Title: Estimating%20Time%20Varying%20Preferences%20of%20the%20FED
1Estimating Time Varying Preferences of the FED
- Ümit Özlale
- Bilkent University,
- Department of Economics
2OUTLINE 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?
3The 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
4Why 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) -
5Estimated 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)
6Estimated 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
7Optimal 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.
8Combining 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
9Combining 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!
10A general framework
- Specify a quadratic loss function and AS-AD
system such as - subject to the following linear constraints
11A 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
12Solving 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.
13Estimation
- 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
14Main 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
15Whats 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.
16What to do?
- We allow for the preference parameters in the
loss function to vary over time, while keeping
the linear constraints
17Estimation 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.
18Main 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.
19Related 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.
20OUTLINE 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
21The 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
22Theoretical 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.
23Theoretical 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.
24Linear 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)
25Empirical 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)
26Estimating 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.
27Estimating 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.
28Estimated Parameters
29Estimating 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.
30Some 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
31Still 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.
32How 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.
33Outline Estimation Results
- Time varying preference series
- Identifying preference shocks
- Comparing observed and optimal interest rates
- Robustness checks
34Time varying preferences
35Time 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.
36Preference Shocks
37Preference 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.
38Actual vs. optimal interest rates
39Actual 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.
40Robustness 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)
41Using the estimated coefficients from Rudebusch
and Svensson
42Using the estimated coefficients from Rudebusch
and Svensson
43Using the estimated coefficients from Rudebusch
and Svensson
44Using the estimated coefficients from Dennis
45Using the estimated coefficients from Dennis
46Using the estimated coefficients from Dennis
47Correlation 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.
48Interest 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.
49Results
- 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.
50Results
- 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.
51Further 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.