Close substitutes vs. perfect substitutes

by on July 25, 2010 at 8:29 am in Economics, Food and Drink | Permalink

For me, pluots and grapes are close substitutes, though not perfect substitutes.

Let's say a house visitor brings a big bag of pluots as a gift.  That distorts my optimum pluot-grape ratio.  But I don't eat all the pluots at once, simply to restore the preferred ratio.  That would be an unbalanced meal.  Instead, I dig into the pluot bag at a higher rate than I would normally eat pluots.  Over a longer period of time the proper ratio is restored, pluot by pluot. 

The closer pluots and grapes are as substitutes, the longer it takes for equilibrium restoration.  But the closeness of substitution is not always the major factor determining the speed of adjustment.  It may be just as important, or more important, how hungry I am, how much of a glutton I am, and how much I like pluots.  It also matters whether I am fearing a large shock, requiring a major pluot reserve, such as when a bevy of pluot-devouring guests might suddenly visit the house.  

In any case, equilibrium restoration eventually comes.  Those pluots will clear my refrigerator, sooner or later.

Apply a similar analysis to cash and T-Bills.  At low nominal interest rates they are close substitutes but not perfect substitutes.  T-Bills are of greater use for clearinghouse collateral, and yield a bit more, but they are not liquid in exactly the same ways.  Even if cash and T-Bills are close substitutes, monetary policy will change the banks' mix and so banks eventually will reequilibrate, converting extra cash into AD, one way or another.  But as with the pluot adjustment, this won't happen all at once.

Equilibration (and the accompanying AD boost) may be slow, maybe too slow for comfort.  But the degree of substitutability is not the only factor determining the speed of this adjustment, just as with the pluots.   The degree of bank and business confidence may be the most important factor.  Other factors will be the cues from the Fed, the corporate cultures of the banks, possible uncertainty, transactional frictions (the difference in returns is small but perhaps the cost of adjusting is small too), and so on.  The degree of substitutability is one factor determining the speed of adjustment but not necessarily a major factor.  I am not sure it should be put in the top three most important factors.

The zero bound argument assumes that the degree of substitutability is, at current margins, the major factor which matters.  You are being "sold" a model of portfolio adjustment with one dominant factor.

Monetary policy is not working well today, but perhaps bank and business confidence is a bigger reason than the degree of substitutability.  From those who promote the relevance of the "zero bound" argument, you will see it implicitly assumed that we have a case of perfect substitutes and that substitutability is the major factor hindering portfolio adjustment, as would lead to an expansion of the broader money supply aggregates.

In many models "close substitutes" and "perfect substitutes" have very different properties.  Current discussions of the liquidity trap usually neglect this point.

Addendum: This is also a framework for thinking about ceasing to pay interest on reserves.  If it creates perfect substitutes, stop the policy immediately.  If it creates closer substitutes, it may matter much less.

1 Bill July 25, 2010 at 9:47 am

Instead of giving you a pluot, let’s assume someone took away your pluot, disturbing your pluot/grape equilibrium (just as the money supply declines when velocity decreases). Let’s assume you can eat pluots, air dry or refrigerate them for future consumption, or juice them for immediate consumption.

Now, having seen your pluots disappear, you’re really hungry for pluots–and the only person that has them is Uncle Ben, who has a magical pluot farm.

Generous Uncle Ben gives you some pluots, but, remembering your loss of the pluots before, you put them in your refrigerator or air dry them in your food dehydrator, and don’t consume or drink their juice.

He keeps giving you pluots, and you keep refrigerating them and drying them, and notice your neighbors are doing the same. No one is eating or drinking pluot juice.

Now you have pluot liquidity crisis.

2 Richard July 25, 2010 at 10:09 am

I think it useful to conisder that cash and T-bills in theory can be substitutes along two different dimensions: as stores of value, and of mediums of exchange.

Now, as mediums of exchange they are imperfect substitutes at best. You just can’t buy things with T-bills like you can with cash.

The problem is that, when confidence drops, people want to buy less stuff. They want to save more. So in that sense the value of cash as a medium of exchange drops. That leaves us its function as a store of value. But it is inferior to T-bills in this regard when T-bills pay interest but cash does not.

Monetary policy then comes along and reduces the interest rate on T-bills. This makes T-bills and cash closer substitutes as stores of value, just when the dimension along which they are never close substitutes — as mediums of exchange — has become less relevant.

So the bottom line is that expansionary monetary policy discourages savings (lower returns on T-bills) but encourages hoarding (less penalty to holding cash). The question for policy makers then is, which is worse? The saving or the hoarding?

3 E. Barandiaran July 25, 2010 at 12:52 pm

Tyler, you have changed your addendum. Let me add another point to my previous comment. The analysis of monetary aggregates –from the monetary base to much larger aggregates including all sorts of bank deposits and T-bills– are based on two contradictory ideas. As aggregates one may think that the components are at least close substitutes on the demand side. Some economists, however, assume that the aggregates include close complements by arguing that the components are demanded in quasi-fixed ratios which facilitate the analysis of the supply of money (look in particular the traditional multiplier analysis of the monetary base and its extension by Brunner and Meltzer in the late 1960s). By aggregating too many things –some close substitutes (pennies and nickels), some close complements (high denomination bills and demand deposits), and some not so close substitutes or complements– the aggregates are useless. The same applies to different assets that are aggregated as bank reserves with the central bank.

4 Steve Sailer July 25, 2010 at 3:48 pm

If you are going to build a complicated analogy on pluots and grapes, you should first explain what a “pluot” is.

5 agnostic July 25, 2010 at 5:20 pm

You’ll improve exposition by using examples that aren’t so obnoxious and… dainty.

6 Bill Conerly July 25, 2010 at 7:56 pm

“Monetary policy is not working well today, but perhaps bank and business confidence is a bigger reason than the degree of substitutability.”

If a carpenter puts down the hammer, do we say that hammers just don’t do the job anymore?

The Fed is not trying to use monetary policy. The growth rate of M2 is less than 2% over the past 12 months (chart here: http://research.stlouisfed.org/fred2/graph/?chart_type=line&s%5B1%5D%5Bid%5D=M2SL&s%5B1%5D%5Btransformation%5D=pc1).

MZM shows a similar pattern.

If the Fed were trying to use monetary policy, they would be buying more and more assets until M2 grew at a reasonable pace. At a first approximation, assume velocity is stable and increase M2 by the rate you’d like to see nominal GDP grow, which is maybe 7% (2% inflation plus 5% real growth). Or be conservative and target just 5% M2 growth. But they are not even trying. Which is why this recovery is so sluggish.

They picked up the hammer after Lehman Brothers fell, but then put the hammer down.

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