The Academy of Economic Studies Doctoral School of Finance and Banking

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The Academy of Economic StudiesDoctoral School
of Finance and Banking

• Monetary Policy Rules Evaluation using a Forward
  
• Looking Model for Romania

MSc student Murarasu Bogdan Coordinator
Professor Moisa Altar
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I motivate the importance of my topic by the
following remark of

• John Taylor (1998) researchers first build a
  structural model of the economy, consisting of
  mathematical equations with estimated numerical
  parameter values. They then test out different
  rules by simulating the model stochastically with
  different policy rules placed in the model. One
  monetary policy rule is better than another
  monetary policy rule if the simulation results
  show better economic performance.

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CONTENTS

• Policy evaluation with a forward looking model
• Estimation (calibration) of the model
• Klein algorithm (generalized Schur decomposition)
• Central banks loss function and the optimization
  problem
• Optimal monetary policy rules

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The forward looking model

• Coats, Laxton, and Rose (2003) argued that in
  order to support the policy decisions necessary
  to respect a target for inflation, the framework
  had to be forward-looking and capable of dealing
  with the process of controlling inflation.

(1)

• Another specification of the system includes the
  real effective exchange rate in the IS curve.
  Taking into consideration that are no great
  differences between the two cases regarding the
  methodology and even the main results, I will
  describe the procedure I follow referring to
  first model.

• This model introduces two layers of complexity
  1. agents actions depend upon expected future
  output and inflation which may cause the
  existence of zero or many reduced form equations
  2. the system must be solved for simultaneity.

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Estimation vs. Calibration

• Problems
• data are very limited, both in terms of the
  coverage and the duration of series
• data sample is very short and describes a period
  of major structural change in the economy and
  major change in policy regimes

These are reasons to expect very imprecise
identification of the parameters from any
estimation.

• Solutions
• I chose a full information method of estimation
  (3SLS) in order to solve for simultaneity
• after estimation I kept the coefficients that
  were statistically or economically significant
• I applied a kind of calibration for the
  coefficient from the Phillips curve which
  is statistically and economically inconsistent

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Data used in estimation

• The model is fitted to quarterly data for the
  Romanian economy for 1998Q1 2006Q2, subject to
  the restriction that the coefficients of the
  policy rule minimize a quadratic loss function.

deviation of inflation from its target
(inflation is measured as a percentage change of
headline CPI, quarter-over-quarter, at annual
rates and is seasonally adjusted using Demetra
(Tramo-Seats))
For the interest rate gap I applied a
Hodrick-Prescott filter to the data and I
computed the gap as a deviation from the trend.
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Structural parameters

• quality of the instruments in 3SLS estimation

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The stability of the coefficients from the two
curves across the interval of variation of
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Structural system is written in Klein format as
(1)
is a vector of predetermined variables

the forward looking or non-predetermined
variables
Reduced form of the system (Klein(2000) algorithm)

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Klein algorithm (generalized Schur decomposition)

• solves systems of linear rational expectations
• the system need to be solved distinctly for the
  predetermined variables (or backward-looking in
  the language of Klein) and non-predetermined ones
  ( or forward looking variables)
• infinite and finite unstable eigenvalues are
  treated in a unified way
• preferable from a computational point of view to
  other similar numerical methods

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• for the pair of square matrices from
  the equation (1) the orthonormal matrices and the
  upper triangular matrices exist
  such that
  (2)
• The generalized eigenvalues of the system are the
  ratios where and are
  the diagonal elements of and
• The decomposition matrices can be transformed so
  that the generalized eigenvalues are arrayed in
  ascending modulus order (stable eigenvalues come
  first corresponding to backward looking variables
  and unstable come next corresponding to forward
  looking variables)

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Solutions
(3)
(4)
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Reduced form

• Now I have the structural system (1) written in
  the reduced form as
• is a
  vector of predetermined variables

(5)

• Taking into account equation (5) we can recover
  the covariance matrix of structural errors from
  the covariance matrix of reduced form errors with
  the relationship

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Loss function

• The central bank chooses the values for the
  coefficients from the reaction function that
  minimize the loss function

• is a matrix of policy weights that represent
  the relative importance to the central bank of
  stabilizing inflation, output and interest rate
  (stabilization objectives).
• These weights range between zero and one and sum
  to one in order to determine whether the
  performance of the policies is sensitive to
  policy objectives (represented by the weights
  assigned to stabilize inflation, output and
  respectively interest rate).

• By minimizing the loss function I also obtain
  optimal values for the coefficients of the
  reaction function

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Computation of the loss function
Because the reduced form errors are linear
combinations of the serially uncorrelated
structural errors, they are serially uncorrelated.
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Correlograms and serial correlation LM test for
the structural errors

• Tests for no autocorrelation of the residual
  (residual from IS curve)

• Tests for no autocorrelation of the residual
  (residual from Phillips curve)

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Alternative policy rules

• The interest rate rules proposed by John Taylor
  are the most used ones. Taylor Rule with Interest
  Rate Smoothing

• Original Taylor Rule (Taylor, 1993) assigns exact
  coefficient values that describe Federal Reserve
  policy

• Optimal Taylor Rule but chooses the
  values for and that minimize the
  loss function of the central bank

• Taylor Backward-Looking Rule, where lagged values
  of output and inflation replace the current
  values of the two variables

• Full State Rule (respond to all, rather than a
  subset, of the variables in the state vector)

• Woodford (2002) attributes to Goodhart a simple
  rule where the central bank responds only to
  deviations of the inflation rate from its target
  value and choosing an optimal value
  for

• Clarida, Gali and Gertler (1998) suggest that
  forecast-based rules are optimal for a central
  bank with a quadratic objective function

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Results

• Table 1 reports the policy rule that achieved the
  lowest loss level for each set of policy
  objective weights considered.

Taylor Rule with Interest Rate Smoothing
Goodhart Rule
Expected Inflation Rule
In the case where NBR gives an important weight
to inflation stabilization, as this is its
primary objective and output represents an
important but secondary objective, the Taylor
Rule with Interest Rate Smoothing is the best
rule to adopt.
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Relative performance of the rules
The figure shows that the Taylor Rule with
Interest Rate Smoothing performs at all times
better than the Taylor Backward Looking Rule.
When the NBR is preoccupied by the stability of
output then it has to respond currently to output
gap and not with a lag.
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Taylor with Interest Rate Smoothing vs. Full
State Rule and Goodhart Rule
The figure shows the superiority of the Taylor
rule against the rule which takes into
consideration the entire state vector. This rule
performs better than the Taylor type rule only
when the stability of inflation is the only
objective of the central bank.
The figure shows that this simple rule can
perform better than the Interest Rate Smoothing
Rule when the output weight is small and also
that the performance of this rule is not
sensitive to weight assigned to interest rate
stabilization.
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Full State Rule vs. Expected Inflation and
Taylor Backward Looking vs. Optimal Taylor

• the central bank should not adopt a policy rule
  in which the nominal rate of interest responds
  only to changes in the current expectation of
  future inflation

• the conclusion is that the central bank performs
  better if it conditions its policy on current
  rather than lagged economic variables

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Impulse responses to positive demand shock for
four policy rules, namely Taylor Rule with
Interest Rate Smoothing Full State Rule
Backward Looking Rule and Goodhart Rule

• Taylor Rule with Interest Rate Smoothing

• Full State Rule

• Backward Looking Rule

• Goodhart(interest conditioned on current
  inflation)

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Impulse responses to positive demand shock of
expected inflation and output
Taylor Rule with Interest Rate Smoothing Full State Rule

• Backward Looking Rule

• Goodhart Rule

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It is clear that the Taylor Rule with Interest
Rate Smoothing achieves a much more stable output
gap and inflation, in spite of a relatively small
increase in the nominal interest rate. This is
achieved by credibly committing to a fixed
coefficient rule that conditions the short-term
interest rate to current economic variables and
to lagged interest rate.
Conclusions

• Taylor Rule with Interest Rate Smoothing responds
  better to economic conditions in Romania

• A central bank like ours, which takes care mostly
  about stabilizing inflation and is concerned
  about the economic stability, should control the
  interest rate using a Taylor Rule with Interest
  Rate Smoothing.

• Paper provides evidence on the practical
  importance to a central bank of analyzing the
  performance of the commitment mechanism

• In future work, I intend to compare the
  performance of fixed coefficients rules to
  unconstrained optimal commitment policy and
  discretionary policy, two alternatives proposed
  by Clarida, Gali and Gertler (1999).

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