Loeb Theorem Cartoon

I can’t say I could describe this theorem after reading this highly entertaining cartoon, but it certainly offers a great deal of food for thought.

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Cost Per Student Per Hour

Let’s say it costs a district $10,000 annually to educate one student. Divide that estimate by 180 days per year, divide again by 7 hours of instruction time per day, and we get $7.94. This back-of-the-envelope calculation shows that, for every ten thousand dollars in annual spending per student, a given student will receive, without charge or obligation, a value of $7.94 each hour she attends class. This money – of course – comes from the local taxpayers.

Now, let’s say we look at a high performing private school. I’m arbitrarily choosing Harvard-Westlake in Los Angelos as an example. At HW, tuition and books runs about $31,000 annually. Do the same rough calculation, and we’ll see that a student receives $24.60 worth of instruction each hour of class she attends. (I’m assuming the public school student and the private school student attend class for the same amount of time). All of that money comes from the student’s family.

Here’s my question, as a sometimes naive non-economist: If the public school student experiences a net value of +$7.94 in her education and the private school student experiences a net value of -$24.60 in her education, why does the public school student perform worse in higher-level academics and careers than the private school student? I can ask the question another way: Why does the private school student perform better in higher-level academics and careers if her financial costs are not supplemented?

The question may be naive because, it seems, the financial burden of acquiring an education differs from the personal enrichment of having acquired an education. The two differ qualitatively, even if we could come up with some way to compare them through an arbitrary quantitative benchmark.

Yet I think there may be another issue at hand – and here’s where someone with a strong background in economics can help me out. It seems to me that when a service provides an individual some value at no risk, the individual has trouble redirecting the given value in meaningful ways.

It’s like if I gave someone a dollar who didn’t ask for it. He may be greatful, but, up until that point, he had no plan for using a dollar. He must now decide what to do with the free money, and his decision may end in frivolity – like buying a lottery ticket.

Based on this story, we might observe that public school gives students far more opportunity to gamble with their education than private schooling does. The incentive to learn does not exist, or, the incentive to learn in public school values at -$7.94. For private school students, the incentive is much higher – as high as +$24.60 – depending on how you factor in being “spoiled” or “pampered.”

Days since last post…

Kind of like:

The Standup Economist Translates Mankiw

How (not) to Assess Teacher Performance

Michele Kerr suggests (1) teachers should be able to remove disruptive students more easily from the classroom; (2) teachers should only be assessed on the results of those students with 90 percent or higher attendance; (3) students who don’t achieve “basic” proficiency in a subject should be prohibited from advancing to the next grade level; and (4) teachers should be assessed on student improvement, not an absolute standard.

Would you agree to tying your performance reviews to student test scores if these four elements were in place?

via Education Week.

I do not agree, since there doesn’t seem to be anything left to review once you take away classroom management, attendance, and – well – teaching. The fourth point looks like a plateau with even less substance.

Test Less?

When it comes to assessment, the United States is an international outlier. As Stanford University’s Linda Darling-Hammond has shown, many nations with better and more equitable educational outcomes test far less than we do. They typically test just one to three times before high school graduation, and use multiple-choice questions sparingly, if at all. Excessive testing wastes educational resources and fosters the use of cheap, low-level tests, while adding high stakes narrows and dumbs down the curriculum. The results provide little instructional value to students, teachers, schools, or districts.

via Education Week: A Better Way to Assess Students and Evaluate Schools.

A great point, however, be careful when comparing across borders: a country’s institutional structures and civic attitudes can and do influence political outcomes. Compared to alternatives, testing may be the best option for American schools … but we have to look at alternatives first.

Definitions: “Incentives” v “Accountability”

Incentives give individuals reasons to act; usually, people act on certain information that signals a positive contribution to one’s own wellness. An incentive might look like this: If I do X, I will gain Y and Y makes me happy.

Accountability enables the collective to sanction individuals for undesired action. In a way, accountability serves as an inverted incentive: you know a failure to perform certain actions will result in a negative contribution to your wellness, so you try harder to perform accordingly. An accountability measure may look like this: If I fail to do X, I will lose Y and Y makes me happy.

Both incentives and accountability can influence the same set of actions. For instance:

X  ->  Y     Johnny works for a living, Johnny gets paid well.

-X -> -Y    Johnny does not work for a living, Johnny does not get paid well.

Notice the subtle difference. Incentives presuppose that individuals do not already have Y and accountability presupposes that individuals do already have Y. (By “presuppose,” I mean that the conditional holds by strength of the consequent term. We don’t care about the cases in which someone doesn’t act on the incentive or doesn’t care about being held accountable.) Y makes the individual happy; but, insofar as the individual has differing interests in increasing her happiness as opposed to avoiding a decrease in her happiness, she will respond differently to incentives than to accountability measures.

For instance: you might act on my offer to give you a free ounce of milk for each cookie you buy from me, but you might not respond if I threaten to take from you an ounce milk every time you don’t buy a cookie.

So be careful when – in arguing questions of policy – you bring up a point about providing incentives when the issue is over accountability, and visa versa. You may have confused your terms.