Tagging and redistributive taxation with imperfect disability monitoring

In 2005, about 80 % of disability recipients suffer from mental disorders and musculoskeletal diseases (e.g., back pain) (Social Security Administration 2006). Generally, most of these disabilities are neither easily observed nor perfectly monitored, even with a deep medical examination (Campolieti 2002). Therefore, disability transfer systems are always imperfect.

Jacquet and Van der Linden (2006) already introduce endogenous and imperfect take-up into the tagging model of Akerlof (1978). Some eligible are deterred from applying by the losses involved in feeling and being stigmatized (stigma being heterogeneous among claimants). Kleven and Kopczuk (2011) also endogenize take-up and model that complexity deters some of the eligible.

In the tagging literature, take-up is usually exogenous but this literature also relies on the assumption that all eligible people, whether they are tagged or untagged, do work (as in Akerlof 1978), or that all eligible do not work (see, e.g., Parsons 1996; Salanié 2002).

The welfare benefit is also called demogrant in the tax literature (e.g., Salanié 2002).

Diamond and Sheshinski (1995), Parsons (1996) and Salanié (2002) show that redistribution can be enhanced by giving more to those who are monitored as disabled, even if the screening is imperfect.

In this paper, the tag (disability) is perfectly correlated with low productivity, which is the basis for redistribution. However, the tag is not perfectly observable; hence, tagging (monitoring) is not perfect. Contrastingly, in the seminal paper of Akerlof (1978), the tag is perfectly observable but correlated more or less perfectly with low productivity. Tagging is also not perfect.

An exception is Boadway et al. (1999), where the accuracy of monitoring depends on the effort level of social workers. Boadway et al. (1999) characterize the optimal payment and monitoring of social workers who shirk. Shirking induces errors in screening between disabled and low-ability claimants (the latter are the able in our model). Contrastingly, the endogenous monitoring of our model depends upon the resources devoted to it and there is no agency problem involved in the tagging process. We also relax Boadway et al.’s assumption that government policy is designed such that all low-ability and disabled people apply for welfare assistance. The other differences between our model and that of Boadway et al. (1999) will become apparent as we proceed. A recent paper by Kleven and Kopczuk (2011) also endogenizes monitoring. The authors study the optimal complexity of transfer program when type I and type II errors co-exist with non-take-up which is induced by the complexity of the transfer program. However, their model does not allow to provide any insight regarding the optimal tax and transfer schedule and the induced distortions simply because no tax revenue is modeled, benefits are exogenously financed and because monitoring is assumed costless.

We want to see whether an EITC or an NIT is optimal. This requires us to describe only the participation tax rates. Therefore, it is appropriate to assume a discrete support for skills, like in Saez (2002). For simplicity, we assume two productivity levels, but increasing the number of productivities would not modify our main results.

It is possible to follow the suggestion by Pestieau and Racionero (2009) to disentangle the disabled’s parameter into two components: \(\delta =\delta _{a}+\delta _{d}\) and again to hold people responsible for their taste parameter \(\delta _{a}\) but not for their disability parameter \(\delta _{d}\). However this complicates the model without bringing further analytical gains.

This is shown in the working paper Jacquet (2010). In the latter paper, the utility when not working is \(v(x)-\sigma \) where \(\sigma \) denotes the (endogenous) reputational stigma à la Besley and Coate (1992) or the take-up cost of snowball (i.e., the take-up by undeserving implies a snowball effect on the take-up by the deserving).

We also assume that \(\lim _{(p,q)\rightarrow (1,0)}M(p,q)=0\). Having \(p=1\) and \(q=0\) corresponds to the situation where none of the applicants receive disability benefits. Therefore, nobody will actually claim disability benefits and the disability benefit will not be observed. Monitoring is then assumed costless. The model boils down to a standard nonlinear income tax system (without tagging) so that welfare benefits are provided to all non-employed people. Similarly, we also assume that \(\lim _{(p,q)\rightarrow (0,1)}M(p,q)=0\). Intuitively, providing benefits to all applicants implies that the level of type II error is maximal (\(q=1\)) but there is no type I error (\(p=0\)). Since this does not require any screening, the cost per applicant can be assumed to be nil, i.e. \(M\left( 0,1\right) =0\). Finally, \(\lim _{(p,q)\rightarrow (0,0)}M(p,q)=+\infty \).

The model does not allow for fines of getting caught because there is no fine in practice.

Recall that we assume \(\delta _{d}\in [0,+\infty )\), however, more generally, this intersection could take place for a negative value of \(\delta _{d}\). In this case, we would have a corner solution where all disabled people apply for disability benefits.

In this model, the decision to work or to apply for disability is independent of \(p\) and tagging forces disabled with \(\delta _{d}>\widetilde{\delta }_{d}\) to work with probability \(p\). We might alternatively think that disabled people are more likely to apply for disability benefits the greater the chance of getting them, i.e. \(p\) being lower. One way to model this could be to introduce a cost of applying for disability benefits, \(k<1\) as follows:so that a higher \(p\) increases the number of disabled choosing to work. This would add behavioral responses to the necessary condition (33) that we neglect here.

When \(p=q=0\) and \(\widehat{\delta }_{a}\rightarrow \infty \), (28) becomesand (31) becomesDividing these two equations by \(v^{\prime }\left( x_{L}\right) \) and \(v^{\prime }\left( x_{D}\right) \), respectively, and adding them givesSubstituting \(\lambda =v^{\prime }\left( x_{H}\right) \) into the latter gives (38).