Different Between Adaptive and Rational Expectation

Working Paper No. 00-01-01 Are Policy Rules Better than the Discretionary System in Taiwan? James P. Cover C. James Hueng and Ruey Yau Are Policy Rules Better than the Discretionary System in Taiwan? James Peery Cover Department of Economics, Finance, and Legal Studies University of Alabama Phone: 205-348-8977 Fax: 205-348-0590 Email: [email  protected] ua. edu C. James Hueng Department of Economics, Finance, and Legal Studies University of Alabama Phone: 205-348-8971 Fax: 205-348-0590 Email: [email  protected] ua. edu and Ruey Yau Department of Economics Fu-Jen Catholic University Taiwan Phone: 619-534-8904 Fax: 619-534-7040 Email: [email  protected] csd. edu Correspondence to: C. James Hueng Department of Economics, Finance, and Legal Studies University of Alabama, Box 870224 Tuscaloosa, AL 35487 Phone: 205-348-8971 Fax: 205-348-0590 Email: [email  protected] ua. edu Are Policy Rules Better than the Discretionary System in Taiwan? ABSTRACT This paper investigates whether th e central bank of Taiwan would have had a more successful monetary policy during the period 1971:1 to 1997:4 if it had followed an optimal rule rather than the discretionary policies that were actually employed.The paper examines the use of two different instruments—the discount rate and the monetary base—with several different targets — growth of nominal output, inflation, the exchange rate, and the money growth. The results show that most of the rules considered would not have significantly improved the performance of the Taiwanese economy. The only rule that is clearly advantageous is one that targets inflation while using the interest rate instrument. Keywords: monetary policy rule, small open economy, dynamic programming JEL classification: E52, F41 1.Introduction How well has the Central Bank of Taiwan implemented monetary policy during the past three decades? With the exception of two inflationary episodes during periods of oil-price shocks (1973-1974 and 1979-1981), as far as inflation is concerned, the historical record suggests that monetary policy in Taiwan has been very successful. Figure 1 shows that during other periods the rate of inflation in Taiwan typically has been relatively low, nearly always being between 2% and 7% per year. But could the Central Bank of Taiwan have performed much better than it actually did?That is, could it have achieved a lower and less variable rate of inflation at little or no cost in terms of lost output? Because Taiwanese monetary policy has been discretionary, rather than based on a formal rule, there is a strand of macroeconomic theory that suggests the answer to this question must be yes. If the structure of the Taiwanese economy is such that an unexpected increase in the rate of inflation causes output to increase, then policy makers have an incentive to increase inflation. This implies that a discretionary monetary policy will have an inflationary bias [Kydland and Prescott (1977) and Barr o (1986)].The existence of this inflationary bias makes it difficult for policy makers to lower expected inflation without first earning a reputation for price stability. If the only way to earn this reputation is through actually achieving low inflation, then the cost of reducing inflation is a significant loss of output. A solution to this reputation or credibility problem is for the monetary authority to follow an explicit formal rule that eliminates its discretion to inflate. It therefore follows that a monetary policy implemented according to a rule will achieve lower inflation than a discretionary monetary policy.For example, Judd and Motley (1991, 1992, 1993) and McCallum (1988) have examined the empirical properties of nominal feedback rules and find that the use of simple feedback rules could have produced price stability for the United States over the past several decades without significantly increasing the volatility of real output. 1 This paper examines whether the cent ral bank of Taiwan would have had a more successful monetary policy if it had followed an explicit rule rather than the discretionary policies it actually implemented.Of the rules considered here, only one yields both an output variance and an inflation variance appreciably lower than those actually realized by the Taiwanese economy. Hence this paper concludes that the discretionary policies implemented by the central bank of Taiwan were very close to being optimal. Svensson (1998) divides proposed rules for monetary policy into two broad groups, instrument rules and targeting rules. Instrument rules require that the central bank adjust its policy instrument in response to deviations between the actual and desired value of one or more variables being targeted by the monetary authority.Examples of this type of rule are those proposed by both Taylor (1993) and McCallum (1988). A rule that requires the Fed to raise the federal funds rate (its instrument of monetary policy) whenever the growth rate of nominal GDP is unexpectedly high (the rate of growth of nominal GDP being the target variable) regardless of other information available to the Fed is an example of an instrument rule. But because instrument rules do not use all information available to the monetary authority, as shown by both Friedman (1975) and Svensson (1998), they are inferior to monetary policy rules that do use all available information.If a monetary policy rule minimizes a specified loss function while allowing the monetary authority to use all available information, then Svensson (1998) calls it a targeting rule. If the monetary authority is following a targeting rule, then it will respond to all information in a manner that minimizes its loss function. The loss function formalizes how important the monetary authority believes are deviations of its various target variables from their optimal values. The policy rule is derived from the optimal solution of the dynamic programming problem that m inimizes the loss function subject to the structure of the economy.The resulting rule expresses the growth of the policy instrument as a function of the predetermined variables in the model. That is, the policy instrument responds not only to the target variables but also to all other variables in the model. Hence a targeting rule would not 2 always require the Fed to raise the federal funds rate when the growth rate of nominal GDP is unexpectedly high because other information might imply that the relatively high rate of growth of nominal GDP is the result of an increase in the growth rate of real GDP (rather than an increase in inflation).Although there appears to be a growing consensus that price stability should be the central long-run objective of monetary policy, there are still continuing debates about the proper selection of the policy instrument and the best target variables. But clearly the choice of the best policy instrument and the best target(s) is an empirical issue. Furthermore, the best choices can vary from country to country because the controllability of any particular policy instrument and the effectiveness of each target most likely vary across countries.Therefore, this paper examines two different policy instruments and several targets to search for the best policy rule for Taiwan. The rest of this paper is organized as follows. Section 2 discusses the instrument and the targets of monetary policy that this paper considers. Section 3 describes the method used to derive the policy rules and conduct the simulations. Section 4 describes the data and presents the simulation results, while Section 5 offers some conclusions. 2. Instruments and Targets of Monetary Policies In discussing how monetary policy should be implemented it is helpful to draw a istinction between the instruments and the targets of monetary policy. The targets of monetary policy are those macroeconomic variables that the monetary authority ultimately desires to influence through its policy actions [Friedman, 1975]. For this reason Svensson (1998) prefers to call target variables only those variables that are important enough to be included in the monetary authority's loss function. The targets of monetary policy therefore are a way to formalize the overall objectives of a monetary authority.On the other hand, the instrument of monetary policy is the variable that the monetary authority chooses to control for the purpose of meeting its overall objectives, i. e. minimizing its loss function. 3 Monetary policy instruments basically fall into two categories: the monetary base and short-term interest rates. Proponents of using the monetary base as the instrument of monetary policy argue that the base is the variable that determines the aggregate level of prices, and therefore is a natural instrument for the control of inflation [McCallum (1988)].But most central banks, including the central bank of Taiwan, use a short-term interest rate as their instrume nt of monetary policy. Proponents of an interest rate instrument point out that it insulates the economy against instability in the demand for money, that interest rates are a part of the transmission channel of monetary policy, and that no useful purpose is served by wide fluctuations in interest rates [Kohn (1994)]. This paper presents simulation results using both types of instruments. The results support the central bank of Taiwan's decision to use an interest rate instrument.This paper examines four target variables: a monetary aggregate, the exchange rate, nominal income and the rate of inflation. 1 The targeting of a monetary aggregate often is advocated by those who believe that business cycles largely result from changes in the growth rate of a monetary aggregate [Warburton (1966), M. Friedman (1960)]. Another reason for choosing a monetary aggregate as the target variable for monetary policy is its ability to serve as a nominal anchor that can prevent policies from allowin g inflation to increase to an unacceptable level.Although this allows a monetary aggregate to communicate long-run policy objectives to the general public, as Friedman (1975) points out, it is by its very nature an inferior choice as a target variable because the monetary authority is only concerned with monetary aggregates to the extent that it provides them with information about inflation and output growth. 2 1 Recent For a more complete discussion about different target variables, see Mishkin (1999). That is, monetary aggregates are intermediate targets rather than true targets of monetary policy. Friedman (1975) shows that the use of intermediate targets is not optimal. Although Svensson's (1998) idea of using forecasts of the target variable as a synthetic intermediate target is implicit in Friedman's (1975) discussion. 4 instability in the velocity of money for the time being has ended any possibility that a monetary aggregate will be used as a target for monetary policy in t he United States. McKinnon (1984) and Williamson and Miller (1987) argue that monetary policy should target the exchange rate in an open economy.For example, the exchange rate has been the sole or main target in most of the EMS countries. Pegging the domestic currency to a strong currency prevents changes in the exchange rate from having an effect on the domestic price level. But exchange rate targeting results in the loss of an independent monetary policy. The targeting country cannot respond to domestic shocks that are independent of those hitting the anchor country because exchange rate targeting requires that its interest rate be closely linked to that in the anchor country.McCallum (1988) suggests a nominal GDP targeting rule because of its close relationship with the price level. The nominal GDP target has intrinsic appeal when instability in velocity makes a monetary target unreliable. As long as the growth rate of real GDP is predictable, there is a predictable relationship between nominal GDP and the price level. However, recent studies on the time series properties of real GDP raise questions about the predictability of real GDP.If real GDP does not grow at a constant rate, then a constant growth rate for nominal GDP does not guarantee a stable price level. Recently there has been a great upsurge of interest in direct inflation targeting, a policy that has been adopted by the central banks of New Zealand, Canada, the United Kingdom, Sweden, Finland, Australia, and Spain. Although this policy has been implemented with apparent success in the above countries, there are theoretical concerns with inflation targeting.One problem with inflation targeting is that the effect of monetary policy actions on the price level occurs with considerably more delay than its effects on financial variables. The use of a financial variable such as monetary aggregates or exchange rates as the target would provide an earlier signal to the public that policy has deviated fr om its goals. In addition, attempts by the central 5 banks to achieve a predetermined path for prices may cause large movements in real GDP, but only if the price level is sticky in the short run.But the apparent success of inflation targeting, where it has been tried, suggests that these concerns are misplaced. 3 Also, because the effect of monetary policy on long-term trends in output and employment is now considered to be negligible, many economists are now advocating that monetary authorities should use only inflation (or the price level) as the sole target for monetary policy. According to this view the main contribution that monetary policy can make to the trend in real output is to create an environment where markets are not distorted by high and volatile inflation.The central bank of Taiwan appears to have accepted this position. It has repeatedly stated that its number one priority is price stability and the reaction function estimated by Shen and Hakes (1995) confirms that it has behaved as if price stability is an important policy goal. So what combination of policy instrument and target variable would result in the best rule for monetary policy in Taiwan? Would the adoption of such a rule have improved Taiwanese monetary policy during the past three decades?To answer these questions this paper experiments over two policy instruments (monetary base and interest rate) and four target variables (the rate of inflation, the growth rate of nominal GDP, the growth rate of the monetary base, and the change in exchange rate) in an attempt to find what would have been the best targeting rule for Taiwan during the period 1971:1-1997:4. The historical performance of the Taiwanese economy is then compared with the performance predicted by the â€Å"best† targeting rule to evaluate how good Taiwanese monetary policy has been.This comparison is made by comparing the volatility of the relevant variables resulting from the proposed rules with those from the historical data. 3 A careful reading of Friedman (1975) and Svensson (1998) also suggests that these concerns are misplaced. 6 Although, as noted above, by their very nature targeting rules are superior to instrument rules. Hence this paper emphasizes targeting rules. But just how much better targeting rules are than instrument rules is an empirical question of some practical importance because instrument rules are more transparent than targeting rules.Hence, for completeness, this paper also presents results for instrument rules using the rate of interest and the monetary base as instruments and the rate of inflation as the target variable. 3. The Model and Methodology 3. 1 The instrument rule An instrument rule adjusts the growth of the policy instrument in response to deviations between the actual and desired value of the target variable. That is, ? It = (? xt-1 – ? xt-1*), (1) where It represents the policy instrument, ? xt is the target variable, the superscript * denot es the target value desired by the central bank, and ? efines the proportion of a target miss to which the central bank chooses to respond. In this paper, variables are expressed as deviations from their own means. Therefore, there is no cost in terms of generality to set the targeted growth rate desired by the central bank to zero. The economy is characterized by an open-economy VARX model which includes five variables: the growth rate4 of real income (? yt), the rate of inflation (? pt), the change in the logarithm of the exchange rate (? et), the growth rate of the monetary base (? mt), and the change in the interest rate (? rt).Since the purpose of this paper only requires a model that fits the Taiwanese economy well during the sample period, we use a general VARX model with a 4 Growth rates in the empirical work are calculated by taking log-first differences. 7 maximum lag length of four and adopt Hsiao’s (1981) method to determine the optimal lags for each variable. 5 S pecifically, the general VARX model can be written as: ? Xt = A0 + A1? Xt-1 + A2? Xt-2 + A3? Xt-3 + A4? Xt-4 + i =0 ? ai ? I t ? i 4 + ? t, (2) where ? Xt is the 4? 1 vector that contains variables other than the growth of the policy instrument.The policy instrument has immediate effects on other variables if the 4? 1 vector a0 is not zero. For example, if the instrument is rt and the target is ? pt, then Xt = [ yt, pt, et, mt ] and equations (1) and (2) can be written as: ? rt = ? ?pt-1, ? Xt = A0 + A1? Xt-1 + A2? Xt-2 + A3? Xt-3 + A4? Xt-4 + (1)’ i =0 ? ai ? rt ? i 4 + ? t. (2)’ Previous studies such as Judd and Motley (1991, 1992, 1993) and McCallum (1988) estimate equation (2) and assume that the economy faces the same set of shocks that actually occurred in the sample period.The estimated equation, the historical shocks, and the policy rule (1) are used to generate the counterfactual data. Statistics calculated from the counterfactual data are then compared to the historical experiences. In these studies, the response parameter ? is arbitrarily set and the results from different ? ’s are compared. However, given linearity of the model and the variance-covariance matrix of historical shocks, one can analytically solve for the value of ? that minimizes the variance of the inflation rates. Specifically, substituting (1) into (2) yields a VAR(5) in ?Xt. For convenience, the VAR(5) system can be written as a more compact expression: 5 We tried to adopt Ball's (1998) open-economy Keynesian type model to Taiwan, but this model was not supported by the Taiwanese data. 8 ?Wt = B0 + B1? Wt-1 + ? t, (3) where Wt = [ Xt, Xt-1, Xt-2, Xt-3, Xt-4 ] and ? t = [? t, 0] are both 20? 1. Assume that ? Wt is stationary. Denote V? W as the variance-covariance matrix of ? Wt and V? the variance-covariance matrix of ?t. Equation (3) implies V? W = B1 V? W B1†² + V?. (4) Given the regression results of (2), the variance of ? t is a function of ? only. Th erefore, the value of ? that minimizes the variance of ? pt, given historical shocks, can be calculated. The advantages of an instrument rule include its simplicity, transparency to the public, and the fact that it is always operational. The central bank responds to observed deviations from the target and does not need to base its policy actions on forecasts that require knowledge of the structure of the economy. However, as noted above, instrument rules are not optimal in the sense that they do not use all available information.The policy instrument only responds to the target variables, which is usually inefficient compared to rules that allow the instrument to respond to all the variables in the model. The following section uses an optimal control problem to derive the optimal policy rule, instead of specifying the rule in advance. 3. 2 The targeting rule A targeting rule is derived from the minimization of a loss function. This loss function reflects the policymaker’s des ired path for the target variable. A commonly used one is a quadratic loss function which penalizes deviations of the target variable from its target value.The policymaker’s optimization problem can be solved with the knowledge of the dynamics of the economic structure, which is equation (2). That is, equation (2) is used as the constraints in the dynamic programming problem. To simplify analysis, equation (2) is written as a first-order system, Zt = b + B Zt-1 + C ? It + ? t, (5) 9 where Zt = [? Xt, ? Xt-1, ? Xt-2, ? Xt-3, ? It, ? It-1, ? It-2, ? It-3]. The constant vector b is 20? 1, B is 20? 20, C is 20? 1, ? t is 20? 1, and their arguments should be obvious. Therefore, the central bank's control problem is to minimize a stream of expected quadratic loss function: T 1 E0 ?Zt ‘ K Zt, T t =1 (6) subject to Zt = b + B Zt-1 + C ? It + ? t, (5) where the expectation E0 is conditional on the initial condition Z0. Again, without loss of generality, the target value is set t o zero since all the variables are expressed as deviations from mean. The elements in the matrix K are weights that represent how important to the central bank are deviations of the target variables from their target values. For example, if the central bank wants to target the inflation rates, then the [2,2] element of K is 1 and the other elements are all zeros.The loss function is equivalent to (1/T) E0 ?t =1? pt 2 . T If the central bank wants to target the nominal GDP, then the 2? 2 block on the upper left corner of K is a unity matrix and the other elements are all zeros. The loss function in this case is (1/T) E0 ?t =1(? yt + ? pt ) 2 . T Now the problem is to choose the policy instrument ? I1, . . . , ? IT that minimizes (6), given the initial condition Z0. By using Bellman's (1957) method of dynamic programming the problem is solved backward. That is, the last period T is solved first, given the initial condition ZT-1.Having found the optimal IT, we solve the two-period prob lem for the last two periods by choosing the optimal IT-1, contingent on the initial condition ZT-2, and so on. Letting T > ? , the optimal policy rule can be expressed as [see Chow (1975, ch. 8) for derivation details]: ? It = G Zt-1 + f , with (7) 10 G = -(C ‘ HC) ? 1 (C ‘ HB), f = -(C ‘ HC) ?1 C ‘ (Hb-h), H = K + (B+CG) ‘ H (B+CG), and h =[I-(B+CG) ‘ ] ?1 [- (B+CG) ‘ Hb]. The rule defines the policy instrument as a function of the predetermined variables in the model. The economy is assumed to face the same set of shocks that actually occurred in the historical period.Therefore, the estimated equations, the policy rule, and the historical shocks are used to generate the counterfactual data. The resulting statistics are compared. Even though it is usually more efficient to let the instrument respond to all the relevant variables than to let it respond only to the target variables, the ad hoc instrument rules are more widely discussed in th e literature. The reason for the preference for simple instrument rules may be that the targeting rule is more sensitive to model specifications. For example, the assumption of full information is generally maintained for the computation of an optimal rule.This tends to make the targeting rule less robust to model specification errors than are the simple instrument rules. In addition, the optimal rule may require larger adjustments of the instrument because it responds to more variables. This would in turn yield undesired higher volatility of the other variables such as output growth. Therefore, again, the choice between the instrument rule and the targeting rule cannot be determined by theory alone and is an empirical issue. 4. Empirical Results 4. 1 Data This paper uses Taiwanese national quarterly time series data for the period 1971:11997:4.The sample starts in 1971:1 because of data availability. All data are taken from two databanks: the National Income Accounts Quarterly and the Financial Statistical Databank. 11 The rediscount rate is used as rt because it indicates the policy intentions of the central Bank of Taiwan most directly. The monetary base mt is defined as the reserve money. The exchange rate target is the NT/US dollar rate. The variable yt is real GDP in millions of 1991 NT dollars, and pt is defined as the GDP deflators. Except interest rates, all variables are in logarithms. All variables are in first-difference form and expressed as deviations from their means.The Augmented Dickey-Fuller (ADF) test is used to ensure that the variables are transformed into stationary processes6. The top row of Table 1 presents the historical standard deviations of the variables in the model in order to allow comparison with the values obtained from the simulations. 4. 2 Estimation results under instrument rules Panel A in Table 1 presents the standard deviations obtained using an instrument rule with inflation as the target variable. The first row of Panel A presents simulation results under an interest rate instrument, while the second row presents results under a monetary base instrument.The simulations using an interest rate instrument yielded standard deviations for output growth, the change in the exchange rate, and money growth that are only slightly higher than those for the historical data, while the standard deviation of inflation is slightly lower than its historical value. The only standard deviation in the first row of Panel A that differs substantially from the historical data is that for the change in the interest rate, which is much lower in the simulation.These results indicate that actual policy in Taiwan achieved results almost as good as those that would have been obtained under an optimal interest-rate instrument rule with the 6 The lag lengths in the ADF regressions are determined by the Akaike Information Criterion (AIC) and the Schwartz's (1978) criterion. The maximum length is set to 12. A time trend is includ ed in the yt, pt, and mt regressions. All results indicate that the original time series are integrated of order one. The results of the tests are available from the authors upon request. 12 xception that the optimal rule would have yielded a more stable rate of interest. The simulation using the monetary base as the instrument yielded slightly higher standard deviations for all variables except the rate of inflation. Those for output growth, the change in the exchange rate, and the rate of interest were only slightly higher than the historical values, while the standard deviation of the growth rate of the monetary base was much higher than its historical value. The standard deviation of the inflation rate is slightly lower than the historical value but is higher than that in the interest rate instrument rule.These results suggest that the discretionary policy implemented in Taiwan was superior to an optimal monetary base instrument rule. They also indicate that an instrument rule u sing the rate of interest would have been superior to one employing the monetary base as instrument, though not by a large margin. 4. 3 Estimation results under targeting rules Panel B of Table 1 presents standard deviations of the variables under the various targeting rules considered here. The first four rows of Panel B present results obtained using an interest rate instrument.In the first row of Panel B the standard deviation of nominal GDP is minimized; in the second row the standard deviation of inflation is minimized; etc. The last three rows of Panel B present results under a monetary base instrument. Notice that for both instruments, if nominal GDP is the target, then the standard deviations of all variables are higher than their historical values. This implies that the growth rate of nominal GDP would not have been a suitable target variable for Taiwan. Furthermore, notice that for all targets under the monetary base instrument the standard deviation of output growth is mu ch higher than its historical value.This effectively rules out consideration of the monetary base as the instrument of monetary policy under a targeting rule for Taiwan. Now notice from the fourth row of Panel B that if the monetary base is the target under an interest rate instrument, the standard deviations of output growth and inflation are both higher 13 than their historical values. This effectively rules out the use of the monetary base as an appropriate target for monetary policy in Taiwan. Finally, by comparing rows â€Å"? pt Target† and â€Å"? t Target† of Panel B, one sees that if the rate of inflation is the target, then the standard deviations of output growth and inflation are lower than if the exchange rate is the target. Also, if inflation is the target, the standard deviations from the simulations for inflation and output are lower than their historical values. Hence it is concluded that Taiwanese monetary policy would have been better than its histor ical performance if it had used an optimal targeting rule with the rate of interest as instrument and inflation as the target. 5. Conclusion Taiwan has been very successful in using discretionary monetary policies.This paper attempts to see whether there exist policy rules that can improve the Taiwanese economy for the past several decades. This paper evaluates several monetary policy rules using Taiwanese quarterly data from 1971:1 to 1997:4. Two types of policy rules are examined. Instrument rules adjust the growth of the policy instrument in response to deviations between the actual and desired values of the target variable. Unlike those in the previous studies where arbitrary instrument rules are proposed, this paper solves analytically for the optimal instrument rules that minimize the standard deviation of the rate of inflation.Targeting rules are derived from the solution to the dynamic programming problem that minimizes a loss function subject to the structure of the economy . The rule expresses the growth of the policy instrument as a function of all the predetermined variables in the model. Two policy instruments (interest rate and monetary base) and four targets variables (nominal GDP growth, inflation rate, changes in exchange rates, and money growth rate) are examined in the paper. Simulations of a simple VARX model and the policy rules suggest that, 14 ompared to the historical policy, the use of a policy rule in Taiwan would not have reduced substantially the volatility of inflation rate. The only policy rule that would appeal to the authority is the direct inflation targeting rule with the interest rate as the instrument. This rule would have reduced the standard deviation of the inflation rate in Taiwan by 0. 7% while maintained similar volatility of the other variables to those in the historical data. 15 References Ball, L. (1998), â€Å"Policy Rules for Open Economies,† NBER Working Paper 6760. Barro, Robert J. (1986). Recent Developme nts in the Theory of Rules Versus Discretion,† The Economic Journal Supplement, 23-37. Bellman, R. E. (1957), Dynamic Programming, Princeton, N. J. : Princeton University Press. Chow, G. C. (1975), Analysis and Control of Dynamic Economic System, John Wiley & Sons Press. Friedman, Benjamin (1975), â€Å"Rules Targets, and Indicators of Monetary Policy,† Journal of Monetary Economics, 1, 443-73. Friedman, Milton (1960), A Program for Monetary Stability. Fordham University Press, New York. Hsiao, C. (1981), â€Å"Autoregressive modelling and money-income causality detection,† Journal of Monetary Economics, 7, 85-106.Judd, J. P. and B. Motley (1991), â€Å"Nominal feedback rules for monetary policy,† Federal Reserve Bank of San Francisco Economic Review (Summer), 3-17. Judd, J. P. and B. Motley (1992), â€Å"Controlling inflation with an interest rate instrument,† Federal Reserve Bank of San Francisco Economic Review 3, 3-22. Judd, J. P. and B. Motley (1993), â€Å"Using a nominal GDP rule to guide discretionary monetary policy,† Federal Reserve Bank of San Francisco Economic Review 3, 3-11. Kohn, D. L. (1994), â€Å"Monetary aggregates targeting in a low-Inflation economy–Discussion,† in J. C.Fuhrer, ed. , Goals, Guidelines, and Constraints Facing Monetary Policymakers, 130135. Federal Reserve Bank of Boston. Kydland, F. E. and Prescott, E. C. (1977), â€Å"Rule rather than discretion: The inconsistency of optimal plans,† Journal of Political Economy 85, 473-491. McCallum, B. T. (1988), â€Å"Robustness properties of a rule for monetary policy,† CarnegieRochester Conference Series on Public Policy 29, 173-204. 16 McKinnon, Ronald (1984). An International Standard for Monetary Stabilization, Washington: Institute for International Economics. Mishkin, F. S. (1999). International experiences with different monetary policy regimes,† NBER Working Paper #6965. Schwartz, S. G. (1978), â€Å"Est imating the Dimension of a Model,† Annals of Statistics 6:461-464. Svensson, Lars E. O. (1998), â€Å"Inflation Targeting as a Monetary Policy Rule,† NBER Working Paper #6790. Shen, C. H. and Hakes, D. R. (1995), â€Å"Monetary policy as a decision-making hierarchy: The case of Taiwan,† Journal of Macroeconomics 17, 357-368. Taylor, John B. (1993). â€Å"Discretion versus Policy Rules in Practice,† Carnegie-Rochester Conference Series on Public Policy, 39: 195:214.Warburton, Clark (1966), â€Å"Introduction,† Depression, inflation, and Monetary Policy: Selected Papers, 1945-1953. Johns Hopkins Press, Baltimore. Williamson, John and Miller, Marcus (1987). Targets and Indicators, Washington: Institute for International Economics. 17 Table 1:Standard Deviations of the Variables (in Percentage) Output Growth ? yt Historical Data: Simulated Data: (A) Instrument Rules: Interest Rate Instrument: ? pt Target Monetary Base Instrument: ? pt Target (B) Targeti ng Rules: Interest Rate Instrument: ? (yt + pt) Target ? pt Target ? et Target ? t Target Monetary Base Instrument: ? (yt + pt) Target ? pt Target ? et Target 5. 346 3. 862 3. 798 4. 964 1. 972 3. 449 2. 767 5. 950 2. 139 14. 63 27. 781 6. 794 0. 185 0. 198 0. 159 4. 348 2. 993 3. 047 4. 446 4. 314 2. 092 3. 064 6. 880 3. 076 2. 469 2. 361 2. 771 5. 421 4. 473 4. 281 4. 058 0. 485 0. 175 0. 332 0. 431 -2. 38 3. 308 2. 748 2. 718 6. 540 0. 178 3. 185 Inflation Rate ? pt 2. 793 Change in Exchange rate ? et 2. 415 Monetary Base Growth ? mt 4. 315 Change in interest rate ? rt 0. 162 Optimal ? : 0. 0133 3. 201 2. 633 2. 601 4. 454 0. 035The sample period is from 1971:1 to 1997:4. The variable ? yt is real GDP growth rate, ? pt is inflation rate, ? et is change in exchange rates, ? mt is monetary base growth rate, and ? rt is change in interest rates. All data are from the National Income Accounts Quarterly and the Financial Statistical Databank data banks. The response parameter ? in the instrument rules defines the proportion of a target miss to which the central bank chooses to respond. 18 Figure 1 Inflation Rate (annual rate %) 70 60 Inflation Rate (% per year) 50 40 30 20 10 0 -10 70 74 78 82 Year 86 90 94 98 19