Forwardlooking Taylors Rule Applied on Slovak Conditions

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Forward-looking Taylors RuleApplied on Slovak
Conditions
Rudolf Gavliak, Vladimír Úradnícek, Emília
Zimková Faculty of Economics Matej Bel
University, Banská Bystrica

• AMSE 2006, August 31 September 1, Trutnov

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1. Theoretical overview2. Specification of
Forward-looking Taylors Rule and Data 3.
Empirical Results4. Conclusion
Content

• AMSE 2006, August 31 September 1, Trutnov

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Rules-versus-Discretion Debate over Monetary
Policy

• AMSE 2006, August 31 September 1, Trutnov

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Rules-versus-Discretion Taylor Rule (1993)

• Where
• is federal funds rate,
• is the rate of inflation over previous 4
  quarters,
• is the deviation of real GDP from target.

• AMSE 2006, August 31 September 1, Trutnov

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Specification of rules and data Forward-looking
rule
The original Taylor rule models the nominal
interest rate in dependence on inflation gap and
GDP gap. If estimating a forward-looking Taylor
rule, the nominal key interest rate model could
be rewritten as Where denotes the
desired nominal rate if output and inflation are
at their target levels, denotes the
percent change in price level at period t,
denotes the target level of inflation in t-th
quarter, is the measure of average output
gap in t-th quarter, is the expectation
operator.

• AMSE 2006, August 31 September 1, Trutnov

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Specification of rules and data Expectations

• The forward-looking equation turns to classical
  Taylor rule equation, if the expected inflation
  and output gap are estimated as a function of
  inflation and output gap reached in previous
  quarter.

• The expected inflation is formed with respect to
  expectations in previous period and to actual
  value.

• If the expectations show some inertia, then
  exponential smoothing is quite good tool to model
  the central bank expectations.

• AMSE 2006, August 31 September 1, Trutnov

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Specification of rules and data Expectations

• If we expect persistence in expectations with
  linear trend and strong seasonal variation the
  Holt-Winters additive (three parameters)
  smoothing is most appropriate.
• The formula used to estimate the inflation
  forecast is
• Where
• is the expected inflation in v (tk)-th
  quarter,
• is the additive seasonal factor.

• AMSE 2006, August 31 September 1, Trutnov

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Specification of rules and data Expectations

• The three coefficients in smoothing equation are
  defined by the following recursions
• Where
• is actual rate of inflation in t-th
  quarter,
• are the damping (smoothing)
  factors,
• is the seasonal frequency (for quarterly
  data s  4).

• AMSE 2006, August 31 September 1, Trutnov

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Specification of rules and data Real interest rate

• If the consideration of central bank are formed
  in respect to real rate values, then the reaction
  function could be derived from the
  forward-looking equation
• Where
• denotes the average target level of
  inflation (long-run equilibrium value).

• AMSE 2006, August 31 September 1, Trutnov

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Specification of rules and data Systematic
reaction
The Taylor rule is quite restrictive to describe
actual changes in key interest rate because of
following reasons

• The central bank meets the decision about
  interest rate setting by consensus (voting in
  governors board).

• Central bank should react only to systematic
  changes in output and inflation and not to
  temporary fluctuations.

• Central bank has the tendency to smooth the
  deviations in output and inflation gap.

• AMSE 2006, August 31 September 1, Trutnov

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Specification of rules and data Interest rates
adjustment
If the actual key interest rate is a smoothed
value of proposed interest rate settings, it
could be modelled as exponential weighted average
of key interest rate past values and interest
rate level proposed by Taylor rule
is interpreted as degree of smoothing of
interest rate changing.

• AMSE 2006, August 31 September 1, Trutnov

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Specification of rules and data Interest rates
adjustment
Substituting interest rate adjustment equation
into forward-looking Taylor rule we get
Part of right side term in this equation
could be considered to equal an error term with
zero mean.

• AMSE 2006, August 31 September 1, Trutnov

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Specification of rules and data Final model
Unfortunately the error term is serially
correlated so, the Generalised Method of moments
(GMM) estimator should be used to estimate the
following model with correlated error term
The condition, which has to be met, means
independence among residuals and instruments
vector

• AMSE 2006, August 31 September 1, Trutnov

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Specification of rules and data Interest rates
adjustment
The estimated adjusted model contains large
number of lagged values of past nominal interest
rates setting. To reduce the number of estimated
parameters, we use the polynomial distributed
lags (PDL) specification. A polynomial
distributed lag model with order p restricts the
coefficients to lie on a p-th order
polynomial of the form

• AMSE 2006, August 31 September 1, Trutnov

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Specification of rules and data Interest rates
adjustment
The formula of the p-th order polynomial holds
for h 1,2,.....n and the constant c is given
by If we have closer look at interest rate
adjustment equation the nominal key interest rate
setting proposed by Taylor rule could be
expressed in this form

• AMSE 2006, August 31 September 1, Trutnov

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Specification of rules and data Interest rates
adjustment
After substituting the parameters in interest
rate adjustment equation and adding constant term
to the formula we have the h-lagged terms model
of key interest rate setting depending of
proposed past settings by the Taylor rule

• AMSE 2006, August 31 September 1, Trutnov

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Specification of rules and data Two-steps
estimation

• Our goal is to estimate the mathematically
  formulated model in two step procedure
• In first step we estimate (using GMM estimator)
  the following model with correlation of an
  unknown form present in residuals
• In second step we substitute the values of key
  interest rate setting proposed by Taylor rule (
  ) to interest rate adjustment equation and
  estimate the one step-ahead setting ( ).

• AMSE 2006, August 31 September 1, Trutnov

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Specification of rules and data Data
The data used to estimate the model in Slovak
conditions are
The dependent variable is the National Bank of
Slovakia (NBS) limit interest rate for 2W REPO
time series (If the interest rate changes during
a quarter, the interest rate is calculated as
weighted arithmetic average with days used as
weights).

• The following independent variables
• quarterly real GDP time series are used (NBS
  forecast),
• quarterly reported y-on-y inflation time series
  (NBS forecast),
• quarterly targeted inflation values (before year
  2005 the NBS prognosis as inflation target
  equivalent were considered).

• AMSE 2006, August 31 September 1, Trutnov

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Specification of rules and data Data
The instrument variables set contains

• quarterly time series of lagged inflation rate,
• lagged National Bank of Slovakia (NBS) limit
  interest rate for 2W REPO time series,
• lagged GDP gap time series,
• lagged M2 growth rate and
• lagged producer price index in coal and oil
  production sector.

The estimation was carried out with help of
Eviews 4.1 and the analysed period was Q12000 to
Q42008.

• AMSE 2006, August 31 September 1, Trutnov

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Empirical results Problems and solutions

• The quarterly targeted inflation values are
  accessible only since year 2005.

• The targeted inflation values for previous
  period are not reported, but we have used the end
  year inflation forecasts published in monetary
  program instead of targeted inflation.

• Using the Winters-Holt additive exponential
  smoothing algorithm we computed forecasts of
  inflation until year 2008.

• The potential GDP was estimated by the
  Hodrick-Prescott filter, which is smoothing out
  the real GDP time series.

• The independent variables (output and inflation
  gap) are stationary.

• AMSE 2006, August 31 September 1, Trutnov

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Empirical results Independent variables

• AMSE 2006, August 31 September 1, Trutnov

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Empirical results Resulting model

• Because of high inflation pressures at the
  beginning of the year 2000 we shifted the
  beginning of input data period to first quarter
  2001.
• The resulting estimation form of the first stage
  estimated equation is

• AMSE 2006, August 31 September 1, Trutnov

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Empirical results Resulting model

• In second step we estimate the autocorrelation
  structure of interest rate setting using the
  polynomial distributed lags (PDL) specification
  and consequently to estimate ?. The estimated
  dependence among proposed key interest rate
  setting ( ), current and historical setting (
  ) is

• AMSE 2006, August 31 September 1, Trutnov

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Empirical results Resulting model

• Expressing the nominal interest rate we could
  compute an one step-ahead forecast as a function
  of interest rate proposed by Taylor rule and past
  nominal key interest rates.
• When replacing the nominal interest rate with
  the one step-ahead estimate, we can estimate a
  projection of key interest rates setting from 3rd
  quarter 2006 till 4th quarter 2008.

• AMSE 2006, August 31 September 1, Trutnov

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Conclusion Concluding remarks
The economic interpretation of estimated
parameters is following

• Parameter ß shows that if inflation gap changes
  per 1 p.p. the nominal key interest rate of the
  central bank will change in average by 0.17 p.p.

• Regarding estimated parameter ?, if GDP gap
  changes per 1 p.p. the nominal key interest rate
  of the central bank will change by 19.47.

• Large differences in estimated parameters
  reflect different volatility of independent
  variables. While the inflation gap is highly
  volatile, the output gap is rather smooth.

• Estimated ? parameter shows that change by 1
  p.p. is in average reflected by 0.46 p.p. in the
  real key interest rate setting change.

• AMSE 2006, August 31 September 1, Trutnov

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Conclusion Concluding remarks

• According forecast of the model the key interest
  rate of the central bank at the end of 2007
  should increase by 1,3 p.p. on the level 5,3.

• An increase of the key interest rate is also
  expected by the financial markets due to fact
  that in the next year the real gross domestic
  product is expected to be above its potential and
  real inflation is expected to be above the
  targeted level.

• The Taylor rule should not be taken as ultimate
  advice but they should serve as a starting point
  for discussions on the key interest rate setting.

• After the Slovak elections in June 2006 the
  prediction of any economic variable became rather
  difficult and it will be more reliable when first
  steps of new government will be known.

• AMSE 2006, August 31 September 1, Trutnov

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Thank you for your attention !
Rudolf Gavliak, Vladimír Úradnícek, Emília
Zimková Faculty of Economics Matej Bel
University, Banská Bystrica

• AMSE 2006, August 31 September 1, Trutnov