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Estimating Time Varying Preferences of the FED. Ümit Özlale Bilkent University, Department of Economics. O UTLINE: Introduction. INTRODUCTION Change in the conduct of monetary policy Estimated policy rules vs. Optimal policy rules What’s missing? What is the contribution of this paper?.

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estimating time varying preferences of the fed

Estimating Time Varying Preferences of the FED

Ümit Özlale

Bilkent University,

Department of Economics

o utline introduction
OUTLINE: Introduction
    • Change in the conduct of monetary policy
    • Estimated policy rules vs. Optimal policy rules
    • What’s missing?
    • What is the contribution of this paper?
the u s economy since late 1970 s
The U.S. economy since late 1970’s
  • General consensus: Favorable economic outcomes in the U.S. economy since the late 1970’s.
  • 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
why is there a change in the conduct of monetary policy
Why is there a change in the conduct of monetary policy?
  • Fed’s 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)
estimated policy rules vs optimal policy rules
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)
estimated policy rules
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
optimal policy rules
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.
combining optimal rule with the data
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
combining optimal rule with the data9
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!
a general framework
A general framework
  • Specify a quadratic loss function and AS-AD system such as:

subject to the following linear constraints:

a general framework11
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
solving via optimal linear regulator
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.
  • 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
main findings
Main findings
  • A substantial change in the Fed’s response to inflation and output gap
  • The response of Fed to inflation has become more aggressive since the late 1970’s.
  • There is an incentive for the Fed to smooth the interest rates
what s missing
What’s 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.
what to do
What to do?
  • We allow for the preference parameters in the loss function to vary over time, while keeping the linear constraints:
estimation method
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.
main contribution of the paper
Main contribution of the paper
  • Generate a time series that will reflect the preferences of the Fed.
  • Identify Fed’s 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.
related work
Related work
  • Sargent, Williams and Zha (2006, AER) find that Fed’s 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.
outline the model
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
the model loss function
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
theoretical support loss function
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.
theoretical support loss function23
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.
linear constraints
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)
empirical support backward looking model
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)
estimating the optimization constraints data
Estimating the optimization constraints: Data
  • We use monthly data from 1970:2 to 2004:10, 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.
estimating the optimization constraints sur
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.
estimating time varying preferences method
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.
some boring stuff
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
still boring
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.
how to estimate the loop
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.
outline estimation results
Outline: Estimation Results
  • Time varying preference series
  • Identifying preference shocks
  • Comparing observed and optimal interest rates
  • Robustness checks
time varying preferences35
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.
preference shocks37
Preference shocks
  • Beginning with the second half of 1980’s 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.
actual vs optimal interest rates39
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.
robustness checks
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)
correlation between preference shocks
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.
interest rate smoothing
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.
  • 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.
  • 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.
further research
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.