VoxEU Column Poverty and Income Inequality Taxation

Heterogeneous returns to wealth and inequality: The comeback of ‘r > g’

A crucial element in the study of wealth inequality is the difference between the rate of return and the growth rate of income. However, the focus on these measures at the aggregate level belies important heterogeneities along the wealth distribution. This column uses rich micro-data from Norway to show that wealthy households enjoy higher rates of return relative to growth, while the opposite is true for poorer household and the lower-middle-income class. It discusses policy implications of these findings for capital and wealth taxation in order to curb the rise of inequality. 

The societal concern over increasing inequality in income and wealth should be addressed in the first place by a precise accounting of the forces at play, so that policymakers can be correctly informed in their decision-making process. To this end, in this column we present novel evidence exploiting rich microdata from Norwegian registers on the relationship between rates of return on wealth, growth rates of income, and inequality. In other words, the interaction between income from financial and human capital is under analysis, as advocated by Kanbur and Stiglitz (2015): “We need to focus on the interaction between income from physical and financial capital and income from human capital in determining snapshot inequality”.

The publication of Piketty’s Capital in The Twenty-First Century (Piketty 2014) in 2014 sparked a surge in interest in the study of wealth inequality and the relation between the rate of return on capital and the growth rate of income. The bottom line in Piketty’s book is that if the rate of return on wealth overcomes the growth rate of income (r > g), wealth-rich individuals – the so-called ‘rentiers’ – would accumulate wealth faster than individuals typically holding low or negative values of wealth and mainly relying on income, thus fostering wealth disparities in the longer run. 

That said, the author himself returns to the debate in Piketty (2015), clarifying that he does not consider "r > g as the only or even the primary tool [...] for forecasting the path of inequality in the twenty-first century. Institutional changes and political shocks [...] played a major role in the past, and it will probably be the same in the future". In our view, a thorough understanding of r > g, its predictive power, relevance, and limitations hinges crucially on the variety of analyses carried out upon it. One important limitation has been that, being originally an aggregate measure (it is estimated for several countries in Jordà et al. 2019, Section VII), it fails to take into account wealth return heterogeneity and potential disparities in growth rates of income. 

How r > g evolves across the wealth distribution 

In recent research (Iacono and Palagi 2021), we present the first micro-level empirical assessment of the relationship r > g across the net wealth distribution (Panel A in Figure 1). By exploiting large-scale administrative data on personal wealth in Norway from 2010 to 2018 (a similar dataset has was the focus of another VoxEU column, see Iacono and Ranaldi 2020), we show that the aggregate measure, R – G, (with an average of 1.1% throughout the period, marked by the horizontal dashed line in Figure 1 below) underestimates its micro counterpart, r – g, for the top half of the wealth distribution, whilst the opposite happens for the bottom half. 

Figure 1 The distribution of r – g

Panel A: Distribution of r – g across net wealth distribution



Panels B and C: Return on wealth (B) and growth rate of income (C) across net wealth distribution


This result can be mostly explained by the positive correlation between rates of return on wealth and position in the distribution (Panel B in Figure 1), whilst growth rates of income display less covariation (Panel C in Figure 1). 

In our paper we also show, through a simple simulation exercise, that the micro r – g predicts a higher level of income and wealth inequality, in comparison to R – G. In other words, our empirical evidence indicates that the distribution of r – g provides insights on the dynamics of inequality of income and wealth that do not arise by exclusively focusing on mean variables.

Sources of heterogeneity

Rates of return on wealth across individuals can differ due to numerous reasons. First, some individuals might have higher entrepreneurial and investment propensities, and thus obtain higher returns on their savings. They can also differ because of other individual characteristics, conducible to education, parental background, or pure luck. All these motives can generate persistent heterogeneity of rates of return. 

Second, wealthier individuals might achieve higher returns due to scale effects in wealth management. Scale economies can originate for instance from the fixed costs associated with raising rates of return, as opening a bank or investment account, or investing in financial knowledge by hiring wealth managers (Gerritsen et al. 2020). In other words, it is only for individuals with substantial portions of wealth that these costs become convenient, leading to a situation for which wealthy individuals are more likely to obtain higher returns to their assets.

We analyse whether our evidence on the micro r – g can be explained only by persistent heterogeneity across the net wealth distribution, or if we can attribute some of its variation to scale dependence. Our results show that approximately half of the variation in r – g when moving up from the bottom to the top decile of the net wealth distribution is associated with scale dependence. 

Policy implications and concluding remarks

The policy implications of our results are numerous, as our evidence interacts with the efficacy of capital and wealth taxation to curb inequalities, assuming that this is desirable from the point of view of policymakers. In recent years, heterogeneity of rates of return on wealth (as documented by Fagereng et al. 2020) and their implication for taxation of capital and wealth have been analysed by several authors in the literature. 

Gerritsen et al. (2020) show that return heterogeneity leads to positive optimal marginal tax rates on capital income, and that desired tax rates are also increasing in capital income. Along similar lines, Rothschild and Scheuer (2016) claim that, if heterogeneous returns are explained by rent-seeking and excess profits, then taxation of capital increases economic efficiency in addition to achieving a more equitable distribution of wealth. The authors differentiate between the effects of capital income and wealth taxation though and claim that the former might be more efficient to target excess profits than a flat tax on wealth. Scheuer and Wolitzky (2016) show that taxing capital must be supported by the majority of citizens to resist the threat of political upheaval. To this end, a positive marginal tax on the wealthy individuals combined with subsidies to capital accumulation for the less wealthy constitute a desirable policy combination.

To sum up, our results indicate that in Norway, the heterogeneity of the rates of return on wealth appears to be an important determinant of increasing inequality, with the growth rates of income playing a smaller role since the latter vary less across the distribution. We also show that the rates of return on wealth are clearly increasing with the share of financial wealth within individual wealth holdings. Hence, our main lessons can be summarised as such: to curb increasing levels of inequality one might either tax capital income (or wealth) more progressively (the current statutory tax on capital incomes in Norway is a flat rate), or incentivise access to ownership of financial wealth also for the less wealthy, in order to reduce the gap in the rates of return between the wealth rich and the wealth poor.


Fagereng, A, L Guiso, D Malacrino and L Pistaferri (2020), "Heterogeneity and Persistence in Returns to Wealth”, Econometrica 88(1): 115-170.

Gerritsen, A, B Jacobs, A V Rusu and K Spiritus (2020), "Optimal Taxation of Capital Income with Heterogeneous Rates of Return", Tinbergen Institute Discussion Papers 20-038/VI, Tinbergen Institute.

Iacono, R and E Palagi (2021), "A micro perspective on r > g", World Inequality Lab Working paper 2021/03.

Iacono, R and M Ranaldi (2020), “The wage curve across the wealth distribution”,, 2 November.

Jordà, O, K Knoll, D Kuvshinov, M Schularick and A M Taylor (2019), "The Rate of Return on Everything, 1870–2015", The Quarterly Journal of Economics 134(3): 1225-1298.

Kanbur, R and J Stiglitz (2015), “Wealth and income distribution: New theories needed for a new era”,, 18 August.

Piketty, T (2014), Capital in the 21st Century, Harvard University Press. 

Piketty, T (2015), “About Capital in the Twenty-First Century”, American Economic Review 105(5): 48-53.

Rothschild, C and F Scheuer (2016), “Optimal Taxation with Rent-Seeking”, The Review of Economic Studies 83(3): 1225-1262.

Scheuer, F and A Wolitzky (2016), "Capital Taxation under Political Constraints", American Economic Review 106(8): 2304-28.

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