Modeling monetary policy in real time: does discreteness matter

1
Modeling monetary policy in real timedoes
discreteness matter?

• Andrei Sirchenko
• European University Institute, Florence, Italy
• This research was supported financially by the
  Global Development Networks grant R05-1861,
  distributed by the Economics Education and
  Research Consortium.
• The author is also grateful to Michael
  Beenstock, Wojciech Charemza and Victor
  Polterovich - for valuable comments and support
  Patrick Graham, Beata Idzikowska, Jaroslaw
  Jakubik, Jakub Jaworowski, Marynia Kruk, Tomasz
  Lyziak, Barbara Sladkowska, Piotr Szpunar, Mark
  Wynne and Reuters-Warsaw for help with getting
  statistical data Joao Santos Silva for useful
  suggestions and explanations TechnoNICOL for
  providing a computer Timo Mitze, Alexis
  Belianin, Michal Brzoza-Brzezina, Dariusz Filar,
  Andrzej Slawinski and other participants at
  XIIIth Spring Meeting of Young Economists and
  Research Seminars at Higher School of Economics
  and National Bank of Poland for useful comments.

2
How do the policy interest rates respond to the
state of the economy?Do discreteness of policy
rates and real-time data matter?

3
The central bank must have a highly regular
and predictable policy rule or response pattern
that links policy actions to the state of the
economy. - William Poole, then-President of
the Federal Reserve Bank of St. Louis

4
It is not possible to make use of a simple
policy rule, which could be known ex ante to
market participants. - National Bank of
Poland, Monetary Policy Council

5
If practitioners in financial markets gain a
better understanding of how policy is likely to
respond to incoming information, asset prices and
bond yields will tend to respond to economic data
in ways that further the central bank's policy
objectives. - Ben Bernanke, President of the
Federal Reserve System

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• Discrete-choice approach
• Real-time data
• MPCs meetings as a unit of observation

7
Frequency distribution of historical NBP
reference rate changes
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• The paper compiles a novel Polish real-time data
  set incorporating historical values of about 140
  economic and financial indicators, truly
  available to policymakers and public at each
  monthly policy meeting during the period 1998
  2007

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• The decision-making meetings of monetary
  authority as a unit of observation

10

• This sample design carefully simulates the actual
  policy-action-generating process

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Brief summary of results
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Policy regime change in 2002

• The systematic policy responses demonstrate
  remarkable structural differences prior to and
  after April 2002

13
Sup-LR test for structural change with unknown
change pointIndependent variables GVARna_Y and
ExInf_T_MSample 1999/02 - 2006/10
14
Sup-LR test for structural change with unknown
change pointIndependent variables EReu and
CPIxac_T_YM Sample 1999/02 - 2006/10
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Switch from backward- to forward-looking behavior

• In its reaction to the deviation of inflation
  from the target the central bank has shifted from
  the backward-looking to forward-looking behavior

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Switch from exchange rate to real activity

• Prior to 2002 the central bank reacted to the
  real activity measures far less, but to the
  exchange rate far more regular than later on

17
Switch from backward- to forward-looking behavior
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Focus on inflation and exchange rate before 2002
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Asymmetric responses to inflationary expectations

• The central bank reacts highly asymmetrically to
  the changes in inflationary expectations,
  depending on whether the expected inflation is
  above or below the inflation target

20
Policy rule in 2002/04 - 2006/10
21
No evidence for policy inertia

• The policy rate appears to be driven by the key
  economic indicators without evidence for
  deliberate interest-smoothing by the central bank

22
Monetary policy inertia in 1999/02 - 2002/03

• The very existence of partial adjustment in the
  context of policy rule in differences does not
  seem to be an issue in the first sub-period at
  all.

23
Tests for monetary policy inertia in 2002/04 -
2006/10
P-Value
 
0.28
0.44
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In-sample fit

• The estimated simple models explain correctly
  about 95 percent of observed policy adjustments.
• The reference rate appears to be changed in
  response to month-to-month change in the spread
  between the expected rate of inflation over the
  next 12 months from Ipsos survey and the
  inflation target, the annual growth rate of index
  of gross domestic product (or, alternatively,
  gross value added) and the positive change since
  the last MPCs meeting in the 12-month WIBOR.

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Policy rule in 2002/04 - 2006/10
P-Value
 
0.28
0.44
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Out-of-sample forecasting

• In forecasting the next twenty policy decisions
  the model correctly predicts seventeen no
  changes and three hikes, erroneously
  forecasting only the timing of one hike with a
  monthly lag and outperforming the market
  anticipation, made one day prior to each policy
  meeting.

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Out-of-sample forecasting of next policy decision
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Out-of-sample forecasting of next policy decision
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Summary of results

• The reported in- and out-of-sample forecasting
  performance, exceeding the typical one in the
  literature, is shown to be partially due to the
  employed methodology, combining the use of
  discrete regression approach, real-time data and
  decision-making meetings of monetary authority as
  a unit of observation.

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This methodological framework carefully mimics
the actual policy-action-generating process since

• most major central banks alter interest rates by
  discrete adjustments
• policy decisions are naturally made using
  information available in the real-time setting
• they are typically made 8-12 times per year at
  special policy meetings

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However, the empirical studies routinely estimate
the monetary policy rules by

• applying the regression methods for a continuous
  dependent variable
• using currently available series of economic
  data
• analyzing the systematic responses of policy
  rates averages to economic data averages for a
  given month or quarter

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Obviously, such practice distorts the actual
data-generating process because

• regression methods for a continuous dependent
  variable are shown to be inadequate when it is
  discrete
• the latest versions of statistical data may
  differ from the real-time ones due to revisions
• time aggregation misaligns the timing of policy
  decisions and availability of statistical data as
  well as raises the problem of simultaneity

33
The discrete-choice approach vs. Conventional
OLS regression

34
Monthly averages of ex post revised datavs. the
real-time non-aggregated data

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Does real-time policy-meeting data matter?

• Yes, the use of real-time data set with the
  policy-making meetings as a unit of observation
  does matter in the econometric identification of
  Polish monetary policy

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Comparison of policy rules, based on revised and
real-time data
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Does discreteness matter?

• Can we address the above problems by the
  conventional simpler linear regression model?

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Does discreteness matter?

• Virtually all measures of fit, constructed for
  the LRM (linear regression model) estimated by
  OLS, cannot be applied for the OPM (ordered
  probit model), and vice versa.

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Does discreteness matter?

• The likelihood functions of GLM (generalized
  linear model) and OPM, have different nature and
  cannot be compared either.

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Does discreteness matter?

• It seems impossible to construct a formal test
  based on the likelihood to compare the LRM and
  OPM. Are there any other appropriate ways to
  compare them?

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Does discreteness matter?

• One possible approach is to define the expected
  value of dependent variable for the OPM and
  compare it with the LRM counterpart.

42
Does discreteness matter?

• For the LRM E(YX) Xb
• For the OPM E(YX)
• Pr(Y-0.5X)(-0.5)
• Pr(Y-0.25X)(-0.25)
• Pr(Y0X)(0) Pr(Ygt0X)(0.50.50.25)/3

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Does discreteness matter?

• An alternative approach is to compute the
  conditional distribution of rate changes by
  defining the probabilities of discrete events for
  the LRM and compare them with the OPM
  counterparts.

44
Does discreteness matter?

• Let us ignore for a moment the discreteness of
  policy rate and evaluate the following simple LRM
  using OLS
• ?RRt Xtß et,
  
• where ?RRt the reference rate change, Xt -
  vector of explanatory variables, and et
  disturbance term, assumed to be normal iid (0,
  s²).

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Does discreteness matter?

• We can define the probabilities of discrete
  outcomes of ?RRt as follows
• Pr (?RRt -0.50) Pr (-8 lt Xtß et lt c1)
• Pr (?RRt -0.25) Pr (c1 Xtß et lt c2)
• Pr (?RRt 0.00) Pr (c2 Xtß et lt c3)
• Pr (?RRt gt 0.25) Pr (c3 Xtß et lt 8),
• where -8 lt c1 lt c2 lt c3 lt 8 are some known fixed
  cut-points.

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Does discreteness matter?

• Let us refer to such a LRM, extended to estimate
  the probabilities of discrete events, as to a
  rounded linear regression model (RLRM). To
  compute the probabilities we just have to choose
  the values of cut-points.

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Does discreteness matter?

• The probabilities of discrete outcomes for the
  RLRM can be now contrasted to the corresponding
  probabilities for the OPM

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Does discreteness matter?

• These measures of fit are useful in comparing
  competing models, but can provide only a rough
  guidance in selecting the preferred model.
  Without doing a formal test, however, it is
  unclear which model is the best one.

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Does discreteness matter?

• Formal comparison of RLRM and OPM can be
  done by noting that the RLRM is a actually a
  special case of interval regression model (IRM),
  while the IRM itself is nested in the OPM.
• Consequently, all three models can be
  estimated by ML and, hence, may be compared
  using, for example, the LR chi-square test.

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Does discreteness matter?
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Does discreteness matter?

• All tests are in favor of the OPM!
• Thus, not only does the OPM reveal considerably
  better measures of fit than the RLRM and IRM, but
  also it is clearly superior on the basis of
  formal statistical test.

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Does discreteness matter?

• The information gained by a more complex
  discrete-response technique like OPM is not
  attainable with the simpler continuous-response
  linear regression techniques.

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• Discreteness does matter!

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Modeling monetary policy in real timedoes
discreteness matter?

• Andrei Sirchenko
• European University Institute, Florence, Italy
• This research was supported financially by the
  Global Development Networks grant R05-1861,
  distributed by the Economics Education and
  Research Consortium.
• The author is also grateful to Michael
  Beenstock, Wojciech Charemza and Victor
  Polterovich - for valuable comments and support
  Patrick Graham, Beata Idzikowska, Jaroslaw
  Jakubik, Jakub Jaworowski, Marynia Kruk, Tomasz
  Lyziak, Barbara Sladkowska, Piotr Szpunar, Mark
  Wynne and Reuters-Warsaw for help with getting
  statistical data Joao Santos Silva for useful
  suggestions and explanations TechnoNICOL for
  providing a computer Timo Mitze, Alexis
  Belianin, Michal Brzoza-Brzezina, Dariusz Filar,
  Andrzej Slawinski and other participants at
  XIIIth Spring Meeting of Young Economists and
  Research Seminars at Higher School of Economics
  and National Bank of Poland for useful comments.

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