Discounting asteroids, again

A while back, I wrote:

It seems to me that history has a direction. For some good things to happen other good things needed to happen first. The transistor had to be invented before the computer could be (well pretty much). I want good things to happen sooner so the other good things that depend on those first good things might happens sooner so that those things can lay the ground work for subsequent good things and, well, you get the picture…

(by the way, its exceedingly cool to quote myself)

and I still believe that. John Quiggin argues that we only have time preferences because we’re afraid to die. An excruciatingly perceptive commentator wrote:

I think John’s substantive point regarding time preferences is that marginal benefits are discounted over time at the individual level because individuals fear they may die before they can consume in the future, but this reasoning doesn’t follow for the everlasting society, thus society shouldn’t have time preferences.

But we should think carefully about what we mean buy ‘consume’. What is the thing that’s providing us the marginal benefits, today and tomorrow? What is the thing that we’d be giving up today in exchange for it in the future?

That I value the marginal benefit of eating today higher than my marginal benefit from eating tomorrow (i.e. I’ve discounted my marginal benefit) seems to follow from my fear of death in the next 24 hours. I might not get the chance to eat tomorrow.

That I value the marginal benefits of ‘consuming’ new knowledge today, on the other hand, doesn’t follow from my fear of death. Knowing something today means I can know more things tomorrow. I have a time preference for learning today versus tomorrow because my consumption of learning today determines my consumption of learning tomorrow.

(The assumption of time separability has precluded my example, but it shouldn’t preclude it from the discussion… We, society, do and should have time preferences independent of our individual fears of death.)

That bit about time separability needs explanation. In the models Quiggin uses, and most economist use, to get a grip on these ideas he assumes benefits in each period are conferred by consumption in that period and only in that period. So your happiness today only depends on your consumption today.

This is a great assumption for two reasons. First, it seems true for most of the things we think about when we think about consumption. It seems right that me eating an apply today has little bearing on the happiness I’ll get tomorrow from eating a banana.

Secondly and perhaps more importantly for us that hate algebra, this assumption greatly simplifies the models we have to deal with.

But there’s lots of “consumption” that we do that does depend on how much was consumed in the past. That I learned stuff today means I can learn even more stuff tomorrow. That the PC was invented in the 70’s meant the internet could flourish in the 90’s. That DNA was mapped in the 90’s means great genetic drugs will be invented in the next couple decades.

It might be weird to think of these things as consumption, but in our models that’s what they’d be.

Who doesn’t have a preference for these things to happen sooner? Does that preference have anything to do with our impending demise? I don’t think so.

In any case, to relate this to the discussion of discount rates… I think the discount rate might be a sort of fudge factor in the models were we assume time separability. If we were better at algebra, we’d directly model the positive effect consumption today has on consumption in the future. Our simple models, however, don’t do this and they undervalue consumption today.

Because we’re not so good at the algebra, we discount future consumption to make up for this modeling error.

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3 Responses to “Discounting asteroids, again”


  1. 1 gabby D February 25, 2007 at 9:57 pm

    hey, about consumption that happens affects future consumption… don’t we call that investment?

  2. 2 Will February 25, 2007 at 10:26 pm

    The nice separation between consumption and investment, one your comment implies, is an implication of the assumption of time-separability of the utility function.

    Consider: Is reading a book about basic physics an investment? Is watching the first part of a mini-series investment? Is upgrading my video card today so I can buy the hottest new computer game tomorrow investment?

    But sticking to the consumption of learning example… You can extend capital to include human capital but when the models are calibrated, does my reading a book get included in the capital stock? What’s the return on my investment to take a intro economics course before I take intermediate economics? Infinite? Zero?

    There’s quite a bit of consumption we do today that doesn’t get counted as investment but still impacts my consumption tomorrow.

    The larger point is that there are other reasons, besides fear of death, that suggest a time preference is appropriate.

  3. 3 Will February 25, 2007 at 11:36 pm

    Gabby, your comments got me thinking about other reasons for a positive time preference in a time separable model.

    Perhaps, in addition to being a modeling error band aid, the discount rate captures measurement error. Because the line between investment and consumption isn’t cut and dry and we have an “apples and oranges” bias in interpreting consumption in our model, we tend to mismeasure capital as consumption. Famously, education was (is?) considered consumption in GDP statistics rather than investment, for example.


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