## Monday, August 12, 2013

### More Perils

In mid-2010, Jim Bullard wrote "Seven Faces of the Peril," which reflected fears at the time that the U.S. economy could be sucked into a long period of deflation such as had been experienced in Japan. Bullard's proposed solution to the problem, quantitative easing (QE), subsequently became a cornerstone of U.S. monetary policy. Bullard's reasoning was as follows. Think in terms of the long run, abstracting from any nonneutralities of money. In the long run, the Fisher relation holds, or

(1) R = i + r,

where R is the short-term nominal interest rate, i is the inflation rate, and r is the real interest rate. Assume that r is a constant. The central bank follows a Taylor rule, of the form

(2) R = max[ai +(1-a)i* + r,0],

where a > 1 is a constant and i* is the target inflation rate. In the Taylor rule, the nominal interest rate cannot fall below the zero lower bound (ZLB). This is a little different from Bullard's nonlinear Taylor rule, but it's the same idea.

In the first figure, (1) and (2) produce two long run steady states, A and B. Point B is the desirable steady state, from the central bank's point of view, as the actual inflation rate is the target rate. But there is another steady state, point A, at which the inflation rate is -r. In a large class of monetary models, point A is the Friedman rule, and r is the rate of time preference, so typically r > 0 and point A is a deflationary steady state. In some of the published work that Bullard cites in his paper, principally Benhabib et al., there are examples where "most" dynamic paths lead to A. Thus Bullard's concern.

In mid-2010, Bullard expressed his concerns, and QE2 (purchases of a total of \$600 billion in long-maturity government debt by the Fed) began in the fall of 2010 and proceeded into mid-2011. The next chart shows the path of the year-over-year pce inflation rate.
As you can see, inflation rose during the QE2 period, and the Fed's approach appeared to be a big success, at least on the inflation side.

But how are we supposed to think about the first figure above, now? New Keynesians (NKs), who are driving Fed policy currently, seem to have settled on a story about what is going on. In the NK story, there was a "real" shock to the economy - that's the financial crisis. That shock is highly persistent. NK models typically don't have much going on of a financial nature, so that's captured as a preference shock - a decrease in the rate of time preference, or in r, in our parlance. Thus, the financial crisis shock becomes a contagious attack of patience.

Figure 2 is the market for nominal bonds, which plays a crucial role in a NK model. Nominal bonds are in zero net supply in equilibrium, and the demand for nominal bonds is increasing in the actual real interest rate ra. The "natural real rate," in NK parlance, is r, which is lower than the equilibrium real rate. Why? In terms of how the FOMC collectively thinks, prices are sticky, the anticipated inflation rate is a constant (expectations are "anchored"), so the real rate of interest cannot go lower because the nominal rate is at the zero lower bound. What has to adjust is the demand for bonds, which falls enough to give an equilibrium at A through a reduction in current consumption. Thus, there is an "output gap."

Though the contagious attack of patience is a persistent shock, apparently, the output gap in NK models is not so persistent. Suppose the nominal interest rate stays at the zero lower bound. As prices adjust, the output gap falls, and the real rate falls to the natural rate r in the figure. Once prices have adjusted, the equilibrium is at B. The output gap has gone away, and the inflation rate has risen.

Until mid-2011 (see the inflation chart above), things seemed to be working according to plan. The inflation rate rose as QE2 proceeded, until mid-2011, but then began to fall, and has continued to do so, on trend. Though real TIPS yields fell, employment growth and real GDP growth remained stubbornly slow. In this instance, a thinking NK person - call him or her NKT - might start thinking there is something missing in the theory that he or she would have to account for. NKT might think that, by 2011, prices had done most of their adjusting. In this person's mind, the sluggish employment and GDP growth no longer represented a sticky-price output gap, but something else. Real GDP could be low because of frictions and inefficiencies that monetary policy might be able to resolve. Or maybe this sluggishness in real economic growth either could not, or should not, be the object of monetary policy actions. In any case, NKT was confused, and in order to be un-confused, he or she went to work to find out what was going on.

But, while NKT was doing his or her work, the FOMC was meeting and wondering what to do. They needed to explain things on the spot, and make policy decisions. What seems to have taken hold is a form of Old Keynesianism (OK). In OK, you can explain essentially anything, and almost any policy can be justified - everything is OK. Without scientific discipline, anything goes. According to OK, high unemployment relative to trend always represents an output gap (an inefficiency); if inflation does not seem to be falling enough given how big you think the output gap is, then there must be some costs that are preventing it from falling more; whatever might reduce nominal interest rates at any maturity is a good thing, etc. Ultimately, given its frustrated attempts to reduce the output gap it thinks it sees, the Fed has resorted to further QE experiments, and increasingly elaborate forward guidance.

In the meantime, NKT might have come up with the following idea. By early 2012, inflation was down to 2%, and we were almost four years past the financial crisis, so the effects of price stickiness as related to the financial crisis shock had pretty much played themselves out. But, for whatever reason, the real rate of interest was still low. NKT read Bullard's 2010 paper, and might have been thinking that the situation in 2012 looked like Figure 3. In the figure, the Taylor rule is now

(3) R =ai + (1-a)i* + re,

where re is what the Fed thinks the long run real rate of interest is. The long-run real rate has fallen to r1, and so now instead of two equilibria, we have one, at point A in the figure. Fortunately, at the zero lower bound the inflation rate is i*, the target.

But, NKT says, what's going on now, in 2013? NKT is beyond thinking about contagious attacks of impatience and is pondering why the real rate of interest should be so low. NKT is thinking about incomplete markets models, borrowing constraints, private information, banking, limited commitment, and New Monetarism. He's read Rocheteau, Wright, Lagos, yours truly, etc. So, NKT thinks, maybe the real rate is low because the financial crisis effectively destroyed the value of some private assets and the sovereign debt of some countries as collateral and in financial exchange. So, there is a low supply of safe assets, which makes the price of those assets high and their real rates of return low.

But, as the financial sector mends itself, and debt problems get resolved, the scarcity of safe assets starts to go away. If the real rate rises from r1 to r2, and the Fed keeps the policy rate at the zero lower bound (and still thinks the real rate is re), we go to an equilibrium at B, with a lower inflation rate.

Further, as NKT reasons, we open up another possibility, which is an equilibrium at C. This results if the private sector anticipates a high inflation rate above i*. The Fed continues to think that re is the long-run real interest rate, and attempts to fight inflation above the target rate, by raising the nominal rate of interest to a level that simply validates the high inflation.

If NKT were really ambitious, however, he or she would have come to the Summer Workshop on Money, Banking, and Payments, at the Chicago Fed. If NKT read this paper, he or she might reason as follows. You can construct examples, using the model in that paper, where the actions of the central bank link the inflation rate to the real rate of interest. Instead of the Fisher relation in equation (1) above, you get (in the example):

(4) R = g(i) + i,

where g(i) is an increasing and concave function, with g(i) < r for i < i**, and g(i) = r, for i >= i**, for i** sufficiently high. In this case you get the equilibrium at B (zero lower bound), and a high-inflation equilibrium at D, with even higher inflation than what NKT finds if the real rate is independent of inflation.

So, if the real rate continues to rise, and the Fed keeps to its current forward guidance commitment, the inflation rate will continue to fall. Under these circumstances, the Fed simply cannot increase inflation without increasing the policy rate - the nominal interest rate on reserves in this case. You can't be in denial about Irving Fisher. But the Fed could gets things wrong in another sense. If it underestimates the actual real rate in the future, and adheres to typical Taylor-rule thinking, then there is a risk of high inflation - the Fed beating its head against the wall in thinking it is tightening, but actually sustaining the high rate of inflation. So there's pre-threshold risk on the low side, and post-threshold risk on the high side.

Modern macroeconomics supports the idea that commitment by policy makers is a good idea. But commitment to what? In the case of simple Taylor rules, there are problems. (i) How do we know what the output gap is? (ii) The short term real interest rate is not a constant in the long run, but reflects how short-term government debt is used in transactions and as collateral. (iii) The Taylor rule may have poor long-run properties.

Rules may not be a good substitute for knowing what is going on.

1. As I was beggining to read your post (which I think gives an incredible insight and is really well explained, even to me, an undergraduate), I drew this conclusion right away: wouldn't it be contradictive then that they are lowering interest rates thereby increasing demand for bonds wich in theory would damage demand for goods and amplify the output gap? This holding everything else constant, but even with other outputs to the model it would still hold the recovery back. I guess this is what you ended up saying?
Thank you for the blog and for this post.

1. I guess what you should take away from this are two things:

(1) There can be important factors influencing interest rates other than central bank policy, even in the long run. Sometimes central banks ignore those things, and that can lead them astray.
(2) Unemployment is currently high, and growth in employment and real gdp is currently low, but it seems unlikely that this is an output gap - i.e. an inefficiency - caused by some sticky-price Keynesian phenomenon associated with the financial crisis. Unemployment is high and growth sluggish for other reasons that we may or may not understand, and that may or may not be amenable to macro policy solutions. Understanding that can help us understand what is going on with inflation, for example.

2. Right, what I said was complete non-sense.
But you say that before (or while) getting to A "What has to adjust is the demand for bonds, which falls enough to give an equilibrium at A through a reduction in current consumption.". Shouldn't the demand for bonds actually have to rise to make the real rate an equilibrium rate?

3. No, greater patience increases the demand for bonds - people want to save for the future they now like so much. But, effectively, in the NK story the price of bonds can't adjust (the price wants to go up - i.e. the real rate wants to go down), so something else has to adjust to reduce demand. In the NK story, what adjusts is current consumption - it goes down.

4. Got it, thank you!

2. Jim Hamilton would maybey say the real shock was oil, which hit almost \$150/barrel in 2008. The financial crisis was a symptom.
Is it a coincidence that most postwar recessions followed oil price spikes ?

1. You could also say that the financial problems leading up to the crisis were the "shock" (speaking loosely), and the oil price path was one of the symptoms.