The Paradoxes of Perfect Policy

So what if I told you the more expansionary monetary policy is, the smaller the Fed’s expected balance sheet will be. And, more curiously, the smaller the Fed’s expected balance sheet will be, the more expansionary current policy will become. These two forces build off each other into perfectly expansive monetary policy. Let me explain why.

Consider two policies. In one, the Fed continues to buy n dollars of Treasuries and mortgage backed securities each month until its expected loss – at any arbitrary sensitivity to deviation from its dual mandate – is minimized. In the other, the Fed continues to buy n dollars of assets each month but, at the end of the year if its target is missed, n becomes kn. This continues ad infinitum.

You would be mistaken to think these policies are functionally equivalent even in the first year. Even though the monetary base would be the same at month 12 under both, inflation would be higher and unemployment lower under the second. Markets know that if the Fed misses its target, purchases will increase substantially in pace next year, which would drive money demand down in the latter months of the year after it becomes clear the Fed’s mandate is missed.

Of course, since deviation from the Fed’s target is falling more rapidly under the latter policy, the expected time of exit from monetary stimulus is also smaller. If k is large enough, markets would expect the Fed to “taper” purchases before the end of year one.

Hence the expected size of the Fed’s balance sheet is smaller under the more aggressive policy, for some parameters k and n.

This deals with almost all the “negative” aspects of quantitative easing suggested by other critics. When more is less, its safer to do more. The scarcity of safe assets, as many worry, would be significantly lower if the Fed’s balance sheet was smaller. Therefore we should be talking about increasing the extent of purchases to the level where people expect a taper because of too much inflation. It’s like walking in a circle.

But the expansionary nature of this is greater still. Paul Krugman, and most Keynesians, correctly worry that expansionary policy isn’t determined by the size of the Fed’s current balance sheet, but expectations of the terminal money base. That is, because Krugman among others believe markets believe the Fed will vacuum money out of the system in the future, there’s a de facto floor on money demand.

Let’s say the Fed can’t really change expectations of its long run “sensibilities” (tolerance of inflation, etc.) without regime change. (This is a point deeply felt in the work of Christina Romer who should be our next chairwomen of the Federal Reserve). That’s not a perfectly true statement, and the expectations channel of monetary policy is still intact, but it still poses an important “drag” on the efficacy of monetary policy. This implies the market would expect a contraction in future money base proportional with the size of the balance sheet. However, if the expected balance sheet at the end of stimulus is smaller, so too is the expectation of future tightness.

So I don’ t think people like Krugman get it all right when they write that quantitative easing works only through signals of “willingness to be easy”. That’s part of it, but more aggressive quantitative easing not only signals a “willingness” on side of the Fed, but more bullish expectations on part of the market that the Fed won’t tighten, not because it doesn’t want to, but because  it doesn’t have to.

In fact, there’s a sweet spot where if k is high enough, markets won’t expect any contraction in money base at all, because the period of expansion would cause inflation so quickly that the Fed can slowly exit its stimulus program without a bloated balance sheet at all.

Because tapering quantitative easing won’t end it completely, there’s a good chance the Fed’s balance sheet is going to end up far larger than it needs to be. It’s about time for the hawks to call for aggressive easing.