Further fine-grained results

Rob Salmond asks some decent questions in comments. I'm going to partially answer them with another set of regressions.

Here, I'm taking the unemployment rate as the dependent variable. In the first column, I run a specification on 15 year olds by themselves: the group one year too young to be hit by the minimum wage change. In the second, I pool 16 and 17 year olds: the group experiencing the change. In the third, I pool 18 and 19 year olds: the group who had been subject to adult rates well prior to June '08. Standard deviations in parentheses under coefficients.

	Unemployment
	15	16 & 17	18 & 19
Adult unemp rate	0.03	1.36	2.06
	[0.21]	[0.11]**	[0.11]**
Post June 2008 indicator	-7.36	-12.52	-1.4
	[6.14]	[3.10]**	[3.16]
Adult unemp rate * indicator	5.42	4.81	1.17
	[1.29]**	[0.65]**	[0.66]
Constant	18.23	9.51	4.39
	[1.21]***	[0.61]**	[0.62]**
R-squared	0.71	0.83	0.8

In all the stuff I've been doing, I've not been using interaction terms and indicator variables for the regime change; we only have a dozen quarters of data since the change.  That's why I prefer conditioning the model on the pre-June 2008 data, running projected unemployment rates going forwards, and just using an eyeball on the difference. But, here are the results instead using an indicator and an interaction term.


If we combine the level and interaction effects to get a net effect at a 5% adult unemployment rate, we get an unemployment rate among 15 year olds 19.7 points higher, 11.53 points higher for 16 & 17 year olds, and 4.5 points higher for 18 & 19 year olds.

Another way of running things: take the unemployment rate among 16 & 17 year olds as predicted by the unemployment rate among 18 & 19 year olds. In that case, when we have a 21% unemployment rate among 18 & 19 year olds, the combination of shift and interaction variables in that specification give us an excess unemployment rate among 16 & 17 year olds of 10.4 percentage points.

Rob asked about goodness of fit measures across the cohorts. I can't easily get that from Stata for OLS with Newey-West standard errors, so the above just has OLS. If we run the above regressions with Newey-West errors, results for 18 & 19 year olds become significant; the coefficients just are much smaller in absolute magnitude than for the younger cohort. But there's no particular action in R-squared above other than that we don't explain as much of the variance in outcomes for 15 year olds. Neither is there any particular action in the R-squared measures if this morning's regressions were run in OLS instead.

But let's go back to my preferred way of running things and just condition the model on quarterly data from 1986 to 2008 and use the established relationship between adult and youth unemployment rates to forecast what those would have looked like from June 2008 onwards had that prior relationship held up, recalling that the period from 1986 to 2008 included periods with adult unemployment rates substantially in excess of anything we have experienced in the current recession.

Unemployment, 16 & 17 year olds

Unemployment, 18 & 19 year olds

Big jump in unemployment rates for 16 & 17 year olds relative to their prior trend given adult unemployment rates; much smaller jump for 18 & 19 year olds. Note further that some unemployment among 18 year olds will be carry-over from having been unemployed when 17.

Rob also asks to what extent I can exclude the global recession. Prior recessions had far higher adult unemployment rates AND lower youth unemployment rates than the current recession. Any effect of the recession ought to be picked up in the effects of adult unemployment rates: recall that we're projecting youth unemployment rates from adult rates. If something in the current recession just has hit youths harder than adults relative to how things have operated in prior recessions, that could be driving things. But it would have to have hit 16 & 17 year olds particularly hard relative to 18 & 19 year olds, and it would have had to have been timed to match the change in the youth minimum wage.