Issue, No.14 (June 2020)

The Role of Inheritance on Wealth Inequality: A Machine Learning Approach

by Pedro Salas Rojo (Complutense University of Madrid, Instituto Complutense de Análisis Económico (ICAE) ), and Juan Gabriel Rodríguez (Complutense University of Madrid, Economics of Inequality and Poverty Analysis (EQUALITAS) )

The debate: The role of inheritance in shaping wealth distribution

There is a general academic consensus that wealth inequality is on the rise (Zucman, 2019). Several factors seem to have contributed to this persisting trend. For instance, the development of financial markets since the 1980s has widened the possibilities for investment at the top of the distribution, thereby increasing their profits. Other authors blame shrinkages in progressive taxation, hindering the effect of distributional policies. Different approaches also suggest that the rising skill premium associated with wages, when accumulated, has led to a number of CEOs accumulating massive stocks of wealth derived from capital gains. However, there is still a matter causing dissent: the role of inheritance in shaping wealth distribution.

On one side, authors such as Karagiannaki (2017) find that inheritances decrease wealth inequality. Through a case-study of the UK, a counterfactual distribution of wealth excluding the value of the bequests received shows that, overall, wealth is much more unequally distributed than inheritances. In this manner, the intergenerational transmission of assets produces a net equalizing effect. However, other authors such as Piketty and Zucman (2015) suggest otherwise. Both authors explain how the annual flow of bequests and gifts, as a percentage of national income, have greatly increased in the last few decades, following the rising share of wealth at the top. Consequently, inheritance would be one of the main vehicles through which wealth inequality is transmitted and increased through generations.

In order to provide more empirical evidence on the actual role of inheritance in wealth distribution, we take a different approach. In this article, we analyze how the bequests received affect the opportunities people have for accumulating wealth. To this end, we use the Luxembourg Wealth Study (LWS) database provided by the Luxembourg Income Survey (LIS), analyzing five countries: Canada, Italy, Spain, the UK and the US.

The measurement of opportunities to acquire wealth

Any social or economic outcome such as wealth, income or health status is a result of the interaction between at least two sets of factors. On the one hand, people face exogenous barriers beyond their control, such as sex at birth, parental education, race or the value of any inheritances received. From this point on, following the seminal work of Roemer (1993), we will call them circumstances. On the other hand, the remaining factors are considered to be endogenous as they are within the individuals’ set of choices. This is the case, for instance, for the number of hours worked or nutritional habits. We call these efforts.1

Based on circumstances, we can divide any society into exhaustive and mutually exclusive groups, also called types. For instance, if we were to consider that the only relevant circumstances in a given society were sex at birth (men, women) and race (black or white), we could generate four types, namely: white men, white women, black men and black women. This society would face equality of opportunity if, and only if, the distribution of economic results was independent from belonging to one type or another. In contrast, if we find prevalent differences between types, we can blame these exogenous factors for conditioning and distorting opportunities for individuals to achieve that particular economic outcome.

Following these ideas, we decompose inequality into two components. The first component collects the between-types inequality, exclusively explained by the different circumstances faced by the individuals. This is what we call Inequality of Opportunity (IOp). The second is the within-type component and is explained by the different efforts exerted by individuals sharing the same circumstances. It is called Inequality of Efforts (IE).

The demarcation of both components is important for social justice as it allows us to isolate and analyze the effect of ‘unfair’ inequality (Rawls, 1971). Moreover, authors such as Marrero and Rodríguez (2013) find that IOp is negatively related to economic growth, as unequal opportunities provoke inefficient allocations of human capital.

In this framework, we consider inheritances and gifts to be circumstances, as they are exogenous shocks received by the individual and is independent of their behavior. Accordingly, we generate different types based on the distribution of inheritances and later decompose total inequality into two components: the part of inequality exclusively explained by the different bequests received and a residual component that includes all remaining uncontrolled circumstances and efforts. This procedure allows us to calculate the share of total inequality explained by inheritances, measuring its actual relevance in the wealth distribution.

The empirical implementation: A Machine Learning approach

Constructing types with discrete variables (race, gender or parental education) is straightforward, as its categories are generally well defined. However, for continuous variables such as the value of the inheritances received, we need to perform a prior discretization. Here we face a choice of procedure. Should we divide the bequests distribution by the median, the terciles, or separate the top decile from the rest? Given the right-skewness of the inheritances distribution, its partition into types is quite tricky, since it could drive the results obtained in the final analysis. In fact, as we describe in the results section (below) we find that by-hand discretizations lead estimates of wealth IOp that are not robust.

To palliate this lack of robustness, we adopt a statistic criterion based on Machine Learning algorithms which split the inheritances received in a consistent way (see also Brunori et al., 2019). In particular, among the algorithms proposed, we lean towards the conditional inference random forests (Hothorn et al., 2006). Based on the conditional distribution of wealth over the continuous circumstance, inheritances, this algorithm applies several statistical tests covering all potential discretizing points. In addition, using a multiple fold cross-validation procedure, we tune an endogenous coefficient of significance, which also erases the researchers’ criteria over the statistical tests performed.

With this algorithm, we discretize the continuous variable under consideration selecting as the final cut points only those for which the types create the most statistically meaningful groups. As a consequence, we are able to extract all the information contained in the distribution of the variables and, at the same time, maximize the out of sample validity.

Main Results: inheritances are important for wealth inequality

The data used is taken from the LWS database (LIS), which includes a complete record of assets and inheritances received. This allows us to employ three different wealth definitions, estimating for each one of them the between-type component of inequality explained by inheritances. Particularly, we analyze financial wealth (consisting of deposits, equities, investment funds and other liquid assets), non-financial wealth (consisting of real estate, garages and other properties) and the sum of both, giving total wealth.

To introduce the matter, Table 1 deploys wealth inequality according to the Gini index for the five countries analyzed. As reported frequently, the United States is the most unequal country regardless of the wealth definition under consideration, while the European countries show the lowest estimates, Canada being in between. These results also highlight the high value that characterizes wealth inequality in general, and financial wealth in particular. For this reason, financial wealth is sometimes considered one of the main causes behind (and also derived from) the rise in capital income inequality.

Table 1: Wealth inequality (measured by Gini).

Country Canada Italy Spain United
Total Wealth 70.66 59.00 59.24 58.70 80.28
Financial Wealth 83.70 73.96 84.13 79.19 91.60
Non-financial Wealth 74.90 60.61 60.20 58.67 82.17

Source: Own elaboration using Luxembourg Income Study (LIS) Database/Luxembourg Wealth Study (LWS) Database.

The first part of our analysis consists of criticizing the use of by-hand discretizations. Thus, Table 2 shows the share of total wealth inequality (that is, the share attributed to the between-type component) explained exclusively by inheritances. Notice that types are constructed according to three different discretization methods. First, we use the median; second, we adopt terciles; third, we separate the individuals at the top quartile from the rest of the distribution.

Table 2: The share of total wealth inequality (Gini) explained by inheritances.

Country Canada Italy Spain United
Gini 70.66 59.00 59.24 58.70 80.28
Inheritances viewed as the median 32,73% 29,54% 42,20% 11,69% 35,03%
Inheritances viewed as terciles 42,17% 38,44% 59,81% 17,14% 47,23%
Inheritances viewed as the third quartile 34,31% 23,59% 25,71% 7,04% 32,09%

Source: Own elaboration using Luxembourg Income Study (LIS) Database/Luxembourg Wealth Study (LWS) Database.

We observe that the different construction of types generates quite different results. For instance, in the US, if we use the median to generate types, around 35% of total wealth inequality is explained by the value of inheritances received. However, if we use terciles to split the population into types, this share rises to a remarkable 47.23%. These results demonstrate that the criterion for separating individuals into types is a fundamental decision in the measurement of the role of inheritances across wealth distribution. The implementation of Machine Learning techniques to generate statistically meaningful types is clearly justified.

Figure 1 represents the share of total, financial and non-financial wealth inequality (Gini index) explained by inheritances for our five countries. The construction of types is now non-discretionary and based on the conditional inference random forests algorithm previously mentioned. The associated paper demonstrates these results to be robust for several different specifications.

We find that, in Canada, around 57% of financial wealth inequality is explained by the inheritances received, while the ratio falls to 36% for non-financial wealth and 42% for total wealth. In Italy, these values range between 37% and 44%. Interestingly, the UK is the country where the reported inheritances received seem to matter the least: around one third of financial wealth inequality is explained by this circumstance, a ratio falling to 16% and 13% for total and real estate inequality, respectively.

Source: Own elaboration using Luxembourg Wealth Study (LWS) Database/Luxembourg Income Study (LIS) Database.

Most notably, our results show that for Spain and the US the value of the inheritances received significantly affect the opportunities of people to accumulate wealth. Particularly in Spain, around 69% of total and 65% of financial wealth inequality is solely explained by the inheritances received, while a remarkable 76% of non-financial wealth inequality is attributed to this circumstance. The US shows similar estimates, interchanging the values for financial and non-financial wealth.

Overall, we find the distribution of inheritances to be a remarkable component of total inequality. However, the importance seems to vary greatly across countries: while it is clearly the most important factor behind wealth distribution in Spain and the US, in other countries, such as Italy and Canada, there seem to be several other important factors shaping wealth distribution. In particular, for the UK, we find that inheritances are relatively unimportant, although not irrelevant by any means, especially for financial wealth.

Complementary analysis: Does parental education provide further insights?

Looking at the results deployed in Figure 1, we propose to consider not only the distribution of inheritances but also the effect of another exogenous factor: parental education. The relation between this variable and wealth distribution shows a prevalent academic consensus. Highly educated parents, in general, transmit their social and human capital to their offspring, facilitating their access to higher levels of education, at better universities, and in which they can develop more profitable social networks. As a result, the opportunities of those individuals with highly educated parents are increased, easing their wealth accumulation through a different channel not necessarily fully captured by inheritances (Palomino et al., 2019). In addition, both circumstances may reinforce each other, so the effect calculated for inheritances could actually reflect, at least in part, the effect of parental education. For this reason, it is convenient to analyze the joint effect of both factors.

For this task, Figure 2 plots the share of wealth inequality for the three previous wealth definitions explained by both circumstances together: parental education and inheritances. Unfortunately, we do not have information of the former variable for either Canada or Spain, so Figure 2 only presents the results for Italy, the UK, and the US.

Source: Own elaboration using Luxembourg Wealth Study (LWS) Database/Luxembourg Income Study (LIS) Database.

We find that, in Italy, more than 60% of financial inequality is explained by the differences in parental education and inheritances received, which also explain up to 52% of total and non-financial wealth inequality. The share attributed to both circumstances also rises in the UK. Now, 49% of financial inequality is explained by them, the ratio rising to around 30% for the other two wealth definitions. Thus, for both countries there is a clear effect of both circumstances on wealth distribution. On the contrary, the already elevated ratios of the US do not vary significantly. It seems that, in this country, the intergenerational transmission of opportunities is essentially captured by the information derived from the distribution of inheritances received.


In this article we use Machine Learning techniques to explore the role of any inheritances received in shaping wealth distribution in five OECD countries. We find this variable explains at least 60% of total, financial and non-financial wealth inequality in Spain and the US. It also explains a remarkable share (more than 40%) in Canada and Italy, while its role is much less important in the UK. Moreover, we find that parental education also accounts for a notable portion of wealth inequality in Italy and the UK but does not add relevant information in the case of the US.

Our results are consistent with the literature that observes important cross-country differences in the factors shaping wealth distribution. Despite finding that inheritance distribution clearly affects the opportunities of individuals for acquiring wealth, we would discourage a deterministic view of the relationship between inheritances and wealth inequality. Rather, we suggest that specific taxation structures, capital flows, general investment behavior and other deep structural factors may be behind the varying opportunities for acquiring wealth across countries.

1The role of luck has also received attention from the literature but, for the sake of simplicity, it is disregarded in this article.

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