میراث، مالیات و توزیع ثروت در یک مدل تعادل عمومی

This paper examines the role of bequests and of taxation on bequests for the distribution of wealth. We investigate a model with overlapping generations and heterogenous households where parents derive utility directly from their bequests. We obtain all results analytically. Using the coefficient of variation as the measure of inequality, bequests per se diminish the inequality of wealth since they raise private savings and hence average wealth holdings more than the variance of wealth. From a policy perspective, taxing bequests and redistributing government revenue lump-sum among the young generation further decreases wealth inequality.

Most industrial countries levy a tax on wealth transfers. However, there are substantial differences in the legal framework of the tax system. In France and Germany, on the one hand, the tax is levied on inheritances. The institutional setting further forces donors to divide their estate equally among their own children (see Cremer and Pestieau, 2003). In the United States and in the United Kingdom on the other hand, there is a tax on estates and donors enjoy more freedom of bequests, although state rules might restrict disinheritance. What many countries seem to have in common is an ongoing and controversial debate about taxation of wealth transfers. Some countries, including the US, contemplate to phase out taxes on wealth transfer in the near future. One of the main arguments in the public and academic discussion is the role of wealth transfers for the inequality of wealth. Wealth is highly concentrated: in many industrial countries, the share of the richest 1% of households in net worth is estimated to be 20–30% (see Davies and Shorrocks, 2000), whereas an equal distribution would imply that any π% of the population hold π% of the total wealth. Wealth transfers in form of bequests or inter-vivo transfers are often seen as one of the major culprits for the inequality of wealth. 1 Since there is some concern about the level of concentration, the taxation of wealth transfers is frequently identified as an adequate policy to mitigate the concentration of wealth. This paper investigates the role of bequests for the distribution of wealth and the effects of redistributive taxation.2 We construct a simple model with stochastic individual income to analyse distributional effects by comparing properties of distributions in an overlapping generations setting. While focusing on steady states for our main results, we provide a complete analysis of transitional dynamics as well. We find that intergenerational wealth transfers per se have an equalizing effect on the distribution of wealth when the coefficient of variation is chosen as the measure of inequality. Since this result can be seen in general equilibrium only, we consider general equilibrium analysis as being important. In our model, bequests have two effects. On the one hand, there is an increase in the variance of wealth. On the other, as these transfers imply that wealth holdings of a family at a certain point in time are determined not only by own income but by a weighted sum of own and ancestor's income, average wealth holdings increase as well. As the greater average wealth compensates for higher variance, the inequality of wealth, as measured by the coefficient of variation, falls. We further find that this result is robust when correlation across parent's and child's income, endogenous labour supply and a CES instead of a logarithmic specification of the utility function are introduced into the model. When we turn to economic policy, we allow the government to tax bequests and redistribute revenue among the young. We find that the redistributive policy reduces the variance of wealth while keeping the average wealth holding constant. As a result, inequality of wealth – again measured by the coefficient of variation – falls. Finally, we analyse how taxation affects the Gini coefficient. Our results are robust to the choice of inequality measure — taxation and redistribution decreases inequality. We are therefore confident that our results can directly be used for policy debates. Note that due to the simplicity of our modeling choice, we are able to derive all results apart from the Gini result in Section 5.3 analytically. The relation between intergenerational transfers and the wealth distribution has already found some attention among economists. In contrast to the frequently alleged concentration increasing influence (e.g. Meade, 1976 and Wilhelm, 1997), the results of some models indicate that intergenerational wealth transfers imply more equality of wealth. The best known argument is the compensation principle between parents and children where bequests serve to compensate differences in random labour income (Becker and Tomes, 1979, Davies, 1986 and Davies and Kuhn, 1991; see Davies and Shorrocks, 2000, ch. 2.3 for a survey3). When it comes to taxation of inheritances, some argue that when “inheritance plays an equalizing role, it seems likely that <…> taxes would be disequalizing” (Davies, 1986, p. 539). In fact, this result has been claimed or shown by Becker and Tomes (1979) or Davies (1986) for a long-run steady state. It was put into some perspective by Davies and Kuhn (1991) who found that in the short-run, taxation could be equalizing. Some seem to summarize the current state of knowledge as if only under exceptional circumstances, taxation of bequests would imply a more equal distribution of wealth: “if there are incomplete markets <…> taxation <…> can reduce <…> inequality” (Gokhale et al., 2001, p. 97).4 Compared to this literature, the present paper confirms that bequests per se imply a more equal wealth distribution indeed. The mechanism stressed here, however, is completely independent of the Becker–Tomes compensation principle. The wealth distribution becomes more equal because of the increase in expected wealth which overcompensates the increase in the variance of wealth such that the coefficient of variation falls. As this mechanism relies on capital accumulation, a general equilibrium setup is important.5 The reason why we find that taxation of bequests has an equalizing effect lies in the assumption about what parents value. Becker (1974) introduced the concept of “social income” which was used by Becker and Tomes (1979) in the form of “family income” or by Davies (1986) and others (again, see the references in Davies and Shorrocks, 2000, ch. 2.3) as “family wealth”. The idea – put simply – is that parents care about total income of children, i.e. labour income plus inheritances after-tax and lump-sum transfers. As a consequence, when maximizing utility, parents take family income as the disposable income which they split optimally between own consumption and total income of children. In the present paper, parents care about (after-tax) bequests per se — we therefore follow the joy-of-giving approach. With this setup, parents do not take family income into account but simply their own income which they split optimally between own consumption and bequests. This simple difference in preferences implies that under joy-of-giving, taxation of bequests is neutral with respect to average wealth and therefore, by decreasing the variance of bequests, implies lower inequality in wealth.6 The rest of the paper is organized as follows. The next section presents the basic model. Section 3 studies the evolution path of the economy and steady state properties. In Section 4, we study the distribution of wealth and the role of bequests for inequality. We also allow for a correlation between parent's and child's income as an extension to the basic model. Section 5 then investigates distributional effects of taxation and checks robustness of our results by using the Gini coefficient as an alternative measure for inequality. The final section concludes.

This paper analysed the impact of bequests on the distribution of wealth assuming a joy-of-giving motive. We distinguish between the effect of bequests per se and taxation of bequests. Bequests per se are captured by a preference parameter (1 − β) which measures the “utility-elasticity of bequests”, i.e. the willingness of parents to bequeath. The higher the parents willingness to give, the higher is the share of parental disposable income the child receives. The paper shows that both expected wealth and the variance of wealth go up with higher joy-of-giving. Since the effect on expected wealth dominates, the coefficient of variation also goes down: More bequests make the distribution of wealth more equal. The reason for this result is the effect bequests have on capital accumulation which we took into account in our general equilibrium analysis. From a policy perspective, by levying a wealth transfer tax and redistributing revenue among the young generation, the government can further reduce the concentration of wealth. The higher the tax τ on bequests, the lower is the variance of wealth, while average wealth holdings are not affected. As a consequence, the coefficient of variation is reduced by the tax. Hence, the government can follow a bequest taxation policy in order to reduce wealth inequality, even though bequests per se – the willingness to bequeath – already result in lower wealth inequality. We find this inequality-reducing effect of taxation (which would also be found in unintended-bequest setups) due to our assumption of a joy-of-giving motive which removes Becker–Tomes type “family wealth” considerations. While these results hold for the coefficient of variation as a measure of inequality, simulation suggests that they also hold for other, “more popular” measures like the Gini coefficient. Taxing bequests reduces not only the coefficient of variation but also the Gini coefficient. The appendix to this paper analyses various extensions — CES utility and endogenous labour supply. We show that the first result – bequests per se increase equality due to capital accumulation – is robust to these extensions. Future work could check whether the taxation result also survives under these more general specifications.