# Re: Market failure to sufficently weigh the future

From: hal@finney.org
Date: Tue Oct 31 2000 - 11:41:31 MST

Robin writes, quoting Hal:
> >The real question is, it seems to me, is would I have been happier over
> >the course of my life if I had generally saved more for the future ...
> >This is what their remedy would do.
>
> The question I asked is exactly the right question to ask given the
> formulation in the paper. If you reject that formulation, then if you
> want to play the formal policy analysis game you are implicitly challenged
> to come up with an alternative formulation which supports the alternative
> conclusions you favor.

I would favor an approach based on rational discounting. I argue that
discounting is rational and appropriate based on future uncertainty.
Any system which proposes to alter discount rates on philosophical or
psychological grounds based on our feelings about whether we would alter
the past would then be seen to be harmful.

Unfortunately I don't have the time or experience to construct a detailed
model for this. Perhaps other researchers have already done so.

My attempts would be to start with a model where you have consumable
goods which are like food, things which you have to consume on a regular
basis but which can be saved into the future. There are diminishing returns
on a per-time-unit basis, so it is better, all else being equal, to consume
equal quantities over time.

Overall utility U = U(x1) + U(x2), where x1 is quantity consumed in the
first time period, and x2 is quantity consumed in the second period,
x1+x2 = constant. This neglects growth of the stock of goods, but I
think growth rates may have historically been negligible compared to
the risk of accidental loss.

U'(x) is positive, U''(x) is negative, to represent diminishing returns.

Now it is possible to show that U is maximized with x1=x2. Presumably
this is an elementary result. (This is what I mean by consuming equal
quantities over time.)

Now we introduce the risk of loss. There is a probability p that we
will not be able to enjoy the goods we have saved into the second period.
Either it goes bad, is stolen, is lost, we are hurt so we can't consume
them, or something else goes wrong.

U = U(x1) + (1-p)*U(x2).

Now optimizing this, with small p and linear or second order approximations,
I get that the optimum x is greater than the x1=x2 value by

delta_x = - p/2 * U'(x1)/U''(x1).

(Don't rely too heavily on this, my algebra is rusty.)

The point is, this is positive, since U'' is negative. Hence we will
rationally consume more in the first period than in the second.

With this calculation built into our preferences via generations of
evolution, it may appear to some that people discount the future as part
of their psychology, a mere matter of taste. Actually the discounting
is fully rational and appropriate in a world of uncertainty.

The authors' argument does not seem to address the possibility that
discounting is rational and appropriate. They view the effect as
purely psychological or even philosophical. Discounting the future
can be modelled as a fully rational process. Unless they can show that
discounting the past can have a similar evolutionary basis (an absurdity,
IMO, since one can't change the past), they are wrong to equate the two
forms of discounting. Since that is the whole basis for their analysis,
I think it is fundamentally misguided.

Now, given this perspective, I do think there is a possible argument
for coercing people to discount less. That would be the claim that
our intuitions about discounting derived from an era whose properties
were very different from the modern world. There was little economic
growth in those days, while we have rapid growth today. Population was
relatively stable, while today it is exploding. It could be that in our
world, the optimal strategy calls for less discounting of the future than
in the primitive world where our instincts developed. In that case it
would be proper to try to get people to discount less.

However this analysis is fundamentally inconsistent with that offered
in the paper, since this starts from the position that some discounting
is rational and appropriate. Nothing in the paper's approach would
prevent it from being applied even to a mature and stable, primitive
society which had evolved discount rates that were perfectly attuned
to the circumstances in which it found itself, for optimum survival.
The authors would step into that society, and armed with their equations,
would ruin it. This in itself demonstrates that their approach is
fundamentally wrong.

Hal

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