interest rate volatility and the macro rational expectations hypothesis

H. SONMEZ ATESOGLU Clarkson University

Potsdam, New York

DONALD H. DUTKOWSKY Syracuse University

Syracuse, New York

Interest Rate Volatility and the Macro Rational kpectations Hypothesis*

In this paper, we augment the Barro-Mishkin quarterly output model with interest rate volatility and test this model for rationality, neutrality, and the distinction for anticipated and unanticipated changes in aggregate demand. The significant role of interest rate volatility indicates that findings from previous studies need to be reexamined with this respecified model. The results reveal that while rationality is maintained, monetary neutrality is rejected. The rejection of zero interest rate volatility effect corroborates previous work by Evans and Tatom. We also find significantly different effects of anticipated and unanticipated variables for money growth. Our findings strengthen Mishkin’s empirical results but reverse those of Frydman and Bappoport. The results provide further evidence that demonstrates the importance of interest rate volatility in determining and explaining business fluctuations.

1. Introduction In a recent paper, Evans (1984) introduces interest rate vol-

atility as a significant variable affecting business fluctuations. Citing Friedman (1982), h e argues that the rise in interest rate volatility brought about by the October 6, 1979, change in Federal Reserve operating procedure increased the risk of agents operating in finan- cial markets. Friedman in turn provides evidence that corporations responded by reducing their long-term bond financing. Since the nonfinancial corporate sector in the United States has traditionally relied upon long-term borrowing to finance purchases of new plants and equipment, Friedman contends that decreased business fixed investment could result.

Other possible detrimental effects have been advanced as well. According to Lombra and Struble (1979), heightened interest rate volatility increases money demand. They argue that the risk-averse investor will seek greater liquidity in response to the increased in-

*We thank two anonymous referees and Chihwa D. Kao for helpful comments.

Journal of Macroeconomics, Winter 1990, Vol. 12, No. 1, pp. 97-109 97 Copyright 8 1990 by Louisiana State University Press 0x4-0704/90/$1.50

H. Sonmz Atesoglu and Donald H. Dutkowsky

terest rate risk. Tatom (1984, 1985) asserts that increased risk also adversely affects the firm’s production and supply. He argues that the increased risk raises the variability of expected profits and increases the cost of using the firm’s capital. The risk-averse firm would respond by reducing output. Tatom provides evidence supporting the dominance of the aggregate supply channel of influence for interest rate volatility.

As shown diagrammatically in Tatom (1984), all the above effects imply that increased interest rate volatility leads to declines in output. Substantial empirical support for this hypothesis has emerged. Evans (1984), estimating the Barro (1981b) output model augmented with a measure of interest rate volatility, demonstrates a significantly negative relationship between unanticipated interest rate volatility and output. Tatom (1985) extends the Evans (1984) model and provides evidence that anticipated volatility ,also matters. The importance of interest rate volatility in explaining business fluctuations has been further reinforced in empirical studies that have utilized several different models of business fluctuation (see Tatom 1984; Dutkowsky and Atesoglu 1986; Dutkowsky 1987).

These studies, however, overlook the testing of several critical issues pertaining to the macro rational expectations hypothesis. In this paper, we augment the Mishkin (1982) output model with interest rate volatility and test for rationality, neutrality, and the need to distinguish between anticipated and unanticipated effects. Ra- tionality, the idea that economic units form expectations optimally using all available information, serves as the foundation of rational expectations-based models. Testing for neutrality, the property that only unanticipated changes in aggregate demand affect business fluctuations, has generated mixed results. Barro (1981b) and Barro and Rush (1980) find evidence supporting neutrality while tests performed by Mishkin (1982) and Makin (1982) reject policy ineffectiveness. Frydman and Rappoport (1987), testing the original Barro and Rush (1980) and Mishkin (1982) models, conclude that anticipated and unanticipated money growth do not exert significantly different effects upon output. They coin the acronym AUDI, which stands for anticipated-unanticipated-distinction-irrelevant, to de- scribe their test results. The significant role of interest rate volatility in determining business fluctuations indicates that all these findings need to be reexamined with this respecified model.

Mishkin’s (1983) estimation and test procedures serve as our empirical approach. The results obtained using quarterly data con- firm rationality but reject monetary neutrality. These results cor-

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lnterest Rate Volatility

roborate Mishkin (1982, 1983) and provide a sharper focus to his empirical findings. On the other hand, the AUDI hypothesis is rejected, reversing the results of Frydman and Rappoport (1987). The overall findings provide additional evidence supporting the importance of interest rate volatility in determining business fluctuations. They also point to the need to develop macroeconomic models along the lines of policy effectiveness with a rational expectations basis. Moreover, the results call for further examination of the separate roles of anticipated and unanticipated variables in aggregate demand.

2. Forecasting Equations In order to generate anticipated and unanticipated money

growth and interest rate volatility, we develop forecasting equations for these variables. Our sample consists of seasonally adjusted quarterly data spanning 1956:&1985:i. All data were obtained from the CITIBASE tape. We use the Mishkin (1983) procedure to avoid criticism raised against the forecasting equations of Barro (1981b) and Barro and Rush (1980) ( see, for example, Pesaran 1982; Mishkin 1982). The dependent variable lagged &om one to four quarters is included to capture persistence effects and to avoid serial correlation. We select the remaining explanatory variables according to the Granger (1969) criterion.

Variables attempted for each forecasting equation other than those appearing below, but found insignificant include one to four quarter lags of the log of the GNP deflator, the Federal budget deficit, the Barro (1981b) unemployment-employment ratio, the Moody’s AAA corporate bond rate, and the logs of the volatilites of Ml money growth, the Moody AAA corporate bond rate, and the six-month Treasury bill rate. We tested each forecasting equation for parameter stability, with two tests conducted for each equation. The first test divided the sample at the midpoint. In the second test, we split the sample at 1979:iu to examine the effects of the October 6 Federal Reserve change in policy procedure. In all cases Chow tests could not reject parameter stability at any reasonable level of significance for either sample break.

With absolute values of t-statistics appearing in parentheses, the estimated forecasting equation for money growth is

DM, = -0.16 + 0. 18DM,e1 + O.l7DM,+ + 0.003DM,-3 - O.l3DM,-, (4.26) (1.76) (1.55) (0.03) (1.36)

99

H. Sonmez Atesoglu and Donald H. Dutkowsky

+ O.O7logY,-, - O.O6logY,-, - 0.0810gY~-~ + 0.0910gY~-~ (1.08) (0.57) (0.92) (1.59)

- 0.005i,-1 + 0.004i,-2 + 0.0004& - 0.001&-4 + DMR,, (7.48) (3.76) @W (0.92)

R2 = 0.66, SE = 0.005, DW= 1.96; (1)

where DM, denotes Ml money growth defined as log M, - log Mtel, Y, refers to real GNP, i, is the six-month Treasury bill rate, and DMR, denotes unanticipated money growth. Equation (1) indicates that lagged output levels affect expectations of money growth. At- tempts to homogenize the units by replacing log Y with output growth generated inferior fit and insignificance of the output effect. The significance of short-term interest rates as a group corresponds to the findings of Mishkin (1982).

Anticipated and unanticipated interest rate volatility are generated according to

log VR, = -3.55 + 0.30 log VR,-I + 0.08 log V&e2 (2.37) (2.99) (0.81)

+ 0.15 log VR,-a - 0.02 log VR,-, - 0.32 log VM,-, (1.57) (0.17) (1.78)

+ 0.32 log VM,-2 + 0.04 log VM,-3 + 0.09 log VM,-, (1.70) (0.22) (0.51)

- 15.16 log G,-, + 35.82 log G,-, - 22.37 log G,-, (2.44) (3.81) (2.28)

+ 2.14 log Gtm4 + VRR, ; (0.32)

R2 = 0.42, SE = 1.23, DW=2.00. (2)

Comparable to Evans (1984), we define interest rate volatility as VR, = [(1/3)X;+ (rit - ft)2]1’2, with ri, denoting the change in the Moody’s AAA corporate bond rate during the ith month of quarter t and F~ = Zpr rit. Money growth volatility, VM,, is constructed in the same way as interest rate volatility; Tatom (1985) argues that the intraperiod standard deviation more accurately describes short-

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Interest Rate Volatility

run money growth variability than does the six-year moving standard deviation measure used by Evans (1984). The variable’s significance as a group in determining expectations of interest rate volatility corresponds to the findings of Tatom (1985). We also f&d the log of real government purchases of goods and services, G,, to be a significant determinant. The variable VRR, denotes unanticipated interest rate volatility.

3. Rationality and Policy Effectiveness Tests Estimates for the output equation appear in Table 1. This un-

restricted output equation allows for contemporaneous and lagged effects of anticipated and unanticipated money growth and interest rate volatility, while imposing cross-equation restrictions implied by the rational expectations model. Following Mishkin (1982, 1983), we include a time trend (t) to allow for increases in the natural level of output as well as to adjust for nonstationarity, the log of real government spending (G) to represent fiscal actions, contemporaneous and lagged anticipated money growth (DME), and current and past unanticipated money growth (DMR). Barro (1981a) argues that permanent income behavior brings about significantly positive effects of anticipated as well as unanticipated current-period real government spending. While Barro (198la) decomposes the government variable into anticipated and unanticipated as well as mil- itary and nonmilitary effects, we follow Barro (1981b) and Mishkin (1982, 1983) and use total government spending.

We augment the Mishkin (1982) equation by including current and lagged anticipated and unanticipated interest rate volatility (VRE and VRR). All anticipated and unanticipated variables extend for eight quarters. Frydman and Rappoport (1987) argue for the shorter lag length relative to the twenty lags used by Barro and Rush (1980) and Mishkin (1982). We employ the Mishkin (1983) procedure to perform joint estimation of the output and both forecasting equations, allowing for fourth-order autocorrelation in the residuals of the output equation. This error structure also accounts for possible residual seasonality effects remaining in the seasonally adjusted quarterly data.

We see from Table 1 that coefficient estimates for anticipated money growth in general are positive and significantly dif&erent from zero throughout the lag structure. In contrast, parameter estimates for unanticipated money growth are positive and significant only for the initial quarters. These results indicate that anticipated money

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TABLE 1. Estimated Unrestricted Outvut Eauation

8 8

log Y, = no + n,t + ITS log G, + 2 cqDME,-, + x f3,DMR,+ i=O i=O

6 6 4

+ 2 Givmt-i + z YiVRRt-i + Pt P t-4 = 2 P&-i + Et

i=O i=O i=l

IrlJ = 6.40 ‘(32.17) % = -0.12 (0.52) 6, = -0.002 (1.20) Tl = 0.006 (4.17) a1 = 0.40 (1.47) 61 = -0.001 (0.19) IT2 = 0.030 (0.77) 0~~ = 0.78 (2.46) 82 = -0.002 (0.57)

ag = 0.70 (2.10) a3 = -0.002 (0.59) a4 = 1.13 (3.76) 84 = 0.001 (0.57) o5 = 0.90 (2.77) a5 = 0.002 (0.82) ol, = 0.98 (3.40) 86 = 0.003 (0.14) CL7 = 0.40 (1.69) S7 = -0.002 (0.98) ct!J = 0.41 (2.00) a* = -0.002 (1.47) po = 0.31 (2.02) yo = -0.001 (0.75) p1 = 0.25 (1.14) y1 = -0.001 (0.58) p2 = 0.57 (2.01) y2 = -0.001 (0.87) p3 = 0.24 (0.75) y3 = -0.002 (1.24) B4 = -0.18 (0.50) y4 = -0.003 (1.25)

p1 = 1.10 (9.23) p5 = -0.34 (0.96) y5 = -0.003 (1.44) p, = 0.10 (0.53) p6 = -0.27 (0.85) y6 = -0.004 (1.77) p, = -0.31 (1.70) p, = -0.37 (1.55) y7 = -0.003 (2.27) p, = 0.08 (0.70) ps = -0.06 (0.35) ys = o.ooo (0.01)

R2 = 0.9946, SE = 0.007, DW = 1.93.

NOTE: Absolute values of t-statistics appear in parentheses.

growth policies produce long and lasting changes in output, while surprise money growth changes generate only short-term output movements.

The insignificance of long lags of unanticipated money growth conflicts with empirical estimations of new classical models such as Barro and Rush (1980). In the context of the new classical formu- lation, lagged effects of unanticipated variables arise from business cycle behavior in aggregate supply (see McCallum 1980). However, Tatom (1985) argues that within a nonneutral rational expectations

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interest Rate Volatility

model, lagged surprises primarily serve to help in forming current anticipations. Consequently, only contemporaneous unanticipated changes and possibly recent lags should exert independent effects. Estimated coefficients for unanticipated interest rate volatility show negative signs for all quarters except the last but are generally insignificant from zero. Anticipated interest rate volatility estimates are of mixed sign and are also insignificant. Multicollinearity or ab- sence of quarterly effect could account for the lack of significance in the estimated interest rate volatility coefficients.

To obtain more definitive results as well as to test for rationality, we perform likelihood ratio tests for restrictions of coefficients as a group. Following Mishkin (1983), we reject the null hypothesis if the likelihood ratio statistic

-2 log LR = n log (SSR”/SSR”) (3)

exceeds the chi-squared value at a critical level of significance. The difference in the dimensionality of the unconstrained and constrained systems determines the degrees of freedom. The variables in (3) are denoted: LR, the likelihood ratio; n, the sum of the num- ber of observations in the output equation, money growth forecasting equation, and interest rate volatility forecasting equation; SSR”, the sum of squared residuals of the constrained system; and SSR”, the residual sum of squares of the unconstrained system estimated with the heteroscedasticity weights of the constrained system (see Mishkin 1983). Besides examining rationality and neutrality, this framework can be utilized to test whether anticipated and unanticipated variables exert identical effects. Acceptance of this AUDI hypothesis supports a conventional aggregate demand-aggregate supply model where such distinctions are not made.

Since numerical maximization difficulties as well as different heteroscedasticity corrections between the constrained and unconstrained models may lead to inaccurate inference, we check our conclusions by performing Wald tests. Following the description in Maddala (1977, 180), suppose that the null hypothesis is Ho: e1 = &, where 0i refers to the r X 1 subset of the parameter vector 8. Let 6i denote the maximum likelihood estimate of 8i in the un- ,. restricted model and V(O,)-’ be the subset of the variance-covari- ante matrix that corresponds to 6,. Then the Wald statistic,

w = (ii, - e,)T(i,)(6, - 6,) ) (4)

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is distributed as chi-squared with r degrees of freedom under HO.

Test results appear in Table 2.’ Observe from Table 2 that the likelihood ratio statistic fails to

reject rationality. Acceptance of this null hypothesis indicates that optimal forecasts of money growth and interest rate volatility in (1) and (2) serve as anticipated and unanticipated variables in determining output. Consequently, cross-equation restrictions between the output and forecasting equations can be imposed without mis- specification.

Both tests reject the neutrality of money growth. The inclu- sion of interest rate volatility sharpens the corresponding findings of Mishkin (1982, 1983), who fails to reject monetary neutrality in his output model with relatively shorter lag length-seven lags of anticipated and unanticipated money growth. The null hypothesis of zero interest rate volatility effect is rejected at the 1% level under both tests. This result reinforces Evans (1984) and points to the importance of interest rate volatility in determining quarterly output movements. Both statistics reject the null hypotheses of identical anticipated and unanticipated effects for the joint case and money growth. Contradictory to Frydman and Rappoport (1987), this finding indicates that expected and surprise effects of monetary policy need to be distinguished in the interest rate volatility augmented model.2

The model, however, fails to reject the null hypothesis of interest rate volatility neutrality at any reasonable level of signifi-

‘The Wald test for the AUDI restrictions requires the variance-covariance matrix of the differences in parameter estimates for anticipated and unanticipated variables. Therefore, we estimate an unrestricted model using actual money growth, the log of interest rate volatility, and the unanticipated components of these variables. Rejection of the AUDI null hypothesis occurs when the Wald test for zero effects of the unanticipated components within this model is rejected. This equation and the model in Table 1 represent equivalent specifications for the unrestricted model; nearly identical partial derivatives are obtained in the estimation. We did not test for rationality with the Wald statistic because of its highly difficult implementation for this test.

‘Some experiments are performed to examine the robustness of our findings under changes in model variables and specification. In particular, we reestimate the model substituting the monetary base for Ml. As another way to consider output nonstationarity, following Frydman and Rappoport (1987), the model is also estimated replacing the time trend with the lagged dependent variable. In this direction we estimate a model using growth rates of output and government spending and lagged output. For all cases, the neutrality and AUDI conclusions for money growth as well as the significance of interest rate volatility remain unchanged.

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TABLE 2. Test Results

Test/Statistic Likelihood Ratio Wald

Rationality

Zero Effect of interest Rate Volatility

Joint Monetary and Znterest 32.069 Rate Volatility Neutrality (0.022)

Monetary Neutrality 18.859 (0.026)

Interest Rate Volatility Neutrality

AUDI for Money Growth and Interst Rate Volatility

AUDI for Money Growth

AUDI for Interest Rate Volatility

14.801 (0.961)

36.209 (0.006)

11.360 (0.252)

34.546 (0.011)

19.378 (0.022)

18.819 (0.027)

-

39.240 (0.003)

33.262 (0.016)

24.196 (0.004)

9.047 (0.401)

33.800 (0.013)

19.828 (0.019)

11.963 (0.215)

NOTES: Significance levels appear in parentheses. AUDI stands for anticipated- unanticipated-distinction-irrelevant. Degrees of freedom are 9 in all the tests except for rationality, zero effect of interest rate volatility, joint neutrality, and AUDI for money growth and interest rate volatility. The rationality test calls for 26 degrees of freedom; all the joint hypothesis tests use 18 degrees of freedom.

cance. The corresponding findings of interest rate volatility neutrality but signi6cance of anticipated money growth differ from results implied by most rational expectations-nonneutrality models such as Fischer (1977), Phelps and Taylor (1977), and Blinder and Fischer (1981). These studies contend that the aggregate supply function brings about nonneutrality, implying significant effects of all anticipated aggregate demand variables. One explanation for this mixed neutrality result is that only unanticipated interest rate volatility affects aggregate supply. Firms may curtail current period production plans made in the previous period only in response to unexpectedly

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increased risk. Alternatively, the findings suggest that risk averse consumers and producers change their money holdings and investment in response to just surprise movements in interest rate volatility. In this way our neutrality results support Blinder (1986), who calls for greater investigation of the separate roles of anticipated and unanticipated variables in aggregate demand.

Still another explanation is suggested by the mixed findings for testing AUDI in interest rate volatility. While the likelihood ratio test rejects the null hypothesis, the Wald test indicates acceptance. Interest rate volatility AUDI suggests a structural system

TABLE 3. Estimated Final Output Equation

8

log Yt = 710 + nit + 7~2 log Gt + z aiDME,+ + i PiDMR,-i i=O 1=0

8

Pt = f: Pik-i + Et i=l

TO = 6.36 (36.54) Tl = 0.005 (3.76) =2 = 0.030 (1.50)

p, = 1.03 (9.21) p, = 0.13 (0.83) p, = -0.35 (2.21) p, = 0.16 (1.44)

t&-j = -0.30 (1.49) a1 = 0.14 (0.59) a2 = 0.51 (1.78) ag = 0.46 (1.60) a4 = 1.03 (3.81) a5 = 0.65 (2.41) a6 = 1.02 (3.75) a, = 0.31 (1.54) a8 = 0.42 (2.46) PO = 0.39 (2.69) p1 = 0.31 (1.53) p2 = 0.65 (2.45) p3 = 0.30 (1.01) p4 = -0.14 (0.43) p5 = -0.22 (0.70) f.& = -0.17 (0.59) p, = -0.23 (1.01) p* = 0.00 (0.00)

yo = -0.002 (2.66) y1 = -0.002 (2.20) y2 = -0.003 (2.56) y3 = -0.004 (2.84) y4 = -0.004 (2.98) y5 = -0.004 (2.76) y,j = -0.003 (2.79) y7 = -0.003 (3.10) ya = o.ooo (0.41)

R2 = 0.9941, SE = 0.007, DW = 1.85.

NOTE: Absolute values of t-statistics appear in parentheses.

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in which the level of volatility affects aggregate supply but exerts no influence on aggregate demand, consistent with Tatom’s (1985) findings. Alternatively, large standard errors reflecting insignificance of anticipated interest rate volatility could account for this AUDI result.3

The test conclusions in Table 2 point to an output model that separates anticipated and unanticipated money growth but allows only for unanticipated interest rate volatility. We report estimates of this model in Table 3. Parameter estimates for anticipated money growth indicate that the effects of anticipated monetary policies be- gin to occur six months from the policy implementation and influence output throughout the two-year period. In contrast, surprise money growth changes produce significant effects only within the initial six months. Coefficient estimates for unanticipated interest rate volatility are negative and significantly different from zero throughout the lag structure.4

4. Conclusion Testing the Barro-Mishkin interest rate volatility augmented

output model confirms rationality while rejecting monetary neutrality. This finding provides additional evidence against the policy ineffectiveness proposition. Our results not only rea&m Mishkin (1982, I983), but they also remove ambiguities in his test results for shorter lag lengths. The results also reject the hypothesis of identical anticipated and unanticipated policy effects, reversing the findings of Frydman and Ftappoport (1987). The findings instead support rational expectations-based nonneutrality models such as Fisher (1977), Phelps and Taylor (1977), and Blinder and Fischer (1981), but also point to the need to consider separate anticipated

We also performed F-tests based upon the two-step estimation method used by Barre (198lb) and Barre and Rush (1980), continuing to allow for fourth-order serial correlation in the output equation. While this statistic is biased due to several factors (see Mishkin 1983; Pagan 1984), the test is easily computed and provides a I&her check on the findings. The F-test rejects at the 5% level of significance the null hypotheses of joint neutrality and joint AUDI. Zero interest rate volatility effect and money growth neutrality are rejected at the 10% level. The F-test does not reject any of the remaining null hypotheses at the 10% level.

41n the estimated model maintaining AUDI for interest rate volatility, we obtain negative estimated volatility parameters from the current-period through the sev- enth-quarter lag. Parameter estimates for the current-period through the fourth- quarter lag are significantly different from zero.

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and unanticipated effects in aggregate demand. In addition, we find that unexpected changes in interest rate volatility produce adverse effects upon business fluctuations, but the role of anticipated interest rate volatility remains unsettled. The results uniformly indicate that announced, rather than surprise, changes in money growth lead to larger and more persistent changes in output. The findings also imply that reducing unexpected interest rate fluctuation serves to improve business fluctuations.

Received: June 1988 Final version: March 1989

References Barro, Robert J. “Output Effects of Government Purchases.” Jour-

nal of Political Economy 89 (October 1981a): 1086-21. -. “Unanticipated Money Growth and Economic Activity in

the United States.” In Money, Expectations, and the Business Cycle: Essays in Macroeconomics, edited by Robert Barro, I37- 69. New York: Academic Press, 1981b.

Barro, Robert J., and Mark Rush. “Unanticipated Money and Eco- nomic Activity in the United States.” In Rational Expectations and Economic Policy, edited by Stanley Fischer, 23-48. Chicago: University of Chicago Press, 1980.

Blinder, Alan S. “Keynes After Lucas.” Eastern Economic Journal 12 (July-September 1986): 209-16.

Blinder, Alan S., and Stanley Fischer. “Inventories, Rational Ex- pectations, and the Business Cycle.” Journal of Monetary Eco- nomics 8 (November 1981): 277-394.

Dutkowsky, Donald H. “Unanticipated Money Growth, Interest Rate Volatility, and Unemployment in the United States.” Review of Economics and Statistics 69 (February 1987): 144-48.

Dutkowsky, Donald H., and H. Sonmez Atesoglu. “Unanticipated Money Growth and Unemployment: Post-Sample Forecasts.” Southern Economic Journal 53 (October 1986): 413-21.

Evans, Paul. “The Effects on Output of Money Growth and Interest Rate Volatility in the United States.” Journal of Political Econ- omy 92 (April 1984): 294-22.

Fischer, Stanley. “Long-Term Contracts, Rational Expectations, and the Optimal Money Supply Rule.” JournaZ of Political Economy 85 (February 1977): 191-205.

Friedman, Benjamin M. “Federal Reserve Policy, Interest Rate

108


Volatility, and the U.S. Capital Raising Mechanism.” Journal of Money, Credit, and Banking 14, part 2 (November 1982): 721- 45.

Frydman, Roman, and Peter Rappoport. “Is The Distinction Be- tween Anticipated and Unanticipated Money Growth Relevant in Explaining Aggregate Output. 2” American Economic Review 77 (September 1987): 693-703.

Granger, Clive W.J. “Investigating Causal Relations by Economet- ric Models and Cross-Spectral Methods.” Econometrica 37 (July 1969): 424-38.

Lombra, Raymond E., and Frederick Struble. “Monetary Aggregate Targets and the Volatility of Interest Rates: A Taxonomic Dis- cussion.” Journal of Money, Credit, and Banking 11 (August 1979): 284-300.

Maddala, G.S. Econometrics. New York: McGraw-Hill, 1977. Makin, John H. “Anticipated Money, Inflation Uncertainty, and Real

Economic Activity.” Review of Economics and Statistics 64 (Feb- ruary 1982): 126-34.

McCallum, Bennett T. “Rational Expectations and Macroeconomic Stabilization Policy: An Overview.” Journal of Money, Credit, and Banking 12, part 2 (November 1980): 716-46.

Mishkin, Frederic S. “Does Anticipated Monetary Policy Matter? An Econometric Investigation.” Journal of Political Economy 90 (February 1982): 22-51.

-. A Rational Expectations Approach to Macroeconometrics: Testing Policy Zneffectiveness and Efficient Markets Models. Chi- cago: University of Chicago Press, 1983.

Pagan, Adrian. “Econometric Issues in the Analysis of Regressions With Generated Regressors.” International Economic Review 25 (February 1984): 221-47.

Pesaran, M.H. “A Critique of the Proposed Tests of the Natural Rate-Rational Expectations Hypothesis.” Economic Journal 92 (September 1982): 529-54.

Phelps, Edmund S., and John B. Taylor. “Stabilizing Powers of Monetary Policy Under Rational Expectations.” JournaZ of Polit- ical Economy 85 (February 1977): 163-90.

Tatom, John A. “Interest Rate Variability: Its Link to the Variability of Money Growth and Economic Performance.” Federal Reserve Bank of St. Louis Review 66 (November 1984): 31-47.

-. “Interest Rate Variability and Economic Performance: Fur- ther Evidence.” Journal of Political Economy 93 (October 1985): 1008-18.

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