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STUDIES THE TAYLOR RULE: APPLICATION AND LIMITS 1 The Taylor rule was popularized in 1996 in a study by Goldman Sachs. It is regularly mentioned in official publications by French and international organizations, notably the OECD, and is now a common part of the monetary policy debate. The rule, which aims to define a code of conduct for the monetary authorities, is based on the calculation of an "optimal" short-term interest rate that is compatible with the central bank's inflation objective and the trend in the output gap. The Taylor rate thus calculated is compared with the actual short-term interest rate in order to assess the suitability of monetary policy in light of economic fundamentals. This paper is firstly devoted to formulating a Taylor rule. When this rule is applied retrospectively to France, the results are inconclusive. Secondly, an illustration is given of the rule's sensitivity to its parameters and the more or less arbitrary way in which these parameters are chosen, which casts doubt on the rule's normative value. FRANÇOISE DRUMETZ ADRIEN VERDELHAN Monetary Research and Statistics Division Monetary Policy Research Unit 1 The study was published in the Banque de France Bulletin No. 45 (September 1997) BANQUE DE FRANCE BULLETIN DIGEST – No. 46 – OCTOBER 1997 35 STUDIES The Taylor Rule: Application and Limits Barro and Gordon1 showed that monetary policy must be credible in order to be efficient and that a policy based on rules of conduct is more credible than a discretionary policy. A school of thought in academic literature has tried to identity operating rules for monetary policy that will minimize or even "discretion". Friedman, for example, advocated an automatic (or non-activist) rule, i.e. independent of the state of the economy, whereby the central bank should aim for a constant rate of growth in the money supply. Since the indiscriminate application of automatic rules risks causing a high degree of variability in output, other writers such as McCallum attempted to define non-automatic (or activist) monetary policy rules. These "activist" rules stipulate that the monetary policy stance may be changed according to events affecting the economy. They therefore include feedback. However, their complexity is often a barrier to operational use. The Taylor rule is part of this search for an "activist" monetary policy rule and ways of inserting it into the central bank's decision-making process. Unlike other rules of this type, it links the very short- term interest rate level, which is controlled by the central bank, to inflation and the output gap and is thus simple and attractive. This has undoubtedly been a factor in its success. The Taylor rule was first presented in 1993 and was refined and popularized by a Goldman Sachs study in 1996. In this later form, it is regularly mentioned in official publications by both French and international organizations, such as the Ministry of Economic Affairs and Finance and notably the OECD in its latest annual study of France. The Taylor rule is thus now a regular feature of the monetary policy debate. 1. Building a Taylor rule and the Results Obtained in the Case of France While the theoretical formulation of the Taylor rule is attractive, its application to France proved inconclusive. 1.1. Attractive Formulation 1.1.1. The Initial Taylor Rule With the aim of studying "the role of monetary policy rules in a world where the simple and algebraic formulation of such rules cannot and should not be applied mechanically by decision makers", Taylor put forward the following "hypothetical yet representative" rule for the United States2: r = 2 + p + 0.5y + 0.5 (p – 2) where r is the Federal Funds rate, p the rate of inflation of the last four quarters and y the gap between real effective GDP and trend GDP. When inflation is equal to its target value of 2% and GDP reaches its trend value, the real interest rate or neutral rate (2%) is equivalent to the economy's trend rate of growth, i.e. 2.2% over the period 1984-1992. Taylor observed that this very simple "hypothetical" rule gives a fairly true representation of the Federal Funds rate trend, i.e. it is close to the reaction function of the American monetary authorities, over the period 1987-1992. The only notable exception was 1987 owing to the impact of the stock market crash. 1 R. Barro and D.B. Gordon, "Rules, Discretion and Reputation in a Model of Monetary Policy", Journal of Monetary Economics No. 12, 1983. 2 J.B. Taylor, "Discretion Versus Policy Rules in Practice", Carnegie-Rochester Conference Series on Public Policy, No. 39, 1993. 36 BANQUE DE FRANCE BULLETIN DIGEST – No. 46 – OCTOBER 1997 STUDIES The Taylor Rule: Application and Limits 1.1.2. The Taylor Rule Generalized Goldman Sachs1 partly adapted the initial Taylor's rule and highlighted the need to take account of inflation expectations as shown in the equation that follows: rnominal = rneutral real + pexpected + 0.5y + 0.5 (p – ptarget) where the notations are the same as in the preceding equation and pexpected is expected inflation and ptarget the inflation target chosen by the central bank. The inflation target can thus vary according to the country and/or the period and the formal introduction of inflation expectations makes it possible to get closer to the behaviour of a central bank, which has to take preventive action. On the other hand, the weightings of the gap between expected inflation and its target and the output gap remain set at 0.5 as with Taylor. Goldman Sachs, followed by the OECD2, generalized the adapted version of Taylor's equation by applying it to all the G 7 countries, particularly to French data. With respect solely to the choice of variables in the equation, their work calls for two remarks: – determining pexpected is delicate. It can either be calculated using an econometric model, be taken from the Consensus Forecasts of the International Monetary Fund (IMF), or approximated using the current rate of inflation. In practice, the latter solution is generally employed; – as McCallum noted3, to calculate the neutral rate at date q, Taylor and the successive users of his rule use data unknown at that date by the central bank because of the time needed to calculate them4. This limits the operational usefulness of the results obtained. 1.2. Inconclusive Results in the Case of France While retrospective application of the Taylor rule to American data made it possible to trace approximately the trend in the short-term Federal Funds rate over the period 1987-1992, a similar calculation with French data gives inconclusive results. In order to highlight this phenomenon, the parameters used in this earlier work should be employed and the Taylor rate should be compared with the actual Pibor 3-month rate. 1.2.1. Building the Taylor Rule In order to take into account in the calculation of the Taylor rate at date q only the data available at this date, the following formula is used: rnominal (q) = rneutral real + psmoothed(q – 1) + 0.5y(q – 1) + 0.5(psmoothed(q – 1) – ptarget) where psmoothed(q – 1) is the inflation rate calculated in the preceding quarter thanks to exponential smoothing of the growth rate of the consumer price index5. The neutral rate will be taken as equal to 3.5% (as advocated by Goldman Sachs) and the inflation target as 2%. The output gap used is that calculated by the Banque de France French Macroeconomic Research Unit (SEMEF). 1 Goldman Sachs, "The International Economic Analyst", volume 11, issue 6, June 1996. 2 Annual study of France 1996-1997, in particular. In practice, the OECD adopted the methodology of Goldman Sachs. 3 B. McCallum, "Discretion Versus Policy Rules in Practice: Two Critical Points. A Comment". Carnegie-Rochester Conference Series on Public Policy, No. 39, 1993. 4 Goldman Sachs and then the OECD thus use the output gap of the current period and the current rate of inflation (as a proxy for expected inflation). By contrast, in his work on the United Kingdom A. Stuart also takes the current rate of inflation, but one quarter removed to take account of the usual time needed to calculate this index - and thus to make it available to the central bank. 5 The smoothed rate of inflation in quarter q is calculated using the actual inflation rate according to the following formula, in which the attenuation coefficient in the exponential smoothing is taken to be equal to 0.5: psmoothed(q) = 0.5p(q) + 0.5psmoothed(q – 1). BANQUE DE FRANCE BULLETIN DIGEST – No. 46 – OCTOBER 1997 37 STUDIES The Taylor Rule: Application and Limits 1.2.2. Retrospective Application to France The following graph shows the trend in the calculated rate and the nominal market rate observed since 1994. TAYLOR RATE COMPARED BREAKDOWN OF TO THE PIBOR 3 MONTH RATE THE TAYLOR RATE 8% 3% 3% 7% 2% 6% 2% 5% 1% 1% 4% 0% 1994-Q1 1995-Q1 1996-Q1 1997-Q1 3% -1% 2% -1% 1994-Q1 1994-Q2 1994-Q3 1994-Q4 1995-Q1 1995-Q2 1995-Q3 1995-Q4 1996-Q1 1996-Q2 1996-Q3 1996-Q4 1997-Q1 1997-Q2 -2% -2% 3-month PIBOR Taylor rate Output gap Inflation gap Smoothed inflation rate Comparison of the Taylor rate and the Pibor 3-month rate over the period 1994-1997 reveals two periods. Analysis of these periods is facilitated by breaking down the Taylor rate: – from 1994 until the last quarter of 1995, the Taylor rate and the market rate were approximately in step. The difference between the calculated rate and the actual rate, due to tensions on the foreign exchange market which necessitated a provisional hike in short-term rates in the first six months of 1995, declined substantially in the second half of the year and reached zero at the end of the year; – beginning in 1996, the actual rate fell below the Taylor rate. The Taylor rate therefore only shows in a very approximate fashion the past trend in the short-term rate. However, one cannot infer a judgement on the suitability of the monetary policy conducted since 1994 with regard to economic fundamentals, since the Taylor rule is highly sensitive to the choice of coefficients and reference variables. 2. Sensitivity of the Taylor Rule to its Coefficients and Reference Variables The retrospective and operational scope of the Taylor rule is undermined by: – the fact that it is more descriptive than normative, which results from the choice of the coefficients used in the equation; – the margin of uncertainty, which affects the determination of the reference variables used in the equation (neutral real interest rate, output gap). 38 BANQUE DE FRANCE BULLETIN DIGEST – No. 46 – OCTOBER 1997 STUDIES The Taylor Rule: Application and Limits 2.1. Is the Taylor Equation Normative or Descriptive? The Problem of the Choice of Coefficients 2.1.1. The Conditions for the Application of the Rule as Envisaged by Taylor It should be remembered that two coefficients are used in the Taylor rule: one (α 1) before the output gap, the other (α 2 ) before the gap between actual inflation and the inflation target. Taylor took these coefficients to be equal to 0.5, without really justifying this choice other than on the grounds that the equation thus formulated reproduced in a satisfactory manner the past behaviour of the American monetary authorities. Moreover, he stated that there was no way of determining whether α 1 should be greater or smaller than α 2 . Accordingly, examining the manner in which this rule could be incorporated in practice into the decision-making process, he concluded that its implementation could only be highly pragmatic. For example, he suggested that the range of indicators available to the Federal Open Market Committee (FOMC) be supplemented by Federal Funds rate forecasts obtained using the rule. If, as was the case from 1987 to 1992, these forecasts proved to be in line with the decisions taken in the absence of the rule, it would be possible for the rule to impose itself gradually, which would be a guarantee of continuity when member of the FOMC are renewed. Alternatively, he proposed that the FOMC examine several versions of the rule resulting from the application of different coefficients. 2.1.2. There is no Precise Basis for the Choice of the Coefficients Used in the Taylor Rule, Particularly in the Case of France As can be seen, the genesis of the Taylor rule is marked by a gradual slide: – from the descriptive towards the normative (or from the notion of central bank reaction function towards that of monetary policy rule), as Taylor suggests in substance that the FOMC sets up its reaction function as a rule; – and from the normative towards the indicative, as Taylor explicitly suggests that his rule be inserted, in any case initially, into the battery of indicators monitored by the Federal Reserve System or that it not be applied mechanically. It should be noted that a reaction function cannot systematically be used as a monetary policy rule. The Taylor equation is based on coefficients that are themselves based on observation of the past behaviour of the monetary authorities. These coefficients influence the trajectories of output and inflation. In order to be able to claim normative rule status for his equation, Taylor would have had to have shown that these trajectories are optimal, which he failed to do. L. Ball1 is aware of this weakness and links these coefficients to a trade-off between output variances and inflation variances: a simple economic model then allows him to suggest a relation between α 1 and α 2 (for example, for α 2 = 0.5, the Taylor rate would be optimal if α 1 = 1). Most later users of the rule kept the value of 0.5 for all countries studied, including France. The rigidity of this option goes against Taylor's suggestions and seems particularly ill-founded in that it cannot, unlike in the case of the United States, be based on the past behaviour of the monetary authorities (see 1.2.). In this respect, it may be noted that the formulation of the rule does not take into consideration strategies involving an intermediate exchange-rate objective. 1 L. Ball, "Efficient Rules for Monetary Policy", NBER Working Paper No. 5952, March 1997. BANQUE DE FRANCE BULLETIN DIGEST – No. 46 – OCTOBER 1997 39 STUDIES The Taylor Rule: Application and Limits 2.2. The Reference Variable Problem The following examples highlight the fact that the assessment likely to be made of monetary policy is closely linked to the way the reference values of the Taylor rule (neutral real interest rate, output gap) are calculated. 2.2.1. Neutral Real Interest Rate Setting the level of the neutral rate is subjective. In the initial Taylor rule, the neutral real rate is a constant, equal to the economy's trend rate of growth over the period studied. Goldman Sachs obtains this rate by making discretionary corrections to the average of the real interest rate of the last ten years, according to the varying degrees of tightness of monetary policy in the course of the period. It would have been equally arbitrary to take as a neutral rate the average of the real short-term rate in the course of the last ten years, i.e. 5.7%, 2.2 points higher than the value used in the Goldman Sachs study. This change, which entails a 2.2 point upward translation of the Taylor rate, would help to substantially reduce the differences observed. TAYLOR RATE COMPARED TO THE PIBOR 3-MONTH RATE Sensitivity to the neutral rate Sensitivity to the output gap 9% 8% 8% 7% 7% 6% 6% 5% 5% 4% 4% 3% 3% 2% 2% 1994-Q1 1994-Q2 1994-Q3 1994-Q4 1995-Q1 1995-Q2 1995-Q3 1995-Q4 1996-Q1 1996-Q2 1996-Q3 1996-Q4 1997-Q1 1997-Q2 1994-Q1 1994-Q2 1994-Q3 1994-Q4 1995-Q1 1995-Q2 1995-Q3 1995-Q4 1996-Q1 1996-Q2 1996-Q3 1996-Q4 1997-Q1 1997-Q2 3-month PIBOR 3-month PIBOR Taylor rate -BDF/SEMEF Taylor rate (neutral interest rate=3.5%) Taylor rate-OECD Taylor rate (neutral interest rate=5.7%) 2.2.2. Influence of the Way the Output Gap is Calculated The potential rate of growth can be calculated by modelling or by trend estimation. The results differ considerably according to the sources and the methods: for example, in 1995, the estimates of the output gap, calculated by the Banque de France, Goldman Sachs or the Direction de la Prévision of the French Ministry for Economic Affairs and Finance, ranged from -0.5% to -3.5% for France1. The above graph makes it possible to compare two Taylor rates, one calculated with SEMEF data, the other with OECD data that was reprocessed into quarterly form. The two estimates differ substantially: the output gap calculated by the SEMEF is less strongly negative than that of the OECD, and this is naturally found in the Taylor rule. A Taylor rate that took account of these SEMEF estimates would thus be higher than an OECD Taylor rate and gap between the actual rate and the calculated rate would be reduced by an average of 110 points over the period 1994-1997. 1 G. Cette, H. Delessy, "Output Gaps: A Wide Variety of Methods and Diagnoses"; Économie Internationale, No. 69, 1st quarter 1997. The Direction de la Prévision calculates a long-term output gap, whereas all the calculations and graphs in this paper use short-term output gap data provided by the SEMEF. The maximum difference between these two output gap estimates is 140 points. 40 BANQUE DE FRANCE BULLETIN DIGEST – No. 46 – OCTOBER 1997 STUDIES The Taylor Rule: Application and Limits It thus appears that the Taylor equation is very sensitive to the choice of reference variables1. The uncertainty that affects the determination of neutral real interest rate levels and output gap levels may lead, from a retrospective point of view, to divergent assessments of the suitability of monetary policy with respect to economic fundamentals. It should be noted, from a prospective point of view, that this uncertainty also undermines the operational scope of the Taylor equation since it is likely to give rise to divergent recommendations as to the direction to be given to monetary policy. In all, the Taylor equation should be analyzed as a reaction function of the Federal Reserve System set up as a decision-making rule, with more indicative than normative value, as the author implicitly recognizes. Given these elements, it appears that rigid application of the initial coefficients of the rule to all of the G 7 countries is improper and undermines the indicative scope of the rule, as does the difficulty in determining the equation's reference values. 1 One could also add, with regard to the inflation target, which is considered constant and taken as equal to the declared or implicit objective of the central bank, that this choice is only valid for short homogenous periods in terms of inflation. Goldman Sachs evaluates the inflation target of the central bank at 2%. This value is more open to criticism if the same target is applied over a long period since the pace of disinflation desired by the monetary authorities is then not taken into account. For example, in 1985, 2% could be a medium-term target but probably not a very short-term target as inflation was still around 5%. BANQUE DE FRANCE BULLETIN DIGEST – No. 46 – OCTOBER 1997 41