## Abstract

Wealth inequality is a major political concern in most OECD countries. Under this premise, we analyze different policy instruments in terms of their impact on wealth inequality and output. In a general equilibrium model, we disaggregate wealth in its capital and land components, and savings in their life-cycle and bequest components. Households are heterogeneous in their taste for leaving bequests. We show that governments have considerable freedom in reducing wealth inequality without sacrificing output: Land rent taxes enhance output due to a portfolio effect and reduce wealth inequality slightly. Bequest taxes have the highest potential to reduce inequality, and their effect on output is moderate. By contrast, we confirm the standard result that capital taxes reduce output strongly and show that they only have moderate redistributive effects. Furthermore, we find that using the tax proceeds for transfers to the young generations enhances output the most and further reduces wealth inequality.

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## Notes

- 1.
- 2.
Recently, Straub and Werning (2014) have called the zero-capital-tax result of Judd (1985) and Chamley (1986) into question. However, Straub and Werning rely on the assumption that consumption taxes are not available—their model thus constitutes an “extreme example of an incomplete set of fiscal instruments” as Chari, Nicolini, and Teles, point out in their manuscript

*More on the taxation of capital*. - 3.
- 4.
Feldstein (1977) was the first to identify the portfolio effect, which Mountford (2004) and Petrucci (2006) further formalized. Edenhofer et al. (2015) extended the analysis of the portfolio effect by introducing a social welfare function as a normative benchmark for evaluating fiscal policy, in particular land rent taxes. The present paper, in contrast, takes a positive approach and focuses on the economic impacts of fiscal policy. Hence, we do not consider a social welfare function. Nevertheless, we find that under land rent taxation the winners of the policy could theoretically compensate the losers. Thus, land rent taxation fulfills the Kaldor–Hicks criterion (see Appendix C).

- 5.
- 6.
We shall make use of the convention that all households choose the same asset composition. More precisely, in every period

*t*there is an \(X_t > 0\) such that \(X_t = k^s_{i,t}/l_{i,t}\) for all \(i \in \{1,\ldots ,N\}\). We use this convention because there is an infinite continuum of possible combinations of individual asset portfolio compositions of each household*i*that have no bearing on any of our results. - 7.
For example, the analytical method applied by Mountford (2004) to a dynamic system with two state variables already leads to inconclusive results if the number of states is increased by one dimension (i.e. bequests are added to his model) and households are still assumed to be homogeneous.

- 8.
Similar to Davies (1986), we can thus separate two different effects of taxation: We first analyze only the distorting effect of different taxes on households’ investment behavior, and do not take into account the effect caused by the redistribution of the tax revenues to the households as transfers. Only in the second step we also consider the impact of the government’s transfers. In contrast to Davies (1986), however, we always allow for general equilibrium effects.

- 9.
In Sect. 3.2, we will discuss conditions under which capital income and bequest taxes may

*increase*inequality. - 10.
Recall that the results we obtain are independent of whether labor supply is fixed or endogenous. Thus, we abstract from a labor-leisure choice here, to keep the analysis as tractable as possible.

- 11.
This can be made plausible by recalling Fig. 1. Compare the set of coordinates in the policy option space that can be reached with the land rent tax alone—the green curve with circles marking the data points—with the coordinates in the policy option space that can be reached with the bequest tax—the blue curve with triangles as data points. When implementing a mix of both taxes it is likely that the coordinates that can be thus reached lie between the green (circles) and the blue (triangles) curve.

- 12.
The difference of 0.13 is a little bit less than the difference between the wealth distributions of the USA (with 0.93, the highest inequality within the sample given by OECD 2015), and France or Finland (both 0.77). The difference of 0.13 corresponds to the difference between the Slovak Republic (with 0.52, the most equal country in the sample), and Greece (0.65). The Gini coefficients of all countries for which OECD (2015) reports wealth distributions are given in Table 6 in Appendix B.

- 13.
Here, we use \(\delta = \frac{1}{2}\). In general, of course, any \(0<\delta <1\) implies transfers to both.

- 14.
See Appendix B, Fig. 6 for a graphical exposition of this fact.

- 15.
As discussed in Sect. 3.1.1, the main channel through which tax reforms change the wealth distribution in our model is the difference in income composition, i.e. the ratio of bequests to wages in total income.

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## Acknowledgements

We would like to thank Mireille Chiroleu-Assouline, Marc Fleurbaey, Robert C. Franks, Beatriz Gaitan, Etienne Lehmann, Linus Mattauch, Christina Roolfs, Marco Runkel, Gregor Schwerhoff, and two anonymous referees, as well as seminar participants at PIK’s RD3 PhD seminar, the PRSE seminar at Universität Potsdam, the OLG days 2016 in Luxembourg, the Journées Louis-André Gérard-Varet 2017, and PET 2017 in Paris for helpful comments and fruitful discussions. Funding by the German Research Foundation (DFG) under grant proposal LE 782/2-1 ist gratefully acknowledged.

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## Appendices

### Model parameters and calibration

### Additional figures and data

See Figures 5, 6, 7 and 8 and Table 6.

### Kaldor–Hicks criterion

Even though we find that recycling all public revenues to the young as lump-sum transfers enhances output and reduced inequality, a Pareto improvement is not possible with such a transfer scheme. However, we find that at least there are cases in which the Kaldor–Hicks criterion is fulfilled. Consider, for instance, the case in which all land rents are skimmed off and redistributed to the young (\(\tau _L = 1\), \(\delta = 0\)) shown in Figs. 9 and 10. Absent any additional transfer mechanism between winners and losers, generations belonging to the top wealth quintile \(i=5\) and possibly all households belonging to the first old generation suffer under the tax. Whether the first old generation suffers under the tax depends on the assumption made about its exogenously fixed level of consumption when young.

Now we introduce a mechanism that allows intertemporal transfers between households. Instead of the lump-sum transfers from public revenues \(g_t\), young and old households may now receive a transfer or have to pay a lump-sum tax *X*. Their budget equations thus are

Further, we assume that funds can be shifted over time via banking and borrowing at the market interest rate *R*. Then, for the total volume of the transfers, it has to hold that

Our numerical experiments confirm that there are feasible combinations of \(\{X^y_{i,t}, X^o_{i,t}\}_{i=1,\ldots ,N,\ t=1,\ldots ,T}\) such that the winners of the 100% land rent tax can compensate the losers, i.e., that

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Franks, M., Klenert, D., Schultes, A. *et al.* Is capital back? The role of land ownership and savings behavior.
*Int Tax Public Finance* **25, **1252–1276 (2018). https://doi.org/10.1007/s10797-018-9486-3

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### Keywords

- Fiscal policy
- Wealth distribution
- Inequality
- Capital tax
- Bequests
- Land rent tax

### JEL Classification

- D31
- E62
- H23
- H24
- Q24