Evaluating the Performance of Monetary Base and M2 Rules

III. Evaluating the Performance of Monetary Base and M2 Rules

Recent research on rules which target nominal income has examined likely macroeco- nomic outcomes in cases where targets are specified in terms of either levels or growth rates. McCallum 1987, 1988, and 1990 defined the ultimate goal in terms of a constant, long-run, price level. But, McCallum 1993 changed the ultimate goal to zero inflation. Others, such as Fair and Howrey 1994, have specified the ultimate goal as a constant inflation rate roughly equal to a recent historical average. Specification of the ultimate goal depends on several factors, including the relative benefits of a constant price level or a stable inflation rate and the costs of disinflation. 9 Rules examined here specify the nominal GDP target in levels, on the assumption that price stability is preferable to inflation stability. In order to assess the relative performance of the monetary base and M2, these policy instruments were used in variations of McCallum’s Rule below to simulate growth paths of nominal GDP in three macro models. DRM t 5 0.00739 2 ~116~X t21 2 X t217 2 M t21 1 M t217 1 l~X t21 2 X t21 . 1 where M is the log of the respective policy instrument e.g., M2; 0.00739 is a 3 annual growth rate expressed in quarterly logarithmic units; X is the log of nominal GDP; X is McCallum’s non-inflationary target path value of nominal GDP i.e., a 3 growth path; l is a partial adjustment coefficient, 10 and t indexes quarters. The rule-specified change in the money supply is DRM, and in cases where there is no money control error, DRM 5 DM, the value of money growth that enters into the models of GDP determination. The second term on the right side of equation 1 is a four-year moving average growth rate of monetary velocity. The third term is a feedback adjustment that is activated when values of nominal GDP deviate from the non-inflationary target path. Although parsimonious, the macroeconomic models utilized represent different, but not improbable, relationships between money and income. Although the models are open to econometric criticism, this doesn’t negate the utility of these simple models in the GDP simulations. As McCallum 1988 noted, model estimation produces parameter values which: 1 represent alternative theories of economic behavior, and 2 are consistent with actual U.S. economic data generated during the sample. The residuals computed in the course of model estimation were recycled in the GDP simulations as estimates of the actual shocks to the respective dependent variables being simulated. Different macroeconomic models were utilized because a lack of consensus regarding the true economic model requires that conclusions regarding rules should be robust for different models of nominal GDP determination. Quarterly data were used and counter- factual simulations were conducted over the sample period 1964:Q1–1995:Q4. 11 9 As Thornton 1996 illustrated, the outcome of cost-benefit comparisons is sensitive to many factors, including: the choice of economic model utilized; the value of the discount rate used in present value computations; the time horizon utilized i.e., finite or infinite; the choice of variable used as the measure of economic welfare, etc. Thornton found that while price stability is not clearly preferable to other potential inflation rates, arguments favoring a positive inflation rate rely on controversial and restrictive assumptions. An examination of the literature regarding the optimal inflation rate is beyond the scope of this paper. For a summary of some other key arguments see Aiyagari 1990 and Marty and Thornton 1995. 10 McCallum recommends using l 5 0.25. Unreported experiments with the policy instruments and macroeconomic models utilized here yield and the same recommendation. 11 All data utilized in this paper were downloaded in 1996 from Citibase data tapes. Suitable Policy Instruments for Monetary Rules 383 Baseline performance measures were computed for each rule under an initial assump- tion of no money control error. By initially assuming that M2 can be controlled precisely, it is possible to assess how sensitive M2 rule performance is to the degree of money control error. The ability of a policy instrument to promote long-run price stability was measured as the root mean square error RMSE of the simulated nominal GDP time path from the targeted, non-inflationary, 3 growth path. Policy instruments which produce smaller RMSEs presumably will deliver a higher degree of price stability. The Keynesian model used in this paper is similar to one used in earlier studies [e.g., McCallum 1988 and 1990; Judd and Motley 1991]. The primary difference is that contemporaneous values of the respective policy instruments do not enter into the aggregate demand equation. 12 Equation 2 is an aggregate demand equation, equation 3 is a wage equation and equation 4 models price adjustments. Augmented Dickey-Fuller tests failed to reject the hypothesis that the price level, real government spending and all measures of the real money stock are integrated of order one. Hypothesis tests suggest nominal wages and real GDP are stationary around a linear time trend. Results for real GDP seem to be sensitive to the sample period selected; however, as real GDP and nominal wages appear I0 over this sample period, co-integrating vectors presumably do not exist for equations 2, 3, and 4. Dy t 5 f 1 1 f 2 Dy t21 1 f 3 Dm t21 1 f 4 DG t 1 f 5 DG t21 1 « 2t ; 2 DW t 5 a 1 1 a 2 ~ y t 2 y9 t 1 a 3 ~ y t21 2 y9 t21 1 a 4 DP t e 1 « 3t ; 3 DP t 5 g 1 1 g 2 DW t 1 g 3 DP t21 1 « 4t , 4 where m is the real value of the respective policy instrument; G is total real government purchases 13 ; y t 2 y9 t is the deviation of real GDP from a fitted trend presumably equal to the natural rate; DP e is expected inflation computed as the average of actual inflation during the prior eight quarters, and W is the nominal, average, hourly earnings of non-agricultural, production, or non-supervisory workers. The system of equations was estimated three times, substituting both measures of the monetary base and M2, respectively, for m. 14 Each version of equation 2, along with equations 3 and 4, was used in combination with the corresponding rule to generate nominal GDP growth paths over the sample period 1964:Q1–1995:Q4. The second model utilized is a variation of the McCallum 1988 simple atheoretic model 15 which incorporates the first differences of nominal GDP and the respective policy 12 The economic models employed here satisfy conditions of admissibility stated by Rasche 1995. Rasche criticized the use of VAR and VECM models in the conduct of counterfactual analysis of policy rules. He argued that it is not always appropriate to first estimate the equations in the system, and then, in GDP simulations, substitute the policy rule for the equation which includes the policy instrument as the dependent variable. Rasche demonstrated that if the policy instrument enters contemporaneously, as an independent variable, into any of the other equations in a simultaneous system, the equations specifying the behavior of the non-policy, endogenous variables are not independent of the omitted equation. A system of equations is considered admissible for counterfactual analysis if the contemporaneous value of the policy instrument appears only once in the system—as the dependent variable in an equation specifying its behavior. 13 As in McCallum 1988, historical values of government purchases were used in the simulations because government spending is assumed to be exogenous. 14 Regression results from the least squares estimation of equations 2–4 are available upon request, as are the regression and simulation results which follow. 15 McCallum’s model is: DX t 5 u o 1 u 1 DX t21 1 u 2 DM t21 1 « to , where X is nominal GDP; M is the nominal value of the respective policy instrument, and « to , is the error term. 384 S. R. Thornton instrument, utilizing four lags of each variable. Augmented Dickey-Fuller tests failed to reject the hypothesis that nominal GDP and all nominal values of the policy instruments, except the Federal Reserve Board monetary base, are integrated of order one. Hypothesis tests suggest the Federal Reserve Board monetary base may be stationary around a linear time trend. Engle-Granger 1987 tests were used in an attempt to identify co-integrating vectors for the models utilizing the St. Louis monetary base and M2. In order to counter the sensitivity of the Engle-Granger approach to the choice of dependent variable in the co-integrating equation, each policy instrument, respectively, and nominal GDP, were considered as dependent variables in an equation utilized to generate a potential co- integrating vector. However, no co-integrating vectors were identified. In the case of the St. Louis monetary base, tests for a co-integrating vector also included the ratio of currency to checkable deposits as recommended by Dickey et al. 1994. The income- velocities of M2 and the St. Louis monetary base were also examined as potential co-integrating vectors. However, augmented Dickey-Fuller tests suggest that over the sample period 1964:Q1–1995:Q4, none of these measures of velocity are I0. 16 As Engle and Yoo 1987 demonstrated, when the economic variables in a system of equations appear to be I1, it is suboptimal to specify a VAR forecasting model in first differences—as is the case in equations 5 and 6 for both M2 and the St. Louis monetary base. Engle and Yoo 1987 demonstrated that in such circumstances, a VECM forecasts more accurately in multi-step forecast horizons. Since a co-integrating vector could not be identified for these systems, a VAR was estimated. Consequently, the multi-step GDP forecasts generated as part of the counterfactual simulations utilizing equation 5, and the corresponding monetary rule, will be less accurate than they would be if a VECM could have been utilized. Results of counterfactual GDP simulations utilizing M2 and the St. Louis monetary base thus provide a lower bounds on potential rule performance in this type of economic model. The two-variable VAR is represented by equations 5 and 6: DX t 5 b 1 O b j DX t2j 1 O a j DM t2j 1 « t5 ; 5 DM t 5 v 1 O v j DX t2j 1 O C j DM t2j 1 « t6 , 6 where j 5 1, 2, 3, 4. The third model utilized is a four-variable VAR which includes the first difference of: real GDP, the GDP price deflator, the three-month Treasury bill rate, and the respective policy instrument, along with four lags of each variable. Because augmented Dickey- Fuller tests suggest that real GDP is stationary around a linear time trend, these systems of equations were estimated as VARs, rather than vector error correction models. All variables, except the three-month Treasury bill rate, are in logarithms. Counterfactual GDP simulations were conducted with three different economic models and three different policy instruments. In each simulation, the root mean square error of simulated nominal GDP from the targeted time path was computed. These RMSEs, along with RMSEs computed using historical data during the sample, appear in Table 1. During the sample, the St. Louis monetary base and M2 always delivered greater levels of long-run price stability than actual discretionary monetary policy. Arguably, a com- parison of RMSEs simulated by rules to the RMSE of actual monetary policy from the 3 16 The non-stationarity of M2 velocity is sensitive to the sample period chosen. Suitable Policy Instruments for Monetary Rules 385 target path biases the analysis in favor of the monetary rules. This occurs because historical monetary policy doesn’t target a stable price level. An alternative is to compare the relative ability of rules and discretionary monetary policy to reduce the variability of nominal GDP around a constant trend. 17 For rules, the constant trend is the targeted 3 GDP growth path. For discretionary policy, the constant trend utilized is the historical, 7.6 average rate of nominal GDP growth over the sample period. Based on this comparison, the M2 rule still substantially reduced the variability of GDP about a fixed trend. The performance of the monetary base rules relative to historical monetary policy was model dependent. Historical policy outperformed both monetary base rules in the four-variable VAR, but not in the Keynesian and two-variable VAR models. The St. Louis monetary base rule always outperformed the Federal Reserve Board monetary base rule. The source of this differential performance is probably due to unreported model estimation results which illustrate a stronger relationship between the St. Louis base and GDP than between the Board base and GDP. However, the performance of both monetary base rules deteriorated substantially in an economic model which also incorporated an interest rate. The relatively inferior perfor- mance of the monetary base and superior performance of M2 in the four-variable VAR model is not surprising. Dotsey and Otrok 1994 and Feldstein and Stock 1993 found that M2 is a significant predictor of nominal GDP— even when interest rates are included in the model. But Feldstein and Stock 1993 found that the predictive content of the St. Louis monetary base is eliminated, when interest rates are included in the model of nominal GDP determination. Although the base may have some predictive content for nominal GDP, this relationship is unstable. Consequently, Feldstein and Stock concluded that when interest rates are included in a model of GDP determination, the more stable interest rate relationship overwhelms the weaker relationship between the monetary base and GDP, causing the base to appear insignificant in models which include interest rates. The M2 rule performed well in all three economic models. The more stable relationship between M2 and GDP was not overwhelmed by the inclusion of interest rates in the model. Figures 1 and 2 illustrate the contrast between M2 and monetary base rules. In the 17 It would be inappropriate to make a comparison of rules and discretionary policy based on simulations using rules which target a nominal GDP growth path consistent with historical levels of inflation. Recall, one purpose of this study is to analyze the performance of rules which target a stable price level—not rules which target a stable inflation rate. Table 1. GDP RMSEs: Rules with No Money Control Error M2 SLMB FRBMB Keynesian model l 5 0.25; 4 yr MA velocity 0.03796 0.03589 0.05375 Two-Variable model l 5 0.25; 4 yr MA velocity 0.02650 0.02638 0.04025 Four-variable VAR l 5 0.25; 4 yr MA velocity 0.02898 0.19052 explosive Historial GDP RMSE: From a 3 growth path: 0.99288 From a 7.6 a growth path: 0.15072 a 7.6 is the historial trend rate of nominal GDP growth from 1964:Q1–1995:Q4. 386 S. R. Thornton former case, simulated GDP closely tracks the target path. M2 appears to be a more robust policy instrument—in the case of no money control error. If the Fed were to adopt an adaptive rule or just utilize a rule to provide added information in the formulation of discretionary monetary policy, it initially appears that because of the more stable rela- tionship between M2 and GDP, an M2 rule would be more suitable for targeting a stable price level. In arriving at this conclusion, it is essential to note that GDP simulations with these constant-coefficient models did not assume stable velocity growth over the sample period. On the contrary, historical variability in a policy instrument’s velocity growth rate affected Figure 1. GDP growth path: M2 rule with no money control error in a four-variable VAR. Figure 2. GDP growth path: St. Louis monetary base rule with no money control error in a four-variable VAR. Suitable Policy Instruments for Monetary Rules 387 the GDP simulations through the size of the observations in the residual vectors i.e., the GDP shocks. This point is particularly important given the recent debate about the reliability of M2 as a monetary policy indicator. 18 During the 1980s, the Fed increasingly utilized M2 as a policy indicator because of its historically stable, long-run relationship with nominal income. Although the long-run average of M2 velocity had been trendless for decades, between 1990 and 1994, M2 velocity exhibited a seemingly transient change in its growth rate. 19 The instability in velocity apparently was related to an expansion of financial assets which serve as substitutes for M2. In 1993, because of the instability in M2 velocity, Alan Greenspan announced the Fed was de-emphasizing M2 as a policy indicator. Yet, in McCallum’s Rule, M2 performed well between 1990 and 1995, keeping nominal GDP close to the target. 20 Why? As M2 velocity trended upwards, the GDP shocks in the macro models increased in size which tended to push simulated GDP away from the GDP target. But, in response, the four-year moving average velocity growth rate in McCallum’s rule gradually rose. This reduced the growth rate of M2 which then reduced deviations of nominal GDP from the target path. The feedback term in equation 1 provides an even more immediate monetary policy response to the changing velocity growth rate. Greenspan’s 1993 announcement highlights a contrast between discretionary monetary policy, as recently implemented by the Fed, and McCallum’s Rule. The responses of the second and third terms on the right side of equation 1 make it unnecessary for M2 velocity to exhibit a pre-1990s level of stability, for the rule to successfully keep GDP close to the target. Although there presumably is a degree of velocity instability which would eradicate the success of the M2 rule, the most recent period of instability in M2 velocity did not exceed this critical threshold. As Section III demonstrates for M2, design features added purposefully by McCallum to make the rule fully operational adjust the growth rate of the policy instrument automatically to accommodate changes in velocity resulting from financial innovations, changes in the business cycle, or other sources. In assessing the M2 rule, it is important to ask whether or not the favorable perfor- mance of M2, relative to the monetary base rule and discretionary monetary policy, persists in the face of money control errors. The performance of the M2 rule was reassessed assuming that money control error causes the actual growth rate of M2 to deviate from that specified by the rule. A likely explanation of money control error is that 18 Carlson and Keen 1996 suggested utilizing MZM as an intermediate, target or indicator variable in the formulation of monetary policy because MZM exhibited a stable demand function during the 1970s, 1980s and 1990s. MZM is Money with Zero Maturity and equals M2 minus small time deposits plus institution-only money market mutual funds. Unreported simulation results with an MZM version of McCallum’s rule indicate that MZM outperformed both measures of the monetary base only in the four-variable VAR model. But, MZM was outperformed by M2 in all three models and in the presence of money control error. Although MZM appears to be a stable function of its opportunity cost and real income, MZM demand is highly interest elastic and consequently, over time, MZM velocity varies over a much wider range than M2 velocity. Thus, the moving average term in McCallum’s rule more accurately forecasts current quarter values of the growth rate in M2 velocity—relative to its forecasts of MZM velocity growth. Therefore, the M2 rule delivers greater levels of price stability than the MZM rule. McCallum wanted his rule to be publicly observable. So, he specified velocity growth as a function of past changes in velocity, rather than movements in interest rates and real income. This design feature makes M2 preferable to MZM as a policy instrument. 19 See Carlson and Keen 1995, Petersen 1995, and Mehra 1997. 20 Figure 1 is a better guide to the performance of the M2 rule between 1990 and 1995 than the RMSEs in Tables 1–3. In the latter case, poor rule performance in the 1990s could be somewhat masked by excellent performance earlier in the sample. However, in Figure 1 large deviations of simulated GDP from the target path, caused by velocity instability, would be visible. 388 S. R. Thornton the Fed generally prefers to attain the rule-specified, quarterly M2 target, but due to factors outside its control, this is sometimes impossible. When money control error is present, the value of DM t that enters into equations of GDP determination is defined as: DM t 5 DRM t 1 MCE t 7 where MCE is the money control error. 21 To understand the operation of equation 7, for simplicity, assume that in time period t 2 1 nominal GDP does not deviate from the target. Thus, in equation 1, M 5 M2 and X t21 5 X t21 . Also assume that in time period t, the four-year moving average growth rate of M2 velocity is 0. Then, in time period t, the rule-determined, target growth rate of M2 is 0.00739 — or 3 in quarterly logarithmic units. Suppose in time t, factors outside Fed control cause M2 growth to be below target. If M2 growth, measured in logarithms, is below target by 0.00249, MCE t 5 20.00249. Using equation 7, we add 0.00739 to 20.00249. So, in time t, the growth rate in M2 which enters into the models of GDP determination is 0.00490 —about 2 in quarterly logarithmic units. In order to realistically simulate GDP time paths, it is necessary to incorporate a likely measure of the money control error over the sample period. This requires specifying a process of monetary control for M2. Imprecise control over M2 forces the Fed to forecast how its policy actions e.g., changes in the Federal Funds rate will affect M2. Deucker’s 1995 model of monetary control is utilized to generate money control errors—assuming the Fed adjusts the federal funds rate to control M2. D ln M t ~1 1 FFR t 5 a 1 a 1 DTB3 t21 1 a 2 DTB10 t21 1 a 3 D ln M t21 1 a 4 D ln y t21 1 « 8t . 8 The change in the log of the money supply i.e., M2, given the federal funds rate FFR, is specified as a function of: a constant; the lagged change in the three-month Treasury bill rate TB3; the lagged change in the ten-year Treasury bond rate TB10; the lagged change in the log of M2 M, and the lagged change in the log of real GDP y. The initial vector of money control errors is generated by estimating equation 8 over the time period 1959:Q4 –1963:Q4 and then forecasting the subsequent quarter value of the dependent variable. The forecast is subtracted from the actual value of the dependent variable to generate the forecast error. The model is re-estimated, forecasts are generated, and forecast errors are computed using a rolling horizon approach until a vector of money control errors is generated for M2 over the sample period 1964:Q1–1995:Q4. The rolling horizon approach was used to produce a time-varying coefficient model, which is desirable because the relationship between money growth and the federal funds rate varies in response to changes in the level of inflation, the economy’s position in the business cycle, etc. The M2, money control error vector derived this way had a mean of 20.00121 in quarterly logarithmic units i.e., 20.5 and a standard deviation of 0.0134 i.e., 5.4. 22 A random number generator was used to create a new money control error 21 Although the specification of equation 7 indicates that the money control errors are added to the rule-determined money growth rate, when the mean money control error is ,0.0, the actual change in money growth tends to be below that specified by the rule. 22 If one takes the midpoint of the M2 targets set since the mid-1970s, and compares actual growth to targeted growth, it is clear that the mean error is not zero. However, the Fed was not attempting to solely control M2 during this time. So, announced M2 targets are not an adequate guide as to what is possible regarding the mean error. Suitable Policy Instruments for Monetary Rules 389 vector with the same statistical distribution as the forecast errors. This simulated error vector was recycled as the money control error vector in equation 7. 23 Because the Fed can make changes in reserve requirements e.g., place a uniform reserve requirement on all depository components of M2 and financial market regulations that would enhance its monetary control, this study doesn’t take the size of the money control error or its correlations with GDP shocks as given. More precisely, the question posed here is: given GDP shocks of historical magnitudes, how is the performance of an M2 rule affected by varying degrees of money control error? The goal of the analysis which follows is to determine if the realm of realistically-sized money control errors includes a threshold of controllability above which an M2 rule consistently produces more variation in nominal GDP around a constant trend than monetary base rules or historical discretionary monetary policy. This tests the operational capabilities of the M2 rule. To conduct this analysis, GDP simulations were conducted with different-sized money control error vectors. The simulated M2 error vector was transformed to generate a grid of twenty-five different vectors of money control errors. The mean errors in the grid are 22, 21, 0, 1, or 2. The standard deviations in the grid are 1, 2, 3, 4, or 5. The grid encompasses the statistical distribution of money control errors generated by equation 8, but in response to arguments that the Fed can more precisely control M2, smaller standard deviations were also included in the grid of potential money control errors. In response to arguments that the Fed might use the existence of money control error as an excuse to violate the rule and pursue stealth discretionary policy, the grid also includes mean errors that are both larger and smaller than the mean money control error generated by equation 8. As the Fed has generally announced annual M2 targets within a band of 4, the difference was split around the mid-point of the roughly 0 mean money control error generated by equation 8. Correlation coefficients between the vectors of GDP shocks generated by estimating each of the three economic models and the initial M2 money control error vector generated by equation 8 are roughly equal to zero. To generate error vectors which exhibited either a moderate positive or negative correlation with the GDP shocks of each economic model, the ordering of the values in the money control error vectors was altered. 24 For the three economic models, positive correlations between the money control error vector and the vector of GDP shocks ranged from 0.46 to 0.50. Negatively-correlated GDP shocks and money control errors were between 20.50 and 20.46, and uncorrelated errors ranged from 20.003 to 20.04. GDP simulations were conducted with equations 1 and 7, in three different eco- nomic models, using the grid of twenty-five different money control error vectors outlined above. This yielded 75 simulations for money control errors which were: uncorrelated 23 It is inappropriate to compute the money control error as the deviation of actual M2 from rule-specified levels over the sample period. Errors computed this way would over-estimate the likely degree of money control error because at no time during this period was the Fed focusing explicitly on M2 as its single instrument of monetary policy. For similar reasons, it would also not make sense to compute the money control error based on deviations of historical M2 growth from the center of Fed specified targets. 24 Rationality would dictate utilizing any information embedded in a systematic correlation between money control errors and GDP shocks to improve economic control. Simulations were conducted with different correlations to assess how the economy might react to the rule in a time period before such information could be successfully utilized. 390 S. R. Thornton with GDP shocks, negatively correlated with GDP shocks, and positively correlated with GDP shocks. Results in Tables 2 and 3 report a subset of simulation results and indicate that the nature of the correlation between GDP shocks and money control errors affects rule Table 2. GDP RMSEs: M2 Rule with Uncorrelated and Positively-Correlated Money Control Errors l 5 0.25 and Four-Year Moving Average Velocity Growth Rate s 5 1 s 5 2 s 5 3 s 5 4 s 5 5 With Uncorrelated Money Control Errors Keynesian Model m 5 22.0 0.04403 0.04539 0.04682 0.04834 0.04986 m 5 0.0 0.03933 0.04078 0.04231 0.04394 0.04556 m 5 2.0 0.04412 0.04537 0.04671 0.04814 0.04958 Two-Variable VAR Model m 5 22.0 0.03165 0.03202 0.03258 0.03333 0.03421 m 5 0.0 0.02467 0.02516 0.02589 0.02685 0.02795 m 5 2.0 0.03144 0.03184 0.03243 0.03322 0.03413 Four-Variable VAR Model m 5 22.0 0.03407 0.03483 0.03572 0.03673 0.03780 m 5 0.0 0.02970 0.03056 0.03156 0.03270 0.03390 m 5 2.0 0.03714 0.03783 0.03864 0.03957 0.04056 With Positively Correlated Money Control Errors Keynesian Model m 5 22.0 0.04476 0.04689 0.04912 0.05148 0.05382 m 5 0.0 0.04023 0.04261 0.04508 0.04766 0.05020 m 5 2.0 0.04501 0.04717 0.04944 0.05183 0.05420 Two-Variable VAR Model m 5 22.0 0.03245 0.03381 0.03549 0.03747 0.03982 m 5 0.0 0.02572 0.02743 0.02951 0.03190 0.03440 m 5 2.0 0.03228 0.03370 0.03543 0.03750 0.03965 Four-Variable VAR Model m 5 22.0 0.03364 0.03408 0.03473 0.03560 0.03661 m 5 0.0 0.02925 0.02978 0.03056 0.03158 0.03276 m 5 2.0 0.03682 0.03727 0.03793 0.03879 0.03978 Table 3. GDP RMSEs: M2 Rule with Negatively-Correlated Money Control Errors l 5 0.25 and Four-Year Moving Average Velocity Growth Rate s 5 1 s 5 2 s 5 3 s 5 4 s 5 5 Keynesian Model m 5 22.0 0.04259 0.04253 0.04258 0.04273 0.04297 m 5 0.0 0.03781 0.03779 0.03789 0.03810 0.03841 m 5 2.0 0.04287 0.04289 0.04301 0.04324 0.04354 Two-Variable VAR Model m 5 22.0 0.03093 0.03074 0.03091 0.03144 0.03226 m 5 0.0 0.02384 0.02372 0.02406 0.02485 0.02598 m 5 2.0 0.03087 0.03088 0.03122 0.03193 0.03290 Four-Variable VAR Model m 5 22.0 0.03248 0.03172 0.03118 0.03086 0.03076 m 5 0.0 0.02800 0.02727 0.02678 0.02655 0.02658 m 5 2.0 0.03591 0.03545 0.03519 0.03513 0.03526 Suitable Policy Instruments for Monetary Rules 391 performance. In simulations where money control errors were either positively correlated or uncorrelated with GDP shocks, RMSEs increased as the mean and standard deviations of the money control error increased. Although the increase in the RMSEs across a given mean or standard deviation in the grid of money control errors was small, it was typically larger in the case of positive correlations. In these cases, there was only a very small increase in the variability of GDP and a very small reduction in the level of price stability attainable by the M2 rule. Even in the cases of the highest degree of money control error, during the sample period, the M2 rule still reduced the variability of nominal GDP by two-thirds, relative to historical monetary policy. In the case of negatively-correlated money control errors and GDP shocks, in the Keynesian and two-variable VAR models, RMSEs increased slightly—suggesting that positive money control errors largely offset negative GDP shocks, and vice-versa. In the four variable VAR model, for any given mean error, the RMSE declined slightly as the standard deviation increased. Even when the money control error was largest, the M2 rule still reduced the variability of nominal GDP to about one-fourth of its historical value. For all types of error correlations, the increases in RMSEs typically ranged from 0.5 to 2.0, relative to the RMSE generated in the case of no M2, money control error. This is a very small increase in the RMSE, as is illustrated by Figure 3 which shows the GDP growth path generated by an M2 rule in the four-variable VAR model, in the case where money control errors are largest. In Figure 3, GDP exhibits only small and temporary deviations from the target path. Even during the period of velocity instability in the 1990s, simulated GDP deviates only slightly from target. The effects of a high degree of money control error, combined with positive correlations between the money-GDP shocks, was mostly mitigated by the feedback adjustment term, which produced subsequent quarter adjustments in M2 growth needed to keep GDP close to target. Simulation results utilizing money control errors do not suggest the economy is insensitive to large changes in M2 growth. Rather, results indicate that the parameters in McCallum’s Rule are set at values which promote long-run price stability and signifi- cantly insulate the economy from undesired swings in money growth. Subject to some Figure 3. GDP growth path: M2 rule with positively-correlated money control errors and GDP shocks in a four-variable VAR mean error 5 2, standard deviation 5 5. 392 S. R. Thornton caveats, addressed below, results suggest that, given GDP shocks of historical magnitudes even those caused by the velocity shocks in the 1990s, the performance of an M2 rule is robust to varying degrees of money control error. Findings regarding the likely success of an M2 rule are in contrast with those obtained by Dotsey and Otrok 1994— even though both studies used money control errors of similar size. The most probable explanation is the use of different M2 rules. The adjustment parameters in McCallum’s rule appear to do a better job of mitigating the impacts of money control error on the GDP growth path. To assess the relative performance of the policy instruments, it is useful to compare the RMSEs in Tables 2–3 with the RMSEs generated by corresponding economic models and monetary base rules. In the four-variable VAR, the M2 rule performed much better than either of the base rules. 25 When comparing monetary base and M2 rules it appears that even the addition of a plausible degree of money control error doesn’t much mitigate M2’s advantage of a relatively stronger and more stable relationship with nominal GDP during this time period. The strength and stability of the relationship between the policy instrument and nominal GDP improves the ability of the feedback adjustment term to offset the undesirable impacts of money control errors. When comparing the performance of specific policy instruments, precise monetary control seems less advantageous than a stronger and more stable link to GDP. In the Keynesian and two-variable VAR models, the St. Louis monetary base rule delivered slightly lower RMSEs than the M2 rule with money control error. But, this difference in performance is small and unlikely to be economically significant. Results suggest that given current monetary control procedures, the Fed could suc- cessfully utilize an M2 rule to maintain much greater levels of price stability and much lower levels of GDP variability than we have achieved under discretionary monetary policy. The M2 rule is operationally sound and imposes the discipline necessary to achieve price stability. Findings also indicate that an M2 rule is likely to outperform a base rule.

IV. Caveats in the Analysis of an Adaptive M2 Rule