- Email: [email protected]
Implementing monetary base rules: The currency problem
~ -
HOtLAND
Implementing Monetary Base Rules: The Currency Problem R. W. Hafer, Joseph H. Haslag and Scott E. Hein
Monetary policy rules which rely on the monetary base have been advocated by Meltzer and McCallum. Proponents claim that following monetary base rules would minimize fluctuations around the target growth rate for nominal GNP. Critics of such rules contend that currency has not been properly accounted for in their analysis. This paper examines McCallum's monetary base rule by explicitly taking the demand for currency into account. Assuming that currency is supplied elastically, our investigation quantifies changes in the composition of the monetary base under these rules and provides an estimate of how these compositional changes might affect the variability around the target nominal GNP growth rate.
© 1996 Temple University Keywords: Monetary base; Rules; Currency demand JEL classification: E58; E52; E50
I. Introduction The movement advocating the use of the monetary base as the Federal Reserve's main policy instrument gained momentum with the research findings of Meltzer (1984, 1987) and McCallum (1987, 1988). These studies suggest that adopting a base rule would have substantially reduced fluctuations in income around some predetermined, noninflationary path. McCallum (1987, 1988, 1993) has provided empirical evidence in support of a base rule for the United States and Japan. With regard to the United States, McCallum claims that his rule "if it had been in effect, [would] have kept nominal GNP for the United States close to a smooth target Department of Economics, Southern Illinois University at Edwardsville, Edwardsville, IL (RWH); Research Department, Federal Reserve Bank of Dallas and Department of Economics, Southern Methodist University, Dallas, TX (JHH); James E. and Elizabeth F. Sowell Professor of Finance and Chairman Area of Finance, Texas Tech University, Lubbock, TX (SEH). Address correspondence to: Professor Scott E. Hein, College of Business Administration, Texas Tech University, Lubbock, TX 79409-2101.
Journal of Economics and Business 1996; 48:461-472 © 1996 Temple University
0148-6195/96/$15.00 PII S0148-6195(96)00034-3
462
R.W. Haler et al. growth path over the period 1954-88 despite the regulatory and financial turmoil that occurred during the latter part of that period" [McCallum (1988, p. 183)]. Critics of monetary base rules, such as B. Friedman (1988), have been quick to point out that currency has become an increasingly large and non-controlled component of the monetary base. Currently, currency represents roughly 80% of the monetary base. But these critics have not fully considered the possible impacts which currency has in the implementation of proposed base rules. Merely noting that currency is a large part of the base does not constitute a priori reason to abandon a monetary base rule approach to policy. The contribution of this paper is to consider explicitly the role of currency in implementing a monetary base rule. Given the behavior of income and the monetary base, we simply ask the question: What is the behavior of currency likely to be under such conditions? Answering this question allows us to consider the heretofore ignored issue of how the monetary base would be distributed between reserves and currency across the simulation period. In essence, we consider whether adherence to a monetary base rule of the type promoted by McCallum would pose an implementation problem for the Federal Reserve if the central bank continued to supply currency elastically. The research plan was to use McCallum's (1988) rule to simulate a path for both the monetary base and currency for the period covering roughly 1960-1991. Within the framework of McCallum's (1988) experimental design, this simulation exercise reveals whether or not a policy conflict would arise from adhering to a monetary base rule path consistent with no inflation and an elastically supplied currency. Second, we have attempted to eliminate the currency problem by briefly examining the usefulness of a total reserves rule. Among the questions answered with such a rule, the main one is: Could the Fed achieve a target inflation rate by influencing only deposit creation? The format of the paper is as follows. Section II specifies the model which links nominal GNP growth to the growth of the monetary base. The steady state behavior of the monetary base is calculated and discussed using this model. The simulated values for GNP growth, using the base rule, are presented in Section III, and Section IV examines the role of currency in a base rule setting. A total reserves rule is specified and simulated in Section V, with Section VI summarizing our results.
II. A Model of N o m i n a l GNP McCallum (1987, 1988, 1993) considered the robustness of a monetary base rule by comparing different empirical models relating base growth and economic activity. 1 He found that the simulation results, for both the United States and Japan, were not sensitive to the model linking base and income. Based on such evidence and to focus the discussion, we have adopted McCallum's (1988) simplest reduced-form specification as our data-generating mechanism for nominal GNP growth.
1Judd and Motley (1992), Feldstein and Stock (1993) and Duecker (1993), among others, also analyzed the efficacyof monetary base rules in targeting nominal income growth.
Monetary Base Rules: The Currency Problem 2.1 E m p i r i c a l
463
Results
Base growth and nominal GNP growth are linked by the equation: (1)
A Y t = o~0 q- O~lAYt_ 1 d- o t 2 A B t _ 1 d- o~t,
where Y is the log of nominal GNP, B is the log of the monetary base, e denotes a stochastic error term, A is the difference operator ( A x t = x t - x t ~) and the a s are parameters to be estimated. Equation (1) was estimated using seasonally adjusted, quarterly observations of nominal GNP and the monetary base (quarterly averages), the latter adjusted for changes in reserve requirements using the St. Louis methodology. The data span the period 1954:1-1991:3. The estimation results are (standard errors are reported in parentheses): AYt = 0.008 = 0.27lAYt_ l + 0.360ABt-~
(2)
(0.002) (0.077) (0.106) Adj R 2 = 0.19 S E E = 0.010 B G = 1.24. The estimates are quite similar to those reported in McCallum (1988) for the period 1954-1985. The coefficients on both lagged income and the base are statistically significant at the 5% level. The Breusch-Godfrey (BG) test for serial correlation yields an F statistic of 1.24, which is well below the critical value of 0.02. This outcome suggests that serial correlation is not a problem. As McCallum (1988) found, this equation captures about 20% of the variation in GNP growth. Because the parameter estimates in equation (2) are used in subsequent simulations, unstable parameter estimates could lead to unreliable simulation results. It is important, therefore, to investigate the temporal stability of the estimated relationship. A battery of stability tests were used, always assuming that a break point is unknown a priori. 2 We tested for break points between 1961:1 and 1985:4, eliminating roughly 15% of the sample from consideration as possible break points. The test results, reported in Table 1, generally failed to reject the null hypothesis of parameter stability at conventional significance levels. Even though
2 In finite s a m p l e s , A n d r e w s (1993) has s u g g e s t e d i m p o s i n g b o u n d a r i e s b e t w e e n w h i c h the hypothesized b r e a k m a y have occurred. W h e n the b r e a k p o i n t is u n k n o w n , the a s y m p t o t i c d i s t r i b u t i o n t h e o r y is well specified w h e n one d o e s not s e a r c h over the e n t i r e sample.
Table 1. Results from Tests for Structural Breaks Nominal GNP Growth with Monetary Base Test procedure
Statistic
QLR
6.322 1.745 1.421 1.416"* 0.514
Mean Chow
A - P exp W P-K max P - K m e a n sq
Notes: QLR = Q u a n d t Likelihood Ratio (maximum of likelihood ratio statistics). Mean Chow = average of likelihood ratio statistics. A - P exp W = Andrews and Ploberger exponential weighted average of likelihood ratio statistics. P - K max = Ploberger and Kramer maximum of squared scaled residuals. P - K mean sq = PIoberger and Kramer average of squared scaled residuals. ** Denotes significance at the 5% level.
464
R . W . H a l e r et al.
the P - K max test statistic indicates that a break occurred, Ploberger and Kramer (1990) have shown that the P - K max test is powerful against the alternative in which breaks occur in the intercept term, not slope parameters. Given this result and the fact that no other test rejected the null hypothesis of stability, we proceeded under the presumption that there was no structural break in the data. 3 2.2 Steady-State Base Growth What does this data-generating mechanism for nominal GNP in equation (2) imply about the steady-state growth rate for the monetary base? The steady-state monetary base characterization provides an insight into how a base rule would function. In McCallum's (1988) approach to testing the base rule, a target growth rate for nominal GNP, denoted Ay*, is determined before the simulation exercise. 4 In the steady-state, AYt = AYt_ ~ = AY*. Substituting steady-state nominal growth into equation (1) and solving for the growth rate of the monetary base yields: AB = (1 - otl)/o~2AY *
--
O/0/Of
2 .
(3)
According to equation (3), the steady-state growth rate of base money depends on four factors: 1) the persistence of nominal income growth, at, 2) the multiplier of lagged monetary base growth on nominal income growth, az, 3) the average drift in nominal income, a0, and 4) the targeted value of nominal income growth, Ay*. Other things being equal, an increase in the persistence of nominal income growth ( a 1) results in slower monetary base growth in steady state. A rise in the average drift of nominal income (a 0) also results in slower monetary base growth. A change in the lagged monetary base multiplier, however, has an ambiguous effect on the steady-state growth rate of the monetary base. 5 Finally, an increase in the target growth rate of nominal income (Ay*) results in faster monetary base growth in the steady state. The parameter estimates from equation (2) allow us to calculate the (expected) steady-state growth rate for monetary base. Inserting the estimates from equation (2) into equation (3) and setting the target growth rate for nominal GNP growth at a 3% annualized rate--the growth rate which would, on average, generate zero inflation across the sample period--the monetary base would need to decrease at a
3 This evidence contrasts with Feldstein and Stock's (1993) finding of a structural break in nominal G N P growth regressions in which the monetary base is used as the money measure. The explanation may lie in the differences between the two estimated relations. For example, the adjusted R L for our regression (0.19) is somewhat higher than what was found by Feldstein and Stock (1993) (see line 1, Table 5 with adjusted R 2 of 0.17). Feldstein and Stock also included more lags (three) of a four-quarter growth rate compared with our specification of one lagged value of a one-quarter growth rate. The slightly lower adjusted R 2 suggests that too many lags were included. In addition, we used 28 more observations in estimating our regression, including the period 1954:2-1960:2. 4 Although McCallum originally used a levels target for nominal GNP, he has recently adopted a growth rate target for nominal GNP. See Hafer et al. (1990), Feldstein and Stock (1993) and McCallum (1993) for a discussion of the merits of growth rate vs. level targeting. 5 Formally, sgn(SAB/c~a 2) = s g n [ a 0 - (1 - Otl)AY*]. This equation indicates that if the average drift in nominal income is greater than the product of the target growth rate and one minus the persistence of nominal income growth, then the steady-state growth rate of the monetary base is positively related to changes in the impact multiplier.
465
Monetary Base Rules: The Currency Problem
2.8% a n n u a l rate in the steady state to achieve the target G N P growth rate. 6 This m e a n s that if n o m i n a l G N P growth evolved according to this simple r e d u c e d - f o r m model, the m o n e t a r y base w o u l d have to decline at a 2.8% a n n u a l rate to hit the desired 3% target n o m i n a l G N P growth rate. 7 T h e steady-state analysis indicates that in o r d e r to achieve 3% n o m i n a l i n c o m e growth using a m o n e t a r y base rule, the m o n e t a r y base m u s t shrink over time. But what h a p p e n s if c u r r e n c y d e m a n d is growing along with n o m i n a l i n c o m e ? W e investigated that q u e s t i o n by s i m u l a t i n g m o n e t a r y base growth, G N P growth a n d c u r r e n c y growth within the f r a m e w o r k of M c C a l l u m ' s (1988) policy rule to focus o n the effects which currency growth may have o n the i m p l e m e n t a t i o n of the base rule.
III. N o m i n a l G N P Simulations T h e s i m u l a t e d p a t h for n o m i n a l G N P growth g e n e r a t e d from e q u a t i o n (2) using M c C a l l u m ' s (1988) m o n e t a r y base rule is p r e s e n t e d in this section. M o n e t a r y base growth is dictated by a rule which can be w r i t t e n as: A B t = 0.00739 - ( 1 / 1 6 ) [ Y t i - Yt-17 -
Bt-1 + Bt
17] + A(AYt*-I - A Y t - I ) . (4)
T h e first t e r m o n the r i g h t - h a n d side of e q u a t i o n (4) is simply the quarterly value of a 3% a n n u a l i z e d growth in G N P . This value was again c h o s e n b e c a u s e it would g e n e r a t e zero inflation, o n average, across the sample period. T h e second t e r m is a four-year m o v i n g average of base velocity growth. I n this model, a p e r m a n e n t increase in base velocity growth results in slower m o n e t a r y base growth. T h e t e r m A is a f e e d b a c k p a r a m e t e r , w h e r e 0 _< A _< 1. This stipulates that m o n e t a r y b a s e growth r e s p o n d s to a 1-percentage p o i n t deviation from last p e r i o d ' s i n c o m e growth rate target by A-percentage points.
6 McCallum (1987) found similar parameter values for his simple reduced-form model. The implication, as he noted, is that base would necessarily decline to achieve a steady-state path in which nominal GNP increases at a 3% annual rate. For the quarterly model, one would use equation (2), substituting [1n(1.03)/4)] = 0.00739 or the quarterly target value of Ay*. The calculation reported here was obtained by substituting the parameter values from equation (1) into equation (2). We then annualized AB by reversing the process used to find the quarterly value of target nominal GNP growth. The parameter values in equation (1) imply that steady-state velocity growth is negatively related to movements in steady-state base growth. To see this, substitute AV + AB, where V denotes (the log of) base velocity, for Ay in equation (2) and solve for AV. For velocity growth to be policy invariant, the following condition must hold: a I + t~2 = 1. There are an infinite number of solutions to this expression. In addition to the results reported in this paper, we looked at several different combinations which yielded policy invariant values for velocity growth. Specifically,we tried (1) a 1 = a 2 = 0.5; (2) a 1 = 0.73; o/2 0.27; (3) a = 0.64, o/2 0.36; (4) a 1 = 0.01, c~2 = 0.09, (5) a I = 0.99, ~2 = 0.01. We found the same qualitative results for each case as those reported in the paper. Note also that as ~1 ---,0.0, the steady-state value of base growth increases algebraically. The results are available from the authors upon request. 7 In an earlier version of this paper [Haler et al. (1990)], we separated the simulation and estimation period, using data from the 1954-1969 period to estimate the nominal GNP growth equation. Judd and Motley (1993) interpreted our declining monetary base finding as the product of inconsistency between average output growth in the period 1954-1985. The fact that steady-state monetary base declines when the nominal GNP equation is estimated over the period 1954-1991 would seem to refute the Judd and Motley claim. Indeed, the steady-state characterization in the text makes clear the factors contributing to monetary base decline. =
=
466
R.W. Hafer et al. Equation (2), together with base rule (4), form a recursive system. The value for base growth is determined for period t, fed into the nominal GNP growth rate equation (2) in period t + 1, which then is fed back into the base rule (4), and so on. Shocks to the system are generated using the realized error term from equation (2) 8. Formally, kt = AYt - A Y t P , where AYtP is the predicted value of nominal GNP growth generated by equation (2). The simulated value of nominal GNP growth, AY,s, is thus the value of GNP growth generated with the parameter estimates in equation (2) plus kr Simulated values of nominal GNP growth were generated for the period 1959:1-1991!3. The summary statistics measuring the rule's ability to hit the target growth rate for nominal GNP, assumed to be 3%, indicate that it does quite well in reducing the volatility of GNP growth relative to actual historical values. 9 McCallum's (1988) base rule produces a root mean squared deviation (RMSD) around the target GNP growth path of 3.87%. For purposes of comparison, the RMSD generated using the actual path of GNP growth is 6.50%. Equally suggestive of the rule's ability to lessen income growth volatility is the mean deviation (MD) of 0.12%, which is not statistically different from zero.
IV. The Role of Currency in a Base Rule The issue taken up in this section is to determine how monetary base generated by McCallum's (1988) rule is distributed between currency and reserves. In addressing this issue, we assume that the Federal Reserve is willing to supply whatever currency is demanded. To estimate currency demand growth, a standard currency demand function is estimated. In our model, currency growth (AC) is specified as a function of lagged income growth (AYt 1), the lagged change in the nominal interest rate ( A i t_ 1) and lagged values of currency growth. The nominal interest rate is measured as the quarterly average of the three-month Treasury bill rate. Our purpose is not to investigate all possible currency demand specifications. Rather, this specification is sufficiently general to demonstrate the evolution of currency under the base rule. The estimates for our currency demand equation, using data for the period 1954:1-1991:3, are (standard errors in parentheses): A C t = 0.001 +0.070AYt l - 0 . 0 0 0 2 A i t _ j +0.580AC t 1
(0.001) (0.035)
(0.0004)
(0.081)
+ 0.242ACt- 2 q- 0.037ACt 3 (0.105) (0.094) Adj-R 2 = 0.76
S E E = 0.004
(5) B G = 0.65.
8 This procedure followsMcCallum's (1988) methodologyfor including non-monetaryshocks. 9 To conserve on space, all results reported here are based on a h value of 0.25. This value was found by McCallum (1987, 1988, 1993) to minimize the deviations from the target growth rate. Using other values between zero and one did not significantlyalter the results reported below. These results are available upon request.
Monetary Base Rules: The Currency Problem
467
T h e coefficient e s t i m a t e s indicate that t h e r e is a non-trivial a m o u n t o f p e r s i s t e n c e in c u r r e n c y growth: the s u m o f t h e coefficients o n lagged c u r r e n c y g r o w t h equal roughly 0.85. This m e a n s that innovations, such as slowing i n c o m e growth, a r e likely to have long-lived effects in o u r simulations. T h e results also show that l a g g e d i n c o m e exerts a statistically significant positive effect o n c u r r e n c y d e m a n d . This result is c o n s i s t e n t with the i d e a that c h a n g e s in i n c o m e influence currency d e m a n d decisions. W e d i d n o t find, however, a significant effect f r o m n o m i n a l i n t e r e s t rates. E v e n so, n o m i n a l i n t e r e s t r a t e s have b e e n r e t a i n e d for the sake o f c o m p l e t e n e s s . 1° U s i n g this c u r r e n c y d e m a n d e q u a t i o n , s i m u l a t e d values o f c u r r e n c y w e r e g e n e r a t e d using s i m u l a t e d n o m i n a l G N P growth. T o d o this, two simplifying a s s u m p t i o n s w e r e necessary: First, shocks to c u r r e n c y d e m a n d w e r e o m i t t e d . S e c o n d , b e c a u s e the m o d e l is n o t rich e n o u g h to d e t e r m i n e t h e p a t h o f t h e n o m i n a l i n t e r e s t rate, we u s e d a c t u a l values in t h e simulations. 11 T h e result o f this s i m u l a t i o n exercise is i l l u s t r a t e d b e s t by c o m p a r i n g t h e p a t h of t h e m o n e t a r y b a s e a n d s i m u l a t e d currency. This c o m p a r i s o n is d o n e in F i g u r e 1, w h e r e plots o f the m o n e t a r y b a s e g e n e r a t e d by t h e M c C a l l u m (1988) rule a n d s i m u l a t e d c u r r e n c y a r e shown. T h e m o s t striking f e a t u r e in F i g u r e 1 is that c u r r e n c y begins to exceed the q u a n t i t y o f m o n e t a r y b a s e d i c t a t e d by the rule a r o u n d t h e mid-1970s. This m e a n s t h a t total r e s e r v e s - - b a s e less c u r r e n c y - - w o u l d have b e e n negative a f t e r t h e c r o s s - o v e r point. In fact, by t h e e n d o f the s i m u l a t i o n p e r i o d , t h e v a l u e o f t h e m o n e t a r y b a s e was $31.2 billion a n d c u r r e n c y was $127.2 billion. This result w o u l d r e q u i r e total reserves to b e $ - 96.9 billion! W e d o n o t b e l i e v e t h a t n e g a t i v e t o t a l r e s e r v e s r e p r e s e n t s a viable e q u i l i b r i u m o u t c o m e , b u t this result p o i n t s to o n e very i m p o r t a n t p r o b l e m which m a n y m o n e t a r y b a s e rule a d v o c a t e s have c h o s e n to ignore. F o r a given reserve r e q u i r e m e n t ratio, falling r e s e r v e s relative to c u r r e n c y m e a n s that t h e q u a n t i t y o f d e p o s i t s relative to c u r r e n c y also m u s t fall. A r e d u c t i o n in d e p o s i t s w o u l d r e q u i r e the b a n k i n g s e c t o r to contract, b u t e c o n o m i c c h a n g e s necessary to m i t i g a t e the b a n k i n g s e c t o r ' s c o n t r a c t i o n u n d e r a b a s e rule w o u l d likely arise. F o r e x a m p l e , b a n k s likely w o u l d raise i n t e r e s t r a t e s on d e p o s i t s in an a t t e m p t to shift t h e c o m p o s i t i o n o f the existing m o n e t a r y b a s e t o w a r d reserves a n d stop the h e m o r r h a g i n g b a n k sector. A s the b a n k i n g s e c t o r r e a c t e d to such changes, it is quite likely t h a t the r e d u c e d - f o r m
l0 We experimented with alternative currency specifications. One equation decomposed the lagged term on nominal income into real income growth and inflation, combined with a lagged ex post real interest rate and the lagged currency terms. Another specification related real currency demand to current real income, the current real interest rate and one lagged currency term. Although the quantitative outcome of the simulation exercises varied somewhat between these currency specifications, the qualitative results presented in this paper were not materially affected by these changes. For this reason, we report only the results based on the currency equations shown in the text. The results for the alternative equations and simulation results are available on request. Cagan (1982) and Sprenkle (1993) provide insights into currency demand estimation. ~1The nominal interest rate is likely to look very different in the simulations. This is because inflation would not have risen to the extent observed in the late 1970s and early 1980s. A more reasonable assumption, without solving for the nominal interest rate path, is to assume that the real interest rate would remain unchanged. Thus, a currency model which uses real interest rates as an explanatory variable was also estimated. The results obtained in the simulations were not materially affected by this change. These results are available on request. We also performed simulations using a currency demand equation with no intercept, as the constant reported above was not significantly different from zero. This modification also did not change the major conclusions reported below.
69
70
71
72
73
74
75
76
77
Figure 1. Simulated paths for monetary base and currency.
30
40
50
60
70
80
90
lO0
II0
120
130
Billion$
78
79
•••°°
..o
80
81
oooOO°°°
82
•e
83
84
°s
85
86
87
88
89
90
Monetary Base
Curreaey
,o'"•'"""
91
7z
~.
469
Monetary Base Rules: The Currency Problem
parameters would be very different from those in the equations estimated above. This potential instability in the reduced-form model raises doubt about the reliability of the simulation results from this and previous studies of base rules. Regardless, using the same methodology as base rule advocates have proposed, our simulation exercises for currency suggest that, at a minimum, some startlingly different behavior in the banking sector likely would unfold. At least within the historical context of the simulation exercise, the distribution of the base between currency and reserves must be more fully considered in analyzing the usefulness of adopting base rules for monetary policy.
V. A Total Reserve Rule The problems associated with currency growth in a monetary base targeting regime might be mitigated if the Federal Reserve supplied currency elastically to accommodate demand, but focused policy actions on hitting a total reserves target instead of a base target. To examine this-alternative rule, we estimated a nominal GNP growth equation identical to equation (1) in all respects except that total reserve growth was substituted for monetary base growth. The full-sample regression results after this substitution was made are (standard errors are in parentheses): AYt = 0.01 + 0.328AYt_l + 0.206ATRt 1 (0.002) (0.075) Adj-R 2 = 0.17
(6)
(0.062)
SEE = 0.010
BG = 1.24.
Compared with the monetary base version, the adjusted R 2 is only slightly lower when total reserves are used instead of the base. Even though total reserves have a smaller point impact than base (0.260 vs. 0.360), the coefficient remains statistically significant. As before, the results from the battery of stability tests indicate one cannot reject the hypothesis that the parameters are constant over time. 12 Substituting total reserves for the monetary base in the rule, nominal GNP growth and the path for total reserves were simulated. The summary statistics for the deviations from target nominal GNP growth under the total reserves rule indicate that the MD and RMSD are slightly larger when compared with the monetary base rule. For example, the MD, using a reserves rule, is - 0 . 2 8 compared with 0.12 using a base rule. The RMSD increases to 4.00 using total reserves compared with 3.87 when the base is used. Setting the target nominal GNP growth rate at 3%, the steady state estimates indicate that total reserves would have to decline at a 9.3% annual rate according to the estimates in equation (6). This means that the Federal Reserve would have to substantially contract the quantity of total reserves in order to achieve zero average inflation. Assuming a constant reserve requirement ratio, this contraction
~2 T h e t e s t statistics f r o m t h e s t a b i l i t y t e s t s a r e as follows: QLR = 2.647; M e a n C h o w = 0.980; A - P e x p W = 0.561; P - K m a x = 0.937; P - K m e a n sq = 0.321. T h e t e s t statistics d i d n o t r e j e c t t h e null of parameter
constancy.
70
4 . . . , . °
71
72
73
i
74
•
i
75
iq
"'76.
i
77
78
i
79
Figure 2. Simulated total reserve paths for the base and reserve rules.
40
-30
-20
-I0
IO
20
69
Billion $
30
80
81
82
83
84
85
86
87
88
i
Base Rule
89
90
Total Reserves Rule
i
91
i
Monetary Base Rules: The Currency Problem
471
again would force deposits in the banking system to shrink as fewer reserves would be available to support deposits. Figure 2 provides the time paths for total reserves, both with the base rule and the total reserves rule. The figure shows that total reserves contract sharply even under the total reserves rule. Thus, even using total reserves as the policy instrument, the non-inflationary path for G N P dictates that total reserves, even though they did not turn negative in the simulations, must decline sharply in a manner similar to that found earlier for the monetary base.
VI. Summary Much research has focused on the ability of monetary base rules to achieve predetermined income growth targets. Within this context, we have addressed a different, but equally important issue" What if the Fed operated under the constraint of a monetary base rule and simultaneously maintained an elastic supply of currency? Using the monetary base rule popularized by McCallum (1988), we find that if the Federal Reserve continued to supply currency elastically and manipulated the growth of the monetary base to achieve a non-inflationary 3% rate of nominal G N P growth, total reserves would decline dramatically, even turning negative. This finding seriously questions assertions that such a monetary base rule is operational. The implication from our simulation exercise is that the banking system would shrink as reserves and deposits decline relative to currency holdings. We have also demonstrated that a total reserves rule does not totally obviate this dilemma. A total reserves rule generates a path for shrinking total reserves which mimics the problems similar to those encountered with the monetary base rules. Proponents of monetary base rules rely extensively on evidence that such rules achieve price stability and lessen the volatility of income growth. The findings in this p a p e r suggest that such gains may be offset by problems in other areas, such as a shrinking banking system. Earlier studies have ignored the distinction between reserves and currency development, and simply treated the two as perfect substitutes. By explicitly considering the role of currency, this p a p e r shows that total reserves and, therefore, the size of the banking system, would be substantially affected by following a non-inflation monetary base rule.
The authors with to thank Phillip Cagan, Thomas Cosimano, Milton Friedman, Evan Koenig, Bennett McCallum, Allan Meltzer, Anna Schwartz, Richard Sheehan, David Small, James Stock, session participants at meetings of the Allied Social Sciences Association, the Western Economic Association, the Southern Economic Association, and anonymous referees for helpful comments on earlier versions of this paper. Any remaining errors are our responsibility. The views expressed herein do not necessarily represent those of the Federal Reserve Bank of Dallas nor the Board of Governors of the Federal Reserve System.
References Andrews, D. K. July 1993. Tests for parameter instability and structural change with unknown change point. Econometrica 61:821-56. Cagan, P. Nov. 1982. The choice among monetary aggregates as targets and guides for monetary policy. Journal of Money, Credit, and Banking 14(4):661-86.
472
R . W . Haler et al. Dueker, M. J. M a y / J u n e 1993. Can nominal GDP targeting rules stabilize the economy? Federal Reserve Bank of St. Louis. Review 15-29. Feldstein, M. and Stock, J. H. March 1993. The use of monetary aggregates to target nominal GDP. NBER Working Paper No. 4304. Friedman, B. M. 1988. Conducting monetary policy by controlling currency plus noise: A comment. Carnegie-Rochester Conference Series on Public Policy 29:205-12. Haler, R. W., Haslag, J. H. and Hein, S. E. 1990. Evaluating monetary base targeting rules. Federal Reserve Bank of Dallas Working Paper No. 9008. Judd, J. P. and Motley, B. 1992. Nominal feedback rules for monetary policy: Alternative operating procedures and targets. Unpublished manuscript. McCallum, B. T. Sept./Oct. 1987. The case for rules in the conduct of monetary policy: A concrete example. Federal Reserve Bank of Richmond. Economic Review 10-18. McCallum, B. T. 1988. Robustness properties of a rule for monetary policy. Carnegie-Rochester Conference Series on Public Policy 29:173-203. McCallum, B. T. Sept. 1993. Specification and analysis of a monetary policy rule for Japan. NBER Working Paper No. 4449. Meltzer, A. H. 1984. Overview. In Price Stability and Public Policy. A symposium sponsored by the Federal Reserve Bank of Kansas City, pp. 209-22. Meltzer, A. H. Jan. 1987. Limits of short-run stabilization policy. Economic Inquiry 1-14. Ploberger, W. and Kramer, W. Sept. 1990. The local power of the CUSUM and CUSUM of Squares Tests. Econometric Theory 6:335-47. Sprenkle, C. M. Fall 1993. The case of the missing currency. Journal of Economic Perspectives 7(4):175-84.
HOtLAND
Implementing Monetary Base Rules: The Currency Problem R. W. Hafer, Joseph H. Haslag and Scott E. Hein
Monetary policy rules which rely on the monetary base have been advocated by Meltzer and McCallum. Proponents claim that following monetary base rules would minimize fluctuations around the target growth rate for nominal GNP. Critics of such rules contend that currency has not been properly accounted for in their analysis. This paper examines McCallum's monetary base rule by explicitly taking the demand for currency into account. Assuming that currency is supplied elastically, our investigation quantifies changes in the composition of the monetary base under these rules and provides an estimate of how these compositional changes might affect the variability around the target nominal GNP growth rate.
© 1996 Temple University Keywords: Monetary base; Rules; Currency demand JEL classification: E58; E52; E50
I. Introduction The movement advocating the use of the monetary base as the Federal Reserve's main policy instrument gained momentum with the research findings of Meltzer (1984, 1987) and McCallum (1987, 1988). These studies suggest that adopting a base rule would have substantially reduced fluctuations in income around some predetermined, noninflationary path. McCallum (1987, 1988, 1993) has provided empirical evidence in support of a base rule for the United States and Japan. With regard to the United States, McCallum claims that his rule "if it had been in effect, [would] have kept nominal GNP for the United States close to a smooth target Department of Economics, Southern Illinois University at Edwardsville, Edwardsville, IL (RWH); Research Department, Federal Reserve Bank of Dallas and Department of Economics, Southern Methodist University, Dallas, TX (JHH); James E. and Elizabeth F. Sowell Professor of Finance and Chairman Area of Finance, Texas Tech University, Lubbock, TX (SEH). Address correspondence to: Professor Scott E. Hein, College of Business Administration, Texas Tech University, Lubbock, TX 79409-2101.
Journal of Economics and Business 1996; 48:461-472 © 1996 Temple University
0148-6195/96/$15.00 PII S0148-6195(96)00034-3
462
R.W. Haler et al. growth path over the period 1954-88 despite the regulatory and financial turmoil that occurred during the latter part of that period" [McCallum (1988, p. 183)]. Critics of monetary base rules, such as B. Friedman (1988), have been quick to point out that currency has become an increasingly large and non-controlled component of the monetary base. Currently, currency represents roughly 80% of the monetary base. But these critics have not fully considered the possible impacts which currency has in the implementation of proposed base rules. Merely noting that currency is a large part of the base does not constitute a priori reason to abandon a monetary base rule approach to policy. The contribution of this paper is to consider explicitly the role of currency in implementing a monetary base rule. Given the behavior of income and the monetary base, we simply ask the question: What is the behavior of currency likely to be under such conditions? Answering this question allows us to consider the heretofore ignored issue of how the monetary base would be distributed between reserves and currency across the simulation period. In essence, we consider whether adherence to a monetary base rule of the type promoted by McCallum would pose an implementation problem for the Federal Reserve if the central bank continued to supply currency elastically. The research plan was to use McCallum's (1988) rule to simulate a path for both the monetary base and currency for the period covering roughly 1960-1991. Within the framework of McCallum's (1988) experimental design, this simulation exercise reveals whether or not a policy conflict would arise from adhering to a monetary base rule path consistent with no inflation and an elastically supplied currency. Second, we have attempted to eliminate the currency problem by briefly examining the usefulness of a total reserves rule. Among the questions answered with such a rule, the main one is: Could the Fed achieve a target inflation rate by influencing only deposit creation? The format of the paper is as follows. Section II specifies the model which links nominal GNP growth to the growth of the monetary base. The steady state behavior of the monetary base is calculated and discussed using this model. The simulated values for GNP growth, using the base rule, are presented in Section III, and Section IV examines the role of currency in a base rule setting. A total reserves rule is specified and simulated in Section V, with Section VI summarizing our results.
II. A Model of N o m i n a l GNP McCallum (1987, 1988, 1993) considered the robustness of a monetary base rule by comparing different empirical models relating base growth and economic activity. 1 He found that the simulation results, for both the United States and Japan, were not sensitive to the model linking base and income. Based on such evidence and to focus the discussion, we have adopted McCallum's (1988) simplest reduced-form specification as our data-generating mechanism for nominal GNP growth.
1Judd and Motley (1992), Feldstein and Stock (1993) and Duecker (1993), among others, also analyzed the efficacyof monetary base rules in targeting nominal income growth.
Monetary Base Rules: The Currency Problem 2.1 E m p i r i c a l
463
Results
Base growth and nominal GNP growth are linked by the equation: (1)
A Y t = o~0 q- O~lAYt_ 1 d- o t 2 A B t _ 1 d- o~t,
where Y is the log of nominal GNP, B is the log of the monetary base, e denotes a stochastic error term, A is the difference operator ( A x t = x t - x t ~) and the a s are parameters to be estimated. Equation (1) was estimated using seasonally adjusted, quarterly observations of nominal GNP and the monetary base (quarterly averages), the latter adjusted for changes in reserve requirements using the St. Louis methodology. The data span the period 1954:1-1991:3. The estimation results are (standard errors are reported in parentheses): AYt = 0.008 = 0.27lAYt_ l + 0.360ABt-~
(2)
(0.002) (0.077) (0.106) Adj R 2 = 0.19 S E E = 0.010 B G = 1.24. The estimates are quite similar to those reported in McCallum (1988) for the period 1954-1985. The coefficients on both lagged income and the base are statistically significant at the 5% level. The Breusch-Godfrey (BG) test for serial correlation yields an F statistic of 1.24, which is well below the critical value of 0.02. This outcome suggests that serial correlation is not a problem. As McCallum (1988) found, this equation captures about 20% of the variation in GNP growth. Because the parameter estimates in equation (2) are used in subsequent simulations, unstable parameter estimates could lead to unreliable simulation results. It is important, therefore, to investigate the temporal stability of the estimated relationship. A battery of stability tests were used, always assuming that a break point is unknown a priori. 2 We tested for break points between 1961:1 and 1985:4, eliminating roughly 15% of the sample from consideration as possible break points. The test results, reported in Table 1, generally failed to reject the null hypothesis of parameter stability at conventional significance levels. Even though
2 In finite s a m p l e s , A n d r e w s (1993) has s u g g e s t e d i m p o s i n g b o u n d a r i e s b e t w e e n w h i c h the hypothesized b r e a k m a y have occurred. W h e n the b r e a k p o i n t is u n k n o w n , the a s y m p t o t i c d i s t r i b u t i o n t h e o r y is well specified w h e n one d o e s not s e a r c h over the e n t i r e sample.
Table 1. Results from Tests for Structural Breaks Nominal GNP Growth with Monetary Base Test procedure
Statistic
QLR
6.322 1.745 1.421 1.416"* 0.514
Mean Chow
A - P exp W P-K max P - K m e a n sq
Notes: QLR = Q u a n d t Likelihood Ratio (maximum of likelihood ratio statistics). Mean Chow = average of likelihood ratio statistics. A - P exp W = Andrews and Ploberger exponential weighted average of likelihood ratio statistics. P - K max = Ploberger and Kramer maximum of squared scaled residuals. P - K mean sq = PIoberger and Kramer average of squared scaled residuals. ** Denotes significance at the 5% level.
464
R . W . H a l e r et al.
the P - K max test statistic indicates that a break occurred, Ploberger and Kramer (1990) have shown that the P - K max test is powerful against the alternative in which breaks occur in the intercept term, not slope parameters. Given this result and the fact that no other test rejected the null hypothesis of stability, we proceeded under the presumption that there was no structural break in the data. 3 2.2 Steady-State Base Growth What does this data-generating mechanism for nominal GNP in equation (2) imply about the steady-state growth rate for the monetary base? The steady-state monetary base characterization provides an insight into how a base rule would function. In McCallum's (1988) approach to testing the base rule, a target growth rate for nominal GNP, denoted Ay*, is determined before the simulation exercise. 4 In the steady-state, AYt = AYt_ ~ = AY*. Substituting steady-state nominal growth into equation (1) and solving for the growth rate of the monetary base yields: AB = (1 - otl)/o~2AY *
--
O/0/Of
2 .
(3)
According to equation (3), the steady-state growth rate of base money depends on four factors: 1) the persistence of nominal income growth, at, 2) the multiplier of lagged monetary base growth on nominal income growth, az, 3) the average drift in nominal income, a0, and 4) the targeted value of nominal income growth, Ay*. Other things being equal, an increase in the persistence of nominal income growth ( a 1) results in slower monetary base growth in steady state. A rise in the average drift of nominal income (a 0) also results in slower monetary base growth. A change in the lagged monetary base multiplier, however, has an ambiguous effect on the steady-state growth rate of the monetary base. 5 Finally, an increase in the target growth rate of nominal income (Ay*) results in faster monetary base growth in the steady state. The parameter estimates from equation (2) allow us to calculate the (expected) steady-state growth rate for monetary base. Inserting the estimates from equation (2) into equation (3) and setting the target growth rate for nominal GNP growth at a 3% annualized rate--the growth rate which would, on average, generate zero inflation across the sample period--the monetary base would need to decrease at a
3 This evidence contrasts with Feldstein and Stock's (1993) finding of a structural break in nominal G N P growth regressions in which the monetary base is used as the money measure. The explanation may lie in the differences between the two estimated relations. For example, the adjusted R L for our regression (0.19) is somewhat higher than what was found by Feldstein and Stock (1993) (see line 1, Table 5 with adjusted R 2 of 0.17). Feldstein and Stock also included more lags (three) of a four-quarter growth rate compared with our specification of one lagged value of a one-quarter growth rate. The slightly lower adjusted R 2 suggests that too many lags were included. In addition, we used 28 more observations in estimating our regression, including the period 1954:2-1960:2. 4 Although McCallum originally used a levels target for nominal GNP, he has recently adopted a growth rate target for nominal GNP. See Hafer et al. (1990), Feldstein and Stock (1993) and McCallum (1993) for a discussion of the merits of growth rate vs. level targeting. 5 Formally, sgn(SAB/c~a 2) = s g n [ a 0 - (1 - Otl)AY*]. This equation indicates that if the average drift in nominal income is greater than the product of the target growth rate and one minus the persistence of nominal income growth, then the steady-state growth rate of the monetary base is positively related to changes in the impact multiplier.
465
Monetary Base Rules: The Currency Problem
2.8% a n n u a l rate in the steady state to achieve the target G N P growth rate. 6 This m e a n s that if n o m i n a l G N P growth evolved according to this simple r e d u c e d - f o r m model, the m o n e t a r y base w o u l d have to decline at a 2.8% a n n u a l rate to hit the desired 3% target n o m i n a l G N P growth rate. 7 T h e steady-state analysis indicates that in o r d e r to achieve 3% n o m i n a l i n c o m e growth using a m o n e t a r y base rule, the m o n e t a r y base m u s t shrink over time. But what h a p p e n s if c u r r e n c y d e m a n d is growing along with n o m i n a l i n c o m e ? W e investigated that q u e s t i o n by s i m u l a t i n g m o n e t a r y base growth, G N P growth a n d c u r r e n c y growth within the f r a m e w o r k of M c C a l l u m ' s (1988) policy rule to focus o n the effects which currency growth may have o n the i m p l e m e n t a t i o n of the base rule.
III. N o m i n a l G N P Simulations T h e s i m u l a t e d p a t h for n o m i n a l G N P growth g e n e r a t e d from e q u a t i o n (2) using M c C a l l u m ' s (1988) m o n e t a r y base rule is p r e s e n t e d in this section. M o n e t a r y base growth is dictated by a rule which can be w r i t t e n as: A B t = 0.00739 - ( 1 / 1 6 ) [ Y t i - Yt-17 -
Bt-1 + Bt
17] + A(AYt*-I - A Y t - I ) . (4)
T h e first t e r m o n the r i g h t - h a n d side of e q u a t i o n (4) is simply the quarterly value of a 3% a n n u a l i z e d growth in G N P . This value was again c h o s e n b e c a u s e it would g e n e r a t e zero inflation, o n average, across the sample period. T h e second t e r m is a four-year m o v i n g average of base velocity growth. I n this model, a p e r m a n e n t increase in base velocity growth results in slower m o n e t a r y base growth. T h e t e r m A is a f e e d b a c k p a r a m e t e r , w h e r e 0 _< A _< 1. This stipulates that m o n e t a r y b a s e growth r e s p o n d s to a 1-percentage p o i n t deviation from last p e r i o d ' s i n c o m e growth rate target by A-percentage points.
6 McCallum (1987) found similar parameter values for his simple reduced-form model. The implication, as he noted, is that base would necessarily decline to achieve a steady-state path in which nominal GNP increases at a 3% annual rate. For the quarterly model, one would use equation (2), substituting [1n(1.03)/4)] = 0.00739 or the quarterly target value of Ay*. The calculation reported here was obtained by substituting the parameter values from equation (1) into equation (2). We then annualized AB by reversing the process used to find the quarterly value of target nominal GNP growth. The parameter values in equation (1) imply that steady-state velocity growth is negatively related to movements in steady-state base growth. To see this, substitute AV + AB, where V denotes (the log of) base velocity, for Ay in equation (2) and solve for AV. For velocity growth to be policy invariant, the following condition must hold: a I + t~2 = 1. There are an infinite number of solutions to this expression. In addition to the results reported in this paper, we looked at several different combinations which yielded policy invariant values for velocity growth. Specifically,we tried (1) a 1 = a 2 = 0.5; (2) a 1 = 0.73; o/2 0.27; (3) a = 0.64, o/2 0.36; (4) a 1 = 0.01, c~2 = 0.09, (5) a I = 0.99, ~2 = 0.01. We found the same qualitative results for each case as those reported in the paper. Note also that as ~1 ---,0.0, the steady-state value of base growth increases algebraically. The results are available from the authors upon request. 7 In an earlier version of this paper [Haler et al. (1990)], we separated the simulation and estimation period, using data from the 1954-1969 period to estimate the nominal GNP growth equation. Judd and Motley (1993) interpreted our declining monetary base finding as the product of inconsistency between average output growth in the period 1954-1985. The fact that steady-state monetary base declines when the nominal GNP equation is estimated over the period 1954-1991 would seem to refute the Judd and Motley claim. Indeed, the steady-state characterization in the text makes clear the factors contributing to monetary base decline. =
=
466
R.W. Hafer et al. Equation (2), together with base rule (4), form a recursive system. The value for base growth is determined for period t, fed into the nominal GNP growth rate equation (2) in period t + 1, which then is fed back into the base rule (4), and so on. Shocks to the system are generated using the realized error term from equation (2) 8. Formally, kt = AYt - A Y t P , where AYtP is the predicted value of nominal GNP growth generated by equation (2). The simulated value of nominal GNP growth, AY,s, is thus the value of GNP growth generated with the parameter estimates in equation (2) plus kr Simulated values of nominal GNP growth were generated for the period 1959:1-1991!3. The summary statistics measuring the rule's ability to hit the target growth rate for nominal GNP, assumed to be 3%, indicate that it does quite well in reducing the volatility of GNP growth relative to actual historical values. 9 McCallum's (1988) base rule produces a root mean squared deviation (RMSD) around the target GNP growth path of 3.87%. For purposes of comparison, the RMSD generated using the actual path of GNP growth is 6.50%. Equally suggestive of the rule's ability to lessen income growth volatility is the mean deviation (MD) of 0.12%, which is not statistically different from zero.
IV. The Role of Currency in a Base Rule The issue taken up in this section is to determine how monetary base generated by McCallum's (1988) rule is distributed between currency and reserves. In addressing this issue, we assume that the Federal Reserve is willing to supply whatever currency is demanded. To estimate currency demand growth, a standard currency demand function is estimated. In our model, currency growth (AC) is specified as a function of lagged income growth (AYt 1), the lagged change in the nominal interest rate ( A i t_ 1) and lagged values of currency growth. The nominal interest rate is measured as the quarterly average of the three-month Treasury bill rate. Our purpose is not to investigate all possible currency demand specifications. Rather, this specification is sufficiently general to demonstrate the evolution of currency under the base rule. The estimates for our currency demand equation, using data for the period 1954:1-1991:3, are (standard errors in parentheses): A C t = 0.001 +0.070AYt l - 0 . 0 0 0 2 A i t _ j +0.580AC t 1
(0.001) (0.035)
(0.0004)
(0.081)
+ 0.242ACt- 2 q- 0.037ACt 3 (0.105) (0.094) Adj-R 2 = 0.76
S E E = 0.004
(5) B G = 0.65.
8 This procedure followsMcCallum's (1988) methodologyfor including non-monetaryshocks. 9 To conserve on space, all results reported here are based on a h value of 0.25. This value was found by McCallum (1987, 1988, 1993) to minimize the deviations from the target growth rate. Using other values between zero and one did not significantlyalter the results reported below. These results are available upon request.
Monetary Base Rules: The Currency Problem
467
T h e coefficient e s t i m a t e s indicate that t h e r e is a non-trivial a m o u n t o f p e r s i s t e n c e in c u r r e n c y growth: the s u m o f t h e coefficients o n lagged c u r r e n c y g r o w t h equal roughly 0.85. This m e a n s that innovations, such as slowing i n c o m e growth, a r e likely to have long-lived effects in o u r simulations. T h e results also show that l a g g e d i n c o m e exerts a statistically significant positive effect o n c u r r e n c y d e m a n d . This result is c o n s i s t e n t with the i d e a that c h a n g e s in i n c o m e influence currency d e m a n d decisions. W e d i d n o t find, however, a significant effect f r o m n o m i n a l i n t e r e s t rates. E v e n so, n o m i n a l i n t e r e s t r a t e s have b e e n r e t a i n e d for the sake o f c o m p l e t e n e s s . 1° U s i n g this c u r r e n c y d e m a n d e q u a t i o n , s i m u l a t e d values o f c u r r e n c y w e r e g e n e r a t e d using s i m u l a t e d n o m i n a l G N P growth. T o d o this, two simplifying a s s u m p t i o n s w e r e necessary: First, shocks to c u r r e n c y d e m a n d w e r e o m i t t e d . S e c o n d , b e c a u s e the m o d e l is n o t rich e n o u g h to d e t e r m i n e t h e p a t h o f t h e n o m i n a l i n t e r e s t rate, we u s e d a c t u a l values in t h e simulations. 11 T h e result o f this s i m u l a t i o n exercise is i l l u s t r a t e d b e s t by c o m p a r i n g t h e p a t h of t h e m o n e t a r y b a s e a n d s i m u l a t e d currency. This c o m p a r i s o n is d o n e in F i g u r e 1, w h e r e plots o f the m o n e t a r y b a s e g e n e r a t e d by t h e M c C a l l u m (1988) rule a n d s i m u l a t e d c u r r e n c y a r e shown. T h e m o s t striking f e a t u r e in F i g u r e 1 is that c u r r e n c y begins to exceed the q u a n t i t y o f m o n e t a r y b a s e d i c t a t e d by the rule a r o u n d t h e mid-1970s. This m e a n s t h a t total r e s e r v e s - - b a s e less c u r r e n c y - - w o u l d have b e e n negative a f t e r t h e c r o s s - o v e r point. In fact, by t h e e n d o f the s i m u l a t i o n p e r i o d , t h e v a l u e o f t h e m o n e t a r y b a s e was $31.2 billion a n d c u r r e n c y was $127.2 billion. This result w o u l d r e q u i r e total reserves to b e $ - 96.9 billion! W e d o n o t b e l i e v e t h a t n e g a t i v e t o t a l r e s e r v e s r e p r e s e n t s a viable e q u i l i b r i u m o u t c o m e , b u t this result p o i n t s to o n e very i m p o r t a n t p r o b l e m which m a n y m o n e t a r y b a s e rule a d v o c a t e s have c h o s e n to ignore. F o r a given reserve r e q u i r e m e n t ratio, falling r e s e r v e s relative to c u r r e n c y m e a n s that t h e q u a n t i t y o f d e p o s i t s relative to c u r r e n c y also m u s t fall. A r e d u c t i o n in d e p o s i t s w o u l d r e q u i r e the b a n k i n g s e c t o r to contract, b u t e c o n o m i c c h a n g e s necessary to m i t i g a t e the b a n k i n g s e c t o r ' s c o n t r a c t i o n u n d e r a b a s e rule w o u l d likely arise. F o r e x a m p l e , b a n k s likely w o u l d raise i n t e r e s t r a t e s on d e p o s i t s in an a t t e m p t to shift t h e c o m p o s i t i o n o f the existing m o n e t a r y b a s e t o w a r d reserves a n d stop the h e m o r r h a g i n g b a n k sector. A s the b a n k i n g s e c t o r r e a c t e d to such changes, it is quite likely t h a t the r e d u c e d - f o r m
l0 We experimented with alternative currency specifications. One equation decomposed the lagged term on nominal income into real income growth and inflation, combined with a lagged ex post real interest rate and the lagged currency terms. Another specification related real currency demand to current real income, the current real interest rate and one lagged currency term. Although the quantitative outcome of the simulation exercises varied somewhat between these currency specifications, the qualitative results presented in this paper were not materially affected by these changes. For this reason, we report only the results based on the currency equations shown in the text. The results for the alternative equations and simulation results are available on request. Cagan (1982) and Sprenkle (1993) provide insights into currency demand estimation. ~1The nominal interest rate is likely to look very different in the simulations. This is because inflation would not have risen to the extent observed in the late 1970s and early 1980s. A more reasonable assumption, without solving for the nominal interest rate path, is to assume that the real interest rate would remain unchanged. Thus, a currency model which uses real interest rates as an explanatory variable was also estimated. The results obtained in the simulations were not materially affected by this change. These results are available on request. We also performed simulations using a currency demand equation with no intercept, as the constant reported above was not significantly different from zero. This modification also did not change the major conclusions reported below.
69
70
71
72
73
74
75
76
77
Figure 1. Simulated paths for monetary base and currency.
30
40
50
60
70
80
90
lO0
II0
120
130
Billion$
78
79
•••°°
..o
80
81
oooOO°°°
82
•e
83
84
°s
85
86
87
88
89
90
Monetary Base
Curreaey
,o'"•'"""
91
7z
~.
469
Monetary Base Rules: The Currency Problem
parameters would be very different from those in the equations estimated above. This potential instability in the reduced-form model raises doubt about the reliability of the simulation results from this and previous studies of base rules. Regardless, using the same methodology as base rule advocates have proposed, our simulation exercises for currency suggest that, at a minimum, some startlingly different behavior in the banking sector likely would unfold. At least within the historical context of the simulation exercise, the distribution of the base between currency and reserves must be more fully considered in analyzing the usefulness of adopting base rules for monetary policy.
V. A Total Reserve Rule The problems associated with currency growth in a monetary base targeting regime might be mitigated if the Federal Reserve supplied currency elastically to accommodate demand, but focused policy actions on hitting a total reserves target instead of a base target. To examine this-alternative rule, we estimated a nominal GNP growth equation identical to equation (1) in all respects except that total reserve growth was substituted for monetary base growth. The full-sample regression results after this substitution was made are (standard errors are in parentheses): AYt = 0.01 + 0.328AYt_l + 0.206ATRt 1 (0.002) (0.075) Adj-R 2 = 0.17
(6)
(0.062)
SEE = 0.010
BG = 1.24.
Compared with the monetary base version, the adjusted R 2 is only slightly lower when total reserves are used instead of the base. Even though total reserves have a smaller point impact than base (0.260 vs. 0.360), the coefficient remains statistically significant. As before, the results from the battery of stability tests indicate one cannot reject the hypothesis that the parameters are constant over time. 12 Substituting total reserves for the monetary base in the rule, nominal GNP growth and the path for total reserves were simulated. The summary statistics for the deviations from target nominal GNP growth under the total reserves rule indicate that the MD and RMSD are slightly larger when compared with the monetary base rule. For example, the MD, using a reserves rule, is - 0 . 2 8 compared with 0.12 using a base rule. The RMSD increases to 4.00 using total reserves compared with 3.87 when the base is used. Setting the target nominal GNP growth rate at 3%, the steady state estimates indicate that total reserves would have to decline at a 9.3% annual rate according to the estimates in equation (6). This means that the Federal Reserve would have to substantially contract the quantity of total reserves in order to achieve zero average inflation. Assuming a constant reserve requirement ratio, this contraction
~2 T h e t e s t statistics f r o m t h e s t a b i l i t y t e s t s a r e as follows: QLR = 2.647; M e a n C h o w = 0.980; A - P e x p W = 0.561; P - K m a x = 0.937; P - K m e a n sq = 0.321. T h e t e s t statistics d i d n o t r e j e c t t h e null of parameter
constancy.
70
4 . . . , . °
71
72
73
i
74
•
i
75
iq
"'76.
i
77
78
i
79
Figure 2. Simulated total reserve paths for the base and reserve rules.
40
-30
-20
-I0
IO
20
69
Billion $
30
80
81
82
83
84
85
86
87
88
i
Base Rule
89
90
Total Reserves Rule
i
91
i
Monetary Base Rules: The Currency Problem
471
again would force deposits in the banking system to shrink as fewer reserves would be available to support deposits. Figure 2 provides the time paths for total reserves, both with the base rule and the total reserves rule. The figure shows that total reserves contract sharply even under the total reserves rule. Thus, even using total reserves as the policy instrument, the non-inflationary path for G N P dictates that total reserves, even though they did not turn negative in the simulations, must decline sharply in a manner similar to that found earlier for the monetary base.
VI. Summary Much research has focused on the ability of monetary base rules to achieve predetermined income growth targets. Within this context, we have addressed a different, but equally important issue" What if the Fed operated under the constraint of a monetary base rule and simultaneously maintained an elastic supply of currency? Using the monetary base rule popularized by McCallum (1988), we find that if the Federal Reserve continued to supply currency elastically and manipulated the growth of the monetary base to achieve a non-inflationary 3% rate of nominal G N P growth, total reserves would decline dramatically, even turning negative. This finding seriously questions assertions that such a monetary base rule is operational. The implication from our simulation exercise is that the banking system would shrink as reserves and deposits decline relative to currency holdings. We have also demonstrated that a total reserves rule does not totally obviate this dilemma. A total reserves rule generates a path for shrinking total reserves which mimics the problems similar to those encountered with the monetary base rules. Proponents of monetary base rules rely extensively on evidence that such rules achieve price stability and lessen the volatility of income growth. The findings in this p a p e r suggest that such gains may be offset by problems in other areas, such as a shrinking banking system. Earlier studies have ignored the distinction between reserves and currency development, and simply treated the two as perfect substitutes. By explicitly considering the role of currency, this p a p e r shows that total reserves and, therefore, the size of the banking system, would be substantially affected by following a non-inflation monetary base rule.
The authors with to thank Phillip Cagan, Thomas Cosimano, Milton Friedman, Evan Koenig, Bennett McCallum, Allan Meltzer, Anna Schwartz, Richard Sheehan, David Small, James Stock, session participants at meetings of the Allied Social Sciences Association, the Western Economic Association, the Southern Economic Association, and anonymous referees for helpful comments on earlier versions of this paper. Any remaining errors are our responsibility. The views expressed herein do not necessarily represent those of the Federal Reserve Bank of Dallas nor the Board of Governors of the Federal Reserve System.
References Andrews, D. K. July 1993. Tests for parameter instability and structural change with unknown change point. Econometrica 61:821-56. Cagan, P. Nov. 1982. The choice among monetary aggregates as targets and guides for monetary policy. Journal of Money, Credit, and Banking 14(4):661-86.
472
R . W . Haler et al. Dueker, M. J. M a y / J u n e 1993. Can nominal GDP targeting rules stabilize the economy? Federal Reserve Bank of St. Louis. Review 15-29. Feldstein, M. and Stock, J. H. March 1993. The use of monetary aggregates to target nominal GDP. NBER Working Paper No. 4304. Friedman, B. M. 1988. Conducting monetary policy by controlling currency plus noise: A comment. Carnegie-Rochester Conference Series on Public Policy 29:205-12. Haler, R. W., Haslag, J. H. and Hein, S. E. 1990. Evaluating monetary base targeting rules. Federal Reserve Bank of Dallas Working Paper No. 9008. Judd, J. P. and Motley, B. 1992. Nominal feedback rules for monetary policy: Alternative operating procedures and targets. Unpublished manuscript. McCallum, B. T. Sept./Oct. 1987. The case for rules in the conduct of monetary policy: A concrete example. Federal Reserve Bank of Richmond. Economic Review 10-18. McCallum, B. T. 1988. Robustness properties of a rule for monetary policy. Carnegie-Rochester Conference Series on Public Policy 29:173-203. McCallum, B. T. Sept. 1993. Specification and analysis of a monetary policy rule for Japan. NBER Working Paper No. 4449. Meltzer, A. H. 1984. Overview. In Price Stability and Public Policy. A symposium sponsored by the Federal Reserve Bank of Kansas City, pp. 209-22. Meltzer, A. H. Jan. 1987. Limits of short-run stabilization policy. Economic Inquiry 1-14. Ploberger, W. and Kramer, W. Sept. 1990. The local power of the CUSUM and CUSUM of Squares Tests. Econometric Theory 6:335-47. Sprenkle, C. M. Fall 1993. The case of the missing currency. Journal of Economic Perspectives 7(4):175-84.