## Monday, August 16, 2010

### When people don't understand regression equations

This article seems to be one of the worst mis-understandings of regression that has been posted in a while. Let us consider the heart of the argument:

When they ran the numbers, the answer their computer spat out had them reviewing their work looking for programming errors. The optimal rate of firing produced by the simulation simply seemed too high: Maximizing teacher performance required that 80 percent of new teachers be fired after two years' probation.

After checking and rechecking their analyses, Staiger and Rockoff came to understand why a thick stack of pink slips are needed to improve schools. There are enormous costs to having mediocre teachers burdening the school system, and once they get their union cards, we're stuck with them for decades. The benefits of keeping only the superstars is enormous, such that it's better to risk accidentally losing some of the good ones than to have deadwood sticking around forever.

The regression equation is assuming that all things remain equal. Presuming that there are 3 million teaching jobs in the United States (which was true in 1999 with 3.1 million), that would require filling 1.2 million vacancies per year. It's hard to get a good number for the total number of college graduates per year, but in 2004 there were 2.6 million freshmen; so one would assume, given a 100% graduation rate, that nearly 50% of college graduates would spend two years teaching (before being fired). Remember, in the long run this is sampling without replacement as we don’t rehire people who have already been fired in previous years.

Two comments come to mind. One, you have to have a powerful incentive to make the majority of college students do this. Either a social expectation (as in a teacher draft) that encourages potential teachers to give two years of service or some sort of extremely lucrative remuneration scheme would have to be developed.

Two, can we really believe that a cross section of 50% of college graduates would have better teaching ability than the median teacher currently does?

Furthermore, a school with a constant staff flux may have different characteristics than the current system. Teachers may be more willing to quite mid-year for another opportunity. Every year nearly 50% of teachers are learning the basics of school operations, administration and the material being taught. How do we get teachers to invest in long term outcomes and how do we handle mentoring new teachers given how few established teachers there are?

Which makes the decision to focus on this particular practical difficulty almost surreal:

And, of course, another issue is politics. It's hard to reconcile an 80 percent dismissal rate with the existence of teachers' unions: Pushback from unions and the government leaders who rely on their support have largely managed to prevent any breach of teacher job security thus far.

I think the bigger concern is to look at how we would overcome structural staffing issues. Or to wonder if the 80% of temporary teachers could possibly be superior to the teachers they replace. Seriously, I think that the existence of unions is far down on the list of concerns here.

Heck, if we reject a "draft based system" and presume that "social shaming" is unlikely to work, one might wonder if there was a way to invest the additional resources that we'd need to put into salary to make HALF of college graduates delay their career plans to teach in k-12 school systems.

All of this is based on a simulation study, which means the authors have failed to account for the degradation in the teaching pool as they increased the rate of rejection of teachers. By holding the job pool constant (i.e. holding the quality of the marginal recruits constant as you decrease the retention rate) they have made one of the classic mistakes of regression analysis.