Obituary: Phillips Curve

The Phillips curve has been the decisive moving part in the central bankers’ theory of the inflation process. It’s not just central bankers. Just as stagflation was gutting Keynesianism, the 1970s rational expectations revolution established the supremacy of the accelerationist Phillips curve in economists’ minds. Modern macroeconomics went all in on a variant wedded to a national frame of reference. Even though it has been shown that global slack has replaced domestic slack as the effective Phillips curve for the US economy, the Fed has been holding fast to its model of the inflation process as it perfects rudderless central banking.

We shall be looking at a conservative measure of underlying inflation, the trimmed mean PCE deflator. This is because we are not interested in mean-reverting short-term fluctuations that make the composite series so volatile at the monthly frequency. The next figure displays US inflation at the monthly frequency in 1983-2019. We already have enough energy to work with. The broad pattern is consistent with the Fed’s achievement in bringing down inflation to moderate levels by the 1990s. But the negative trend has arguably continued. The risk since the financial crisis has been on the downside. So the Fed has constantly had to worry about inflation expectations getting unanchored on the downside.

USinf.png

We split the time-series for 1983-2019 into five year periods. (Years begin in April.) For each five year period we project inflation onto the unemployment rate and returns on Brent. We include a lagged term of the left-hand side variable and perform Durbin-Watson tests to make sure that the residuals are no longer autocorrelated. Keeping the periods at arms length allows us to not worry about detrending the series.

We display the estimated model in the representation we proposed in the previous dispatch. The dichronic pattern is unmistakable. The Phillips curve can be said to have been alive as late as 15 years ago. But then it died.

PhillipsCurve.png

While the Phillips curve was giving up the ghost another pretender was vying for the throne. The elasticity of underlying inflation to innovations in the price of crude seemed to be a significant factor in the five years to Lehman. In the next five years the relationship became statistically insignificant perhaps because China was driving the price of crude. In the last five years, that is since the Shale revolution, the fixed effect has declined ever so slightly but the pattern has become more stable with the result that it is again statistically significant (by the slimmest margin). This does not herald a return to the mid-2000s. To the contrary. The elasticity of American supply puts a definite upper bound on how high the price of crude may stabilize for (say) a few quarters.

Crude.png

Even if the price of crude was not effectively capped by the response function of American frackers, US inflation is quite insensitive to the oil price. This is manifest once we compare the two sets of fixed effects. In its heyday, the oil price approached the scale of the normal Phillips curve. But roughly speaking, both have since vanished. The juxtaposition highlights the Fed’s predicament as it seeks to pilot rudderless. The best theory of inflation we have is the neutral model. Chance reigns supreme.

Predicament.png

The following tables reports my estimates for each period.

Table 1. Fixed-effect of Unemployment Rate Shocks.
Slope SE pVal iqr
2014-2019 -0.126 0.091 0.169 1.150
2009-2014 -0.159 0.099 0.116 1.700
2004-2009 -0.247 0.151 0.106 0.750
1999-2004 -0.346 0.115 0.004 1.650
1994-1999 0.732 0.166 0.000 0.950
1989-1994 -0.765 0.190 0.000 1.650
1984-1989 -0.397 0.197 0.050 1.500
Table 2. Fixed-effect of Oil Price Shocks.
Slope SE pVal iqr
2014-2019 1.620 0.715 0.027 0.114
2009-2014 2.359 1.595 0.145 0.081
2004-2009 3.295 1.242 0.010 0.134
1999-2004 2.045 0.957 0.037 0.099
1994-1999 0.645 1.063 0.546 0.118
1989-1994 0.715 1.451 0.624 0.087
1984-1989 2.095 1.357 0.130 0.100

It is also interesting to note the stability of interquartile ranges of our predictors. There is no trend in either series and they appear to be stationary. Moreover, they appear to be extraordinarily stable. Furthermore, the scales are off by an order of magnitude. We cannot compare the magnitudes of the slopes in Table 1 with those in Table 2 without rescaling them. The normal solution to the problem is to standardize both predictors to have mean zero and variance one. The problem with that approach — that I have used often enough myself — is that z-scores tell us nothing about the relative magnitude of their influence over the left-hand side variable. That’s why it is more informative to weight the predictors by a measure of their variation. Interquartile range turns out to be much more useful than we imagined.

repstability.png

 

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