, Equations (3 and (4. The Lagrangian expression is: { γ u(c T { (c T, c, c h, σ, δ, λ1, λ2, λ3 G( σ σ δ +(1 γ u(c h F ( δ 0 0 σg(σdσ + u(c (1 G( σ} δf(δdδ + u(c (1 F ( δ } +λ 1 [π T (w c T + π (w c + π h (w h c h ] +λ 2 [u(c h δ u(c ] + λ 3 [u(c T σ u(c ] (8 From the assumptions on the utiity function, the optima c T, c and c h are necessariy positive. If, at the optimum, σ = 0, by Equation (4, c T = c. Therefore, no ow-abiity person wi choose to caim the targeted transfer. 5 In that sense, tagging is not optima. In contrast, if at the optimum σ > 0, by Equation (4, c T > c, i.e. tagging is optima. Constraints (3 and (4 can be rewritten respectivey as φ 1 (c, c h, δ = 0 and φ 2 (c T, c, σ = 0. It can be checked that φ 1 and φ 2 are quasiconcave. The necessary but not the sufficient 5 Those characterized by σ = 0 are actuay indifferent between caiming the targeted transfer or not. 8

9 conditions for φ to be quasiconcave are fufied. Triviay the objective W (c T, c, c h, σ, δ is in genera not quasiconcave. So, a vector (c T, c, c h, σ, δ, λ1, λ2, λ3 satisfying the foowing first-order conditions is not necessariy an optimum. These conditions are nevertheess instructive. The first-order conditions can be written as 6 : (π T + λ 3 u (c T = λ 1π T (9 (π λ 2 λ 3 u (c = λ 1 π (10 (π h + λ 2 u (c h = λ 1 π h (11 σ = 0 and 0 (12 σ σ with = λ1 γg( σ[c c T ] λ 3 (13 σ δ = 0 and 0 (14 δ δ with = λ1 (1 γf ( δ[wh ch (w c ] λ 2 (15 δ and Equations (3, (4 and (7. Proposition 1 Whatever the vaue of σ, the inverse of the margina cost of pubic funds is equa to the margina cost of increasing by a unit the utiity of each individua in each group weighted by the share in the popuation (Diamond and Sheshinski, 1995: 1 λ 1 = πt u π h π + + (c T u (c u (c h (16 Proof. The proof is straightforward by adding Equations (9, (10 and (11. Having scrutinized the first-order conditions, it turns out that both the case with tagging ( σ > 0 and the one without tagging ( σ = 0 can verify these conditions. The rest of this section is divided into three parts. First, we expain intuitivey why σ = 0 can be optima, when this property shoud not hod and why δ has to be positive. Then, theoretica properties are derived when tagging is optima and finay when it is not Basic mechanisms affecting σ and δ Let us first anayticay show that σ = 0 satisfies the first-order condition $ σ Equations (9 and (13, we can write: σ = 1 6 The constraint quaifications have been checked. = 0. From u (c T πt [u (c T λ 1] + λ1γg( σ[c c T ] (17 9

10 From (4, taking c constant, a margina increase in σ requires an increase in c T such that dct d σ = 1 u (c T. The socia margina vaue of giving dc T to a wefare caimants is π T u (c T whie, πt λ 1 is the socia margina cost of the corresponding increase in pubic expenditures. Finay, λ1 γg( σ[c c T ] is the net cost due to margina individuas shifting from c to the higher c T. If σ = 0, the fraction of the tagged popuation, πt, is zero. Moreover c = c T. Hence, from (17, $ = 0. The intuition behind this property is σ the foowing. By (4, the margina individuas who enter the tagged popuation are aways indifferent because their utiity eves are the same whether they are tagged or not. Therefore, there is no direct impact on the utiitarian criterion W. Their earnings, w, and hence their contribution to aggregate output are aso the same. Moreover, in σ = 0, c T = c. A margina increase in σ has therefore no impact on net resources. 7 Under which circumstances, is it pausibe that a positive vaue of σ aso soves the first-order conditions? It wi turn out that the shape of the distributions of σ and δ is critica. From the discussion above, a necessary condition is that $ > 0 for some positive σ vaues of σ. From (17, σ shoud increase if: dc T d σ [u (c T λ 1 > g( σ [c T ] c ]λ 1 (18 G( σ As σ starts increasing from zero, c T aso grows (otherwise there woud be ess redistribution from the high-abiity to the ow-abiity peope. It wi be shown that λ 3 < 0 when σ > 0. Hence from (9, u (c T > λ 1. The eft-hand side of (18 is then positive. As σ starts increasing from zero, c T c increases too and it becomes more difficut to fufi (18. So, a decine of g( σ g(σ G(σ G( σ as σ rises heps to fufi (18. A distribution for which is decreasing is said to have decreasing monotone reversed hazard (or faiure rate. Equivaenty, the og of the cumuative distribution function, G, has to be concave. This condition is satisfied by most of the usua distributions. 8 The distribution of δ aso affects the chances of finding a positive vaue of σ that soves the first-order conditions. From Equations (11 and (15, we can rewrite: δ = (1 γf ( δ u (ch [u (ch λ 1 ] λ 1 (1 γf ( δ[ch wh (c w ] (19 If δ = 0, F ( δ = 0 and c h = c therefore $ δ δ=0 = λ 1(1 γf (0(w w h > 0. So, δ has 7 It shoud be mentioned that σ = 0 can aso sove the first-order conditions when w > 0 and the tagged popuation does not work. 8 A sufficient condition for G to be og-concave is that the density is og-concave. Famiies of distributions that aways have og-concave density functions incude the uniform, the norma, the ogistic, the extremevaue, the chi-square, the chi, the exponentia and the Lapace distributions. However some famiies of distributions do not have og-concave density for a their parameter vaues. Sti they may have a ogconcave distribution function. This is the case with the Gamma, the power function and the Weibu distributions for instances. See Bagnoi and Bergström (

11 to be positive. As ong as δ shoud increase, one has dch d δ [u (ch λ 1 ] > λ 1 f ( δ F ( δ [c h w h (c w ] (20 The structure of this expression and the one of (18 are simiar. If many high-abiity workers are characterized by ow vaues of δ, δ wi be such that a arge proportion of high-abiity individuas wi work in skied jobs. This reduces the margina cost of pubic funds, λ 1, and from (18, increases the probabiity that a positive vaue of σ is optima. Section 5 wi be devoted to numerica simuations which wi provide additiona insights on situations where tagging is or not optima. Meanwhie, the anaytica properties derived in each environment wi be presented Anaytica properties under tagging ( σ > 0 The reative vaue of c T and c h is a major issue here. The next emma wi be usefu ater on. Lemma 1 If σ > 0 : where θ = πt π T +λ [ 3 1 u (c θ 1 with strict inequaities if δ > u (c T u 0, (c h 1 π T λ 3 1 π T ] 1. Proof. Equation (9 can be rewritten as: 1 λ 1 = π T πt + λ 3 1 u (c T (21 Putting this in (16 and dividing by π + π h 1 π T yieds: θ u (c T = x u (c + 1 x u (c h (22 where x = π is the probabiity of occupying an unskied job conditiona on being π +π h untagged (0 < x < 1 and θ = πt 1 π T λ 3 π T +λ [ ]. Hence, θ is nonnegative. According to 3 1 π T the sign of λ3, θ can be higher or ower than 1. Since δ 0, Equation (3 ensures that u(c h u(c. Therefore, θ u (c T ies (stricty between 1 u (c and 1 u (c (if δ > 0. h Proposition 2 If σ > 0, then consumption eves are ordered in the foowing way: c h > c T > c (23 Proof. First, σ > 0 and Equation (4 insures that c T > c. Hence, u (c T < u (c. Second, from (16, λ 1 > 0. So, since g( σ > 0, the first-order conditions (12-(13 impy that λ 3 < 0. Therefore, θ > 1. This and Lemma 1 yied that u (c h < u (c T. Hence, putting these two resuts together, one has : u (c h < u (c T < u (c. This is equivaent to (23. Proposition 2 is in ine with Parsons (

12 Proposition 3 If σ > 0, the tax evied on those occupied in skied jobs is stricty higher than the tax paid by workers occupied in unskied jobs: w h c h > w c. Proof. Section has shown that δ > 0. Then, Equations (14 and (15 impy that the sign of λ 2 is the one of w h w (c h c. The atter is apparenty ambiguous because w h w and c h c are both positive (see Proposition 2. By contradiction, it can however be shown that λ 2 is positive. Let us assume that w h c h w c. Then λ 2 0. Recaing that λ 3 < 0, u (c < λ 1 is then a consequence of (11. However, from (9, u (c T > λ 1. Combining these two resuts eads to u (c T > (c u or c T < c, which is in contradiction with Proposition 2. Therefore, λ 2 > 0, which impies that w h c h > w c. Proposition 4 If σ > 0, it cannot be rued out that untagged individuas with ow abiity pay taxes. Proof. From the budget constraint (7, it can be shown that: w c = π T (ct c π h [w h c h (w c ] (24 From Propositions 2 and 3, both c T c and w h c h (w c are positive. Hence, the sign of w c is ambiguous. In other words, the gross income of untagged ow-abiity and high-abiity individuas can be increased (in case of a transfer: w c < 0 or decreased (in case of a tax: w c > 0 by the optima tax-transfer system Anaytica properties when tagging does not prevai ( σ = 0 Some quite intuitive propositions can be shown when σ = 0. Proposition 5 If σ = 0, then consumption eves are ordered in the foowing way: c h > c = c T (25 Proof. This property foows immediatey from σ = 0, δ > 0 (see Section and Equation (4. Proposition 6 If σ = 0, w h c h > w c, with w h c h > 0 and w c < 0. Proof. The proof of this proposition foows the same ines as the proof of Proposition 3 above. From Proposition 3, δ > 0 (see Section and the resut λ 1 > 0, since λ 2 > 0 and λ 2 = λ 1 (1 γf ( δ[(w h c h (w c ], w h c h > w c. Moreover, from the budget constraint, it is immediatey seen that w h c h and w c have opposite signs. 12

13 Figure 2 summarizes our previous resuts. As iustrated by the upper pane of Figure 2, when tagging is suboptima, a ow-abiity workers (that is a proportion γ of the popuation and a proportion 1 F ( δ of the high-abiity peope are in unskied jobs and have u(c as utiity eve. Their consumption eve (i.e. their gross abor income increased by a transfer is (stricty ower than the one of the high-abiity workers in skied job. The atter (whose proportion is represented by the grey area have their utiity eves incuded between u(c h and u(c. The ower pane of Figure 2 represents an economy where tagging is optima: A proportion G( σ of ow-abiity workers (the dark area have a consumption eve c T (stricty higher than c (which, in this case, can be ower than gross income and (stricty ower than c h. FIGURE 2 ABOUT HERE 3.2 The maxi-min wefare criterion If the utiitarian objective is repaced by the Rawsian one, the consumptions eves shoud maximize (6 subject to the budget constraint and the two conditions (3 and (4 defining the cut-off eves. Intuitivey, introducing tagging enabes the government to increase the transfer given to the targeted individuas. Yet, to finance this, more highabiity workers have to opt for a skied job. This requires a decine of the consumption eve of the ow-abiity workers who do not caim the targeted transfer. Since these peope are the east we-off, such a change cannot be advocated in a maxi-min perspective. Put another way: Proposition 7 The maxi-min optimum requires σ = 0. Proof. Totay differentiating the budget constraint and the two conditions defining the cut-off eves, (3 and (4, and rearranging yieds: [ T π u (c T u (c T + π u (c + [ π + u (c + [ π h u (c h π h u (c h γg( σ ( c T c ] dc T = ] d σ (1 γf ( δ (w h c h (w c π h u (c h ] d δ (26 and dc = u (c T dct d σ u (c (27 Substituting (26 into (27, it is easiy seen that c σ = 1 u (c π + π h ( u (c u (c h γg( σ π T u (c + π T u (c + π h u (c h c T c 1 (28 13

14 This partia derivative is zero at σ = 0 and is negative for any σ > 0. Put differenty, extending the size of the tagged popuation from σ > 0 to σ +d σ impies that the untagged ow-abiity group wi be worse off. Since the utiity which is maximized under the maximin criterion (6 is the one of this group, a Rawsian cannot accept such an extension. Conversey, for any σ > 0, a margina decrease in σ has a positive effect on c. This hods true unti σ = 0. The maxi-min optimum definitey requires σ = 0. The same concusion obviousy aso hods if the owest consumption eve, namey c, is maximized. 4 Two extensions First, we consider a more genera socia wefare function and show how the aversion to inequaity affects the decision to use tagging. Second, we show that our resuts are robust to the introduction of a socia recognition of the ow-abiity individuas who fend for themseves. The atter can be seen as the counter-part of stigmatization. 4.1 A genera socia wefare function Consider the foowing standard genera socia wefare function σ [u(c γ{ T σ]1 v u(c 1 v g(σdσ + g(σdσ 0 1 v σ 1 v +(1 γ{ δ [u(c h δ] 1 v 0 1 v f(δdδ + δ u(c 1 v 1 v } f (δdδ } for v 1 where v is aversion to inequaity. We have aready studied the case in which v = 0 (utiitarian and that in which v (maxi-min. Consider now an intermediate vaue of v and assume that the conditions under which tagging is optima are satisfied. The first-order condition with respect to c T v σ = 1 u (c T [γ σ 0 [u(c T u (c T and (13 now ead to: σ]v g(σdσ λ 1 πt ] + λ1 γg( σ(c c T where v denotes the Lagrangian. As previousy, from (4, taking c as constant, a margina increase in σ requires an increase in c T vaue of giving dc T to a wefare caimants is γ such that dct d σ = 1 u (c T σ 0. The socia margina u (c T [u(c T σ]v g(σdσ whie, πt λ 1 is the socia margina cost of the corresponding increase in pubic expenditures. Finay, the ast term is the same as in (17. If σ > 0, the first-order condition is vioated if 1 u (c T [ γ σ 0 [u(c T u (c T σ]v g(σdσ λ 1 πt ] < λ 1 γg( σ(c c T (29 14

15 From (4, the right-hand side of this ast expression is stricty positive when σ > 0. As the aversion to inequaity v rises, ess and ess weight is given to the margina utiity of the tagged popuation (through the decreasing mutipier 1/[u(c T σ]v. The foowing property is therefore to be expected. Starting from a case where tagging is optima under a utiitarian criterion v = 0, there exists a higher eve of aversion to inequaity v under which tagging is optima and above which it is not. 4.2 Introducing socia approva" Imagine peope who are not tagged benefit from socia approbation. This counter-part of stigmatization increases the utiity of peope who fend for themseves (i.e. everyone in the economy except tagged peope. Let us denote socia approbation by a scaar a > 0. The threshod eve for ow-abiity workers satisfies now the foowing equaity: u(c T σ = u(c + a (30 The threshod eve δ is sti defined by (3. Let us first examine if the suboptimaity of tagging which prevais with a maxi-min criterion is affected when considering socia approva. The appropriate maxi-min criterion becomes: u(c + a It can easiy been shown that (28 is sti vaid in this case. Therefore, the suboptimaity of tagging with a maxi-min criterion is maintained when socia approbation is considered. Let us now turn to a utiitarian criterion. The utiitarian criterion without socia approbation (5 is sighty modified by considering socia approbation: a new term [1 γg( σ]a has to be added. It can easiy be checked that the first-order conditions with respect to c T and c remain unchanged. Moreover the first-order condition with respect to σ is exacty the same because the effect of a margina change in σ on the utiitarian criterion, namey: γ[u(c T σ u(c a]g( σ is sti zero by (30. In sum, the introduction of socia approva does not change the concusions of the theoretica anaysis. 5 A numerica anaysis under utiitarianism This section focuses on the utiitarian criterion (5. With a og-concave distribution for δ, there aways exists a soution ( σ = 0, δ > 0 to the first-order conditions (see Appendix 7.2. In addition, there can exist (at east one other soution such that σ > 0, δ > 0. 15

16 Then, severa oca optima are observed. Numerica methods are therefore needed to see when tagging is optima and when it is not. The foowing numerica exercise emphasizes the crucia roe of the densities of σ and δ. The numerica anaysis shows that tagging is ony optima when the distribution of σ is characterized by a density highy concentrated on ow vaues of σ (i.e., simutaneousy, sma mean and variance, where ow shoud be understood reative to u(w. However, a distribution sufficienty concentrated on reativey ow vaues of σ is ony a necessary condition because the distribution of δ aso pays a crucia roe. In some cases, where σ is highy concentrated on ow vaues, tagging is not optima because the distribution of the abiity parameters, δ, has a very ow or a very arge variance (and mean. This section iustrates and expains these resuts. The presentation is organized as foows. First, we rewrite and caibrate the mode. Second, we iustrate how the parameters space can be divided into an area where tagging is optima and another where a utiitarian woud avoid it. It is shown that very restrictive assumptions on the distributions of σ and δ are needed in order to concude that tagging is optima. Third, we conduct a sensitivity anaysis. 5.1 Reformuation of the mode and caibration Combining constraints (3, (4, (7 and the utiitarian criterion (5, it is convenient to rewrite the probem as: W (c, σ, δ γ[ σg( σ σ +(1 γ[ δf ( δ δ 0 ] σg(σdσ + ] δf (δdδ + u(c (31 0 with c = 1 + γg( σ[ ct c w + (1 γf ( δ(w h w 1] + (1 γf ( δ[ c h c 1] (32 Equation (32 can be rewritten as φ 3 (c, c T, c h, σ, δ = 0. Using a ogarithmic utiity function, u(. og k (. with k > 1 and again Equations (3, (4, it is convenient to rewrite φ 3 as: c ( σ, δ = w + (1 γf ( δ(w h w σ δ 1 + γg( σ(k 1 + (1 γf ( δ(k 1 Substituting (33 into the objective function (31, the probem becomes a maximization with respect to ( σ, δ. (33 FIGURE 3 ABOUT HERE 16

17 Let δ and σ be distributed according to Gamma distributions. 9 Figure 3 represents Gamma densities with parameter r respectivey equa to 0.2, 0.42, 1, 1.5 and 3. These vaues iustrate the variety of shapes of the Gamma density. Moreover, r = 0.42 wi be a critica vaue for our resuts. As r decreases beow 1, the density, f(x, becomes quicky negigibe when x increases. This phenomenon captures what is here meant by concentration. This notion is a reative one. It depends on the vaues of w h and w and on the shape of u(.. Let r δ, r σ be the parameters characterizing Gamma distributions respectivey for δ and σ. To emphasize the roe of these parameters, the density and distribution functions can be rewritten as F ( δ r δ, f( δ r δ, G( σ r σ and g( σ r σ in (31 and (33. With two eves of skis, one can hardy base our assumption about w h and w on actua wage distributions. Hence, we take w h = 100, w = 20 and deveop, in Subsection 5.3, a sensitivity anaysis. We assume a ogarithmic utiity function with a basis k equa to 2 (u(wh = og 2 (wh = 6.64 and u(w = og 2 (w = 4.32 and aso deveop a sensitivity anaysis in Subsection 5.3. The proportion of ow-abiity individuas, γ, is assumed to be equa to 0.5. The roe of γ is aso discussed in Subsection The effect of r σ and r δ Methodoogy Let W ( σ, δ, rσ, rδ denote (31 after substitution of (33. The optimum ( σ, δ verifies W σ ( σ, δ, rσ, rδ = 0 (34 and W ( σ, δ, rσ, rδ = 0 (35 δ This system is highy noninear. Therefore, according to the chosen initia vaues and the numerica method used, a soution to (34-(35 need not be a goba optimum. So, for each pair (rσ, rδ, the objective function (31 (with c defined by (33 is evauated for a wide range of vaues of the endogenous variabes ( σ, δ. Through this, we check whether the soution found to (34-(35 is the goba optimum. The above system defines an impicit reationship between the optima vaues of σ, δ and rσ and rδ. This system is however too compex to be studied anayticay. 9 A positive random variabe foows a Gamma aw of parameter r if its density is given by: f(x = 1 Γ(r exp( xxr 1 The parameter r of a Gamma distribution is equa to the mean and the variance of the distribution. We have checked that our concusions are maintained with other continuous distributions defined on the infinite support [0, +. 17

18 Since (34 and (35 characterize an optimum, we can totay differentiate them with respect to σ, δ, rδ and r σ as 2 W σ 2 d σ + 2 W δ σ d δ = 2 W rσ σ dr σ 2 W rδ σ dr δ (36 and 2 W d σ + 2 W σ δ δ 2 d δ = 2 W drσ 2 W rσ δ rδ δ drδ (37 This formuation wi be hepfu in the numerica anaysis to study the effect(s of sma changes in r σ and r δ. The effects of dr σ and dr δ on d σ are given by: d σ = dr σ 2 W 2 W 2 W δ σ rσ δ rσ σ 2 W σ 2 2 W δ 2 2 W δ 2 (38 ( 2 W 2 σ δ d σ = dr δ 2 W 2 W 2 W δ σ r δ δ r δ σ 2 W σ 2 2 W δ 2 The effects of drσ and drδ on d δ are given by: 2 W δ 2 ( 2 W 2 (39 σ δ d δ drσ = 2 W σ δ 2 W δ 2 d σ dr σ 2 W rσ δ 2 W δ 2 (40 d δ dr δ = 2 W σ δ 2 W δ 2 d σ dr δ 2 W r δ δ 2 W δ 2 (41 The signs of these expressions are in genera ambiguous. In the foowing numerica exercise, the components of (38-(41 wi be evauated. This information wi be usefu to understand how and why σ and δ vary withr σ and r δ, respectivey. A necessary condition for the optimaity of tagging: a ow r σ In a (r δ, r σ space, Figure 4 dispays the area where tagging is optima (see the shaded area. It highights that tagging can ony be optima for ow vaues of r σ. This resut turns out to be true in a reported and unreported simuations. When r σ decreases, the distribution of σ is more concentrated on ow vaues. In our exampe, tagging can never be optima if r σ > a σ which is nonnegigibe compared to u(w. This iustrates the idea of concentration: Very few peope have FIGURE 4 ABOUT HERE 10 If rσ = 0.42, 45.8% of the ow-abiity workers have a σ above 0.2 and 9.7% of the ow-abiity workers have an σ above 1.2. The utiity from the gross wage in a unskied job is u(w = 4.3, and therefore, σ = 0.2 (respectivey σ = 1.2 is ony 4.6% (respectivey 27.8% of u(w, which is reativey ow. 18

19 This first resut is quite intuitive. If stigmatization is considered as a negigibe phenomenon (in the sense that the density of σ is concentrated on very ow vaues of σ reative to u(w, then the mode confirms the traditiona resut in the tagging iterature (Akerof, 1978; Parsons, 1996; Saanié, This iterature shows that if a portion of the ow-abiity peope can be costessy tagged (i.e., without neither administrative costs nor prejudices due to stigma, the tota utiitarian wefare is raised by giving an aowance targeted on this sub-popuation. There is an incentive to do so because the benefits paid to tagged ow-abiity workers (c T provide no work disincentive to the high-abiity workers so that the former sub-popuation can be treated more generousy. In our mode, with a density of σ sufficienty concentrated on very ow vaues of σ reative to u(w, the prejudice due to stigma is much ower than the disadvantages inked to a redistributive system purey administered by the tax authority. Then, the traditiona resut hods: tagging is optima. However, a distribution of the intensity of stigmatization highy concentrated around reativey ow vaues is ony a necessary condition. Simuations resuts wi show that the dispersion of abiities among those who can perform skied jobs aso pays a crucia roe. A ook at the area where tagging is optima Looking at the area where tagging is optima, we wi describe what happens when r σ (respectivey r δ increases. Thanks to the methodoogy previousy defined and the simuations, we wi be abe to ocay study the signs of Expressions (38 to (41. Due to space imitation, we expain genera features by considering a few exampes. What happens in the interior of the tagging region when r σ increases? Tabe 2 dispays the main features of the optima when r σ increases and r δ is fixed to 1.3. As the dispersion and the mean of the intensity of stigmatization gets wider, c increases (starting from vaues beow w, c T somewhat decreases, therefore, π T decines, π increases and π h decreases. In the area where tagging is optima, σ and δ decrease with r σ. r σ [0.1; 0.42[, we compute that 2 W < rσ σ 0, 2 W < 2 W δ 2 0, > 2 W 0, < 0 and 2 W 2 W > 2 W δ σ rσ δ σ 2 δ 2 ( 2 > 0. Remembering σ δ (38, this expains why d σ < 0. The sign of these effects can then be introduced in (40 drσ to understand why < d δ drσ 0 r σ [0.1; 0.42[. TABLE 2 ABOUT HERE TABLE 3 ABOUT HERE What happens in the interior of the tagging region when r δ increases? Let us take the case where r σ = 0.2 and consider a few vaues of r δ. For sufficienty ow vaues of r δ (here 0.1, the distribution of δ is highy concentrated around ow vaues. With moderate 19

20 differences c h c, neary a high-abiity workers opt for a skied occupation. Given the avaiabe resources, stigmatization can be avoided by giving reativey high eves of transfer to a ow-abiity workers. For r δ [0.2; 0.5], Tabe 3 indicates that c T increases, c decreases and π decreases. So, as the dispersion and the mean of δ increases, tagging is first used more intensivey. From the vaues taken by the components of (39, d σ dr δ is positive but ess and ess so as r δ increases in the interva [0.2; 1.05[. Around r δ = 1.05, sti expoiting (39, d σ becomes negative. Actuay, for high vaues of r dr δ (reative to u(w h u(w, δ the share of high-abiity workers with a high δ becomes so arge that redistribution has to decrease. The substitution away from skied jobs acceerates drasticay (see the evoution of π h in Tabe 3. Looking at the components of d δ dr δ in (41 carifies why the optima vaue of δ does not vary monotonicay with r δ. This effect and the change in the distribution function nevertheess ead to a monotonic decine in π h. The we-being of those earning w is therefore more heaviy weighted in the wefare function. Therefore, c increases and c T decreases. In other words tagging is ess and ess used (c T c 0. This numerica resut confirms the intuition provided in Subsection To sum up, even if the intensity of stigmatization is highy concentrated around ow vaues in comparison with u(w, tagging is not optima if the distribution of the disutiity of skied jobs is either very concentrated on ow vaues or on the contrary if it has a arge variance (and arge mean. 5.3 Sensitivity anaysis Subsection 5.2 emphasized the roe of the distributions of σ and δ on the optimaity of tagging. Let us now ook at the effect of the other parameters. We consider in turn the basis of the ogarithmic utiity function, the wage differentia and the proportion of ow-abiity individuas in the tota popuation. First, if the basis of the ogarithmic utiity function (k > 1 increases, the area where tagging is optima in (r σ, r δ space is reduced (see Figure 5. Figure 5 dispays how the area where tagging is optima shrinks when k increases from 2 to 2.6. Intuitivey, when tagging is optima, it is used to reduce the difference in utiity eves between u(c h and u(c T, that is og k (c h og k (ct. It can be checked that og k (c h/c T with respect to k > 1. So, for any given c h c T is decreasing convex > 1, the former difference in utiity eves softens by itsef when k increases. Tagging is then ess needed. So, for any pair (r σ, r δ where tagging is optima but c T is cose to c, tagging becomes suboptima (c T = c when k increases. Second, if the difference between the gross wage rates, w h w, decreases, tagging is again ess needed. Actuay, as in the case of an increase of k, the inequaity in utiity 20

21 eves is reduced when the difference is reduced. Therefore, the area where tagging is optima is reduced as iustrated Figure 5, yet with a scope of reduction depending on the parameter s variation. FIGURE 5 ABOUT HERE Third, if the proportion γ of ow-abiity individuas in the popuation increases, the area where tagging is optima is aso reduced. Let us see why by considering a point in the tagging area. If γ increases, the high-abiity popuation receives a ower weight in the utiitarian criterion. In addition, keeping the aocation of resources unchanged is not feasibe because of the growing share of ow-abiity persons. Simuations show that a utiitarian reacts party through an increase in taxation, w h c h, and party through a decrease of c T. Moreover, to prevent δ from decreasing too much, c is reduced too but to a ower extent than c T. Therefore, cose to the boundary of the tagging area where initiay c T c, an increase in γ eads to c T c 0 (and σ 0. 6 Concusion This paper has questioned the optimaity of conditioning income transfers on persona characteristics of the potentia wefare recipients instead of basing them ony on reported incomes. In our anaysis, wage formation and the demand for abor are assumed to be exogenous. We have deveoped a simpe framework with two categories of (unobservabe abiities, in which individuas with ow abiities decide whether or not to caim the targeted transfer and wefare authorities assess eigibiity perfecty and costessy. This assumption about wefare agencies is deiberatey in favor of tagging. Being a wefare recipient is however sociay disapproved because a socia norm is vioated. This sti widespread norm states that anyone shoud fend for onesef and one s famiy. It has been assumed that the disutiity of being stigmatized is exogenousy distributed in the popuation. The main concusions are as foows. First, with a utiitarian criterion, tax-transfer systems with and without tagging can sove the first-order optimaity conditions. These are not necessariy sufficient however for determining the (goba optimum. Therefore, we have deveoped a numerica anaysis that suggests that tagging can ony be recommended if the distribution of the intensity of stigmatization is highy concentrated around ow vaues, where ow is a reative notion. The intensity of stigmatization is measured in comparison with the eve of earnings in unskied jobs. However, this is ony a necessary condition. The dispersion of the disutiity of effort among those who can perform a skied job ( the high-abiity peope aso pays a crucia roe. Even when the intensity of stigmatization can be considered as a minor factor, tagging is not optima if the dispersion of abiities 21

22 among the high-abiity peope is too arge or too narrow. After a sensitivity anaysis, we concude that the above properties are robust. Second, tagging is aways suboptima under a maxi-min socia criterion (for which the aversion to inequaity parameter tends to infinity. As this paper focuses on stigmatization, utiity costs such as transaction costs or the oss of privacy that appying for and receiving assistance benefits entai have not been considered. However, the mode coud easiy be interpreted as incuding such utiity cost. To sum up, stigmatization which has often been negected in the economics iterature questions the robustness of previous normative concusions about the advantages of tagging. 7 Appendix 7.1. A wefare criterion ony based on income eves The utiitarian and maxi-min criteria are standard in the iterature. They take preferences as given and consider that utiity functions are appropriate for a normative anaysis. However, some authors have criticized this approach when individuas differ in severa dimensions. For exampe, Feurbaey and Maniquet (2002 have argued in favor of a distinction between reevant and irreevant characteristics: Whereas the former ca for compensation, the atter do not, because they are considered as faing within the responsibiity of the individuas. In the same vein, Arneson (1990 defends a conception of socia justice as equa opportunity for wefare. He aso makes a distinction between the part of one s utiity for which one is responsibe and the part for which is not. Foowing these authors, this appendix excudes from the normative criteria the parts of the utiities under contro of peope. Being a parameter of disutiity of effort, δ shoud then be eft aside. One coud aso argue that individuas are responsibe for the intensity of the impact of stigmatization on their we-being (σ. Then, income shoud not be transferred in order to compensate for high vaues of σ and δ. This principe coud be transated into normative criteria where σ and δ are simpy ignored. This appendix is then devoted to the anaysis of a wefare criterion which is ony based on income eves. The socia wefare functions coud then use any stricty increasing and concave function of consumption. For simpicity, we here use the function u(. Our aternative normative criterion is then a sum of such corrected utiity functions weighted by the share in the popuation: { V γ +(1 γ } G( σ + u(c (1 G( σ u(c T { u(c h F ( δ + u(c (1 F ( δ } (42 22