Monday, 6 July 2009

Errata

When Matt and I drafted our report on the BERL study, we sent it on to BERL for comment. Reverse engineering anything like this can't be done perfectly, and we didn't have access to their underlying workings, so we were looking for any bits where we misunderstood what BERL was doing. The only reply we received was that they didn't have time to look at it. So, we released it. Wednesday night, I had the chance to chat with Adrian Slack, the study's main author. He pointed out lots of areas of disagreement. On some of these, like that someone going to a company-sponsored Christmas party imposes an externality on his employer if he shows up at work hung over the next day, we're not going to agree. But, on two points, I think he was right. And so I sent him an email Sunday (or, rather, Matt did as I haven't his email address) telling him so and showing the effect on the final figures. Here are the two corrections.

First, we misinterpreted Rayner on excess unemployment. But, correcting it adds almost nothing to our overall costs. Rayner argues that about 5.15% (he uses measures for prevalence rates of 4.3% and 6%) of the working age population suffers reduced employment rates due to alcohol use. The 2004 working age population was 3,094,400. The employment rate in 2004 was 63%. So, the employment rate among 159,362 individuals was ten percentage points lower, for a workforce reduction of 15,936 individuals. BERL argued for reduced employment of 31,100 workers; we apply Rayner and get about 16,000 (our first estimate was 9,200). BERL gave a cost measure of \$877.5 million. Of that, \$469.25 was forgone earnings and the rest was multiplier. So, to adjust BERL's figure, we just apply the fraction [15,936/31100] to their measure of forgone earnings, [update: and make a minor adjustment for cohort heterogeneity] then inflate by our preferred 1.1 multiplier rather than their preferred 1.87 multiplier. Our costs on this measure then are \$192 million in private costs and \$19 million in external costs (where we'd previously said \$11.1 million in external costs). So, we increase our policy-relevant costs measure by about \$8 million.

There's one other bit worth noting in Rayner, that BERL chose to ignore: Rayner says that applying the full wage costs is the upper bound, not the lower bound. Here's Rayner:
At one extreme, the economy is assumed to be at full employment, in the sense of output being subjected to a labour constraint. In this case, the loss of a person from the workforce means that the total output is reduced by the value of his/her marginal productivity, which will equal his/her gross wage if employers are profit maximizers.

The opposite extreme sees unemployment in the economy caused by demand constraint. The loss of a worker now has little output implications, since he/she can be replaced by another from those unemployed, at the cost of only a small initial retraining.
Rayner goes on to remind the reader that his use of the first assumption is an upper-bound estimate. So adding a 1.87 multiplier would be inappropriate, and so too is our 1.1 multiplier.