A couple of blog posts ago, we looked into the feasibility of running a highpressure economy and discussed if a more aggressive monetary policy response was warranted, when getting close to the ‘effective lower bound’ (ELB). In this macro note I thought I would provide a short rebuttal, showing that there might be other processes at play, which would invalidate any such efforts.
Is the Phillipsrelation nonlinear, and is it possible to utilize this relationship in current tight labor markets to jumpstart inflation?
Let’s start by altering the specifications of our previous travails somewhat and use: an intercept, an unemployment gap (actual UNR minus the CBO’s estimate of NAIRU), and a couple of lags of inflation (to improve on the DWstats and as a proxy for inflation expectations). In short, this way we get more robust estimations (more observations).
First, no matter if we use coreCPI or corePCE we still get the infamous flattening results when comparing across time, as the coefficient for the unemployment gap decreases from the early to the late sample (In the table I have chosen only to look at core PCE, but downloading the mbndfile at the bottom you can play around with it on your own). And this becomes even more pronounced the closer in time you push the start data for the late sample:

Full sample (1959Q1 –2019Q1) 
Early sample (1959Q1 – 1987Q4) 
Late sample (1988Q1 – 2019Q1) 
Unemployment gap 
0.07658 (0.00271)*** 
0.12969 (0.02211)** 
0.02528 (0.11291) 
Lagged inflation coefficients, sum 
0.96 
0.97 
0.95 
Unemployment gap, positive 
0.07862 (0.08824)* 
0.15579 (0.19541) 
0.03016 (0.20476) 
Lagged inflation coefficients, sum 
0.93 
0.93 
0.92 
The corePCE inflation is positively correlated with the unemployment gap, but it’s hard to see any clear tendencies towards nonlinearity, at least over the full sample (note, also/however, the weak pstats).
Showing that evidence for nonlinearities seems very weak or is perhaps nonexistent is no great feat when we simultaneously imply there might be no Phillipsrelationship at all!
In all honesty, the breakdown in the very simple Phillipsrelationships we tend to look at in these exercises can reflect a number of other, structural, issues. Academics and others have – of course – offered numerous other explanations, often with a tilt towards supplyside changes, of which improved anchoring of inflation expectations is but one. Others include increased globalization and competition or susceptibility to exchange rate movements etc. etc.
The thing I’m getting at is that if more and more of the pricing decisions are related to factors not necessarily related to the business cycle – to demand – we should perhaps explore other avenues to validate this key relationship in economics when conducting monetary policy. Do, for instance, note that the flattening of the Phillips curve is generally much less obvious when using wage inflation instead of price inflation measures, an indication as good as any that the reflexive response of “anchoring inflation expectations” does not suffice.
One way of approaching this issue is instead using “cyclically sensitive” measures of inflation such as the FED NY’s underlying inflation gauge (UIG) or the equivalent measure of the SF FED’s– supposedly – strips inflation of, for example, the effects of globalization. When using these measures in our model, we do indeed see a more traditional relationship (without having to resort to nonlinear relationships), and even with simple median/trimmed mean measures of inflation the Phillips relationship is reanimated. In the below tables, I have used two versions but there are others in the mbnddocument for those interested:
Dallas FED: Trimmed mean 
Full sample (1977Q1 –2019Q1) 
Early sample (1977Q1 – 1997Q4) 
Late sample (1998Q1 – 2019Q1) 
Unemployment gap 
0.10365 (0.02047)** 
0.20018 (0.03183)** 
0.13688 (0.00235)** 
Lagged inflation coefficients, sum 
0.93 
0.94 
0.41 
Unemployment gap, positive 
0.07834 (0.20969) 
0.11058 (0.40890) 
0.17381 (0.00435)** 
Lagged inflation coefficients, sum 
0.88 
0.88 
0.30 
Note: There might be some nonlinear effects in the late sample (as the coefficient is higher for positive unemployment gaps), but they are counteracted by what I interpret as an “anchoring”effect as the sum of the lagged inflation coefficients have also dropped markedly. This, of course, borders on wild speculation but what fun is life without it?
SF FED: Cyclical core PCE inflation 
Full sample (1986Q1 –2019Q1) 
Early sample (1986Q1 – 2002Q4) 
Late sample (2003Q1 – 2019Q1) 
Unemployment gap 
0.05914 (0.00040)*** 
0.10350 (0.00070)*** 
0.0905 (0.00027)*** 
Lagged inflation coefficients, sum 
0.87 
0.91 
0.66 
Unemployment gap, positive 
0.07023 (0.00242)** 
0.14134 (0.05078)* 
0.09278 (0.00138)** 
Lagged inflation coefficients, sum 
0.84 
0.87 
0.70 
Note: We see no indications of nonlinear effects in the late sample, but the “anchoring”effect that I speculated in is perhaps visible here also, as the sum of the lagged inflation coefficients have also dropped markedly. Together with the NY FED measure this adjusts explicitly for the structural changes the US economy has experienced over the past decades.
Feel free to vary sample periods and interchange with different inflation measures. As you can see the results are quite robust – the Phillips relationship becomes more intact over time and there is, again, no obvious nonlinear relationship implied at higher levels of resource utilization. Also, no matter what ‘nonconventional’ inflation measure we use, the sum of lagged inflation coefficients falls dramatically in the late sample, which indicates that inflation persistence has fallen off, and/or that expectations have become more well anchored. Whether this is a good thing always and everywhere remains to be seen.
In the end, then, what we have achieved is to cast a fair share of doubt on the existence of a (stable) nonlinear Phillips relationship. This is good news as it means that we don’t need to construct additional theoretical layers on top of “traditional macro” to model economic developments. We can also, especially with inflation measures stripped of supply side effects, show that the Phillips relationship is both stable and robust.
Now, it wouldn’t be me if I didn’t leave you with a small seed of selfdoubt (of which I myself have plenty); How do you really adjust for supplyside effects, hmm..?