On the Relevance of Distinctions Between Anticipated ...directory.umm.ac.id/Data...

On the Relevance of Distinctions BetweenAnticipated, Unanticipated Expansionary,and Unanticipated ContractionaryMonetary Policy

Joonsuk Chu and Ronald A. Ratti

It has been found that distinctions among positive innovations, negative innovations, andanticipated monetary policy change are relevant for explaining movement in real output.An asymmetry in the effects of anticipated expansionary and anticipated contractionarymonetary policy on output also was found to be statistically significant, and the nullhypothesis of no asymmetry in stimulative/contractionary policy was rejected. There isevidence that unanticipated stimulative, unanticipated contractionary, anticipated stimu-lative, and anticipated contractionary monetary policy each have statistically significanteffects on output. Recognition of these asymmetries was found to make the finding ofnon-neutrality more likely. © 1999 Elsevier Science Inc.

Keywords:Expansionary; Contractionary; Monetary policy

JEL classification:E52, E58

I. IntroductionThe policy ineffectiveness proposition advanced by Lucas (1973) and Sargent andWallace (1975) conjectures that anticipated nominal changes have no effect on real output.The hypothesis that differentiation between anticipated and unanticipated change innominal variables is important for explaining movement in real output was tested by Barro(1977), who found support for the neutrality hypothesis. In contrast, Mishkin (1982) foundthat when lag length was increased in the nominal variables, the neutrality hypothesis was

Youngsan University of International Affairs, Yangsan, Korea (JC); Department of Economics, Universityof Missouri-Columbia, Columbia, Missouri (RAR).

Address correspondence to: Dr. R. A. Ratti, University of Missouri-Columbia, Department of Economics,118 Professional Building, Columbia, MO 65211.

Journal of Economics and Business 1999; 51:109–131 0148-6195 /99 /$–see front matter© 1999 Elsevier Science Inc., New York, New York PII S0148-6195(99)00029-0

rejected. In a further extension, Frydman and Rappoport (1987) presented evidencecasting doubt on the relevance of the distinction itself between anticipated and unantic-ipated nominal change in explaining real output. Work by De Long and Summers (1988)and Cover (1992) has drawn attention to a different asymmetry and concluded thatnegative-money shocks have a greater effect on output than positive-money shocks.1

Macklem et al. (1996) found evidence for Canada that asymmetric effects on output existin anticipated policy.2

This paper examines the relevance of distinctions among anticipated monetary policychange, unanticipated positive-money change, and unanticipated negative-money changein explaining movement in real output. The role of a possible asymmetry in policy actions,e.g., stimulative versus contractionary policy, is also considered.3 Growth in M1 will beone of the measures of monetary policy. The spread between the commercial paper rateand the Treasury bill rate will be another. Work by Friedman and Kuttner (1992) indicatesthat spread contains highly significant information about movement in real output.Kashyap et al. (1993) viewed spread as a proxy for the stance of monetary policy. A tightmonetary policy causes firms to compete for funds, leading to an increase in the issuanceof commercial paper. Hence, the commercial paper rate rises more than the Treasury billrate when money is tight.4

The change in the federal funds rate will also be used as a measure of monetary policy.This will allow the issue of possible asymmetry in the effects of anticipated policy to betested.5 Bernanke and Blinder (1992) have argued that innovations in the federal funds

1 Cover (1992, p. 1261) went so far as to state that “positive-money shocks have no effect on output, whereasnegative-money shocks cause output to decline.” Cover noted that this outcome is consistent with either a rigidlyvertical aggregate supply curve and sticky prices in the face of unexpected changes in demand, or with a situationin which wages are sticky downwards but flexible upwards and a vertical aggregate supply curve at the point offull employment. A zero effect of positive money shocks is, of course, not predicted by either the new classicalmodel with rational expectations, in which prices are flexible, or the nonclassical rational expectations modelwith contracts. Recent work by Lucas (1990), Christiano (1991), and Fuerst (1992) within a cash-in-advance realbusiness-cycle framework, provides some motivation for assuming an asymmetry in the effect of positive andnegative money shocks, but not a basis for concluding that positive shocks are unimportant.

2 A number of papers have addressed ways in which there may be asymmetric effects of policy on the realeconomy. This includes work by Bernanke and Gertler (1989), Caplin and Leahy (1991), and Ball and Mankiw(1994). Empirical evidence of asymmetric effects of monetary policy has been reported by Morgan (1993), Huh(1994), Thoma (1994), Ammer and Brunner (1995), and Garcia and Schaller (1995). Macklem et al. (1996)provide an excellent survey of work on asymmetric effects of monetary policy.

3 In this paper, monetary policy innovations are formed by using a method used by Mishkin (1982), Cover(1992), and Macklem et al. (1996). This involves a forecast equation for the monetary policy indicator. Residualsfrom this equation are then used as innovations to be used in an output equation. This method of constructioncontrasts with that used to identify policy shocks in a large literature using structural vector autoregression(VAR) models [see, for example Sims (1980, 1992); Bernanke (1986); Bernanke and Blinder (1992)]. Cochrane(1995) argued that the VAR technique implicitly assumes that only unanticipated shocks matter. Bernanke andMihov (1995) and Cochrane (1995) maintained that it is important to allow for the possible effect of anticipatedmoney on output. In addition, Macklem et al. (1996) stressed that when asymmetric effects are being considered,scarcity of degrees of freedom becomes even more of a problem with the VAR approach.

4 Friedman and Kuttner (1992) held that the gap between the Commercial Paper rate and the Treasury billrate better captures information about occurrences in financial markets relevant for the determination of outputthan movements in an interest rate or fluctuations in money. In another paper, Friedman and Kuttner (1993) pointout that monetary policy is only one of several factors that can account for movement in spread and itsrelationship to output. Kashyap et al. (1993) have shown that monetary policy influences a firm’s mix of externalfinancing and that this implies that a loan supply channel of monetary policy exists.

5 We are grateful to two referees for suggesting that we consider asymmetry in anticipated policy betweenstimulative and contractionary components, and also in policy action overall, as between stimulative andcontractionary operations. Exploration of these issues with the other measures of monetary policy is not possible(anticipated growth in M1 is nearly always positive, and anticipated spread is always positive).

110 J. Chu and R. A. Ratti

rate are a good measure of changes in monetary policy and are informative about futuremovements in real activity.6

It was found in our study that distinctions between positive innovations, negativeinnovations, and anticipated monetary policy change are relevant for explaining move-ment in real output. There is evidence that unanticipated expansionary monetary policy isjust as likely to have a statistically significant effect on output as is unanticipatedcontractionary monetary policy.7 These results appear to be robust across differentmeasures of monetary policy, different specifications of the monetary policy and outputequations, and over different sample periods.

For monetary policy measured by change in the federal funds rate, an asymmetry in theeffects of anticipated expansionary and anticipated contractionary monetary policy onoutput was found. The null hypothesis of no asymmetry in stimulative/contractionarypolicy was rejected. Anticipated expansionary monetary policy and anticipated contrac-tionary policy were each found to have statistically significant effects on output. A majorfinding of the study is that allowing asymmetries in anticipated and unanticipatedmonetary policy between stimulative and contractionary components makes the finding ofneutrality of money less likely.

In Section II, the model and the hypotheses to be considered are presented. Empiricalresults for growth in money and for spread are presented in Sections III and IV,respectively. The issue of asymmetry in stimulative/contractionary policy is taken up inSection V, when the change in the federal funds rate is used as the measure of monetarypolicy. Section VI is the conclusion.

II. The Model and HypothesesThe procedure adopted in this paper involves nonlinear joint estimation of a money policyindicator equation—from which monetary policy innovations will be constructed—and areal output growth equation. The setup of the relationship between money and outputfollows that in Barro (1977) and Mishkin (1982).8 The monetary policy indicator processis characterized by:

MPIt 5 Zt21g 1 ut, (1)

where t 5 2, . . . , T. In equation (1), the monetary policy indicator,MPIt, can berepresented by the growth in M1, spread, the change in the federal funds rate, or someother measure of the stance of monetary policy.Zt21 is a vector of variables used toforecastMPIt available at timet 2 1, andg is a vector of coefficients.ut is an error termassumed to be serially uncorrelated and independent ofZt21.

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 onsensitivity to changes in bank reserves. They also felt that a credit channel is at work in the monetarytransmission mechanism.

7 The cumulative effects of unanticipated positive, unanticipated negative, or anticipated monetary policy onthe 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 inorder to estimate both M1 growth and output growth equations.

Expansionary/Contractionary Monetary Policy 111

GYt 5 a0 1 Oi51

m

a1iGYt2i 1 Oi50

n

b iu1MPIt2i

u1 1 Oi50

n

b iu2MPIt2i

u2 1 Oi50

n

b ieMPIt2i

e 1 Wtu

1 et. (2)

In equation (2),GYt is growth in real gross domestic product;Wt is a vector of variablesinfluential in determining real growth;u is a vector of coefficients, andet is an error term.9

Thebiu1, bi

u2, bie, i 5 0, 1, . . .n, are the effects of positive innovations (MPIt2i

u1), negativeinnovations (MPIt2i

u2), and anticipated (MPIt2ie ) monetary policy on real growth, respec-

tively. In a later section of the paper, when the change in the federal funds rate isconsidered as the monetary policy indicator, anticipated monetary change will also beseparated into positive and negative components. This will allow the possible role ofasymmetry in stimulative/contractionary policy to be considered.

The residuals from equation (1),ut, form the basis for measures of monetary policyindicator shocks and anticipated monetary policy used in equation (2). A positive mon-etary policy shock is defined asMPIt

u1 5 ut if ut is positive; otherwise, it equals zero. Anegative monetary policy shock is defined asMPIt

u2 5 ut if ut is negative; otherwise itequals zero. Anticipated monetary policy for timet is defined asMPIt

e 5 Zt21g. For MPIgiven by growth in M1, Cover (1992) jointly estimated equations (1) and (2), and testedthe null hypothesis that the positive-negative innovation distinction is irrelevant forexplaining output (henceforth, PNDI) by testingbi

u1 5 biu2, i 5 0, 1, . . .n. Cover found

that PNDI was rejected, and that the null hypothesisbiu1 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 oranother. Frydman and Rappoport (1987) tested the null hypothesis that the anticipated-unanticipated distinction is irrelevant (AUDI) for explaining output by implicit impositionof the restriction thatbi

u1 5 biu2(5 ki

u), i 5 0, 1, . . .n. The difference stationary form oftheir output equation is given by:

GYt 5 a0 1 Oi51

m

a1iGYt2i 1 Oi50

n

k iuMPIt2i

u 1 Oi50

n

k ieMPIt2i

e 1 Wtu 1 ht. (3)

Frydman and Rappoport tested the null hypothesis thatkiu 5 ki

e, i 5 0, 1, . . .n (AUDI).They reported results forn $ 7 for M1 over the period 1954:I–1976:IV which suggestedAUDI could not be rejected.

This paper examines the null hypothesis that distinctions among anticipated monetarypolicy, unanticipated positive policy shocks, and unanticipated negative policy shocks areirrelevant for explaining output (SYMMETRY). SYMMETRYwill be tested by setting upthe null hypothesis ofbi

u1 5 biu2 5 bi

e, i 5 0, 1, . . .n.11 It is argued in this paper thata distinction between anticipated and unanticipated monetary policy shocks might be

9 Analysis of the time series properties ofGYt indicated a stationary process. With the presence of moneyshock terms in equation (2), tests indicated that the error term does not show first-order or higher-order serialcorrelation.

10 The Cover (1992) conclusion that expansionary monetary has statistically insignificant effects on outputwas formed given imposition of the constraint thatbi

e 5 0, i 5 0, 1, . . .n.11 Note that if SYMMETRYcannot be rejected, equation (2) reduces down to an equation in which

expectations about monetary policy do not affect output, asMPIt2i1 1 MPIt2i

2 1 MPIt2ie 5 MPIt2i.


rejected by failure to account for a possible asymmetry between positive and negativemonetary policy surprises. It is also contended that if such an asymmetry exists in effectson output, taking account of this distinction will affect findings on neutrality.

The underlying reason for these results can be seen intuitively by supposing that thetrue output equation is given by equation (2). In this case, the error term in equation (3)is defined as:

ht 5 Oi50

n

~b iu1 2 k i

u! MPIt2iu1 1 O

i50

n

~b iu2 2 k i

u! MPIt2iu2 1 et. (4)

Equation (4) demonstrates that in equation (3),ht is not orthogonal to theMPIt2iu

(5MPIt2iu1 1 MPIt2i

u2) terms whenbiu1 Þ bi

u2, i 5 0, 1 . . .n. This leads to inconsistentestimators of the parameters in equation (3) and inconsistent test statistics on hypothesesconcerning these parameters.12

The estimation procedure is as follows. Equations (1) and (2) are estimated by OLS. Inequation (2),MPIt2i

u1 andMPIt2iu2(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) InformationCriterion (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 bynonlinear generalized least-squares, treating the estimated variance-covariance matrix asgiven. It is assumed that the residuals in the monetary policy equation and in the outputequation are uncorrelated. A new variance-covariance matrix is re-estimated with eachnew set of coefficient estimates until the change in this estimated matrix is infinitesimal.13

III. Empirical Results for M1To separate monetary policy into anticipated and unanticipated positive and negativecomponents, growth in M1 (GM) is regressed on lagged values of itself, lagged values ofgrowth in the monetary base (GB), lagged values of the unemployment rate (UR), laggedgrowth rates of GDP (GY), lagged changes in the T-bill rate (DTBR), and lags of thefederal government surplus (FEBS).14 This specification is similar to that in Mishkin(1982), Frydman and Rappoport (1987), and Cover (1992). The growth rate in output isregressed on lag distributions ofMGe, MGu1, and MGu2, and lags of changes in theTreasury-bill rate and growth in output.15 Results of joint estimation of money and output

12 It should also be noted that inconsistent estimators might be obtained if an asymmetry exists in anticipatedpolicy. However, for measures of monetary policy given by growth in M1 and spread, it is not possible with themethod outlined above to identify stimulative and contractionary components of anticipated policy. This issueis considered when change in the federal funds rate is used as measure of monetary policy.

13 This procedure iterated until the relative change in the value of the function was less than 0.000001. TheBHHH algorithm was used for optimization. The resulting estimates are approximately maximum-likelihoodestimates [Mishkin (1982, p. 26)]. The coefficient estimates obtained from joint estimation are more efficientbecause of cross-equation restrictions.

14 Data are from CITIBASE, except for M1 prior to 1959:I. As in Cover (1992), M1 during the third monthof the quarter was used as the money supply. Prior to 1959:I, data on M1 obtained from Friedman and Schwartz(1970) was multiplied by 0.990302 (the ratio of the M1 series in CITIBASE to the M1 series in Friedman andSchwartz for the period 1959:I–1960:IV).

15 The Treasury-bill rate did not appear in the output equations of Barro and Rush (1980), Mishkin (1982),or Frydman and Rappoport (1987). Results when changes in the Treasury-bill rate were excluded from the outputequation were found to be very similar and, for that reason, are not reported. Cover (1992) reported results onoutput specifications that both included and excluded lags of changes in the Treasury-bill rate, with similar


equations forn 5 4 appear in Tables 1 and 2 for the period 1951:I–1979:III, and in Tables1 and 3 for the period 1951:I–1992:II.16 Money equations are reported in Table 1 andoutput equations in Tables 2 and 3. In these tables, Set I corresponds to equations (1) and(2), and Set II corresponds to equations (1) and (3).

results on an asymmetry between positive and negative policy shocks. Note that lagged changes in theTreasury-bill rate were found to be statistically significant in the output equations.

16 Results for the period ending in 1979:III are reported, as during October 1979, Fed operating procedureschanged and results could be more easily compared with those obtained by Barro and Rush (1980), Mishkin(1982), and Frydman and Rappoport (1987). Results are also reported for the period ending in 1992:II. Thisprovides an update and also facilitates comparison with the work of Cover (1992), whose sample period endedin 1987:IV. n 5 4 was chosen by AIC applied to the initial OLS estimate of the output equation. Results forhigher values ofn will be reported.

Table 1. M1 Growth Equations: Nonlinear Joint Estimation(standard errors in parentheses)

Variable

Set I Set II

Coefficient (se.) p Value Coefficient (se.) p Value

1951:I–1979:IIIConstant 20.153 (0.245) 0.5349 0.233 (0.180) 0.1933GM{1} 0.174 (0.080) 0.0306 0.241 (0.085) 0.0044GM{2} 0.261 (0.078) 0.0008 0.260 (0.089) 0.0035GM{3} 0.155 (0.070) 0.0276 0.093 (0.077) 0.2272GM{4} 0.019 (0.058) 0.7408 20.018 (0.066) 0.7793GB{1} 0.156 (0.087) 0.0731 0.143 (0.086) 0.0957GB{2} 0.084 (0.087) 0.3358 0.163 (0.095) 0.0866DTBR{1} 20.349 (0.081) 0.0000 20.384 (0.091) 0.0000UR{1} 0.064 (0.041) 0.1189 20.016 (0.028) 0.5590FEBS{1} 0.002 (0.004) 0.6818 0.001 (0.002) 0.5836GY{1} 20.004 (0.034) 0.8994 20.006 (0.039) 0.8670Std. error 0.544 0.549DW 1.987 2.057R2 0.485 0.4751951:I–1992:IIConstant 0.246 (0.174) 0.1548 0.332 (0.173) 0.0551GM{1} 0.276 (0.066) 0.0000 0.250 (0.070) 0.0003GM{2} 0.222 (0.069) 0.0013 0.277 (0.075) 0.0002GM{3} 20.089 (0.069) 0.1938 20.098 (0.071) 0.1681GM{4} 20.079 (0.057) 0.1623 20.080 (0.058) 0.1682GB{1} 0.129 (0.071) 0.0664 0.094 (0.061) 0.1232GB{2} 0.114 (0.073) 0.1149 0.093 (0.062) 0.1295DTBR{1} 20.399 (0.048) 0.0000 20.371 (0.050) 0.0000UR{1} 0.030 (0.029) 0.3120 0.015 (0.029) 0.5819FEBS{1} 20.002 (0.001) 0.0816 20.002 (0.001) 0.0079GY{1} 0.025 (0.043) 0.5495 0.031 (0.044) 0.4685Std. error 0.713 0.713DW 2.006 1.923R2 0.509 0.509

Notes:GM{ i} 5 log difference in M1 with lagi; GB{ i} 5 log difference in monetary base with lagi; DTBR{1} 5 changein the T-bill rate lagged one period;UR{1} 5 civilian unemployment rate lagged one time period;FEBS{1} 5 federal budgetsurplus lagged one period;GY{1} 5 log difference in real GDP lagged one period. In output equation for Set I, a distinctionbetween the effects of positive and negative money shocks was recognized. This distinction was suppressed in Set II.


From the Set I results in Tables 1, 2, and 3, it can be seen that the null hypothesis—thatdistinctions among the effects ofMGe, MGu1, and MGu2 on growth in output areirrelevant (SYMMETRY)—is rejected at the 0.05 level for both time periods. From the SetII results, it is also apparent that AUDI is also rejected. These results are summarized inthe first column of the upper part of Table 4 which brings together a number of results as

Table 2. Output Equations with Growth in M1 as Monetary Policy Indicator: Nonlinear JointEstimation 1951:I–1979:III(standard errors andx2 statistics* in parentheses)

Set I Set II

Variable Coefficient p Value Variable Coefficient p Value

Constant 0.442 (0.255) 0.0836 Constant 0.859 (0.404) 0.0334GY{1} 0.327 (0.086) 0.0001GY{1} 0.256 (0.134) 0.0549DTBR 0.377 (0.151) 0.0124DTBR{1} 0.280 (0.159) 0.0777DTBR{1} 20.071 (0.349)0.8395DTBR{1} 20.883 (0.607)0.1455GMe 20.157 (0.865)0.8563GMe 22.195 (1.395)0.1157GM3{1} 1.067 (0.567) 0.0602GMe{1} 1.486 (0.656) 0.0234GMe{2} 20.856 (0.592)0.1481GMe{2} 0.094 (0.724) 0.8965GMe{3} 1.451 (0.634) 0.0221GMe{3} 1.513 (0.591) 0.0104GMe{4} 21.454 (0.461)0.0016GMe{4} 21.080 (0.419)0.0099GMu2 0.088 (0.330) 0.7888GMu 0.347 (0.153) 0.0235GMu2{1} 0.490 (0.381) 0.1987GMu{1} 0.939 (0.477) 0.0488GMu2{2} 0.043 (0.402) 0.9142GMu{2} 0.943 (0.555) 0.0894GMu2{3} 0.202 (0.334) 0.5449GMu{3} 0.141 (0.335) 0.6723GMu2{4} 20.771 (0.361)0.0329GMu{4} 20.180 (0.264)0.4944GMu1 0.375 (0.284) 0.1863GMu1{1} 0.103 (0.325) 0.7502GMu1{2} 0.137 (0.380) 0.7192GMu1{3} 20.818 (0.328)0.0127GMu1{4} 0.290 (0.334) 0.3845HypothesisGMe{ i} 5 0a, i 5 0, . . . 4 (13.273)* 0.0209 GMe{ i} 5 0a, i 5 0, . . . 4(9.860)* 0.0792¥ (GMe) 5 0b, (0.083)* 0.7729¥ (GMe) 5 0b, (0.330)* 0.5658GMu2{ i} 5 0a, i 5 0, . . . 4 (5.702)* 0.3363 GMu{ i} 5 0a, i 5 0, . . . 4(10.814)* 0.0552¥ (GMu2) 5 0b, (0.005)* 0.9433¥ (GMu) 5 0b, (3.143)* 0.0762GMu1{ i} 5 0a, i 5 0, . . . 4 (8.700)* 0.1217¥ (GMu1) 5 0b, (0.015)* 0.9014GMu2{ i} 5 GMu1{ i} c, i 5 0, . . . 4(8.202)* 0.1454¥ (GMu2) 5 ¥ (GMu1)d (0.001)* 0.9695GMu2{ i} 5 GMu1{ i}

5 GMe{ i} c, i 5 0, 1 . . .4 (19.744)* 0.0317GMe{ i} 5 GMu{ i} c, i 5

0, 1 . . . 4 (12.833)* 0.0249¥ (GMu2) 5 ¥ (GMu1) 5 ¥

(GMe)d (0.002)* 0.9988¥ (GMe) 5 ¥ (GMu)d (2.965)* 0.0851Std. error 0.764 0.773DW 2.126 2.094R2 0.432 0.420

a x2(5)-test of the null hypothesis that the coefficients onGMe (GMu1, GMu2, or GMu) terms are jointly zero.b x2(1)-test of the null hypothesis that the sum of the coefficients on theGMe (GMu1, GMu2, or GMu) terms is zero.c x2(5)-test andx2 (10)-test of joint pairwise equality and of joint triple-wise equality, respectively, of coefficients on

variables indicated.d x2(1)-test andx2 (2)-test of pairwise equality and of triple-wise equality, respectively, of sums of coefficients on variables

indicated.GMe{ i}, GMu2{ i}, and GMu1{ i} represent anticipated, unanticipated negative, and unanticipated positive growth in M1,

respectively.


lag distributions of the nominal variables are increased. For example, forn 5 8 andgreater, the result noted by Frydman and Rappoport (1987), of the anticipated-

Table 3. Output Equations with Growth in M1 as Monetary Policy Indicator: Nonlinear JointEstimation 1951:I–1992:II(standard errors andx2 statistics* in parentheses)

Set I Set II


Constant 0.746 (0.268) 0.0054 Constant 0.661 (0.264) 0.0122GY{1} 0.311 (0.103) 0.0025GY{1} 0.343 (0.121) 0.0045DTBR 0.300 (0.064) 0.0000DTBR 0.270 (0.065) 0.0000DTBR{1} 20.550 (0.294)0.0614DTBR{1} 20.749 (0.292)0.0103GMe 21.583 (0.689)0.0214GMe 22.126 (0.740)0.0040GMe{1} 0.840 (0.363) 0.0207GMe{1} 1.077 (0.406) 0.0079GMe{2} 0.998 (0.351) 0.0044GMe{2} 1.277 (0.423) 0.0025GMe{3} 20.084 (0.201)0.6743GMe{3} 20.204 (0.234)0.3834GMe{4} 20.157 (0.175)0.3695GMe{4} 20.151 (0.206)0.4607GMu2 0.690 (0.193) 0.0003GMu 0.219 (0.090) 0.0156GMu2{1} 0.537 (0.306) 0.0789GMu{1} 0.558 (0.283) 0.0485GMu2{2} 0.366 (0.278) 0.1869GMu{2} 0.695 (0.289) 0.0161GMu2{3} 20.502 (0.282)0.0746GMu{3} 20.693 (0.251)0.0058GMu2{4} 20.362 (0.255)0.1555GMu{4} 20.460 (0.227)0.0423GMu1 20.189 (0.165)0.2493GMu1{1} 0.462 (0.297) 0.1198GMu1{2} 0.594 (0.284) 0.0363GMu1{3} 20.676 (0.234)0.0038GMu1{4} 20.379 (0.231)0.1013HypothesisGMe{ i} 5 0a, i 5 0, . . . 4 (12.428)* 0.0293 GMe{ i} 5 0a, i 5 0, . . . 4(11.518)* 0.0420¥ (GMe) 5 0b, (0.005)* 0.9434¥ (GMe) 5 0b, (0.525)* 0.4684GMu2{ i} 5 0a, i 5 0, . . . 4 (19.949)* 0.0012GMu{ i} 5 0a, i 5 0, . . . 4(18.401)* 0.0024¥ (GMu2) 5 0b, (2.946)* 0.0860¥ (GMu) 5 0b, (1.087)* 0.2971GMu1{ i} 5 0a, i 5 0, . . . 4 (12.792)* 0.0254¥ (GMu1) 5 0b, (0.201)* 0.6538GMu2{ i} 5 GMu1{ i} c, i 5 0, . . . 4(9.501)* 0.0906¥ (GMu2) 5 ¥ (GMu1)d (2.455)* 0.1171GMu2{ i} 5 GMu1{ i} 5 GMe{ i} c, i

5 0, 1 . . . 4 (22.016)* 0.0150GMe{ i} 5 GMu{ i} c, i 5

0, 1 . . . 4 (12.487)* 0.0286¥ (GMu2) 5 ¥ (GMu1) 5 ¥

(GMe)d (3.140)* 0.2080¥ (GMe) 5 ¥ (GMu)d (1.067)* 0.3014Std. error 0.767 0.786DW 2.107 2.125R2 0.405 0.375

a x2(5)-test of the null hypothesis that the coefficients onGMe (GMu1, GMu2, or GMu) terms are jointly zero.b x2(1)-test of the null hypothesis that the sum of the coefficients on theGMe (GMu1, GMu2, or GMu) terms is zero.c x2(5)-test andx2(10)-test of joint pairwise equality and of joint triple-wise equality, respectively, of coefficients on

variables indicated.d x2(1)-test andx2(2)-test of pairwise equality and of triple-wise equality, respectively, of sums of coefficients on variables

indicated.GMe{ i}, GMu2{ i}, and GMu1{ i} represent anticipated, unanticipated negative, and unanticipated positive growth in M1,

respectively.


unanticipated distinction being irrelevant for the period 1954:I–1976:IV, comes into play(on the first line of Table 4).17

Note however that these results on the rejection of AUDI contrast sharply with thoseobtained at longer lags when distinctions among positive shocks, negative shocks, andanticipated money growth are simultaneously allowed. The null hypothesis that distinc-tions among the three types of monetary change are irrelevant is rejected at the 0.01 levelfor n $ 8 for the period ending in 1979:III. In comparison to the conclusion of Frydmanand Rappoport, it appears that distinctions between anticipated and unanticipated changesin nominal values do matter for explaining movement in output, at least when a distinctionis allowed between the impact of positive and negative shocks. This outcome is relativelystable for both sample periods and over various lag lengths.

As reported in Table 5, at longer lags for both sample periods, the null hypotheses thatneither positive money nor negative money surprises have an effect on output is rejectedat the 0.05 level. Thus positive money surprises matter (as do negative money surprises).This result seems to differ from that reported by Cover (1992), to the effect that positive

17 Frydman and Rappoport (1987) reported results for a period ending in 1976:IV and forn $ 7. They statedthat results with regard to AUDI would be similar for a period ending in 1979, as was indeed the case for resultsreported in Table 4.

Table 4. Test Results of Null Hypotheses of Irrelevance of Distinctions Among Anticipated,Unanticipated Positive, and Unanticipated Negative Growth in M1 for Explaining Movement inReal Output(p values reported)

Equation Hypothesisa

Lag Lengthb

n 5 4 n 5 8 n 5 12 n 5 16

M1 (1951:I–1979:III)AUDI 0.0249 0.2378 0.2781 0.4979PNDI 0.1454 0.0119 0.0037 0.0090SYMMETRY 0.0317 0.0050 0.0018 0.0001

M1 (1951:I–1992:II)AUDI 0.0286 0.0233 0.0364 0.1146PNDI 0.0906 0.1671 0.1002 0.0369SYMMETRY 0.0150 0.0135 0.0215 0.0195

Structural Shifts in Money Equationc

M1 (1951:I–1979:III)AUDI 0.0248 0.1870 0.1619 0.1859PNDI 0.1172 0.0001 0.0000 0.0000SYMMETRY 0.0232 0.0001 0.0000 0.0000

M1 (1951:I–1992:II)AUDI 0.1139 0.3654 0.0297 0.0615PNDI 0.1404 0.0032 0.0040 0.0036SYMMETRY 0.0701 0.0057 0.0001 0.0005

a SYMMETRY-distinctions among anticipated, unanticipated positive, and unanticipated negative monetary policy changeare irrelevant. Null hypothesis:bi

e 5 biu1 5 bi

u2, i 5 0, 1, . . .n.AUDI-distinction between anticipated and unanticipated monetary policy change is irrelevant. Null hypothesis:bi

e 5 biu, i 5

0, 1, . . .n (restrictionbiu1 5 bi

u2, i 5 0, . . .n).PNDI-distinction between unanticipated positive and unanticipated negative monetary policy change is irrelevant. Null

hypothesis:biu1 5 bi

u2, i 5 0, 1, . . .n.b For n 5 4, regressions start from 1951:I. Asn increases, regressions start at successively later dates.c Intercept differs before and after 1963:III, and coefficients on first and second lags of money growth terms differ before

and after 1971:III. No Treasury-bill rate variables appear in output equation.


money shocks did not affect output growth, and negative shocks had a highly significanteffect in reducing output (at least for the period 1951:I–1987:IV). The results of Cover(1992), however, hold in an equation (which is not reported here), in which the anticipatedmoney terms were suppressed. Results for the period ending in 1987:IV, whenGMu1,GMu2, andGMe terms appear in the output equation, are similar to those for a periodending in 1992:II, and over both periods, money was found to be non-neutral. The

Table 5. Test of Null Hypotheses of Irrelevance of Unexpected Expansionary, UnexpectedContractionary, and Anticipated M1 Growth for Explaining Movement in Real GDP


Lag Length

n 5 4 n 5 8 n 5 12 n 5 16

M1 (1951:I–1979:III)Un. expansionary 0.1217 0.0190 0.0006 0.0004Un. contractionary 0.3363 0.0187 0.0111 0.0013Anticipated 0.0209 0.0079 0.0137 0.0017With restrictionbi

u1 5 biu2, i 5

0, . . .n{Anticipated}b 0.0792 0.1211 0.0650 0.1147Unanticipated 0.0551 0.0136 0.0015 0.0020

M1 (1951:I–1992:II)Un. expansionary 0.0254 0.0119 0.0110 0.0075Un. contractionary 0.0012 0.0141 0.0794 0.1555Anticipated 0.0293 0.0405 0.1328 0.0506With restrictionbi

u1 5 biu2, i 5


Structural Shifts in Money EquationM1 (1951:I–1979:III)

Un. expansionary 0.6226 0.0254 0.0019 0.0102Un. contractionary 0.0001 0.0001 0.0001 0.0000Anticipated 0.9771 0.0006 0.0012 0.0000With restrictionbi

u1 5 biu2, i 5


M1 (1951:I–1992:II)Un. expansionary 0.6757 0.0325 0.0228 0.0093Un. contractionary 0.0158 0.0143 0.0018 0.0047Anticipated 0.2334 0.4116 0.0355 0.0057With restrictionbi

u1 5 biu2, i 5

0, . . .n{Anticipated}b 0.4259 0.5456 0.1351 0.0736

Unanticipated 0.0387 0.2138 0.0637 0.2654

a For Un. Expansionary (unanticipated positive growth in M1), null hypothesis isbiu1 5 0, i 5 0, 1, . . .n. For Un.

Contractionary (unanticipated negative growth in M1), null hypothesis isbiu2 5 0, i 5 0, 1, . . .n. For Anticipated, null

hypothesis isbie 5 0, i 5 0, 1, . . .n.

b Null hypothesis for {Anticipated}:bie 5 0, i 5 0, 1, . . .n, given restrictionbi

u1 5 biu2, i 5 0, . . .n. Null hypothesis for

Unanticipated:biu 5 0, i 5 0, 1, . . .n, given restrictionbi

u1 5 biu2, i 5 0, . . .n.


inclusion of anticipated money in the output equation yielded positive money shocks(EXPANSIONARYpolicy in Table 5) which were statistically significant. Anticipatedmoney was found, for the most part, to matter, and as noted in Table 5, did so morestrongly when a distinction between positive and negative money surprises was recog-nized.18

In Tables 2 and 3, forn 5 4, it is reported that the null hypothesis that the sums of thecoefficients on positive money shocks, on negative money shocks, and on anticipatedmoney growth are significantly different from zero could not be rejected at the 0.05level.19 This result (not reported) was robust for various lag lengths and for both sampleperiods. The implication of alternative specifications for the money equation will now bebriefly considered.

Alternative Specifications of the Equations

Intercept and slope dummy variables will now be introduced into the money equation toaccount for structural change. This will have the effect of altering the measure ofexpectations. Following Frydman and Rappoport (1987), in equation (1), the intercept isallowed to differ before and after 1963:III and the coefficients of each of the variablesGMt21 and GMt22 are allowed to differ before and after 1971:III.20 It was found thatmoney equations estimated with these changes were much improved. Results under theheading of “structural shifts in money equation” appear in Tables 4 and 5. There, it canagain be seen that for both sample periods,SYMMETRYwas rejected over alln, whereasAUDI could not be rejected except forn 5 4. Other results were similar to those alreadynoted.

IV. Spread as Monetary Policy IndicatorIn a number of recent papers, the importance of various interest-rate measures asindicators of the stance of monetary policy has been emphasized. In this section, therelevance of distinctions among unanticipated expansionary, unanticipated contractionary,and anticipated policy, when the indicator of monetary policy is taken to be spread, isinvestigated.21 Spread was regressed on four-lagged values of itself and on four-laggedvalues of a number of economic variables. These variables wereGM, GY, GB, UR, FEBS,

18 Cover (1992) noted the non-neutrality of money for the period 1951:I–1987:IV. However, because thecoefficients on theGMt

1 terms were of the wrong sign in the presence of anticipated money terms, Cover’spreferred regression equation is one in which anticipated money growth terms were excluded. Note that the mainfinding of Cover concerning an asymmetry between positive and negative money shocks in explainingmovement in output continues to be confirmed in this paper.

19 Cover (1992) also reported a similar result when anticipated money was included in the output equation[see Cover (1992, Tables VI and VII, pp. 1273, 1275)]. He found that the sums of coefficients on the positiveshocks (SUM(POS)) and on negative shocks (SUM(NEG)) were not statistically significant at the 0.05 level.When anticipated money terms did not appear in the output equation, Cover (1992, pp. 1269–70) found thatSUM(NEG) was statistically significant at the 0.01 level (and thatSUM(POS) was insignificant).

20 Frydman and Rappoport (1987) introduced these dummy variables to test the robustness of tests of AUDI.They pointed out that the intercept dummy was introduced to catch the observation that money growth roseappreciably during the early 1960s, and the slope coefficients on the first and second lags ofGM were allowedto change after 1971.III to capture structural shifts associated with the collapse of the Bretton Woods regime.

21 Spread was measured by the difference between the 3-month commercial paper rate and the 3-monthTreasury bill rate from 1971:II. Prior to 1971:II, the 6-month commercial paper rate was used. The spread serieswas found to be level stationary.


and GDP inflation (GDINF).22 GY, GB, andGDINF were not statistically significant for1949:II–1992:II. Thus, four-lagged values ofGM, UR, and FEBS appear along withfour-lagged values of spread in the forecasting equation for spread.

To begin with, four-lagged values of the dependent variable,GYt, and current andfour-lagged values of anticipated change, and positive and negative innovations in spreadappear in the output equation.23 A positive (negative) surprise in spread indicates thatspread was greater (less) than expected and, hence, that monetary policy was morecontractionary (expansionary) than expected. The coefficients on the monetary policyvariables should be negative (at least at first). To avoid confusion,MPIt

e, MPItu1, and

MPItu2 refer to anticipated, unexpected expansionary, and unexpected contractionary

policy, respectively.The results of joint estimation of equations for spread and for output for the period

1950:II–1992:II appear in Tables 6 and 7, respectively. Sets I and II are again estimatesof equations (1) and (2), and of equations (1) and (3). In the spread equations in Table 6,it can be seen that increases in the rate of money growth and in the budget surplus tended

22 Four-lagged values of each of these variables were retained in the equation explaining spread only if theywere jointly significant at the .05 level or stronger. This was the method employed by Mishkin (1982, p. 30).

23 Four lags in the spread terms are indicated by AIC from examination of the output equation beforeapplying a joint estimation. The residuals of the output equation do not show first-order or higher-order serialcorrelation.

Table 6. Monetary Policy Equations with Spread as Monetary Policy Indicator: Nonlinear JointEstimation 1950:II–1992:II(standard errors in parentheses)

Set I Set II

Variable Coefficient p Value Coefficient p Value

Constant 0.200 (0.077) 0.0098 0.147 (0.099) 0.1386MPI{1} 0.630 (0.055) 0.0000 0.690 (0.073) 0.0000MPI{2} 20.038 (0.067) 0.5739 20.083 (0.089) 0.3512MPI{3} 0.076 (0.067) 0.2556 0.066 (0.089) 0.4544MPI{4} 0.057 (0.053) 0.2885 0.168 (0.078) 0.0313UR{1} 20.004 (0.047) 0.9331 20.122 (0.061) 0.0445UR{2} 0.118 (0.080) 0.1422 0.272 (0.110) 0.0136UR{3} 20.336 (0.085) 0.0001 20.356 (0.112) 0.0015UR{4} 0.212 (0.048) 0.0000 0.191 (0.061) 0.0018FEBS{1} 0.427 (0.109) 0.0001 0.320 (0.135) 0.0176FEBS{2} 20.036 (0.133) 0.7896 0.182 (0.163) 0.2659FEBS{3} 20.485 (0.133) 0.0003 20.597 (0.180) 0.0008FEBS{4} 0.170 (0.127) 0.1830 0.167 (0.155) 0.2823GM{1} 0.038 (0.024) 0.1200 0.071 (0.028) 0.0112GM{2} 20.015 (0.024) 0.5376 20.048 (0.031) 0.1141GM{3} 20.014 (0.025) 0.5834 0.002 (0.030) 0.9214GM{4} 0.086 (0.022) 0.0002 0.057 (0.027) 0.0353Std. error 0.307 0.301DW 1.933 1.957R2 0.534 0.549

Notes:GM{ i} 5 log difference in M1 with lagi; UR{ i} 5 civilian unemployment rate laggedi time periods;FEBS{ i} 5federal budget surplus laggedi time periods. In output equation for Set I, a distinction between the effects of positive andnegative money shocks was recognized. This distinction was suppressed in Set II.


Table 7. Output Equations with Spread as Monetary Policy Indicator (MPI): Nonlinear JointEstimation 1950:II–1992:II(standard errors andx2 statistics* in parentheses)(1 indicates expansionary shock and2 indicates contractionary shock)

Set I Set II


Constant 0.750 (0.298) 0.0119 Constant 1.216 (0.288) 0.0000GY{1} 0.372 (0.083) 0.0000 GY{1} 0.210 (0.085) 0.0137GY{2} 0.131 (0.082) 0.1146 GY{2} 0.102 (0.083) 0.2178GY{3} 20.193 (0.088) 0.0282 GY{3} 20.169 (0.085) 0.0469GY{4} 20.054 (0.081) 0.5054 GY{4} 20.062 (0.082) 0.4529MPIe 1.401 (0.728) 0.0543 MPIe 1.676 (0.741) 0.0237MPIe{1} 22.739 (0.954) 0.0041 MPIe{1} 21.981 (0.877) 0.0238MPIe{2} 0.741 (0.928) 0.4253 MPIe{2} 0.081 (0.795) 0.9185MPIe{3} 0.605 (0.846) 0.4749 MPIe{3} 20.591 (0.760) 0.4365MPIe{4} 20.296 (0.495) 0.5502 MPIe{4} 0.093 (0.489) 0.8487MPIu1 20.631 (0.574) 0.2721 MPIu 20.714 (0.218) 0.0010MPIu1{1} 24.435 (0.818) 0.0000 MPIu{1} 21.915 (0.598) 0.0013MPIu1{2} 2.734 (0.862) 0.0015 MPIu{2} 20.043 (0.583) 0.9410MPIu1{3} 0.014 (0.829) 0.9866 MPIu{3} 0.005 (0.529) 0.9909MPIu1{4} 0.201 (0.758) 0.7912 MPIu{4} 0.722 (0.510) 0.1571MPIu2 21.057 (0.356) 0.0030MPIu2{1} 0.044 (0.588) 0.9398MPIu2{2} 20.898 (0.589) 0.1276MPIu2{3} 20.330 (0.559) 0.5551MPIu2{4} 0.086 (0.548) 0.8761Hypothesis HypothesisMPIe{ i} 5 0a, i 5 0, . . . 4 (11.483)* 0.0425 MPIe{ i} 5 0a, i 5 0, . . . 4 (13.684)* 0.0177¥ (MPIe) 5 0b, (0.447)* 0.5034 ¥ (MPIe) 5 0b, (5.078)* 0.0242MPIu1{1} 5 0a, i 5

0, . . . 4 (37.892)* 0.0000 MPIu{ i} 5 0a, i 5 0, . . . 4 (22.527)* 0.0004¥ (MPIu1) 5 0b, (3.764)* 0.0523 ¥ (MPIu) 5 0b, (4.121)* 0.0423MPIu2{ i} 5 0a, i 5

0, . . . 4 (12.477)* 0.0287¥ (MPIu2) 5 0b, (5.457)* 0.0194MPIu1{ i} 5 MPIu2{ i} c, i

5 0, . . . 4 (35.947)* 0.0000¥ (MPIu1) 5 ¥ (MPIu2)d (0.001)* 0.9764MPIu1{ i} 5 MPIu2{ i} 5

MPIe{ i} c, i 5 0, 1 . . . 4 (46.562)* 0.0000MPIe{ i} 5 MPIu{ i} c, i 50, 1 . . . 4 (12.782)* 0.0255

¥ (MPIu1) 5 ¥ (MPIu2)5 ¥ (MPIe)d (3.647)* 0.1614 ¥ (MPIe) 5 ¥ (MPIu)d (1.275)* 0.2588

Std. error 0.712 0.794DW 2.098 2.092R2 0.529 0.412

a x2(5)-test of the null hypothesis that the coefficients onMPIe (MPIu1, MPIu2, or MPIu) terms are jointly zero.b x2(1)-test of the null hypothesis that the sum of the coefficients on theMPIe (MPIu1, MPIu2, or MPIu) terms is

zero.c x2(5)-test andx2(10)-test of joint pairwise equality and of joint triple-wise equality, respectively, of coefficients on

variables indicated.d x2(1)-test andx2(2)-test of pairwise equality and of triple-wise equality, respectively, of sums of coefficients on variables

indicated.


to raise spread one quarter later, after which time the effect was eroded, and a rise in theunemployment rate tended to reduce spread after three quarters followed by a reversal inthe fourth quarter. In the output equation in Table 7, the null hypothesis that distinctionsamong anticipated, unanticipated positive, and unanticipated negative changes in spread isirrelevant in explaining growth in output (SYMMETRY) was rejected.

The effects of increasingn for the period ending in 1992:II, and for a period ending in1979:III, are reported in Table 8. Also, results are presented for a period starting in1957:III. This sample period was included because it matches the period for which resultswere available on the federal funds rate as the measure of monetary policy. From Table8, it can be seen that as lag length increased in the spread variables, the null hypothesisof equality of coefficients onMPIu1, MPIu2, andMPIe continued to be rejected at the 0.01level.24

Expansionary monetary policy, signaled by spread, usually had a statistically signifi-cant effect on output in Table 8. The exception was for the sample ending in 1979:III withn 5 16. It is interesting that contractionary monetary policy signaled by spread was notusually quite as potent, especially for the sample ending in 1979:III. Consistent with theM1 results, spread as an indicator of monetary policy reinforces the conclusion thatasymmetries among the effects of anticipated, expansionary unanticipated, and contrac-tionary unanticipated monetary policy on aggregate output are of some empirical impor-tance.25

V. Federal Funds Rate as Monetary Policy IndicatorThe use of change in the federal funds rate as a monetary policy indicator provides anopportunity to test a stimulative/contractionary distinction in the effect on output. Antic-ipated changes in the federal funds rate are divided into positive (anticipated contraction-ary) and negative (anticipated stimulative) components,MPIe2 andMPIe1, respectively.The output equation is given by:

GYt 5 a0 1 Oi51

m

a1iGYt2i 1 Oi50

n

b iu1MPIt2i

u1 1 Oi50

n

b iu2MPIt2i

u2 1 Oi50

n

b ie1MPIt2i

e1

1 Oi50

n

b ie2MPIt2i

e2 1 Wtu 1 et. (29)

It is now possible to test the following two hypotheses:26

H0 (SC):No stimulative/contractionary asymmetry given bybie1 5 bi

e2 andbiu1 5 bi

u2,i 5 1, . . .n.H0 (AU): No anticipated/unanticipated asymmetry given bybi

e1 5 biu1 andbi

e2 5 biu2,

i 5 1, . . .n.

24 As a check for robustness, an alternative specification of the spread equation was tried in which four lagsof real growth (GY) and of inflation (GDINFL) were added to those listed in the spread equation in Table 6.Results were found to be very similar to those given in Tables 7 and 8 (concerning effects of spread as MPI) and,thus, are not reported here.

25 In contrast to results when monetary policy was measured by growth in M1, results in Table 8 suggest thatanticipated change in spread has, at best, only marginal effects on output (except whenn 5 4).

26 The authors are grateful to a referee for suggesting this formulation for theAC andAU hypotheses.


Table 8. Test Results of Null Hypotheses When Spread is Monetary Policy Indicator(p values reported)


Lag Lengthb

n 5 4 n 5 8 n 5 12 n 5 16

Spread (1950:II–1979:III)SYMMETRY 0.0049 0.0001 0.0001 0.0000PNDI 0.0026 0.0000 0.0000 0.0000Un. expansionary 0.0017 0.0179 0.0223 0.4890Un. contractionary 0.3818 0.3058 0.4120 0.0082Anticipated 0.0007 0.0704 0.1384 0.4302With restrictionbi

u1 5bi

u2, i 5 0, . . .n{Anticipated} 0.0616 0.4415 0.5884 0.9426Unanticipated 0.2939 0.4106 0.2190 0.4695AUDI 0.1091 0.5425 0.5453 0.9406

Spread (1950:II–1992:II)SYMMETRY 0.0000 0.0000 0.0000 0.0000PNDI 0.0000 0.0000 0.0000 0.0000Un. expansionary 0.0000 0.0000 0.0000 0.0000Un. contractionary 0.0287 0.0503 0.0326 0.0262Anticipated 0.0425 0.2139 0.0821 0.0801With restrictionbi

u1 5bi


Spread (1957:III–1992:II)SYMMETRY 0.0000 0.0000 0.0000 0.0000PNDI 0.0000 0.0000 0.0000 0.0000Un. expansionary 0.0000 0.0000 0.0000 0.0000Un. contractionary 0.0053 0.0002 0.0004 0.0000Anticipated 0.3477 0.3800 0.2576 0.1083With restrictionbi

u1 5bi


a SYMMETRY-distinctions among anticipated, unanticipated positive, and unanticipated negative monetary policy areirrelevant. Null hypothesis:bi

e 5 biu1 5 bi

u2, i 5 0, 1, . . .n.AUDI-distinction between anticipated and unanticipated monetary policy is irrelevant. Null hypothesis:bi

e 5 biu, i 5 0,

1, . . .n (restrictionbiu1 5 bi

u2, i 5 0, . . .n).PNDI-distinction between unanticipated positive, and unanticipated negative monetary policy is irrelevant. Null hypothesis:

biu1 5 bi

u2, i 5 0, 1, . . .n.Un. expansionary refers to unanticipated negative spread (null hypothesis isbi

u1 5 0, i 5 0, 1, . . .n).Un. contractionary refers to unanticipated positive spread (null hypothesis isbi

u2 5 0, i 5 0, 1, . . .n).Anticipated-null hypothesis isbi

e 5 0, i 5 0, 1, . . .n.Null hypothesis for {Anticipated}:bi

e 5 0, i 5 0, 1, . . .n, given restrictionbiu1 5 bi

u2, i 5 0, . . .n. Null hypothesis forUnanticipated:bi

u 5 0, i 5 0, 1, . . .n, given restrictionbiu1 5 bi

u2, i 5 0, . . .n.b For n 5 4, regressions start from 1950:II (or 1957:III). Asn increases, regressions start at successively later dates.


The change in the federal funds rate is now regressed on four-lagged values of itselfand on four-lagged values of a number of economic variables which have been previouslyintroduced.27 The variables tried on the righthand side of equation (1) as explanatoryvariables include four lags of the variablesGM, GY, UR, FEBS, andGDINF. Four-laggedvalues of each of these variables were retained in the equation explaining spread only ifthey were jointly significant at the .05 level or stronger. It was found that the laggeddependent variable,GY, andGDINF were statistically significant.

In the output equation, two-lagged values of the dependent variable,GY, and currentand five-lagged values of anticipated and unanticipated positive and negative innovationsin the change in the federal funds rate appear on the basis of AIC. The current and laggedvalue of the change in the T-bill rate (DTBR) are also included as explanatory variablesin the output equation.28 Innovations in the change in the federal funds rate should benegatively associated with real output growth (at least, at first).

The federal funds rate equation and the output equation were jointly estimated and theresults are presented in Tables 9 and 10. Set I refers to joint estimation of equations (1)and (29), and Set II refers to joint estimation of equations (1) and (3). In the federal fundsequations, it can be seen that increases in the rate of real growth raised the change in thefederal funds rate for several quarters, and that an increase in the rate of inflation had thesame effect for about two quarters.

27 The level of the federal funds rate is non-stationary and the change in the federal funds rate is stationary.28 As emphasized by Bernanke and Blinder (1992), when interpreting movement in the federal funds rate, it

helps to know the current level of market rates of interest.

Table 9. Monetary Policy Equations with Change in Federal Funds Rate as Monetary PolicyIndicator: Nonlinear Joint Estimation 1957:III–1992:II(standard errors in parentheses)

Set I Set II

Variable Coefficient p Value Coefficient p Value

Constant 21.122 (0.199) 0.0000 20.726 (0.244) 0.0029MPI{1} 0.069 (0.059) 0.2402 0.063 (0.084) 0.4517MPI{2} 20.300 (0.066) 0.0000 20.356 (0.082) 0.0000MPI{3} 0.034 (0.052) 0.5138 0.087 (0.088) 0.3234MPI{4} 0.027 (0.054) 0.6103 0.018 (0.080) 0.8172GY{1} 0.294 (0.059) 0.0000 0.373 (0.095) 0.0000GY{2} 0.116 (0.054) 0.0328 0.154 (0.089) 0.0853GY{3} 0.216 (0.052) 0.0000 0.119 (0.078) 0.1255GY{4} 0.088 (0.050) 0.0810 0.002 (0.065) 0.9716GDINF{1} 0.250 (0.121) 0.0395 0.216 (0.131) 0.0993GDINF{2} 0.537 (0.136) 0.0000 0.469 (0.167) 0.0049GDINF{3} 20.326 (0.124) 0.0089 20.039 (0.138) 0.7738GDINF{4} 0.009 (0.101) 0.9193 20.396 (0.167) 0.0178Std. error 0.978 0.949DW 1.930 1.981R2 0.238 0.276

Notes:GY{ i} 5 log difference in real GDP with lagi; GDINF{ i} 5 log difference in GDP-deflator laggedi time periods.In the output equation for Set I, distinctions among the effects of positive and negative anticipated and unanticipated change inthe federal funds rate are recognized. In the output equation for Set II, only a distinction between anticipated and unanticipatedchange in the federal funds rate is recognized.


Table 10. Output Equations with Change in Federal Funds Rate as Monetary Policy Indicator(MPI): Nonlinear Joint Estimation 1957:III–1992:II(standard errors andx2 statistics* in parentheses)(1 indicates expansionary policy and2 indicates contractionary policy)

Set I Set II


Constant 0.223 (0.199) 0.0000 Constant 0.285 (0.170) 0.0941GY{1} 0.367 (0.143) 0.0102 GY{1} 0.554 (0.225) 0.0137GY{2} 0.325 (0.157) 0.0390 GY{2} 0.050 (0.208) 0.8086DTBR 0.818 (0.190) 0.0000 DTBR 0.597 (0.188) 0.0014DTBR{1} 0.121 (0.218) 0.5779 DTBR 0.203 (0.201) 0.3107MPIe1 21.152 (0.417) 0.0058 MPIe 21.298 (0.506) 0.0103MPIe1{1} 0.388 (0.443) 0.3816 MPIe{1} 0.618 (0.555) 0.2656MPIe1{2} 20.429 (0.304) 0.1582 MPIe{2} 20.735 (0.458) 0.1086MPIe1{3} 20.140 (0.282) 0.6190 MPIe{3} 0.350 (0.410) 0.3939MPIe1{4} 20.096 (0.266) 0.7171 MPIe{4} 20.147 (0.261) 0.5708MPIe1{5} 0.010 (0.237) 0.9663 MPIe{5} 20.117 (0.155) 0.4499MPIe2 20.844 (0.485) 0.0822 MPIu 20.131 (0.156) 0.3990MPIe2{1} 21.431 (0.611) 0.0191 MPIu{1} 20.045 (0.185) 0.8041MPIe2{2} 1.574 (0.508) 0.0019 MPIu{2} 20.671 (0.232) 0.0039MPIe2{3} 20.340 (0.401) 0.3956 MPIu{3} 0.247 (0.279) 0.3747MPIe2{4} 0.334 (0.396) 0.3986 MPIu{4} 20.278 (0.215) 0.1948MPIe2{5} 20.678 (0.345) 0.0496 MPIu{5} 20.200 (0.138) 0.1477MPIu1 20.285 (0.207) 0.1691 HypothesisMPIu1{1} 20.128 (0.222) 0.5633 MPIe{ i} 5 0a, i 5 0, . . . 5 (11.459)* 0.0751MPIu1{2} 20.507 (0.205) 0.0136 ¥ (MPIe) 5 0b, (7.985)* 0.0047MPIu1{3} 20.414 (0.231) 0.0733 MPIu{ i} 5 0a, i 5 0, . . . 5 (26.054)* 0.0002MPIu1{4} 0.128 (0.190) 0.4987 ¥ (MPIu) 5 0b, (12.675)* 0.0003MPIu1{5} 0.011 (0.155) 0.9401MPIu2 20.283 (0.186) 0.1288 MPIe{ i} 5 MPIu{ i} a, (7.771) 0.2553MPIu2{1} 20.053 (0.191) 0.7779 ¥ (MPIe) 5 ¥ (MPIu)b (0.347) 0.5559MPIu2{2} 20.326 (0.175) 0.0626MPIu2{3} 20.185 (0.201) 0.3576 Std. error 0.744MPIu2{4} 0.122 (0.176) 0.4856 DW 2.028MPIu2{5} 20.535 (0.170) 0.0016 R2 0.431HypothesisMPIe1{ i} 5 0a, (14.929)* 0.0208 ¥ (MPIe1) 5 0b, (7.969)* 0.0047MPIe2{ i} 5 0a, (19.866)* 0.0029 ¥ (MPIe2) 5 0b, (5.957)* 0.0146MPIu1{ i} 5 0a, (17.419)* 0.0078 ¥ (MPIu1) 5 0b, (10.481)* 0.0012MPIu2{ i} 5 0a, (23.707)* 0.0005 ¥ (MPIu2) 5 0b, (14.168)* 0.0001MPIe1{ i} 5 MPIe2{ i} a (19.194)* 0.0038 ¥ (MPIe1) 5 ¥ (MPIe2)b (0.001)* 0.9660MPIu1{ i} 5 MPIu2{ i} a

i 5 0, 1 . . . 5 (7.763)* 0.2559 ¥ (MPIu1) 5 ¥ (MPIu2)b (0.038)* 0.8450SC: No stimulative/contractionary:MPIe1{ i} 5 MPIe2{ i} and MPIu1{ i} 5 MPIu2{ i} c

(25.259)* 0.0136AU: No anticipated/unanticipated:MPIe1{ i} 5 MPIu1{ i} and MPIe2{ i} 5 MPIu2{ i} c

(20.913)* 0.0516Std. error 0.625DW 1.994R2 0.602

a x2(6)-test of the null hypothesis for coefficients on variables indicated.b x2(1)-test of the null hypothesis for coefficients on variables indicated.c x2(12)-test of the null hypothesis for coefficients on variables indicated.


In Table 10, it is reported, based on exclusion tests, that each of the four componentsof policy had statistically significant effects on output. The cumulative effects were alsoeach found to be statistically significant. This latter result is different from that obtainedwhen MPI was measured by growth in M1.

Results on the no stimulative/contractionary asymmetry (SC) and no anticipated/unanticipated (AU) hypotheses are reported at the bottom of Table 10. It was found thatSCwas rejected at the 0.0136 level. This result would seem to be based on the finding ofasymmetry in anticipated policy between stimulative and contractionary actions. Thisfollows, as the null hypothesis ofbi

e1 5 bie2, i 5 0, 1 . . . 5 wasrejected withp value

0.0208, compared to failure to reject the null hypothesis ofbiu1 5 bi

u2, i 5 0, 1, . . . 5. Inaddition, it will be noted from Set II, that the exclusion test for anticipated money had ap value of only 0.0751. Thus, recognition of an asymmetry in anticipated policy wouldagain seem to be of importance to results. In Table 10,AU was rejected at the 0.0516 level.

The results discussed here forn 5 5 generally held for longer lag lengths and arereported in Table 11.29 For the purpose of comparison with the results obtained in theearlier part of the paper, results are presented in Table 12 for the federal funds rate, inwhich an asymmetry in anticipated policy was not recognized (these results can becontrasted with those for spread summarized in Table 8).

In Table 11, asymmetries are to be found in both stimulative versus contractionarypolicy, and in anticipated versus unanticipated effects. For changes in the federal fundsrate, as a measure of monetary policy, it would seem that an asymmetry in the effects onoutput of anticipated policy between stimulative and contractionary components is ofsome empirical importance.

To illustrate these asymmetries, a simple five-variable VAR(GY, MPIu2, MPIu1,MPIe2, MPIe1) was estimated and impulse response functions forGY obtained.30 Theimpulse responses of growth in GDP (GY) to one-standard-error shocks toMPIu2 andMPIu1 are shown in Figure 1, and toMPIe2 and MPIe1 in Figure 2. In Figure 1, thenegative effect of unanticipated contractionary policy was initially somewhat larger inabsolute value than the positive effect of unanticipated stimulative policy. Both effects onGY fluctuated and decayed fast (with eight quarters). In Figure 2, the negative effect ofanticipated contractionary policy was larger in absolute value in the first two quarters thanthe positive effect of anticipated stimulative policy.MPIe2 showed a positive effect aftertwo quarters. Thus, it seems that anticipated contractionary policy has a relatively large,but short-lived, negative effect onGY. The impulse responses from the VAR are consis-

29 Results are not reported for a period ending in 1979:III because there was an inadequate number of degreesof freedom available for test statistics. As a check for robustness for the results over the period 1957:III–1992:II,an alternative specification of the federal funds rate equation in Table 9 was tried. In addition to four lags ofGYand ofGDINFL, four lags each ofUR, FEBS, andGM were added as explanatory variables in the federal fundsrate equation. The main difference in results concerned unanticipated policy.AU was more likely to be rejected,with p values that the anticipated/unanticipated distinction not being relevant (H0 (AU): bi

e1 5 biu1 andbi

e2 5bi

u2, i 5 1, . . .n.) now being 0.0905 (n 5 5), 0.0008 (n 5 8), 0.0000 (n 5 12), and 0.0000 (n 5 16). In addition,the hypothesis of no asymmetry in unanticipated policy (H0: bi

u1 5 biu2) was also more likely to be rejected with

p values 0.8628 (n 5 5), 0.0061 (n 5 8), 0.0000 (n 5 12), and 0.0000 (n 5 16). Results for asymmetry inanticipated policy were similar to those already reported. Given limitations of space, these results are notreported here.

30 MPIu2, MPIu1, MPIe2, MPIe1 were obtained for change in the federal funds rate implied by Set I inTables 9 and 10. The VAR had five lags, constant and deterministic variables,DTBR{0} and DTBR{1}, and wasestimated over the period 1957:III–1992:II. We are grateful to a referee for suggesting impulse responsefunctions be used to illustrate the impact of the components of monetary policy.


Table 11. Test Results of Null Hypotheses with Federal Funds Rate as Measure of MonetaryPolicy for 1957:III–1992:II(p values reported;x2 ( )-statistics in parentheses)

Hypothesis Lag Length

n 5 5 n 5 8 n 5 12 n 5 16

No Anticipated Expansionary EffectHo: bi

e1 5 0, i 5 0, 1 . . .na

0.0208 (14.929) 0.0074 (22.483) 0.0683 (21.236) 0.0038 (36.534)Ho: ¥ bi

e1 over i 5 0, 1 . . .nb

0.0047 (7.969) 0.0001 (14.414) 0.0019 (9.576) 0.0442 (4.047)No Anticipated Contractionary Effect

Ho: bie2 5 0, i 5 0, 1 . . .na

0.0029 (19.866) 0.0011 (27.523) 0.0019 (32.570) 0.0191 (31.151)Ho: ¥ bi

e2 over i 5 0, 1 . . .nb

0.0146 (5.957) 0.0014 (10.093) 0.0064 (7.428) 0.2394 (1.383)No Unanticipated Expansionary Effect

Ho: biu1 5 0, i 5 0, 1 . . .na

0.0078 (17.419) 0.0157 (20.374) 0.0083 (28.259) 0.0013 (39.821)Ho: ¥ bi

u1 over i 5 0, 1 . . .nb

0.0012 (10.481) 0.0001 (14.310) 0.0002 (13.265) 0.0146 (5.961)No Unanticipated Contractionary Effect

Ho: biu2 5 0, i 5 0, 1 . . .na

0.0005 (23.707) 0.0001 (33.439) 0.0019 (32.585) 0.0017 (39.039)Ho: ¥ bi

u2 over i 5 0, 1 . . .nb

0.0001 (14.168) 0.0001 (14.765) 0.0037 (8.425) 0.1335 (2.250)No Asymmetry in Anticipated Policy

Ho: bie1 5 bi

e2 5 0, i 5 0, 1 . . .na

0.0038 (19.194) 0.0178 (20.002) 0.0329 (23.811) 0.0064 (34.863)Ho: ¥ bi

e1 5 ¥ bie2 over i 5 0,

1 . . .nb

0.9660 (0.001) 0.7835 (0.075) 0.8094 (0.068) 0.9297 (0.007)No Asymmetry in Unanticipated Policy

Ho: biu1 5 bi

u2 5 0, i 5 0, 1 . . .na

0.2559 (7.763) 0.2693 (11.094) 0.1216 (19.047) 0.0033 (37.012)Ho: ¥ bi

u1 5 ¥ biu2 over i 5 0,

1 . . .nb

0.8450 (0.038) 0.9310 (0.007) 0.8966 (0.152) 0.4404 (0.595)No Stimulative/Contractionary Asymmetry

Ho (SC): bie1 5 bi

e2 andbiu1 5 bi

u2 i5 0, 1 . . .nc

0.0136 (25.259) 0.0538 (28.573) 0.0062 (47.459) 0.0003 (69.193)No Anticipated/Unanticipated Asymmetry

Ho (AU): bie1 5 bi

u1 andbie2 5 bi

u2 i5 0, 1 . . .nc

0.0516 (20.913) 0.0726 (27.350) 0.0964 (35.743) 0.0470 (48.906)

a x2 test withn 1 1 degrees of freedom.b x2 test with one degree of freedom.c x2 test with 2n 1 2 degrees of freedom.


tent with the results noted in Table 11, concerning an asymmetry in anticipated policybetween stimulative and contractionary effects.

VI. ConclusionFor monetary policy measured by change in the federal funds rate, an asymmetry in theeffects of anticipated expansionary and anticipated contractionary monetary policy onoutput was found. The null hypothesis of no asymmetry in stimulative/contractionarypolicy was rejected. Anticipated expansionary, anticipated contractionary, unanticipatedexpansionary, and unanticipated contractionary monetary policy were each found to havestatistically significant effects on output. Each of the four components of monetary policywere also found to have statistically significant cumulative effects on output.

Table 12. Test Results of Null Hypotheses When Federal Funds Rate is Monetary PolicyIndicator. Asymmetry in Anticipated Policy not Recognized (bi

e1 5 bie2)

(p values reported)


Lag Lengthb

n 5 5 n 5 8 n 5 12 n 5 16

Federal Funds (1957:III–1979:III)SYMMETRY 0.3598 0.0000 0.0000 0.0000PNDI 0.2632 0.0000 0.0000 0.0000Un. expansionary 0.8846 0.0063 0.0930 0.0000Un. contractionary 0.0195 0.0005 0.0001 0.0000Anticipated 0.6415 0.4207 0.9365 0.0011With restrictionbi

u1 5 biu2, i

5 0, . . .n{Anticipated} 0.6014 0.9028 0.1590 0.4211Unanticipated 0.5689 0.0192 0.0030 0.0169AUDI 0.4260 0.6435 0.2691 0.5539

Federal Funds (1957:III–1992:II)SYMMETRY 0.2383 0.1140 0.0558 0.0118PNDI 0.3147 0.1322 0.0133 0.0004Un. expansionary 0.1421 0.0585 0.0028 0.0024Un. contractionary 0.0003 0.0003 0.0015 0.0000Anticipated 0.0357 0.0055 0.0855 0.0716With restrictionbi

u1 5 biu2, i

5 0, . . .n{Anticipated} 0.0751 0.0245 0.4450 0.3898Unanticipated 0.0002 0.0004 0.0000 0.0006AUDI 0.2553 0.3239 0.6074 0.8436

a SYMMETRY-distinctions among anticipated, unanticipated positive, and unanticipated negative monetary policy areirrelevant. Null hypothesis:bi

e 5 biu1 5 bi

u2, i 5 0, 1, . . .n.AUDI-distinction between anticipated and unanticipated monetary policy is irrelevant. Null hypothesis:bi

e 5 biu, i 5 0,

1, . . .n.PNDI-distinction between unanticipated positive, and unanticipated negative monetary policy is irrelevant. Null hypothesis:

biu1 5 bi

u2, i 5 0, 1, . . .n.Un. Expansionary refers to unanticipated negative change in federal funds rate (null hypothesis isbi

u1 5 0, i 5 0, 1, . . .n).Un. Contractionary refers to unanticipated positive change in federal funds rate (null hypothesis isbi

u2 5 0, i 5 0, 1, . . .n).Anticipated-null hypothesis isbi

e 5 0, i 5 0, 1, . . .n.Null hypothesis for {Anticipated}:bi

e 5 0, i 5 0, 1, . . .n, given restrictionbiu1 5 bi

u2 5 kiu, i 5 0, . . .n. Null hypothesis

for Unanticipated:biu 5 0, i 5 0, 1, . . .n, given restrictionbi

u1 5 biu2, i 5 0, . . .n.

b For n 5 5, regressions start from 1957:III. Asn increases, regressions start at successively later dates.


For different measures of monetary policy, different specifications of the monetarypolicy and output equations, and over different sample periods, distinctions amongpositive innovations, negative innovations, and anticipated monetary policy change werefound to be relevant for explaining movement in real output. Unanticipated expansionarymonetary policy was found to be just as likely to have a statistically significant effect onoutput as unanticipated contractionary monetary policy. In addition, recognition of asym-metries in anticipated and unanticipated monetary policy between stimulative and con-tractionary components made the finding of neutrality of money less likely.

Figure 1. Impulse response of GDP to money shocks.

Figure 2. Impulse response of GDP to anticipated policy.


The results provide some empirical evidence that modeling of asymmetric effects ofexpansionary and contractionary policy, particularly when policy is anticipated, should bethe focus of further work.

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