Welfare stigma and risk taking in the welfare state

Thomas Eichner; Daniel Weinreich

doi:10.1007/s00355-014-0836-5

Social Choice and Welfare

February 2015, Volume 44, Issue 2, pp 319–348 | Cite as

Welfare stigma and risk taking in the welfare state

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Thomas EichnerEmail author
Daniel Weinreich

Article

First Online: 21 August 2014

Received: 11 October 2013

Accepted: 28 July 2014

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Abstract

The welfare state provides social insurance for lifetime risks. In that framework welfare stigma in form of a social norm against living off (net-)transfers is introduced, and the impact of welfare stigma on self-insurance and social insurance that works through redistributive taxation is analyzed. It turns out that introducing welfare stigma reduces the socially optimal self-insurance and raises the socially optimal social insurance. It may be efficient for the society to operate at a point on its opportunity frontier where an increase in risk taking decreases mean post-tax income and welfare stigma. In the presence of moral hazard self-insurance efforts are invariant with respect to welfare stigma whereas social insurance increases upon introducing welfare stigma. Furthermore, it is shown that self-insurance and social insurance are inefficiently low or high depending on the preference intensity of the social norm.

Fig. 1
Efficient risk taking in dependence of the social norm

Keywords

Social Norm Moral Hazard Marginal Benefit Social Optimum Preference Intensity

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Appendix

Appendix 1: Derivation of (18) and (21)

Differentiation of the first-order condition for $\sigma ^*_X$

$$\begin{aligned} A:= - (1-\tau ) \cdot i(\mu _Y, \sigma _Y) + \bar{\mu }'(\sigma _X) + \tau c k - \frac{a \Phi '(s)}{U_{\mu }} \cdot \frac{\partial s}{\partial \sigma _X} \end{aligned}$$

(33)

yields

$$\begin{aligned} A_{\sigma _X}&= - (1-\tau ) \left[ (\bar{\mu }' + c \tau k) i_{\mu } + (1-\tau ) i_{\sigma }\right] + \bar{\mu }'' - \frac{a \Phi ''(s)}{U_{\mu }} \cdot \left( \frac{\partial s}{\partial \sigma _X} \right) ^2 \nonumber \\&+ \frac{a \Phi '(s) \frac{\partial s}{\partial \sigma _X}}{U_{\mu }^2} \left[ (\bar{\mu }' + c \tau k) U_{\mu \mu } + (1-\tau ) U_{\mu \sigma }\right] - \frac{a \Phi '}{U_{\mu }} \cdot \frac{\partial ^2 s}{\partial \sigma ^2_X} \nonumber \\&= -(1-\tau )^2 \frac{d^2 \mu _Y}{d \sigma ^2_Y} + \bar{\mu }'' - \frac{a \Phi ''}{U_{\mu }} \left( \frac{\partial s}{\partial \sigma _X} \right) ^2 - \frac{a \Phi '}{U_{\mu }} \frac{\partial ^2 s}{\partial \sigma _X^2} \nonumber \\&+ \frac{(a \Phi ')^2 U_{\mu \mu }}{U_{\mu }^3} \left( \frac{\partial s}{\partial \sigma _X} \right) ^2 - \frac{2 (1-\tau ) a \Phi ' i_{\mu }}{U_{\mu }} \frac{\partial s}{\partial \sigma _X} \end{aligned}$$

(34)

$$\begin{aligned} A_a&= - \frac{\Phi '(s)}{U_{\mu }} \cdot \frac{\partial s}{\partial \sigma _X}>0, \end{aligned}$$

(35)

$$\begin{aligned} A_{\tau }&= (1-\tau ) \left[ c i_{\mu } (m-k\sigma _X) + \sigma _X i_{\sigma } \right] + i + ck \nonumber \\&- \frac{a \Phi ' \frac{\partial s}{\partial \sigma _X}}{U_{\mu }^2} \left[ c U_{\mu \mu } (m-k\sigma _X) + \sigma _X U_{\mu \sigma } \right] \end{aligned}$$

(36)

The second equality in (34) follows from making use of the fist-order condition (33), (14) and $i_{\mu } = - \frac{U_{\sigma \mu } U_{\mu } - U_{\sigma } U_{\mu \mu }}{U_{\mu }^2} = - \frac{1}{U_{\mu }} (U_{\sigma \mu } + i U_{\mu \mu })$. Observe that the first three summands in (34) are negative. Then a sufficient (but not necessary) condition for the second-oder condition being satisfied, formally $A_{\sigma _X} < 0$, is $U_{\mu \mu } <0$ (which displays risk aversion if expected utility approach and mean-variance approach are compatible) and

$$\begin{aligned} \frac{\partial ^2 s}{\partial \sigma ^2_X} = - \frac{m c \sigma _{\theta }}{\sigma ^3_X} \left( 2 F' + \frac{m c \sigma _{\theta } F''}{\sigma _X} \right) < 0. \end{aligned}$$

(37)

Note that $F'$ is strictly positive while $F''$ can be positive or negative. If $F''<0$, then a sufficient condition for $\frac{\partial ^2 s}{\partial \sigma ^2_X}<0$ might be $F'' > - \frac{2 \sigma _X F'}{m c \sigma _{\theta }}$ as the bracket term in (37) must be positive. Then, (18) follows from ${\mathrm {sign}} \,\frac{\partial \sigma ^*_X}{\partial _a} = - {\mathrm {sign}} \,\frac{A_a}{A_{\sigma _X}} = {\mathrm {sign}} \,A_a$.

Next, differentiation of the first-order condition for $\tau ^*$

$$\begin{aligned} B:= - c (m-k \sigma _X) + \sigma _X i(\mu _Y, \sigma _Y) \end{aligned}$$

(38)

leads to

$$\begin{aligned} B_{\tau }&= \sigma _X [-c (m-k \sigma _X) i_{\mu } - \sigma _X i_{\sigma }] = - \sigma ^2_X \frac{{\mathrm {d}}^2 \mu _Y}{{\mathrm {d}}\sigma ^2_Y} < 0, \nonumber \\ B_a&= 0,\end{aligned}$$

(39)

$$\begin{aligned} B_{\sigma _X}&= c k + i + \sigma _X [(\bar{\mu }' (\sigma _X) + \tau c k) i_{\mu } + (1-\tau ) i_{\sigma }] \nonumber \\&= c k + i + \sigma _Y \frac{{\mathrm {d}}^2 \mu _Y}{{\mathrm {d}}\sigma _Y^2} + \frac{\sigma _X i_{\mu } a \Phi '}{U_{\mu }} \cdot \frac{\partial s}{\partial \sigma _X} > 0. \end{aligned}$$

(40)

Observe that the second-order condition $B_{\tau } + B_{\sigma _X} \frac{\partial \sigma ^*_X}{\partial \tau }<0$ is satisfied if $\frac{\partial \sigma ^*_X}{\partial \tau } = -\frac{A_\tau }{A_{\sigma _X}} >0$. Under this presupposition

$$\begin{aligned} \frac{\partial \tau ^*}{\partial a} = - \frac{B_a + B_{\sigma _X} \frac{\partial \sigma ^*_X}{\partial a}}{B_{\tau } + B_{\sigma _X} \frac{\partial \sigma ^*_X}{\partial \tau }} = \frac{-B_{\sigma _X}}{B_{\tau } + B_{\sigma _X} \frac{\partial \sigma _X^*}{\partial \tau }} \end{aligned}$$

(41)

establishes (21).

Appendix 2: Derivation of (24)

Differentiating the first-order condition for $\tilde{\sigma }_X$

$$\begin{aligned} C:= - (1-\tau ) i (\mu _Y, \sigma _Y) + \bar{\mu }' (\sigma _X) + \tau k \end{aligned}$$

(42)

subject to $\mu _Y = \bar{\mu } (\sigma _X) - c \tau (m-k \sigma _X)$ and $\sigma _Y = (1-\tau ) \sigma _X$ we obtain

$$\begin{aligned} C_{\sigma _X}&= -(1-\tau )^2 \frac{\mathrm{d}^2 \mu _Y}{\mathrm{d} \sigma _Y^2} - \frac{(1-\tau ) i_{\mu } a \Phi '}{U_{\mu }} \frac{\partial s}{\partial \sigma _X} + \bar{\mu }'' < 0 \nonumber \\&= - (1-\tau )^2 \frac{{\mathrm {d}}^2 \mu _Y}{{\mathrm {d}}\sigma ^2_Y} + \tau (1-\tau ) k (1-c) i_{\mu } + \bar{\mu }''(\sigma _X) <0, \end{aligned}$$

(43)

$$\begin{aligned} C_a&= 0, \end{aligned}$$

(44)

$$\begin{aligned} C_{\tau }&= i + (1-\tau ) \sigma _X \frac{\mathrm{d}^2 \mu _Y}{\mathrm{d} \sigma _Y^2} + k > 0 . \end{aligned}$$

(45)

The comparative static effect (24) follows immediately from $\frac{ \partial \tilde{\sigma }_X}{\partial \tau } = - \frac{C_\tau }{C_{\sigma _X}}$.

Appendix 3: Robustness check

In order to examine the robustness of the results in Sect. 5 we run further examples with different parameter values. We do so in Table 1 where we have changed the parameter $c$ in row 1–6 all else equal as in the example of Sect. 5, $\beta $ in row 7–12 all else equal as in the example of Sect. 5, and $m$ in row 13–18 all else equal as in the example of Sect. 5. For each parameter constellation we have taken three different parameter values of $a$. For a low value of $a$, $\tilde{\sigma }_X$ is inefficiently high and $\tilde{\tau }$ is inefficiently low. For a middle value of $a$, $\tilde{\sigma }_X$ and $\tilde{\tau }$ are approximately efficient, and for a high value of $a$, $\tilde{\sigma }_X$ is inefficiently low and $\tilde{\tau }$ is inefficiently high. This does not only hold for $c=0.01$ and $c=0.13$ as shown in rows 1–6, but also for all $c \in [0.01, 0.13]$. In addition, the Figs. 3, 4, 5, 6, 7, 8 9, and 10 remain qualitatively unchanged. For $c \notin [0.01,0.03]$ we obtain corner solutions. Either one of the pre-tax standard deviations is negative or one of the tax rate is outside of the interval $[0, 1]$. Analogous arguments apply to variations in $\beta $ and $m$.³⁰

Table 1

Robustness check

No.	c	$\beta $	m	a	$\sigma _X^*$	$\tilde{\sigma }_X$	$\tau ^*$	$\tilde{\tau }$
1	0.01	2.0	0.8	5	0.216063	0.231384	0.954398	0.564451
2	0.01	2.0	0.8	28	0.258273	0.258262	0.973566	0.973767
3	0.01	2.0	0.8	30	0.261062	0.25974	0.974482	0.998841
4	0.13	2.0	0.8	0.5	0.209583	0.210725	0.35334	0.284817
5	0.13	2.0	0.8	1.12	0.224575	0.224579	0.470269	0.470153
6	0.13	2.0	0.8	2.0	0.242166	0.238543	0.578199	0.66681
7	0.075	1.0	0.8	0.5	0.206666	0.206971	0.223769	0.177062
8	0.075	1.0	0.8	1.1	0.216972	0.21697	0.3242	0.324374
9	0.075	1.0	0.8	2.0	0.230069	0.228995	0.431093	0.505263
10	0.075	5.0	0.8	2.0	0.23351	0.245597	0.891188	0.78859
11	0.075	5.0	0.8	3.92	0.254644	0.254653	0.916967	0.9169
12	0.075	5.0	0.8	5.0	0.264807	0.258113	0.926984	0.971614
13	0.075	2.0	0.5	2.0	0.228351	0.23911	0.924859	0.675088
14	0.075	2.0	0.5	5.57	0.258032	0.258038	0.970107	0.970001
15	0.075	2.0	0.5	6.0	0.261023	0.259656	0.97364	0.997412
16	0.075	2.0	1.2	0.1	0.194389	0.194836	0.14325	0.0792682
17	0.075	2.0	1.2	0.9	0.212464	0.212482	0.308831	0.30793
18	0.075	2.0	1.2	2.0	0.23171	0.22889	0.442163	0.529586

References

Andersen TM (2013) Incentive and insurance effects of income taxation. Bull Econ Res, in pressGoogle Scholar
Andersen TM (2008) Unemployment insurance and taxation: incentives vs. insurance, discussion paper. Sept 2008Google Scholar
Aronsson T, Sjögren T (2010) Optimal income taxation and social norms in the labor market. Int Tax Public Financ 17(1):67–89CrossRefGoogle Scholar
Besley T, Coate S (1992) Understanding welfare stigma: taxpayer resentment and statistical discrimination. J Public Econ 48(2):165–183CrossRefGoogle Scholar
Bird EJ (2001) Does the welfare state induce risk-taking? J Public Econ 80:357–383CrossRefGoogle Scholar
Clark AE (2003) Unemployment as a social norm: psychological evidence from panel data. J Labor Econ 21(2):323–351CrossRefGoogle Scholar
Conlin M, Lynn M, O’Donoghue T (2003) The norm of restaurant tipping. J Econ Behav Org 52(3):297–321CrossRefGoogle Scholar
Dufwenberg M, Lundholm M (2001) Social norms and moral hazard. Econ J 111(473):506–525CrossRefGoogle Scholar
Eaton J, Rosen HS (1980a) Optimal redistributive taxation and uncertainty. Quart J Econ 95(2):357–364CrossRefGoogle Scholar
Eaton J, Rosen HS (1980b) Taxation, human capital, and uncertainty. Am Econ Rev 70(4):705–715Google Scholar
Eaton J, Rosen HS (1980c) Labor supply, uncertainty and efficient taxation. J Public Econ 14(3):365–374CrossRefGoogle Scholar
Ehrlich I, Becker GS (1972) Market insurance, self-insurance, and self-protection. J Polit Econ 80(4):623–648CrossRefGoogle Scholar
Eichner T (2008) Mean variance vulnerability. Manag Sci 54(3):586–593CrossRefGoogle Scholar
Eichner T, Wagener A (2004) The Welfare State in a Changing Environment. International Tax and Public Finance 11(3):313–331CrossRefGoogle Scholar
Elster J (1989) Social norms and economic theory. J Econ Perspect 3(4):99–117CrossRefGoogle Scholar
Evanc C (2008) Taxation compliance and administrative costs an overview. In: Lang M, Obermair C, Schuch J, Staringer C, Wenninger P (eds) Tax compliance costs in an enlarged European community. Vienna and Kluwer Law International, Linde Verlag, London, pp 447–468Google Scholar
Fehr E, Fischbacher U, Gächter S (2002) Strong reciprocity, human cooperation, and the enforcement of social norms. Human Nature 13(1):1–25CrossRefGoogle Scholar
Gong M, Baron J, Kunreuther H (2009) Group cooperation under uncertainty. J Risk Uncertain 39(3):251–270CrossRefGoogle Scholar
Homans GC (1974) Social behavior: its elementary form. Harcourt, Brace and World, New YorkGoogle Scholar
Lajeri-Chaherli F (2003) Partial derivatives, comparative risk behavior and concavity of utility functions. Math Soc Sci 46:81–99CrossRefGoogle Scholar
Lajeri F, Nielsen LT (2000) Parametric characterizations of risk aversion. Econ Theory 15:469–475CrossRefGoogle Scholar
Lindbeck A (1995) Hazardous welfare-state dynamics. Am Econ Rev 85(2):9–15Google Scholar
Lindbeck A, Nyberg S, Weibull JW (1999) Social norms and economic incentives in the welfare state. Q J Econ 114(1):1–35CrossRefGoogle Scholar
Lindbeck A, Nyberg S, Weibull JW (2003) Social norms and welfare state dynamics. J Eur Econ Assoc 1(2–3):533–542CrossRefGoogle Scholar
Lindbeck A, Nyberg S (2006) Raising children to work hard: altruism, work norms, and social insurance. Q J Econ 121(4):1473–1503Google Scholar
Linde J, Sonnemans J (2012) Social comparison and risky choices. J Risk Uncertain 44(1):45–72CrossRefGoogle Scholar
Maccheroni F, Marinacci M, Rustichini A, Taboga M (2009) Portfolio selection with monotone mean-variance preferences. Math Financ 19(3):487–521CrossRefGoogle Scholar
Markowitz H (1952) Portfolio selection. J Financ 7(1):77–91Google Scholar
Meltzer AH, Richard SF (1981) A rational theory of the size of government. J Polit Econ 89(5):914–927CrossRefGoogle Scholar
Meyer J (1987) Two-moment decision models and expected utility maximization. Am Econ Rev 77(3):421–430Google Scholar
Mirrlees JA (1971) An exploration in the theory of optimum income taxation. Rev Econ Stud 38(2):175–208CrossRefGoogle Scholar
Moffitt R (1983) An economic model of welfare stigma. Am Econ Rev 73(5):1023–1035Google Scholar
OECD (2013) Tax administration 2013: Comparative information on OECD and other advanced emerging economies. OECD PublishingGoogle Scholar
Ormiston MB, Schlee EE (2001) Mean-variance preferences and investor behaviour. Econ J 111(474):849–861CrossRefGoogle Scholar
Rege M (2004) Social norms and private provision of public goods. J Public Econ Theory 6(1):65–77CrossRefGoogle Scholar
Rege M, Telle K (2004) The impact of social approval and framing on cooperation in public good situations. J Public Econ 88(7):1625–1644CrossRefGoogle Scholar
Roberts K (1977) Voting over income tax schedules. J Public Econ 8(3):329–340CrossRefGoogle Scholar
Sherif M (1936) The psychology of social norms. Harper and Brothers, New YorkGoogle Scholar
Sinn H-W (1983) Economic decisions under uncertainty. North Holland, AmsterdamGoogle Scholar
Sinn H-W (1995) A theory of the welfare state. Scand J Econ 97(4):495–526CrossRefGoogle Scholar
Sinn H-W (1996) Social insurance, incentives and risk taking. Int Tax Public Financ 3(3):259–280CrossRefGoogle Scholar
Stutzer A, Lalive R (2004) The role of social work norms in job searching and subjective well-being. J Eur Econ Assoc 2(4):696–719CrossRefGoogle Scholar
Traxler C (2010) Social norms and conditional cooperative taxpayers. Eur J Polit Econ 26(1):89–103CrossRefGoogle Scholar
Varian HR (1980) Redistributive taxation as social insurance. J Public Econ 14(1):49–68CrossRefGoogle Scholar
Wenzel M (2004) An analysis of norm processes in tax compliance. J Econ Psychol 25(2):213–228CrossRefGoogle Scholar
Yamamura E (2008) Impact of formal and informal deterrents on driving behavior. J Socio-Econ 37(6):2505–2512CrossRefGoogle Scholar
Yamamura E (2011) Effects of social norms and fractionalization on voting behaviour in Japan. Appl Econ 43(11):1385–1398CrossRefGoogle Scholar

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Thomas Eichner
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Daniel Weinreich
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1.Department of EconomicsUniversity of HagenHagenGermany

Welfare stigma and risk taking in the welfare state

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