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Optimal monetary policy: A new test
Optimal Monetary Policy: A New Test Costas Christou, University of Muryland, Harris Dellas, University of Murylund, and Anastassios Gagales, Bunk of Greece
Tests of the optimality (given some well-specified criterion) of uc*~ai monetary policy are scarce in the macro litcraturc. The purpose of this paper is twofold: first to examine how the nature of economic shocks (that is. their type. frequency. persistence. etc.) dctcrmincs the optimal degree and sign of cyclical activism; and second, to test whether actual monetary policy has satisticd a simple optimality criterion. The criterion states that if policy is motivated by price :md output stability objectives. it ought to react countereyclically to transitory shocks under the presumption that transitory shocks are mostly of demand origin; and procyclically toward past persistent supply disturbances. We subject this contention to a test in the United States. Canada and the United Kingdom by using a variety of measures ofdisturbances (the BlanchardQuah. the Solow-Prescott residuals. as well as oil price shocks) and the monetary base and the federal funds rate as monetary policy instruments. The empirical evidence failed to uncover any systematic pattern in actual policy that would be consistent with the suggested criterion.
1. INTRODUCTION The theoretical literature on optimal monetary policy is perhaps one of the most voluminous in economics. Numerous optimality criteria have been dcvclopcd catering to any conceivable environment involving policy (for some references consult the recent conference volume by Haraf and Cagan (1990) or any macro text (e.g., Blanchard and Fischer, 1989). It is thus very startling that all this literature has not generated any explicit empirical tests of the optimality of ut-tml policy. Although a great deal of empirical work in economics concerns itself with the examination of the optimality of economic behavior, no similar attempt has yet been made to apply the same tools to evaluate the
180
C. Christou,
H. Delks,
and A.
Gag&s
optimality of monetary policy according to some well-specified model.’ Of course, there has been some work on related issues such as examining whether the monetary authorities have followed particular policy rules (e.g., nominal interest rate targeting-see Ban-o, 1989or nominal income targeting-see Papell, 1989, etc.); however, the more fundamental question of whether monetary policy has been conducted in an optimal manner when it attempts to satisfy its traditional objectives of price and employment stability remains unexplored. Our objective in this paper is to make a first step in closing this gap. We start by deriving a simple optimality criterion for the conduct of cyclical policy when the exogenous disturbances are of different types and consist of elements with varying degrees of frequency of occurrence and persistence. We then examine whether the actual behavior of monetary policy has subscribed to a subset of that criterion. Work sharing our first objective and methodology can be found in the literature on supply shocks and monetary policy that was inspired by the energy shocks of the 1970s (Blinder, 198 1, Rotenberg, 1983, and Gordon, 1984). It is has not, however, led to explicit empirical testing of the type proposed here. In this paper, we follow the suggestion deriving from Lucas’s policy critique to relate the characteristics of optimal policy to the parameters of the stochastic process that entices government activity (see Cooley, Leroy, and Raymon 1984). We adopt a popular model of economic stabilization that relies on short-term price rigidities and on policy preferences that are defined over output and price stability. We ignore the issue of intermediate targets completely because targets only constitute intermediate steps in achieving the truly fundamental objectives of price and output stability. The main feature of the solrlition for optimal policy is that it reacts countercyclically to current demand shocks (independent of their persistence), procyclically to past persistent supply disturbances, and ambiguously (depending on preferences) to current supply shocks; moreover, in the last case, countercyclically policy may not be exercised if the transitory shocks have a large probability of occurrence. Countercyclical reaction to perceived persistent past shocks is suboptimal because it may lead to permanently higher prices without any compensating long-run gains in employment (because of rational expectations). Under the presumption that transitory shocks are mostly of demand origin while persistent of supply, one will expect that optimal monetary policy will ‘With
the exception of Mankiw (1987).
inflation to smooth tax distortions.
who has examincd whether the government USC’S
OPTIMAL
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181
be countercyclical toward transitory, and procyclical toward, pclst persistent disturbances. We then examine the behavior of policy in the United States, Canada, and the United Kingdom. Testing the predictions of the model involves two difficulties. First, one must be able to identify the disturbances that trigger policy. And second, one must deal with the controversies regarding what constitutes a legitimate policy instrument. With regard to the latter issue, we chose the monetary base in the hope that its movements incorporate a “stabilization” motive, but ;Nealso experimented with an alternative measure in the United States, namely, the federal funds rate.’ We are aware of the heated debates that have taken place in policy circles regarding the identification of “the” policy instrument. We do not take a position, and we let the data tell their story and the readers draw their own conclusions by presenting the results with both policy instruments. With regard to the former difficulty, we employed three constructions of disturbances. The first one was applied to the United States and Canada only and relies on the Solow-Prescott residuals. The second one is the price of oil (both nominal and real), and its choice was motivated by the findings of Hamilton (1983) that oil price changes are truly exogenous to macroeconomic developments and that they have preceded all but one recessions since World War II. The third construction employs a technique recently developed by Blanchard and Quah ( 1989) for decomposing shocks into transitory and permanent components. Although these shocks may or may not be truly exogenous (that is, some may have been caused by past policies), this does not cause any problems for the simple reason that there is nothing that rules out that optimal policy does not involve present policy reacting to events caused by past policies.’ The analysis failed to provide strong support to the theory. In many cases the reaction coefficients were insignificant; and although they had the predicted sign in several cases in which they were significant, we feel that they did not reveal a robust, systematic pattern. ‘McCallum
(1983) in his criticism of Sims make? the claim that U.S. monetary policy has
been implemented throughout the postwar period by means of interest rate instruments rather than through the monetary base. Bemanke and Blinder ( 1989) reach a similar conclusion. Nonetheless. in the models developed in this paper. the choice of the monetary instrument is irrelevant. Rather than deriving an optimal rule for money as a function of current and past disturbances we would have derived a similar rule corresponding to interest rates. It must be noted. however. that there exists some controversy with regard to whether interest rate targeting is consistent with a price-/t%pc/stability objective. ‘For example. one can argue tt
rh contractionary monetary policy in the early 1980s was
a policy response to past inflation that itself had been partly caused by past inflationary policy.
C. Chrislou.
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H. Dellas. and A. Gagalcs
Whether this finding reflects problems with the data and the modeling strategy or the failure of monetary authorities to behave optimally remains an important open question that is certainly worth further investigation. The rest of the paper is organized as follows. Section 2 offers an illustrative model and derives the characteristics of optimal monetary policy. Section 3 considers the special case of frequent transitory disturbances in the context of noncontinuous (trigger) intervention. Section 4 reports the empirical results, and a few concluding remarks follow in Section 5. 2. CONTINUOUS
INTERVENTION
The objective in this section is to use a popular macroeconomic model (see Blanchard and Fischer, 1989) to examine the relation between the rzature of exogenous shocks and the type of optimal policy activism. In this section we assume that policy intervention is continuous. The next section offers an example with policy based on trigger points. Let the level of output in period t be determined by the following equation ?‘I= ?” + I@, - p:‘, +
hu,,
(1)
where _Y,and _v’are the actual and long-run level of output respectively, p, and p” , are the actual and expected prices for period t, and u, is a supply (productivity) shock. Equation 1 says that the equilibrium rate of output depends on both short-” and long-term supply factors (u and _Y’)and also on unanticipated inflation. The second term in Equation 1 is the expectations augmented (short-run) aggregate supply (Phillips) curve; its slope is given by l/b. Aggregate demand is given by the following equation 1P1, = p, + ?‘,- 11,.
(2)
where m is the supply of money and 1’is a demand (velocity) shock. The policymaker’s objective in period 0 is to choose a sequence of money stocks {M,},~..,, to minimize the function
w=
I?,,
x P’W,. 0
(3)
“We li~llow Blanchad and Fischer ( IWO) in assuming that u does not affect the long-run growth of output (v’) hecausc it can he thought as rcprcsenting a wage push factor or a protitmargin change.
OPTIMAL
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where l3 is the discount factor (0 < l3 < I), E is the expectations operator and W, is a social welfare cost function defined as w, = .J”Cp,.?‘,) = p; + C(-‘,- JV’J2 C’> 0.
(3’)
According to Equation 3a, social cost rises with both price and output instability. The parameter c represents the weight in the policymaker’s welfare function attached to price and output objectives respectively. The demand and supply shocks follow AW(I ) processes “, = PI”, u, = pg,
I + El,
(4)
, +
(3
E:,.
with pI and p2 taking values in the interval (8, 1I and E] and e2 being white noise. To motivate the use of policy for countercyclical purposes we must introduce some rigidity.” We will assume that the economy is characterized by one-period labor contracts. This, in combination with full information on the current realization of the disturbances makes policy an effective means of achieving the objectives specified in Equation 3. Maximization of Equation 3 with regard to the money supply, m,, leads to the following optimal monetary policy rule (we are abstracting from issues of time inconsistency) I -
mj = -“,
cb
+ (, + (.b)?be,, + bpzu, ,.
The optimal conduct of policy entails a countercyclical response to the current demand shock; a procyclical response to a past persistent supply shock; and an ambiguous response to the current transitory supply disturbance: countercyclical if output concerns are dominant (large c) or the Phillips curve is steep (large 6), and procyclical in the converse case. The analysis so far has assumed that the monetary authorities have a price-level objective. We could have alternatively assumed that they have an inflation-rate objective. It is straightforward to see that with this modification there is no policy response to past (persistent) supply shocks-which have persistent effects on the price level-because there is no incentive to reverse a past change in the absolute level of prices. Note, however, that a procyclical response to past, permanent supply shocks can obtain under an inflation objective if supply shocks have permanent effects on the injkztion rate. ‘Or allow monetary authorities to possesssome informational advantage over the privatesector.
C. Christou. H. D&IS. and A. Gayles
184
3. TRIGGER-POINT
INTERVENTION
assumption that E,, has a zero mean and that intervention is continuous, the model of Section 2 did not address the issue of how the frequency of intervention affects its effectiveness and hence its desirability. Consider the condition Equation 6 with 1 > cb. so that the optimal policy response to a transitory supply disturbance is countercyclical. If the probability of getting a transitory negative supply shock in the next period is high and rational individuals understand that the policymakers’ reaction to such an event will be an expansion of the money supply, then inflationary expectations will be high. This will make intervention ineffective and hence undesirable. Consequently (abstracting for a moment from time-inconsistency issues. which, however, will be incorporated into the analysis later). the optimal response may be to not counter the disturbance at all. In this section we construct a simple example with trigger-point intervention to allow for such scenarios, which enables us to examine the relationship between frequency and effectiveness. For tractability purposes we will use a special case of the model of Section 2. The main difference is that supply shocks are assumed not to have any major effect on their own on prices (say, because the aggregate demand curve is flat). And we also employ a triggerintervention strategy. Let output in period t be determined by the following equation Due to the
?I = ?” + (Q,- 1,;1
-
I(,
(7)
and the welfare objective function be given by w, = fC&.?;, = -p’lZ + (‘(?;)(J,- ?“I.
(8)
Without loss of generality, we specialize c(_\;) to’ (‘, = (aif
y’ - 11,< _v*
(9)
= 0. othmvise.
We can now proceed to characterize the equilibrium under alternative policy intervention rules. To make it easier to understand the factors involved we will assume the simplest possible behavior for u, that of purely transitory noise’ with zero mean. Let us consider the case of a
‘Our specification of trigger strategies is rather primitive compared 10 the regulated Brownian motion literature (e.g..
see Bertola and Drazen, 190):
however. it is quite sufticient for the
purposes of this paper. ‘Dellas (IYYO) sludies the case when II is a two-state Markov process.
OPTIMAL
MONETARY
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185
nonintervention rule, p:. = p, = 0 for every I. The probability then that employment concerns become active is 4. y = probf_v’ - 14,< _v*) = prob( - II, < f Let
A = {u,: -u,
- _v’).
- $1. The welfare cost of such a policy. W,,
is
w, = - [ 141
-
h)]
I
cu~G(u,).
(10)
4
where C is the probability distribution of 14. Now suppose that the policymaker follows activist policy. The probability of intervention is 9. Under rational expectations. inflationary expectations are p: = cq because the optimal discretionary level of prices is dW/dP, = c. As intervention takes place when _v’ - u, < _v* only. we have that social welfare under discretion. W,. is given by w,, =
[l/f
I -
b)]
I
{-t-‘/z 4
Combining Equations 10 and
•+ c[(c - cq) I
14) ~GW.
(11)
1 gives
w,, - M’R= c-‘(IQ - 414.
(12)
A sufficient condition for nonactivism to be preferred to activism is that 4 > l/2. The intuition behind this result is straightforward. If very adverse supply shocks are rare. then the probability of intervention and hence of inflationary expectations are low. Consequently, monetary policy is highly effective (because it is mostly unanticipated), which increases the appeal of activism. A common problem associated with rules is that they usually require a technology for policy precommitment that may not be available. it is then of interest to inquire whether reputational considerations can substitute for explicit policy precommitment in supporting an optimal policy rule. We want to know the circumstances under which a policymaker facing zero inflationary expectations (that is, believed to be following the nonintervention rule) and an adverse productivity shock that creates employment concerns will engage in countercyclical policy and hence signal his inability to follow the rule. The level of welfare associated with the one-time deviation from the rule (when people expect adherence to the rule) is the one-time gain from surprise inflation plus a term similar to Equation 9, which arises from the subsequent switch to discretion, and is given by --F/2 + L’(C- II,) + [bl(I
- b)] [ - c.72 + c-(c-- cy - u,)]dG(rr ,I. I .a
(131
C. Christou. H. Dellas. and A. Gagales
186
For the temptation to cheat (deviate from the rule) to be dominated by the rule, Equation 13 must be less than 10. Combining 10 and 13 gives the following condition cl2 - 14,+ [h/l
- hjc( IQ -
y) < II, - E(u,~L~,E A).
(14)
As can be seen from 14, the condition 9 > l/2 is no longer sufficient to guarantee the dominance of the nonintervention rule because of the welfare gain generated by the monetary surprise. Let 9* be the value of q that satisfies 14 as an equality and q** the value of 9 that satisfies 12 as an equality. Note that 9** > 9*. It is straightforward but cumbersome to show, that pure strategy equilibria exist in the intervals 9 > y** and 9 > 9* with the rule p, = 0 being optimal for 9 > 9** and countercyclical discretion for 9 < 9”. whereas only mixed strategy equilibria exist in the interval 9* < 9 < y**. In the latter case, the monetary authorities randomize the choice of inflation between p, = 0 and p, = c’. However, if the discount rate is low or the one-time gains from intervention are not enormous, then 9* and 9** will be very close to l/2, so the previous analysis without randomization (which is thought as an unrealistic description of policy) will almost always be valid. 4. THE EMPIRHCAL ANALYSIS In this section we test the implications of the model of Section 2 regarding the optimal conduct of monetary policy. There exists a presumption that persistent shocks tend to be mostly of supply origin, whereas transitory disturbances tend to be predominantly of demand origin. Under this presumption one expects that optimal policy will involve a procyclical response toward past permanents shocks and a countercyclical one toward present transitory ones. The secrecy surrounding the conduct of monetary policy, the lack of credibility characterizing public statements of objectives, and finally the difficulty associated with the construction of measures of exogenous (non-policy-induced) transitory and persistent disturbances create severe problems in testing models of policy. These difficulties led us to experiment with several alternative approaches. The first one relies on a method employled by Blanchard and Quah ( 1989) to disentangle the effects of permanent and transitory shocks. The other two approaches identify as exogenous disturbances the Solow-Prescott residuals (fol-
hUndcr a price-level objcclivc or when pcrmancnl supply shock\ have a permanent et’tixt on Ihe inflation rate. BUI in my C;IW. the policy rcsponsc 11)pat persistent supply bhocks cannot tie countercyclical.
OPTIMAL MONETARY POLICY: A NEW TEST
187
lowing Prescott, 1986) and oil price changes (following Hamilton, 1983), respectively. We mostly use the monetary base as the cyclical policy instrument, but we also follow the suggestion of McCallum (1983) and Bemanke and Blinder (1989) to utilize the federal funds rate as the instrument of monetary policy in the United States. Before proceeding to discuss the measures of disturbances we must address an issue that is of theoretical relevance and may be of some practical importance too. The sample period included two different exchange rate regimes. Theory says that if capital controls are absent and the countries under the fixed regime abide by the ruies of the game (that is, they do not engage in devaluations), then the monetary base cannot serve as a policy instrument (note that this argument does not apply to the United States, which was both a large ecomomy as well as a reserve issuer). Our reading of the historical record is that the fixity of the exchange rate regime did not really impose much monetary discipline on countries such as the United Kingdom. If the reader disagrees with this claim he or she can selectively discard the samples before 1973 that use the monetary base in Canada and the United Kingdom. 4A. The Blanchard-Quah Residuals Let y, and p, denote the logarithm of real GNP and GNP deflator respectively, and let e:’ and e!’be the period-t transitory and permanent shocks respectively (for more details, see Blanchard and Quah, 1989). Assuming that the processes for y and p contain a unit root, the corresponding rates by and Ap are stationary and have the following representation x, = c
BJ,
,
+ AC,
E(ee’)
= a
(15)
where x = (Ay,Ap)’ and e = (4”. eP). The elements of the A matrix give the within-period response of real output growth and inflation to transitory and permanent shocks. Once Equation 15 has been estimated, one can recover the series for the transitory and permanent shocks. The moving average representation of 15 is x, = [I - $(L)j
’ AE,.
(16)
The A and a matrices cannot be estimated without some identifying restrictions. Since x is a stationary process, it has a Wold moving average representation X, = 11- R(L)lb ‘11 ,
E(d)
=
zi.
(17)
C. Christou.
188
H. Dellas. and A. Gagales
Table 1: The A Matrices for the United States, and United Kingdom and Canada
1.23 0.02
Canada
United Kingdom
United States
0.86
1.39
0.34
0.04
-0.1;
-0.13
0.69
0.68
0.07
- O.OH
All data with the exception of Canadian GNP are seasonally unadjusted. All series were taken for the IFS with the following exceptions: U.S. GNP: Survry of Current Business. Bureau of Ecenomic An;:!ysis. U.S. Department of Commerce: U.K. GNP G*or~mic~ Trends Annuul
Slcpphnenr
(1989): Prescott-Wow
( 1989). London. U.K. Central Statistical Office; Oil price: Mork
residuals: Backus. Kehoe. and Kydland ( IYXY).
From 16 and 17, one has E = AilA’.
(18)
Under the additional assumption that the conditional variance of transitory and permanent shocks is time invariant, R is a diagonal matrix and can be normalized to the identify matrix. Condition 18 can then be used to identify three of the elements of A. To uncover the fourth element, an additional identification restriction is needed. Following Blanchard and Quah (1989), we postulate that temporary shocks do not affect the long-run level of GNP.’ This assumption requires that the sequence of matrices in 16 be such that the sum of the upperleft entries (which is lim(@, +,/de:/)) equals zero. We examine the behavior of real GNP and inflation (we use the Consumer Price Index [CPI] to measure inflation) in the United States of America, Canada, and the United Kingdom in a sample that extends from 1957: 1 to 1989:2. Inspection of the GNP growth and inflation series revealed that the mean growth rate of output fell, whereas the average inflation rate increased after the mid-1970s. As in Blanchard and Quah we tried to eliminate this potential source of non-stationarity by taking 1974: 1 as the break point and subtracting from the series used in the analysis the average output and inflation rates for the two subperiods. The pre-and post- 1974: I quarterly rates are: I .08 and 0.48 for U.S. GNP, 0.75 and 1.58 for U.S. inflation; 1.22 and 0.78 “In recent theories of multiple equilibria with non- convexiries. rcmporary disturbances. whether demand or supply, can have permanent effects on output (Galor and Tsiddon. IYHY. and Stadler. 1990). As in Blanchard and Quah ( 19X9). wc have decided to ignore this complicalion in the formulation of the nests.
OPTIMAL
MONETARY
POLICY: A NEW TEST
189
for Canadian GNP and 0.76 and 1.79 for Canadian inflation; 6.78 and 0.31 for U.K. GNP and 1.1 I and 2.51 for U.K. inflation. Table 1 reports the A matrix for the United States of America, Canada. and the United Kingdom irespectively. In all three countries the coefticient that gives the impact of a temporary shock on inflation is positive. which indicates the dominance of demand disturbances as a source of short-run variation. whereas the coefficient of the permanent shock is negative. which is consistent with our priors on the nature of shocks that can have pemlanent effects (that is, supply). There is a theoretical presumrrion that transitory shocks ought to have larger effects on economic activity than permanent ones (because of the intertemporal substitution effects), and there exists some evidence supporting this contention (see Barro, 198 I. for the differential effects of transitory and permanent changes in government expenditure). Table 1 is consistent with this presumption. Using the A matrix we constructed a series for transitory and permanent disturbances. I” Aicording to the criterion suggested in Section 2 changes in the monetary base (the cyclical policy instrument) should be positively (that is. procyclically) related to lagged values of permanent disturbances; the contemporaneous response to supply disturbances is ambiguous; and under the presumption that transitory shocks are mostly of demand origin. one would expect a countercyclical reaction to temporary disturbances. The exact timing of policy reaction will depend on the length of private-sector rigidity (length of labour contracts). on the delay of wicognition of the shocks by the policymaker, the time it takes for policy to have an impact, and so on. Not having any priors on any of those we experimented with various numbers of lags, Tables 2-4 report some of the results from a regression of the growth rate of high- power money (MBj and the federal funds rate (FFR) on eight lags of the transitory (demand) and permanent (supply) disturbances” and on deterministic seasonal dummies. Two subperiods (with 1974:l being the separating period) were used (because of coefficient instability in the whole sample). In Canada the only reaction coefticient that is statistically significant at the 5-percent confidence level concerning past supply shocks in the post-1974 pe‘“Alternatively. we could have wnstrwted
two output series: one reflecting only the effects
of pwnanent disturbances tohtained by wttinp all realizations of transitory disturbances to zero) and the other r&ctins
only the elkts
these two writs in the rqrcssion
of tmnsitory disturbances. We could then have used
in the place of the disturbances. These
however. quiwlent. “Regressions with various nun~txxs 01 lass wre the results.
IWO
approachesare.
run hut did not produce any difference in
Table 2:
Regression of the Monetary Base on the Transitory Component (USA)
No.
Label
I
Constant Transit. Transit. Transit. Transit. Transit. Trdnsit Transit. Transit. Season.
2 3
4 5 6 7 8 9 IO II I2
Var.
Lag
0
0
I6 16
I 2
I6 I6 I6 I6 16 I6 9 9 9
3 4 5 6 7 8 -2 -I 0
Dependent variable: MB From 1961:3 until 1973:4 Total observations: SO Usable observations: SO R**2: 0.756855 I8 SSR: 55.089938 Durbin-Watson: I .78 1550.1 I Zi) = !8.2053 Q(
Table
- 0.9638400 - 0.2305754 0.444 I752 -0.5289032 0.1630576 0.3368761 E-02 0.7095956E-01 - O.l57738SE-01 0.295661 I 2.653519 ___ 2.850735 4.136095
Stand. error 0.4605908 0.2517188 0.2619867 0.2668660 0.2709730 0.2583585 0.2366932 0.2125989 0.1896285 0.7928952 0 ._5’5’0’5 _. _ _. 0.7715333
T-statistic - 2.09’617 - 0.9160036 I.69541 I - 1.981906 0.6017484 0.1303910E-01 - 0.2997891 -0.7419539E-01 I .ss9159 3.346620 5.427877 5.360877
Skipped/missing: 0 Degrees of freedom: 37 RBAR**>._. 0 .67799740 SEE: I. 2202 I20 Significance
level: 0.635975
3: Regression of the FFR on the Transitory Component
No.
Label
I
Constant Transit. Transit. Transit. Transit. Transit. Transit. Transit. Transit. Season. Season. Season.
2 3 4 5 6 7 8 9 IO II I’*
Coefficient
Var. 0 I6 I6 I6 I6 I6 I6 I6 I6 9 9 9
Dependent variable: FFR From 1961:3 until 1973:4 Total observations: SO Usable observations: SO R**l: 0.42403348 SSR: 16.768830 Durbin-Watson: I .90485039 Q(21) = IX.XS41
Lag
Coefficier.!
0 I 2 3 4 5 6 7 8 - 2 -I 0
- 0.23324% 0.1938004 0.4777349 - 0.7644548E-01 O.l49419OE-01 0.923079OE-0 I 0.8801086E-01 0.9104620E-01 0.6310106E-02 0.5328669 0.7143436 0.1244376
Stand. error 0.2342815 0. I39825 I 0. I39507 I 0.1304490 0.1287148 0. I226550 0. I193079 0. I I88958 0. I026667 0.2773557 0.3015104 0.2708777
Skipped/missing: 0 Degrees of freedom: 37 RBAR**‘._. 0 .*. ‘37’3353 &_. . . SEE: 0.67320994 Signilicance
level: 0.594500
T-statistic - 0.9955574 I .3X6020 3.424450 0.586OlH3 0. II60853 0.7525815 0.7376786 0.7657649 -0.6146203E-01 I .92 I240 2.369217 0.4593867
OPTIMAL
Table 4 No.
MONETARY
POLICY: A NE\\’ TEST
191
Regression of the FFR on the Pemuncnt Conywnent (USA) Label
Var.
I 2 3 4 5
Constant
0
Perman.
17
Perman.
17
Pemian.
17
Perman.
17
6
I7
7
Pemiul . Pemun.
8
Perman.
I7
9
Perman.
10
Season.
I7 9
II
Season.
9
12
Season.
9
Lag
c’oellkknt
stand. ecroT
r-statistic -0.6961291 2.tiu59 0.61457.U I .737$X2 O.75298S3 O.Jx67x9 O.32M%9E-Ol 0.4117444s - 0.786KM I .014067 0.6026II3 0.707883
I7
Dependent variable: FFR From 19712 until 1988:J Total observations: 59
Skipptut mishg:
Usable observations: SO
Degrees of tkxdom: 46
R**2: 0.26174991
RBAR**Z:
SSR: 97.765773
SEE: I .4S7XSS6
Durbin-Watson: Q(Zl,
0
tkO69l6294
I .76314X.5
= 15.1281
Signiticance Icwl: 0.227431
riod, and it has the predicted sign (positive). In the United Kingdom all coefficients are statistically insignificant. In the United States of America, the regressions that use the monetary base as the policy instrument produce insigniticant coefhcients for all types of shocks and time periods. The federal funds rate fares somewhat better with a countercyclical response to demand shocks in the pre-74 and to c~trtemporuneous supply shocks in the post-74 period. Although the results do not contradict the theory and are consistent with it in some cases, we feel that they are not strong enough to support any claims of optimality of monetary policy. Note again that the Blanchard-Quah residuals are not truly exogenous in the sense that they may incorporate the effects ofpast policy actions. As explained in the introduction, this does not affect the interpretation of the results as optimal policy reacts to t?pes of disturbances independently from their particular soun-e (private versus public sector). 4l3.. The Oil Price
We now turn to a variable that was suggested by the work of Hamilton (1983). Hamilton found that: (I 1 all but one of the U.S. recessions since World War II have been preceded with some lag by a dramatic increase in the price of crude petroleum: and (ZB that crude oil price
C. Christou. H. Deltas. and A. Gagales
192
changes were exogenous in the sense that they were unpredictable on the basis of what was happening in the U.S. macroeconomy up until that point. These two findings imply that we have a truly exogenous disturbance whose cyclical implications could not have escaped the attention of a policymaker concerned about economic downturns. The real oil price is the nominal price deflated by the CPI deflator and extends from 1956: 1 to 1988:2 (the nominal price series comes from Mork, 1989). Oil price changes were found to be very persistent, so we used the first difference of the real oil price (l-6 lags) as the independent variable, as well as seasonal dummies. In the United States, the FFR registers an immediate rise in response to an oil price increase (which points in the direction of dominant price concerns) in the pre- 1974: 1 sample, whereas the money supply responds countercyclically with some lag in the same sample (Tables 5-6). An immediate countercyclical response is also found in the United Kingdom in the first sample (Table 7). In Canada there is an interchange of sign of statistically significant coefficients in the second sample (post 1974) that is hard to interpret (Table 8). All coefficients were statistically insignificant in both subsamples in the United Kingdom. Note that the United Kingdom was an oil importer until the mid-1970s and an oil exporter thereafter, which may have affected the actions of policymakers. Whatever the effect may have been, however, it is not captured by the estimated policy equations. Table 5:
Regression of the FFR on the Oil Price (USA)
No.
Label
I 2 3
Constant Pr. oil Pr. oil
0 II II
Pr. oil Pr. oil Pr. oil Pr. oil Season. Season. Season.
I I I I
4 5 6 7 8 9 IO
Var.
I I I I 6 6 6
Lag 0 I 2 3 4 5 6 2 - I 0
Coefficient
Stand. error
-0.6176756E-01 0.3700545 0. I589785E-01 -0.1744215 -0.3301001 O.l990333E-01 - 0.2602856E-0 0.2810578
I
0.2102862 - 0.3806279E-01
0.2266782 0.1682421 0. I826936 0.2262546 0.2224868 0.1962464 0.3617887E-01 0.2014906 0.2261894 0.2010486
Dependent variable: FFR From 1959:2 until 1973:4 Total observhons: 59 Usable observations: 59 R**2* . 0 .34572554 SSR: 20.563061 Durbin-Watson: I .744 I8388
Skipped/missing: 0 Degrees of freedom: 48 RBAR**2. . 0 .20941836 SEE: 0.6545205 I
Q(2l)
Sipnifcance
= 20.6532
level: 0.480292
T-statistic - 0.2724901 2.199536 0.8701919E-01 - 0.7709083 - I .483683 0.1014201 -0.7194410 I .394892 0.9296909 -0.1893213
OPTIMAL
MONETARY
POLICY:
A NEW TEST
193
Table 6: Regression of the Monetary Base on the Oil Price (USA) No.
Label
I 2 3 4 5 6 7 8 9 10
Constant Pr. oil Pr. oil Pr. oil Pr. oil Pr. oil Pr. oil Season. Season. Season.
Var.
Lag
Coefficient
Stand. error
0 II II II II II II 6 6 6
0 I 2 3 4 5 6 - 2 -I 0
- I .337731 0.6579392 -0.2102771 0.8640173 -0.1716106 0.8624684 -0.6142616 3.131303 3.059469 4.583357
0.4511503 0.36705OY 0.3654374 0.4324991 0.4300415 0.4324341 0.4475363 0.5231216 0.5309809 0.5283702
Dependent variable: MB From lY59:2 until lY73:4 Total observations: 5Y Usable observations: 59 SSR: R**2*.91.346474 0 .67419451 Durbin-Watson: 2.34657718 Q(2l) = 46.2306
T-s:atistic - 2.965156 I .I92501 -0.5754121 I .997732 - 0.3990559 I .99445 I - I .372540 5.985906 5.761919 8.6744517
Skipped/missing: 0 Degrees of freedom: 4H SEE: RBAR**2: I.3795113 0.60631877Signiticance
level: 0. Il906lE-02
Table 7: Regression of the Monetary Basg c- the Oil Price (UK) No.
Label
Var.
I 2 3 4 5 6 7 8 9 IO
Constanl Pr. oil Pr. oil Pr. oil Pr. oil Pr. oil Pr. oil
0
9 Y Y Y 9 9 5 5 5
Lag 0
I 2 3 4 5 6 --2 - .I 0
u&lkient - I .531489 0.8058338 -0.5185263 0.4143337 - 0.9850894E-0 0.4lE5SQI -0.3343313 5.517017 0.3622421 8.856391
Stand.
I
I .396889 0.402936 I 0.444568 I 0.5463710 0.5684302 0.53973Y2 0.4725235 0.9846327 I .070107 0.9867652
Dependent variable: MB From 1959:2 until 1973:4 Total observations: 59 Usable observations: 59 R**2*. 0 .72570142 SSR: 420.00420 Durbin-Watson: I .X3 196437 Q(2l) = 20.3996
Skipped/missing: 0 Degrees of freedom: 48 RBAR**2. , 0 .66855588 ..SEE: 2.9580547 Signilicance
error
level: 0.4YAOYO
T-statistic - I .096357 I .999YO5 - I.166360 0.7583375 - 0.1733000 0.7155243 - 0.7075442 5.603122 0.3385103 8.975176
C. Christou.
194
Table 8: Regression of the Monetary No.
Label
1
Constant
0
0
2
Pr. oil
I
3 4 5 6 7 8 9 10
Pr. oil
7 7 7 7 7 7 3 3 3
Var.
Pr. oil Pr. oil Pr. oil Pr. oil Season. Season. Season.
Base on the Oil Price (Canada)
Coefficient
Stand.
5.584801
0.5059658 0.3157719E-01 0.33274lOE-01 0.3337886E-01 0.3324344E-0 0.3310748E-01 0.3204819E-01 0.6839257 0.7 192524 0.7016179
Lap: -
2 3 4 5 6
0.2851667E-01 0.4129338E-01
-
O.l243516E-01 0.1005989
-
0.7229538E-01 0.2057947E0
I
I I. 16730
-2 -I
5.426201 0
H. Dellas, and A. Gagales
12.77122
T-statistic
error
I
- I I .03790 - 0.9030782 I .241007 - 0.3725460 3.026129 - 2.183657 0.6421414 16.32824 7.544224 18.20254
Dependent variable: MB From 1974:2 until 198X:2 Total observations: 57
Skipped/missing: 0
Usable observations: 57
Degrees of freedom: 46 0.87753073 - .
R**2: 0.89940024
RBAR**2:
SSR: 153.16545
SEE: I .824742 I
Durbin-Watson: 2.06764443 Q(21) = 23.1544
Signiticance level: 0.335803
4C. The Prescott-Solow Residuals The third method for constructing measures of exogenous’” disturbances uses the Prescott-Solow residuals for the United States and Canada from 1974:l to 1984:2. Preliminary analysis of the data indicated that the series could be best described as a highly persistent process, which implies mat changes are almost permanent. ‘We regressed high-power money (and the FFR for the United States on six lags of the first difference of the technology shock. The only statistically significant coefficient is found in the United States for the federal funds rate (Table 9), and it has the predicted sign; namely a procyclical response to past distant shocks. But again, this finding does not seem strong enough to support the suggested policy optimality criterion. A possible criticism of the tests conducted is that they may not be informative enough for the following reason: The theoretical analysis in Section 2 did not entertain the possibility that policy may have been state dependent. This implies, for instance, that a countercyclical reaction to a transitory negative supply shock is more likely when the “Evan\ (1990~ shows that the Solou-Prescott
residuals may not be exogenous as they are
Granper-caused by money. govrrnmrnt expenditure. and so on. Thi\ does not cauw any problems lo our testing stralqy.
OPTIMAL MONETARY POLICY: A NEW TEST
!95
Table 9: Regression of the FFR on the Prescott--Solow Residuals (USA) No.
Label
Var.
1 2 3 4 5 6 7
Constant Technol. Technol .
0 IO IO IO IO IO IO
Technol .
Technol. Technol. Technol.
Lag 0 I
2 3 4 5 6
Coefficient O.l15758OE-01 54.17480 - 0.7159676 - 2 I .58224 6.797248 80.94772 46.70994
Stand. error
0.2981048 37.85527 37.67268 37.78966 37.89785 37.33266 37.33628
T-statistic 0.388313OE-OI I .431103 -0.1900496E-01 -0.5711151 0. I79357 I 2.168282 1.251060
Dependent variable:FFR From 1974:2 until 1984:l Total olservations: 40
Skipped/missing: 0
Usable observations: 40
Degrees of freedom: 32
R**2* . 0 . 20812776
RBAR**2. . 0 .03490083
SSR: 96.98698; Durbin-Watson: Q(l8,
=
SEE: I .7409317
I .90239732
10.0409
Significance level: 0.930562
current rate of inflation is low and/or unemployment is high and a procyclical one when inflation is high and/or unemployment is low. In other words, the coefficient of the transitory shock in Equation 6 is state dependent rather than constant. Consequently, one could suggest the inclusion of unemployment and inflation variablesI in the tests of the optimality of policy. Although this is a legitimate point, it does not affect the validity of our empirical tests for the following reason. Suppose there is a sporadic interchange of policy from pro to counter. Then a possible outcome is that the policy reaction coefficient to transitory supply shocks may turn out not to differ significantly from zero, even when policy is, in reality, activist. It is still, however, unquestionable that the optimal response to past persistent supply shocks ought to be procyclical; and that in light of the presumption that transitory shocks tend to originate in demand, one should expect a countercyclical response to transitory shocks. 5. CONCLUSIONS In this paper we have made a first attempt to evaluate the optimality of actual monetary policies given a simple optimality criterion. An important determinant of policy turned out to be the distinction between “One can divide the unemployment-inflation
space into four regions according to high and
low and examine policy behavior within each region. We plan to pursue this in the future.
C. Christou.
196
H. Dellas.
and A. Gagales
transitory and persistent supply disturbances as well as the frequency of the various transitory shocks. We employed a decomposition into transitory-permanent components of disturbances based on the Blanchard-Q&l method, the Solow-Prescott residuals, and the price of crude oil to test the former aspect. We used the monetary base (and the federal funds rate for the United States only) as the instrument of monetary policy in the United States, Canada, and the United Mingdom. Our results did not indicate strong support for the suggested theory of optimal policy. Whether this finding reflects the policymakers’ failure to behave optimally or a mispecification of the policy instrument or the nature of the disturbances considered requires further investigation to be determined. One cannot explain this failure by making the claim that monetary policy uses intermediate targets because the selection of intermediate targets must be consistent with the stated more fundamental objectives of price and output stability. More work aiming at subjecting observed policy to optimality criteria is needed. Given the secrecy surrounding policy and the possible lack of credibility of announcements, the indirect approach employed in this paper seems most promising in spite of the considerable difficulties involved. REFERENCES Backus. D.. Kehoe. P.. and Kydland. F. ( 1989) lmemational Trade and Business Cycles. Mitnat. Federal Reserve Bank of Minneapolis, MN. Barro. R. ( I98 I ) Output Effects of Government Purchases. Jourtd IOX6-I 121. Barro. R. ( 1989) Imerest rate targeting. Jourtutl
ctj Motactu~
rtj’ Polirid
Ervttotny.
X9:
Ecotrttntir:~ 23: 3-30.
Bemanke. B.. and Blinder. A. ( 1989) The Federal Funds Rate and the Channels of Monetary Transmission. Mitttco.
Princeton University.
Benola. G.. and Drazen. A. (1990) Tripper Points and Budget Cuts. Mittrect, University of Maryland. Blanchard, 0..
and Fischer, S. ( 1989) Lccnms
ott Mtrc.r~t~~1.ottotttic.s.Cambridge. MA: MIT
Press. Blanchard. 0..
and Quah. D. (19X9) The Dynamic Effccrs of Aggregate Demand and Supply
Disturbances. Atnzricxttt Ecottutttric Rmkv
79: 655-673.
Blinder. A. ( 1981) Monetary Accommodation of Supply Shocks under Rational Expectations. Jourttd
of Mom*! Ct-dit
trtd Rctttkit~aq13: 425-438.
Cooley. T., Leroy, S., and Raymon, N. (1983) Modeling Policy Interventions. Mimcvt. ?Iniversity of California,
Santa Barbara.
Dellas. H. (1990) Optimal Monetary Policy. Mittrco. Luibersity of Maryland. Evans, C. ( 1990) Productivity Shocks and the Business Cycle. Mitnm.
New York University.
Galor, 0. and Tsiddon. D. ( 1989) Transitory Productivity Shocks and Long-Run Outpul. Mitttco. Brown University. Gordon. R. ( 1984) Supply Shocks and Monetary Policy Revisited. Atttvricutt 74: 38-43.
Ecottcttttic~ Rmim
OPTIMALMONETARY
POLICY: A
197
NCWTEST
Hamilton. J. ( 1983) Oil and the Macroeconomy since World War II. JOWTJ~J/ of Poliricul Ecorrotn~ 91: 22X-248. Haraf.
W..
and Cagan. P. ( 1990) MOIJ&JI-.VPoliq
for
CfJcJrJ~irJg FitJiJtJciul
( 1987) Optimal Seignorage Collection: Theory and Evidence. JoJ~rnul of Mmefary Economics 20: 327-34 I . McCallum.
B. (1983) A Reconsideration of Sims’ Evidence Concerning Monetarism. &conomic.s
Letrers 13: 167-171. Mark. K. ( 1989) Oil and the Macroeconomy When Prices Go Up and Down: An Extension of Hamilton’s Results. hurnu~ of Poliricul Economy 97: 740-744. Papell. D. ( 1989) Monetary Policy in the United States under Flexible Exchange Rates. hnericun Economic Review 79: I IO6- I I 16. Prescott. E. ( 1986) Theory Ahead of Business Cycle Measurement. Clrrnegie Rcrchesrer Corkference series
011
Public Policy. 2% 11-u.
Rotenberg. J. (1983) Supply Shocks. Sticky Prices. and Mc netary Policy.
JOJtrtJUl
of MntJq
Credit and 6utJkirJg IS: 489-498 Stadler. G. (1990) Real Business Cycle Models with Endogenous ‘fechnology. AmericutJ Ewnomic Review 80: 163-778.
Tests of the optimality (given some well-specified criterion) of uc*~ai monetary policy are scarce in the macro litcraturc. The purpose of this paper is twofold: first to examine how the nature of economic shocks (that is. their type. frequency. persistence. etc.) dctcrmincs the optimal degree and sign of cyclical activism; and second, to test whether actual monetary policy has satisticd a simple optimality criterion. The criterion states that if policy is motivated by price :md output stability objectives. it ought to react countereyclically to transitory shocks under the presumption that transitory shocks are mostly of demand origin; and procyclically toward past persistent supply disturbances. We subject this contention to a test in the United States. Canada and the United Kingdom by using a variety of measures ofdisturbances (the BlanchardQuah. the Solow-Prescott residuals. as well as oil price shocks) and the monetary base and the federal funds rate as monetary policy instruments. The empirical evidence failed to uncover any systematic pattern in actual policy that would be consistent with the suggested criterion.
1. INTRODUCTION The theoretical literature on optimal monetary policy is perhaps one of the most voluminous in economics. Numerous optimality criteria have been dcvclopcd catering to any conceivable environment involving policy (for some references consult the recent conference volume by Haraf and Cagan (1990) or any macro text (e.g., Blanchard and Fischer, 1989). It is thus very startling that all this literature has not generated any explicit empirical tests of the optimality of ut-tml policy. Although a great deal of empirical work in economics concerns itself with the examination of the optimality of economic behavior, no similar attempt has yet been made to apply the same tools to evaluate the
180
C. Christou,
H. Delks,
and A.
Gag&s
optimality of monetary policy according to some well-specified model.’ Of course, there has been some work on related issues such as examining whether the monetary authorities have followed particular policy rules (e.g., nominal interest rate targeting-see Ban-o, 1989or nominal income targeting-see Papell, 1989, etc.); however, the more fundamental question of whether monetary policy has been conducted in an optimal manner when it attempts to satisfy its traditional objectives of price and employment stability remains unexplored. Our objective in this paper is to make a first step in closing this gap. We start by deriving a simple optimality criterion for the conduct of cyclical policy when the exogenous disturbances are of different types and consist of elements with varying degrees of frequency of occurrence and persistence. We then examine whether the actual behavior of monetary policy has subscribed to a subset of that criterion. Work sharing our first objective and methodology can be found in the literature on supply shocks and monetary policy that was inspired by the energy shocks of the 1970s (Blinder, 198 1, Rotenberg, 1983, and Gordon, 1984). It is has not, however, led to explicit empirical testing of the type proposed here. In this paper, we follow the suggestion deriving from Lucas’s policy critique to relate the characteristics of optimal policy to the parameters of the stochastic process that entices government activity (see Cooley, Leroy, and Raymon 1984). We adopt a popular model of economic stabilization that relies on short-term price rigidities and on policy preferences that are defined over output and price stability. We ignore the issue of intermediate targets completely because targets only constitute intermediate steps in achieving the truly fundamental objectives of price and output stability. The main feature of the solrlition for optimal policy is that it reacts countercyclically to current demand shocks (independent of their persistence), procyclically to past persistent supply disturbances, and ambiguously (depending on preferences) to current supply shocks; moreover, in the last case, countercyclically policy may not be exercised if the transitory shocks have a large probability of occurrence. Countercyclical reaction to perceived persistent past shocks is suboptimal because it may lead to permanently higher prices without any compensating long-run gains in employment (because of rational expectations). Under the presumption that transitory shocks are mostly of demand origin while persistent of supply, one will expect that optimal monetary policy will ‘With
the exception of Mankiw (1987).
inflation to smooth tax distortions.
who has examincd whether the government USC’S
OPTIMAL
MONETARY
POLICY: A NEW TEST
181
be countercyclical toward transitory, and procyclical toward, pclst persistent disturbances. We then examine the behavior of policy in the United States, Canada, and the United Kingdom. Testing the predictions of the model involves two difficulties. First, one must be able to identify the disturbances that trigger policy. And second, one must deal with the controversies regarding what constitutes a legitimate policy instrument. With regard to the latter issue, we chose the monetary base in the hope that its movements incorporate a “stabilization” motive, but ;Nealso experimented with an alternative measure in the United States, namely, the federal funds rate.’ We are aware of the heated debates that have taken place in policy circles regarding the identification of “the” policy instrument. We do not take a position, and we let the data tell their story and the readers draw their own conclusions by presenting the results with both policy instruments. With regard to the former difficulty, we employed three constructions of disturbances. The first one was applied to the United States and Canada only and relies on the Solow-Prescott residuals. The second one is the price of oil (both nominal and real), and its choice was motivated by the findings of Hamilton (1983) that oil price changes are truly exogenous to macroeconomic developments and that they have preceded all but one recessions since World War II. The third construction employs a technique recently developed by Blanchard and Quah ( 1989) for decomposing shocks into transitory and permanent components. Although these shocks may or may not be truly exogenous (that is, some may have been caused by past policies), this does not cause any problems for the simple reason that there is nothing that rules out that optimal policy does not involve present policy reacting to events caused by past policies.’ The analysis failed to provide strong support to the theory. In many cases the reaction coefficients were insignificant; and although they had the predicted sign in several cases in which they were significant, we feel that they did not reveal a robust, systematic pattern. ‘McCallum
(1983) in his criticism of Sims make? the claim that U.S. monetary policy has
been implemented throughout the postwar period by means of interest rate instruments rather than through the monetary base. Bemanke and Blinder ( 1989) reach a similar conclusion. Nonetheless. in the models developed in this paper. the choice of the monetary instrument is irrelevant. Rather than deriving an optimal rule for money as a function of current and past disturbances we would have derived a similar rule corresponding to interest rates. It must be noted. however. that there exists some controversy with regard to whether interest rate targeting is consistent with a price-/t%pc/stability objective. ‘For example. one can argue tt
rh contractionary monetary policy in the early 1980s was
a policy response to past inflation that itself had been partly caused by past inflationary policy.
C. Chrislou.
182
H. Dellas. and A. Gagalcs
Whether this finding reflects problems with the data and the modeling strategy or the failure of monetary authorities to behave optimally remains an important open question that is certainly worth further investigation. The rest of the paper is organized as follows. Section 2 offers an illustrative model and derives the characteristics of optimal monetary policy. Section 3 considers the special case of frequent transitory disturbances in the context of noncontinuous (trigger) intervention. Section 4 reports the empirical results, and a few concluding remarks follow in Section 5. 2. CONTINUOUS
INTERVENTION
The objective in this section is to use a popular macroeconomic model (see Blanchard and Fischer, 1989) to examine the relation between the rzature of exogenous shocks and the type of optimal policy activism. In this section we assume that policy intervention is continuous. The next section offers an example with policy based on trigger points. Let the level of output in period t be determined by the following equation ?‘I= ?” + I@, - p:‘, +
hu,,
(1)
where _Y,and _v’are the actual and long-run level of output respectively, p, and p” , are the actual and expected prices for period t, and u, is a supply (productivity) shock. Equation 1 says that the equilibrium rate of output depends on both short-” and long-term supply factors (u and _Y’)and also on unanticipated inflation. The second term in Equation 1 is the expectations augmented (short-run) aggregate supply (Phillips) curve; its slope is given by l/b. Aggregate demand is given by the following equation 1P1, = p, + ?‘,- 11,.
(2)
where m is the supply of money and 1’is a demand (velocity) shock. The policymaker’s objective in period 0 is to choose a sequence of money stocks {M,},~..,, to minimize the function
w=
I?,,
x P’W,. 0
(3)
“We li~llow Blanchad and Fischer ( IWO) in assuming that u does not affect the long-run growth of output (v’) hecausc it can he thought as rcprcsenting a wage push factor or a protitmargin change.
OPTIMAL
MONETARY
POLICY: A NEW TEST
183
where l3 is the discount factor (0 < l3 < I), E is the expectations operator and W, is a social welfare cost function defined as w, = .J”Cp,.?‘,) = p; + C(-‘,- JV’J2 C’> 0.
(3’)
According to Equation 3a, social cost rises with both price and output instability. The parameter c represents the weight in the policymaker’s welfare function attached to price and output objectives respectively. The demand and supply shocks follow AW(I ) processes “, = PI”, u, = pg,
I + El,
(4)
, +
(3
E:,.
with pI and p2 taking values in the interval (8, 1I and E] and e2 being white noise. To motivate the use of policy for countercyclical purposes we must introduce some rigidity.” We will assume that the economy is characterized by one-period labor contracts. This, in combination with full information on the current realization of the disturbances makes policy an effective means of achieving the objectives specified in Equation 3. Maximization of Equation 3 with regard to the money supply, m,, leads to the following optimal monetary policy rule (we are abstracting from issues of time inconsistency) I -
mj = -“,
cb
+ (, + (.b)?be,, + bpzu, ,.
The optimal conduct of policy entails a countercyclical response to the current demand shock; a procyclical response to a past persistent supply shock; and an ambiguous response to the current transitory supply disturbance: countercyclical if output concerns are dominant (large c) or the Phillips curve is steep (large 6), and procyclical in the converse case. The analysis so far has assumed that the monetary authorities have a price-level objective. We could have alternatively assumed that they have an inflation-rate objective. It is straightforward to see that with this modification there is no policy response to past (persistent) supply shocks-which have persistent effects on the price level-because there is no incentive to reverse a past change in the absolute level of prices. Note, however, that a procyclical response to past, permanent supply shocks can obtain under an inflation objective if supply shocks have permanent effects on the injkztion rate. ‘Or allow monetary authorities to possesssome informational advantage over the privatesector.
C. Christou. H. D&IS. and A. Gayles
184
3. TRIGGER-POINT
INTERVENTION
assumption that E,, has a zero mean and that intervention is continuous, the model of Section 2 did not address the issue of how the frequency of intervention affects its effectiveness and hence its desirability. Consider the condition Equation 6 with 1 > cb. so that the optimal policy response to a transitory supply disturbance is countercyclical. If the probability of getting a transitory negative supply shock in the next period is high and rational individuals understand that the policymakers’ reaction to such an event will be an expansion of the money supply, then inflationary expectations will be high. This will make intervention ineffective and hence undesirable. Consequently (abstracting for a moment from time-inconsistency issues. which, however, will be incorporated into the analysis later). the optimal response may be to not counter the disturbance at all. In this section we construct a simple example with trigger-point intervention to allow for such scenarios, which enables us to examine the relationship between frequency and effectiveness. For tractability purposes we will use a special case of the model of Section 2. The main difference is that supply shocks are assumed not to have any major effect on their own on prices (say, because the aggregate demand curve is flat). And we also employ a triggerintervention strategy. Let output in period t be determined by the following equation Due to the
?I = ?” + (Q,- 1,;1
-
I(,
(7)
and the welfare objective function be given by w, = fC&.?;, = -p’lZ + (‘(?;)(J,- ?“I.
(8)
Without loss of generality, we specialize c(_\;) to’ (‘, = (aif
y’ - 11,< _v*
(9)
= 0. othmvise.
We can now proceed to characterize the equilibrium under alternative policy intervention rules. To make it easier to understand the factors involved we will assume the simplest possible behavior for u, that of purely transitory noise’ with zero mean. Let us consider the case of a
‘Our specification of trigger strategies is rather primitive compared 10 the regulated Brownian motion literature (e.g..
see Bertola and Drazen, 190):
however. it is quite sufticient for the
purposes of this paper. ‘Dellas (IYYO) sludies the case when II is a two-state Markov process.
OPTIMAL
MONETARY
POLICY: A NEW TEST
185
nonintervention rule, p:. = p, = 0 for every I. The probability then that employment concerns become active is 4. y = probf_v’ - 14,< _v*) = prob( - II, < f Let
A = {u,: -u,
- _v’).
- $1. The welfare cost of such a policy. W,,
is
w, = - [ 141
-
h)]
I
cu~G(u,).
(10)
4
where C is the probability distribution of 14. Now suppose that the policymaker follows activist policy. The probability of intervention is 9. Under rational expectations. inflationary expectations are p: = cq because the optimal discretionary level of prices is dW/dP, = c. As intervention takes place when _v’ - u, < _v* only. we have that social welfare under discretion. W,. is given by w,, =
[l/f
I -
b)]
I
{-t-‘/z 4
Combining Equations 10 and
•+ c[(c - cq) I
14) ~GW.
(11)
1 gives
w,, - M’R= c-‘(IQ - 414.
(12)
A sufficient condition for nonactivism to be preferred to activism is that 4 > l/2. The intuition behind this result is straightforward. If very adverse supply shocks are rare. then the probability of intervention and hence of inflationary expectations are low. Consequently, monetary policy is highly effective (because it is mostly unanticipated), which increases the appeal of activism. A common problem associated with rules is that they usually require a technology for policy precommitment that may not be available. it is then of interest to inquire whether reputational considerations can substitute for explicit policy precommitment in supporting an optimal policy rule. We want to know the circumstances under which a policymaker facing zero inflationary expectations (that is, believed to be following the nonintervention rule) and an adverse productivity shock that creates employment concerns will engage in countercyclical policy and hence signal his inability to follow the rule. The level of welfare associated with the one-time deviation from the rule (when people expect adherence to the rule) is the one-time gain from surprise inflation plus a term similar to Equation 9, which arises from the subsequent switch to discretion, and is given by --F/2 + L’(C- II,) + [bl(I
- b)] [ - c.72 + c-(c-- cy - u,)]dG(rr ,I. I .a
(131
C. Christou. H. Dellas. and A. Gagales
186
For the temptation to cheat (deviate from the rule) to be dominated by the rule, Equation 13 must be less than 10. Combining 10 and 13 gives the following condition cl2 - 14,+ [h/l
- hjc( IQ -
y) < II, - E(u,~L~,E A).
(14)
As can be seen from 14, the condition 9 > l/2 is no longer sufficient to guarantee the dominance of the nonintervention rule because of the welfare gain generated by the monetary surprise. Let 9* be the value of q that satisfies 14 as an equality and q** the value of 9 that satisfies 12 as an equality. Note that 9** > 9*. It is straightforward but cumbersome to show, that pure strategy equilibria exist in the intervals 9 > y** and 9 > 9* with the rule p, = 0 being optimal for 9 > 9** and countercyclical discretion for 9 < 9”. whereas only mixed strategy equilibria exist in the interval 9* < 9 < y**. In the latter case, the monetary authorities randomize the choice of inflation between p, = 0 and p, = c’. However, if the discount rate is low or the one-time gains from intervention are not enormous, then 9* and 9** will be very close to l/2, so the previous analysis without randomization (which is thought as an unrealistic description of policy) will almost always be valid. 4. THE EMPIRHCAL ANALYSIS In this section we test the implications of the model of Section 2 regarding the optimal conduct of monetary policy. There exists a presumption that persistent shocks tend to be mostly of supply origin, whereas transitory disturbances tend to be predominantly of demand origin. Under this presumption one expects that optimal policy will involve a procyclical response toward past permanents shocks and a countercyclical one toward present transitory ones. The secrecy surrounding the conduct of monetary policy, the lack of credibility characterizing public statements of objectives, and finally the difficulty associated with the construction of measures of exogenous (non-policy-induced) transitory and persistent disturbances create severe problems in testing models of policy. These difficulties led us to experiment with several alternative approaches. The first one relies on a method employled by Blanchard and Quah ( 1989) to disentangle the effects of permanent and transitory shocks. The other two approaches identify as exogenous disturbances the Solow-Prescott residuals (fol-
hUndcr a price-level objcclivc or when pcrmancnl supply shock\ have a permanent et’tixt on Ihe inflation rate. BUI in my C;IW. the policy rcsponsc 11)pat persistent supply bhocks cannot tie countercyclical.
OPTIMAL MONETARY POLICY: A NEW TEST
187
lowing Prescott, 1986) and oil price changes (following Hamilton, 1983), respectively. We mostly use the monetary base as the cyclical policy instrument, but we also follow the suggestion of McCallum (1983) and Bemanke and Blinder (1989) to utilize the federal funds rate as the instrument of monetary policy in the United States. Before proceeding to discuss the measures of disturbances we must address an issue that is of theoretical relevance and may be of some practical importance too. The sample period included two different exchange rate regimes. Theory says that if capital controls are absent and the countries under the fixed regime abide by the ruies of the game (that is, they do not engage in devaluations), then the monetary base cannot serve as a policy instrument (note that this argument does not apply to the United States, which was both a large ecomomy as well as a reserve issuer). Our reading of the historical record is that the fixity of the exchange rate regime did not really impose much monetary discipline on countries such as the United Kingdom. If the reader disagrees with this claim he or she can selectively discard the samples before 1973 that use the monetary base in Canada and the United Kingdom. 4A. The Blanchard-Quah Residuals Let y, and p, denote the logarithm of real GNP and GNP deflator respectively, and let e:’ and e!’be the period-t transitory and permanent shocks respectively (for more details, see Blanchard and Quah, 1989). Assuming that the processes for y and p contain a unit root, the corresponding rates by and Ap are stationary and have the following representation x, = c
BJ,
,
+ AC,
E(ee’)
= a
(15)
where x = (Ay,Ap)’ and e = (4”. eP). The elements of the A matrix give the within-period response of real output growth and inflation to transitory and permanent shocks. Once Equation 15 has been estimated, one can recover the series for the transitory and permanent shocks. The moving average representation of 15 is x, = [I - $(L)j
’ AE,.
(16)
The A and a matrices cannot be estimated without some identifying restrictions. Since x is a stationary process, it has a Wold moving average representation X, = 11- R(L)lb ‘11 ,
E(d)
=
zi.
(17)
C. Christou.
188
H. Dellas. and A. Gagales
Table 1: The A Matrices for the United States, and United Kingdom and Canada
1.23 0.02
Canada
United Kingdom
United States
0.86
1.39
0.34
0.04
-0.1;
-0.13
0.69
0.68
0.07
- O.OH
All data with the exception of Canadian GNP are seasonally unadjusted. All series were taken for the IFS with the following exceptions: U.S. GNP: Survry of Current Business. Bureau of Ecenomic An;:!ysis. U.S. Department of Commerce: U.K. GNP G*or~mic~ Trends Annuul
Slcpphnenr
(1989): Prescott-Wow
( 1989). London. U.K. Central Statistical Office; Oil price: Mork
residuals: Backus. Kehoe. and Kydland ( IYXY).
From 16 and 17, one has E = AilA’.
(18)
Under the additional assumption that the conditional variance of transitory and permanent shocks is time invariant, R is a diagonal matrix and can be normalized to the identify matrix. Condition 18 can then be used to identify three of the elements of A. To uncover the fourth element, an additional identification restriction is needed. Following Blanchard and Quah (1989), we postulate that temporary shocks do not affect the long-run level of GNP.’ This assumption requires that the sequence of matrices in 16 be such that the sum of the upperleft entries (which is lim(@, +,/de:/)) equals zero. We examine the behavior of real GNP and inflation (we use the Consumer Price Index [CPI] to measure inflation) in the United States of America, Canada, and the United Kingdom in a sample that extends from 1957: 1 to 1989:2. Inspection of the GNP growth and inflation series revealed that the mean growth rate of output fell, whereas the average inflation rate increased after the mid-1970s. As in Blanchard and Quah we tried to eliminate this potential source of non-stationarity by taking 1974: 1 as the break point and subtracting from the series used in the analysis the average output and inflation rates for the two subperiods. The pre-and post- 1974: I quarterly rates are: I .08 and 0.48 for U.S. GNP, 0.75 and 1.58 for U.S. inflation; 1.22 and 0.78 “In recent theories of multiple equilibria with non- convexiries. rcmporary disturbances. whether demand or supply, can have permanent effects on output (Galor and Tsiddon. IYHY. and Stadler. 1990). As in Blanchard and Quah ( 19X9). wc have decided to ignore this complicalion in the formulation of the nests.
OPTIMAL
MONETARY
POLICY: A NEW TEST
189
for Canadian GNP and 0.76 and 1.79 for Canadian inflation; 6.78 and 0.31 for U.K. GNP and 1.1 I and 2.51 for U.K. inflation. Table 1 reports the A matrix for the United States of America, Canada. and the United Kingdom irespectively. In all three countries the coefticient that gives the impact of a temporary shock on inflation is positive. which indicates the dominance of demand disturbances as a source of short-run variation. whereas the coefficient of the permanent shock is negative. which is consistent with our priors on the nature of shocks that can have pemlanent effects (that is, supply). There is a theoretical presumrrion that transitory shocks ought to have larger effects on economic activity than permanent ones (because of the intertemporal substitution effects), and there exists some evidence supporting this contention (see Barro, 198 I. for the differential effects of transitory and permanent changes in government expenditure). Table 1 is consistent with this presumption. Using the A matrix we constructed a series for transitory and permanent disturbances. I” Aicording to the criterion suggested in Section 2 changes in the monetary base (the cyclical policy instrument) should be positively (that is. procyclically) related to lagged values of permanent disturbances; the contemporaneous response to supply disturbances is ambiguous; and under the presumption that transitory shocks are mostly of demand origin. one would expect a countercyclical reaction to temporary disturbances. The exact timing of policy reaction will depend on the length of private-sector rigidity (length of labour contracts). on the delay of wicognition of the shocks by the policymaker, the time it takes for policy to have an impact, and so on. Not having any priors on any of those we experimented with various numbers of lags, Tables 2-4 report some of the results from a regression of the growth rate of high- power money (MBj and the federal funds rate (FFR) on eight lags of the transitory (demand) and permanent (supply) disturbances” and on deterministic seasonal dummies. Two subperiods (with 1974:l being the separating period) were used (because of coefficient instability in the whole sample). In Canada the only reaction coefticient that is statistically significant at the 5-percent confidence level concerning past supply shocks in the post-1974 pe‘“Alternatively. we could have wnstrwted
two output series: one reflecting only the effects
of pwnanent disturbances tohtained by wttinp all realizations of transitory disturbances to zero) and the other r&ctins
only the elkts
these two writs in the rqrcssion
of tmnsitory disturbances. We could then have used
in the place of the disturbances. These
however. quiwlent. “Regressions with various nun~txxs 01 lass wre the results.
IWO
approachesare.
run hut did not produce any difference in
Table 2:
Regression of the Monetary Base on the Transitory Component (USA)
No.
Label
I
Constant Transit. Transit. Transit. Transit. Transit. Trdnsit Transit. Transit. Season.
2 3
4 5 6 7 8 9 IO II I2
Var.
Lag
0
0
I6 16
I 2
I6 I6 I6 I6 16 I6 9 9 9
3 4 5 6 7 8 -2 -I 0
Dependent variable: MB From 1961:3 until 1973:4 Total observations: SO Usable observations: SO R**2: 0.756855 I8 SSR: 55.089938 Durbin-Watson: I .78 1550.1 I Zi) = !8.2053 Q(
Table
- 0.9638400 - 0.2305754 0.444 I752 -0.5289032 0.1630576 0.3368761 E-02 0.7095956E-01 - O.l57738SE-01 0.295661 I 2.653519 ___ 2.850735 4.136095
Stand. error 0.4605908 0.2517188 0.2619867 0.2668660 0.2709730 0.2583585 0.2366932 0.2125989 0.1896285 0.7928952 0 ._5’5’0’5 _. _ _. 0.7715333
T-statistic - 2.09’617 - 0.9160036 I.69541 I - 1.981906 0.6017484 0.1303910E-01 - 0.2997891 -0.7419539E-01 I .ss9159 3.346620 5.427877 5.360877
Skipped/missing: 0 Degrees of freedom: 37 RBAR**>._. 0 .67799740 SEE: I. 2202 I20 Significance
level: 0.635975
3: Regression of the FFR on the Transitory Component
No.
Label
I
Constant Transit. Transit. Transit. Transit. Transit. Transit. Transit. Transit. Season. Season. Season.
2 3 4 5 6 7 8 9 IO II I’*
Coefficient
Var. 0 I6 I6 I6 I6 I6 I6 I6 I6 9 9 9
Dependent variable: FFR From 1961:3 until 1973:4 Total observations: SO Usable observations: SO R**l: 0.42403348 SSR: 16.768830 Durbin-Watson: I .90485039 Q(21) = IX.XS41
Lag
Coefficier.!
0 I 2 3 4 5 6 7 8 - 2 -I 0
- 0.23324% 0.1938004 0.4777349 - 0.7644548E-01 O.l49419OE-01 0.923079OE-0 I 0.8801086E-01 0.9104620E-01 0.6310106E-02 0.5328669 0.7143436 0.1244376
Stand. error 0.2342815 0. I39825 I 0. I39507 I 0.1304490 0.1287148 0. I226550 0. I193079 0. I I88958 0. I026667 0.2773557 0.3015104 0.2708777
Skipped/missing: 0 Degrees of freedom: 37 RBAR**‘._. 0 .*. ‘37’3353 &_. . . SEE: 0.67320994 Signilicance
level: 0.594500
T-statistic - 0.9955574 I .3X6020 3.424450 0.586OlH3 0. II60853 0.7525815 0.7376786 0.7657649 -0.6146203E-01 I .92 I240 2.369217 0.4593867
OPTIMAL
Table 4 No.
MONETARY
POLICY: A NE\\’ TEST
191
Regression of the FFR on the Pemuncnt Conywnent (USA) Label
Var.
I 2 3 4 5
Constant
0
Perman.
17
Perman.
17
Pemian.
17
Perman.
17
6
I7
7
Pemiul . Pemun.
8
Perman.
I7
9
Perman.
10
Season.
I7 9
II
Season.
9
12
Season.
9
Lag
c’oellkknt
stand. ecroT
r-statistic -0.6961291 2.tiu59 0.61457.U I .737$X2 O.75298S3 O.Jx67x9 O.32M%9E-Ol 0.4117444s - 0.786KM I .014067 0.6026II3 0.707883
I7
Dependent variable: FFR From 19712 until 1988:J Total observations: 59
Skipptut mishg:
Usable observations: SO
Degrees of tkxdom: 46
R**2: 0.26174991
RBAR**Z:
SSR: 97.765773
SEE: I .4S7XSS6
Durbin-Watson: Q(Zl,
0
tkO69l6294
I .76314X.5
= 15.1281
Signiticance Icwl: 0.227431
riod, and it has the predicted sign (positive). In the United Kingdom all coefficients are statistically insignificant. In the United States of America, the regressions that use the monetary base as the policy instrument produce insigniticant coefhcients for all types of shocks and time periods. The federal funds rate fares somewhat better with a countercyclical response to demand shocks in the pre-74 and to c~trtemporuneous supply shocks in the post-74 period. Although the results do not contradict the theory and are consistent with it in some cases, we feel that they are not strong enough to support any claims of optimality of monetary policy. Note again that the Blanchard-Quah residuals are not truly exogenous in the sense that they may incorporate the effects ofpast policy actions. As explained in the introduction, this does not affect the interpretation of the results as optimal policy reacts to t?pes of disturbances independently from their particular soun-e (private versus public sector). 4l3.. The Oil Price
We now turn to a variable that was suggested by the work of Hamilton (1983). Hamilton found that: (I 1 all but one of the U.S. recessions since World War II have been preceded with some lag by a dramatic increase in the price of crude petroleum: and (ZB that crude oil price
C. Christou. H. Deltas. and A. Gagales
192
changes were exogenous in the sense that they were unpredictable on the basis of what was happening in the U.S. macroeconomy up until that point. These two findings imply that we have a truly exogenous disturbance whose cyclical implications could not have escaped the attention of a policymaker concerned about economic downturns. The real oil price is the nominal price deflated by the CPI deflator and extends from 1956: 1 to 1988:2 (the nominal price series comes from Mork, 1989). Oil price changes were found to be very persistent, so we used the first difference of the real oil price (l-6 lags) as the independent variable, as well as seasonal dummies. In the United States, the FFR registers an immediate rise in response to an oil price increase (which points in the direction of dominant price concerns) in the pre- 1974: 1 sample, whereas the money supply responds countercyclically with some lag in the same sample (Tables 5-6). An immediate countercyclical response is also found in the United Kingdom in the first sample (Table 7). In Canada there is an interchange of sign of statistically significant coefficients in the second sample (post 1974) that is hard to interpret (Table 8). All coefficients were statistically insignificant in both subsamples in the United Kingdom. Note that the United Kingdom was an oil importer until the mid-1970s and an oil exporter thereafter, which may have affected the actions of policymakers. Whatever the effect may have been, however, it is not captured by the estimated policy equations. Table 5:
Regression of the FFR on the Oil Price (USA)
No.
Label
I 2 3
Constant Pr. oil Pr. oil
0 II II
Pr. oil Pr. oil Pr. oil Pr. oil Season. Season. Season.
I I I I
4 5 6 7 8 9 IO
Var.
I I I I 6 6 6
Lag 0 I 2 3 4 5 6 2 - I 0
Coefficient
Stand. error
-0.6176756E-01 0.3700545 0. I589785E-01 -0.1744215 -0.3301001 O.l990333E-01 - 0.2602856E-0 0.2810578
I
0.2102862 - 0.3806279E-01
0.2266782 0.1682421 0. I826936 0.2262546 0.2224868 0.1962464 0.3617887E-01 0.2014906 0.2261894 0.2010486
Dependent variable: FFR From 1959:2 until 1973:4 Total observhons: 59 Usable observations: 59 R**2* . 0 .34572554 SSR: 20.563061 Durbin-Watson: I .744 I8388
Skipped/missing: 0 Degrees of freedom: 48 RBAR**2. . 0 .20941836 SEE: 0.6545205 I
Q(2l)
Sipnifcance
= 20.6532
level: 0.480292
T-statistic - 0.2724901 2.199536 0.8701919E-01 - 0.7709083 - I .483683 0.1014201 -0.7194410 I .394892 0.9296909 -0.1893213
OPTIMAL
MONETARY
POLICY:
A NEW TEST
193
Table 6: Regression of the Monetary Base on the Oil Price (USA) No.
Label
I 2 3 4 5 6 7 8 9 10
Constant Pr. oil Pr. oil Pr. oil Pr. oil Pr. oil Pr. oil Season. Season. Season.
Var.
Lag
Coefficient
Stand. error
0 II II II II II II 6 6 6
0 I 2 3 4 5 6 - 2 -I 0
- I .337731 0.6579392 -0.2102771 0.8640173 -0.1716106 0.8624684 -0.6142616 3.131303 3.059469 4.583357
0.4511503 0.36705OY 0.3654374 0.4324991 0.4300415 0.4324341 0.4475363 0.5231216 0.5309809 0.5283702
Dependent variable: MB From lY59:2 until lY73:4 Total observations: 5Y Usable observations: 59 SSR: R**2*.91.346474 0 .67419451 Durbin-Watson: 2.34657718 Q(2l) = 46.2306
T-s:atistic - 2.965156 I .I92501 -0.5754121 I .997732 - 0.3990559 I .99445 I - I .372540 5.985906 5.761919 8.6744517
Skipped/missing: 0 Degrees of freedom: 4H SEE: RBAR**2: I.3795113 0.60631877Signiticance
level: 0. Il906lE-02
Table 7: Regression of the Monetary Basg c- the Oil Price (UK) No.
Label
Var.
I 2 3 4 5 6 7 8 9 IO
Constanl Pr. oil Pr. oil Pr. oil Pr. oil Pr. oil Pr. oil
0
9 Y Y Y 9 9 5 5 5
Lag 0
I 2 3 4 5 6 --2 - .I 0
u&lkient - I .531489 0.8058338 -0.5185263 0.4143337 - 0.9850894E-0 0.4lE5SQI -0.3343313 5.517017 0.3622421 8.856391
Stand.
I
I .396889 0.402936 I 0.444568 I 0.5463710 0.5684302 0.53973Y2 0.4725235 0.9846327 I .070107 0.9867652
Dependent variable: MB From 1959:2 until 1973:4 Total observations: 59 Usable observations: 59 R**2*. 0 .72570142 SSR: 420.00420 Durbin-Watson: I .X3 196437 Q(2l) = 20.3996
Skipped/missing: 0 Degrees of freedom: 48 RBAR**2. , 0 .66855588 ..SEE: 2.9580547 Signilicance
error
level: 0.4YAOYO
T-statistic - I .096357 I .999YO5 - I.166360 0.7583375 - 0.1733000 0.7155243 - 0.7075442 5.603122 0.3385103 8.975176
C. Christou.
194
Table 8: Regression of the Monetary No.
Label
1
Constant
0
0
2
Pr. oil
I
3 4 5 6 7 8 9 10
Pr. oil
7 7 7 7 7 7 3 3 3
Var.
Pr. oil Pr. oil Pr. oil Pr. oil Season. Season. Season.
Base on the Oil Price (Canada)
Coefficient
Stand.
5.584801
0.5059658 0.3157719E-01 0.33274lOE-01 0.3337886E-01 0.3324344E-0 0.3310748E-01 0.3204819E-01 0.6839257 0.7 192524 0.7016179
Lap: -
2 3 4 5 6
0.2851667E-01 0.4129338E-01
-
O.l243516E-01 0.1005989
-
0.7229538E-01 0.2057947E0
I
I I. 16730
-2 -I
5.426201 0
H. Dellas, and A. Gagales
12.77122
T-statistic
error
I
- I I .03790 - 0.9030782 I .241007 - 0.3725460 3.026129 - 2.183657 0.6421414 16.32824 7.544224 18.20254
Dependent variable: MB From 1974:2 until 198X:2 Total observations: 57
Skipped/missing: 0
Usable observations: 57
Degrees of freedom: 46 0.87753073 - .
R**2: 0.89940024
RBAR**2:
SSR: 153.16545
SEE: I .824742 I
Durbin-Watson: 2.06764443 Q(21) = 23.1544
Signiticance level: 0.335803
4C. The Prescott-Solow Residuals The third method for constructing measures of exogenous’” disturbances uses the Prescott-Solow residuals for the United States and Canada from 1974:l to 1984:2. Preliminary analysis of the data indicated that the series could be best described as a highly persistent process, which implies mat changes are almost permanent. ‘We regressed high-power money (and the FFR for the United States on six lags of the first difference of the technology shock. The only statistically significant coefficient is found in the United States for the federal funds rate (Table 9), and it has the predicted sign; namely a procyclical response to past distant shocks. But again, this finding does not seem strong enough to support the suggested policy optimality criterion. A possible criticism of the tests conducted is that they may not be informative enough for the following reason: The theoretical analysis in Section 2 did not entertain the possibility that policy may have been state dependent. This implies, for instance, that a countercyclical reaction to a transitory negative supply shock is more likely when the “Evan\ (1990~ shows that the Solou-Prescott
residuals may not be exogenous as they are
Granper-caused by money. govrrnmrnt expenditure. and so on. Thi\ does not cauw any problems lo our testing stralqy.
OPTIMAL MONETARY POLICY: A NEW TEST
!95
Table 9: Regression of the FFR on the Prescott--Solow Residuals (USA) No.
Label
Var.
1 2 3 4 5 6 7
Constant Technol. Technol .
0 IO IO IO IO IO IO
Technol .
Technol. Technol. Technol.
Lag 0 I
2 3 4 5 6
Coefficient O.l15758OE-01 54.17480 - 0.7159676 - 2 I .58224 6.797248 80.94772 46.70994
Stand. error
0.2981048 37.85527 37.67268 37.78966 37.89785 37.33266 37.33628
T-statistic 0.388313OE-OI I .431103 -0.1900496E-01 -0.5711151 0. I79357 I 2.168282 1.251060
Dependent variable:FFR From 1974:2 until 1984:l Total olservations: 40
Skipped/missing: 0
Usable observations: 40
Degrees of freedom: 32
R**2* . 0 . 20812776
RBAR**2. . 0 .03490083
SSR: 96.98698; Durbin-Watson: Q(l8,
=
SEE: I .7409317
I .90239732
10.0409
Significance level: 0.930562
current rate of inflation is low and/or unemployment is high and a procyclical one when inflation is high and/or unemployment is low. In other words, the coefficient of the transitory shock in Equation 6 is state dependent rather than constant. Consequently, one could suggest the inclusion of unemployment and inflation variablesI in the tests of the optimality of policy. Although this is a legitimate point, it does not affect the validity of our empirical tests for the following reason. Suppose there is a sporadic interchange of policy from pro to counter. Then a possible outcome is that the policy reaction coefficient to transitory supply shocks may turn out not to differ significantly from zero, even when policy is, in reality, activist. It is still, however, unquestionable that the optimal response to past persistent supply shocks ought to be procyclical; and that in light of the presumption that transitory shocks tend to originate in demand, one should expect a countercyclical response to transitory shocks. 5. CONCLUSIONS In this paper we have made a first attempt to evaluate the optimality of actual monetary policies given a simple optimality criterion. An important determinant of policy turned out to be the distinction between “One can divide the unemployment-inflation
space into four regions according to high and
low and examine policy behavior within each region. We plan to pursue this in the future.
C. Christou.
196
H. Dellas.
and A. Gagales
transitory and persistent supply disturbances as well as the frequency of the various transitory shocks. We employed a decomposition into transitory-permanent components of disturbances based on the Blanchard-Q&l method, the Solow-Prescott residuals, and the price of crude oil to test the former aspect. We used the monetary base (and the federal funds rate for the United States only) as the instrument of monetary policy in the United States, Canada, and the United Mingdom. Our results did not indicate strong support for the suggested theory of optimal policy. Whether this finding reflects the policymakers’ failure to behave optimally or a mispecification of the policy instrument or the nature of the disturbances considered requires further investigation to be determined. One cannot explain this failure by making the claim that monetary policy uses intermediate targets because the selection of intermediate targets must be consistent with the stated more fundamental objectives of price and output stability. More work aiming at subjecting observed policy to optimality criteria is needed. Given the secrecy surrounding policy and the possible lack of credibility of announcements, the indirect approach employed in this paper seems most promising in spite of the considerable difficulties involved. REFERENCES Backus. D.. Kehoe. P.. and Kydland. F. ( 1989) lmemational Trade and Business Cycles. Mitnat. Federal Reserve Bank of Minneapolis, MN. Barro. R. ( I98 I ) Output Effects of Government Purchases. Jourtd IOX6-I 121. Barro. R. ( 1989) Imerest rate targeting. Jourtutl
ctj Motactu~
rtj’ Polirid
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Blinder. A. ( 1981) Monetary Accommodation of Supply Shocks under Rational Expectations. Jourttd
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trtd Rctttkit~aq13: 425-438.
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OPTIMALMONETARY
POLICY: A
197
NCWTEST
Hamilton. J. ( 1983) Oil and the Macroeconomy since World War II. JOWTJ~J/ of Poliricul Ecorrotn~ 91: 22X-248. Haraf.
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and Cagan. P. ( 1990) MOIJ&JI-.VPoliq
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B. (1983) A Reconsideration of Sims’ Evidence Concerning Monetarism. &conomic.s
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Rotenberg. J. (1983) Supply Shocks. Sticky Prices. and Mc netary Policy.
JOJtrtJUl
of MntJq
Credit and 6utJkirJg IS: 489-498 Stadler. G. (1990) Real Business Cycle Models with Endogenous ‘fechnology. AmericutJ Ewnomic Review 80: 163-778.