Should you leave your house to your grandchildren?

Last week, housing minister Gavin Barwell suggested that people should leave their houses to their grandchildren when they die, rather than their children. The reasoning is straightforward: young people are much less likely to own a property than their parents were at the same age, so the inheritance of a lump sum will help them get on the housing ladder. In contrast, if you leave your house to your children it is less likely to make a big impact on their lives, as they are likely to already own a house.

Not everyone was happy with the suggestion. Number 10 immediately distanced itself from the idea, pointing out that Barwell was giving his personal views and not government policy. The line was clear: “It is not for the government to dictate how [people] complete their wills.”

But putting government intervention to one side, would writing wills to benefit grandchildren, or great-grandchildren, produce a more equitable society? It’s not only to do with giving the money to younger people. In “The Hidden Wealth of Nations”, David Halpern made an argument around the expected wealth of the beneficiaries of a will. The correlation between your wealth and your children’s wealth is quite strong, but between yours and your grandchildren’s it gets weaker, and so on through the generations. So, by leaving your assets to descendants further down the family tree, you are more likely to benefit someone who would otherwise have very little.

The arguments seem valid, but let’s see how they would play out in practice. At Sandtable we build agent-based models (ABMs) – simulated populations that link individual behaviour to macroscopic outcomes. To look at inheritance we put together a model of the UK population in which agents (the individuals in the model) are born, grow up, earn a living, find a partner, have children and, in the end, die. We can then test the idea by running two different versions: one where people give their wealth to their children when they die, and one where they set up “intergenerational trusts” that pay out to their grandchildren and greatgrandchildren when they turn 20 (or immediately if they’re already over 20).

The models start off with 10,000 agents, but this number varies as agents are born and die. Reflecting current projections, the population gradually grows over the course of the simulation. There’s a fairly simple economic model in agents earn an income based on their age and educational attainment, with some random variation too. Their education itself is linked to that of their parents, again with some variation. As the agents earn money they save or invest a fraction of it, and whatever they have put aside grows with time too. We’ll provide more details of the model in a future blog post, so watch this space!

Before we look at the large-scale results, let’s take a look at some of the individual histories in the model. One of the great things about ABMs is that you can actually look at individuals and track their actions all the way through the simulation. For example, here’s the brief life story of one of the agents from the first model, where people give directly to their children:

Mary’s life history, with direct inheritance

As well as the important life events, the plot shows how the agent’s wealth changed over time. We’re counting everything that could be passed down in a will, so as well as cash there’s home equity and any investments, including any pension fund that’s not yet been used for an annuity.

This agent – we’ll call her Mary – is born in 2032, enters a relationship at age 22 and has three children over the next seven years. Her relationship ends in 2072 when she’s aged 40. She retires at age 65, putting half her wealth into an annuity to guarantee some future income, and then her wealth gradually declines as she uses up her savings. In 2103 both her parents die, and their wealth is split between Mary and her two siblings. This causes Mary’s wealth to suddenly jump up by about £100,000. Unfortunately Mary dies just 6 years later at age 77.

Like many people, Mary inherits wealth relatively late in life – arguably too late to make a big difference. While she surely appreciated the windfall, might it have been more use earlier on?

Let’s look now at an agent from the second model, where inheritance happens via trusts:

Paul’s life history, with intergenerational trusts

This agent – Paul – has a similar family background to Mary. He is born in 2021. At age 20 he gets a small amount of money from a trust fund set up by two of his great-grandparents, who died when he was a child. He enters into a relationship at age 22, and they have their first baby the following year. A further four children follow in the next 15 years. In 2044, the same year as Paul’s first child is born, his grandmother dies and leaves him about £40,000. He inherits a further £60,000 when his grandfather dies in 2054. His parents die in 2066 and 2072, but he doesn’t inherit from them because they have left everything to their grandchildren and great-grandchildren. Paul retires at 65, like Mary, and lives off his pension and savings until he dies in 2107, aged 86.

Paul and Mary inherit and earn about the same amounts as each other over the course of their lives, but because Paul gets that inheritance earlier in life he is always wealthier than Mary at each step.

Looking at the population as a whole, we can measure how the different inheritance methods affect the overall level of equality. A common metric for this is the Gini coefficient, which looks at how unevenly a resource (in this case wealth) is distributed. A high Gini coefficient means high inequality. If each agent had exactly the same wealth as all the others we would get a Gini coefficient of zero, while the maximum value of one occurs if one person has all the wealth and everybody else has nothing.

The models are run out to 150 years in the future, so we can watch how the Gini coefficient varies through time:

Gini coefficient for all adults

For the model using direct inheritance the Gini coefficient stays fairly constant over the next 150 years – not too surprising, as we’ve not changed anything from the current situation. The intergenerational trusts, on the other hand, produce a significant and lasting decrease in the Gini coefficient.

A key driver of this effect is that you’re taking wealth from people in their 50s and above and giving it to younger adults, who on average have less. But could this just be entrenching inequality within each generation? Are you just setting things up so that those who had rich ancestors get an early boost, while everyone else is left behind?

To answer that we can look at the Gini coefficient again, but this time only including younger adults (age 20-39):

Gini coefficient for young adults (age 20-39)

Even within a single generation there is still a strong shift brought about by the intergenerational trusts. The reason is that they massively increase the number of people who inherit something while they’re young – out of four grandparents and eight great-grandparents you’ll likely get something, even if it’s not too much. So, even though the amounts are biased towards people in rich families, the injection of wealth across a large fraction of the population helps reduce inequality overall.

It’s not all good news though. Despite reducing inequality, the trusts can actually increase the correlation between your wealth and your parents’ wealth. This is because the trusts pay out to two generations, so their wealth becomes more strongly tied together. They quite literally get the same opportunities in life. This effect goes away again if the trusts only pay out to one generation.

There are also other factors that influence the effectiveness of intergenerational trusts. One important factor is assortative mating. This is the tendency for people to choose partners who are like themselves, in terms of things like wealth, education and race. We don’t have race in this model but we can look at the other factors, and see how the results vary as you change the strength of assortative mating.

Gini coefficient for young adults with different levels of assortative mating (colours are as before)

Here, “standard” means at the level we currently see in real life, while “strong” is twice that level. It’s clear that this is an important effect – the stronger you make assortative mating, the less the improvement in the Gini coefficient. Put simply, if people only choose partners with similar levels of wealth, then some people will inherit lots from all their ancestors while others inherit little or nothing. However, even with the strong assortative mating, intergenerational trusts do still decrease inequality relative to direct inheritance.

Of course there are some caveats that must be attached to this modelling. The comparison here is between the most extreme cases, where everyone uses one or the other of the two inheritance methods, so any outcomes in real life would be almost certainly be smaller. Also, the economics in this model are quite simple and optimistic – the agents all have reliable incomes, they always manage to save some of their income, and they always get reliable returns from their savings and investments. The next step in modelling would be to loosen these assumptions and incorporate effects such as unemployment, varying savings ratios or failed investments, all of which will be strongly correlated with existing wealth. Another mechanism to add would be a link between wealth as a young adult and educational attainment – for example, if you’ve just inherited a lump sum you may be less worried about the cost of going to university, and hence more likely to get a degree.

But even this fairly simple model gives us a good picture of how intergenerational trusts would likely affect inequality in the UK, and allows us to answer some key questions:

• Would these trusts reduce overall inequality? Yes, primarily by moving wealth from older to younger adults.
• Would they reduce inequality within generations? Yes, although they may strengthen the link between your wealth and that of your parents.

So overall the effect appears to be positive, but they may require other policies to help ensure that your opportunities in life are not dependent on whether you had wealthy ancestors.