Fertility, Inheritance, and the Concentration of Wealth

Epistemic status: Shower thoughts

This is just something I have been thinking about recently. It’s an obvious fact that wealth inequality has been rising across the west for a long time since a low point in the mid 20th century (perhaps since 1971). Similarly, birth rates have been falling across the developed world since the mid 20th century in the West and since the 1970s in East Asia as part of the demographic transition across the world. While certainly not the only story ¹, I think these two factors are deeply intertwined through numerous mechanisms, but one crucial and underappreciated one is inheritance law.

The effects of inheritance and demographics on economic trends are often not well recognized since they operate on long timescales, but they are extremely powerful. Inheritance law ², especially, has an massive effect in the long run on shaping the distribution of wealth in a society, as remarked upon by many observers and especially de Tocqueville ³. Specifically, allowing or requiring the equal distribution of wealth between heirs (partible inheritance) tends strongly towards the diminishment of wealth over generations ⁴ since fortunes are regularly split up and shared while primogeniture (all wealth handed to oldest child, typically male heir) results in wealth being maintained and compounded along a single individual in the family line ⁵.

The reasons for this are extremely simple. Partible inheritance both splits up a fortune with N children N ways and also increases the total consumption of all heirs which increases the drawdown of the wealth, leading ultimately to rapid dissolution within a few generations for all but the largest fortunes. Under primogeniture, however, the fortune is maintained and only the single primary heir can maintain their full income, allowing a significantly reduced drawdown fraction which often makes the difference between wealth compounding or diminishing. The mathematics of wealth accumulation and aristocracy are actually extremely simple and can be understood simply from reading a Jane Austen novel or from the modern day incarnation in the FIRE community (simply swap “land” for “index funds”).

To make this simple, let’s pretend you are an idealized aristocrat. As an aristocrat, you have some significant amount of wealth – which historically has almost always been ‘land’ – i.e. estates which are rented out to tenants. In a feudal economy, the land has some extremely high price which is technically wealth, but in practice estates were rarely tradeable so the market was exceptionally thin. Crucially this land produced an income from the tenants which you, the aristocrat, can use to fund your lavish lifestyle. In a modern context, wealth is usually in the form of stocks which go up in value, on average, and which can pay out dividends providing direct income. This does not matter much since the key point is that you never want to sell the principal and live solely off the income produced by it. In an ideal world, we can measure the rate of return on the principal $r$ out of which you can draw an income. The rate of return times the amount of principal is the amount of ‘breakeven’ income that you have. If you spend more than that, you start spending principal which means that the next year you receive less income from it. If the rate of return on principal holds true forever (a big assumption clearly) then it is trivial to model what happens. If you spend more per year than the breakeven income, your wealth exponentially goes to zero. If you spend exactly that amount your wealth stays the same forever. If you spend less, then your wealth exponentially increases – i.e. compounds – assuming you can reinvest your income from the principal into an identical asset ⁶.

Now let’s add inheritance to the picture. Every N years you die and the wealth is split between heirs ⁷. In the case of primogeniture one heir inherits the vast majority of the wealth, so if you are in the compounding regime this simply continues under the new heir. However, if there is partible inheritance then the fortune is split between all heirs approximately equally. In this case, not only is the principal divided multiple ways, but each heir will want to maintain a high standard of living given their fortune which also increases the spend from the return of the diminished principal per heir. It is easy to see how this can very often push over a fortune from the exponential growth compounding regime into the exponential diminishment spending-down-the-principal regime, ultimately reducing wealth inequality.

However, for this to occur there needs to be enough heirs to split the wealth between for there to be any effect. As birthrates have decreased below two across the developed world, we defacto end up with a system very similar to primogeniture where the inheritance law does not matter and one heir gets everything because they are the only heir. As the birth rate approaches and drops below 1, wealth is guaranteed to concentrate under any inheritance law since primogeniture and partible become identical. Each child will then inherit wealth from both sides of the family which will thus cause increasing wealth concentration per generation even without any other economic fundamentals changing.

The importance of inheritance and the compounding growth of inherited fortunes is also at the center of Piketty’s arguments in Capital in the 21st century which essentially argues that inequality depends primarily on the rate of return on capital $r$ vs the growth rate of the economy $g$, and that if $r > g$ then inequality must be increasing. In some sense this must be true – if the growth rate of value of capital is growing faster than the economy as a whole then the share of capital in the total value of the economy must be increasing and hence the relative economic position of the owners of capital vs others must be improving ⁸. If the owners of capital are conceptualized as a fixed group – i.e. in a feudal society with ‘aristocrats’ who own capital vs ‘peasants’ who do not, then this means that wealth inequality must increase between the aristocrats vs peasants. In practice, due to the lognormal distribution of wealth, most capital is owned by a relatively small proportion of the population and hence this is not as unreasonable assumption as it seems. However, $r$ and $g$ must be interpreted broadly for this to make sense and can’t just be read off as simple e.g. economic growth rate and the interest rate. Specifically $r$ has to refer to some real growth of fortunes over a long temporal period per capita – so that ‘random’ shocks such as wars and long term laws such as inheritance laws are correctly taken into account.

I think that this framework provides an interesting lens to reason about long term demographic effects on economies and the impact of inheritance laws. For instance, a growing population would seem to have two equalizing effects. First, it increases $g$ through economic growth causing productivity improvements. Secondly, with average birthrates $>2$, the return ‘per heir’ will be substantially lower than the return over the full fortune, and ultimately this is what matters since it is mortal humans who end up holding wealth and not immortal economic beings. There is a countervailing effect, however, in that a rapidly growing population would also increase $r$, the rate of return on capital, since a rapidly growing population has many more potential labourers for its capital stock and hence capital is concomitantly scarcer and can earn a higher return. The world of declining population should be expected to face opposite pressures. $g$ declines since the total population becomes smaller and older. $r$ also declines since capital becomes much more plentiful relative to labour (old people have lots of capital and cannot contribute much labour), however inheritances concentrate larger amounts of wealth in the hands of fewer individuals. Broadly, this makes specific predictions. We should expect economics characterized by growing populations to have relatively fast growth, decreasing levels of wealth inequality, and high interest rates (returns on capital). Conversely we should expect shrinking, low birthrate economies to have slower growth, lower interest rates (low return on capital), and slowly increasing wealth inequality.

It is interesting to think about the degree to which long term trends like this in economics come from demographic factors or other factors such as government regulations, trade, improving technology etc. Ultimately it is some combination of both but I feel that deep demographic factors seem generally underappreciated since they are slow and relatively unnoticeable while also being easy to predict ahead of time given that demographic growth and basic contours of inheritance laws can both be known or predicted with good certainty decades ahead. Moreover, it feels like forces like these exert deep pressures on the general shape of society and its web of much faster moving interactions.