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Social welfare effects of tax-benefit reform under endogenous participation and unemployment: an ordinal approach

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Abstract

This paper analyzes the social welfare effects of tax-benefit reforms in a framework integrating endogenous labor supply and unemployment. We adopt an ordinal approach to social welfare comparisons by searching for “socially desirable” reforms that would improve social welfare for an entire class of social welfare functions. In the model, there is a discrete distribution of individuals’ productivities and individuals are heterogeneous with respect to leisure preferences (or disability of work). Labor supply decisions are limited to the participation decision. Unemployment is modeled in a search and matching framework with individual wage bargaining. For the social welfare analysis, the model is calibrated for Switzerland. Starting from a situation with an unemployment benefit scheme, the introduction of in-work benefits is shown to be a “socially desirable” reform: it would be unanimously preferred to the current situation according to all social welfare functions based on the criteria of Pareto, anonymity, and the principle of transfers. This result holds for two different types of preference heterogeneity (leisure preferences or disability of work) and also for the case where job search effort cannot be monitored.

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Notes

  1. These necessary conditions are derived from two special cases of this class of social welfare functions (SWF): the utilitarian SWF and the Rawlsian SWF. Note also that second-order social welfare dominance does not exclude the case where a reform produces winners and losers as long as the former are on average poorer than the latter.

  2. If the desirability of reforms were evaluated using a single social welfare function, a loss in efficiency could always be traded off against a reduction in inequality and a decrease in the poorest individual’s welfare could always be traded off against an increase in the welfare of other individuals. Our main result—that the introduction of in-work benefits leads to a situation which dominates the current situation in terms of social welfare—cannot be inferred from the description of optimal tax schedules.

  3. In a model with discrete participation decisions and a continuous effort level, Choné and Laroque (2011) show that financial incentives to work for low-skill individuals are part of the optimal tax schedule when participation costs are pecuniary. See also Beaudry et al. (2009) for a similar contribution in a different setup (discrete productivities).

  4. See also Choné and Laroque (2010) for a rigorous analysis of this question in the Mirrlees model.

  5. See also Lehmann (2003) who analyzes the introduction of a basic income in a search-matching model with two skill categories and exogenous labor supply.

  6. In a first-best world where it observes individuals’ types (skill and preference parameters), an inequality-averse government would choose a policy that would equalize utility levels of all individuals (Choné and Laroque 2005). Those who have a strong taste for leisure would be taxed whereas the government would pay an unemployment benefit only to those whose preference for leisure is below a certain threshold.

  7. Calibration of monitoring parameters would be somehow arbitrary.

  8. Because of the absence of capital in the model, we adopt the conservative assumption that there is no tax on firm profits. The entrepreneurs’ income could be taxed away without creating distortions in our model, but such an outcome would be unrealistic. Indeed, in a more complete model with capital accumulation, a tax on profits would have detrimental effects on growth.

  9. In our simulations of Sects. 4.2 and 4.3, we assume that the marginal tax rate is unique and independent of skill. For given benefits, the marginal tax rate on labor income is then determined by the government’s intertemporal budget constraint.

  10. This assumption is analogous to the hypothesis, which is standard in the literature of optimal taxation, that different labor types are perfectly substitutable.

  11. Note that, because of wage bargaining, the difference W i −U i depends only on θ i . Indeed, Eqs. (3) and (8) imply

    $$W_i-U_i= \biggl(\frac{\beta}{1-\beta} \biggr) \frac{p_i c}{(1+\tau_i) m(\theta_i)}. $$

  12. Alternatively, if a shock decreases the participation rate, some of the unemployed will quit the queue, thereby decreasing the unemployment rate.

  13. Most inactive individuals are also better off than most of the working individuals of the same skill. In the model, the utility of being employed is higher than the utility of being unemployed, but this difference is rather small due to the fast turnover in the labor market.

  14. The equivalence between the two versions of the model holds only if individuals experience the same level of disutility from being employed and from being unemployed. This assumption might seem strong, but can be justified by the fact that it is not necessarily easier for a disabled person to actively seek for work than to be employed.

  15. There have been very small changes in unemployment rates and the structure of wages between 1998 and 2008 in Switzerland, by contrast to other European countries.

  16. For example, Gerfin and Leu (2007) report for Switzerland participation elasticities of 0.36 for married women and 0 for single women, single men, and men in couples.

  17. The anonymity criterion is equivalent to symmetry of the SWF with respect to individual utilities. The Pareto criterion states that the SWF is weakly increasing in individual utilities. The transfer principle states that a mean-preserving equalizing transfer does not decrease social welfare. This is equivalent to saying that the SWF is S-concave (Note that S-concavity implies symmetry).

  18. This choice is sometimes justified by the fact that other search models lead to an equilibrium outcome where the Hosios condition is satisfied. See Moene (1997) and Mortensen and Pissarides (1999). In our simulations, we use a Cobb–Douglas matching function for which η(θ i ) is constant and identical for all skill levels.

  19. The difference in net tax payments between employment and unemployment is T i =τ i w i −z wi −z u . Define the average “employment tax rate” as \(\tau_{i}^{e}= T_{i}/w_{i}\). Assuming that η is constant, condition (21) can then be rewritten as \(\bar{\tau}_{i}^{e}-\tau_{i} = (\eta-\beta)/[\eta(1-\beta)]\).

  20. To understand this point, it should be emphasized that any increase in z wi is neutral with respect to the participation decision of skill i if it is offset by a budget-neutral increase in the tax rate τ i : both changes apply to the same employment state and their incentive effects on participation cancel out because the average tax rate remains unchanged. The same cannot be said of unemployment assistance: z u is received when an individual is unemployed, but the corresponding tax is paid when the individual is working. An individual who is out of the labor force and begins to search for a job will first be unemployed before being able to find a job. Hence, the increase in unemployment benefits will be of more value for him than the fall in the net wage due to the corresponding tax increase. Therefore, a rise in z u tends to increase participation even if the government budget is balanced. A positive benefit paid to individuals outside the labor force, as defined in Eq. (22), counterbalances this effect.

  21. The population share s J is calibrated in such a way that the entrepreneur’s initial utility level is twice the utility level of the average worker. The contribution of individuals outside the labor force to social welfare is not straightforward to compute because of their heterogeneity (an appendix describing the approximation procedure is available on request).

  22. These social indifference curves were calculated using version L-PM of the model. Results with version L-MI are identical for the SWF with ϵ=0 and are available on request.

  23. Generalized Lorenz dominance is equivalent to second-order stochastic dominance (Thistle 1989). See also Sen (1997, p. 132–138).

  24. Condition (A.4) is implied by the following conditions of the maximum principle: ∂H c /∂θ i =0 and \(\dot{\mu}_{i} -r\mu_{i}=-\partial H_{c}/\partial\ell_{i}\) where H c is the current-value Hamiltonian and μ the multiplier associated with (A.3). Close inspection of necessary conditions reveals that \(\dot{\mu}_{i}=0\) since μ i jumps to its steady state value.

  25. Note that (16) can be written as

    $$\frac{r+q+\theta_i m(\theta_i)}{1+\theta_i c} \ c=(1-\beta) \biggl(1-\frac{(1+\tau)(z_u-z_w)}{p_i(1+\theta_i c)} \biggr) m( \theta_i). $$

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Acknowledgements

We thank Bruno van der Linden, Jaime de Melo, and two anonymous referees for very helpful comments on earlier versions.

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Authors and Affiliations

  1. Swiss Federal Tax Administration, Schwarztorstrasse 50, 3003, Berne, Switzerland

    Brigitte van Baalen

  2. Department of Economics, University of Geneva, 40 boul. du Pont-d’Arve, 1211, Geneva 4, Switzerland

    Tobias Müller

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  1. Brigitte van Baalen
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  2. Tobias Müller
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Correspondence to Tobias Müller.

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Support by the Swiss National Science Foundation (Grant No. 4045-59741, National Research Programme 45: “Future Problems of the Welfare State”) is gratefully acknowledged.

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Appendix A: Economic efficiency: optimality conditions

Appendix A: Economic efficiency: optimality conditions

According to the utilitarian criterion, aggregate welfare Ψ (at time t=0) is defined as the sum of individual utilities:

$$ \varPsi = \sum_i s_i \bigl[ (1-\pi_i) \bar{N}_i + \bigl( \pi_i-\ell_i(0)\bigr) U_i + \ell_i(0) (W_i+J_i) \bigr], $$
(A.1)

where π i =H(ξ i ), ℓ i (0) is the initial employment rate and \(\bar{N}_{i} =\int_{\xi_{i}}^{\infty} x H'(x)\,\mathrm{d}x/\allowbreak(1-\pi_{i})+z_{n}\) is average utility of inactive individuals. It can be shown that (A.1) is equal to

$$ \varPsi= \sum_i s_i \int_{0}^{\infty} \biggl\{\int _{\xi_i}^{\infty} x H'(x)\,\mathrm{d}x + \ell_i(t) p_i - \bigl(\pi_i- \ell_i(t)\bigr) p_i c \theta_i \biggr\} \mbox{e}^{-rt} \,\mbox{d}t, $$
(A.2)

where ℓ i (t) evolves according to (1). The initial employment rates ℓ i (0) are fixed and the problem of efficiency maximization consists in maximizing Ψ subject to

$$ \dot{\ell}_i(t) = \theta_i m( \theta_i)\pi_i - \bigl[q+\theta_i m( \theta_i)\bigr] \ell_i(t), \quad\pi_i = H( \xi_i), \quad\ell_i(0) = \ell_{i}^0 . $$
(A.3)

Consider first the optimal level of labor market tightness, denoted by \(\hat{\theta}_{i}\). According to the necessary conditions of the maximum principle, \(\hat{\theta}_{i}\) is the solution ofFootnote 24

$$ \bigl[r+q+\theta_i m(\theta_i) \bigr]c/(1+\theta_i c) = m(\theta_i) \bigl[1-\eta( \theta_i)\bigr], $$
(A.4)

where η(θ i )=|θ i m′(θ i )/m(θ i )| is the absolute value of the elasticity of m(θ i ).

What policies can the government use to attain maximum efficiency? In the decentralized equilibrium, θ i is determined by Eq. (16). Combining this equation with the optimality condition (A.4) and using (9) yields Eq. (21) in the main text.Footnote 25

Now turn to the optimal choice of labor market participation, denoted by \(\hat{\pi}_{i}=H(\hat{\xi}_{i})\). The optimal reservation level of the leisure parameter is given by \(\hat{\xi}_{i}=g_{i}(\hat{\theta}_{i})\), where g i is derived from the following first-order condition, obtained by maximizing the Hamiltonian with respect to ξ i :

$$ \xi_i = \frac{m(\theta_i)-(r+q)c}{r+q+\theta_i m(\theta_i)} p_i \theta_i \equiv g_i(\theta_i). $$
(A.5)

What policies are compatible with optimal participation rates? Combining (A.5) with the job creation condition (15) yields

$$ \xi_i = \frac{ \theta_i m(\theta_i)}{r+q+\theta_i m(\theta_i)} \ w_i (1+ \tau). $$
(A.6)

Comparison of (A.6) with the determination of ξ i in the decentralized equilibrium (11) leads to the following condition:

$$ \tau w_i = z_w-z_n + \frac{r+q}{\theta_i m(\theta_i)} \ (z_u- z_n). $$
(A.7)

Equation (A.7) leads to the conclusion that a laissez-faire policy without government intervention ensures maximum efficiency with respect to the participation decision. As there are no externalities involved, this does not come as a surprise. A more interesting question is whether there exist other policies that can ensure an efficient outcome. To address this question more clearly, the government’s budget constraint has to be taken into account. Substituting (A.7) into the intertemporal budget constraint (14) yields condition (22) in the main text.

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van Baalen, B., Müller, T. Social welfare effects of tax-benefit reform under endogenous participation and unemployment: an ordinal approach. Int Tax Public Finance 21, 198–227 (2014). https://doi.org/10.1007/s10797-012-9263-7

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