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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
The relevance of (conditional) welfare stigma for the design of welfare state programs is further studied by Lindbeck (1995), Dufwenberg and Lundholm (2001), Lindbeck et al. (2003) and Lindbeck and Nyberg (2006).
It is worth mentioning that welfare stigma is also analyzed in the context of private provision of public goods (Rege 2004; Rege and Telle 2004) and tax compliance and tax evasion (Wenzel 2004; Traxler 2010).
Eichner and Wagener (2004) extend the analysis by welfare costs (administrative costs or shadow costs for public funds) and background risks. Within these extensions the efficient tax rate may be less than one.
Gong et al. (2009) analyze the case of group cooperation under uncertainty which is clearly related to social norms. However, we abstract from considering group settings.
The model at hand satisfies the location-scale condition of Meyer (1987) and Sinn (1973) and hence expected utility becomes a function of mean and variance. However, we do not assume that mean-variance preferences and expected utility need to be consistent and follow Ormiston and Schlee (2001) and Eichner (2008) and take the mean-variance framework as an approach that stands on its own.
Individuals are ex ante identical. After the veil of ignorance has lifted they differ with respect to income losses and incomes. Applying the law of large numbers the distribution of \(Y\) is then the ex post realized income distribution.
In the absence of welfare costs \((c=0)\) the share of net-transfer recipients cannot be influenced by variations of self-insurance efforts and we obtain the results of Sinn (1995), Sinn (1996).
One might argue that living on welfare is a matter of luck in our setting and is therefore not subject to feelings of stigma. However, Lindbeck et al. (1999) considers productivity differences, reflected by a wage distribution, which constitute the share of transfer recipients in society. From an ex ante perspective, the revelation of this distribution could then also be interpreted as a matter of luck. Nevertheless, the question of how responsible and irresponsible factors shape stigma preferences is an interesting question but not subject to our analysis.
The specific functional form in (12) can be microfounded as follows. Suppose the individual is expected utility maximizer and let \(\breve{u}\) denote the von Neumann-Morgenstern utility function of income \(y\). The utility under certainty is given by
where \(\breve{\Phi }(s)\) represents welfare stigma. Then we obtain the expected utility
$$\begin{aligned} \mathbf E u(y) = (1-s) \mathbf E \breve{u}(y) + s \left[ \mathbf E \breve{u}(y)- a \breve{\Phi }(s) \right] = \mathbf E \breve{u}(y) - a s \breve{\Phi }(s). \end{aligned}$$
The identities \(\mathbf E \breve{u}(y) \equiv U(\mu _Y, \sigma _Y)\) and \(\Phi (s) \equiv s \breve{\Phi }(s)\) establish (12).
Self-insurance affects \(\mathbf E \breve{u}(y) - a s \breve{\Phi }(s)\) from footnote 12 through \(s\) in two ways. It affects the ex-ante probability of getting a net-transfer reflected by the \(s\) before the stigma function \( \breve{\Phi }(s)\), and it changes the ex-post share of net-transfer recipients captured by \(s\) as argument of the stigma function \( \breve{\Phi }(s)\). In Sect. 2–5 we assume that the ex-post share effect overcompensates the ex-ante probability effect. This assumption goes back to the heart of the concept of welfare stigma (see Lindbeck et al. 1999 or Aronsson and Sjögren 2010). In view of expected utility in footnote 12 the ex-post share effect dominates, if and only if \(\Phi '(s)=\breve{\Phi }(s) +s \breve{\Phi }'(s)<0 \). The other case \(\Phi '(s) > 0\), where the ex-ante probability effect overompensates the ex-post stigma effect, is discussed in Sect. 6.
In our model expected utility and mean-standard deviation preferences are perfect substitutes. Since the interaction between individual’s choice (self-insurance or pre-tax standard deviation) and the source of uncertainty is linear, the model satisfies the location-scale property (Meyer 1987; Sinn 1983) such that all income distributions differ only by mean \(\mu _Y\) and standard deviation \(\sigma _Y\) of post-tax incomes.
Inserting the fiscal budget constraint (3) with \(\mathbf E T\) from (8) in (9), the mean post-tax income \(\mu _Y\) simplifies to \(\mu _Y = \bar{\mu }_X - c \tau (m-k \sigma _X)\). It is then obviously, that the fiscal budget is balanced in the social optimum.
This is line with the literature on welfare stigma. Lindbeck et al. (1999) employ a similar model structure. When individuals decide on working or not they treat the tax and transfer and therefore the share of transfer recipients in society as exogenously given. In a balanced-budget equilibrium a relationship between the tax and transfer system and the share of transfer recipients is established.
Given the highly stylized nature of our model the numerical example is not based on empirical data. Nevertheless, concerning the parameter \(c\) reflecting the operating costs we have chosen a value from the literature. OECD (2013) reports that administrative costs for tax administration as percentage of tax revenues range from 0.5 - 3 %. Evanc (2008) refers to different studies that estimate the compliance costs of income taxation between 2 % and 10 % of tax revenues. In the numerical example we have set the operating costs (as sum of administrative costs and compliance costs) \(c=0.075\) which amounts to 7.5 % and is in the middle of the range identified by Evanc (2008) and OECD (2013).
We cannot generalize our findings from the numerical example by induction, of course. We have run several other examples in the Appendix 3. The graphs corresponding to all examples under scrutiny turned out to be qualitatively the same as those in Figs. 3–10.
In this case, the model could be extended by a different norm type similar to the work hours norm of Aronsson and Sjögren (2010) which focuses on the decisions at the intensive margin of labor supply.
The value \(\theta _{\mathrm {min}} = 0.3\) constitutes a lower boundary for the feasibility of the optimization problems. However, we can increase the minimum income loss to \(\theta _{\mathrm {min}} = 0.5\) without changing our results.
