The Ideal Inflation‐Indexed Bond and Irving Fisher's Impatience Theory of Interest with Overlapping Generations*

Abstract Irving Fisher long advocated inflation‐indexed bonds. But with what index? I prove in the context of a multicommodity CAPM world that the best welfare‐improving bond pays the minimum money needed to achieve the same utility, and not the minimum needed to buy an ideal commodity bundle. Irving Fisher also developed and advocated the impatience theory of interest. But in OLG economies, the rate of interest is determined by population growth, not impatience. I reconcile this contradiction by proving that in stationary OLG economies with land, the interest rate at the unique steady state does depend on impatience. Indeed, the proposition that greater impatience creates higher interest rates holds more generally in OLG with land than in Fisher's two‐period model, because then income effects and substitution effects naturally work in the same direction.     

线性和非线性视角下的费雪效应实证检验

基于2000年1月~2009年12月我国名义利率和通货膨胀率均为非平稳时间序列的事实,采用Johansen协整检验和门限协整(threshold cointegration)两种方法对我国是否存在费雪效应进行检验;实证发现,两种方法均支持我国存在弱费雪效应,但得出来的弱费雪效应程度却存在差别,前者认为我国通货膨胀率的变化只有6%反应到名义利率上面,而后者认为这个比例达到42.4%。     

Panel cointegration tests of the Fisher effect

Most empirical evidence suggests that the Fisher effect, stating that inflation and nominal interest rates should cointegrate with a unit slope on inflation, does not hold, a finding at odds with many theoretical models. This paper argues that these results can be attributed in part to the low power of univariate tests, and that the use of panel data can generate more powerful tests. For this purpose, we propose two new panel cointegration tests that can be applied under very general conditions, and that are shown by simulation to be more powerful than other existing tests. These tests are applied to a panel of quarterly data covering 20 OECD countries between 1980 and 2004. The evidence suggest that the Fisher effect cannot be rejected once the panel evidence on cointegration has been taken into account. Copyright © 2007 John Wiley & Sons, Ltd.     

Interest rate risk in an emerging economy

The sharp decrease in inflation over the last decade—from 26% in 1990 to 4% in 2001—led the Central Bank of Chile to set its monetary policy interest rate in nominal terms since August 2001. This paper analyzes the effect of nominalization on the behavior of nominal, inflation-linked, and real interest rates, and its subsequent effects on the financial market. We find that nominalization has made nominal interest rates less volatile, while the opposite holds for inflation-linked interest rates. The effect on real interest rates is less unambiguous, but nominalization appears to have increased the cost of borrowing.     

Inflation illusion and the Taylor principle: An experimental study

We develop a simple experimental setting to evaluate the role of the Taylor principle, which holds that the nominal interest rate has to respond more than one-for-one to fluctuations in the inflation rate to exert a stabilizing effect. In our setting, the average inflation rate fluctuates around the inflation target if the computerized central bank obeys the Taylor principle. If the Taylor principle is violated, the average inflation rate persistently deviates from the target. These deviations from the target are less pronounced, if inflation rates cannot be as readily observed as nominal interest rates. This result is consistent with the interpretation that subjects underestimate the influence of inflation on the real return to savings if the inflation rate is only observed ex post.     

Fisher equations inverted and not

Regressions of the realized real after-tax interest rate on theex post rate of inflation are shown to be incapable of discriminating between the competing hypotheses that the real after-tax interest rate is not effected by expected inflation due to the substitutability between debt and equity (the Fisher hypothesis); and, that the nominal after-tax interest rate is not effected by expected inflation due to the substitutability between money and debt (the inverted Fisher hypothesis). An alternative regression which is so capable, is shown to reject the inverted and support the original Fisher hypothesis.     

Nonlinear dynamics of interest rate and inflation

According to several empirical studies US inflation and nominal interest rates as well as the real interest rate can be described as unit root processes. These results imply that nominal interest rates and expected inflation do not move one‐for‐one in the long run, which is incongruent with theoretical models. In this paper we introduce a new nonlinear bivariate mixture autoregressive model that seems to fit quarterly US data (1953 : II–2004 : IV) reasonably well. It is found that the three‐month Treasury bill rate and inflation share a common nonlinear component that explains a large part of their persistence. The real interest rate is devoid of this component, indicating one‐for‐one movement of the nominal interest rate and inflation in the long run and, hence, stationarity of the real interest rate. Copyright © 2006 John Wiley & Sons, Ltd.     

Impact of macroeconomic surprises on the Brazilian yield curve and expected inflation

This study investigates how unexpected announcements in Brazilian and U.S. macroeconomic indicators affect the term structure of nominal interest rates, as well as implicit inflation expectations and real interest rates. Using daily data from March 2005 to December 2012, we employ an extended Vector Error Correction Model to take into account nonstationarity and the long-term equilibrium among different maturities of those curves. We found empirical evidence that macroeconomic surprises, domestic (Brazilian) and external (U.S. American), which lead the market to believe that there might be a higher risk of inflation or an overheated economy, raise nominal interest rates, implicit expected inflation and real interest rates. Surprisingly, in relation to the efficient-market hypothesis, we found that some macroeconomic surprises have a lagged effect on the yield curves. We also tested the impact of the global financial crisis of 2007–09 and found that the crisis affected significantly the direction and magnitude of the responses to macroeconomic news.     

Fisher's The Nature of Capital and Income*

Abstract . In this essay James Tobin reminds us of the importance of Irving Fisher's great book and how that book was favorably received by economists. Fisher presented fundamental definitions and supplied a path breaking exposition of the mathematics of interest rates and their relationship to the valuation of assets. This essay was originally published as the “Editorial Introduction to Volume 2 of The Works of Irving Fisher, 14 vols London: Pickering & Chatto, 1997; 2:1–6.     

Nominal interest rate policy rules and the feasibility of real interest rate control

In this paper the author builds a financial market model to demonstrate that policy aimed at reducing the variance in nominal interest rates reduces the information content of these variables. This has the undesirable effect of destabilizing real interest rates. The researcher demonstrates that nominal interest rate policy rules stabilize the component of the variance in the ex ante real interest rate attributable to the variance in the nominal rate. The variability of the expected inflation rate can, however, be increased by such policy rules, making the net effect of a nominal interest rate policy on the variance in the real interest rate ambiguous.     

Do Wall Street economists believe in Okun’s Law and the Taylor Rule?

We use data from the Wall Street Journal’s semi-annual survey of professional economists to test whether individual economists’ six-month-ahead predictions of real GDP growth, unemployment, short-term interest rates and inflation reflect Okun’s Law and the Taylor Rule. We conclude the economists believe real growth is less responsive to unemployment-rate changes than the textbook version of Okun’s Law; we also find the economists believe the Federal Reserve sets short-term interest rates by placing more weight on unemployment and less weight on inflation than the Taylor Rule prescribes.     

Interest rate movements and US consumers’ inflation forecast errors: is there a link?

The Fisher effect maintains that movements in short-term interest rates largely reflect changes in expected inflation. Since expected inflation is subject to error, we ask whether interest rates move in response to over- and under-predictions of inflation. In answering, we measure expected inflation by the consumers’ forecast of inflation derived from the Michigan Surveys of Consumers (MSC). Our findings for 1978–2013 indicate that the MSC inflation forecasts were unbiased, efficient, and directionally accurate. For 1978–2007, (i) interest rates moved downward (upward) in response to MSC over-predictions (under-predictions) of inflation, and (ii) MSC inflation forecast errors had directional predictability for interest rates. However, no link between interest rate movements and MSC inflation forecast errors is detected for 2008–2013 when monetary policy kept short-term interest rates unusually low.     

A fractional cointegration analysis of Fisher hypothesis: evidence from Turkey

This paper examines the validity of Fisher hypothesis in Turkey over the period from 1990:01 through 2010:03 by using cointegration and fractional cointegration approaches. The findings from Engle and Granger cointegration test indicate that inflation and nominal interest rate series are cointegrated. Since the conventional cointegration tests do not provide strong evidence on the long run relationship, we also use fractional cointegration definition suggested by Cheung and Lai (J Bus Econ Stat 11:103–112, 1993) which requires only a mean reverting (d < 1) relationship between the series. The results from fractional cointegration tests based on GPH and Robinson methods show that inflation and nominal interest rate series are fractionally cointegrated. These findings support the validity of the Fisher hypothesis in Turkey.     

The monetary policy strategy of the Bank of England in 2020–21: An assessment

Excessive money creation during the Covid pandemic has resulted in Britain's worst episode of inflation since 1990–91. The backdrop to this failure of monetary policy is the Bank of England's aggregate demand/aggregate supply framework together with the Monetary Policy Committee's neglect of broad money. An alternative way to operate monetary policy is urgently needed. A significantly improved monetary policy outcome could be achieved by shifting from trying to steer the economy using interest rates and quantitative easing or quantitative tightening to reliance on the relative stability of income velocity (the ratio of nominal GDP to broad money) as a means of managing aggregate demand.     

Discounting inflation — a note

The aim of this paper is to clarify the confused issue of the effect of inflation on the discounting procedure for investment appraisal. The standard approach is considered, together with the impact of inflation, and the problem of how to adjust the standard approach to take account of inflation. The point is made that it is usually easiest to estimate expected returns in current prices, in which case the discount rate should reflect the real opportunity cost of capital, to avoid mixing real returns and nominal interest in a manner which leads to the rejection of worthwhile projects. An example is given of how the real rate of interest can be computed from the nominal rate of interest and the rate of inflation, and the difference this makes to discounting a sample project. The paper then illustrates how real rates of interest have frequently been negative over the past decade and how this implies that projects may be acceptable even if the sum of future undiscounted returns is less than the initial outlay. The conclusion drawn is that investors should maximize economic profit defined as the surplus over opportunity cost, which reduces the deterrent of nominally high interest rates, for the maximization of surplus over opportunity cost has the corollary of minimization of opportunity loss.     

The London Business School with Gower Publishing

In October we forecast 1 per cent output growth in 1993 accompanied by little change in retail price inflation, an increase in unemployment to 3.2 million by the end of the year and a £20bn deficit on the current account of the balance of payments. Since then we have revised our view of the international outlook and the Chancellor has made his Autumn Statement. There are also some hopeful signs in the latest data on retail sales, manufactured exports and the money supply that demand may be picking up both domestically and overseas. How do these developments affect our short-term forecast? The simple answer is very little: the outlook on output and inflation in 1993 is barely changed since October (Table I). We have lowered our forecasts for world inflation and for German interest rates which means that the pound can be held steady against the DM at lower UK interest rates and that the inflationary consequences of devaluation, though significant, are slightly less over the medium term than we made out in October. There is one revision of major significance, and that relates to the PSBR, which is now likely to reach f45bn in 1993-4, more than 7per cent of nominal GDP. The change is not on the spending side - the Autumn Statement confirmed existing expenditure plans - but on revenues, notably corporate taxes and tares 011 spending, which have fallen far more quickly than we envisaged. This, in combination with a projected near-2'per cent of GDP deficit on the balance of payments, poses a difficult medium-term policy dilemma. To escape from the twin deficits requires either deflation of demand, which conflicts with the Government's new-found commitment to growth, or a more buoyant economy to boost tax revenues and a competitive pound to underpin export-led growth. Of the two the latter is self-evidently more inflationary. This highlights the policy dilemma: at some stage the Government may have to choose between reducing the deficits and its 1–4 per cent inflation target or sacrifice its commitment to growth.     

Price dynamics when there are alternatives to cash payment

Empirical evidence from the 1980s and 1990s indicates that cash use in the U.S. remains high even though there has been a proliferation of alternatives to cash. This paper examines the dynamics of inflation and asset prices in response to innovations in the efficiency of processing noncash transactions. The quantitative results suggest that inflation is more sensitive than nominal interest rates or real equity prices to innovations in the efficiency of non-cash payments processing. Thus, as alternatives to cash payment become more prominent, the volatility of real interest rates may increase.(JELE31, E41, G12) This research is supported by a Swarthmore College Faculty Research Grant and a Eugene M. Lang Faculty Fellowship.     

BARGAINING FOR LOWER INFLATION

Industrialists are concerned about the high level of interest rates. The government is refusing to take deliberate steps to cut them, particularly at a time when the exchange rate has been falling in response to events in oil markets. However, the government has suggested that wage moderation offers the best chance of a fall in interest rates. Can this be interpreted as a promise of a reward for good behaviour? The idea of a policy bargain, whereby the authorities promise some kind of fiscal or monetary stimulus as a reward for moderation in wage settlements, is not new. An explicit bargain of this type was offered by Mr Healey in 1976 and again in 1977. In each year he offered tax cuts contingent on the negotiation of a new pay policy. Some have interpreted Mr. Lawson's comments at the recent NEDC meeting as offering a similar type of bargain on interest rates. As far as we can tell, that interpretation is incorrect; there are however interesting and important questions about whether policy should respond to lower inflation. We argue that, in general, lower inflation will itself produce favourable automatic responses for real demand within a nominal policy framework. The question of the effects of wage moderation is rather more complex. We believe that no policy adjustment is necessary. This also appears to be the government's view.     

Unconditional tests for association in 2 × 2 contingency tables in the total sum fixed design

The asymptotic approach and Fisher's exact approach have often been used for testing the association between two dichotomous variables. The asymptotic approach may be appropriate to use in large samples but is often criticized for being associated with unacceptable high actual type I error rates for small to medium sample sizes. Fisher's exact approach suffers from conservative type I error rates and low power. For these reasons, a number of exact unconditional approaches have been proposed, which have been seen to be generally more powerful than exact conditional counterparts. We consider the traditional unconditional approach based on maximization and compare it to our presented approach, which is based on estimation and maximization. We extend the unconditional approach based on estimation and maximization to designs with the total sum fixed. The procedures based on the Pearson chi‐square, Yates's corrected, and likelihood ratio test statistics are evaluated with regard to actual type I error rates and powers. A real example is used to illustrate the various testing procedures. The unconditional approach based on estimation and maximization performs well, having an actual level much closer to the nominal level. The Pearson chi‐square and likelihood ratio test statistics work well with this efficient unconditional approach. This approach is generally more powerful than the other p‐value calculation methods in the scenarios considered.     

Optimal discretionary monetary policy in a micro-founded model with a zero lower bound on nominal interest rate

This paper investigates optimal discretionary monetary policy under the zero lower bound on the nominal interest rate (ZLB) in the case of a distorted steady state due to monopoly and taxation. Solving a fully nonlinear micro-founded (FNL) model using a global method, I find that the central bank in a more distorted economy would cut the interest rate less aggressively under a particularly adverse demand shock. This occurs because inflation and nominal interest rates are higher on average, making the ZLB less likely to bind and causing the economy to escape from the ZLB sooner. However, the social planner would choose the optimal inflation rate of approximately zero. The result emerges because the unconditional benefit of avoiding the ZLB is not big enough to offset the cost of higher relative price dispersion when inflation is significantly positive. In addition, I show that the conventional linear-quadratic (LQ) method is inaccurate in the case of a sufficiently distorted steady state.