Monthly Archives: August 2010

What Happens When the Interest Rate is Fixed?

Narayana Kocherlakota, president of the Minneapolis Fed made the following statement in a speech last week:

Long-run monetary neutrality is an uncontroversial, simple, but nonetheless profound proposition. In particular, it implies that if the FOMC maintains the fed funds rate at its current level of 0-25 basis points for too long, both anticipated and actual inflation have to become negative.

This set off a firestorm of criticism among a variety of folks in the blogosphere (just do a quick Google search). With that in mind, I thought that I would revisit an influential paper on the topic.

In 1992, Peter Howitt wrote a paper entitled, “Interest rate control and nonconvergence to rational expectations.” The purpose of the paper was to illustrate to many economists at the time the central insight of Wicksell’s cumulative process in which the control of interest rates by the central bank might lead to accelerating inflation (or deflation).

To illustrate this point, he used a model with the following two equations (an IS equation and a Phillips curve, respectively):

y(t) = -a[i(t) - pe(t) - r*]

p(t) = pe(t) + by(t)

where y(t) is output, i(t) is the nominal interest rate, pe(t) is expected inflation, r* is the natural real rate of interest, p(t) is inflation, and a and b are parameters.

Now suppose that the central bank decides to leave the interest rate fixed at ‘i’. Under rational expectations, in which p(t) = pe(t), there is one unique solution:

p(t) = p(t)* = i – r

where p(t)* is used to denote the rational expectations equilibrium rate of inflation. Thus, if the nominal interest rate is fixed at zero, the rate of inflation that prevails is

p(t) = -r

This seems to be where Kocherlakota is getting his conclusion. According to the model, under rational expectations the equilibrium inflation rate will be negative.

Now suppose that rational expectations does not hold. What will happen to inflation? Typically, it is assumed that even in the absence of rational expectations, individuals are able to learn from their forecast errors and therefore they ultimately end up at the ratex solution. Thus, it is important to consider what would happen in this model if forecast errors exist.

To obtain the possible forecast error, we can replace i(t) – r* in the IS equation with p(t)*, the rational expectations equilibrium solution. Now combine the IS equation and the Phillips curve by substituting for y in the Phillips curve. Doing so allows us to express the forecast error as follows:

p(t) – pe(t) = ab[pe(t) - p(t)*] (1)

Now suppose that the central bank sets the nominal interest rate such that the real rate of interest is lower than the natural rate of interest. Wicksell argued that in this scenario accelerating inflation would result. How can we test this in our model. Well, if the real rate of interest is less than the natural rate it must be true that:

r < r*


i – pe(t) < i – p(t)*

and thus

pe(t) > p(t)*

In other words, if the nominal rate of interest is set by the central bank such that the real rate of interest is lower than the natural rate, inflation expectations will be greater than the rational expectations equilibrium rate of inflation. Returning to equation (1), if inflation expectations are higher than the rational expectations equilibrium rate of inflation, the actual rate of inflation will be higher than the expected rate of inflation. If we assume that individuals have adaptive expectations, this means that they will revise their expectation of inflation upward. The importance of this finding is that even if individuals are able to learn from their forecast error, they will be led AWAY from the rational expectations equilibrium. In other words, it will not follow that expectations will eventually converge on the rational expectation.

So why is any of this important? Isn’t Kocherlakota simply claiming that we live in a world of rational expectations, which most macroeconomists endorse use?

It is important because Kocherlakota subsequently makes this statement:

If the FOMC hews too closely to conventional thinking, it might be inclined to keep its target rate low. That kind of reaction would simply re-enforce the deflationary expectations and lead to many years of deflation.

This statement seems to imply that the Fed should start thinking about raising interest rates. However, unless individuals have rational expectations from the outset (they perfectly forecast inflation), raising the interest rate is likely to push the real rate of interest (further) above the natural rate thereby causing (accelerating) deflation.

[A quick note: Howitt's finding is robust to different learning mechanisms and to a flexible price framework. Interestingly enough, Howitt actually identifies what has come to be known as the Taylor principle in this paper as well.]

Signs of Tight Money?

Even David Beckworth’s undergraduate students are forecasting lower nominal GDP.

Unemployment Benefits

In a couple previous posts (here and here), I considered the claim that unemployment benefits are stimulative for the economy. My focus mainly centered on the determinants of consumption and disregarded the discussion regarding the disincentives to work. My position on the latter has always been that if you lengthen the duration of unemployment benefits, you will increase the average duration of unemployment at the margin. This is straightforward economics.

Today, Robert Barro considers the effects of disincentives to work in the WSJ:

The peak unemployment rate of 10.1% in October 2009 corresponded to a mean duration of unemployment of 27.2 weeks and a share of long-term unemployment of 36%. The duration of unemployment peaked (thus far) at 35.2 weeks in June 2010, when the share of long-term unemployment in the total reached a remarkable 46.2%. These numbers are way above the ceilings of 21 weeks and 25% share applicable to previous post-World War II recessions. The dramatic expansion of unemployment-insurance eligibility to 99 weeks is almost surely the culprit.

This is the important point in the debate. It is likely that a number of individuals have increased the duration of unemployment at the margin due to the lengthening of benefits. I do, however, remain skeptical that the magnitude of the effect is as large as Barro claims.

Finally, I would point out that it is not necessarily a bad thing for the duration of unemployment to increase if it ultimately results in a better match between the skills of the worker and the firm than would have otherwise taken place. Of course, this last point is nearly impossible to determine.

The Death of the Federal Funds Rate?

I referenced a paper nearly a month ago by Michael Woodford and Vasco Curdía that examined the Federal Reserve balance sheet as an instrument of monetary policy. Hopefully, I will have some time soon to briefly discuss the dynamics of their model. Nonetheless, the recent behavior of the Federal Reserve has been considerably different than in the past. Since the federal funds rate reached (or nearly reached) its zero lower bound, the Federal Reserve enacted a number of measures through the expansion of its balance sheet. As Benn Steil and Paul Swartz note in a recent op-ed in WSJ Europe, this poses interesting questions about the exit strategy of the Federal Reserve, in particular, the role of the federal funds rate:

Between August and November 2008, the Federal Reserve swelled its balance sheet to $2.2 trillion from $940 billion to ease a potentially catastrophic credit crunch brought on by fears of cascading defaults. The assets added to the balance sheet are today comprised overwhelmingly of mortgage securities. The purchase of these securities had the parallel purpose of shoring up a collapsing housing market.

Much of the money the Fed conjured to buy these assets made its way into reserves, which the banks chose to hold at the Fed. Excess reserves—reserves held above and beyond what the Fed requires of the banks as a minimum—soared to more than $1 trillion from $2 billion.

As long as this money remains parked at the Fed, it poses no risk of fuelling inflation—just like cars parked in garages can’t tie up traffic. But at some point the banks will muster the courage to begin transforming these near zero-yielding reserves into credit, and the Fed knows it then will have to act to prevent exuberance from pushing up prices too far and too fast—in traffic terms, to stop the cars from streaming onto the roads all at once.

In normal times, the Fed would do this by selling Treasury securities from its balance sheet, which the banks pay for using the excess dollars they’ve parked in reserves. Those dollars are then no longer available to the banks to create credit.

But these are not normal times. The Fed doesn’t have an excess stock of Treasurys to sell—its holdings are at roughly what they were before the crisis. It has only a vast excess pile of politically toxic assets—the mortgage securities it has amassed since 2008. Dumping them would depress the housing market further by pushing up mortgage rates and enrage an already Fed-wary Congress.

So what will the Fed do? Chairman Bernanke has been anxious to assure the markets that he has other tools in his chest, two in particular. The first is to entice the banks to move a portion of their reserves to term deposits, which would lock up that money for a fixed period. The second is to use “reverse repos,” in which the Fed continuously borrows money from the banks, using its Treasury securities as collateral. Both strategies soak up reserves.

But both strategies have a hidden “catch”—the Fed will lose control over interest rates. Since 1994, the Fed has announced its so-called fed-funds target rate, or the rate at which it intends to see banks lend reserves to each other overnight. By buying or selling securities, the Fed jiggers interest rates to keep them at the target. But if the Fed is no longer willing to sell securities to tighten policy, and if it is instead determined to drain a specific quantity of reserves through term deposits, it will have to pay whatever rate the market demands. Logically, then, the fed-funds rate will mechanically shadow the term deposit auction rate.

Reserves have always been the tool of the Federal Reserve through open market operations. The Fed has, for some time now, targeted the federal funds. What this means is that the Fed accommodates fluctuations in the demand for reserves with corresponding changes in supply in order to keep the federal funds rate at its target.

With the federal funds rate at the zero lower bound, the Fed has used a number of other means to conduct monetary policy as Steil and Swartz detail above. A number of people have pointed out that, with the federal funds rate effectively at zero, the Fed can use the interest paid on excess reserves as a policy tool. However, I believe that a number of these individuals have missed the fact that this change in policy tools involves a significant change in operating procedures.

The Fed does not directly control the federal funds rate. As a result, the Fed adjusts the level of reserves to maintain its target. The Fed does, however, control the interest rate on excess reserves. As a result, they can change the interest rate to adjust the level of bank reserves. There is a significant difference in policy. In the first scenario, the Fed is adjusting bank reserves to change the path of the federal funds rate. In the second scenario, the Fed is adjusting the interest paid on excess reserves to change the path of bank reserves. As a result, the size and composition of the Federal Reserve’s balance sheet is increasingly more important. In fact, one could argue that the Fed’s balance sheet will be a better indicator about the path of monetary policy than the federal funds rate — even after the funds rate rises above the zero lower bound.

Another Quick Announcement

I apologize for the light blogging lately. I am in the process of moving my office as I have taken a visiting position at the University of Toledo for the 2010 – 2011 academic year. For those interested, here is my current contact information:

Josh Hendrickson
Department of Economics
University of Toledo
4110-H University Hall
2801 W. Bancroft
Toledo, OH 43606
joshua {dot} hendrickson {at} utoledo {dot} edu

Congrats to Bill Woolsey

I have been very busy as of late, but I need to extend congratulations to our friend Bill Woolsey, who was elected mayor of James Island, South Carolina last week.