تنظیمات موضعی در زمان و مکان: مالیات بر درآمد مطلوب با مقایسه اجتماعی پویا

Abstract This paper concerns optimal redistributive non-linear income taxation in an OLG model, where people care about their own consumption relative to (i) other people's current consumption, (ii) own past consumption, and (iii) other people's past consumption. We show that both (i) and (iii) affect the marginal income tax structure whereas (ii) does not. We also derive conditions under which atemporal and intertemporal consumption comparisons give rise to exactly the same tax policy responses. On the basis of the available empirical estimates, comparisons with other people's current and past consumption tend to substantially increase the optimal marginal labor income tax rates. Yet, such comparisons may either increase or decrease the optimal marginal capital income tax rates.

1. Introduction A rapidly growing body of evidence suggests that people have positional preferences in the sense of deriving utility from their own consumption relative to that of others.1 Alongside this development, a corresponding literature dealing with optimal policy responses to positional concerns has evolved, showing that such concerns may have a substantial effect on the incentive structure underlying public policy. Within the literature on optimal income taxation,2 it has for example been shown that social comparisons may motivate substantially higher marginal income tax rates than without such comparisons; see, e.g., Boskin and Sheshinski (1978), Layard (1980), Oswald (1983), Tuomala (1990), Blomquist (1993), Ireland (2001), Aronsson and Johansson-Stenman, 2008, Aronsson and Johansson-Stenman, 2010 and Aronsson and Johansson-Stenman, 2013, Wendner and Goulder (2008) and Wendner (2010a). Yet, almost all earlier studies on optimal policy responses to positional concerns that we are aware of assume that people only make “atemporal” consumption comparisons, by valuing their own current consumption relative to other people's current consumption. A much more general approach has recently been presented by Rayo and Becker (2007). According to their evolutionary model, selfish genes would prefer that the humans they belong to are motivated by their own current consumption relative to (i) their own past consumption, (ii) other people's current consumption, and (iii) other people's past consumption. In the macroeconomic literature of dynamic consumption behavior, (i) corresponds to what is typically denoted habit formation (sometimes denoted internal habit formation), (ii) corresponds to keeping up with the Joneses, while (iii) corresponds to catching up with the Joneses (sometimes denoted external habit formation). 3 The present paper takes these three types of consumption comparisons as a point of departure in a study of optimal income taxation in a dynamic economy. 4 We develop and analyze an overlapping generations (OLG) model with endogenous labor supply and savings, where the consumers are concerned with their relative consumption and where nonlinear taxes of labor income and capital income are used for purposes of externality correction and redistribution. A dynamic model allows us to explore intertemporal aspects of consumption comparisons, and provides a natural framework for studying capital income taxation. The latter is important not least due to the difficulties of explaining the widespread use of capital taxes with conventional public economics models. Earlier research shows that relative consumption concerns may motivate such taxes (Aronsson and Johansson-Stenman, 2010), and one might perhaps conjecture such concerns to be particularly important when the concept of relative consumption has more than one dimension, as we assume here. The literature on optimal redistributive taxation under relative consumption concerns is scarce, and almost all earlier studies are based on static models. The only exception that we are aware of is Aronsson and Johansson-Stenman (2010), who analyze optimal nonlinear income taxation in a dynamic economy where each consumer compares his/her own current consumption with other people's current consumption. Hence, their study neglects internal habit formation as well as the catching up with the Joneses type of comparison mentioned above, and focuses solely on consumption comparisons based on keeping up with the Joneses preferences. The present paper, in contrast, addresses the implications of such atemporal comparisons for optimal income taxation simultaneously with the implications of relative consumption comparisons over time. Another study related to ours is Ljungqvist and Uhlig (2000), who consider optimal labor income taxation in a dynamic representative agent model where the consumer preference for relative consumption is driven by a catching up with the Joneses motive. We generalize their approach in several different ways by (1) considering a broader set of tax instruments, (2) analyzing redistribution policy alongside externality correction, and (3) allowing keeping up and catching up with the Joneses mechanisms to be operative simultaneously. These extensions are important. In addition to the empirical evidence for between-people comparisons mentioned above, there is evidence suggesting that people also make comparisons with their own past consumption (e.g., Loewenstein and Sicherman, 1991 and Frank and Hutchens, 1993); indeed, such comparisons were discussed already by Veblen (1899). It also makes intuitive sense that old people compare their own consumption with several different reference levels, including what they recall about their own and others’ consumption when they were young. Moreover, when growing up, most people are likely to receive information from parents and grandparents about the consumption (and other living conditions) characterizing earlier generations. The results from happiness studies have also documented that people's happiness adapts to income changes, consistent with the idea that the reference income increases over time when actual income increases; see, e.g., Stutzer (2004) and Di Tella et al. (2010). Specifically, Senik (2009) presents recent estimates regarding the importance of different kinds of comparisons over time, showing that subjective well-being is dependent on one's own standard of living relative to both internal and external reference points. Such comparisons are also consistent with the empirical pattern of some financial puzzles,5 and (as mentioned) they are in line with recent research based on evolutionary models. Section 2 presents the model and the outcome of private optimization. In Section 3, we consider optimal income taxation in a first-best setting with full information about individual productivity, where the government can deal with its distributional objectives through lump-sum taxes. This provides a simple benchmark by which to compare our results with some earlier literature on optimal labor income taxation under positional concerns (which is based on similar models). Our results show that relative comparisons with one's own past consumption (internal habit formation) do not directly affect the policy rules for marginal income taxation (although they may, of course, influence the levels of marginal income tax rates). The intuition is that such comparisons are fully internalized at the individual level and do not generate any externalities. However, positional concerns governed by comparisons with other people's current and past consumption give rise to externalities and will, therefore, also directly affect the incentive structure underlying marginal income taxation. We show that positional concerns with respect to other people's current and past consumption tend to increase the optimal marginal labor income tax rates. We also show how the marginal capital income tax rates are governed by differences in positional concerns over the individual life cycle, where the relevant measure of reference consumption is again based on both the current and past consumption of others. In general, positional concerns governed by other people's past consumption give rise to much more complex policy responses than do comparisons based on other people's current consumption. This is so because consumption comparisons over time give rise to an intertemporal chain reaction with welfare effects in the entire future, whereas comparisons with other people's current consumption only lead to “atemporal externalities.” We can nevertheless derive strong results for a natural benchmark case in which the concerns for relative consumption are constant over time, implying that relative consumption comparisons over time (based on the catching up with the Joneses preferences) give rise to exactly the same marginal tax rate responses as comparisons with other people's current consumption (based on the keeping up with the Joneses preferences). In practice, informational limitations are likely to prevent governments from using differentiated lump-sum taxation as a basis for redistribution. Therefore, in Section 4, we introduce asymmetric information between the government and the private sector with respect to individual ability (worker productivity), where the public decision problem is described by a variant of the two-type optimal income tax model originally developed by Stern (1982) and Stiglitz (1982). Although simple, the two-type model provides a powerful framework for analyzing externality correction and redistribution simultaneously. In such a second-best framework, tax distortions are the outcome of an optimal choice made by the government, subject to informational limitations, and not of any arbitrary restrictions on the tax instruments (such as linearity) or the necessity to raise revenue per se. Therefore, our approach enables us to capture that the optimal income tax responses to positional concerns may involve purely corrective as well as redistributive elements. In a second-best setting where ability is private information, there is also another policy incentive involved beyond positional externalities: the government may relax the incentive constraint by exploiting differences in positional concerns across ability types. Our results show that while the externality-correcting mechanism unambiguously works to increase the marginal labor income tax rates, independently of whether individuals compare their own current consumption with other people's current or past consumption (or use a combination of these two reference measures), the direction of the mechanism through the incentive constraint is ambiguous. We both present general optimal taxation results and derive sufficient conditions for when the overall net effect of positional concerns works to increase the marginal labor income tax rates. Section 5 illustrates with a particular Cobb-Douglas functional form and shows, based on parameter estimates from the literature, that positional preferences of both the keeping up with the Joneses and the catching up with the Joneses types substantially increase the optimal marginal labor income tax rates. Section 6 summarizes and concludes the paper; proofs are presented in the Appendix.

. Conclusion The present paper simultaneously recognizes three mechanisms behind relative consumption concerns: comparisons with (i) other people's current consumption (keeping up with the Joneses), (ii) own past consumption (habit formation), and (iii) other people's past consumption (catching up with the Joneses). We are not aware of any previous normative economic analysis in such a setting. We start by deriving a first-best tax policy to correct for the positional externalities in the case where the government is able to redistribute through lump-sum instruments. We show that comparisons with one's own past consumption do not affect the optimal policy rules, since such comparisons are internalized by each individual (although internal habit formation may, of course, affect the levels of marginal income tax rates), whereas comparisons with other people's current and past consumption generate positional externalities. In a stationary regime where the degrees of positionality are time-invariant, the optimal tax policy is derived in terms of the average degree of time-inclusive consumption positionality, which is essentially the sum of the average degree of current consumption positionality and the average degree of intertemporal consumption positionality. Results derived in earlier literature such as Ljungqvist and Uhlig (2000) and Dupor and Liu (2003) follow as special cases of our first-best model. We also show that the optimal marginal labor income tax rates become larger the more positional people are on average, in terms of the average degree of time-inclusive consumption positionality. The second-best analysis carried out in Section 4 is based on the two-type optimal income tax model with asymmetric information between the government and the private sector. In this case, the net effects of relative consumption concerns also depend on whether the low-ability type is more or less positional (broadly speaking) than the mimicker. The reason is that this determines whether an increase in the reference consumption works to relax or tighten the self-selection constraint. If the degrees of positionality are constant over time, there are no direct effects of relative consumption concerns on the marginal capital income tax rates; in a second-best setting, such concerns will, nevertheless, affect the marginal capital income tax structure through the self-selection constraint. We are also able to reproduce the well-known result of Ordover and Phelps (1979) for when there should be no capital income taxes on the margin, in a model where people compare their own current consumption with several different measures of reference consumption. When we generalize the model to allow for time variation also with regard to the positionality degrees, the population size, and the interest rate, the optimal policy responses become considerably more complex and the optimal policy rules are no longer possible to express in a simple way in terms of time-inclusive positionality degrees. This applies both to the first-best and the second-best model. Yet, we were able to obtain important findings regarding the qualitative effects of positional concerns on the optimal marginal income tax rates, and in particular, when such concerns unambiguously work to increase or decrease these tax rates. Finally we illustrate with a Cobb–Douglas functional form and show, based on parameter estimates from the literature, that positional preferences of both the keeping up with the Joneses and catching up with the Joneses types substantially increase the optimal marginal labor income tax rates for both types. Since the leisure separability conditions are fulfilled for this form, the optimal marginal capital income tax rates are consequently zero for both types. We believe that the research area consisting of normative economic analysis when relative consumption matters is still underexplored. Examples of important issues that remain to be analyzed include multi-country settings, public provision of private (non-positional) goods, public good provision in a dynamic economy, and long-term social discounting.