Does QE actually reduce inflation?

There's a counterintuitive meme floating around in the blogosphere that quantitative easing doesn't do what we commonly suppose. Somehow QE reduces inflation or causes deflation, rather than increasing inflation. Among others, here are Nick Rowe, Bob Murphy, David Glasner, Stephen Williamson, David Andolfatto, Frances Coppola, and Bill Woolsey discussing the subject. Over the holidays I've been trying to wrap my head around this idea. Here are my rough thoughts, many of which may have been cribbed from the above sources, though I've lost track from which ones.

Let's be clear at the outset. Inflation is a rise in the general price level, deflation is a fall in prices. QE is when a central bank purchases assets at market prices with newly issued reserves.

In equilibrium, the expected returns on all goods and assets must be equal. If they aren't equal then people will rebalance towards superior yielding assets until the prices of these assets have risen high enough to iron out their superior return (and away from low yielding assets until their prices have fallen enough so that their expected return is once again competitive with all other assets).

Central bank reserves are one of the many assets whose yield is included in this calculus of returns. The return on reserves can be decomposed into two specific categories of return: expected capital gains, or price appreciation, and a liquidity return, sometime referred to on this blog as a monetary convenience yield.

Regarding the first return, this is typically negative. People expect the purchasing power of central bank reserves to be lower in the future than in the present—they anticipate inflation.*

The liquidity return exists because reserves are highly marketable. The ability to quickly mobilize reserves to deal with unanticipated events yields a flow of liquidity services, specifically the alleviation of felt uncertainty. The expected return on these liquidity services outweighs the expected capital loss on reserves, providing reserve owners with a combined return that is competitive with other assets like cars, olive oil, education, t-bills or houses.

When a central bank conducts QE, the quantity of reserves in the economy increases so that they are less scarce. All else staying the same, the marginal value that people attribute to the flows of liquidity services provided by reserves declines. With their liquidity return having fallen, reserves now yield a lower overall return than competing assets.

Given these unequal returns, reserve owners will want to rebalance their portfolios into higher yielding alternatives. However, existing owners of these assets will be unwilling to accept this trade since the return they can expect to receive on reserves is no longer competitive with the return on the assets that they would be forgoing. Reserve owners will have to sweeten the deal by offering potential counterparties an improved return on reserves held. The way they can do this is to offer to sell their reserves at a reduced price today relative to their price tomorrow. In doing so, reserve owners are offering counterparties an improved potential for capital appreciation to counterbalance the diminished liquidity return on reserves.

Another way to describe this trade is that reserve owners must create some inflation, or a higher price level, in order to attract interested buyers. From this higher plateau, prices will rise at a much slower rate than before, or, put differently, the purchasing power of reserves will fall much slower than previously expected. The new expected price trajectory of reserves may even be a deflationary one—the market anticipating prices tomorrow to be lower than those today. In any case, only when the expected capital gain on reserves has been sweetened enough to sufficiently compensate would-be owners of reserves for bearing their diminished liquidity return will potential counterparties be willing to trade away their existing assets for reserves.

So back to our initial question: does QE reduce inflation? Not quite. By diminishing the liquidity return on reserves, QE reduces *expected* inflation. This change in expected inflation occurs via a leap in inflation in the present. Subsequent rounds of QE will continues to breed inflation and lower expected inflation until the liquidity return has been reduced to zero, at which point further QE will have no effect.

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But let's introduce another wrinkle. What happens if other assets also carry a liquidity return? And let's assume that there are different kinds of liquidity returns, so that the liquidity services provided by one asset can't be easily substituted with the liquidity services of another. Thus, when the economy is flooded with reserves and their marginal liquidity return hits zero, the liquidity return on alternative assets needn't also decline to zero.

Let's take up where we left off. QE has reduced the liquidity return on reserves to zero and subsequent rounds of QE no longer cause inflation or reduce expected inflation. Let's assume that short term bills, specifically those issued by, say, Microsoft, provide a unique set of collateralizability services, and therefore yield a liquidity return > 0.

When our central bank purchases Microsoft bills, the supply of Microsoft collateral in the economy shrinks, which increases the liquidity return on Microsoft bills. The total return on Microsoft bills, the sum of their liquidity return and expected capital gain, is now superior to all other assets. This spawns a mass effort by investors to sell other assets for Microsoft bills. The only way that existing bill owners will agree to sell away their superior yielding Microsoft debt is if potential buyers offer to pay a higher price. As short term Microsoft bill prices are bid up, the expected capital gain on bills is reduced, counterbalancing the higher liquidity return. At some appropriately higher bill price, the total expected return on bills will be reduced to a level competitive with all other assets, restoring equilibrium.

This process, however, doesn't have any impact on inflation. All that is happening is that the relative price of a certain asset—the short term Microsoft bill—is rising.

Subsequent rounds of QE will further reduce the supply of short term Microsoft bills, increasing their liquidity return and eventually driving their price above par. At any price above par, capital returns on bills are effectively negative—bills, after all, never pay out more than their par value. People will continue to be attracted to a <0% yielding short term bill as long as it sports a sufficiently large liquidity return. The latter can outweigh the negative capital return, providing a total return that is competitive with other assets.

One problem with QE is that it drives the price paid for the liquidity service on Microsoft short term bills above the cost that Microsoft must incur in maintaining those liquidity services. People are effectively paying more to enjoy Microsoft liquidity services than they would in a competitive economy in which prices are pushed down to the cost of production. The artificially high price for bills that has been caused by QE incentivizes people to acquire a smaller flow of Microsoft liquidity services than they would otherwise prefer. This represents a deadweight loss to the economy, or what is termed an allocative inefficiency by economists. The surplus that consumers enjoy is smaller than it would be in a world in which large scale purchases of Microsoft bills had not pushed their liquidity return to artificially high levels.

This loss of allocative efficiency, however, does not equate to deflation. While QE involving Microsoft bills may not be ideal for the economy, it doesn't cause the price level to fall.

Given QE's effect on Microsoft bills, it would be odd if Microsoft did not choose to continually issue new short term bills until the marginal value of liquidity services yielded by bills was driven back down to the cost of maintaining those services. This would goose Microsoft's profits while simultaneously increasing the consumers' surplus, removing all of the inefficiency created by QE.

However, if the issuer of these unique collateralizable bills is the government, not Microsoft, things might be different. Because the government isn't profit-driven, it may be less motivated to issue new bills and reduce the allocative inefficiency created by QE. Is this a big deal? The excess of liquidity's price over cost is similar to any other monopolistic distortion, take for intance the diamond or potash oligopolies that price their products above cost. Situations like these are unfortunate, but I'm not so sure that they have large macroeconomic consequences. The benefit of not doing QE because one might create inefficiencies in a few lone markets for collateral are surely not as large as the benefits of doing QE in order to boost the economy's price level.

So the best I can do in my mental meandering is that QE either produces inflation or is irrelevant. It does not cause lower inflation or deflation. The by-product of any QE-inspired jump in inflation is lower *expected* inflation than before. A few inefficiencies may be created in various markets targeted by purchases, but as interesting as these inefficiencies are I don't see how they produce severe macroeconomic consequences.

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*For the sake of simplicity I assume that reserves don't pay interest.