Turns out that there is nothing new under the sun. The Australian result (that inflation only decelerates during recessions) also appears in US data … and others already did better work on the relationship.
Stock and Watson (my academic heros) had a look at the unemployment / inflation relationship in their 2010 Jackson Hole paper. In part, the paper was a response to disjunction between those that (correctly) pointed out that inflation tended to fall in recessions, and those that (accurately) demonstrated that activity variables didn’t improve on naive auto-regressive forecasts.
Their specification was a little different to mine – they split the sample into periods when the unemployment rate is below the minimum unemployment rate over the prior twelve quarters and periods where it is not. So I’ve done the same for Australia below.
In periods where the unemployment rate is above the 12q minimum, S+W found that US inflation tends to fall – confirming the conventional wisdom that inflation tends to fall during recessions (and after recession, given the implicit lag introduced by the 12q min).
The histograms for Australian recession are above. There is also a clear tendency for inflation to fall in Australia in periods where there the unemployment rate is below the 12q min.
The average change in the QoQ inflation in periods where the unemployment rate is above the 12q minimum is an unemployment gap is -3.4 basis points (standard deviation+27.6bps), and the average change in periods where the unemployment rate is below the recent minimum is +2.1bps (standard deviation19.6bps).
As you’d expect given that inflation fell from 10% to 2%, there are more quarters with a gap (74) than without (41). And due to the lag, we’ve presently still got a gap (though if the unemployment rates starts heading down again, we’ll flip to no-gap).
I still think that this is interesting and instructive, despite the fact that we cannot reject the hypothesis that both means are equal to the full sample mean (of -1.4bps). The probability that the gap-mean is the same as the full sample mean is ~54%, and for the nogap-mean that same probability is ~25%
My three-way split did better, with the probability that the unemployment-is-rising-mean is the same as the full sample mean sample mean is 10.48% — ohh so close to a conventional level of significance!
unemployment is rising = -10.2bps (sd 23.6bps, p-value = 10.5%)
unemployment is steady = +3.2bps (sd 23bps, p-value = 36.4%)
unemployment is falling = +1bps (sd 28.4bps, p-value = 40.7%)
Given that this is an a priori specification, i am pretty sure I could find some unemployment classification which gave me an unemployment-is-rising mean that is significantly different from the full sample mean.
If you’re willing to take that leap with me, the probability that the ‘up’ mean is the same as the to the ‘not-up’ mean is 2.8% – a robust result. Using a two sample Welch test (not assuming equivalent variance), I get 4.95%. I’m persuaded that there is something different happening when the unemployment rate is rising.
You can clearly see the difference between the sub-groups in these boxplots.