Estimating%20Time%20Varying%20Preferences%20of%20the%20FED

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Estimating Time Varying Preferences of the FED

• Ümit Özlale
• Bilkent University,
• Department of Economics

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OUTLINE Introduction

• INTRODUCTION
• Change in the conduct of monetary policy
• Estimated policy rules vs. Optimal policy rules
• Whats missing?
• What is the contribution of this paper?

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The U.S. economy since late 1970s

• General consensus Favorable economic outcomes in
  the U.S. economy since the late 1970s.
• Little consensus Role of monetary policy
• Several papers, including Clarida et al (2000,
  QJE) report a change in the conduct of monetary
  policy, which contributes to overall improvement
  in the economy

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Why is there a change in the conduct of monetary
policy?

• Feds preferences have changed over time
• References Romer and Romer(1989, NBER), Favero
  and Rovelli (2003, JMCB), Ozlale (2003, JEDC),
  Dennis (2005, JAE)
• Variance and nature of shocks changed.
• References Hamilton (1983, JPE), Sims and Zha
  (2006, AER)
• Learning and changing beliefs about the economy
• References Sargent (1999), Taylor (1998), Romer
  and Romer (2002)

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Estimated Policy Rules vs. Optimal Policy Rules

• To understand the changes in the monetary policy,
  two main approaches
• Estimate interest rate rules, which started with
  the celebrated Taylor Rule
• Some references Taylor (1993, Carnegie-Rochester
  CS), Boivin (2007, JMCB)
• Derive optimization based policy rules
• Some references Rotemberg and Woodford (1997,
  NBER), Rudebusch and Svensson (1998, NBER)

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Estimated Policy Rules

• Advantages
• Capturing the systematic relationship between
  interest rates and macroeconomic variables
• Empirical support
• Disadvantages
• Do not satisfy a structural understanding of
  monetary policy
• Unable to address questions about policy
  formulation process or policy regime change

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Optimal Policy Rules

• Advantages
• Optimization based policy rules
• Theoretical strength
• Disadvantages
• Cannot adequately explain how interest rates move
  over time.
• Estimate more aggressive responses to shocks than
  typically observed.

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Combining optimal rule with the data

• Combine the two areas by
• Assuming that monetary policy is set optimally
• Estimating the policy function along with the
  parameters that characterize the economy
• References
• Salemi (1995, JBES) uses inverse control
• Favero and Rovelli (2003, JMCB) uses GMM
• Ozlale (2003, JEDC) uses optimal linear regulator
• Dennis (2004, OXBES and 2005, JAE) uses optimal
  linear regulator

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Combining optimal rule with the data

• Advantages
• Assess whether observed outcomes can be
  reconciled within optimal policy framework
• Assess whether the objective function has changed
  over time
• Allows key parameters to be estimated
• Disadvantages
• None!

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A general framework

• Specify a quadratic loss function and AS-AD
  system such as
• subject to the following linear constraints

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A general framework

• Each period, the central bank attempts to
  minimize a loss function
• Which depends on the deviations from inflation,
  output gap and interest rate targets
• The preferences of the central bank are
• The linear constraints are inflation and output
  gap equations.
• Inflation is expected to have an inertia and it
  is affected from the output gap.
• The output gap is affected from the real interest
  rate

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Solving via Optimal Linear Regulator

• When the loss function is quadratic and the
  constraints are linear, the problem can be
  regarded as a stochastic optimal linear regulator
  problem, for which the solution takes the form
• which means that the control variable, which is
  the interest rate, is a function of the state
  variables in the model
• The vector contains both the loss function
  (preference) and the system parameters to be
  estimated.

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Estimation

• One way to estimate the parameters is to
• Cast the model in state space form
• Developing a MLE for the problem
• Under certain conditions, executing the Kalman
  filter provide consistent and efficient estimates

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Main findings

• A substantial change in the Feds response to
  inflation and output gap
• The response of Fed to inflation has become more
  aggressive since the late 1970s.
• There is an incentive for the Fed to smooth the
  interest rates

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Whats missing?

• The preferences that characterize the loss
  function are assumed to stay constant over time.
• In technical terms, previous studies did not
  allow for a continual drift in the policy
  objective function.
• Thus, these studies could not identify preference
  shocks of the Federal Reserve.

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What to do?

• We allow for the preference parameters in the
  loss function to vary over time, while keeping
  the linear constraints

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Estimation method

• We use a two-step procedure
• 1st step Estimate the linear optimization
  constraints, which are the parameters in the
  inflation and the output gap equation.
• 2nd step Conditional upon the estimated
  constraints, estimate the time-varying
  preferences of the Fed.

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Main contribution of the paper

• Generate a time series that will reflect the
  preferences of the Fed.
• Identify Feds preference shocks from the data.
• In technical terms Given the linear constraints
  and the state variables, estimate the
  time-varying parameters in a quadratic objective
  function.

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Related work

• Sargent, Williams and Zha (2006, AER) find that
  Feds optimal policy is changing because of a
  change in the parameters of the Phillips curve
  (not because of a change in the parameters of the
  objective function)
• Boivin (2007, JMCB) uses a time-varying set-up to
  investigate the changes in the parameters of a
  forward-looking Taylor-type rule. However, he
  does not consider a change in the preferences of
  the objective function.

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OUTLINE The Model

• The Model
• Introducing the model
• Theoretical support for the loss function
• Empirical support for the backward-looking model
• Estimating the optimization constraints
• Estimating time-varying preferences

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The Model Loss Function

• We assume that the loss function is
• The preferences vary over time.
• We specify a random walk process
• For simplicity, we assume that

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Theoretical Support Loss Function

• A quadratic loss function, although hypothetical,
  is convenient set-up for solving and analyzing
  linear-quadratic stochastic dynamic optimization
  problems
• Supporting references Svensson (1997) and
  Woodford (2002)
• Since inflation data is constructed as deviation
  from the mean, we did not specify any inflation
  target.

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Theoretical Support Loss Function

• The assumption of random walk
• Cooley and Prescott (1976, Ecta) state that a
  random walk assumption is the best way to account
  for the Lucas critique.
• A TVP specification has the ability to uncover
  changes of a general and potentially permanent
  nature for each parameter separately.

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Linear Constraints

• The linear constraints of the model are
• To satisfy the long-run Phillips curve,
  coefficients of the lagged inflation terms sum up
  to unity.
• This backward looking model is adopted from
  Rudebusch and Svensson and it is used in several
  studies, including Dennis (2005, JAE)

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Empirical Support Backward Looking Model

• Forward looking models tend not to fit the data
  as well as the Rudebusch-Svensson model, which is
  also reported in Estrella and Fuhrer (2002)
• There is no evidence of parameter instability in
  this version of the backward-looking model, as
  stated in Ozlale (2003)

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Estimating the optimization constraints Data

• We use monthly data from 19702 to 200410, where
  the output gap is derived by using a linear
  quadratic trend.
• For robustness purposes, we also use quarterly
  data, where inflation is derived from GDP chain
  weighted price index, the output gap series is
  taken from CBO.
• In each case, we use federal funds rate as the
  policy (control) variable.

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Estimating the optimization constraints SUR

• We estimate the parameters in the backward
  looking model by using the Seemingly Unrelated
  Regression.
• Estimating each equation by OLS returns similar
  results, implying weak/no correlation between the
  residuals.

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Estimated Parameters
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Estimating Time Varying Preferences Method

• Step 1
• The solution for the optimal linear regulator is
• Step 2
• Let be the
  difference (control error) between the observed
  control variable and the optimal control
  variable.

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Some Boring Stuff!

• In the Kalman filtering algorithm, the estimate
  for the state vector is
• which can also be written as
• Since the optimal feedback rule for the linear
  regulator is

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Still Boring!

• The new state vector is
• For simplicity, let
• Then, the problem reduces down to obtaining the
  elements of at each step .
• Keep in mind that the matrix includes the
  parameters of the model.

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How to estimate the loop

• The model can be cast in a non-linear state space
  model.
• The linear Kalman filter is inappropriate for the
  non-linear cases.
• Thus, we use the extended Kalman filter and
  estimate both the optimal control sequence and
  the time-varying parameters in the model.

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Outline Estimation Results

• Time varying preference series
• Identifying preference shocks
• Comparing observed and optimal interest rates
• Robustness checks

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Time varying preferences
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Time varying preferences

• Regardless of the starting values, the preference
  parameter for output stability goes down to zero.
• Such a finding is consistent with Dennis (2005,
  JAE), which states that output gap enters the
  policymaking process only because its indirect
  effect on inflation.
• The estimated series follow random walk, which is
  consistent with our initial assumptions.

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Preference Shocks
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Preference shocks

• Beginning with the second half of 1980s we do
  not observe any significant shocks in the policy
  preferences. Thus, the Greenspan period is silent
  in terms of preference changes.
• The significantly positive shocks, which indicate
  an increased emphasis on price stability occur in
  the Volcker period.
• Such a finding supports the view that Volcker
  period is a one-time discrete change in the
  policy.
• These shocks are found to be normally distributed
  and autocorrelated.

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Actual vs. optimal interest rates
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Actual vs. optimal interest rates

• The estimated interest rate is slightly sharper
  than the observed interest rate, which may be
  related to the absence of interest rate smoothing
  in the loss function.
• The correlation between the two series is found
  to be 0.93.
• Such a finding implies that the observed control
  sequence (interest rate) can be generated by
  putting increasingly more emphasis on price
  stability.

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Robustness Checks

• In order to see whether the estimated results are
  robust, we set the optimization constraints
  according to the findings of two studies, which
  use the same model
• Rudebusch and Svensson (1998, NBER)
• Dennis (2005, JAE)

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Using the estimated coefficients from Rudebusch
and Svensson
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Using the estimated coefficients from Rudebusch
and Svensson
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Using the estimated coefficients from Rudebusch
and Svensson
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Using the estimated coefficients from Dennis
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Using the estimated coefficients from Dennis
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Using the estimated coefficients from Dennis
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Correlation between preference shocks

• Corr (RS, DE)0.98
• Corr (RS, OZ)0.90
• Corr (OZ, DE)0.91
• These findings provide robustness for the
  estimation methodology and the results.

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Interest rate smoothing

• Several studies, including mine!, except
  Rudebusch (2002, JME) have found that interest
  rate smoothing is an important criteria for the
  Fed.
• Rudebusch (2002) states that lagged interest
  rates soak up the persistence implied by serially
  correlated policy shocks.
• Given that, we find a serial correlation in
  preference shocks, Rudebush (2002) argument seems
  to be valid.

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Results

• In this paper, we showed that, given the state of
  the economy, it is possible to estimate the
  hidden time-varying preferences of the Fed.
• Such a methodology also allows us to generate the
  preference shocks of the Fed.

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Results

• The results are consistent with the literature
• The weight of the output gap in the loss function
  goes down to zero, implying that output gap is
  important as long as it affects inflation
• There is a one-time discrete change in policy in
  the Volcker period. The Greenspan period is
  silent.
• It is possible to generate almost identical
  interest rates, even without imposing interest
  rate smoothing incentive to the loss function.

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Further research

• The paper can be significantly improved if the
  parameters in the constraints and the preferences
  are simultaneously estimated.
• Estimating time-varying preferences for inflation
  targeting and non-inflation targeting countries
  will provide important clues about whether the
  overall decrease in inflation rates for IT
  countries can be explained by a preference change.