# Discount factors and death

What is a discount factor? A discount factor tells us the rate of time preferences between periods of time – in other words it gives us a measure for how much “stuff” we are willing to sacrifice in the future in order to consumer now.

Economists often use “exponential discounting“. Furthermore Rauparaha has discussed how hyperbolic discounting more accurately reflecting peoples true time preference at a given point in time. However, there are other issues that influence the way people discount. The one I want to focus on today is death.

In an interesting post over at 26 Econ, Aaron Schiff discusses the “marginal life expectancy” you have as you get older. The inspiration for this post came from another post at Flowing Data which discussed how your probability of dieing lifted as you became older.

Now the fact that your probability of dieing rises as you become older is extremely useful when thinking about discount factors. However, before doing this lets try to describe what a person’s inter-temporal choice looks like. For an example we will look at consumption choices through the lens of the permanent income hypothesis.

Say that you are “young”, if you have no time preference for consumption and the real effective interest rate is zero then the composition of your savings and borrowing will be such that, given your expectation of future income, consumption is the same in every period.

If we now introduce a probability of death this all changes. As there is some probability that you will be dead tomorrow you develop an automatic preference to consuming today – as savings become wasted consumption and therefore forgone utility (leaving aside the issue of bequests for the moment).

The greater the probability of death, the more likely you would be “wasting” income by not consuming it now (or not borrowing on a future that doesn’t occur 😉 ), as a result, the more you will consume now.  As your probability of death rises as you get older, this implies that your natural time preference shifts more towards the here and now, rather than the future.

Why is this useful?

Well, it implies several things.  Firstly, the marginal propensity to consume of the old will be higher then that of the young – when incomes are equalised.  Secondly, and more interestingly, it implies that old people would be more likely to deviate in a prisoners dilemma game then the young.

Why is this important?  Well we are coming up to a point in time where a significant portion of the population (baby boomers) will view themselves as old.  If they start deviating in all the prisoners dilemma games they are playing, social efficiency will fall significantly.

This might seem like a cold and ultra-rationalist way of viewing the generational breakdown, but given NZ history I don’t think it is unreasonable.

Think of it this way – this generation has always been the dominant generation in the population demographics.  When they were young they got free education (70’s), when they worked they got lower taxes (80s), in their savings years they got cheap houses (90s) which have now appreciated substantially, and now that they are planning to retire and “dis-save” they seem to want lower GST rates so they can buy more.

I’m not usually a fan of the holistic way of viewing issues – but it looks to me like this generation may have taken a whole bundle of surplus from its parents and children.  If a group this powerful then decides to deviate on all the co-operative equilibrium that exist in our communities and in our political structure then we can expect a large social cost for their children to pick-up.

1. CPW says:

Nice post Matt. To nitpick, however, education expenditure was much lower in the 70s, taxes were rising in the 80s (check if you don’t believe me), and buying cheap houses will screw the boomers over when they go to sell if price appreciation is purely weight of numbers.

The real fast one pulled by the boomers is the explicit promise that NZ super will be maintained and the implicit promise that healthcare will remain free and comprehensive, both of which are large unfunded liabilities for future generations.