Inflation and the "Risk-Free" Interest Rate

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grondeau's picture
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Inflation and the "Risk-Free" Interest Rate

Two years ago, with the price of oil at all time highs, there was concern that we could start seeing run-away inflation again.  A few months later, the financial system was on the verge of a total meltdown, credit dried up, and the specter of  a deflationary spiral appeared on the scene as oil fell to a third of its peak price.  Gradually, the economy seems to be righting itself, but the turmoil has left us with ever larger government debt.  With all this going on - I'm going to ask a few simple questions with the hope that finding the answers will also bring insight to the bigger questions.

In our credit-based economy you need to have borrowers and lenders making transactions to keep the liquidity flowing in the economic engine. The parties have to agree on the time value of money - that is - the interest rate. How do they do that?

Risk-Free Interest Rate

What should the risk-free interest rate be?  That's the question I'll started with.  Central banks, the FED in the U.S., adjust interest rates to achieve economic goals, but central banks cannot impose interest rate policy without  investors willing to buy bonds at the rates set by the central bank.  Hence, the question - from the perspective of both the bond holder and the investor, what should the risk-free interest rate be?

A low-risk investment will be short-term.  Uncertainty of  future events adds risk.  Inflation puts a lower limit on the interest rate a bond holder will tolerate.  Since we are talking about short-term loans, it is the current inflation rate that is important.  A bond holder could loan money short-term at just the current inflation rate but an investor would almost guarantee a positive return if he could procure funds at precisely the rate of inflation.   All he would have to do is invest in the "average" economy, which has quite a "risk-free" long-term growth history.  Hence, there would be a large demand for money at just the rate of inflation.  Rather, this reasoning would suggest that the "correct" risk-free short-term interest rate - the rate where neither lender nor borrower can see immediate profit, would be the current rate of inflation plus the long-term real GDP growth rate.   Long-term trends for GDP and population are shown on the chart below.

Growth Trends

The relentless GDP growth, here shown on a logarithmic scale, averaging merely 1% above population growth, is arguably the reason for our affluent standard of living.  The booms and busts that make the headlines are the wiggles on the graph that seem barely significant compare to the relentless growth.  For the curious I included total U.S. energy consumption on the chart as well.  Before the oil shocks of the 1970's, energy consumption was growing at about the same rate as the overall economy.  Since then energy consumption growth has more closely followed population growth.

Federal Funds Rate and Risk Free Market Rate

To test the hypothesis that the natural level of short-term interest rates should be about equal to inflation plus trend GDP growth, I made the chart below from data available from several sources. (BEABLSFed) The best proxy for the "risk free" loan rate is the overnight federal funds rate.  Keep in mind that the Federal Reserve can have other agendas as well as providing a market for short-term funds.

Also plotted in green is the percent change in annual GDP.  This is an amplified version of the little wiggles on the GDP line in the first chart.  Trend GDP growth at 1.35% is the orange line.  The two pink bars show the major oil price shocks that hit the economy.

Note that indeed the Federal Funds rate, in red, closely approximates the inflation rate plus 1.5% trend GDP which I'll call the "market rate", shown in purple.  During the 60's and early 70's the fit is very close. In the mid 70's, Arthur Burns was Fed chairman under President Nixon.  In the recession brought on by the oil shocks, Burns dramatically cut rates in an effort to spur the economy.  Loose money and high oil prices dramatically drove inflation through the roof.  We can see the onset of modern monetary policy that began in earnest with Paul Volker as fed chairman in 1980.  The Fed pushed interest rates significantly higher than the market rate (purple), and kept them there for several years in order to bring down the high inflation that started under Burns.

Fed Policy and Taylor Rules

The Fed sets interest rates based upon a two main policy goals.  They need to keep inflation under control and can raise rates to shrink the money supply to accomplish this goal.  They also need to keep the economy at "full output", keep people employed, and keep the economy growing.  On the chart above, when the red line is above or below the purple line, the Fed is trying to push or pull the economy one way or another.  During the boom years of the late 90's the Fed kept the funds rate slightly above our market rate to prevent the economy from overheating and fueling inflation.  With the dot-com bust at the turn of the century, the Fed dropped the funds rate below the market rate in an effort to stimulate the economy, spur full employment and pull the nation out of recession.  Every month the Fed's Board of Governors  sets the current interest rate.  How they decide, no one knows for sure, but observers have come up with empirical rules that closely agree with the Fed's actions.

One version of the Taylor Rule, as it is known, says that

Target fed funds rate = 2.07 + 1.28 x inflation – 1.95 x excess unemployment

The Fed has only one knob that it can turn in its effort to control two variables -- inflation and excess unemployment.  During a normal business cycle a downturn generates unemployment, depressed demand, and less inflationary pressure.  As the Taylor rule dictates, the Fed would decrease the Funds rate in these circumstances.  Similarly, during boom times we have full employment, commodity bubbles easily form, and inflation will rise as demand outstrips supply for goods and services.  The Fed's response is to raise rates so as to put a crimp on the availability of easy money that fuels such a boom.


The problem comes when there is high inflation as well as high unemployment.  Stagflation struck after the oil shocks in the 70's.  The Fed's initial response was to let rates rise with inflation, but to keep rates slightly below the market rate in an effort to move the economy out of the recession caused by the oil shocks.  This laissez-faire approach allowed inflation to get out of hand, and by the end of the second oil shock inflation was running at 14% per year and took Volker's extraordinarily high interest rates to bring on yet another recession that was needed to bring the inflation under control.

The success of that policy started the new era of active monetary control by the Fed that we have to this day.  But it doesn't always get it right.  The very low rates in the early 00's are now seen as part of the reason the real estate bubble was able to grow so large.

When oil prices were rising rapidly in 2008, there was fear that another round of inflation, or worse yet stagflation, was imminent.  That never happened, however, because we never really had a supply shock.  Prices reach very high levels and consumption dropped, but the supply was always there.  There were no gas lines this time.  The collapsing housing market and the resulting financial crisis quickly led to a recession, demand for oil evaporated, and with it any concern about inflation.

Fed Funds Spread

The last chart shows the spread between the Fed Funds rate and our "risk-free" market rate along with a few historical notations.  It has been argued that the easy money policy of the Burns Fed was responsible for the very high inflation in the 80's.  This certainly was the largest period of protracted stimulus on our chart.

The Zero Bound

With the recent downturn, the Fed has new challenges.  The Fed Funds rate has reached zero.  The Taylor Rule suggests that the Fed Funds rate should be at a negative 5% or there about.  But interest rates can't be negative, so the Fed's influence on the economy via this interest rate is limited. This is the so-called "Zero Bound", and we have hit it.  On the last chart, we notice that despite the severity of the present economic recession, the spread is barely in the green.  As a result, the Fed had to come up with a multitude of "extraordinary" facilities to inject more money into the falling economy during the height of the crisis.  One of the largest programs was the purchase of mortgage-backed securities to the tune of a trillion dollars.


Despite the simplistic model for a risk-free market rate, many of the Fed's policy goals can be better understood by looking at this rate spread than by absolute interest rates.  Presently low inflation is hampering the effectiveness of the usual interest rate mechanism for injecting money into the economy by stimulating private bank lending.

JAG's picture
Status: Diamond Member (Offline)
Joined: Oct 26 2008
Posts: 2492
Re: Inflation and the "Risk-Free" Interest Rate

Nice post, and I like your blog as well. 

One question though, what does this analysis imply for the future of interest rates? It wasn't clear to me.  I did understand your Tomato Futures post however, lol.


grondeau's picture
Status: Bronze Member (Offline)
Joined: Nov 10 2008
Posts: 35
Re: Inflation and the "Risk-Free" Interest Rate


I do better at predicting the past...  That said, the Fed has demonstrated that it can bring down inflation by raising interest rates high enough to cause a recession.  In quasi normal times, I'm sure the Fed could do the same thing again.  Control is more difficult on the deflation side because of the zero bound.  

If I was in the drivers seat, I would shoot to hold inflation at about 4% for the foreseeable future.  That's a bit higher than current targets, but it gives more leverage on the deflation side when that become necessary.  It also allows for positive nominal returns on savings accounts, etc. even if GDP growth goes to zero.  Psychologically, positive nominal returns, even if negative in real terms, are more acceptable than overt losses.


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