# Interest rate volatility and the macro rational expectations hypothesis

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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 reex- amined with this respecified model. The results reveal that while rationality is maintained, monetary neutrality is rejected. The rejection of zero interest rate vol- atility effect corroborates previous work by Evans and Tatom. We also find signif- icantly different effects of anticipated and unanticipated variables for money growth. Our findings strengthen Mishkins empirical results but reverse those of Frydman and Bappoport. The results provide further evidence that demonstrates the impor- tance 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 firms production and supply. He argues that the increased risk raises the variability of expected profits and in- creases the cost of using the firms capital. The risk-averse firm would respond by reducing output. Tatom provides evidence supporting the dominance of the aggregate supply channel of influence for in- terest rate volatility.

As shown diagrammatically in Tatom (1984), all the above ef- fects 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 fluc- tuations 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 in- terest 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 per- formed by Mishkin (1982) and Makin (1982) reject policy ineffec- tiveness. Frydman and Rappoport (1987), testing the original Barro and Rush (1980) and Mishkin (1982) models, conclude that antici- pated 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 vola- tility in determining business fluctuations indicates that all these findings need to be reexamined with this respecified model.

Mishkins (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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roborate Mishkin (1982, 1983) and provide a sharper focus to his empirical findings. On the other hand, the AUDI hypothesis is re- jected, reversing the results of Frydman and Rappoport (1987). The overall findings provide additional evidence supporting the impor- tance 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 de- mand.

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 quar- terly 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 correla- tion. 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 Moodys 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)

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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 gen- erated 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]12, with ri, denoting the change in the Moodys 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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run money growth variability than does the six-year moving stan- dard deviation measure used by Evans (1984). The variables sig- nificance as a group in determining expectations of interest rate vol- atility 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, contempora- neous 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 gov- ernment 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 equa- tions, 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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H. Sonmez Atesoglu and Donald H. Dutkowsky

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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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 in- significant 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 ration- ality, 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 con- strained 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 fore- casting 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 unanti- cipated...

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