## Tuesday, 30 August 2011

### 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.

1. Hi Eric

Thanks for running these. Certainly these disaggregated data are really helpful for this purpose. Are they publicly available, or did you have to ask / pay for them?

I think you do a good job of showing that, whatever happened post 2008, it affected 16-17 year olds more than 18+ year olds. But I’m not sure I buy your account about why a minimum wage change would affect 15 year olds as well, which your regressions show is happening. You suggested that rational employers might shun 15 year olds because one day they will turn 16 and get the adult minimum wage. I don't buy it. It is pretty easy for employers in these sectors to employ 15 year olds on fixed term contracts that happen to expire soon after their 16th birthday, limiting their exposure drastically. Worker turnover is also typically very high at these ages, further limiting employers’ exposure.

I would have thought that an increase in the relative price of 16-17 year olds would help prospective workers both just older and just younger than them.

At best, your argument would imply a partial pass-through of wage effects to 15 year olds. The fact that this change appears to have hurt 15 year olds even more than 16-17 year olds suggests to me that, whatever role the youth minimum wage change had, there is something else at play here, too. The global recession is a good candidate, and while I understand and respect your view that the other recession we have data for shows a different pattern, the number of recessions we are dealing here is only two. It would not surprise me if the two recessions did not have identical relative impacts on adult / youth unemployment rates.

If you agree that there are two factors at play here, then I guess the challenge is to figure out a way to parse one effect from the other.

Cheers,
Rob

2. @Rob: I'll put up the .do and .dta files next week once I've tidied them; bit swamped this week. Had to ask for the data...

I need to look more at the 15 year olds to figure out what's going on there. But in the period prior to 2008, there's basically no relationship between the adult unemployment rate and the unemployment rate for 15 year olds. It's all noise.

Another way of thinking about the current change for 15 year olds: suppose you can get a task performed either by hiring a couple of low skilled workers and engaging in intense supervision or by hiring one more highly skilled worker and engaging in little supervision, but you need to invest effort into structuring the job before going to market. If the only potential pool of applicants for the former is 15 year olds, you just create fewer of those jobs.

Or, finally, consider the position of a 15 year old with marginal attachment to education - he's doing poorly at it and isn't a good fit for school. If employment prospects look good going forward, he exits. Otherwise, he drifts at school for a couple more years. If all of his 16 & 17 year old friends aren't getting jobs, the marginal one stays in school (lfpr for 15 year olds did drop substantially); the ones left in the labour market are substantially worse bets than they were prior to the change.

I worry less about defined recessions and more about periods in which the adult unemployment rate was higher than that currently experienced. And there, we have 49 quarters of >5% adult unemployment prior to 2008 and only 5 since.

3. Thanks, Eric. I'll look forward to seeing the .dta on here a bit later on. These are interesting results you have.