Optimal income taxation and migration

See Atkeson et al. (1999) and Chari et al. (1999).

The difference between the government and individuals’ discount rates can be explained in terms of myopia of the latter, or of political instability, where a government takes into account that it might lose office and therefore values the future less than individuals do (see Grossman and Van Huyck 1988).

By the same reasoning, the asymmetry disappears in the special case of logarithmic utility function, since the anticipated policy path does not affect current individual choices and, thus, the cumulative distortionary effect of taxes is ruled out (see also Lansing 1999 and Reinhorn 2013). For a recent discussion on nonzero taxation of capital income, see also Straub and Werning (2014).

Another extension of the basic framework aimed at obtaining a positive taxation of capital consists in the introduction of uncertainty. However, even if Zhu (1992) points out that in such a case the capital income tax may be nonzero in the long run, Chari et al. (1994) show via simulations that the average value of the optimal capital income tax is very close to zero. Other authors have explored the role of market incompleteness in stochastic environments: Chari and Kehoe (1999), for example, consider an economy with state contingent returns on debt acting as shock absorbers. They show that if the government cannot issue bonds with state contingent returns, capital income taxes can be chosen to overcome this problem. More recently, on the role of idiosyncratic uncertainty and private information in invalidating the Chamley–Judd result, see Golosov et al. (2003), Kocherlakota (2005) and Albanesi and Sleet (2006).

See Atkinson and Sandmo (1980) and Erosa and Gervais (2002).

The relevance of the “disconnectedness” of the economy has been firstly analysed by Weil (1989) in the context of the validity of the Ricardian equivalence proposition.

For a presentation of this model in continuous time, see Barro and Sala-i-Martin (1999), chapter 9.

See, for instance, Razin et al. (2002) and Occhino (2008) on fiscal incentives and the relationship between migration and welfare policies; Solé-Auró and Crimmins (2008) on the differences in consumption patterns of natives and immigrants; Czaika and Parsons (2017) for a recent contribution on the effects of international policy agreements on the characteristics of immigrants; and Bell and Eiser (2016) for the effects of the interplay of migration and fiscal policies on the performance of labour markets.

For example, Ramsey (1928) considered constant discounting unacceptable from an ethical standpoint; see, among others, Bernheim (1989), Michel (1990) and Caplin and Lehay (2004).

A notable exception is the work by Farhi and Werning (2005), who obtain a time-varying social discount rate by assuming that the government values future generations directly and not simply through the altruism of the current generation and in the absence of an OLG framework. See also Spataro and De Bonis (2008) for an analysis of the issue in the context of a perpetual youth economy.

For a general analysis of the taxation of savings and, in particular, inheritance taxes in a similar framework, see De Bonis and Spataro (2010).

To see this, consider period 0: the dynasty of the natives consists of 1 native (the founder, born in period − 1) and n children, so that \({{P}}_{-1,0} = (1 +n)\) and the dynasties of the first immigrants are formed by \({{P}}_{0,0} = \alpha (1+n)\) individuals, with \({{N}}_{0} = (1 + \alpha ) (1+n)\). In period 1, the dynasty of natives is formed by the founder, n children and \(n (1+ n)\) nephews, such that \({{P}}_{-1,1} = (1+n)^{2}\). In the same period 1, the dynasties of the first immigrants are formed by \(\alpha (1+ n)\) founders and \(\alpha (1+ n) n\) children, so that \({{P}}_{0,1} = \alpha (1 + n)^{2}\), while new immigrants have entered the economy, equal to a fraction \(\alpha \) of the previous period population and their current children, i.e. \({{P}}_{1,1} = \alpha (1 + \alpha ) (1 +n)^{2}\), so that \({{N}}_{1}= (1 + \alpha )^{2} (1+ n)^{2}\). Generalizing, we end up with the above expressions for \({{P}}_{\mathrm{s,t}.}\) and \({{N}}_{\mathrm{t}}\).

See Stiglitz (2015) for a review.

See Atkinson and Stiglitz (1980); the alternative “dual” approach takes prices and tax rates as control variables (see, for instance, Chamley 1986).

As for the first dynasty, the implementability constraint takes the form: \(\sum \limits _{t=s}^\infty {({\frac{1+n}{1+\beta }})}^{t-s} ({U_{c_{s,t}} c_{s,t} + U_{l_{s,t}} l_{s,t}}) = U_{c_{0,0}} (1+\tilde{r}_{0,0}) {\bar{k}}_{-1}.\)

In our model, thus, the reference point in the government maximization problem is the utility of the dynasties. The dynastic dimension of income has been recently put forward in the context of the distributional effects of taxation (Piketty 2014; Atkinson 2015; Kanbur and Stiglitz 2015; Halvorsen and Thoresen 2017). Even if our framework is very simple, since dynasties only differ as for their date of entry into the economy and we adopt an utilitarian welfare function, we contribute to this literature by adding efficiency aspects to the analysis of the taxation of dynastic income.

We omit the government budget constraint since, by Walras’ law, it is satisfied if the implementability and feasibility constraints hold.

From now onward, we omit the s and t indicators, whenever this does not cause ambiguity: hence, notation \({{X}}^{+1}\) stands for \({{X}}_{{s}, {t}+1}\).

This case occurs, for instance, when the utility function is of the form: \(U=\frac{c^{1-\frac{1}{\sigma }}}{1-\frac{1}{\sigma }} +V(l)\), where \(H_c =-\frac{1}{\sigma }\).

Generally speaking, differences in weight can be connected to different characteristics of natives and immigrants, and of different generations of immigrants; this would be of relevance for the choice of taxation instruments other than capital income taxation.