How economic incentives shape wealth transmission

Parental wealth transmission to children can take many forms. Primogeniture refers to a preferred (usually first-born) child getting all the wealth, whereas a completely egalitarian transmission would mean each child getting the same share. Then there is everything in-between.

Which one of these societies tended towards historically varied quite a bit by time and place. Surely, there are cultural and historical reasons for this. But there are also economic ones.

Augustins et al. (2014) build an evolutionary model to study this question. They study how wealth transmission can evolve in closed, rural societies. Suppose everyone has a certain wealth (as measured in land). Each year, there is a harvest, which has a noisy yield (i.e. sometimes the land over-performs its nominal potential, sometimes it under-performs it).

There is a maintenance cost to land (like the cost of buying seeds, etc.), which is equal to the land’s nominal value. So families whose harvest yield is above the land’s potential (due to the noise mentioned above) will have positive profits, but families whose yield is below the potential will have losses. On average, these will cancel each other out (as the noise has mean zero). There is also a flat (percentage) tax on wealth, whose proceeds are then equally redistributed.

Families with positive profits can then buy lands from families with losses. So in the next period, everyone will once again start with a balanced wealth and no debts. Total land supply is constant over time.

First, the authors show that the wealth disribution in such a society converges to a stationary power law distribution. As the figures below illustrate (left one for simulated values, right one for theoretical ones), as the noise in harvest yield increases (sigma), the distribution has a fatter right tail. So there will be more inequality in a more uncertain environment.

Wealth distribution vs. environmental uncertainty

Second, evolution is introduced assuming that the type of wealth transmission selected by families is a heritable trait. To achieve this, the researchers add fertility into the model. This is done the following way: the model is simulated for 25 years (one generation), then each household engages in some reproduction with a probability that is increasing in wealth. There is thus already a selection effect on wealth here. Then if a household does have positive reproduction, their number of children is drawn from a Poisson distribution.

Upon giving birth, the parent dies so there are no overlapping generations. At this point, the parent also transfers their wealth to the children. A parameter rho controls how egalitarian this transmission mechanism is. Rho measures the degree of primogeniture with the property that rho=1 means the first-born child gets everything and rho=0 means completely egalitarian sharing amongst children.

Rho is then allowed to mutate slightly from period to period in a random way with mean zero. So if the average rho changes over many generations, that is due to selection. I.e. people who prefer primogeniture (if rho increases) or those who prefer a more egalitarian sharing (if rho decreases) are more successful in the long-run.

Simulations show that as environmental variance (as measured by the uncertainty in harvest yield) increases, more people will choose an egalitarian sharing (i.e. rho goes down). This is illustrated in the figure below.

Evolution of primogeniture trait vs. uncertainty

Some of the intuition behind these results is as follows. If the wealth distribution is egalitarian (happens when sigma is low as shown above, or if there is high wealth redistribution due to taxation), then many people will be moderately rich or poor. Individuals will then have a relatively low probability to reproduce (low wealth). So those who split their wealth among many offspring will create offspring who are themselves poor and unlikely to reproduce. Those who give all their wealth to one offspring will make their offspring more likely to reproduce. Thus primogeniture increases chances of reproduction in the long run.

On the other hand, when wealth distribution is unequal (many very poor and very rich people; can happen if harvest yield variance is high or there isn’t a lot of redistributive taxation), then rich people will find it more useful to split their large wealth among their offspring. This ensures that more of their children will be able to reproduce. Poor people might prefer primogeniture but on average they will have fewer children (because of their lower wealth) and thus rho will decrease overall. This happens because the large number of rich people in this case prefer egalitarian wealth transmission.

One important thing to keep in mind is that this is clearly a model that is more applicable to historical periods than to today. As the whole idea is to model a closed rural society where the main source of wealth is land.

Additionally, there is definitely room here to come up with some clever empirical analysis to test the hypotheses put forward in this paper. It would be interesting to see whether data backs this all up. Data on the variance of harvest yields or at least on the degree of climatic fluctuations across years could probably be obtained (see here) to measure environmental variability. Data on wealth transmission mechanisms across societies might be more difficult to come by for a large enough number of closed and rural societies. Still, if it does exist, this could make for another interesting paper.

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