challenge of **monetary** **policy** is to interpret current data on the economy and financial markets with an eye to anticipat- ing future inflationary or contractionary forces and to coun- tering them by taking action in advance.” Governor Meyer (April 24, 1997) noted that he is “inclined to believe in the forward-looking approach and therefore in preemptive pol- icy.” Moreover, he justified forward-looking **policy** in his comments on March 16, 1998, that “[a] good reason for responding to forecasts of inflation is that the effects of **monetary** **policy** on the economy mostly occur about a year from now.” In a discussion of **monetary** **policy** in Canada, Duguay and Poloz (1994) noted that a key implication of the interaction between **policy** objectives and mainstream views of **how** the economy works is that **policy** formulation must be forward-looking. Using Federal Reserve forecasts and preliminary data available at the time **policy** choices were made, McNees (1986) found evidence that **monetary** policymaking has been forward-looking as well as back- ward-looking. Orphanides (1997) used Federal Reserve forecasts of inflation to estimate forward-looking **policy** **rules**. Clarida, Gali, and Gertler (1998b) estimate for- ward-looking **policy** **rules** for pre- and post-1979. Clarida, Gali, and Gertler (1998a) report that Germany, Japan and the U.S. have pursued forward-looking **monetary** **policy**. Batini and Haldane (1999) use the Bank of England fore- casting model to show that inflation-forecast-based **rules** confer some real benefits.

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In order to estimate a central bank’s real-time interest rate reaction function, it is crucial to develop real-time forecasts of the inflation rate and the output gap when this data is not available. The Greenbook U.S. output gap forecast can be well described by a simple quadratic detrending, while many other popular detrending methods produce results significantly different from the Fed’s internal estimates. Greenbook inflation forecasts can be closely replicated using Bayesian model averaging over various lag lengths of the ADL model in inflation and the GDP growth rate. Other aggregate methods also typically produce forecasts superior to single model projections. The paper proceeds to use these forecasts in order to estimate forward-looking **Taylor** **rules** in the absence of forward-looking data. The results show that since the 1980s, the Fed, the Bank of Canada, the Bundesbank, and the Bank of England have pursued inflation- targeting **monetary** **policy**. However, while the United States and Germany targeted inflation one-year-ahead, the United Kingdom and Canada focused on the middle-term of roughly two quarters hence. Despite these differences, all four central banks obeyed the **Taylor** principle of having an inflation response coefficient greater than one.

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considered indicative of the **Taylor** rule as a description of **monetary** **policy**, and with this in mind, the following sub-periods be identified for the UK. With such an erratic history, it is of interest whether the effectiveness of British **monetary** **policy** has changed in a significant way. **Taylor** (1993) introduced a positive metric for determining the goals of **monetary** policymakers, expressed in simple interest-rate reaction functions as well as normative **rules** for judging the effectiveness of **policy**, particularly through an analysis of the magnitude of the coefficients on the reaction function. Since then, the literature on **Taylor** **Rules** has expanded considerably and various authors have estimated **Taylor**-type reaction functions for a wide cross-section of countries. Prior approaches to estimating **Taylor** **Rules**, whether in the UK or more generally, either tend to estimate a single rule for long time periods, or exploit the narrative history to identify changes in announced central bank **policy** and estimate separately for each period. The first approach ignores the possibility of structural breaks in the **monetary** **policy** reaction function and risks biased coefficients on the parameters of interest. The second approach offers an improvement by acknowledging the possibility of structural change in the reaction function, but implicitly assumes that the change in actual policymaking occurs at the moment of the announcement of a change in **policy**. However, it is plausible that these two events may occur with a lag: an announced change in **policy** may reflect a change in de facto policymaking some quarters prior, or an announced change in **policy** may only be implemented with a These possibilities pose serious challenges to the determining the timing of breaks in sub-periods. For estimations purposes then, sub-periods for estimation might follows as Nelson (2002), Adams et al (2005) and David (2011):

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Laubach, Mishkin and Posen [7]). Thus, there has been commitment to objectives rather than to simple instrument **rules**. Second, central banks have developed very elaborate and complex decision-making processes, where large amounts of information are collected, processed and analyzed, and where considerable judgment is exercised (see, for instance, Brash [13]). Third, any simple **rules** of thumb actually used are conditions for target variables or forecasts of target variables, rather than explicit formulas for the instrument rate. This is the case, for instance, for the rule of thumb expressed by the Bank of England and Sveriges Riksbank (the central bank of Sweden), that normally, the interest rate should be adjusted such that the resulting inflation forecast at an appropriate horizon (usually about two-years ahead) is on target. 5 No central bank has so far made a commitment to a simple instrument rule like the **Taylor** rule or variants thereof. Neither has any central bank announced a particular instrument rule as a “guideline.” Thus, there appears to be a substantial gap between the research on instrument **rules** and the practice of **monetary** **policy**. This paper discusses and proposes a way to bridge that gap. From a descriptive perspective, it argues that, in order to be **useful** for discussing real-world **monetary** **policy**, the concept of **monetary**-**policy** **rules** has to be broadened and defined as “a prescribed guide for **monetary**-**policy** conduct,” including “targeting **rules**” as well as “instrument **rules**.” 6 Furthermore, it argues that the **monetary**-**policy** practice is better discussed in terms of targeting **rules** than instrument **rules**. A general targeting rule specifies the objectives to be achieved, for instance, by listing the target variables, the targets (target levels) for those variables, and the (explicit or implicit) loss function to be minimized. A specific targeting rule specifies conditions for the target variables (or forecasts of the target variables), for instance, like the above rule of thumb of the Bank of England and the Riksbank. From a prescriptive perspective, this paper argues that a commitment to targeting **rules** has a number of advantages, for instance, in 5 This rule furthermore refers to constant-interest-rate forecasts, since both the Bank of England and the Riksbank mainly rely on such forecasts.

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This paper is structured as follows. In Section 1 the existing literature on time- varying **monetary** **policy** **rules** is reviewed. Theoretical models based on asymmet- ric central-bank preferences imply a time-varying reaction to economic variables. Though empirical research on this topic is still in the beginning, non-linearities in **monetary** **policy** **rules** seem to be of importance. Section 2 discusses the speciﬁcation of the Markov-switching model and the estimation procedure. It is assumed that the **monetary** **policy** regime switches according to a ﬁrst-order Markov process, while a second independent Markov process determines switching in the residual variance of the **monetary** **policy** rule. The countries investigated are France, Germany, Italy, the United Kingdom and the United States. Section 3 discusses the data and Section 4 presents the estimation results. Results show that the weights assigned to inﬂation and the output gap follow two distinct regimes. The ﬁrst **monetary** **policy** regime is associated with a high weight on inﬂation, while in the second regime the central bank follows an accommodative **policy**. Following the terminology of Owyang and Ramey (2000) one regime can be classiﬁed as “hawkish” because a high weight on inﬂation is associated with a low one on output, whereas the other regime can be termed as “dovish” with a high weight on output and a low weight on inﬂation. In addition, the consequences of participation in the EMS for France and Italy are explored. Switching in the residual variance is relevant for all countries and con- tributes signiﬁcantly to an improvement over a simple linear model. Results are found to be robust against changes in the deﬁnition of expected inﬂation and the output gap. Section 5 concludes.

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With BoJ **policy** under intense scrutiny in recent years, it is no surprise that there have been many efforts to use reaction function analysis to assess its reaction to the onset of the recession early in the decade. There is little agreement among these studies, however: Some find that the BoJ was too tight over this period, while others suggest its reaction was appropriate, or even that the call rate was set too low. Even those who agree that BoJ **policy** went from being “too loose” in the late 1980s to “too tight” in the early 1990s differ considerably as to exactly when the change took place. The variety of divergent assessments of the Japanese experience illustrates some of the pitfalls, discussed above, regarding the measurement problems inherent in the reaction function approach. In this section, we show that assumptions concerning the output gap are particularly important: Both the specification for the underlying trend in potential output and the use of real-time versus ex-post estimates in the analysis play a role. Whether assessments are made using a forward-looking specification, rather than Taylor’s original backward-looking equation, also makes a big difference in the appraisal.

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In an influential paper, **Taylor** (1993) proposed a simple **policy** rule for computing the nominal Fed Funds rate. **Taylor** argued that the nominal Fed Funds rate is the sum of four terms: the real interest rate, the inflation rate; the weighted deviation of inflation from the inflation target and the weighted output gap. Kohn (2007) evaluates this contribution of John **Taylor** and concludes that “his framework has been enormously important to policymaking in the Federal Reserve, and it has yielded many benefits. Nevertheless, it is important to keep in mind that some significant practical limitations also are associated with the application of such **rules** in real time. In other words, “it is not so simple to use simple **rules**” (p.3). Cochrane (2011) gives a comprehensive evaluation of the theoretical foundations of the **Taylor** Rule and argues that such a rule is not identified without unrealistic assumptions.

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The objective of this article is to determine if the Phillips curve is a relevant tool to conduct **monetary** **policy** in African countries wishing to adopt an inflation-targeting regime. I choose Nigeria as a case of study because it is in the early stage of the implementation of this regime. I estimate a medium-sized model for **monetary** **policy** analysis. The model reflects a synthesis between the New Keynesian and the Real Business Cycle (RBC) approaches. Then I estimate the model by using Bayesian econometric technique in order to overcome the shortage of data availability. The study concludes that there is evidence that central banks can control the inflation rate through a Phillips curve, a **Taylor** rule that includes the exchange rate, and the sterilization of the resources from oil exports. Nevertheless, there are limits to the stabilization program. The same evidence suggests that it is important to implement a credible inflation- targeting regime to reduce inflation gradually, instead of abrupt stabilization attempts with high costs in lost output.

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i t|t−1 denotes previous market expectations of the instrument rate, but with a systematic and transparent **monetary** **policy** as in current inflation targeting, instrument-rate surprises are small anyhow. In practical **monetary** **policy**, there are recent conspicuous deviations from instrument- rate smoothing, in Fed interest-rate reductions in the first half of 2001 and previously Willem Buiter’s voting in the Bank of England MPC. Deviations from Milton Friedman’s (1969) optimal quantity of money could motivate a quadratic interest-rate term (cf. Woodford 1999b), but since most money pays some interest these days, the distortion would seem to be minor, and it is diﬃcult to see that such costs could be significant compared to the costs of variability of inflation and the output gap. Woodford (1999c) has shown that an instrument-smoothing objective under discretion can induce a desirable history-dependence of **monetary** **policy**. In the perspective of this paper, though, a commitment to an optimal specific targeting rule is a more direct way of achieving such history-dependence. The practical importance of history- dependence also remains to be established, as noted above. Rudebusch (2002b) suggests that the high coeﬃcient on the lagged federal funds rate in estimated Fed reaction functions can be explained by the Fed reacting to persistent shocks rather than to some separate interest-rate smoothing objective. 56

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A potential shortcoming of the aforementioned analyses is the fact that all assume homogeneity of agents in the economy, despite the fact that heterogeneity is a universal feature in reality. Heterogeneity, if captured by structural parame- ters, can have an impact on the dynamics of an economy and affect the dynamic properties of **rules**. We focus on heterogeneity of expectations in the economy. Agents form either RE or adaptive expectations. In particular, we focus on het- erogeneous expectations in a NK model as elaborated in Branch and McGough (2009). We examine the consequences for local stability when the central bank conducts **monetary** **policy** by several simple **rules**. Thus, the analysis herein may be viewed as a kind of robustness-check for the numerical results of Bullard and Mitra (2002, 2007) mentioned above.

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For the first period (Table III), we obtain signs and coefficients quite close to those expected for the inflation and the output gap, when introducing inflation as an average of backward and forward values (equation III.1). However, the degree of interest rate smoothing is below the expected ( ρ = 0.19). Worse results are found when introducing the **monetary** aggregate (see III.2) and the exchange rate (see III.3). In the former, inflation does not appear to be significant and the implicit inflation target increases strongly (57.41 versus the 6.68 reference value). In contrast, the **monetary** aggregate is significant and shows the expected sign. That result would allow us to conclude that the nominal interest rate path might be explained by **monetary** variables during the first period of our sample. On the other hand, when introducing the exchange rate, all the variables but the exchange rate are significant and show the expected sign. For those reasons is difficult to describe this period by a **Taylor** rule.

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We conclude that, without assuming a forward-looking attitude of ECB **policy**-makers, past **policy** rate changes are identified as having been too small with respect to changes in inflation and the ECB’s **policy** reaction function does clearly differ from that of the Bundes- bank. However, once forward-looking behaviour of the ECB is taken into account, it has followed a stabilising course, i.e. nominal **policy** rate changes were large enough to actually influence real short term interest rates. In that case, it becomes more difficult to statistically distinguish between the way the Bundesbank has carried out its mandate of achieving price stability in the nineties and the way the ECB has done it since. Specifications using survey information, and therefore combining a forward-looking aspect with the use of real-time data, result in by far the best fit. Unlike for the US, the use of real-time – instead of ex-post data – does not make such a clear difference for any of our conclusions for the euro area.

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inconsistency principles. His survey also clarified important theoretical issues such as uniqueness and determinacy and he reviewed research on alternative targets and instruments, including both money supply and interest rate instruments. Like McCallum we focus on the robustness of **policy** **rules**. We focus on **policy** **rules** where the interest rate rather than the money supply is the **policy** instrument, and we place more emphasis on the historical performance of **policy** **rules** reflecting the experience of the dozen years since McCallum wrote. We also examine issues that have been major topics of research in academic and **policy** circles since then, including **policy** inertia, learning, and measurement errors. We also delve into the issues that arose in the recent financial crisis including the zero lower bound on interest rates and dealing with asset price bubbles. In this sense, our paper is complementary to McCallum’s **useful** Handbook of

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Farrell, 2007). Further, the **Taylor** rule has been criticised for being too simplistic, as it does not include all of the relevant information needed to conduct **monetary** **policy**. An omission that is a likely cause of the misspecification in the estimated reaction functions is only the inclusion of inflation and the output gap. Central banks may have other objectives, such as the maintenance of financial stability or an exchange rate objective which are not included with specific variables used in the **Taylor** rule. This issue becomes more important for countries where the exchange rate is not flexible and where their governments depend heavily on seignorage revenues due to their inability to generate revenues from other sources and to counter a larger budget deficit (Malik, 2007). Thus, an alternative variable has been included to enhance and better reflect the broader considerations of the central banks. The inclusion of additional or other production or **monetary** variables may help in a fuller analysis. An interesting point is to estimate if the **monetary** **policy** actually pursued can be captured satisfactorily by the estimated specification of the **Taylor**-type function.

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Although **monetary** aggregates have been traditionally used as a framework for **monetary** **policy**, Nelson (2003) comments that models where the only effect of **monetary** **policy** is via the short-term interest rate can be consistent with the quantity theory of money. Laxton and Pesenti (2003) also find that inflation forecast based **rules** perform better than conventional **Taylor** **rules** in small open emerging economies. Not surprisingly, **monetary** **policy** in emerging markets has increasingly moved towards inflation targeting and marked-based instruments (Fry et al., 1996).Given that other indicators may also be crucial in emerging markets, the **Taylor** rule has been extended to accomodate such features. One of such additional elements is the exchange rate (Filosa, 200; Mohanty and Klau, 2005; Devereux et al., 2006; Batini et al., 2009), which supports the “fear of floating” hypothesis. More recently, Mehrotra and Sánchez- Fung (2010) show that McCallum-**Taylor** specifications with an interest rate instrument and a nominal income gap target perform better than benchmark **Taylor** **rules** in describing **monetary** **policy** in inflation targeting emerging market economies.

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Several extensions could be considered in the future research. First, in the thesis, we evaluated **Taylor**-type **rules** which respond to the current inflation and output gap. Several contributions argue that responding to the past/expected inflation in **monetary** **policy** **rules** might improve welfare (see e.g. Benhabib et al., 2001; Clarida et al., 1998). So an investigation on improving welfare could be conducted by introducing backward/forward specifications of inflation gaps to interest-rate **rules**. Second, it is worth to introducing the Zero Lower Bound on nominal interest rates when analysing performance of **monetary** **policy** **rules**. As point out by **Taylor** and Williams (2010) and McCallum (2000), the zero-lower-bound problem might cause **monetary** **policy** inefficiency, leading variability on inflation and aggregate demand. An interesting analysis would be investigating **how** the zero-lower-bound problem affects ranking across different **monetary** **policy** **rules** considered in this thesis. The third extension would be, instead of using interest-rate **rules**, it would be interesting to consider the exchange rate exclusively in a **monetary** **policy** rule. The exchange rate-based **monetary** **policy** would be extremely **useful** for small and extremely open to trade economies (McCallum, 2007) – therefore, explore the potential benefit of **rules** which take the exchange rate as a targeting variable could be one possible future research.

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In the conditional variance equation, the negative ARCH(1) term for the Czech inflation suggests corrective or offsetting responses to the shocks to volatility in the previous period. The positive ARCH(1) terms for inflation in the remaining two countries would imply propagation of previous-period shocks, but the obtained estimates are not significant. The ARCH(1) term for the exchange rate is significant only in Poland, which is consistent with the pure float mechanism prevailing there. Its negative sign suggests corrective appreciation of previous- period local currency depreciation (or depreciation responding to a prior appreciation). The GARCH(1) terms for the Czech and Polish inflation series are positive, implying inter-period transmission of persistency in volatility. The same term is positive for the Czech and Hungarian exchange rates. It has a negative value for the Polish exchange rate series, implying reverse corrections to the persistency of volatility. It is worth noting that in all examined cases the sums of ARCH and GARCH coefficients do not exceed unity, suggesting an ongoing compression of volatility, or declining risk associated with the time-varying pattern of these variables. This is an important finding for their expected stability in the future and, therefore, for feasibility of application of a **policy** instrument rule that is based on these indicator variables. It shall be, however, noted that higher order ARMA and GARCH terms would likely yield more robust results, more suitable for forecasting purposes. Nevertheless, from the standpoint of examination of time-varying properties of individual variables their simplified treatment provides some **useful** information.

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Since John **Taylor** (1993) estimated the Federal Reserve **monetary** **policy** rule, there has been an increasing interest in building the model and the expla- nation of the efficiency of “active **monetary** **policy** **rules**”, that is a police that respond to an increase in inflation more that one-to-one increase in nominal interest rate. The basic idea is that in order to get a unique stable solution, poli- cymakers should use active **monetary** **policy** taking into account current infla- tion (Kerr and King, 1996) or future inflation expectations (Bernanke and Woodford, 1997; Clarida, Gali and Gertler, 2000).

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Since John **Taylor** (1993) estimated the Federal Reserve **monetary** **policy** rule, there has been an increasing interest in building the model and the expla- nation of the efficiency of “active **monetary** **policy** **rules**”, that is a police that respond to an increase in inflation more that one-to-one increase in nominal interest rate. The basic idea is that in order to get a unique stable solution, poli- cymakers should use active **monetary** **policy** taking into account current infla- tion (Kerr and King, 1996) or future inflation expectations (Bernanke and Woodford, 1997; Clarida, Gali and Gertler, 2000).

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We start in the next section with a review of the development of optimal simple **monetary** **policy** **rules** using quantitative models. We then consider the robustness of **policy** **rules** using comparative model simulations and show that simple **rules** are more robust than fully optimal **rules**. The most recent paper in the Elsevier Handbook in Economics series on **monetary** **policy** **rules** is the comprehensive and widely-cited survey published by Ben McCallum (1999) in the Handbook of Macroeconomics (**Taylor** and Woodford, 1999). Our paper and McCallum’s are similar in scope in that they focus on **policy** **rules** which have been designed for normative purposes rather than on **policy** reaction functions which have been estimated for positive or descriptive purposes. In other words, the **rules** we study have been derived from economic theory or models and are designed to deliver good economic performance, rather than to fit statistically the decisions of central banks. Of course, such normative **policy** **rules** can also be descriptive if central bank decisions follow the recommendations of the **rules** which they have in many cases. Research of an explicitly descriptive nature, which focuses more on estimating reaction functions for central banks, goes back to Dewald and Johnson (1963), Fair (1978), and McNees (1986), and includes, more recently, work by Meyer (2009) on estimating **policy** **rules** for the Federal Reserve.

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