# Visualizing Paths with the Short-run Natural Real Rate… via Miles Kimball

I wrote a post with many graphs to visualize the various paths that interest rates can take in order to normalize monetary policy in the Long-run. (link to previous post) Here is a basic graph from that post… To recap… Nominal rates on the y-axis. Real rates on the x-axis. Up-sloping lines represent constant rates of inflation. Inflation increases Northwest in the model.

The basic equation guiding the model is the Fisher equation…

Nominal rate = real rate + expected inflation

The vertical dashed line represents the Long-run natural real interest rate at any nominal rate. The Long-run natural real rate is independent of monetary policy and inflation (at least in theory, but there are qualifications to that which I will not go into here.) The yellow star represents where the Long-run natural real rate crosses the inflation target of a central bank. The blue star shows where the US economy is now. The blue star would like to get to the yellow star in the Long-run.

### OK… Now Bring in Miles Kimball

Miles Kimball wrote a post in June 2013 (link) defining the difference between short-run and Medium-run natural real interest rates. His Medium-run is my Long-run. He is up-to-date with the terminology. Medium-run is the better accepted term nowadays, so I will use Medium-run for the rest of the post. The graphs show Long-run but they are actually Medium-run.

“The reason I wrote this post is because many people don’t seem to understand that low levels of output lower the net rental rate and therefore lower the short-run natural interest rate. Leaving aside other shocks to the economy, monetary policy will not tend to increase output above its current level unless the interest rate is set below the short-run natural interest rate. That means that the deeper the recession an economy is in, the lower a central bank needs to push interest rates in order to stimulate the economy.” – Miles Kimball

Why is the distinction between Short-run and Medium-run natural real rates important? Short-run monetary policy should seek the Short-run natural real rate instead of the Long-run. So that means that we have to draw a second vertical line in the graph above for the Short-run natural real rate. I have placed the Short-run natural rate below the real rate in the US currently… to show a problem that arises. What is the problem? Well, we would like the blue star to go right toward the yellow star… and we would like economic momentum to build as we move there, but the real interest rate would need to go to the Short-run natural rate on the left first in order to build that momentum according to the logic of Miles Kimball. So how would that happen? How can the real rate go left and right?

### Visualizing Paths Again

I presented this path in the previous post which represents the view of Paul Krugman and others. We see that inflation expectations are increased which lowers the real rate below its Short-run natural rate. Then the economy picks up momentum. Then the Federal Reserve would be able to start raising the nominal rate upon this economic momentum.

Miles Kimball has a path that he favors. He would drop the nominal rate below the zero lower bound at the current inflation rate. His path would be something like this… The advantage to Miles Kimball’s approach is that the Short-run natural real rate is reached quicker and more directly, instead of trying to build change inflation expectations…. which may not even be possible since inflation expectations are so well-anchored.

Another point… As the Short-run natural real rate shifts right toward the blue star during the recovery, there would come a time when economic momentum would appear on its own. Then inflation momentum would appear too. Some Fed officials are waiting for this sign. We would then see conditions building for raising nominal rates. Then the blue star would start heading back to the yellow star in the Medium-run.

### Where might the Short-run Natural Real Rate be?

Have we seen any sign that economic momentum has picked up? Yes… Miles Kimball gives an equation for the rental rate of capital.

• R for the the rental rate,
• K for the amount of capital,
• W for the wage, and
• L for the amount of total worker hours,

RK = constant * WL.

Dividing both sides of this equation gives an equation for the rental rate:

R = constant * WL/K.

His equation is similar to the profit-rate equation I have posted before. (link)

Profit rate = (Productivity – Real compensation) * Total labor hours/Capital stock

Modified Profit rate = Capital share of income * Total labor hours/Capital stock

In both equations, as labor hours increase, so does the rental rate. My point is that labor hours have increased in 2014 with the relatively rapid decrease in unemployment. Thus via Miles Kimball, the rental rate increases, and the Short-run natural real rate shifts right in the graph. Like this… If the Short-run natural real rate has shifted to the right of the blue star, then monetary policy can now start normalizing. Remember that Miles Kimball wrote his post in June 2013. The Short-run natural real rate has certainly moved since then.

However, the question is whether the vertical Short-run natural real rate has crossed the current real rate (blue star) or if it is still to the left of the current real rate.  If it has crossed, then the time for raising the nominal rate would be coming soon. But still, is there enough left in the gas tank of the business cycle to give enough sustainable momentum to reach the yellow star of normalized monetary policy? Or is the US economy too uncertain with Europe, Japan and China slowing down? Or is the fragility of emerging markets to a rise in the US Fed rate slowing down normalization of monetary policy?

If the US falls into another recession, the Short-run natural real rate will shift left again, and monetary policy will have the same problem all over again.

So there are obstacles and uncertainties to normalizing monetary policy even though it may be the time to start doing just that.