Post for capital theory geeks

Bryan Caplan (now a permanent blogger at Arnold Kling's ever-excellent EconLog) argues that we do not need time preference to generate positive rates of interest.  He claims that diminishing marginal utility will suffice.  Lawrence White and Doug MacKenzie offer commentary...

Bryan's central argument is the following:

In the modern world, the typical person gets richer in the typical year. Once again, this gives even perfectly patient people a reason to increase their demand for current consumption. Imagine you are going to inherit $1,000,000 next year. According to the law of diminishing marginal utility, you would want to increase your consumption now when the marginal utility is high, and pay for it by cutting back your consumption in the future when the marginal utility is low. No time preference story need apply.

I would put it differently.  The argument for positive interest rates does not require "pure time preference," but it does require assumptions about the intertemporal substitutability of consumption. Diminishing marginal utility, in the classic sense, is defined at a single point in time. But how do differing marginal utilities of consumption vary across time? How does my two millionth dollar next year compare to my one millionth dollar today (Steve Miller asks the same)? This variable is distinct from either classic time preference or classic diminishing marginal utility. For Caplan's argument to work, we must assume that consumption tomorrow is a relatively close substitute for consumption today. 

So the Austrians are correct that we must consider "preferences across time" as a broad category behind the phenomenon of interest.  That being said, the intertemporal substitutability of consumption is closer to Irving Fisher's notion of time preference as a marginal allocation than it is to Mises. 

Why does all this matter?  There is no quick, easily bloggable explanation.  But to race ahead to the conclusion, this extra dimension of preferences offers us some hope in explaining apparent anomalies in equity returns and market pricing of debt securities (though here is one critique).  And here are some implications for the conduct of monetary policy. 

Intertemporal consumption involves local complements, not substitutes, when habit formation (this link is for Bryan) is sufficiently strong.  If you would like a fun exercise, try to figure out what this implies for the term structure of interest rates in a world with zero time preference... 

And if you don't already understand what this post is about, don't bother trying to learn.