The publication of the best-selling book, *Capital in the Twenty-First Century,* by Thomas Piketty (2013) has spurred renewed academic and public debate about wealth formation and wealth inequality, as witnessed – for example – by the symposium about wealth and inequality in the Winter 2015 volume of the *Journal of Economic Perspectives*, and the many recent Vox columns on the topic.

A large and contentious economics literature focuses on understanding the determinants of the personal distribution of income. Wealth inequality is even more complicated. It may be generated by inequality in earnings capacity, differences in savings propensities or risk-taking, and differences in inter vivos wealth transfers and bequests across generations.

## Are bequests necessarily a source of wealth inequality?

In recent research, we zoom in on the effect of bequests on wealth inequality (Boserup et al 2016). It may seem intuitive that bequests create wealth inequality. From a theoretical point of view it is not necessarily the case, though. The answer depends on bequest patterns – to what extent bequests flow from rich parents to rich kids and to what extent they move poor kids up in the distribution – and whether we measure inequality in terms of *absolute* or *relative* wealth differences. An example of an absolute inequality measure is the variance of the distribution. An example of a relative inequality measure is the share of total wealth owned by the wealthiest 1%.

To understand how bequests might affect different measures of inequality, it is useful to consider a simple example where everyone receives a bequest proportional to their wealth. In that case, the variance of the wealth distribution increases, while wealth shares remain constant. Thus, absolute inequality increases and relative inequality is unchanged. A less than proportional increase in wealth may increase absolute inequality, while decreasing relative inequality. Another twist on this argument that further advances the possibility of a decline in relative inequality is the incidence of zero or even negative net worth – bequests will rarely make heirs more indebted so that the bottom of the distribution is likely to gain in proportional terms and lead to a decline in relative inequality unless the rich inherit disproportionately relative to their initial wealth.

## So do bequests create wealth inequality?

Our answer to this question is “yes” and “no”. It depends on whether we look at absolute or relative wealth inequality as shown in the graphs below. Our analysis is based on administrative wealth records for the Danish population of people who are 45-50 years old and divided into ‘treatment’ and ‘control’ groups, based on whether the last surviving parent dies in 2010 (time zero in the figures below). These groups are not exactly identical – by definition, parents die in one group but not in the other group – but they do follow similar trends before 2010. In Figure 1, we look at absolute wealth and compare the variance of the wealth distribution of the two groups. It shows that the variance of the distribution increases by around 30% after people receive bequests. When looking at the different percentiles in the distribution, we find that they all increase, and that the monetary increase is larger, the larger the percentile. This confirms that absolute inequality increases throughout the distribution.

**Figure 1**. Effect of bequests on the variance of the wealth distribution

However, we obtain the opposite conclusion when looking at relative measures of wealth inequality, such as top wealth shares. In Figure 2 we show the top 1% wealth share for the two groups. The top wealth shares in the treatment and control groups vary over time due to fluctuations in market values of assets, but follow parallel trends until parental death. Afterwards the gap between the two curves widens considerably. The top 1% wealth share decreases by more than 5 percentage points relative to the control group, a very large effect when compared to the baseline level of around 30%. Thus, relative inequality declines. We get the same conclusion if looking at other top wealth shares.

**Figure 2.** Effect of bequests on top 1% share of wealth

## Concluding remarks

Our work suggests – contrary to the popular belief – that bequests need not increase inequality even if rich parents have rich kids. In fact, in Denmark, the post-bequest distribution is more equal (if measured in relative terms) than the pre-bequest distribution. Having said that, this work does not by itself answer the question of a longer-term impact of bequests. For example, if individuals at the bottom of the distribution primarily consume out of their bequest while individuals at the top primarily save, the longer-term dynamics may reverse short-term inequality effects. Like all studies, ours is also necessarily limited to what we can observe – Danish administrative data do not cover wealth hidden from tax authorities, which may be substantial (Zucman 2013). Naturally, bequests are just one form of intergenerational transfers. Inter vivos gifts and parental investments in children's human capital are very important other channels. In ongoing work we integrate all these effects by studying intergenerational wealth mobility; that is, the relationship between the wealth of parents and children.

## References

Boserup, S, W Kopczuk and C Kreiner (2016) “The role of bequests in shaping wealth inequality: Evidence from Danish wealth records”, CEPR Discussion Paper, DP11059, forthcoming in the *American Economic Review: Papers and Proceeding*s.

Piketty, T (2013) “Capital in the Twenty-First century”, Harvard University Press.

Zucman, G (2013) “The missing wealth of nations: Are Europe and the US net debtors or net creditors?”, *Quarterly Journal of Economics*, 128(3): 1321-1364.