Monday, September 28, 2009

Hamilton on Sumner 2

When I read Sumner's article, I thought his citation of Hume was a nice touch. Sumner's point was that monetary disequilibrium can be caused by an increase in the demand to hold money as well as a decrease in the quantity of money. Locking up coin in a strong box is the same as having the coin disappear. How clever.

Because orthodox monetarists spent so much effort trying to argue that velocity is sufficiently stable so that a money supply rule--slow steady growth of some measure of the quantity of money--would result in stable growth of nominal income, monetary disequilibrium theorists constantly must point out that monetary disequilibrium doesn't solely come from changes in the quantity of money. The problem is an imbalance between the quantity of money and the demand to hold it.

Like many monetary disequilibrium theorists, Sumner likes the supply and demand approach to the problem rather than the equation of exchange. That is because he focuses on the medium of account function of money, and has spent much time thinking about the gold standard in that way, where the nonmonetary uses of gold must be analyzed using supply and demand.

But Sumner brought up the equation of exchange, and Hamilton responded with a discussion of the ambiguous nature of the concept of "velocity." What exact version of the equation of exchange does Sumner have in mind?

I think the real answer is no version. Monetary disequilibrium theorists all understand that income velocity is the reciprocal of the Cambridge k. So, "velocity" is most definitely the ratio of nominal income to the quantity of money, just as k is the ratio of money to nominal income. And that is related to a notion of treating the demand for money in proportion to nominal income. As shown by Sumner's quote of Hume about how locking coins in a strongbox has the same effect as a decrease in the quantity of coin, it is clear that there is no assumption that money demand, k, or V are constant.

The current crisis exists because the demand for money rose, and the quantity of money didn't increase enough to match the increase in demand. That velocity fell and the quantity of money didn't rise enough to offset the drop in velocity is just another way of saying the same thing.

Hamilton then raises concerns regarding "long and variable lags." On this view, a change in the quantity of money will only impact nominal income after many months, and maybe it could be as much as a year or two. This is the orthodox monetarist view, and it leads them to look at the huge increase in base money over the last year and to worry that within the next few months, quarters or years, massive inflation will occur. Those of us who claim that the drop in nominal GDP proves that however large was the increase in the monetary base by historical standards, it was evidently too small, supposedly fail to recognize the lag issue. Nominal income today depends on the quantity of money created in the past, and changes in the quantity of money today will have no impact on nominal income today, but will only add to the tremendous inflationary pressures that will be generated in the future, which will be coming any time now.

Hamilton then shows a chart of M1 and M1 velocity since 1980, and it looks to me like changes in M1 are matched by opposite changes in velocity. Certainly, this seems plausible enough. My view is that if new money is created, and it is placed in someone's hands, then the immediate effect is that the individual holds more money. If the demand to hold money was unchanged, then it takes some time for that person to choose how to spend the excess money balances. But that is the relevant issue--how long does it take people to decide how to spend excess money balances.

If we imagine an exogenous change in the quantity of money, with a given demand for money, and we consider how fast that excess money will be spent, I think that little will be spent in the first few minutes or even hours. And, it is possible that not all will be spent in the first month. But to imagine that the issue is a single individual gradually spending money ignores a key part of the process. Excess money balances are spent, and then those receiving them have excess balances, and they must decide how to spend it. At each step of the process, there is increased demand for assets, goods or services, and so only gradually does the growing demand for the goods and services raise nominal expenditure. That the full impact of a given change in the quantity of money might only gradually be felt is entirely reasonable. But that isn't the same thing as saying that a change in the quantity of money, no matter how large, will not have any effect on nominal expenditures for several months, quarters or years.

Further, suppose that there was an increase in the demand for money, and people are gradually figuring out what expenditures to cut in order to build up money balances. It might take some time for any individual to determine how to cut spending to build up money balances. And as one person cuts spending, those who would have received the money have reduced money balances, and they in turn must cut spending. It could be a long, drawn out process.

Now, suppose that an increase in the quantity of money occurs simultaneously with the increase in the demand for money. To what degree does the gradual, drawn out process get short circuited? Someone who was working out ways to cut spending to build money balances now has more money balances. There is no need to figure out how to spend excess balances. They just have less need to cut expenditures. Similarly, some of those who would have ended up with less money as those short on money cut spending, will receive extra money from those spending excess money balanceces. Such persons have no need to adjust their actual money holdings to desired money holdings at all.

So what about Hamilton's charts of M1 and M1 velocity? Suppose that Sumner's proposal of index futures targeting was implemented and it worked better than his wildest dreams. Nominal expenditures remained exactly on a 5% (or 3%, 0r 2%) growth path. If the demand for money changes, then the quantity of money would change with it. In other words, the quantity of money would exactly change to offset any change in velocity, generating the exact pattern shown by Hamilton.

Of course, the Federal Reserve has not used index futures convertibility. However, the Fed has targeted interest rates, making the quantity of money endogenous. The traditional rationale for this policy is that the open market trading desk will cause changes in the monetary base and the broader money aggregates to accommodate changes in the demand for them. This is fully consistent with Wicksellian monetary economics, and as long as the target for the interest rate is just right, changes in bank lending will generate bank monetary liabilities that do exactly match the demand to hold them. The result should be changes in the quantity of money that exactly offset changes in velocity. Of course, when the central bank fails to make the appropriate changes in interest rates--to match changes in the natural interest rate--changes in the quantity of money will passively accommodate changes in nominal expenditure. That the "Great Moderation" shows a period where changes in the quantity of money largely offset changes in velocity should be what is expected. If the Fed had failed to make the proper adjustments in interest rates, it wouldn't have been quite so moderate.

None of this proves that changes in the quantity of money don't just result in people passively increasing their money balances and leaving excess balances unspent. If we imagine that increases in money demand occur on one isolated island, and the expansions in the quantity of money occur on another isolated island, then it could well be that lagged effects of the added money demand will hit at a time when the increased quantity of money is having little effect. Without trade between the islands, as the excess money gradually spreads to more and more people, it will never be to any of those being hit with reduced sales and so reduced money balances.

Sumner tends to focus more on rational expectations. Everyone knows that the increase in money balances will raise nominal expenditure eventually, and expectations of higher prices and output in the future raise spending today. My view is that to the degree people understand that Paulson and Bush's threats of another Great Depression are false, and that nominal expenditure will not fall in half and remain depressed for a decade, then they will not be so motivated to cut spending and accumulate money balances at this time. I admit, however, that I also insist on a market process that generates increased nominal expenditure even with pigheaded market participants who listen to the likes of Paulson and Bush.

Hamilton then argues that using monetary policy to target nominal expenditure is problematic because monetary policy will impact commodity prices faster than wages or the prices of services. I was entirely puzzled as to why Hamilton would think that the goal of the policy is to raise wages or the prices of services. The goal is to avoid a drop in nominal expenditure and the associated drop in output and employment. If that cannot be avoided, then the goal is to return nominal expenditure back to its previous growth path in order to generate a recovery of output and employment. Ideally, price and wage changes should be avoided, and if that has failed, and falling nominal expenditure has already lead to a deflation of commodity prices, then reflating them is appropriate.

Hamilton's comment sometimes gives the impression that he is commenting on a proposal to stabilize the price level, or even to cause inflation. No, the proposal is to stabilize nominal expenditure. How this impacts various measures of the price level or real output will depend on the particular measures and more importantly, on the market forces determining production and pricing at a given growth path of nominal expenditure.


  1. Hi Bill,

    It's nice to see you blogging.

    --"The current crisis exists because the demand for money rose, and the quantity of money didn't increase enough to match the increase in demand."--

    Although I am inclined to agree with the above statement (if pushed to explain the crisis in one sentence), should we not also be concerned with the specific locations that new money enters the economy? One problem with the Federal Reserve (and its allies in the Treasury) seems to be that monetary expansion is used to suppress relative price adjustments and prevent malinvestment from being purged.

    When money demand rises so should money supply, but more concern should be given to where that money enters the economy, because aiming at monetary equilibrium ought to aid in relative price adjustments, not stand in their way. This seems to me to be a major drawback of relying on a central bank rather than a free banking system.

  2. Lee:

    Thanks for your comment.

    You are right that what I call the new Federal Reserve is working to funnel money into "weak" sectors of credit markets. I don't think they are trying to prop up malinvestments, but they are trying to prevent overshooting in those sectors because of failures in credit markets. The ruination of the mortgage securitzation market is resulting in excessively low relative prices for houses, too little home production, and the like. I don't think the Fed is trying to return to the extremely high prices or levels of production from a few years ago. I think the consensus view is that there was a bubble.

    While it might sound like I am defending them, I am a critic of their approach. I think the Fed should avoid trying to direct credit.

    Read again the story of the two islands as well as how the secondary effects of a simultaneous increase in money demand and increase in the quantity of money can "cancel." Those who would be receiving more money from those spending excess balances may also be receiving less money from those building up their balances. They have no need to adjust their money balances at all. The real world will be somewhere between he separate islands and this perfect offsetting of secondary effects.

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