Empirical Evidence on Inflation and Unemployment in the Long Run July 2011 Alfred A. Haug (University of Otago) and Ian P. King (University of Melbourne) 1

Goal: Analyze the time-series properties for: inflation unemployment Establish stylized facts about the relation between the two variables in the long run 2

Theoretical Issues:  Friedman’s 1977 Nobel lecture: long-run “Phillips curve” may be positively sloped  Generally accepted in mainstream macro nowadays: a vertical long-run Phillips curve  Empirical evidence is not so clear: King & Watson (1997)  Recent theoretical developments ◦ Berentsen, Menzio & Wright (2011, AER) argue for a positive long-run relation between inflation and unemployment 3

Econometric Tools: As much as possible free from statistical and economic models Theory of spectral analysis provides rigorous framework extract components with specific frequencies we are interested in co-variability of series over frequencies lower than the business cycle (the long-run behavior) 4

Data: Postwar U.S. data from 1952Q1 to 2010Q1 from Fed of St. Louis FRED data base Civilian unemployment rate, 16 years of age and older CPI-based inflation and GDP-deflator based inflation (ln( P t -P t-4 ))100 and (ln( P t -P t-1 ))400 5

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Basic Idea: Search for regularities in the relationship between inflation and unemployment Main frequency bands 8 – 50 years per cycle also: years per cycle 8

What we do in this paper: Apply the band-pass filter of Christiano and Fitzgerald (2003; CF) Compare results to those from the Baxter-King (BK) filter Study dynamic cross-correlation patterns of CF filtered components of inflation and unemployment contemporaneously and at leads and lags Test for structural breaks in the raw data and filtered data Carry out a sensitivity analysis 9

Methodology: Spectrum Coherences Ideal (but not feasible) filter in the time domain is: 10

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Methodology: Spectrum of the filtered series : where is the gain of the ideal filter given by 12

Methodology: For symmetric filters it can be shown that the phase shift is zero for all The ideal filter is not feasible as one would need infinite observations Various approximations of the ideal filter have been proposed 13

The Hodrick-Prescott filter: Finite sample problems: Is asymmetric and can produce phase-shift “spurious” cycles : no - see Pedersen (2001) but: the long-run or trend component inherits the nonstationarity of the raw series HP filter cannot be used for long-run analysis it is not a band-pass filter 14

The Baxter-King filter: Ideal filter is approximated by a symmetric finite MA Filter weights are chosen in the frequency domain by minimizing the following loss function: 15

The Baxter-King filter: This is a band-pass filter Filter weights are adjusted to ensure that the filtered series are covariance stationary BK-filter renders stationary series that are I(1) and I(2), and also series with a linear or quadratic deterministic trend 16

Problems: Trade-off between a better approximation to the ideal filter by making k larger and a loss of 2k observations for further analysis It is not consistent because the approximation errors does not go to zero as T goes to infinity (k is fixed); would need k as an increasing function of T 17

Christiano-Fitzgerald filter: This filter minimizes the mean squared error criterion instead: In the frequency domain the problem can be stated as: 18

Christiano-Fitzgerald filter: The solution depends on the spectrum of Filter weights are adjusted according to the importance of the spectrum at a given frequency Christiano and Fitzgerald assume a random walk process (avoids estimating the spectrum every time) 19

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Empirical Analysis Model with constant only:constant and deterministic trend: inflationunemploymentinflationunemployment 95% confidence band a – – – – Table 1. Confidence Bands for the Largest Autoregressive Root 21

Empirical Analysis 22

Empirical Analysis 23

Empirical Analysis The filtered components are generated series so that standard critical values and standard confidence bands can not be used for the cross-correlations We calculate critical values with the bootstrap method 20,000 replications with Gaussian errors generated under the null hypothesis of zero cross-correlations in the data generating process 24

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Structural breaks: Apply break tests of Bai and Perron (1998, 2003) to the dynamic cross-correlations; filtered components are covariance stationary First apply the double maximum test UDmax, then Sup-F if there is a break at all; estimate break dates; allow for multiple breaks 10,000 replications to calculate critical values for the UDmax test UDmax test for the stability of relationship between the filtered components of inflation and the unemployment rate for cycles of 8 to 50 years at lead 13: cannot reject null of no break Same results for other significant cross-correlations 28

Summary of the results: Highest level of cross-correlation occurs when cycles are 8-50 years in length, and where unemployment responds to inflation after 13 quarters (3.25 years): Only correlations that are significant at or better than the 10% level are those where inflation leads unemployment by 1 to 6 years; all are positive There are no breaks in significant 8-50 year correlations Our results are robust to modifications of the cycle length and different filtering methods (CF and BK); no breaks despite different fiscal and monetary policies over time 29