(Don't Fear) The Taper

In this blog entry, I explain why I argue that Quantitative Easing (QE) is meaningless for the real economy, and thus why backing away from QE ("Tapering") is not to be feared.

Economists who follow Modern Monetary Theory (MMT) have been arguing this for some time. For example, Bill Mitchell outlined in detail in this article from 2009, Quantitative easing 101, why QE is essentially a pointless exercise.

What I find interesting is that you did not need to resort to heterodox economic theories to understand the logic.  The ineffectiveness of QE can be diagnosed with mainstream models, as I discuss further below. (And in fact, there has been some skepticism about the effectiveness of recent rounds of QE, even within the ranks of the central banks implementing the policy.) The operation of the money markets is highly efficient, so that MMT and mainstream descriptions largely coincide.

It is clear that the initial round of QE, where the Fed purchased risky assets in disrupted markets, was effective. This was an example of the Fed acting as a lender of last resort, which was what the Bank of England was doing more than 100 years ago. It was therefore not a great new innovation in central bank policy, and it reflects the reversal of a what some saw as a previous policy error (the Fed had long ceased operating in private markets, which has isolated the central bank from the conditions in the banking system). But the central bank balance sheet size expansion is a side effect of lender of last resort operations, and not an objective of policy.

But the credit markets have since stabilised, to the point that investors are again chasing yield without heed to the consequences. Why continue the policy of QE? With nominal policy rates locked at the zero bound already, there were few other options legally open to the Fed to stimulate the economy. I was tempted to use the metaphor of saying the latest round of QE is a Hail Mary pass by the Fed. Unfortunately, that metaphor is inapplicable – a correctly executed Hail Mary has a possibility of succeeding. Instead, a better analogy is: The Fed was down by 6 points, 2 seconds left on the clock, and they dropped back into their end zone and punted, hoping that the other team fumbles the ball.

Returning to the question of how we can see that QE is ineffective, we can look at the basic model of the core of the monetary system. Any mathematical model of the economy which attempts to simulate the monetary system will have to model one concept: the weighting of “money” versus interest-paying financial assets in private portfolios. (In a Dynamic Stochastic General Equilibrium (DSGE) model, the “private sector” is the “Representative Household” that undertakes an optimisation problem to maximise its present and future utility.)

If we ignore the other components of the model, at the end of the period the private sector (“representative household”) has to decide how to allocate its portfolio among two financial assets.

	Name In Model	Real World Equivalent	Holding Period Expected Return
	Money	Notes (e.g., dollar bills) and coins.	0%
	Treasury Bills	Treasury Bills (T-Bills)	r%

If the private sector agent is going to optimise the expected return on its financial assets, it is straightforward to see that it should have 0% in “Money” and all of its portfolio in T-Bills (as long as r>0). But a quick glance at real world data shows that households do in fact hold dollar bills and coins, and so some kludges have to be thrown into the model to force the model household to hold money.

Once the kludges are in place, there is a function which describes the trade-off between holding money and T-Bills. The higher the interest rate, the larger the opportunity cost for holding money, so money holdings as a percentage of financial assets drops.  One could determine the trade-off function by either econometric analysis, or arbitrarily imposing a form on the objective function which determines the trade-off. This function creates a direct mapping between “money” and the short-term interest rate in mainstream models. (This makes the models unable to distinguish between the “quantity of money” and the interest rate as policy variables.)

But what about other financial assets, like bonds? Within the context of a simple DSGE model, the expected one-period return for a bond will equal the return for a T-Bill. The representative agent is indifferent between holding T-Bills and bonds, and so it could choose any portfolio allocation between:

•  0% T-Bills, 100% bonds, and
• 100% T-Bills, 0% bonds.

(The household solves an optimisation of the expected utility in most versions of these models, and so risks around expected returns have no impact on the solution.)

This indeterminacy means that there is no unique solution to the optimisation problem, so the bond market has to be abolished from the model (or else another kludge introduced to force a unique weighting). Other financial assets within the model will also be folded into T-Bill holdings for the same reason.

What happened to required reserves? They do not appear in the model. In the U.S., required reserves are a liability of the consolidated Federal government which bear no interest. (In Canada, required reserves were abolished as an anachronism. Yes, the reserve ratio is 0% and loans did not go to infinity.) Required reserves therefore appear to be equivalent to “Money” in my table above. But the private sector is explicitly not allowed to be indifferent between required reserves and money; there is a regulatory constraint to hold them. Therefore, required reserves do not map properly onto the mathematical variables of a DSGE model.  (And since bank lending do not appear in the most basic of the most versions of these models, modelled required reserves would be zero anyway.)

And now we return to the asset created by QE: excess reserves, which do pay interest. These are an asset that have a holding period rate of interest. They are mathematically equivalent to T-Bills, and they would have to drop out of the model in the same fashion bonds do. From the standpoint of a mainstream economic model, the purchase of Treasury assets by the Fed just creates a change of mix between equivalent assets (T-Bills and excess reserves), and thus has no impact on the model solution (e.g., the trajectory of economic variables).

What about the increased ability of banks to “lend out reserves”? This does not happen in DSGE models (where the banking system is generally not modelled), nor in the real world. See the previously referenced article by Bill Mitchell for more details, but in summary, the central bank will always have to expand its balance sheet to meet the demand for required reserves (or cause a financial crisis). Reserves do not constrain lending: bank capital ratios and demand by creditworthy borrowers do. This concept has been very heavily discussed by MMT theorists already, and I have nothing further to add.

In order to come up with some sort of justification for QE, analysts have had to resort to desperate measures: appealing to supply and demand for the determination of interest rates. In a DSGE world, the financial markets are typically assumed to be efficient, and so rate expectations determine interest rates, not supply and demand. But the proposed fix is: by buying Treasurys and Mortgage-Backed Securities, the Fed can force a portfolio reallocation by private investors (alternatively reduce the supply of long duration assets). It is assumed that this reallocation will reduce the observed risk premia in bond yields. There have been new iterations of DSGE models which attempt to model this behaviour.

Unfortunately, there is no good evidence that supply and demand factors have anything more than a trivial impact on the term structure of interest rates.  I will have to look at this argument in a follow-up entry, as that is a big topic.

(c) Brian Romanchuk 2013