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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

				
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