Inflation Persistence and
the Taylor Rule
Christian Murray,
David Papell, and
Oleksandr Rzhevskyy
Workshop, Fall 2005
motivation

Inflation persistence is central to
macroeconomics




Standard New Keynesian model
My favorite example – Taylor’s staggered
contracts macro model
No trade-off between the level of inflation and the
level of output (natural rate hypothesis)
Trade-off between output variability and inflation
persistence
Workshop, Fall 2005
motivation

We normally measure persistence through
estimating autoregressive/unit root models




Unit root – shocks are permanent
Stationary – shocks dissipate over time
Measure persistence through half-lives
What do we know about unit roots and
inflation?
Workshop, Fall 2005
answer - not much
Year
Author(s)
Framework
Findings about inflation
1977
Nelson and Schwert
Analysis of autocorrelation structure
Nonstationary behavior of inflation
1987
Barsky
Estimation of autocorrelations
I(0) until 1960 and I(1) thereafter
1988
Rose
Dickey-Fuller test
I(0)
1991
Neusser
Cointegration tests
I(0)
1993
Brunner and Hess
Dickey-Fuller-type test with
bootstrapped critical values
I(0) from 1947 to 1959, and I(0) from 1960 till 1992
1993
Evans and Wachtel
Markov Switching
I(1) during 1965-1985, I(0) elsewhere
1996
Baillie et al
ARFIMA
Long memory process with mean reversion
1997
Culver and Papell
Panel UR test
I(0) for 3 countries out of 13 using UR test with breaks, I(1) for 7
of them; the last 3 countries are marginal
1999
Ireland
Phillips-Perron test
the unit root hypothesis for inflation can be rejected, but only at
the 0.10 significance level; in the post-1970 sample, the unit
root hypothesis cannot be rejected.
1999
Stock and Watson
DFGSL test
p-values are larger that 10% for both CPI and PCE inflations
before 1982, and less than 10% after 1985
2000
McCulloch and Stec
ARIMA
In the early portion of our period, a unit root in inflation may be
rejected, while in the later portion, it generally cannot be.
Whole period: Jan. 1959 - May, 1999
2001
Bai and Ng
PANIC
Cannot reject a UR at 5%
2003
Henry and Shields
Two regime TUR
Cannot reject a UR for the US inflation rate
Markov Switching
Assumed to be I(0) because of theoretical concerns
Workshop, Fall 2005
2005
Ang et al.
main idea

Suppose that the empirical evidence is correct



Inflation is sometimes stationary and sometimes
has a unit root
Nonsensical statement for most macro
variables
Real variables


Real GDP, real exchange rates
Theory predicts either stationary or unit root
Workshop, Fall 2005
main idea

Nominal variables



Nominal exchange rates, nominal interest rates,
stock prices
Market efficiency arguments for unit root
Inflation is a policy variable


Milton Friedman, “Inflation is everywhere and
always a monetary phenomenon”
Monetary policy can change over time
Workshop, Fall 2005
main idea

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

Textbook macro model
Taylor rule, IS curve, and Phillips curve
Inflation persistence depends on Fed’s policy rule
δ is the key variable – chosen by the Fed
it   t   ( t   * )   yˆ t  Rt*
yˆt   ( Rt  R* )
 t   t 1   yˆt   t

Inflation is stationary if the Taylor rule obeys the Taylor
principle
Workshop, Fall 2005
econometric model


A typical models used to pick policy changes
in time is the Markov Switching Model
Throughout the paper, we assume

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2 states of nature
First-order Markov switching process
We start with looking at the inflation series
alone, then move towards Taylor rule
estimation
Workshop, Fall 2005
the ms-ar(p) model



We start from looking at inflation series alone,
and estimate ADF-type regression with statedependent parameters
Inflation is constructed using the GDP deflator
with quarterly data
Setup
p
yt   st   st yt 1   st i yt i   t
 t ~ N (0,  s2 )
t
st  0, 1
Workshop, Fall 2005
i 1
the ms-ar(2) model: results
MS-AR(2) MODEL
Prob[S=i]
δ
φ1
μ
σ
Loglik
Workshop, Fall 2005
Garcia χ
State 0
State 1
0.985***
0.974***
(0.01)
(0.02)
-0.138
-0.305***
(0.09)
(0.06)
-0.398***
-0.256***
(0.12)
(0.08)
0.961*
0.717***
(0.56)
(0.16)
1.681***
0.845***
(0.15)
(0.06)
-309.38
2
42.63
the ms-ar(2) model: states
Workshop, Fall 2005
the ms-taylor rule model

We take into account

interest rate smoothing
i t  (1   )i t*  i t 1  v t

real-time GDP data with a quadratic trend


deviations from trend are constructed using only past
data
synchronization of information flows

the quarterly interest rate is the last month’s FFR
Workshop, Fall 2005
the ms-taylor rule: setup

Markov specification of the Taylor rule
 (1   )

*
ˆ
it


(



)


y

R
 sit 1   t
s
t
s
t
s
 t ~ N ( 0,  s2 )
s  0, 1



*
R* - the equilibrium real interest rate - assumed to
be fixed at 2%
ω – the GDP gap parameter – is the same in both
states
δ – inflation parameter – is allowed to switch; so
can the target inflation rate π*
Workshop, Fall 2005
the ms-taylor rule: results
MS-Taylor Model
Prob[S=i]
δ
ω
State 0
State 1
0.951***
0.788***
(0.02)
(0.08)
0.765
0.991***
(0.52)
(0.44)
0.921***
(0.28)
ρ
σ
π*
Workshop, Fall 2005
0.718***
0.936***
(0.02)
(0.02)
2.233***
0.432***
(0.30)
(0.03)
4.181*
2.904***
(2.36)
(0.69)
the ms-taylor rule: states
Workshop, Fall 2005
the ms-taylor rule: robustness

Robust to:

various assumptions about the GDP gap

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linear trend
stochastic trend with BN decomposition
Not robust to:

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middle-period FFR instead of end-of-the-period
Standard linear or quadratic, instead of real-time,
trend
Workshop, Fall 2005
conclusions

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There two are states for inflation
We cannot reject the unit root in one of them;
the second one is stationary
Fed actions can also be characterized by two
state behavior
The Taylor Rule model with Markov switching
fits the data well
Workshop, Fall 2005
conclusions

The 1960s, 1980s, and 1990s


The 1950s and 1970s

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
Inflation stationary and the Taylor rule obeys the
Taylor principle
Inflation has a unit root and the Taylor rule does
not obey the Taylor principle
Consistent with other evidence for the 1970s
Interest rate ceilings in the 1950s
Workshop, Fall 2005