The Fisher Theory of Nominal Interest Rates and Inflation Rate - Essay Example

The Fisher Theory of Nominal Interest Rates and Inflation Rate Table of Contents Description of Fisher Theory 3 Adjustment for Variation in Tax Rates 4 Adjustment for Variation in Risk 4 Underlying Assumptions of Irving Fisher 5 Mechanics behind the Hypothesis of Relationship between Rate of Inflation and Nominal Interest Rate 6 Complete Illusion 6 Adaptive Lag 7 Rational Expectations 7 Empirical Evidences: Irving Fisher Theory of Interest Rates 12 12 A Critique To the ‘Real’ Notion of Fisher’s Theory of Interest 13 Expected Inflation Has No Effect on the Nominal Interest Rate 13 Condition of Indifference Is Not a Relevant One 14 Transfer of Real Income over Time 14 Theory of the Rate of Interest 14 Fisher’s Indifference Condition as a Definition 15 Conclusion / Findings of the Research 16 References 17 Bibliography 20 Introduction The essay is based on the Fisher Theory of nominal interest rates and inflation rate. The objective of the essay is to describe the Fisher Theory and based on the understanding of the theory, the mechanism behind the hypothesis (that there should be a positive link between the rate of inflation and nominal interest rate) will be tested. In other words, the instinct of the Fisher theory of interest rates will be proved. This will be done by researching various evidences both on theoretical aspect as well as practical aspects. Fisher has his own way of defining the term ‘interest’. According to the economist, interest is ‘an index of a community’s preference for a dollar of present (income) over a dollar of future income’ (Library of Economics and Liberty, 2008). The label that he has put to his theory of interest rate is ‘the impatience and opportunity’. Fisher has postulated in this theory that interest rate results from interface between two forces: the time preference that people have for capital at present and the principle of investment opportunity (Library of Economics and Liberty, 2008). The above instincts will be supported through theoretical and practical evidences by collecting data from various sources. Description of Fisher Theory Irving Fisher’s theory of interest establishes a link of nominal interest rate (i) to the rate of inflation (П) and the real rate of interest (r). The rate which is derived after making adjustment for the inflation is the real interest rate. This is the interest rate which the lenders should consider for lending their funds. The relationship that has been presented by Fisher between these three interest rates is: (1+i) = (1+r) (1+П); which is equivalent to I = r + П (1+r) Thus, the above relationship states that if rate of inflation increases by 1 percent, then the nominal interest rate increases by more than 1 percent. This means that there is a positive relationship between the rate of inflation and nominal interest rate (University of Missouri-Kansas City, 2010). Adjustment for Variation in Tax Rates In the next step of the analysis, the effect of taxes on the real rate of return will be taken into account. Let a country be considered with currency C. Then let ic be the nominal risk-free rate of interest, rc be the real interest rate and Пc be the expected rate of inflation. Let tc be the rate of tax on the interest income and r*c be the after tax real rate of return. The after tax rate of return is ic (1-tc). Then, R*c = [ic (1-tc) – Пc] / (1+Пc). From the above expression, it can be explained that with the increase in rate of inflation, the nominal interest rate also increases by a few proportion of the increase in inflation rate (Mulligan, 2002). Adjustment for Variation in Risk The analysis in the previous stage assumed that the level of risk is equal in all the countries. In reality, the risk perception is different. If there is a difference, then there should be a risk premium for the lenders and investors, that is, an increased interest rate for the purpose of compensating them for taking higher risk. Let sc be the risk premium in the country with currency C. Let the international market be in equilibrium, then the real and after tax rates of return will have to be equal in different countries. Then, rc – sc = r* for all countries and thus, Ic = [(r* + sc) (1+Пc) + Пc] / (1-tc) The above expression shows that for increase in the expected rate of inflation, the nominal interest rate also increases by some proportion (Watkins, n.d.). Underlying Assumptions of Irving Fisher According to Irving Fisher, the real rate of interest is the most important price in the economy. This is because real rate of interest provides the worth of consumption at present in terms of consumption in the future. Fisher was pretty much interested in measuring inflation and hence was a leading supporter of inflation-indexed bonds. For measuring the inflation, he had created an inflation index and carefully published its value (Geanakoplos, 2005). Mechanics behind the Hypothesis of Relationship between Rate of Inflation and Nominal Interest Rate For understanding the assumptions of Fisher Theory or the later arguments towards the position of inflation expectation, three behavioural patterns will have to be used: complete illusion, adaptive lag and rational expectations. These patterns show consistency with the deviation of market and real interests during the changes of price level. They will reflect the various ways of adjustment that they make to bring the deviation that should occur. A complete understanding of these patterns will lead to the support behind the hypothesis that there is a positive link between the rate of interest and nominal interest rate (University of Detroit Mercy, 2006). Complete Illusion This behaviour pattern is reflected during the periods of price stability which people were habituated during 1952-1964. During the period, the entrepreneurs used to enjoy no profit at all. The people were susceptible towards inflation effect. As inflation started during 60s, the people showed little concern. According to their mindset, the observation in the market was real for them. With the first oil shock in 1973, they began to feel the pressure of decreasing income as real rates decreased (Thaler, 1997). Adaptive Lag With the lag in 1973, people began to adjust their expectations and began to approach to the inflation premiums in the form of higher rate of interest. They were approaching to compensate for the loss that they have incurred due to capital investment. It should be noted here that in the behavioural pattern of complete illusion, all the adjustments were done by the real interest rates. Here as the people began to understand the inflation reality, they approached to take on the premium. When inflation accelerates rapidly, the nominal or market rate of interest rises but the real interest rates continue to fall. This is evident from the happenings of the mid 1970s. Here, the basic nature of the people is backward looking and thus the actual acceleration faces hindrance. Rational Expectations Finally, the people understood the inflation reality and thus the nominal interest rate started to increase. It is the rational part of this pattern. The market tries out all initiatives to influence the knowledge of people. With the influence, people began to protect themselves in the economy. In this part of the economy, the entrepreneurs earn profit by selling new products to the investors (Evans & Honkapohja, 2001). During the period of late inflation during the 1970s, many products were offered in the market like the financial futures, variable rates mortgage and so on. (University of Detroit Mercy, 2006). Complete Illusion: ‘a’ as acceleration in inflation occurs, but the nominal rates do not change, a fall in the real interest rate is observed ‘b’ vice versa. Adaptive Lag: ‘a’ as inflation accelerates and nominal rates do not change, the real rate falls, ‘b’ as acceleration in inflation continues and nominal rates adjust upward, the real rate level off, ‘c’ as inflation decelerates but nominal rate still on a rise, the real rate moves upward and‘d’ as inflation continues to decelerate, the nominal rate begins to amended downward and the real rate also levels off. Rational Expectations: ‘a’ according to the acceleration of the inflation, nominal rates also increase for compensating but the real rate remains unaffected, ‘b’ as inflation decelerates and the nominal rate decreases; there is no alteration in the real rate (University of Detroit Mercy, 2006). (University of Detroit Mercy, 2006). The above data representation has been done by comparing the CPI (Consumer Price Index) with the 10 year U. S. Treasury bond. CPI has been collected from the Bureau of Labor statistics. The effect of the behavioural patterns described before can be seen from the plotted figure. The discussion above leads to a rational towards the positive relationship between the rate of inflation and nominal interest rate (University of Detroit Mercy, 2006). Empirical Evidences: Irving Fisher Theory of Interest Rates There has been an age-old debate as to whether the Fisher Effect of expected inflation on real interest rate holds good at all times or not. The following section of the paper will present an overview of the various empirical evidences that sometimes supported the effect and sometimes not. Mitchener & Weidenmier (2010) has presented an evidence to discard the debate on whether the Fisher effect worked during the typical gold standard period or not. They did so by the development of a market-based measure of common inflation expectation. During the period of standard gold, inflation was used to be tracked by gold-silver price ratio. Thus, they derived a measure of inflation expectation by differentiating the interest rate between Austrian silver and gold perpetuity bonds. The empirical evidence suggested by them mentioned that inflation expectations showed significant perseverance at the annual, monthly and weekly occurrence. The evidences also suggested that market participants reviewed long-run inflation expectations following changes in the short-run forward price. Thus, these prove the workings of long-run Fisher effect during the typical gold standard period (Mitchener & Weidenmier, 2010). A Critique To the ‘Real’ Notion of Fisher’s Theory of Interest Although there have been many evidences to prove the basic assumptions of the Fisher’s Theory of interest rates in the economy, there have been even some critiques towards the concept. In the following section of the paper, the other side of the coin will be presented. The critique is based on five aspects of the Fisher’s theory that are assumed to be irrelevant to the economic analysis (Tymoigne, 2006). Expected Inflation Has No Effect on the Nominal Interest Rate Keynes in the General Theory (1936) provided the first criticism to the Fisher’s Theory of interest rate. On the assumption that a change in inflation rate leads to changes in nominal rate of interest, Keynes implied criticism that money rates should be compared and not the real rates because money rates are the only observable element in the economy. Next, Keynes suggested that capital goods are not a fair substitute for monetary assets. Thirdly, he mentioned that changes in interest rates do not mean changes in the opportunity cost influenced by inflation (Tymoigne, 2006). Condition of Indifference Is Not a Relevant One According to the assumptions of Fisher, the best way to safeguard purchasing power, when rising inflation is expected, is to raise the monetary assets’ interest rates. This assumption completely discards the effect of increased rate of interest on the assets prices. This might lead to a capital loss for the people (Tymoigne, 2006). Transfer of Real Income over Time Fisher’s assumption that arbitrage in the micro level is appropriate for macro level, has been criticized by Keynes. Aggregate demand is achievable only from present consumption. The profitability provided at present in advance for the future cannot be just pushed into the future (Tymoigne, 2006). Theory of the Rate of Interest Fisher’s assumption that real interest rate is calculated on terms of money has been criticized in the sense that marginal capital efficiency is an identical concept as the rate of return. This criticism has again been criticized that Keynes should not have puzzled marginal capital efficiency and rate of return as in Fisher’s theory money is a veil (Tymoigne, 2006). Fisher’s Indifference Condition as a Definition Following Fisher’s assumption, interest rates are set by the ultimate provider of credit, which is the Central Bank. The interest rate is also the real interest rates, not just the nominal. In Fisher’s definition, real interest rate is the expected inflation deducted from the nominal. Thus, the Central bank can determine the real rate according to its wishes (Tymoigne, 2006). Conclusion / Findings of the Research The research paper has tried to make an in-depth study of the Fisher’s theory of interest rates. The in-depth study has helped so far to come up with the conclusion that there is really a positive link between the rate of inflation and nominal interest rate. The practical evidences of the past and various citations of the supporters of Fisher’s theory have helped in establishing the relationship. Although, in one part of the research, the criticisms of the theory have been presented, no practical evidences of those aspects have been found from the research. Hence, it would be viable to say that the empirical evidences confirm the fact that there is a direct relationship between the rate of inflation and nominal interest rate. References Evans G. W. & Honkapohja, S., 2001. Learning and Expectations in Macroeconomics. Princeton University. [Online] Available at: http://press.princeton.edu/chapters/s7097.pdf [Accessed December 04, 2010]. Geanakoplos, J., 2005. The Ideal Inflation-indexed Bond and Irving Fisher’s Impatience Theory of Interest with Overlapping Generations. Yale University. [Online] Available at: http://cowles.econ.yale.edu/~gean/art/p1111.pdf [Accessed December 03, 2010]. Library of Economics and Liberty, 2008. The Concise Encyclopaedia of Economics. Liberty Fund. [Online] Available at: http://www.econlib.org/library/Enc/bios/Fisher.html [Accessed December 03, 2010]. Mitchener, K. J., & Weidenmier, M. D., 2010. Searching for Irving Fisher. National Bureau of Economic Research. [Online] Available at: http://lsb.scu.edu/~kmitchener/research/Fisher_15670.pdf [Accessed December 04, 2010]. Mulligan, C. B., 2002. Capital, Interest, and Aggregate I Intertemporal Substitution during the 20th Century. University of Chicago and NBER. [Online] Available at: http://hubcap.clemson.edu/~sauerr/seminar_papers/capries.pdf [Accessed December 04, 2010]. Thaler, R. H., 1997. Irving Fisher: Modern Behavioral Economist. The American Economic Review. [Online] Available at: http://faculty.chicagobooth.edu/richard.thaler/research/pdf/IrvingFisher.pdf [Accessed December 04, 2010]. Tymoigne, E., 2006. Fisher’s Theory of Interest Rates and the Notion of “Real”: A Critique. California State University. [Online] Available at: http://www.levyinstitute.org/pubs/wp_483.pdf [Accessed December 04, 2010]. University of Detroit Mercy, 2006. Fisher Effect. 2003 Volume, Issue 3. [Online] Available at: http://byrned.faculty.udmercy.edu/2003%20Volume,%20Issue%203/Fisher%20Effect.htm [Accessed December 04, 2010]. University of Missouri-Kansas City, 2010. Fisher’s Relation, Purchasing Power Parity and the Interest Rate Parity Theorem (including Covered and Uncovered Interest Arbitrage). College of Arts and Science. [Online] Available at: http://cas.umkc.edu/ECON/economics/faculty/Kregel/645/Winter2003/Readings/Fisher%27s%20Relation.pdf [Accessed December 04, 2010]. Watkins, T., No Date. The Original Fisher Model. San Jose State University. [Online] Available at: http://www.sjsu.edu/faculty/watkins/fisher1.htm [Accessed December 03, 2010]. Bibliography Fama, E. F., 2010. Short-Term Interest Rates as Predictors of Inflation. The American Economic Review. [Online] Available at: http://www.jstor.org/pss/1804833 [Accessed December 04, 2010]. Mundell, R., 2010. Inflation and Real Interest. The Journal of political Economy. [Online] Available at: http://www.jstor.org/pss/1828985 [Accessed December 04, 2010]. Tanzi, V., 2010. Inflationary Expectations, Economic Activity, Taxes and Interest Rates. The American Economics Review. [Online] Available at: http://www.jstor.org/pss/1814734 [Accessed December 04, 2010]. Read More