Introduction

I wrote my senior thesis on the Fisher effect – the one-to-one relationship between inflation and the nominal interest rate. Most of us know of the Fisher effect from the Fisher equation:

i_t = r_t   E(pi_t)

where i_t is the nominal interest rate, r_t is the real interest rate and E(pi_t) is the expected inflation rate over the current period. The Fisher effect is named after Irving Fisher, who first proposed the idea in his 1930 book The Theory of Interest. Fisher hypothesized that there is a “real” interest rate that is unaffected by money and a “nominal” interest rate that covaries positively with inflation. The Fisher effect has strong intuitive appeal. Consider a creditor giving a $100 loan to a borrower. This creditor just wants all of his money paid in full after one year, nothing more. But, say that there will be a 6% increase in the price level between the time he loans that $100 and the time he gets that $100 back. He wants $100 back in today’s dollars so he would ask for $106 at the end of one year with an interest rate of 6%. In other words, all interest rates reflect the expected change in purchasing power over the maturity of the loan.

The intuition behind the Fisher effect is so powerful that most people accept the Fisher effect at face value. It is taught in every introductory macroeconomics course as fact. However, finding the Fisher effect in the data is extremely difficult. This literature review covers empirical tests of the Fisher effect.

Empirical roadblocks

I made the claim that it is hard to find the Fisher effect in data. This is because of the fact that the real interest rate and market participants' inflation expectations are unobservable variables. Hence, economists have had to make a few assumptions when testing the Fisher effect. Most economists have used actual inflation and an assumption of rational expectations to test the Fisher effect. Economists have assumed a constant real interest rate. This is a tough pill to swallow, but there is no good substitute for the real interest rate. The last big roadblock is the fact that interest rates aren’t just a function of the real interest rate and inflation expectations. They also include different premia like risk premia or liquidity premia. These premia are also unobservable. Economists generally assume these premia are all zero when testing the Fisher effect because economists use government bond yields to do their tests. This is not a bad assumption, as most people think of government bonds as nominally risk free and government bonds are quite liquid.

Testing the Fisher effect

Irving Fisher himself was the first person to test the Fisher hypothesis. He found that interest rates and inflation have a positive relationship and in the long run the relationship is close to but below unity. He finds, in general, that interest rates tend to be high while inflation is rising and low when inflation is falling. In summary, he writes:

>When the effects of price changes upon interest rates are distributed over several years, we have found remarkably high co-efficients of correlation, thus indicating that interest rates follow price changes closely in degree, though rather distantly in time. (Fisher, 451)

In other words, the Fisher effect happens in the long-run, but not in the short-run.

In the post-War era, landmark research into the Fisher effect came from Fama and Gibbons (1982). Under the assumption of a constant real interest rate and a rational bond market, they tested the ex ante interest rate with ex post inflation. The equation they tested took the form:

pi_t = -(r_t-1)   i_t-1

Fama and Gibbons tested this equation using 1-month and 3-month US Treasuries yields from 1954 to 1979. They found that the Fisher effect does exist in this data. This research shows that the short-run Fisher effect exists. Fama and Gibbons also set the stage for further research: if market actors are rational, inflation can be used for expected inflation and errors from regressions will be white noise. So, most other researchers have used actual inflation with the assumption of rational expectations in their estimation of the Fisher effect

In 1992 Frederic Mishkin updated the Fama-Gibbons arrangement of the Fisher equation with new US Treasury data through 1990. Mishkin (1992) wasn’t able to confirm the results of Fama and Gibbons. However, Mishkin’s research did test for a long-run Fisher effect using cointegration tests. Mishkin found that when interest rates are high, inflation is also high. As Mishkin himself wrote in his paper, his findings (both in the short-run and long-run) are consistent with Irving Fisher’s original findings in 1930.

Evans and Lewis (1995) tested the Fisher equation using conventional time-series methods as well as a Markov switching model – a model where market actors anticipate inflation process changes. Evans and Lewis rejected the Fisher effect with their time-series estimation, showing that the inflation coefficient was less than unity. However, if there was a structural break in inflation processes, that would confound the results. Evans and Lewis found that inflation did have structural breaks and thus modeled these breaks using a Markov switching model. Using this model, they were unable to reject the hypothesis that inflation moves one-to-one with the nominal interest rate in the long-run. Evans and Lewis not only use actual inflation, but also the Livingston Survey as a measure of inflation expectations.

In 1996, William Crowder and Dennis Hoffman tested the Fisher equation before and after adjusting for tax effects associated with making money on bonds. Without adjusting for taxes, Crowder and Hoffman found an inflation coefficient larger than one. However, after adjusting for taxes, they found that the coefficient for inflation is insignificantly different from one. This runs contrary to the other authors thus far. Most were unable to find even a one-to-one relationship between inflation and the nominal interest rate, but Crowder and Hoffman did. Other researchers did not adjust for taxes and yet their coefficient on inflation was consistently below unity.

Alternative measures of inflation expectations

The authors I’ve covered so far have all been using government bonds and actual inflation for the variables in their regressions. However, Evans and Lewis (1995) include the Livingston Survey as well. There exist alternative measures of inflation expectations mostly in the form of surveys. The two surveys people are most familiar with are the Survey of Professional Forecasters and the Livingston Survey. These surveys ask economists and other forecasters what they expect inflation to be over certain time periods. The surveyors then release this data publicly. Unfortunately, surveys of forecasters are about as useful as proxies for inflation expectations as sun spots are. So what other recourse is there?

In the 1980s the United Kingdom and Australia both introduced inflation-indexed government bonds. The US and Canada followed suit in the late 1990s. These bonds promised a real return as opposed to a nominal return like regular government bonds do. In 1990, Woodward was the first author to develop a data set of market derived inflation expectations. Woodward utilized inflation indexed UK gilts and regular UK gilts to create a series of inflation expectations using quarterly data. The amazing thing about this is that Woodward made an unobserved variable, inflation expectations, completely observable. In 1992, he updated his 1990 methodology using monthly data and explicitly tested the Fisher effect for different maturities. Like Crowder and Hoffman, Woodward found that, when yields are not adjusted for taxes, the coefficient for inflation is higher than one. However, when adjusted for taxes, the coefficient for inflation is either slightly below or insignificantly different than one on long-term maturities. The coefficients for inflation on short-termed securities were less than one. Thus, Woodward corroborated Fisher’s original findings that inflation manifests itself in interest rates over the long-run but not in the short run.

Summary of findings

Nearly all researchers find some support for the Fisher effect but it is one-to-one in nearly all studies. No author finds short-run support for the Fisher effect besides Fama and Gibbons, but Mishkin showed that Fama and Gibbons’ results were unique to the data set Fama and Gibbons used. Adjusting for taxes pushes down the coefficient for inflation in two papers but papers that don’t adjust for taxes do not find a coefficient for inflation above unity. Only one author uses a realistic measure of inflation expectations. However, all the data seems to point in the direction of “Irving Fisher was right.” The research is certainly not an emphatic “yes”, but it gives the Fisher effect two thumbs up and the research doesn’t warrant any asterisks in macroeconomics textbooks.

Okay, but who cares?

More politely “what useful conclusions can you draw from this research?” While a few things come to mind, I think the most important thing for me is that all of this research points to Milton Friedman being right in Friedman (1968). Friedman states that the conventional wisdom of judging the stance monetary policy by what the federal funds rate is, is entirely wrong. Since the Fed lowers the federal funds rate to expand the money supply we think that low interest rates signals easy monetary policy. However, when the Fed lowers interest rates, inflation goes up after some time. Market actors include this increase in inflation in the interest rate due to the one-to-one relationship between inflation and the nominal interest rate, so interest rates rise - especially on long-termed maturities. If the Fed thinks that high interest rates means tight money, then the Fed will lower the federal funds rate further, thus increasing inflation. This increase in inflation then makes interest rates go even higher. Since high interest rates coincide with high inflation, this means that high interest rates - especially on long-term maturities - are a sign of easy monetary policy.

Final remarks

I hope some of you found this interesting. If anyone has any other questions, feel free to ask me. If you want to know what I did in my senior thesis, I can give you a run down. I've run out of space here to discuss it.

References

Crowder, William J and Dennis L. Hoffman, “The Long-Run Relationship between Nominal Interest Rates and Inflation: The Fisher Equation Revisited” Journal of Money, Credit and Banking, (February, 1996), 102-119

Evans, Martin D. D. and Karen K. Lewis, “Do Expected Shifts in Inflation Affect Estimates of the Long-Run Fisher Relation?” The Journal of Finance (March 1995), 225-253

Fama, Eugene F. and Michael R. Gibbons “Inflation, Real Returns and Capital Investment” Journal of Monetary Economics (1982), 297-323

Fisher, Irving, The Theory of Interest (New York: Macmillan, 1930)

Friedman, Milton “The Role of Monetary Policy” The American Economic Review (March 1968), 1-17

Mishkin, Frederic S. “Is the Fisher effect for real? A reexamination of the relationship between inflation and interest rates”, Journal of Monetary Economics (1992) 195-215

Woodward, G. Thomas, “The Real Thing; A Dynamic Term Structure of Real Interest Rates and Inflation Expectations in the United Kingdom: 1982-1988,” *Journal of Business *(July 1990), 373-398

_________, “Evidence of the Fisher Effect From U.K. Indexed Bonds” The Review of Economics and Statistics (May 1992) 315-320