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

2. 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

3. 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?

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

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

12. 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

13. 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*

14. 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)

15. Workshop, Fall 2005 the ms-taylor rule: states

16. 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

17. 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

18. 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