The Model and Hypotheses

rate are a good measure of changes in monetary policy and are informative about future movements in real activity. 6 It was found in our study that distinctions between positive innovations, negative innovations, and anticipated monetary policy change are relevant for explaining move- ment in real output. There is evidence that unanticipated expansionary monetary policy is just as likely to have a statistically significant effect on output as is unanticipated contractionary monetary policy. 7 These results appear to be robust across different measures of monetary policy, different specifications of the monetary policy and output equations, and over different sample periods. For monetary policy measured by change in the federal funds rate, an asymmetry in the effects of anticipated expansionary and anticipated contractionary monetary policy on output was found. The null hypothesis of no asymmetry in stimulativecontractionary policy was rejected. Anticipated expansionary monetary policy and anticipated contrac- tionary policy were each found to have statistically significant effects on output. A major finding of the study is that allowing asymmetries in anticipated and unanticipated monetary policy between stimulative and contractionary components makes the finding of neutrality of money less likely. In Section II, the model and the hypotheses to be considered are presented. Empirical results for growth in money and for spread are presented in Sections III and IV, respectively. The issue of asymmetry in stimulativecontractionary policy is taken up in Section V, when the change in the federal funds rate is used as the measure of monetary policy. Section VI is the conclusion.

II. The Model and Hypotheses

The procedure adopted in this paper involves nonlinear joint estimation of a money policy indicator equation—from which monetary policy innovations will be constructed—and a real output growth equation. The setup of the relationship between money and output follows that in Barro 1977 and Mishkin 1982. 8 The monetary policy indicator process is characterized by: MPI t 5 Z t2 1 g 1 u t , 1 where t 5 2, . . . , T. In equation 1, the monetary policy indicator, MPI t , can be represented by the growth in M1, spread, the change in the federal funds rate, or some other measure of the stance of monetary policy. Z t2 1 is a vector of variables used to forecast MPI t available at time t 2 1, and g is a vector of coefficients. u t is an error term assumed to be serially uncorrelated and independent of Z t2 1 . The output equation is initially given in difference stationary form by: 6 Bernanke and Blinder 1992 argued that the forecasting performance of the federal funds rate is based on sensitivity to changes in bank reserves. They also felt that a credit channel is at work in the monetary transmission mechanism. 7 The cumulative effects of unanticipated positive, unanticipated negative, or anticipated monetary policy on the other hand were not found to be statistically different from one another for each measure of monetary policy. 8 Mishkin 1982 employed a nonlinear joint estimation method by nonlinear generalized least squares in order to estimate both M1 growth and output growth equations. ExpansionaryContractionary Monetary Policy 111 GY t 5 a 1 O i5 1 m a 1i GY t2i 1 O i5 n b i u1 MPI t2i u1 1 O i5 n b i u2 MPI t2i u2 1 O i5 n b i e MPI t2i e 1 W t u 1 e t . 2 In equation 2, GY t is growth in real gross domestic product; W t is a vector of variables influential in determining real growth; u is a vector of coefficients, and e t is an error term. 9 The b i u1 , b i u2 , b i e , i 5 0, 1, . . . n, are the effects of positive innovations MPI t2i u1 , negative innovations MPI t2i u2 , and anticipated MPI t2i e monetary policy on real growth, respec- tively. In a later section of the paper, when the change in the federal funds rate is considered as the monetary policy indicator, anticipated monetary change will also be separated into positive and negative components. This will allow the possible role of asymmetry in stimulativecontractionary policy to be considered. The residuals from equation 1, uˆ t , form the basis for measures of monetary policy indicator shocks and anticipated monetary policy used in equation 2. A positive mon- etary policy shock is defined as MPI t u1 5 uˆ t if uˆ t is positive; otherwise, it equals zero. A negative monetary policy shock is defined as MPI t u2 5 uˆ t if uˆ t is negative; otherwise it equals zero. Anticipated monetary policy for time t is defined as MPI t e 5 Z t2 1 gˆ . For MPI given by growth in M1, Cover 1992 jointly estimated equations 1 and 2, and tested the null hypothesis that the positive-negative innovation distinction is irrelevant for explaining output henceforth, PNDI by testing b i u1 5 b i u2 , i 5 0, 1, . . . n. Cover found that PNDI was rejected, and that the null hypothesis b i u1 5 0, i 5 0, 1 . . . n, could not be rejected. 10 The hypotheses to be tested are basically checks for asymmetries of one type or another. Frydman and Rappoport 1987 tested the null hypothesis that the anticipated- unanticipated distinction is irrelevant AUDI for explaining output by implicit imposition of the restriction that b i u1 5 b i u2 5 k i u , i 5 0, 1, . . . n. The difference stationary form of their output equation is given by: GY t 5 a 1 O i5 1 m a 1i GY t2i 1 O i5 n k i u MPI t2i u 1 O i5 n k i e MPI t2i e 1 W t u 1 h t . 3 Frydman and Rappoport tested the null hypothesis that k i u 5 k i e , i 5 0, 1, . . . n AUDI. They reported results for n 7 for M1 over the period 1954:I–1976:IV which suggested AUDI could not be rejected. This paper examines the null hypothesis that distinctions among anticipated monetary policy, unanticipated positive policy shocks, and unanticipated negative policy shocks are irrelevant for explaining output SYMMETRY. SYMMETRY will be tested by setting up the null hypothesis of b i u1 5 b i u2 5 b i e , i 5 0, 1, . . . n. 11 It is argued in this paper that a distinction between anticipated and unanticipated monetary policy shocks might be 9 Analysis of the time series properties of GY t indicated a stationary process. With the presence of money shock terms in equation 2, tests indicated that the error term does not show first-order or higher-order serial correlation. 10 The Cover 1992 conclusion that expansionary monetary has statistically insignificant effects on output was formed given imposition of the constraint that b i e 5 0, i 5 0, 1, . . . n. 11 Note that if SYMMETRY cannot be rejected, equation 2 reduces down to an equation in which expectations about monetary policy do not affect output, as MPI t2i 1 1 MPI t2i 2 1 MPI t2i e 5 MPI t2i . 112 J. Chu and R. A. Ratti rejected by failure to account for a possible asymmetry between positive and negative monetary policy surprises. It is also contended that if such an asymmetry exists in effects on output, taking account of this distinction will affect findings on neutrality. The underlying reason for these results can be seen intuitively by supposing that the true output equation is given by equation 2. In this case, the error term in equation 3 is defined as: h t 5 O i5 n ~b i u1 2 k i u MPI t2i u1 1 O i5 n ~b i u2 2 k i u MPI t2i u2 1 e t . 4 Equation 4 demonstrates that in equation 3, h t is not orthogonal to the MPI t2i u 5MPI t2i u1 1 MPI t2i u2 terms when b i u1 Þ b i u2 , i 5 0, 1 . . . n. This leads to inconsistent estimators of the parameters in equation 3 and inconsistent test statistics on hypotheses concerning these parameters. 12 The estimation procedure is as follows. Equations 1 and 2 are estimated by OLS. In equation 2, MPI t2i u1 and MPI t2i u2 i 5 0, 1, . . . n have been given by the residuals from equation 1. In this second stage, n is determined by the Akaike 1973 Information Criterion AIC. The OLS residuals of both equations are used to construct the variance- covariance matrix for the system, and equations 1 and 2 are re-estimated jointly by nonlinear generalized least-squares, treating the estimated variance-covariance matrix as given. It is assumed that the residuals in the monetary policy equation and in the output equation are uncorrelated. A new variance-covariance matrix is re-estimated with each new set of coefficient estimates until the change in this estimated matrix is infinitesimal. 13

III. Empirical Results for M1