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Workshop, Fall 2005 Inflation Persistence and the Taylor Rule Christian Murray, David Papell, and Oleksandr Rzhevskyy

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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

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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?

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Workshop, Fall 2005 answer - not much YearAuthor(s)FrameworkFindings about inflation 1977Nelson and SchwertAnalysis of autocorrelation structureNonstationary behavior of inflation 1987BarskyEstimation of autocorrelationsI(0) until 1960 and I(1) thereafter 1988RoseDickey-Fuller testI(0) 1991NeusserCointegration testsI(0) 1993Brunner and HessDickey-Fuller-type test with bootstrapped critical values I(0) from 1947 to 1959, and I(0) from 1960 till 1992 1993Evans and WachtelMarkov SwitchingI(1) during 1965-1985, I(0) elsewhere 1996Baillie et alARFIMALong memory process with mean reversion 1997Culver and PapellPanel UR testI(0) for 3 countries out of 13 using UR test with breaks, I(1) for 7 of them; the last 3 countries are marginal 1999IrelandPhillips-Perron testthe 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. 1999Stock and WatsonDFGSL testp-values are larger that 10% for both CPI and PCE inflations before 1982, and less than 10% after 1985 2000McCulloch and StecARIMAIn 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 2001Bai and NgPANICCannot reject a UR at 5% 2003Henry and ShieldsTwo regime TURCannot reject a UR for the US inflation rate 2005Ang et al.Markov SwitchingAssumed to be I(0) because of theoretical concerns

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Workshop, Fall 2005 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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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

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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 Inflation is stationary if the Taylor rule obeys the Taylor principle

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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

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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

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Workshop, Fall 2005 the ms-ar(2) model: results MS-AR(2) MODEL State 0State 1 Prob[S=i]0.985***0.974*** (0.01)(0.02) δ-0.138-0.305*** (0.09)(0.06) φ1φ1 -0.398***-0.256*** (0.12)(0.08) μ0.961*0.717*** (0.56)(0.16) σ1.681***0.845*** (0.15)(0.06) Loglik-309.38 Garcia χ 2 42.63

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Workshop, Fall 2005 the ms-ar(2) model: states

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Workshop, Fall 2005 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 month’s FFR

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Workshop, Fall 2005 the ms-taylor rule: setup Markov specification of the Taylor rule 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*

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Workshop, Fall 2005 the ms-taylor rule: results MS-Taylor Model State 0State 1 Prob[S=i]0.951***0.788*** (0.02)(0.08) δ0.7650.991*** (0.52)(0.44) ω0.921*** (0.28) ρ0.718***0.936*** (0.02) σ2.233***0.432*** (0.30)(0.03) π*4.181*2.904*** (2.36)(0.69)

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Workshop, Fall 2005 the ms-taylor rule: states

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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

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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

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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

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