Inflation Persistence and the Taylor Rule

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Inflation Persistence andthe Taylor Rule
Christian Murray, David Papell, and Oleksandr
Rzhevskyy
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motivation

• Inflation persistence is central to
  macroeconomics
• Standard New Keynesian model
• My favorite example Taylors 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

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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?

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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
2005 Ang et al. Markov Switching Assumed to be I(0) because of theoretical concerns
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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

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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

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main idea

• Textbook macro model
• Taylor rule, IS curve, and Phillips curve
• Inflation persistence depends on Feds policy
  rule
• d is the key variable chosen by the Fed
• Inflation is stationary if the Taylor rule obeys
  the Taylor principle

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econometric model

• A typical models used to pick policy changes in
  time is the Markov Switching Model
• Throughout the paper, we assume
• 2 states of nature
• First-order Markov switching process
• We start with looking at the inflation series
  alone, then move towards Taylor rule estimation

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the ms-ar(p) model

• We start from looking at inflation series alone,
  and estimate ADF-type regression with
  state-dependent parameters
• Inflation is constructed using the GDP deflator
  with quarterly data
• Setup

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the ms-ar(2) model results
  MS-AR(2) MODEL MS-AR(2) MODEL
  State 0 State 1
ProbSi 0.985 0.974
  (0.01) (0.02)
d -0.138 -0.305
  (0.09) (0.06)
f1 -0.398 -0.256 
  (0.12) (0.08) 
µ 0.961 0.717
  (0.56) (0.16)
s 1.681 0.845
  (0.15) (0.06)
Loglik -309.38
 Garcia ?2 42.63
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the ms-ar(2) model states
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the ms-taylor rule model

• We take into account
• interest rate smoothing
• 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 months
  FFR

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the ms-taylor rule setup

• Markov specification of the Taylor rule
• R - the equilibrium real interest rate - assumed
  to be fixed at 2
• ? the GDP gap parameter is the same in both
  states
• d inflation parameter is allowed to switch
  so can the target inflation rate p

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the ms-taylor rule results
  MS-Taylor Model MS-Taylor Model
  State 0 State 1
ProbSi 0.951 0.788
  (0.02) (0.08)
d 0.765 0.991
  (0.52) (0.44)
? 0.921  
  (0.28)  
? 0.718 0.936
  (0.02) (0.02)
s 2.233 0.432
  (0.30) (0.03)
p 4.181 2.904
  (2.36) (0.69)
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the ms-taylor rule states
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the ms-taylor rule robustness

• Robust to
• various assumptions about the GDP gap
• linear trend
• stochastic trend with BN decomposition
• Not robust to
• middle-period FFR instead of end-of-the-period
• Standard linear or quadratic, instead of
  real-time, trend

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conclusions

• 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

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conclusions

• The 1960s, 1980s, and 1990s
• Inflation stationary and the Taylor rule obeys
  the Taylor principle
• The 1950s and 1970s
• 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