Narayana Kocherlakota is now blogging. His most recent post concerns the equilibrium rate of interest, or natural rate of interest as it is sometimes referred. Kocherlakota argues that those who would like to see higher interest rates should stop harping on the Federal Reserve and instead write their Congressman to encourage more fiscal stimulus. I think that this view is both conventional and also odd. Allow me to explain.

Consider the following simple thought experiment. Suppose that the market rate of interest targeted by the Federal Reserve, the federal funds rate, is equal to the equilibrium rate that would prevail in a perfect, frictionless world. We can think of this equilibrium rate as being the rate consistent with a consumption Euler equation. In particular, this implies that the real rate of interest is given by

Real natural interest rate = Rate of time preference + Expected Growth

Now suppose that the economy enters a recession and expected growth declines. This implies that the natural interest rate declines also. If the central bank stands firm and does not adjust its target for the federal funds rate, then monetary policy is too tight. The market interest rate is above the natural interest rate. In a standard Wicksellian world the fact that the market interest rate is "too high" would imply a further reduction in the economic activity, which would further reduce the natural rate of interest. Again, if the central bank continues stand firm, monetary policy actually tightens. The implication is that the central bank can passively tighten even though they haven't taken any action. In the pure credit economy of Wicksell, this process would continue to produce a deflationary spiral until the central bank equated the market interest rate with the natural rate.

Note this important point. In the Wicksellian model, there is an accelerationist effect. The accelerationist effect is due to the fact that tight monetary policy actually reduces the natural rate. Thus, to get back to normalcy what the central bank needs to do is not only to lower the market interest rate, but to lower the market rate *below* the natural rate. Once they do this, economic activity starts to increase and therefore so does the natural rate. To get back to normalcy, the central bank then has to increase the market rate faster than the natural rate is increasing until the two ultimately converge.

Note that this seems to be an odd way to conduct monetary policy. For example, imagine that you have a bow and arrow and there is some target in the distance. Suppose that every time you move the arrow to adjust your aim, the target moves as well. Nonetheless, this is the basic concept behind the Wicksellian model.

Kocherlakota argues in his post that the natural rate of interest is too low and that the market interest rate cannot get low enough to accomplish the task described above to correct for previously tight monetary policy. As a result, we need our Congressmen to go out and pass legislation that will get the economy moving and raise the natural interest rate toward the market interest rate.

I find this view strange for several reasons. First, in a Wicksellian framework if the natural interest rate is below the market rate, this results in a deflationary spiral. Since this seems to be Kocherlakota's model of choice, how does he explain the economic recovery? Second, standard economic theory suggests that the natural interest rate is the sum of the rate of time preference and expected growth. Real GDP growth (and expected real GDP growth) has been positive for some time. Even if we ignore my first point, why hasn't this increase in growth led to an increase the natural interest rate?

My answer to these questions is that the federal funds rate essentially becomes a useless indicator at the zero lower bound. Quantitative easing is just open market operations by a different name. To demonstrate this, consider that measures of the so-called shadow federal funds rate have actually plummeted far below zero. Estimates of the shadow rate come from the framework initially described by Fischer Black in his paper "Interest Rates as Options." In that paper, Black pointed out that the benefit of holding short term debt is that it includes an option to switch to currency if the yield ever becomes negative. What this implies, however, is that while the market interest rate can never go below zero, it is possible to estimate a shadow rate when the observed market rate hits the zero lower bound. Estimates of the shadow rate have gone as low as -3%. If we are to believe this methodology, what this says to me is that quantitative easing succeeded in doing what monetary policy was thought not to be able to do.

One could argue perhaps that the rounds of QE did not go far enough. For example, for the central bank to produce a significant recovery, the Wicksellian model suggests that the central bank must not only reduce the market interest rate, but that they should reduce the market interest rate below the natural rate. If they simply reduce the market rate to the natural rate, then this just stops the decline in economic activity rather than providing some catch-up growth.

Regardless of whether you believe that latter claim, this post essentially makes the following claim. If I am correct in saying that the shadow rate is preferable to the federal funds as an indicator of monetary policy, then even if you believe in the Wicksellian model, you needn't believe that we need to have to rely on fiscal policy to raise the natural rate of interest. What my discussion implies is that the central bank need only to lower the shadow interest rate below the natural rate.