Updated: 5/12/2006


Fisher Effect

For nearly forty years both before and after the turn of the 20th Century (1867 – 1947), an American economist, Irving Fisher, contributed heavily to the topic of money, inflation and interest rates.  His ideas are reflected in the development of the concept of Purchasing Power Parity.  Fisher is a precursor of the modern concept of Rational Expectations.  When the Fisher effect is fully manifested in the behavior of interest rates, we have Rational Expectations.


To understand the relationship of inflation (deflation) to interest rates, we must first distinguish between the rates you can see in the markets.  This rate is usually called the nominal or market interest rate.  When price levels are changing as in the case of inflation, the principal of a loan is shrinking in real value.  Inflation has the same effect as a negative rate of interest.  If, on a one year loan compounded annually at 6 percent, the inflation rate over the year is 2 percent, the real interest rate is 4 percent or 6 percent, the nominal interest, less 2 percent the inflation rate.  This is true by definition.  If instead the prices fell at a 2 percent rate over the year (deflation rate of 2 percent), the real interest rate would be 8 percent of the nominal interest rate of 6 percent plus the deflation rate of 2 percent.  Deflation increases the real value of the principal and is like an additional rate of interest accrued to the lender.  Again, this is true by definition.  The real interest rate is the nominal or market rate of interest adjusted for price level changes.  During inflationary periods, the nominal or market interest rate will be higher than its price level adjusted counterpart, the real interest rate.  During deflationary periods, the nominal or market rate of interest will be lower than its price level adjusted counterpart, the real interest.  


The nominal or market interest rate and the real interest rate must diverge when price levels are changing, whether it be inflation or deflation occurring.  Only when price levels are stable, neither rising nor falling, on the average, will the nominal or market rate of interest be equal to the real interest rate.  This is all tautological, i.e. true by definition.


To understand what Fisher was assuming, or that later those arguing the position of Rational Expectations explained, we shall use three behavior patterns: complete illusion, adaptive lag, and rational expectations.  They are consistent with the divergence of market and real interests during price level changes, but show how the three behavior patterns reflect different routes of adjustment to bring about the divergence that must occur.


Complete Illusion

This market behavior pattern is dominant towards the end of prolonged periods of price stability such as the period from 1952-64 reflected.  The public was habituated to price stability.  No profit was to be had by entrepreneurs is selling insurance or safeguards against inflation.  It would be like selling refrigerators to Inuits in the Artic during winter.  The public was at the height of vulnerability to the damage that inflation causes, especially to savers, investors, etc. 


As inflation started in the late 1960s, very mildly for a few years, and then began to accelerate in the early 1960s, little concern was shown by the public.  To their mindset at the time, what they observed in the market was to them real.  When the first oil shock occurred in 1973 ( a barrel of crude oil quadrupled from $3.50 to $14.00 in a nanosecond, an increasing number of people began to feel the sting of falling incomes as real rates of interest began to plummet.


Adaptive Lag

With a lag, the public began to adjust their expectations and lenders, savers, and investors began to tack on an inflation premium in the form of higher interest rates, to compensate for the loss of real principal invested. 


Note than until the oil shock of 1973, the milder inflation drove real interest downward as nominal or market interest rates did not yet reflect the inflation that was occurring.  In the behavior pattern of Complete Illusion, the real interest rate does all the adjusting (in this case downward as a result of the public’s failure to compensate for inflation in the form of an inflation premium to be embedded in the market or nominal interest rates.


As the public begins to realize the reality of inflation and its redistributive effects, it begins to tack on inflation premiums to interest rates but with a lag.  If the public embeds a premium in interest rates, it is usually based on past experience (with the more remote having lesser weights and the more proximate including the present, heavier weights).  If inflation is accelerating rapidly as it was in the mid to late 1970s, the nominal or market interest rates can be rising while the real interest rats continue to fall.  The public in effect is backward looking and underestimates the actual acceleration occurring.  This was actually occurring in the mid-1970s. 


Rational Expectations

Finally, the public fully understood the reality of inflation and the nominal or market interest rates began to reflect the new reality fully.

This is the intellectual part of Rational Expectations.  But just knowing is not enough.  The market must adapt and adjust to enable the public to manifest their newly found knowledge.  A parallel evolution is going on in the financial markets to enable the public to make Rational Expectation complete.


Many changes began to occur in the financial markets in the early 1970s.  As the public began to see the reality of inflation, they wanted to protect themselves in their financial behavior.  Now financial entrepreneurs could profit from selling new products and processes to savers, lenders, and investors.  Imagine if global warming were to prove to be a reality and the Artic warmed up.  Inuits would begin buying refrigerators once they recognized the problem of warming was going to stay around.


Similarly, those harmed by inflation, (savers, investors, lenders, and fixed income recipients in general began to realize inflation was here and   not likely to seen go away.  About 1970, new products and processes were rolled out.  Some already existed but were rather small in importance until it was realized they could help protect the public from the financial damage of inflation.  Financial futures, variable rate mortgages, stripping of coupon bonds to create zero derivatives, securitization of many kinds of loans, expanded use of duration analysis, money market mutual funds, etc., etc..



The growth in intellectual understanding of inflation, its causes, and its effects along with developments in the financial markets as mentioned above, brought the economy close to what was to be termed rational expectations.  This is similar to what Irving Fisher assumed nearly three quarters of a century earlier.  The Rational in Rational Expectations is not that of Aristotle nor Max Weber but rather a kind of clairvoyance.  The markets inflation premiums were based upon their estimates of inflation in the future.  When the actual rate of inflation matched that expected to occur, the real or inflation adjusted rate of inflation was not affected by inflation.  The nominal or market rate of interest adjusted upward but by the correct amount so the real rate was not impacted by inflation.  This is equivalent to saying that the market was correctly predicting the future inflation rates.


Text Box: Patterns of Behavior Responding to Inflation


Complete Illusion: a: As inflation accelerates and the nominal interest rate remains unchanged, real interest rates fall b: As inflation decelerates, real interest rates rise.

Adaptive Lag: a: As inflation accelerates and the nominal rate remains unchanged, the real rate falls.  b: Inflation continues to accelerate, and the nominal rate begins to be adjusted upward.  The real rate levels off.  c: Inflation begins to decelerate while the nominal rate is still rising.  Thus the real rate spikes upwards.  d: Inflation continues to decelerate.  The nominal rate begins to be adjusted downward.  The real rate levels off.
e: Inflation returns to zero.  Thus the real and nominal rates are the same, and both continue downward. 

Rational Expectations: a: As inflation accelerates the nominal rate is increased to compensate, and the real rate remains unchanged.  b: As inflation decelerates the nominal rate is decreased.  Again there is no change in the real rate.

(Inflation accelerates linearly in all diagrams.  In the adaptive lag model, the nominal rate at each point in time is adjusted by the rate of inflation at the time a half cycle prior.  The implicit model is thus oversimplified: real world adjustments would be based on a weighted average of prior inflation rates).


Since the editors of this newsletter are New Paradigmers, we warn the reader that the occurrence of deflationary episodes has been one again  occurring and it is expected t occur more frequently as an increasingly competitive economic is elimination the inflationary bias that occurred due the lack of competition in many more markets in the past.  While the former Secretary of the Treasury takes credit for the much lower rates of inflation and the FOMC (Federal Reserve Board Federal Open-Market Committee https://www.federalreserve.gov/fomc/) also takes credit, the real cause is the increasingly significant and widespread growth of competition in markets.  The only seriously inflationary sector currently is energy.  This is due to the FTC (Federal Trade Commission - http://www.ftc.gov/os/2000/03/opectestimony.htm; http://www.ftc.gov/ftc/oilgas/index.html) and Justice Department’s unwillingness to curb the re-cartelization of the American portion of the oil market and is distribution channels  (Important…http://tonto.eia.doe.gov/FTPROOT/presentations/hrt310/hrt310.html Justification for allowing merger of Exxon and Mobil 1999 and BP Amoco 1998).  While a serious deflationary bias is not expected to develop, increasing competition in the product markets should cause a change in the distribution of the productivity dividend from that going to productive resources employed by firms in cartelistic markets to the consumer surplus by eliminating economic rent or what is sometimes called producer surplus.


The increased understanding by the public of this ongoing development could be a major reason why the FOMC’s upward pressure on short term interest rates such as the Fed Funds rate had little impact on the longer term rates.  As we have suggested in this newsletter on more than one occasion, Greenspan's conundrum is more likely the lack of understanding that the economy has evolved significantly and has impacted the public’s expectations of the future inflation rates and short term interest rates and thus the term structure of interest rates and its graph the yield curve.


In the Chapter Six (The Effects of Changing Price Levels on Interest Rates) of Dr. Byrne’s manuscript, Financial Economics, it was seen that inflation affects interest rates by driving a wedge between nominal and real interest rates.  In the model of rational expectations, the nominal interest rate does all of the adjusting with inflation having no effect on the real interest rate.  If two nations, alike in all other respects but have different inflation rates, according to the Fisher effect, in a model of rational expectations, the nation with the higher inflation should have the higher nominal interest rates.  If we continue to assume that the U.S. inflation rate expected over the coming year is 4% and in Germany is 12%, nominal interest rates on similar securities should be 8% higher in Germany than in the U.S.


If the real interest rate in both nations is 2% on one year T-bills, the nominal one year T-bill rate in the U.S. will tend to be 6% and in Germany will tend to be 14%.  Note that differing inflation rates have two impacts.  Through purchasing power parity, the forward premium on the dollar in respect to the mark is 8% (difference in expected annual inflation rates).  Through the Fisher effect, the difference in nominal interest rates on similar securities is 8% (difference in expected annual inflation rates), being higher in Germany than in the U.S.



By extension, the concept of Interest Rate Parity pursues the Fisher effect argument…

Interest Rate Parity


A second principle, Interest Rate Parity, ties the interest rates of two nations with their exchange rates.  According to the Interest Rate Parity principle, the difference in similar nominal or market rates of interest should be equal to the forward premium of the nation with the lower inflation rate.  Otherwise arbitrage will occur, the profitability of which will cease only when interest rate parity once again prevails.


Assume that the one-year T-bill rate in the U.S. is 8% while that in Germany is 14%.  All other facts are as given above.  Arbitrage will occur.  Marks can be sold spot and Dollars purchased at the rate of 2 marks for one dollar.  The dollars thus acquired will be invested for one year at 8% while concurrently the dollars just purchased spot will be sold one year forward at the rate of $.46 for one mark.  This is profitable, since while 6% less is earned for one year on the dollar, 8% is earned on the round trip.  As a result, the spot dollar will appreciate and the forward dollar will depreciate until the forward premium on the dollar falls to 6%.  Alternately, the adjustment could come from the one year interest rates in the U.S. falling and in Germany rising until they differ by 8%.  More likely, both could adjust.  If the Fisher effect is fully manifested so that nominal or market interest rates, the final adjustment will be in the U.S. interest rate falling to 6% until the differential on one year T-bills is 8% and interest rate parity once again prevails.


Should the difference in inflation rates differ from the forward premium or discount on the current arbitrage will force a reconfiguration on nominal or market interest rates and spot and forward exchange rates until interest rate parity is reestablished.  Studies show that except under conditions of massive intervention by central banks, interest rate parity gives a pretty reliable explanation of the difference in nominal interest rates and the spot and forward exchange rates.



Purchasing Power Parity


Last, but certainly not least, we can now examine some underlying principles that help explain the relationship between spot prices of futures and forward contracts for foreign exchange.  Each underlying asset has a similar set of principles relating spot to forward and futures prices.  Futures or forward prices in the foreign exchange markets are expected spot prices as they are expected to be on the delivery date of the futures contracts.  This relationship is similar for interest rates as imbedded in both interest rate futures and forward contracts.  This is called the expectations theory of futures price determination.  There is another approach called the cost of carry theory of futures price determination.  We leave this more complicated approach to more specialized texts and will concentrate on the expectations approach.  Assume that the following spot and forward dollar/mark exchange rates currently exist.


Spot        $0.50

90 day      0.49

180 day    0.48

One year  0.48


Recall from the chapter on exchange rate determination that when the dollar price of foreign exchange decrease, the dollar is said to appreciate against the currency in question.  In the case above, it is clear that the market expects the dollar to appreciate over the coming year against the mark since the rates for delivery at a future date show the dollar cost of the mark to be less and less the further away is delivery.  When it costs less in dollars (cents) to buy marks for forward delivery, the dollar is said to be at a forward premium against the mark (the mark is concurrently at a forward discount against the dollar).  We can calculate the forward premium on the dollar in respect to the mark.  It is in annualized percentage terms as follows.



On a 180 day basis:            ($0.50 - $.48)   x   365  

               $0.50               180  

= 0.081 or in percentage terms, a forward premium of 8.1%



On a one year basis: $0.50 - $0.46 


= 0.08 or in percentage terms, a forward premium of 8%



Why would such a relationship exist?  Why should the dollar appreciate against the mark over the coming year and by a rate of about 8%?  From the chapter on exchange rate determination, it is shown that a number of factors could be the cause either independently or in combination.  However, a major cause of many exchange rate changes is due to different rates of inflation of the two nations involved.  If the expected rates of inflation in the U.S. over the coming year is 4% and in Germany is 12%, the principle of Purchasing Power Parity could explain the forward premium on the dollar in respect to the mark.


According to the Purchasing Power Parity principle, nations with higher inflation rates will tend to find their currencies depreciating against the currencies of nations with lower inflation rates.  One could also say that the currencies of nations with lower inflation rates tend to find their currencies appreciating against the currencies of nations with higher inflation rates.  The rate of appreciation expressed in annual terms (equal to forward premium on the currency of the nation with the lower inflation rate) being equal to the difference in inflation rates, all else equal.  Capital flights due to increasing political instability of a nation, massive and persistent intervention on foreign exchange markets and other causes of the dollar being at a forward premium to the mark are ruled out in this interpretation of exchange rate changes.






Click here to return to Main Page


(Opinions expressed on this web page are those of a faculty member or employee and do not necessarily reflect the position of University of Detroit Mercy)