## Saturday, October 10, 2009

### More on Money and Interest

But would you agree that if the Fed moved the interest rate on reserves from below the rate on T-bills, to a rate above the yield on T-bills, at the same time they doubled the money supply, then prices would not even rise in the long run? (And that is what they did.) I realize that combines two separate policy changes, and looking at it from your side I see why it would be frustrating to mix the two issues.

When I first read this, I was puzzled. Why should a change in the interest rate paid on reserves be expected to exactly offset the impact of a simultaneous doubling of the quantity of base money simply because it crossed this threshold, going from less to more than the interest rate on T-bills? My first thought was no, and after further consideration, the answer remains no.

What could Sumner be thinking? First, consider a banking system that only holds T-bills as earning assets. The assumption is unrealistic, but it has some relevance for the post-crisis banking system. Last year, many believed that the banking system was capital constrained. Because of the nature of capital regulations, reserve balances at the Fed and government bonds are especially close substitutes. Both are counted as zero when calculating risk-weighted assets. Since some banks have sold stock to repay TARP money, it is clear that not all banks are completely capital constrained, but presumably some are and, of course, all banks are always somewhat constrained by capital regulation.

Consider a simple money multiplier formula:

mm = (1+c)/(c+r)

where c is the currency-deposit ratio, and r is the reserve-deposit ratio.

Suppose that c = 1, (which is close to current conditions if "deposits" means reported transactions accounts.) Suppose that with interest rate on reserves less than interest rates on T-bills, banks hold no reserves, so r = 0. Then:

mm = (1+1)/(1+0) = 2.

Now, suppose that the interest rates paid on reserve balances is set above the T-bill rate, so that banks replace all T-bills in their asset portfolios with reserve balances. Ignoring any other sort of earning asset, the reserve ratio becomes 1 and so:

mm = (1+1)/(1+1) = 1.

The money multiplier falls exactly in half.

If the Fed doubled base money, and at the same time increased the interest rate paid on reserve balances so that the money multiplier fell exactly in half, then the money supply and the price level would not be affected, even in the long run. However, once the money multiplier is equal to one, changes in base money should again return to causing proportional changes in the price level.

Further, it is only the very special assumptions made above that cause the money multiplier to fall exactly in half when the interest rate on reserve balances crosses that particular threshold. For example, if the currency- deposit ratio were less than one, then the money multiplier would have been more than 2 and would have fallen by more than 50%. A simultaneous doubling of base money would be inadequate to prevent a decease in the quantity of money and deflation.

On a more positive note, if banks already were holding some reserves because of regulation or liquidity needs, then the money multiplier would initially be lower, and so the decrease caused by the change in interest rates smaller. Most importantly, if the assumption that T-bills are the only earning assets is dropped, then changes in the interest rate on reserves relative to T-bill rates doesn't reduce the money multiplier to one. Banks would continue to hold earning assets with yields sufficiently higher than the interest rate being paid on reserve balances.

So what actually happens if the Fed increases the interest rate it pays on reserves to a level above the yields on T-bills of particular terms to maturity? The demand for reserves rises by an amount equal to the amount of those particular T-bills banks were holding in their asset portfolios. If base money happened to increase by exactly that same amount, then the quantity of money and the price level would not be affected, even in the long run.

In my view, by far the best way to see the problem is that if the Fed increases the interest rate it pays on reserve balances, the real demand for reserves will rise, and the level of base money needed to keep nominal expenditure on its target growth path will be greater. In other words, the Fed will need to purchase more assets, the higher the interest rate it pays on reserve balances. The Bernanke Fed considers this a good thing. I consider it undesirable, and worry that their efforts to manipulate flows of credit by purchasing just the right assets have distracted them from what should be their most important task, keeping the quantity of base money at a level so that nominal expenditure remains on a stable growth path.

1. Bill, I don't follow your argument. Are you assuming that the M1 multiplier cannot fall below 1? It already has. Bank holdings of T-bills could be much larger than transactions deposits. Am I misunderstanding something here?

2. Scott:

All I did was describe a special situation where a change in the interest rate on reserves from below to above "the" T-bill rate would exactly offset a doubling of base money.

If the reserve ratio on measured transactions deposits rises above one, then the M1 money multiplier can fall below one. In reality, both the reserve ratio is above one and the currency deposit ratio is greater than one, both pushing the M1 money mulitplier below one.

The commercial banks held \$1,220 billion worth of government bonds in September 2006. It dropped until January 2008, hitting a trough of \$1,100 billion. Since that time it has increased to \$1,360 billion. Oddly enough, the previous peak was passed just about October 2008.

So, the banks have increased both reserve balances and their holdings of government bonds. Presumably, because the Fed began paying interest on reserve balances, banks increased their holdings of government bonds less than they would have. We know that all the measures of the money supply have increased. It is just they have not not increased as much as velocity has fallen.

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