My prior post noted the big jump in youth unemployment rates since the abolition of the separate youth minimum wage. Let's go back to this briefly.
If we assume that the youth rate will always be some fixed amount above the adult rate, then the current run-up, as I noted earlier, is highly anomalous and seems very plausibly explained by the minimum wage change.
Some folks reckon the better measure is the ratio: the youth unemployment rate will always be some multiple of the adult rate. If you measure the ratio of the two over time, the current ratio is high, but there isn't an obvious break point in 2008.
The graph below has (thanks Stephen Hickson!) the unemployment rate for those aged 15-19 and the unemployment rate for everyone else (aged 19 and up). It looks to me like the proper relationship is a combination of a level shift and a multiplicative effect. When the adult rate is very low - below four percent or so - the youth rate bounces around at a point about 10 to 12 points higher than the adult rate. When the adult rate is high, the youth rate exceeds that constant by a multiple of the adult rate.
As always, I take this kind of thing over to Stata to find out what's going on. First, let's rule out that what we have going on is only a level shift or only a multiplicative effect. I run ordinary least squares with the youth unemployment rate (15-19 year olds) as dependent variable and the adult rate (20 and up) and a constant as independent variables. If it's just a level shift, the coefficient will be significant, close to 1 in magnitude, and with a significant constant term around 10. If it's just a ratio effect, the constant will be insignificant and we'll have a coefficient somewhere around 3.
Both the constant and the adult rate come up highly significant. So, over the period 1986 to present, we can expect the youth rate to be 1.44 times the adult rate (the multiplicative effect - about 44% above the adult rate) plus a constant of 9 percentage points. So if the adult rate is 5, the youth rate should be 16.2. We've ruled out the "it's just ratios" argument - there is a constant term in there; we've also ruled out that it's just a level shift because the coefficient is significantly greater than 1.
Moreover, when we plot the residuals, we find something pretty interesting. Recall that the residuals are the difference between the model's expected youth unemployment rate and the actual youth unemployment rate. A positive residual means that youth unemployment was higher than the model predicted; negative means it was lower.
If we look at the top graph, we see youth unemployment rates went up a lot during the recession of the early 1990s. But over that period, youth unemployment rates were never more than a couple of points above what the very simple model predicted (residuals graph, above). In recessions, it does look like the youth rate gets hit harder than the adult rate. But look at what happens starting around fourth quarter 2008. We now have residuals that blow up the model. Something really weird starts happening to the youth unemployment rate at the end of 2008. Youth unemployment is now about 10 points higher than we'd expect using the simple model. Again, the residual here is telling us that the current youth unemployment rate is about 10 points higher than would be expected given the prior relationship between the youth and adult unemployment rates.
I tried a few different variations allowing the constant and the slope to shift for high and for low levels of adult unemployment. But none of that made any substantial difference. Putting in a variable allowing the slope and constant to vary with regime (youth rate or no youth rate) made a big difference, but you'd of course expect that given the residuals plot above.
This remains very much a first cut: something I may someday assign as an honours project for more thorough sorting out. The econometrics here are very simplistic and do nothing to account for differences in labour force participation rates or the obvious problem of serial correlation in the time series data. But the simple model is still pretty telling. If we allow youth unemployment rates to vary both as a level shift above the adult rate and as a multiple of the adult rate, which is what we're doing when we run the simple regression with a constant term, we still have a jump in the current youth unemployment rate that is well above that seen in prior recessions.
My first cut explanation remains the abolition of the youth minimum wage.