Williamson on Quantitative Easing

In comments on an earlier post, David Beckworth asked for my view on Stephen Williamson's argument that quantitative easing cannot be effective.

I think that the element of truth in Williamson's argument is that if the Fed purchases government bonds with yields lower than the interest rate it is paying on reserves, it unlikely to have much of an effect. (The situation is ambiguous because not everyone is allowed to hold reserve balances at the Fed.)

I disagree with his view that having the Fed purchase long term to maturity government bonds would have no expansionary effect. My view is that as long as the Fed purchases assets with yields higher than the yield it is paying on reserves, it can correct an excess demand for money.

So, what is Williamson's argument?

The Fed can swap reserves for T-bills or reserves for long-maturity Treasuries all it wants, but because this essentially amounts to intermediation activities the private sector can accomplish as well, this will have no effect.

Williamson is correct that there might be some offsetting change in private sector intermediation when the Fed purchases assets--for example, banks might sell long term government bonds and reduce their issue of short term to maturity certificates of deposit. However, he is implicitly assuming that the supply of private financial intermediation services is perfectly elastic.

DeLong makes much the same point.

But such swaps take various forms of duration and default risk onto (or off of) the Fed's and thus taxpayers' balance sheets and off of the private market and thus investors' balance sheets. These are different (but overlapping) groups who perceive risks differently, have different resources, and react to risks differently. The fact that the private market could undo any particular Federal Reserve policy intervention does not mean that it will.

So, why do I bring up "perfectly elastic" supply? I guess it involves my constant return to ordinary economics.

When the Fed undertakes quantitative easing, it is increasing the supply of intermediation services--issuing short and safe reserve balances and purchasing long term to maturity government bonds. The result will be a reduction in the equilibrium price of those services, which is the difference between the yields on the earning assets financial intermediaries buy and the yields they must pay on the liabilities they issue to fund those assets.

This reduction in the price received by financial intermediaries will ordinarily reduce the quantity of those services supplied (and increase the quantity demanded.) In equilibrium, the price of the services is lower and the quantity is higher. While the "quantity" is specifically the quantity of intermediation services, it is simultaneously the quantity of liabilities issued by the financial intermediaries. To the degree those liabilities serve as media of exchange or are (near) perfect substitutes, that is also at least part of the quantity of money.

The more elastic the supply of intermediation serivces, then given any increase in supply (quantity of long term bonds purchased by the Fed,) the larger will be the decrease in quantity supplied and the smaller the increase in the quantity of money. If the supply of intermediation services is perfectly elastic, then the decrease in quantity supplied will exactly equal the increase in supply and the quantity of money will be left unchanged.

That is Williamson's implicit assumption.

The following series of diagrams show a given increase in supply, and shows how the increase in the equilibrium quantity depends on the elasticity of supply.

Suppose supply is slightly more elastic.

The given increase in supply (the Fed's purchases of assets) results in a smaller increase in the quantity of money, because the decrease in quantity supplied by private financial intermediaries is larger.

Suppose supply is even more elastic.

The increase in supply is almost entirely offset by the decrease in quantity supplied.

And finally, with perfectly elastic supply, the decrease in quantity supplied entirely offsets the increase in supply, leaving the quantity unchanged.

In my view, as long as supply is not perfectly elastic, all that Williamson's argument means is that amount of long term government bonds the Fed must purchase to generate the desired increase in the quantity of money is larger.

And what if the supply of private financial intermediation is perfectly elastic? Does the Fed have to purchase infinite amounts of assets?

No.

Suppose the elasticity of supply of private intermediation was so high that the Fed must purchase enough assets to nearly match Q2, the desired quantity of money. The private sector will sell off nearly all of the assets it holds because the price they receive drops (even if it is only a slight amount.) This immediately shows what the Fed must do. If the supply of private intermediation services were perfectly elastic, then the Fed must purchase assets equal to the entire desired quantity of money.

If, of course, the supply of private intermediation services is really perfectly elastic.

Given all of this supply and demand analysis, would quantitative easing impact expenditure on output? If the quantity demanded for financial intermediation rises, it certainly suggests that any increases in the quantity of money will be matched by an increase in the demand to hold money.

However, this analysis is ambiguous regarding monetary disequilibrium. The price of intermediation services is the difference between the interest rates paid on the liabilities of financial intermediaries and what they receive on earning assets. Because money serves as a medium of exchange, there is no requirement that financial intermediaries issuing money pay an interest rate on that money so that people are willing to hold the amount of money issued. (Or rather, competing private issuers are usually limited by redeemability, and central banks are not constrained.)

It is certainly possible that such a decrease in price and increase in quantity could occur without there being any monetary disequilibrium. For example, if the Fed were to increase the interest rate it pays on reserves so that the amount banks want to hold increases with the additional quantity, then no excess supply of money would develop.

(Something like that appeared to be the goal of QE1. Pay interest on reserves to raise the demand for reserves, so that the Fed could expand the quantity of reserves and lend them to a variety of Wall Street firms whose financial health was considered essential to the operation of credit markets. Or, as I prefer to say, rebuild the house of cards that was the shadow banking system.)

If, on the other hand, the interest rate paid on money doesn't rise, and so the demand to hold money doesn't rise, and the quantity of money rises, there would an excess supply of money--or at least an excess supply of money given current, depressed level of nominal expenditure on output.

Further, if quantitative easing is expected to cause increases in nominal expenditure in the future, those expectations should cause various private investors to sell off government bonds to fund the purchase of capital and consumer goods. If that were to happen, the lower equilibrium price of intermediation would be consistent with an increase in both the interest rates the Fed earns and the interest rate the Fed pays on reserves.

Anyway, I agree with Williamson that a decrease in the interest rate the Fed pays on reserves could raise nominal expenditure on output, and consider that better than quantitative easing, at least until the interest rates fall to the cost of holding currency. (Having the Fed, and so, the taxpayer, accept additional risk so that traders on money markets can earn brokerage fees seems like a travesty to me.)

I don't think a traditional liquidity trap is an example of Friedman's optimal quantity of money. I don't think that it is all about expected deflation reducing the nominal interest rate to zero with real interest rates remaining constant. While that could happen, what actually happened was a shift in the demand for assets--away from more risky assets to safer assets. One element of risk is interest rate risk, and so there was also a shift in demand away from longer towards shorter term to maturity assets. It is the real yields on short and safe assets that have fallen to a point where open market operations using short and safe assets to target the interest rate on short and safe assets is failing to prevent massive monetary disequilibrium.

Of course, I think the goal of monetary policy should be keeping GDP (nominal) on a stable growth path. Williamson, I think, sees no value in such a goal, and so, it makes it difficult for me to decipher what he thinks the Fed might be up to.