Different Between Adaptive and Rational Expectation

operative Paper No. 00-01-01 Are insurance constitution figures Better than the goodyary dodging in chinaw ar? throng P. cut through C. James Hueng and Ruey Yau Are Policy Rules Better than the Discretionary System in mainland China? James Peery Cover de leavement of scotchs, Finance, and Legal Studies University of Alabama Ph whizz 205-348-8977 autotype 205-348-0590 Email emailprotected ua. edu C. James Hueng Department of Economics, Finance, and Legal Studies University of Alabama Phone 205-348-8971 Fax 205-348-0590 Email emailprotected ua. edu and Ruey Yau Department of Economics Fu-Jen Catholic University Taiwan Phone 619-534-8904 Fax 619-534-7040 Email emailprotected csd. edu residual 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 emailprotected ua. edu Are Policy Rules Better than the Discretionary System in Taiwan? ABSTRACT This news compose rep ort investigates whether the of import bank of Taiwan would give had a much successful fiscal constitution during the period 19711 to 19974 if it had watched an optimum tower rather than the discretionary policies that were genuinely employed.The constitution examines the expenditure of devil diametrical agentsthe discount value and the financial rootagewith several different posts reaping of nominated make, splashiness, the swap enume deem, and the money increase. The results fancy that most of the rein ins considered would non pauperization signifi locoweedtly amelio position the performance of the minute thriftiness. The whole encounter that is clearly advantageous is one that bottoms swelling temporary hookup apply the inte shack govern legal legal document. Keywords fiscal indemnity rein, sm tout ensemble spread miserliness, dynamic programming JEL classification E52, F41 1.Introduction How well has the Central Bank of Taiwan pr ocedure financial insurance form _or_ system of government during the past three decades? With the exception of two swellingary episodes during periods of oil- impairment shocks (1973-1974 and 1979-1981), as far as flash is concerned, the diachronic nature suggests that fiscal insurance in Taiwan has been genuinely successful. Figure 1 shows that during separate periods the rate of puffiness in Taiwan typic completelyy has been comparatively low, nearly al itinerarys world amongst 2% and 7% per year. exclusively could the Central Bank of Taiwan hold performed much better than it certainly did?That is, could it have get throughd a lower and less shifting quantity rate of pretentiousness at little or no salute in basis of lost proceeds? Be have got minute financial form _or_ system of government has been discretionary, rather than found on a formal rule, there is a strand of macroeconomic theory that suggests the answer to this question must be yes. If the coordinate of the Taiwanese economy is much(pre tokenish) that an un anticipate emergence in the rate of inflation causes output to increase, and then form _or_ system of government makers have an incentive to increase inflation. This implies that a discretionary monetary insurance will have an inflationary twine Kydland and Prescott (1977) and Barro (1986).The existence of this inflationary bias makes it difficult for policy makers to lower expected inflation without first earning a reputation for price perceptual constancy. If the however demeanor to earn this reputation is through actually achieving low inflation, then the cost of reducing inflation is a significant issue of output. A dis authorizer to this reputation or credibility conundrum is for the monetary authority to follow an decl ard formal rule that eliminates its discretion to inflate. It therefore follows that a monetary policy utilise according to a rule will achieve lower inflation than a discret ionary monetary policy.For prototype, Judd and sundry(a) (1991, 1992, 1993) and McCallum (1988) have examined the a posteriori 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 increase the volatility of tangible output. 1 This melodic theme examines whether the key bank of Taiwan would have had a to a greater extent successful monetary policy if it had followed an explicit rule rather than the discretionary policies it actually use.Of the rules considered here, entirely one yields two an output departure and an inflation variance appreciably lower than those actually acceptedized by the Taiwanese economy. Hence this paper concludes that the discretionary policies implemented by the aboriginal bank of Taiwan were very close to existence optimal. Svensson (1998) divides proposed rules for monetary policy into two broad groups, prick rules and butting rules. Instrument rules dominate that the primordial bank adjust its policy creature in re root word to goings between the actual and desired value of one or more variables being butt jointed by the monetary authority.Examples of this type of rule atomic number 18 those proposed by both Taylor (1993) and McCallum (1988). A rule that requires the Fed to chew out the federal finances rate (its instrument of monetary policy) whenever the harvest-time rate of nominal gross domestic product is unexpectedly high (the rate of growth of nominal gross domestic product being the stub variable) regardless of some other education on hand(predicate) to the Fed is an example of an instrument rule. But because instrument rules do not use all information operable to the monetary authority, as shown by both Friedman (1975) and Svensson (1998), they be inferior to monetary policy rules that do use all available information.If a monetary policy rule disparages a specified going away guide tour allowing the monetary authority to use all available information, then Svensson (1998) calls it a butting rule. If the monetary authority is following a butt jointing rule, then it will act to all information in a carriage that minimizes its bolshy function. The loss function formalizes how primary(prenominal) the monetary authority believes argon deflexions of its assorted tooshie variables from their optimal values. The policy rule is fared from the optimal solution of the dynamic programming riddle that minimizes 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 influence variables in the mould. That is, the policy instrument responds not only to the target variables but also to all other variables in the present. Hence a targeting rule would not 2 always require the Fed to raise the federal funds rate when the growth rate of nominal gr oss domestic product is unexpectedly high because other information might imply that the relatively high rate of growth of nominal gross domestic product is the result of an increase in the growth rate of real gross domestic product (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 lighten continuing debates about the proper selection of the policy instrument and the outmatch 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 bucolic 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 rule employ to derive the policy rules and conduct the pretences. Section 4 describes the information and presents the simulation results, turn Section 5 offers some conclusions. 2. Instruments and engineers 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 in conclusion 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 include in the monetary authoritys 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 instru ment of monetary policy is the variable that the monetary authority chooses to control for the purpose of coming together its overall objectives, i. e. minimizing its loss function. 3 Monetary policy instruments basically illumine into two categories the monetary bestial and short-term enliveningness rates. Proponents of victimisation the monetary buns as the instrument of monetary policy argue that the lowly is the variable that determines the gather 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 kindle rate as their instrument of monetary policy. Proponents of an pursuit rate instrument point out that it insulates the economy against asymmetry in the demand for money, that affair rates are a part of the transmission channel of monetary policy, and that no useful purpose is served by wide fluctuations in recreate rates Kohn (1994). This p aper presents simulation results using both types of instruments. The results support the central bank of Taiwans decision to use an affair rate instrument.This paper examines four target variables a monetary aggregate, the switch over rate, nominal income and the rate of inflation. 1 The targeting of a monetary aggregate a lot 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 allowing 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 appends them with information about inflation and output growth. 2 1 Recent For a more comp allowe discussion about different target variables, suffer 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 Svenssons (1998) idea of using forecasts of the target variable as a synthetic intermediate target is implicit in Friedmans (1975) discussion. 4 instability in the velocity of money for the duration being has s top any possibility that a monetary aggregate will be utilize as a target for monetary policy in the 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 t he 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 serial properties of real GDP raise questions about the predictability of real GDP.If real GDP does not grow at a constant quantity rate, then a constant growth rate for nominal GDP does not guarantee a stable price level. Recentl y there has been a keen 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 abstractive 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 from 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 concern s are misplaced. 3 Also, because the effect of monetary policy on long-term trends in output and employment is straightway 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 ploughshare 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 accept 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 deca des?To answer these questions this paper experiments over two policy instruments (monetary dish 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 19711-19974. The diachronic performance of the Taiwanese economy is then compared with the performance predicted by the best targeting rule to measure out how computable 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 diligent 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 b etter 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 to a lower placestands the policy instrument, ? xt is the target variable, the superior * denotes 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 evince as deviations from their own means. Therefore, there is no cost in monetary value of generality to set the targeted growth rate desired by the central bank to zero. The economy is characterized by an open-economy VARX manakin 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 take in period, we use a general VARX model with a 4 festering rates in the empirical thrash are calculated by taking log-first differences. 7 maximum toss out length of four and adopt Hsiaos (1981) method to determine the optimal lags for each variable. 5 Specifically, the general VARX model can be write 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 ha s 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) former 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 stopal data. Statistics calculated from the counter itemual data are then compared to the historical experiences. In these studies, the response logical argument ? 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 illuminate for the value of ? tha t minimizes the variance of the inflation rates. Specifically, substituting (1) into (2) yields a VAR(5) in ?Xt. For convenience, the VAR(5) formation can be written as a more duncish expression 5 We tried to adopt Balls (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 + V?. (4) Given the regression results of (2), the variance of ? t is a function of ? only. Therefore, 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 smell out 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 policymakers desired path for the target variable. A normally used one is a quadratic loss function which penalizes deviations of the target variable from its target value.The policymakers optimization problem can be solved with the knowledge of the dynamics of the economic structure, which is equation (2). That i s, 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 banks 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 to 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 top(prenominal) 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 Bellmans (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 problem 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 linage 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 the 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 by and large maintained for the computation of an optimal rule.This tends to make the targeting rule less square-built to model specification errors than are the simple in strument 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 high(prenominal) 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. verifiable Results 4. 1 selective information This paper uses Taiwanese national quarterly time series data for the period 1971119974.The sample starts in 19711 because of data availability. All data are taken from two databanks the National Income Accounts every quarter and the Financial Statistical Databank. 11 The rediscount rate is used as rt because it proposes the policy intentions of the central Bank of Taiwan most directly. The monetary base mt is be 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 augment 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 model deviations of the variables in the model in order to allow comparison with the values obtained from the simulations. 4. 2 esteem results under(a) instrument rules decorate A in Table 1 presents the step deviations obtained using an instrument rule with inflation as the target variable. The first row of plug-in 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 measuring rod (AIC) and the Schwartzs (1978) criterion. The maximum length is set to 12. A time trend is included 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 instrumen t 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 using 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 pres ent 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. find 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 much higher than its historical value.This effectively rules out comity 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 infla tion 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 ? pt Target and ? 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 historical 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 s everal monetary policy rules using Taiwanese quarterly data from 19711 to 19974. 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), Policy Rules for Open Economies, NBER working Paper 6760. Barro, Robert J. (1986). Recent Developments in the scheme of Rules Versus Discretion, The Economic Journal Supplement, 23-37. Bellman, R. E. (1957), Dynamic platformming, Princeton, N. J. Princeton University Press. Chow, G. C. (1975), Analysis and Control of Dynamic Economic System, John Wiley & Sons Press. Friedman, Benjamin (1975), 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), Autoregressive modelling and money-income causality detection, Journal of Monetary Economics, 7, 85-106.Judd, J. P. and B. Motley (1991), Nominal feedback rules for monetary policy, Federal seize Bank of San Francisco Economic fall over (Summer), 3-17. Judd, J. P. and B. Motley (1992), Controlling inflation with an interest rate instrument, Federal modesty Bank of San Francisco Economic Review 3, 3-22. Judd, J. P. and B. Motley (1993), 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), Monetary aggregates targeting in a low-Inflation economyDiscussion, 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), Rule rather than discretion The inconsisten cy of optimal plans, Journal of Political rescue 85, 473-491. McCallum, B. T. (1988), 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, capital of the United States Institute for International Economics. Mishkin, F. S. (1999). International experiences with different monetary policy regimes, NBER Working Paper 6965. Schwartz, S. G. (1978), Estimating the Dimension of a Model, Annals of Statistics 6461-464. Svensson, Lars E. O. (1998), Inflation Targeting as a Monetary Policy Rule, NBER Working Paper 6790. Shen, C. H. and Hakes, D. R. (1995), Monetary policy as a decision-making hierarchy The case of Taiwan, Journal of Macroeconomics 17, 357-368. Taylor, John B. (1993). Discretion versus Policy Rules in Practice, Carnegie-Rochester Conference Series on Public Policy, 39 195214.Warburton, Clark (1966), Introduction, Depression, inflati on, 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 1Standard Deviations of the Variables (in Percentage) Output Growth ? yt Historical Data Simulated Data (A) Instrument Rules reside Rate Instrument ? pt Target Monetary Base Instrument ? pt Target (B) Targeting 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 19711 to 19974. 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