Inflation Persistence and the Taylor Rule

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

2. 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. 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. answer - not much

5. 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. 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. 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. 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. 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. the ms-ar(2) model: results

11. the ms-ar(2) model: states

12. 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. 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. the ms-taylor rule: results

15. the ms-taylor rule: states

16. 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. 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. 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