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Inflation Persistence and the Taylor Rule

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					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            I(0) from 1947 to 1959, and I(0) from 1960 till 1992
                                  bootstrapped critical values
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
  Workshop, Fall 2005
2005    Ang et al.           Markov Switching                        Assumed to be I(0) because of theoretical concerns
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

   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   * )   yt  Rt*
                                                    ˆ
                      yt   ( Rt  R* )
                      ˆ
                       t   t 1   yt   t
                                       ˆ

   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
         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 state-
    dependent parameters
   Inflation is constructed using the GDP deflator
    with quarterly data
   Setup                     p
                      yt   st   st yt 1    st i yt i   t
                                                 i 1
                       t ~ N (0, s2 )
                                      t



                      st  0, 1
Workshop, Fall 2005
the ms-ar(2) model: results
                                         MS-AR(2) MODEL
                                     State 0       State 1
                      Prob[S=i]      0.985***      0.974***
                                      (0.01)        (0.02)
                         δ            -0.138       -0.305***
                                      (0.09)        (0.06)
                         φ1          -0.398***    -0.256***
                                      (0.12)        (0.08)
                         μ            0.961*       0.717***
                                      (0.56)        (0.16)
                         σ           1.681***      0.845***
                                      (0.15)        (0.06)
                       Loglik        -309.38
                                 2
Workshop, Fall 2005
                      Garcia χ        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

                                                                 
                 it  (1  s )  t   s ( t   s )   y  R*  sit 1   t
                                                  *
                                                           ˆ
                  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
                                  State 0       State 1
                      Prob[S=i]   0.951***     0.788***
                                   (0.02)       (0.08)
                         δ         0.765       0.991***
                                   (0.52)       (0.44)
                         ω        0.921***
                                   (0.28)
                         ρ        0.718***     0.936***
                                   (0.02)       (0.02)
                         σ        2.233***     0.432***
                                   (0.30)       (0.03)
                         π*       4.181*       2.904***
Workshop, Fall 2005                (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
              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


Workshop, Fall 2005
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


Workshop, Fall 2005
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

Workshop, Fall 2005

				
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