I've modified things a bit since the last time I posted on it. As we have more and more quarters under the new regime, including those quarters' data in the estimation of parameters starts messing with the estimates if the point is figuring out what youth unemployment would look like if it had followed its prior trend relative to the adult rate.
It's a very simple model. I take the youth unemployment rate as a function of the adult unemployment rate and the square of the adult unemployment rate (to capture non-linearities) for all quarters prior to Quarter 90: June 2008. I then ask Stata to predict the youth unemployment rate given the estimated parameters (and the adult unemployment rate) and to measure the difference between the predicted results and the observed results in all quarters. Then, I ask it to tell me what the largest difference was in any quarter prior to June 2008. I subtract that difference from the residuals from June 2008 onwards and call that excess youth unemployment. That tells me how much worse youth unemployment is now, relative to the adult rate, than it was in the worst possible quarter prior to mid 2008. I multiply that excess unemployment rate by the youth labour force in each quarter from June 2008 onwards to get the number of kids unemployed who would have been employed had the youth unemployment rate been no worse relative to the adult rate than it had been in the worst quarter prior to June 2008.
The table below has the number of kids, in thousands, who were unemployed and who would have been employed had the youth unemployment rate performed no worse relative to the adult rate than it had in its worst quarter prior to the abolition of the differential youth minimum wage.
| Quarter | Adult unemployment rate | Expected youth unemployment rate | Actual youth unemployment rate | Excess youth unemployment, in thousands |
| Jun-08 | 2.9 | 15.8 | 15.4 | -0.7 |
| Sep-08 | 3.2 | 16.2 | 15.7 | -0.8 |
| Dec-08 | 3.3 | 16.2 | 17.9 | 3.0 |
| Mar-09 | 4.5 | 17.8 | 19.1 | 2.2 |
| Jun-09 | 4.5 | 17.8 | 22.9 | 8.2 |
| Sep-09 | 4.9 | 18.3 | 25.1 | 10.5 |
| Dec-09 | 5.3 | 18.8 | 26.5 | 13.2 |
| Mar-10 | 5.2 | 18.7 | 25.2 | 10.5 |
| Jun-10 | 5.4 | 19.0 | 24.7 | 8.7 |
| Sep-10 | 5.1 | 18.5 | 23.3 | 6.8 |
| Dec-10 | 5.3 | 18.8 | 25.5 | 10.4 |
Excess youth unemployment peaked at just over 13,000 youths in December quarter 2009, dropped to just under 7,000 at September quarter 2010 and rose again to over 10,000 in December quarter. And again, excess here is defined relative to the worst possible performance of youth unemployment (as compared to adult) experienced between 1986 and 2008, including more than a few periods in which adult unemployment rates were far in excess of those currently experienced.
Any reasonable explanation has to say why things are so different this time than in prior recessions. The abolition of the youth minimum wage seems the most plausible explanation.
I don't have access to Stata so I can't extract the data you've made available, but I do have some questions about your method.
ReplyDeleteFirstly, why do you suppose there is a simple linear relationship between adult and youth unemployment rates? Surely you'd need to consider differences in the relative sizes of each cohort: the adult cohort probably doesn't change much, but the youth one does (based on the size of school leavers each year).
If there is something other than a linear relationship here, calculating linear regressions probably doesn't mean very much.
Secondly, why use the data for Quarter 90 as your point of reference? What happens to the model if you select other Quarters?
Thirdly, how well does your model correspond to the data you used to derive it?
Regards,
Craig
@Craig: Good questions.
ReplyDelete1. I'm using adult unemployment and its square on the right hand side. A crude way of handling non-linearities, but having it or leaving it out makes no substantive difference in results.
1.(a, on cohort sizes) I don't correct for this directly. But I have run things using employment rates instead of unemployment rates (no substantive difference). And, just look at HLFS. SAD3AA gives you the total working age population in the 15-19 age bracket; SAD3AZ gives you the total all ages working age population. You don't need Stata to run the ratio of those in Excel. In the 1980s, that age group was about 12% of the population. It dropped through the 90s from about 10% to about 9%. And it's hovered through the 2000s from 9-10%. It's now at 9.2%. The average since Q90 is very slightly lower than the average through the 2000s until Q90. There's no big cohort shock that's driving results. If anything, the 15-19 age group is a smaller part of the working age population than it was in the 80s and 90s.
1(b) In the absence of some really good reason to think that a linear model is the wrong one, casting about for specifications starts getting into problems of specification search.
2. Q90 is when Labour abolished the lower differential youth minimum wage: Q2 2008. I chose that quarter because that's when Labour's law change became effective. My results would get stronger if I moved the quarter forward to Q4, because that's when youth unemployment rates really started diverging from adult rates; they'd get weaker if I moved things back because the really strong effects from Q4 onwards would start being averaged out by the prior period. I didn't do any quarter searching. First, I don't roll that way. Second, there was a good reason for choosing the quarter of the law change. Third, it won't make a whole lot of difference unless you do something really stupid in quarter selection, like going backwards a couple of years before the law change.
3. The biggest divergence between hypothesis (increasing youth minimum wage to adult level increases youth unemployment) and test (relationship between youth unemployment and adult unemployment before and after the change) is that the data lumps together 15-19 year olds while the law change hit the 15-17 year olds; 18-19 year olds had previously been brought up to the adult rate. I've not had a chance to look yet at disaggregated data. But I'd expect that the previously non-binding increase in the 18-19 year old minimum wage became binding about the same time.