Abstract
This paper investigates the possible effects upon expected real interest rates (hereinafter referred to as real rates) arising from programs of monetary restraint. The investigation focuses on the unobservable real rate because it is typically regarded as the mechanism whereby slower money growth results in observable changes, such as a rise in nominal interest rates, a slowdown in economic activity, and currency appreciation. Thus, debate over the economic costs and international effects associated with policies to reduce monetary growth centers on the magnitude of their impact on real rates.
I. Summary
This paper investigates the possible effects upon expected real interest rates (hereinafter referred to as real rates) arising from programs of monetary restraint. The investigation focuses on the unobservable real rate because it is typically regarded as the mechanism whereby slower money growth results in observable changes, such as a rise in nominal interest rates, a slowdown in economic activity, and currency appreciation. Thus, debate over the economic costs and international effects associated with policies to reduce monetary growth centers on the magnitude of their impact on real rates.
Concern over the stance of fiscal policy also centers on possible effects on real rates. The expectation that large future deficits will be monetized increases anticipated inflation and thereby increases nominal interest rates. Another view sees large deficits resulting in an increased flow of securities, which will be held only at higher real rates. In turn, the higher real rates will crowd out some private borrowers, thereby depressing private investment and economic activity.
Major findings of this paper fall into three categories: (1) Programs of monetary restraint tend to result in higher real interest rates because when they are initially implemented, they result in “surprise” monetary stringency. The negative money surprises in the second quarter of 1981 were of sufficient magnitude to have added an estimated 2 to 3 percentage points to both real and nominal interest rates.
(2) An increase in the fiscal deficit can raise the real rate if it raises the ratio of total borrowing to gross national product (GNP), but the usual effect of a larger ratio of the budgetary deficit to GNP is to lower the real rate. This apparent paradox is caused by the fact that total borrowing relative to GNP typically moves inversely with respect to the budgetary deficit relative to GNP, since deficits often rise during recessions, when total demand on credit markets is low.
(3) The equation estimated to explain interest rate behavior consistently underpredicts interest rates in 1981. This suggests not only some change in underlying structural relationships but also possible effects of special circumstances, such as the new tax incentives for business and the large projected budgetary deficits in the United States.
Overall, the study suggests two general conclusions. First, programs of inflation control involving monetary stringency may produce temporary, largely unavoidable upward pressure on real rates, since the initial measures may come as a surprise in the wake of past expansionary policies. Second, such programs should be implemented with careful attention paid to the implications of fiscal policy for total credit demand.
II. Introduction
This paper investigates the possible effects upon expected real interest rates arising from programs of monetary restraint and attendant policies. The expected real interest rate (hereinafter referred to as the real rate) is the focus of the investigation, because it typically is seen as transmitting the effects of changes in the money growth rate to the economy. According to this view, slower money growth results in a number of observable changes in important economic variables—including a rise in market or nominal interest rates, a slowdown in economic activity, and currency appreciation—and these observable effects can ultimately be traced to the impact of slower money growth on the unobservable real rate. Since policies aimed at controlling inflation involve a reduction in money growth, debate over the economic costs and international effects associated with the control of inflation centers on the magnitude of the attendant positive impact on real rates; an increase in real rates, in turn, results in a slowdown in economic activity or a currency appreciation.
Views differ on the magnitude of these by-products of inflation control. On the one hand, those who see prices as highly flexible tend to view “real” variables, such as the real rate, as largely independent of monetary policy, except for very brief periods and, therefore, see lower costs associated with the control of inflation. On the other hand, those who view prices as sticky tend to attribute persistent and sometimes costly real effects, transmitted by the real rate, to the monetary restraint associated with programs of inflation control.
Concern over the stance of fiscal policy in conjunction with monetary policy also centers on possible effects on the real rate and the attendant costs and international repercussions of the policy mix. An easy fiscal policy that produces large actual and/or expected deficits may raise nominal interest rates for either of two reasons. According to one view, the expectation that large future deficits will be monetized increases anticipated inflation and thereby increases nominal interest rates. According to the alternative view, large deficits result in an increased flow of securities, which will only be held at higher real rates. In turn, the higher real rates will crowd out some private borrowers, thereby depressing private investment and resulting in the slowdown in economic activity discussed earlier. Those holding the first view tend to argue that deficits will not raise nominal interest rates if the public is convinced they will not be monetized. Those who emphasize the impact of deficits on the real rate argue that slower money growth or nonmonetization of deficits will produce a liquidity shortage, so that higher real rates will be required to squeeze out private borrowers in order for a large quantity of government securities to be sold. Those who see a possible positive impact on the real rate arising from large deficits will clearly be more concerned about negative effects on economic activity associated with crowding out and about a possible export of a slowdown as real rates rise abroad than will those who emphasize the impact on expected inflation. The former see real economic effects associated with larger deficits, while the latter see largely nominal effects.
In order to investigate the possible costs and international repercussions of a program of monetary stabilization and inflation control, this paper tests a number of hypotheses regarding the behavior of the real rate. Specifically, tests of the hypothesis that surprise changes in the money supply are inversely related to the real rate are conducted that simultaneously allow for operation of the Mundell-Tobin effect1 of anticipated inflation on the real rate. In addition, the paper tests the hypothesis that larger actual or anticipated government deficits relative to GNP will raise the real rate owing to the crowding out phenomenon. Section III reviews highlights of recent empirical literature investigating behavior of the real rate and describes the methodology to be employed here. Section IV describes the model to be tested, briefly reviews some recent investigations that focus on the effects of monetary shocks on real rates, and discusses the measurement of monetary surprises. Results of estimating the model are reported in Section V. Implications of the results for explaining interest rate behavior during 1980-81 are presented in Section VI, and some concluding remarks are presented in Section VII.
III. Empirical Investigations of the Expected Real Interest Rate
Statistical investigations regarding the possibility of movements in the real rate have appeared with increasing frequency since publication of Fama’s (1975) provocative article.2 Nelson and Schwert (1977) argued that Fama’s test of the joint hypothesis of market efficiency and constancy of the real rate was not sufficiently powerful and, after applying more powerful tests, concluded that the data permitted rejection of the hypothesis of constancy of the real rate. Other investigations, including those by Hess and Bicksler (1975), Carlson (1977), Garbade and Wachtel (1978), and Levi and Makin (1979), have rejected the hypothesis of constancy of the real rate while tending to support the hypothesis that market interest rates include an efficient inflationary premium.
More recently, investigators have moved from merely testing the hypothesis of constancy of the real rate to searching for an explanation for the real rate movements suggested by a large body of statistical evidence. Mishkin (1981) has investigated the relationship between the real rate and anticipated inflation suggested by Mundell (1963) and Tobin (1965). Levi and Makin (1979,1981) and Hartman (1981) have considered effects of inflation uncertainty on the real rate. Dwyer (1981) has found that the real rate is independent of predictable changes in the money supply.
This paper investigates the hypothesis that surprise changes in the money supply are inversely related to the real interest rate, while simultaneously allowing for operation of the Mundell-Tobin effect of anticipated inflation on the real rate.3 Tests are also conducted of the possible positive impact upon the real rate arising from larger government budget deficits. The three novel aspects of the investigation are tests of the hypothesized impact of money surprises on real rates in conjunction with tests of the Mundell-Tobin hypothesis, tests of possible evidence of crowding out associated with larger budget deficits, and estimation employing transfer function methodology developed by Box and Jenkins (1970).
The transfer function methodology employed to estimate the empirical relationships investigated in this study has a number of advantages over the usual linear econometric estimation techniques. With this methodology, it is possible to entertain any autoregressive (AR), moving average (MA), or combined (ARMA) representation of residuals and to estimate it simultaneously with relationships between the endogenous and exogenous variable(s), while the usual methodology allows only iterative estimation of a first-order autoregressive process to represent residuals. The transfer function also enables parsimonious representation of possible distributed lag relationships between the endogenous variable and exogenous variables. It is worth noting that the transfer function in its simplest representation produces estimation results identical to the usual ordinary-least-squares (OLS) methodology with serially uncorrelated residuals. As is well known, however, the standard assumptions required for OLS estimation are often violated; and in such cases, the transfer function technique provides the investigator with a useful and more flexible tool with which to test for empirical relationships.
Overall, the transfer function is reasonably well described as a means to combine time series and structural explanations of behavior of economic variables such as interest rates. Problems encountered in estimation of the impact of monetary surprises and other variables upon real interest (see Section IV) provide a particularly good illustration of its advantages.
IV. Natural and Cyclical Components of the Real Rate
COMPONENTS OF THE REAL RATE
The hypothesis to be tested here involves decomposition of the real rate into a long-run underlying, or natural, component and a short-run cyclical component. The analogy with the decomposition by Lucas (1973) of real output into natural and cyclical components is obvious.
The natural portion of the real rate is determined by the expected marginal productivity of capital and the marginal rate of time preference of consumers.4 The equilibrium natural real rate equates, at the margin, the subjective rate at which investors are willing to exchange current and future consumption, with the rate representing the marginal product of capital—that is, the objective, technological marginal rate of transformation between current and future goods. Under the Mundell-Tobin effect, the natural portion of the real rate can be affected by changes in anticipated inflation. A rise in anticipated inflation causes a shift out of money balances and into real capital, thereby depressing the marginal product of capital and the equilibrium real rate. This is the Tobin effect set out in Tobin (1965). Mundell (1963) describes a similar phenomenon whereby a rise in anticipated inflation depresses equilibrium real cash balances and consequently increases the steady-state level of flow saving owing to the real balance effect. Equilibrium is restored by means of a lower real interest rate, which increases the level of investment until it equals the higher level of saving. This effect, operating as it does on the steady-state level of saving, is not expected to be subsequently reversed in the absence of further change in the rate of anticipated inflation.
The hypothesized impact of a money surprise on real interest arises from an assumption of sticky price adjustment. Money growth above its anticipated level results in an excess supply of money if prices are sticky in the short run, assuming also that surprise money growth does not immediately cause a rise in real income sufficient to absorb excess money supply. Until prices adjust fully to absorb the excess money supply, the only alternative is for real interest rates to fall, thereby (ceteris paribus) lowering nominal interest rates by an amount sufficient to clear the money market.5
The impact of a money surprise on the real rate ought to be temporary, lasting only as long as stickiness of prices prevents adjustment to monetary equilibrium without some adjustment of the real rate. Its duration and existence is an empirical question, the answer to which ought to shed some light on the speed of adjustment of overall prices.
The real rate may also be affected by budget deficits. In addition to the possible impact of budget deficits on anticipated inflation, a larger budget deficit relative to GNP, which raises overall private and public sector borrowing relative to the GNP proxy for the economy’s ability to absorb debt, will require a higher real rate to induce investors to hold a larger real stock of securities. Alternatively, the higher real rate may be viewed as necessary to crowd out private sector borrowing. A higher level of borrowing relative to GNP is hypothesized to increase the cyclical portion of the real rate. More specifically, an increase in the ratio of borrowing to GNP creates an excess supply of securities, which, in turn, causes a temporary increase in the real rate.
The exact formulation to be investigated here includes the Fisher equation and a hypothesis dividing the real rates into natural and cyclical components (where all rates are continuously compounded).
where
it = nominal interest rate at time t
rt = expected real interest rate (with
FDOG = net funds raised in U.S. credit markets divided by GNP7
πt = anticipated inflation, or the log of the price level at t + 1, as expected at t, less the log of the actual price level,
et = an error term, normally distributed with mean zero8
Substituting equation (2) into (1), equations (3) and (4) give an expression for the nominal interest rate in terms of a constant term, anticipated inflation, the ratio of net borrowing to GNP, a money surprise, and an error term9
Equation (5) suggests that regression of nominal interest on a constant, a measure of net borrowing relative to GNP, a money surprise, and anticipated inflation ought to: (1) provide, from the constant term, an estimate of the portion of the natural real rate unaffected by anticipated inflation; (2) test the hypothesized positive impact upon the real rate of a rise in the level of borrowing relative to GNP; (3) test the hypothesized negative impact of a money surprise on the real rate by checking to see if the coefficient on the surprise is significantly less than zero; and (4) test the hypothesized negative impact of anticipated inflation on the real rate by checking to see if the coefficient on anticipated inflation is significantly below unity. Examination of the impact of lagged values of anticipated inflation and lagged values of borrowing relative to GNP on contemporary nominal interest ought not to indicate subsequent reversal of the initial negative impact. Alternatively, the hypothesized temporary negative impact of a money surprise ought not to persist, in which case distributed lag coefficients on the money surprise term ought to sum to zero.
OTHER INVESTIGATIONS OF MONEY SHOCKS AND REAL RATE
The notion being advanced here that monetary shocks cause the real rate to diverge temporarily from its long-run equilibrium value is also investigated in a study by Cornell (1981) that extends the work of Fama and Gibbons (1980). Cornell finds that monetary shocks connected with U.S. banks’ reserve settlements on Wednesdays cause temporary (one-day) movements in the (Federal funds) real rate of the sort hypothesized previously in equation (3).10 He suggests further that a possible reason for the failure of Fama and Gibbons to detect such effects is prompt action by the Federal Reserve System to offset such shocks. Cornell explicitly recognizes, however, that given “a dramatic shift to a policy of slow, constant growth in the monetary base …, it may turn out that reserve problems which develop on Wednesday suddenly have a large and sustained impact on the ex ante real rate” (p. 18). In short, while Cornell’s investigation of the impact of monetary shocks on the real rate is conceptually similar to this investigation, his explicit finding of a one-day impact resulting from Wednesday (lagged) reserve settlement shocks says nothing explicit about the possible impact of surprise money growth over one quarter on real rates of return on 90-day Treasury bills investigated here, since he appears to believe that shocks are essentially offset within a day. However, the previous quotation clearly indicates a view that a shock lasting for a quarter would have an impact on the real rate, measured at quarterly intervals.
In another related study, Grossman (1981) considers the response of interest rates on Treasury bills to weekly money supply announcements by the Federal Reserve System. With the change in the bill rate between 3:30 p.m. and 5:00 p.m. on announcement day (Friday) as the dependent variable, Grossman finds a positive link running from money surprises (positive if the increase in the money supply exceeds a consensus, predicted level) to the change in interest rates. This positive relationship reflects, in Grossman’s view, “the System’s technique of operation,” whereby faster money growth results in movement toward the upper bound and causes the public to anticipate tightening by the Federal Reserve System.
The positive sign of the relationship between a money surprise and the change in interest rates hypothesized by Grossman is the reverse of the relationship hypothesized by Cornell (1981) and this study. There is, however, no real conflict with the behavior hypothesized here. In effect, Grossman’s rationale for this positive relationship is a policy reaction function built into Federal Reserve System operating procedures during the September 1977-September 1979 sample period examined. Grossman assumes that money growth above the targeted level would cause the Federal Reserve System to move to raise the federal funds rate and that the public would anticipate such action, thereby bidding up interest rates in anticipation of such a move. While such a response may be possible during a single day for a given policy regime, the findings of Cornell and this study (reported later on) suggest that controlling for anticipated inflation reveals that money growth that is greater than anticipated will temporarily depress the real rate. This results holds for both daily and quarterly data.
MEASUREMENT OF MONEY SURPRISES
This study employs residuals from an ARMA (1,5) model11 of money (M1-B) growth as money surprises.12 It would be possible to estimate money surprises using alternative measures of money such as M2 and/or using alternative representations of anticipated money growth such as those linking behavior of the money supply to targets of monetary policy that appear in Barro (1977). While the range of possible measures of money surprises is wide, experimentation with a number of conceptually different measures in Makin (1982) produced highly correlated measures (all exceeding 0.90) of money surprises and had little impact upon the results of testing the natural rate hypothesis.
There also arises the issue of sample data employed to estimate the model of money supply behavior. If either the form of the ARMA model or the coefficients of a given ARMA model change over time, then forecasts as of time t should employ only data available as of time t. This problem, alluded to by Sheffrin (1979), also appears to be more serious in principle than in practice (see Makin (1982)). It is worth noting here that Khan (1981) uses a far more tractable alternative than Sheffrin’s procedure of periodic re-estimation for estimation of surprises using only data that were available to forecasters at the time forecasts were being made. The technique of sequential estimation used by Khan employs the procedure of Brown, Durbin, and Evans (1975) to produce for a given ARMA model a series of any length of updated coefficient estimates, which requires only one matrix inversion to produce the initial ARMA model estimate. This procedure is appealing and can be used with a wide range of data series from which one desires to extract surprises in a logically consistent manner. For postwar U.S. money series, however, it appears that the procedure produces little impact on actual measures of surprises. For the sample period extending from March 1973 to June 1981, a series of M2 surprises estimated using Khan’s method was regressed on a surprise series estimated for the identical sample period with ARMA. The result yielded a constant term not significantly different from zero (t-statistic = +0.97) and an estimated surprise coefficient of 0.93, which is only 1.21 standard errors less than unity. The two series are presented later on in Chart 2, a glance at which will reveal the high degree of their correlation.
M1-B Surprises (At Annual Growth Rates): Pre-Sample Estimation, March 1973-June 19801
(In per cent)
Citation: IMF Staff Papers 1982, 002; 10.5089/9781451946888.024.A003
Source: United States, Federal Reserve Bulletin, various issues.1 The residual from the ARMA model of money growth, the mean values and standard deviations of which are shown in Table 5.M2 Surprises (At Annual Growth Rates): March 1973-September 19811
Citation: IMF Staff Papers 1982, 002; 10.5089/9781451946888.024.A003
Source: United States, Federal Reserve Bulletin, various issues.1The residual from the ARMA model of money growth, the mean values and standard deviations of which are shown in Table 5. The pre-sample and in-sample methods are described in Section IV.The overall result of careful consideration of alternative measures of postwar U.S. money surprises, which may very well not generalize to other series, is to suggest that in-sample ARMA models serve as well as any. This is a useful piece of information, as it suggests that the simplest method of estimating money surprises serves as well as any of the more complex alternatives.
PROBLEMS OF IDENTIFICATION AND OBSERVATIONAL EQUIVALENCE
An identification problem that can arise in attempting to estimate an equation such as (5) has been elucidated by Buiter (1980). His discussion, which is applied largely to implementation of tests of the natural rate hypothesis of Lucas (1973), makes clear the requirement that identification of the parameter describing the impact of a money surprise in equation (5) requires an assumption that money growth is independent of the other variables in the equation. There is also a related problem of “observational equivalence,” which is noted by Sargent (1976) and McCallum (1979), whereby it is impossible to distinguish between the hypothesized impacts upon the real rate of (1) money surprises and (2) actual money growth unless money growth is independent of innovations in nominal interest rates.
Since there is no unique method of solving this identification problem, this study shall proceed on the assumption that monetary innovations cause contemporaneous interest rate innovations, rather than vice versa. Independence of actual money growth from contemporary anticipated inflation and borrowing relative to GNP is no stronger an assumption than many of the others required for empirical investigation of this issue.
V. Testing for Constancy of Real Rate
Results of estimating interest rate equations are presented in three stages. First, results are presented that focus upon the impact of monetary surprises and anticipated inflation; also, implications of proper modeling of residuals with the transfer function are discussed. Next, the impact of including the borrowing/GNP ratio is investigated. Finally, the “best” model is employed to generate post-sample forecasts in order to consider the possibility of a recent (since the end of 1980) structural shift in the true parameters of the model describing behavior of interest rates.
CORRECTING CORRELATED RESIDUALS
Results of estimating interest rate equations excluding the borrowing/GNP variable are presented in Table 1. It is clear from equation (9) that after dealing with the problem of properly modeling residuals, it is impossible to reject the two hypotheses advanced in Section III about behavior of the real rate. A 1 per cent positive money surprise produces a significant negative impact on the real interest rate (estimated to be about 28 basis points), while a 1 per cent rise in anticipated inflation significantly depresses the real interest rate by an estimated 25 (1 - 0.746 ≅ 0.25) basis points. The relevant test of the hypothesized negative impact of anticipated inflation on the real rate is whether the coefficient on πt, is significantly less than unity. The estimated coefficient of 0.746 in equation (9) is 2.71 standard errors less than unity and is significant at the 0.01 level.
Money Surprises and Real Interest: First Quarter 1959-Fourth Quarter 19801
(Dependent variable: 3-month Treasury bill rate)
Figures in parentheses are t-statistics. D-W denotes the Durbin-Watson statistic.
The money surprise is measured by residuals from an AR-1, MA-5 model of M1-B growth estimated using quarterly data for the period extending from the first quarter of 1959 to the fourth quarter of 1980. The chi-square test of the hypothesis that residuals are white noise has a significance level of 0.94.
Anticipated inflation is based on data supplied by the Federal Reserve Bank of Philadelphia on 6-month inflationary expectations. Interpolation is employed to obtain a quarterly series.
Equation (8) is estimated with the Cochrane-Orcutt correction for serial correlation (ρ = 0.725; t = 9.06).
Equation (9) is estimated as a transfer function. Residuals are modeled by an AR-1; MA-3 model (t-statistics are 5.78, 5.59). A chi-square test fails to reject the hypothesis that the first 24 residuals from equation (9) are white noise at a significance level of 0.55.
Money Surprises and Real Interest: First Quarter 1959-Fourth Quarter 19801
(Dependent variable: 3-month Treasury bill rate)
| Antici- | ||||||
|---|---|---|---|---|---|---|
| Money | pated | |||||
| Equation | Constant | Surprise2 | Inflation3 |
|
D-W | n |
| (6) | 2.53 | 0.756 | 0.77 | 0.58 | 87 | |
| (12.38) | (17.23) | |||||
| (7) | 2.46 | −0.424 | 0.777 | 0.78 | 0.67 | 87 |
| (12.14) | (2.21) | (17.68) | ||||
| (8) | 2.39 | −0.138 | 0.814 | 0.43 | 4 | 86 |
| (4.55) | (1.26) | (7.97) | ||||
| (9) | 2.66 | −0.277 | 0.746 | 0.90 | 5 | 88 |
| (5.59) | (2.66) | (7.97) |
Figures in parentheses are t-statistics. D-W denotes the Durbin-Watson statistic.
The money surprise is measured by residuals from an AR-1, MA-5 model of M1-B growth estimated using quarterly data for the period extending from the first quarter of 1959 to the fourth quarter of 1980. The chi-square test of the hypothesis that residuals are white noise has a significance level of 0.94.
Anticipated inflation is based on data supplied by the Federal Reserve Bank of Philadelphia on 6-month inflationary expectations. Interpolation is employed to obtain a quarterly series.
Equation (8) is estimated with the Cochrane-Orcutt correction for serial correlation (ρ = 0.725; t = 9.06).
Equation (9) is estimated as a transfer function. Residuals are modeled by an AR-1; MA-3 model (t-statistics are 5.78, 5.59). A chi-square test fails to reject the hypothesis that the first 24 residuals from equation (9) are white noise at a significance level of 0.55.
Money Surprises and Real Interest: First Quarter 1959-Fourth Quarter 19801
(Dependent variable: 3-month Treasury bill rate)
| Antici- | ||||||
|---|---|---|---|---|---|---|
| Money | pated | |||||
| Equation | Constant | Surprise2 | Inflation3 |
|
D-W | n |
| (6) | 2.53 | 0.756 | 0.77 | 0.58 | 87 | |
| (12.38) | (17.23) | |||||
| (7) | 2.46 | −0.424 | 0.777 | 0.78 | 0.67 | 87 |
| (12.14) | (2.21) | (17.68) | ||||
| (8) | 2.39 | −0.138 | 0.814 | 0.43 | 4 | 86 |
| (4.55) | (1.26) | (7.97) | ||||
| (9) | 2.66 | −0.277 | 0.746 | 0.90 | 5 | 88 |
| (5.59) | (2.66) | (7.97) |
Figures in parentheses are t-statistics. D-W denotes the Durbin-Watson statistic.
The money surprise is measured by residuals from an AR-1, MA-5 model of M1-B growth estimated using quarterly data for the period extending from the first quarter of 1959 to the fourth quarter of 1980. The chi-square test of the hypothesis that residuals are white noise has a significance level of 0.94.
Anticipated inflation is based on data supplied by the Federal Reserve Bank of Philadelphia on 6-month inflationary expectations. Interpolation is employed to obtain a quarterly series.
Equation (8) is estimated with the Cochrane-Orcutt correction for serial correlation (ρ = 0.725; t = 9.06).
Equation (9) is estimated as a transfer function. Residuals are modeled by an AR-1; MA-3 model (t-statistics are 5.78, 5.59). A chi-square test fails to reject the hypothesis that the first 24 residuals from equation (9) are white noise at a significance level of 0.55.
The significance of employing the transfer function technique to estimate equation (9) can be seen by comparing equations (6) through (8) with equation (9). In equation (6), it is clear that anticipated inflation alone leaves highly autocorrelated residuals (Durbin-Watson statistic = 0.58). Addition of the money surprise term raises the Durbin-Watson statistic somewhat and adds to overall explanatory power but leaves an unacceptably high level of indicated autocorrelation in residuals. The usual procedure would be to correct equation (7) for autocorrelated residuals. The result of employing the Cochrane-Orcutt procedure is reported as equation (8). There is a drop in overall significance levels, leaving one to conclude from equation (8) that a money surprise does not produce a statistically significant negative impact on the real rate. However, inspection of the residuals from equation (7) suggests that they are not adequately represented by an ARMA (1,0) model. Estimation of a transfer function (equation (9)) reveals that an ARMA (1,3) model is required to leave white-noise residuals. Proper modeling of residuals produces a substantially changed result—namely, that the data do not permit rejection of the hypothesis that a positive money surprise has a negative impact on the real rate. This result carries with it the implication that prices are somewhat sticky, at least for a period of up to one quarter.
It would, of course, be desirable to provide prior hypotheses regarding implications for estimated parameter values or estimated standard errors of mismodeling residuals. Hendry (1977) has investigated the question and found that little can be said about it, particularly where higher-order processes are involved.13 The best operational rule is to model residuals in a way that leaves white-noise residuals and not simply to assume that an ARMA (1,0) representation is correct.
POSSIBLE IMPACT OF MONEY SURPRISE ON ANTICIPATED INFLATION
It is worth noting that the estimated coefficient on anticipated inflation is little affected by inclusion of a money surprise term. The possibility exists that the level of anticipated inflation may be positively correlated with a money surprise, which, given a negative impact of a money surprise on the real rate, would tend to bias downward the estimated impact of anticipated inflation on nominal interest when the money surprise is omitted from the equation. Such a possibility deserves consideration in the light of a persistent tendency for the estimated impact of anticipated inflation upon nominal interest to lie below the value of unity anticipated under the Fisher hypothesis.14 The fact is, however, that, at least for the sample under investigation here, the correlation coefficient between anticipated inflation and money surprise is only 0.21. The overall implication is that the persistent finding that the estimated coefficient on anticipated inflation is less than unity may well be due to the negative impact of anticipated inflation on the real rate rather than to bias associated with omission of a money surprise. Failure to entertain this hypothesis led investigators to consider a wide range of alternative explanations, including measurement error on anticipated inflation, “fiscal illusion” (Tanzi (1980)), and failure to control adequately for changes in other variables (such as the level of economic activity or the inflation rate) that might also affect the real rate. All of these possible effects may be valid, but it would be useful to reconsider them in the light of a possible Mundell-Tobin effect.15
PERSISTENCE OF MONEY SURPRISE AND ANTICIPATED INFLATION EFFECTS
If it is found that the impact of a money surprise is not reversed after a quarter or more, the implication is that prices tend to be sticky over a longer period of time. A persistent impact of anticipated inflation on subsequent real rates would suggest a permanent impact upon the rate of capital formation under the Mundell-Tobin hypothesis. These possibilities can easily be checked using output from the transfer function estimation procedure. Gross correlations between unexplained changes in the dependent variable and each of the exogenous variables enable one to check on possible distributed-lag relationships. For the money surprise, the chi-square test statistic for cross correlations with 12 degrees of freedom is 14.3 with a marginal significance value of 0.28. While this result constitutes only a marginal rejection of possible lagged relationships over 12 periods, inspection of the plot of cross correlations reveals that all of the cross correlations lie within a range of two standard errors from zero. The most significant cross correlation, at lag 3, did not enter significantly when added to equation (9). A hypothesis of price stickiness for periods of more than one quarter is supported by these findings, whereby the initial downward pressure on the real rate is not subsequently reversed. Such a finding is contrary to the views of many economists regarding the degree of price flexibility. In view of the marginal rejection of a lagged relationship between money surprises and the real rate that was suggested earlier, more investigation may be called for. For now it is worth noting that the (insignificant) lagged cross correlations between the money surprise and the unexplained portion of the dependent variable are all positive for the period extending from the first quarter through the third quarter. This suggests a tendency for (negative) effects of the surprise to be erased over a cycle spanning about 9 months.
The chi-square test statistic for cross correlations with anticipated inflation given 12 degrees of freedom is 8.52, which carries a marginal significance value of 0.744. This constitutes a highly significant rejection of a possible lagged relationship between the real rate and anticipated inflation and suggests, as does the Mundell-Tobin hypothesis, that a rise in anticipated inflation has a permanent negative impact on the real rate.16
CONTROLLING FOR OTHER VARIABLES
In an earlier study of the effects of anticipated inflation on nominal interest, Levi and Makin (1979, 1981) controlled for the impacts of output growth and inflation uncertainty upon the real rate, finding both to have negative impacts. Bomberger and Frazer (1981) also found that a Livingston measure of inflation17 uncertainty had a significant negative impact on interest rates.
More recently, Hartman (1981) has argued that the real rate ought to be defined as the nominal rate minus the expected inflation rate plus the variance of the inflation rate. This implies a measure of inflation variance on the right-hand side of equation (4) with a coefficient of minus 1. Neither real growth nor inflation uncertainty entered significantly when they were added to equation (9), either separately or together. This result suggests that the money surprise term in equation (9) is capturing the impact on the real rate of inflation uncertainty and output growth. Larger money surprises may well increase inflation uncertainty. The natural rate hypothesis suggests that money surprises raise the level of real output but not its growth rate. However, price stickiness within a quarter or inventory effects may cause money surprise effects on real output growth. The price stickiness requirement is consistent with the finding that a money surprise is inversely related to the real rate. Full reconciliation of the results reported here with earlier investigations will require further investigation but should provide additional insights into short-run real effects of monetary disturbances.
INCLUSION OF A MEASURE OF BUDGET DEFICITS IN INTEREST RATE EQUATION
As was noted earlier, if budget deficits increase net borrowing relative to GNP (FDOG), the crowding out hypothesis suggests a positive impact of deficits upon the real rate. If, as some analysts suggest, FDOG is positively correlated, via anticipated monetization of debt, with anticipated inflation, this will impart an upward bias to the estimated coefficient on anticipated inflation when FDOG is omitted from the equation.
Equation (10) in Table 2 reports the result of adding FDOG to the interest rate equation. None of the conclusions drawn from discussion of Table 1 is seriously affected. The negative impact of a money surprise on the real rate is slightly reduced, as is the estimated coefficient attached to anticipated inflation. The latter result reflects some positive correlation between anticipated inflation and FDOG. 18
Budget Deficits and Real Interest1
(Dependent variable: 3-month Treasury bill rate)
Figures in parentheses are t-statistics.
Budget Deficits and Real Interest1
(Dependent variable: 3-month Treasury bill rate)
| Antici- | Borrow- | ||||||
|---|---|---|---|---|---|---|---|
| Money | pated | ing/GNP | Noise | ||||
| Equation | Constant | Surprise | Inflation | (FDOG) |
|
Model | n |
| (10) | 1.30 | -0.237 | 0.711 | 10.86 | 0.92 | AR-1, | 86 |
| (1.58) | (2.28) | (5.43) | (2.89) | MA-2,3 | |||
| (11) | -0.14 | -0.228 | 0.378 | 11.36 | 0.93 | AR-1, | 89 |
| (0.03) | (2.50) | (1.77) | (2.93) | MA-2,3 | |||
| (12) | 0.0 | -0.151 | 0.490 | 10.22 | 0.94 | AR-1, | 89 |
| (2.09) | (2.27) | (3.11) | MA-1,2 |
Figures in parentheses are t-statistics.
Budget Deficits and Real Interest1
(Dependent variable: 3-month Treasury bill rate)
| Antici- | Borrow- | ||||||
|---|---|---|---|---|---|---|---|
| Money | pated | ing/GNP | Noise | ||||
| Equation | Constant | Surprise | Inflation | (FDOG) |
|
Model | n |
| (10) | 1.30 | -0.237 | 0.711 | 10.86 | 0.92 | AR-1, | 86 |
| (1.58) | (2.28) | (5.43) | (2.89) | MA-2,3 | |||
| (11) | -0.14 | -0.228 | 0.378 | 11.36 | 0.93 | AR-1, | 89 |
| (0.03) | (2.50) | (1.77) | (2.93) | MA-2,3 | |||
| (12) | 0.0 | -0.151 | 0.490 | 10.22 | 0.94 | AR-1, | 89 |
| (2.09) | (2.27) | (3.11) | MA-1,2 |
Figures in parentheses are t-statistics.
Based on the estimated coefficient attached to the ratio of net borrowing to GNP in equation (10), a government deficit accruing at the rate of $100 billion annually that pushed up total borrowing by the full amount of the deficit would raise the 3-month Treasury bill rate by about 68 basis points during the first quarter it was in effect.19 The positive impact would not persist beyond one quarter and would reflect a rise in the real rate. The two-standard-error range of the estimate covers 21 to 116 basis points. These estimates should be viewed as upper bounds if it is supposed that during any given period, a rise in government borrowing, in addition to crowding out private investments, is associated with a downward shift in the private borrowing schedule.
STRUCTURAL SHIFT
It is interesting to investigate the possibility of a structural shift in the estimated relationship just discussed (reported as equation (10) in Table 2). Since the end of 1980, a policy regime change has occurred, at least proximately, on account of the change in the United States Administration. In order to test for structural change, equation (10) was re-estimated adding observations for the first three quarters of 1981. The result is given as equation (12). A Chow test of the null hypothesis that the three 1981 observations obey the same relationship as that given by equation (10) yields an F-statistic of 6.68, which is well above the critical value of 4.07 required for rejection of the null hypothesis at the 0.01 level. These results constitute evidence of a structural shift after the end of 1980 in the interest rate equation (10).
The nature of the shift becomes clear from examination of the post-sample performance of equation (10) in predicting the interest rate. Employing actual values of post-sample exogenous variables, the model consistently and badly underpredicts interest rates during the first three quarters of 1981. As is clear from the upper portion of Table 3, actual interest rates during 1981 lie well above the upper end of the 95 percent confidence range for forecasts based on the model estimated with data ending in the fourth quarter of 1980. This result seems attributable to parameter change, since actual post-sample values of explanatory variables are used to generate these post-sample forecasts.
Model Forecasts of Interest Rates
Confidence limits are at the 95 per cent, or two standard error, level.
Model Forecasts of Interest Rates
| Forecast Lower Confidence1 | Upper Confidence | ||||
|---|---|---|---|---|---|
| For: | Limit | Forecast | Limit | Actual | Error |
| Origin fourth quarter 1980: out-of-sample | |||||
| First quarter 1981 | 9.76 | 11.35 | 12.94 | 14.39 | 3.04 |
| Second quarter 1981 | 7.93 | 9.99 | 12.06 | 14.91 | 4.91 |
| Third quarter 1981 | 8.36 | 10.50 | 12.64 | 15.05 | 4.55 |
| Origin fourth quarter 1980: in-sample | |||||
| First quarter 1981 | 12.25 | 13.66 | 15.06 | 14.39 | 0.73 |
| Second quarter 1981 | 10.37 | 12.76 | 15.15 | 14.91 | 2.15 |
| Third quarter 1981 | 9.87 | 12.65 | 15.44 | 15.05 | 2.39 |
Confidence limits are at the 95 per cent, or two standard error, level.
Model Forecasts of Interest Rates
| Forecast Lower Confidence1 | Upper Confidence | ||||
|---|---|---|---|---|---|
| For: | Limit | Forecast | Limit | Actual | Error |
| Origin fourth quarter 1980: out-of-sample | |||||
| First quarter 1981 | 9.76 | 11.35 | 12.94 | 14.39 | 3.04 |
| Second quarter 1981 | 7.93 | 9.99 | 12.06 | 14.91 | 4.91 |
| Third quarter 1981 | 8.36 | 10.50 | 12.64 | 15.05 | 4.55 |
| Origin fourth quarter 1980: in-sample | |||||
| First quarter 1981 | 12.25 | 13.66 | 15.06 | 14.39 | 0.73 |
| Second quarter 1981 | 10.37 | 12.76 | 15.15 | 14.91 | 2.15 |
| Third quarter 1981 | 9.87 | 12.65 | 15.44 | 15.05 | 2.39 |
Confidence limits are at the 95 per cent, or two standard error, level.
A policy regime change could affect parameter estimates in an equation like (10). Alternatively, some other exogenous event that put upward pressure on interest rates may have taken place during 1981. In an attempt to distinguish between these two possibilities, equation (10) was re-estimated for “best fit” employing the full sample used to estimate equation (11). The result was a change in the noise model coupled with a reduction in the estimated impact of a money surprise. The impact of anticipated inflation fell also, compared with the estimate reported in equation (10) for the shorter sample period. The equation (12) model also produced the superior forecasts reported in the lower portion of Table 3, although as in-sample forecasts, they are not strictly comparable with the out-of-sample forecasts above. Still, it appears that some of the out-of-sample forecast errors were due to parameter shifts, possibly reflecting a policy regime change coincident with a change in the U.S. Administration.
The fact that even after re-estimation using 1981 data, the model continues to underpredict interest rates, with the magnitude of the error increasing as 1981 goes on, suggests that some exogenous force(s) are operating to push up interest rates. These may include political changes in Europe, the impact of the Economic Recovery Act of 1981 on expected real returns on investment and on projected future deficits, and the increased uncertainty surrounding money surprises and real returns; the last of these factors may cause a rise in the risk premium to be built into observable interest rates, as suggested by Hartman (1981). As more data becomes available, it will be useful to investigate these hypotheses.
VI. Recent Behavior of Real and Nominal Interest Rates
The association of money surprises and budget deficits with movements in expected real rates of interest suggests that, if one controls for expected inflation, the behavior of such surprises and budget deficits ought to give an indication of the behavior of the unobservable expected real interest rate.20 Inspection of Table 4 suggests that expected inflation rates rose steadily from 1973 through 1974, fell until the end of 1976, and then rose steadily until 1980, after which they dropped by over 1.6 per cent from December 1980 to June 1981. It appears, however, that volatility of expected inflation over the period was moderate (a standard deviation of 1.22 per cent for the December 1972-December 1978 period) and even fell during the June 1979-June 1981 period (to a standard deviation of 1.05 per cent). During the latter period, expected inflation rates were high but fairly stable.
Mean and Standard Deviation of Six-month Forecasts Using Data at Annual Rates
Mean and Standard Deviation of Six-month Forecasts Using Data at Annual Rates
| Standard Deviation | |||
|---|---|---|---|
| Date | Mean | Cross section | Over time |
| December 1972 | 3.22 | 0.83 | |
| June 1973 | 4.00 | 1.31 | |
| December 1973 | 5.17 | 2.10 | |
| June 1974 | 7.12 | 2.38 | |
| December 1974 | 7.70 | 2.32 | |
| June 1975 | 5.64 | 2.12 | 1.22 (December 1972- |
| December 1978) | |||
| December 1975 | 5.84 | 1.38 | |
| June 1976 | 5.30 | 1.30 | |
| December 1976 | 5.23 | 1.81 | |
| June 1977 | 5.92 | 1.36 | |
| December 1977 | 5.99 | 1.23 | |
| June 1978 | 6.40 | 1.57 | |
| December 1978 | 6.97 | 1.75 | |
| June 1979 | 8.31 | 2.35 | |
| December 1979 | 10.14 | 2.37 | |
| June 1980 | 10.67 | 2.57 | |
| December 1980 | 10.51 | 2.58 | 1.05 (June 1979- |
| June 1981) | |||
| June 1981 | 8.86 | 2.83 | |
Mean and Standard Deviation of Six-month Forecasts Using Data at Annual Rates
| Standard Deviation | |||
|---|---|---|---|
| Date | Mean | Cross section | Over time |
| December 1972 | 3.22 | 0.83 | |
| June 1973 | 4.00 | 1.31 | |
| December 1973 | 5.17 | 2.10 | |
| June 1974 | 7.12 | 2.38 | |
| December 1974 | 7.70 | 2.32 | |
| June 1975 | 5.64 | 2.12 | 1.22 (December 1972- |
| December 1978) | |||
| December 1975 | 5.84 | 1.38 | |
| June 1976 | 5.30 | 1.30 | |
| December 1976 | 5.23 | 1.81 | |
| June 1977 | 5.92 | 1.36 | |
| December 1977 | 5.99 | 1.23 | |
| June 1978 | 6.40 | 1.57 | |
| December 1978 | 6.97 | 1.75 | |
| June 1979 | 8.31 | 2.35 | |
| December 1979 | 10.14 | 2.37 | |
| June 1980 | 10.67 | 2.57 | |
| December 1980 | 10.51 | 2.58 | 1.05 (June 1979- |
| June 1981) | |||
| June 1981 | 8.86 | 2.83 | |
Charts 1 and 2 and Table 5 suggest a contrast between the level and volatility of money surprises. The mean absolute monetary surprise, which measures the pressure on U.S. expected real interest rates, rose sharply after October 1979 for both M1-B and M2. So, too, did the standard deviation of absolute money surprises.
Absolute Mean and Standard Deviation of U.S. Monetary Surprises 1
Numbers are expressed as annual percentage rates. They were calculated using seasonally adjusted monthly data.
Surprises measured by residuals from an AR-3 model of M1-B growth estimated over the period extending from January 1965 through February 1973 and updated monthly through July 1981. See Khan (1981).
Surprises measured by residuals from an AR-1 model of M2 growth estimated over the period specified in footnote 1.
Absolute Mean and Standard Deviation of U.S. Monetary Surprises 1
| M1-B2 | M 2 3 | |||
|---|---|---|---|---|
| Standard | Standard | |||
| Time Period | Mean | deviation | Mean | deviation |
| March 1973-October 1978 | 3.34 | 2.38 | 2.61 | 2.19 |
| October 1978-July 1981 | 6.84 | 5.74 | 3.30 | 3.16 |
| March 1973-September 1979 | 3.56 | 2.56 | 2.45 | 2.10 |
| October 1979-July 1981 | 8.21 | 6.27 | 4.21 | 3.49 |
Numbers are expressed as annual percentage rates. They were calculated using seasonally adjusted monthly data.
Surprises measured by residuals from an AR-3 model of M1-B growth estimated over the period extending from January 1965 through February 1973 and updated monthly through July 1981. See Khan (1981).
Surprises measured by residuals from an AR-1 model of M2 growth estimated over the period specified in footnote 1.
Absolute Mean and Standard Deviation of U.S. Monetary Surprises 1
| M1-B2 | M 2 3 | |||
|---|---|---|---|---|
| Standard | Standard | |||
| Time Period | Mean | deviation | Mean | deviation |
| March 1973-October 1978 | 3.34 | 2.38 | 2.61 | 2.19 |
| October 1978-July 1981 | 6.84 | 5.74 | 3.30 | 3.16 |
| March 1973-September 1979 | 3.56 | 2.56 | 2.45 | 2.10 |
| October 1979-July 1981 | 8.21 | 6.27 | 4.21 | 3.49 |
Numbers are expressed as annual percentage rates. They were calculated using seasonally adjusted monthly data.
Surprises measured by residuals from an AR-3 model of M1-B growth estimated over the period extending from January 1965 through February 1973 and updated monthly through July 1981. See Khan (1981).
Surprises measured by residuals from an AR-1 model of M2 growth estimated over the period specified in footnote 1.
Since U.S. nominal interest rates have been highly volatile since October 1979, the implication of Tables 4 and 5 and Charts 1 and 2 is that, at least in view of the behavior of monetary surprises, volatility of expected real interest rates has accounted for more movements of nominal interest rates than has volatility of expected inflation rates.
The level of real interest rates in 1980-81 also reflects the pressure on credit markets, as measured by the ratio of total borrowing to GNP. The ratio was well above its average level for 1959-80 during the period extending from the beginning of 1980 until the third quarter of 1981. (The only exception was the second quarter of 1980, during which credit controls were in effect.) The mean ratio is about 14 per cent, while the average ratio during the period extending from the fourth quarter of 1980 to the second quarter of 1981 was about 18 per cent, or about one standard deviation above the mean. Based on estimates in Table 2, a change of 4 per cent in the ratio would raise the real rate by about 40 basis points. Part of the reason for the atypically high level of the ratio of total borrowing to GNP during this period was the unusual coincidence of a rise in fiscal deficits (government demand for credit) and a strong private demand for credit.
Some of the most intense upward pressure on real interest rates in the United States appears to have materialized during the second quarter of 1981. Charts 1 and 2 suggest that an additional reason for this is a sequence of negative money surprises during that time. It appears that in the wake of the very large negative, and then positive, monetary surprises inherent in the imposition and subsequent removal of credit controls during 1980, another sequence of surprises—this time positive-negative ones—materialized in the first half of 1981. Added to negative money surprises was the impact of the strong demand for credit just discussed. This combination of factors tended to create a situation in which high (real) interest rates were more likely to be linked to budget deficits.
In addition to the persistent upward pressures exerted by higher-than-normal total borrowing demands, forces operating on nominal interest rates during the first half of 1981 can be described in terms of events affecting expected inflation rates and expected real interest rates. Election of a new president and expectations of budget-balancing and/or monetary control tended to lower expected inflation over the first six months of 1981 (see Table 4). The brief acceleration of money supply growth above expected levels tended to depress real interest rates during the first quarter of 1981; consequently, nominal interest rates, particularly short rates, fell during the first quarter of 1981. However, an apparent “mini-accord” at the end of March 1981 between the U.S. Treasury and the Federal Reserve System sharply increased pressure on the latter to keep monetary aggregates, then above target, at or below targeted levels. The result was a sharp deceleration of money growth during the second quarter of 1981 that came as a surprise to most observers (see Charts 1 and 2). Such large negative surprises put strong upward pressure on expected real interest rates, swamping the depressing impact of lower inflationary expectations. Most of the drop in inflationary expectations may have come during the first quarter of 1981, so that most of the sharp rise in expected real interest rates (estimated, based on Tables 1 through 5, to be between 2 and 3 per cent) that took place during the second quarter was transmitted directly to nominal rates without being offset by expectations of decreased inflation.
VII. Concluding Remarks
This paper has tested the hypotheses that money surprises and anticipated inflation are inversely related to the expected real rate of interest while total credit demand relative to GNP is positively related to the real rate. The results obtained, which are based on quarterly data for the period extending from the first quarter of 1959 to the fourth quarter of 1980, fail to reject any of these hypotheses.
An examination of the behavior of money surprises before and after institution of new operating procedures by the Federal Reserve Board in October 1979 indicates sharp increases in both the level and volatility of such surprises. The results reported here—which indicate that there was increased volatility of money surprises when the volatility of anticipated inflation had, if anything, decreased since October 1979—suggest that since October 1979, movements of nominal interest rates have been influenced more by changes in expected real interest rates than by changes in anticipated inflation.21 This would explain Hodrick’s (1981) observation of a change in the sign of the observable relationship between nominal interest differentials and exchange rates that has been prevalent since October 1979, as well as the apparent failure of nominal interest rates to respond to the drop in inflationary expectations during the first half of 1981.
In addition to the impact of money surprises on the level and volatility of real interest rates, the persistence of heavy demands on the credit markets created by an unusual coincidence of high levels of private and public sector borrowing kept real rates higher than they otherwise would have been during 1980-81.
The primary implication for monetary policy of the findings reported here is that the result of Fama and Gibbons (1980), whereby a sudden transition to a sharply reduced growth rate of the money base would reduce short-term nominal rates, may not be valid. On the contrary, empirical findings reported in Section V suggest that, unless a negative money surprise results in an instantaneous and equal percentage decrease in inflationary expectations, the overall result will be an increase, at least temporarily, in the nominal rate owing to an increase in the real rate. Such an increase appears likely, since no such close relationship between money surprises and anticipated inflation is evident from the data examined here.
Added to this result is the finding that easy fiscal policy that results in higher actual or anticipated budget deficits and in heavier total demands on credit markets will, in conjunction with a surprise decrease in money growth, produce abnormally high real rates, such as those that materialized during the second quarter of 1982. It should be noted, however, that large budget deficits per se may not typically increase total credit demand, since they usually arise during recessions, when total demand for credit is low.
In general, a program of inflation control that involves monetary stringency may produce some temporary, largely unavoidable upward pressure on real rates, since the stringency necessary to cut inflation may come as a surprise in the wake of past expansionary policies that created the need for a program of inflation control. Such programs should, however, be implemented with careful attention paid to the implications of fiscal policy for total credit demand. Increase in fiscal deficits that occur when private demand for credit is already strong will increase total credit demand, which, in conjunction with negative money surprises, will create intense—though temporary—upward pressure on real rates. In sum, the risk of a slowdown in economic activity and the international repercussions associated with inflation control programs can be minimized, though probably not eliminated, if a slowdown in money growth is not accompanied by policies that give rise to large actual or anticipated budget deficits.
REFERENCES
Alamouti, Kaveh, “An Analysis of the International Relationship Among Real Rates of Return” (unpublished, London Business School, January 1980).
Barro, Robert J., “Unanticipated Money Growth and Unemployment in the United States,” American Economic Review, Vol. 67 (March 1977), pp. 101–15.
Bomberger, William A., and William J. Frazer, Jr., “Interest Rates, Uncertainty and the Livingston Data,” Journal of Finance, Vol. 36 (June 1981), pp. 661–75.
Box, George E. P., and Gwilym M. Jenkins, Time Series Analysis: Forecasting and Control (San Francisco, 1970).
Brown, R. L., and others, “Techniques for Testing the Constancy of Regression Relationships Over Time,” Journal of the Royal Statistical Society, Series B, Vol. 37 (No. 2, 1975), pp. 149–63.
Buiter, Willem H., “Some Problems of Estimation and Hypothesis Testing in Models of Unanticipated Monetary Growth: A Simple Example” (unpublished, International Monetary Fund, August 22, 1980).
Carlson, John A., “Short-Term Interest Rates as Predictors of Inflation: Comment,” American Economic Review, Vol. 67 (June 1977), pp. 469–75.
Cornell, Bradford, “Can Monetary Policy Affect the Ex-Ante Real Rate: New Tests Using Daily Data” (unpublished, Graduate School of Management, University of California, Los Angeles, 1981).
Darby, Michael R., “The Financial and Tax Effects of Monetary Policy on Interest Rates,” Economic Inquiry, Vol. 13 (June 1975), pp. 226–76.
Dwyer, Gerald P., Jr., “Are Expectations of Inflation Rational? Or Is Variation of the Expected Real Interest Rate Unpredictable?” Journal of Monetary Economics, Vol. 8 (July 1981), pp. 59–84.
Fama, Eugene F., “Short-Term Interest Rates as Predictors of Inflation,” American Economic Review, Vol. 65 (June 1975), pp. 269–82.
Fama, Eugene F., and Michael Gibbons, “Inflation, Real Returns, and Capital Investment” (unpublished, Graduate School of Business, University of Chicago, 1980).
Feldstein, Martin, “Inflation, Income Taxes, and the Rate of Interest: A Theoretical Analysis,” American Economic Review, Vol. 66 (December 1976), pp. 809–20.
Fisher, Irving, The Theory of Interest (New York, 1930).
Garbade, Kenneth, and Paul Wachtel, “Time Variation in the Relationship between Inflation and Interest Rates,” Journal of Monetary Economics, Vol. 4 (November 1978), pp. 755–65.
Grossman, Jacob, “The ‘Rationality’ of Money Supply Expectations and the Short-Run Response of Interest Rates to Monetary Surprises,” Journal of Money, Credit and Banking, Vol. 13 (November 1981), pp. 409–24.
Hartman, Richard, “On the Appropriate Definition of the Real Rate of Interest” (unpublished, University of Washington, October 1981).
Hendry, David F., “Comments on Granger-Newbold’s ‘Time Series Approach to Econometric Model Building’ and Sargent-Sims’ ‘Business Cycle Modeling Without Pretending to Have Too Much A Priori Economic Theory,’” in New Methods in Business Cycle Research: Proceedings from a Conference, ed. by Christopher Sims (Federal Reserve Bank of Minneapolis, 1977), pp. 183–202.
Hess, Patrick J., and James L. Bicksler, “Capital Asset Prices Versus Time Series Models as Predictors of Inflation: The Expected Real Rate of Interest and Market Efficiency,” Journal of Financial Economics, Vol. 2 (December 1975), pp. 341–60.
Hodrick, Robert J., “Exchange Rates, Nominal and Real Interest Rates, and the Role of Monetary Policy” (unpublished, International Monetary Fund, July 1981).
Keran, Michael, and Charles Pigott (1980 a), “Interest Rates and Exchange Rates: I (The Relationship),” Federal Reserve Bank of San Francisco, Weekly Letter (September 12, 1980), pp. 1–3.
Keran, Michael, and Charles Pigott (1980 b), “Interest Rates and Exchange Rates: II (Policy Implications),” Federal Reserve Bank of San Francisco, Weekly Letter (September 19, 1980), pp. 1–3.
Khan, Mohsin S., “Monetary Shocks and the Dynamics of Inflation,” Staff Papers, Vol. 27 (January 1980), pp. 250–84.
Khan, Mohsin S., “Estimating Models of Expectations: A Simplified Sequential Approach” (unpublished, International Monetary Fund, July 1981).
Levi, Maurice D., and John H. Makin, “Anticipated Inflation and Interest Rates: Further Interpretation of Findings on the Fisher Equation,” American Economic Review, Vol. 68 (December 1978), pp. 801–12.
Levi, Maurice D., and John H. Makin, “Fisher, Phillips, Friedman and the Measured Impact of Inflation on Interest,” Journal of Finance, Vol. 34 (March 1979), pp. 35–52.
Levi, Maurice D., and John H. Makin, “Fisher, Phillips, Friedman and the Measured Impact of Inflation on Interest: A Reply,” Journal of Finance, Vol. 36 (September 1981), pp. 963–69.
Lucas, Robert E., Jr., “Some International Evidence on Output-Inflation Tradeoffs,” American Economic Review, Vol. 63 (June 1973), pp. 326–34.
Makin, John H., “Anticipated Money, Inflation Uncertainty and Real Economic Activity,” Review of Economics and Statistics, Vol. 64 (February 1982), pp. 126–34.
McCallum, Bennett, “On the Observational Inequivalence of Classical and Keynesian Models,” Journal of Political Economy, Vol. 87 (April 1979), pp. 395–402.
Mishkin, Frederic S., “The Real Interest Rate: An Empirical Investigation,” in The Costs and Consequences of Inflation, ed. by Karl Brunner and Allan H. Meltzer, Carnegie-Rochester Conference Series on Public Policy, Vol. 15 (Amsterdam, 1981), pp. 151–200.
Mundell, Robert A., “Inflation and Real Interest,” Journal of Political Economy, Vol. 71 (June 1963), pp. 280–83.
Nelson, Charles R., and G. William Schwert, “Short-Term Interest Rates as Predictors of Inflation: On Testing the Hypothesis that the Real Rate of Interest is Constant,” American Economic Review, Vol. 67 (June 1977), pp. 478–86.
Sargent, Thomas J., “The Observational Equivalence of Natural and Unnatural Rate Theories of Macroeconomics,” Journal of Political Economy, Vol. 84 (June 1976), pp. 631–40.
Sheffrin, Steven M., “Unanticipated Money Growth and Output Fluctuations,” Economic Inquiry, Vol. 17 (January 1979), pp. 1–13.
Tanzi, Vito, “Inflation, Indexation and Interest Income Taxation,” Banco Nazionale del Lavoro, Quarterly Review, Vol. 29 (March 1976), pp. 64–76.
Tanzi, Vito, “Inflationary Expectations, Economic Activity, Taxes, and Interest Rates,” American Economic Review, Vol. 70 (March 1980), pp. 12–21.
Tobin, James, “Money and Economic Growth,” Econometrica, Vol. 33 (October 1965), pp. 671–84.
Mr. Makin, Consultant in the Research Department when this paper was prepared, is Professor of Economics at the University of Washington in Seattle and a Research Associate with the National Bureau of Economic Research. This article represents a part of a large body of work that he has undertaken investigating the effects of monetary policy and associated phenomena, both nationally and internationally. He is a graduate of Trinity College (Hartford, Connecticut) and the University of Chicago.
This is defined and discussed in Section IV.
Long before the investigations discussed here, Irving Fisher reported, based on an investigation of market interest rates during the late nineteenth and early twentieth centuries in London, New York, Berlin, Calcutta, and Tokyo, that “the real rate of interest in terms of commodities is from seven to thirteen times as variable as the market rate of interest expressed in terms of money” (Fisher (1930), p. 415).
Mishkin (1981) found a significant negative impact upon the real rate of a lagged actual (consumer price index) inflation rate taken as a proxy for anticipated inflation. An autoregressive integrated moving average (ARIMA) (0,1,1) inflation model with a seasonal MA-1 term also provided an expected inflation proxy with a significant negative impact on the real rate.
Alamouti (1980) provides a similar description of the determination of the real rate. Determination of the real rate in this manner is suggested directly by the full title of Fisher’s (1930) classic—The Theory of Interest as Determined by Impatience to Spend Income and Opportunity to Invest it.
This view of dynamic adjustment to monetary shocks is investigated empirically for a number of developing countries in Khan (1980).
Since actual money growth less anticipated money growth is written as
Both figures are expressed as seasonally adjusted annual rates. Net funds raised in U.S. credit markets are based on data drawn from the U.S. Federal Reserve Board’s Flow-of-Funds Accounts. See Federal Reserve Bulletin, Table 1.58, “Funds Raised in U.S. Credit Markets,” Line 60.
The nature of the error process is the subject of investigation in Section III.
Tax effects alluded to by Darby (1975) and Feldstein (1976) are ignored. Mishkin (1981) finds that their inclusion has little impact on conclusions regarding non-constancy of the real rate.
Cornell is clearly thinking of shocks to the monetary base in the form of shortages or excesses of bank reserves.
The first number in parentheses indicates the order of the autoregressive process, and the second number the order of the moving average.
The chi-square test statistic for the hypothesis that the residuals of the ARMA(1,5) model is 6.84 with 14 degrees of freedom, which implies a significance level of 0.94. The model was estimated using quarterly data for the period extending from the first quarter of 1959 to the fourth quarter of 1980.
Hendry also suggests that identifying the correct order of error autocorrelation is more important than the form (AR or MA). More specifically, had the true error process been ARMA (0,1), an ARMA (1,0) would do reasonably well. But since the true process in equation (9) was ARMA (1,3), ARMA (1,0) represents a serious misspecification.
A value above unity is anticipated if tax effects articulated by Darby (1975), Tanzi (1976), and Feldstein (1976) are considered. See Tanzi (1980) for a discussion of these articles and others that investigate the quantitative impact of changing inflationary expectations on nominal interest. Tanzi argues that “fiscal illusion,” or failure to account for taxes, may be responsible for lower-than-expected coefficients obtained when nominal interest rates are regressed on anticipated inflation.
Levi and Makin (1978, 1979, 1981) have investigated a number of these effects in a model including a Mundell-Tobin effect. This paper, however, adds consideration of money surprise effects on the real rate.
The problem of inference here is complicated by the fact that the Mundell-Tobin hypothesis hinges upon the difference of the coefficient of anticipated inflation from unity and not from zero. However, both the incorporation of a change in anticipated inflation into nominal interest and the real impact under the Mundell-Tobin hypothesis are expected to be permanent. This generates a prior hypothesis of persistence with no subsequent reversal that is not contradicted by the data.
That is, the standard deviation across sample participants of the expected rate of inflation as reported in surveys conducted by the Philadelphia Inquirer under the guidance of Joseph Livingston and compiled semiannually by the Federal Reserve Bank of Philadelphia.
Despite some correlation with FDOG, anticipated inflation remains a highly significant explanatory variable in an equation such as (10). The F-statistic for the significance of including anticipated inflation in equation (10) is 14.65, well above the critical value of 7.01 required for significance at the 0.01 level.
It is important to realize that total borrowing relative to GNP—and not the government budget deficit relative to GNP—is included in equation (10). If the budget deficit relative to GNP were to be employed in place of the variable used in equation (10), the estimated coefficient would indicate that larger deficits cause interest rates to fall. The reason for this seemingly odd result is that during the 1959-80 sample period, government deficits typically rose in recessions when private borrowing fell. As the latter category is roughly three times government borrowing, the net effect is a reduction in total credit demand. Therefore, a larger government budget deficit is serving as a proxy for a fall in total credit demand, which, in turn, results in a drop in the real rate.
The term “budget deficits” refers here only to government borrowing that raises the ratio of total borrowing to GNP.
A similar suggestion has been advanced in Keran and Pigott (1980 a) and (1980 b).
