Optimal redistributive taxation with both extensive and intensive responses

Abstract

We derive a general optimal income tax formula when individuals respond along both the intensive and extensive margins and when income effects can prevail. Individuals are heterogeneous across two dimensions: their skill and their disutility of participation. Preferences over consumption and work effort can differ with respect to the level of skill, with only the Spence-Mirrlees condition being imposed. Employing a new tax perturbation approach that integrates the nonlinearity of the tax function into the behavioral elasticities, we derive a fairly mild condition for optimal marginal tax rates to be nonnegative everywhere. Numerical simulations using U.S. data confirm the mildness of our conditions. The extensive margin strongly reduces the level of optimal marginal tax rates Résumé Nous déterminons une formule générale de taxation optimale pour le cas où les individus ont des réponses intensives et extensives de leur offre de travail et où des effets revenus peuvent survenir. Les individus diffèrent selon deux caractéristiques : leur productivité et leur désutilité à participer. Des individus de productivité différents peuvent avoir une fonction d'utilité différente tant que la condition de Spence-Mirrlees reste vérifiée. En utilisant une nouvelle méthode de perturbation de la fonction de taxe qui intègre dans la définition des élasticités comportementales les non-linéarités de la fonction de taxe, nous obtenons une condition suffisante assez peu restrictive qui garantit que les taux marginaux optimaux sont partout positifs ou nuls. Nos simulations numériques basées sur des données américaines confirment le caractère plausible de notre condition suffisante. Elles montrent également que l'introduction d'une marge extensive réduit singulièrement le niveau des taux marginaux optimaux.

Short- and long-term participation tax rates and their impact on labor supply

“…This division barely changes over time. Interestingly, some PTRs in the bottom decile are negative in 2006 which coincides with the theoretical results of Diamond (1980), Saez (2002) and Jacquet et al (2013). This is due to the additional child benefit (Kinderzuschlag) which is an in-work benefit introduced in 2005 to raise the household income of working families above the threshold of social assistance.…”

“…In optimal tax theory, work incentives inherent in the tax-benefit system are captured by the Effective Marginal Tax Rate (EMTR) at intensive margin and the Participation Tax Rate (PTR) at the extensive margin. Diamond (1980), Saez (2002) and, more recently, Jacquet et al (2013) find that the optimal PTR can be negative for lower income levels. The empirical literature has shown that the behavioral response at the extensive margin exceeds the response at the intensive margin.…”

Political preferences for redistribution in Sweden

“…3 Another interesting crosscountry application of the inverse-taxation methodology is Spadaro et al (2015), with a focus on the poverty-aversion of European policy-makers. 4 Zoutman et al (2014) analyze the re-distributive preferences in the Netherlands by inverting the continuous optimal income tax model with both intensive and extensive margins developed by Jacquet et al (2013). Relatedly, Zoutman et al (2015) and Jacobs et al (2017) analyze the political preferences for redistribution of Dutch political parties.…”

“…13 The key intuition behind this equation is that it trades off the mechanical increases in tax revenue resulting from increases in taxes on the working population against the behavioral losses in tax revenue resulting from participation responses. As explained in Jacquet et al (2013), in the presence of intensive-margin responses [ε(z) = 0], optimal participation taxes will deviate from formula (5) since one needs to take into account the distortions induced by the tax schedule on intensive-margin responses. 14 In the presence of intensive-margin responses, Eq.…”

“…5 instead defines a "target" for the participation tax. In this case, using Zoutman et al (2015), appendix, equation 34 (or equation 18d in Jacquet et al 2013) an average of Eq. 5 should hold in the optimum, i.e.…”