EVALUATING CORE INFLATION INDICATORS

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EVALUATING CORE INFLATION INDICATORS Carlos
Robalo Marques Pedro Duarte Neves Luís Morais
Sarmento
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WHY SHOULD CENTRAL BANKS AVOID THE USE OF THE
UNDERLYING INFLATION INDICATOR Carlos Robalo
Marques Pedro Duarte Neves Afonso Gonçalves da
Silva
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MOTIVATION

• PURPOSE OF THE FIRST PAPER
• To propose a set of testable conditions to
  evaluate alternative core inflation indicators.
• PURPOSE OF THE SECOND PAPER
• To test the excluding food and energy
  indicators for several countries using the
  criteria suggested in the first paper.

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CORE (OR TREND) INFLATION DEFINITION

• We assume that, for any given period t, we have
  by definition
• Where
• Inflation
• Core or trend inflation
• Temporary component, with .
• Note that we cannot have , because in
  this case will include a permanent component
  (the expected value of ), which, by
  definition, must be included in

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COMMENTS ON SOME COMMONLYSUGGESTED EVALUATION
CRITERIA

• HABILITY TO FORECAST FUTURE HEADLINE INFLATION
• Laflèche (1997), Bryan and Cecchetti(1994),
  Freeman(1998) Vega and Wynne (2001)
• First comment Evaluation is made in relative
  rather than absolute terms, and so no conclusion
  can be drawn on the properties of the selected
  indicator(s).

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• Second comment the forecast ability is not a
  sensible requirement for a core inflation
  indicator. In fact, we should not expect a core
  inflation measure to be a good predictor of
  future headline inflation because is the
  long run component of and the long run
  component has no information about the short run.
• By definition - and so in the
  model ƒ( ) we have in fact
  ƒ( ).
• Can we expect to be able to forecast (
  ), as has no information about ? Of
  course, not.
• Statistical argument
• A smooth series ( ) cannot (by definition)
  be able to accurately forecast a volatile series
  ( ).

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THE REFERENCE MEASURE APPROACH

• Ex Bryan and Cecchetti (1994), Bryan, Cecchetti
  and Wiggins II (1997), Bakhshi and Yates (1999),
  Coimbra and Neves (1997), Vega and Wynne (2001)
• The selected indicator is the one that best
  approximates the reference measure (minimises
  the MSE) usually a centred moving average of the
  inflation rate.

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Comment

• The properties of the reference measure are
  unknown
• If the reference measure is not the best proxy
  for the unknown true trend of inflation, this
  approach does not guarantee that the best
  indicator is selected, as the core inflation that
  best approximates the reference measure is not
  necessarily the one that best approximates the
  true trend of inflation

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NECESSARY CONDITIONSIMPORTANT ASSUMPTIONS

• . We assume that, for any given period t, we have
  by definition

• . The temporary disturbances in the inflation
  rate, , are caused by developments such as
  changes in weather conditions, disturbances in
  the supply of goods, etc.

3. By definition is expected to have zero
mean and finite variance, and therefore,
non-stationary is excluded on theoretical
grounds. 4. In what follows it is assumed that
, the inflation rate, is I(1). 5. The candidates
to be a core inflation measure are timely and not
subject to revisions.
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NECESSARY CONDITIONS (CONT.)

• When inflation, , is I(1), we say that is
  a core inflation measure if

I) is I(1) and and are
cointegrated with unitary coefficient, i.e.,
- is a stationary variable with zero
mean

• Condition i) follows directly from the definition
  of core or trend inflation and implies that
  inflation and the core inflation measure cannot
  exhibit a systematically diverging trend, in
  which case the latter will give false signals to
  the monetary authority.
• This condition was first proposed in Freeman
  (1998).

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NECESSARY CONDITIONS (CONT.)

• If does not have zero mean, then
  is not capturing the whole
  systematic component of .
• Also, if is stationary, but
  , does not account for the whole
  permanent component of . The net result
  shall correspond to either a faster (if )
  or slower (if ) systematic growth of
  vis-à-vis and therefore the two variables
  tend to drift apart.

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NECESSARY CONDITIONS (CONT.)

• ii) There is an error correction mechanism given
• by
• for , i.e.,
  may be
• written as
• Condition ii) implies that if is a trend
  measure of then must be an attractor
  for , in the sense that in the long run,
  must converge to . So, we must have
• in the ECM model.

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NECESSARY CONDITIONS (CONT.)

• If this is not the case the use of as a
  core inflation measure is not useful at all. If
  there is no reason to expect that will
  converge to , there is no point in knowing
  whether in a given period is above or below
  . However, if condition ii) holds, we can
  ensure that if in a given period is above
  (below) , there is a reason to expect that,
  sooner or later, will start to decrease
  (increase) and converge to .
• Condition ii) is a special case of Granger
  causality. In particular, this condition requires
  that Granger causes through the error
  correction term. In this sense, is a
  leading indicator of .

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NECESSARY CONDITIONS (CONT.)
iii) is strongly exogenous for the
parameters of the previous equation.

• Condition iii) aims at preventing that condition
  ii) does occur the other way around, i.e. that
  is not an attractor for and also that is
  not sensitive to observed outliers in .
  Otherwise it will be very difficult, if not
  impossible, to anticipate the future path of
  inflation by looking at .
• The fact, for instance that in a given period
  is above , allows us to anticipate
  the
• future path of only if is not a
  function of .

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NECESSARY CONDITIONS (CONT.)

• Strong exogeneity of implies simultaneously
  that the error correction term does not appear in
  the equation for (i.e., that is weakly
  exogenous for the parameters of the cointegrating
  vector) and also that does not Granger cause
  .
• In other words, condition iii) implies that in
  the error correction model for
• we must have

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HYPOTHESIS TESTING

• Condition i) use unit root tests on the
• series , in order to
  assess if
• is a zero mean stationary variable.
• Alternative Johansen approach to test for
  cointegration between and and see
  whether (1, -1) is a cointegrating vector.
• Condition ii) test the hypothesis
  using the conventional t-ratio of in
  following ECM
• Alternative use the Johansen approach to show
  that is not weakly exogenous for the
  parameters of the cointegrating vector.

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HYPOTHESIS TESTING (CONT.)

• Condition iii) test the hypothesis
• in the following ECM model
• The test of this condition is carried out in two
  steps
• i) week exogeneity is tested (? 0) using the
  t-ratio of or the Johansen approach (weak
  exogeneity of )
• ii) Test (?1 ?2 ?s 0) only for the
  weakly exogenous indicators, i.e. meet the first
  step.

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EVALUATING THE CORE INFLATION INDICATORS FOR THE
UNITED STATES

• (1) The Excluding food and energy indicator
  (EFE)
• (2) The 8 (symmetric) trimmed mean (TM8)
• (3) The median of price changes distribution
  (MED)
• MAIN CONCLUSIONS
• TM8 and MED meet the three conditions and so can
  be used as useful core inflation indicators.
• TM8 is slightly less volatile than MED.
• The EFE indicator does not meet conditions ii)
  and iii).

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EVALUATING THE EXCLUDING FOOD AND ENERGY
INDICATOR FOR 6 COUNTRIES
(1) USA (2) Germany (3) France (4) Italy (5)
Spain (6) Portugal MAIN CONCLUSION For none of
the six countries does the EFE indicator meet the
3 conditions. For USA, Germany and France the
EFE indicator fails conditions ii) and iii)For
Italy and Portugal fails condition i) For Spain
fails condition ii)
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Comment on the results
The conclusion that the EFE indicator does not
meet conditions ii) and iii) was to be expected.
In fact, in order to compute the EFE indicator we
exclude from the CPI, the prices of energy and
unprocessed food, which are goods that enter as
intermediate inputs into the production process.
Therefore, changes in the energy or in the
unprocessed food directly and contemporaneously
affect the CPI inflation, but affect the prices
of the other CPI items, i.e. the EFE indicator,
only with a lag. This being so, the prices of
energy and unprocessed food are a leading
indicator of the EFE indicator, and as they
affect prices contemporaneously, the inflation
rate itself also appears as a leading indicator
of the EFE indicator.