Tuesday, November 10, 2009

Throwing Money at the Problem

Ran across this graphic today on the rate of return states get from the money they spend on education as measured by high school graduation rates. (Click through to see the a larger version.)

High school graduation is an important indicator of later financial success, with high school graduates earning $14,000 more annually than high school dropouts.

The first thing I noticed is that this is a really, really bad graphic representation of the data. What do you get from looking at this picture? Not much. There is no order, there is no representation of magnitude. Just not very effective, so I shoved the numbers from the graphic into a spreadsheet and got something a little more interesting.

Now in this graph you get a better feel for the data. The x-axis (on the bottom) is the amount each state spends per student, and the y-axis is the high school graduation rate.

You can click on the graph for a larger image - but the actual numbers are not particularly interesting. What is interesting is the randomness of the data. And why is randomness interesting? Because if spending more money on education was related to high school graduation rates you would expect the points to start in the lower left corner and move up to the upper right corner. The randomness of the points indicates the stunning lack of correlation between spending and graduation rates.

Those three points way out to the right are (from top to bottom), New Jersey, New York, and Washington, D.C. All three spend over $12,000 per child annually, but get extraordinarily different graduation results.

For those of you interested in geeky numbers, r-squared for a linear regression is 0.0373, and even for a six-degree polynomial regression (remember, there are only 51 points), the r-squared only gets to 0.2191. How low a correlation is that? If you try to correlate the first letter of the state (a pretty random value) with the graduation rate the linear r-squared is 0.0873, more than twice as high as the r-squared for dollars per student. That is a stunning lack of correlation.

Now, there are huge problems with compressing the entire education system down to two numbers. It ignores any quality factors like what the actual graduation requirements are (some states will have more demanding graduation requirements), and also what each state considers a student (are special education students included in both figures, or incarcerated youths, or students in private schools), so it's easy to quibble and get defensive on a case-by-case basis. You could also argue these figures should be weighted in importance based on population size (which these figures are not). No question that there are some apples and oranges comparisons.

What is clear in spite of those differences is that money alone does not fix the education system. Money, is probably not even the primary factor in educational success. Utah and Colorado have identical graduation rates, but Utah spends $2400 less per student. How does that happen? New York spends almost twice as much as Texas, but has a lower graduation rate. How does that happen?

Education is not a simple problem and, as this data shows, it does not have a simple answer, not even money.



  1. What about life-cost and teacher salary? What about teacher-per-student? What about school infrastructure? And how does spending money now affects graduation of those that are studying for the past 14 years? Is that spending an average? Knowledge is path dependant, people who have learnt how to learn in the past (when perhaps expediture was higher) will have better performance, for example.

    These numbers say nothing, rather than try and fail (if you go just a little beyond the number) to criticize the government's strategy. Look at South Korea, Finland, China, and so many other countries history of education investment and you'll see that their relative fast economic (and life standards) growth is directly related to education expenditure - but of course with the delay of students actually getting into the market place.

  2. I appreciate your add'l graphic. Brings a little more clarity. We have three children in two different public schools in NYC, and even then, the parents are expected to donate additional monies ($250/student in one and $600/student in another) to augment what the DOE doesn't give us.

  3. Innovationtool: I understand your points. That's why I put in the bit about the dangers of compressing the data.

    To rebut:

    Life-cost and teacher salary: I doubt this is impacts the data. Is New York really 67% more expensive than California? Somehow I doubt it, yet their graduation rates are similar (California is higher).

    Teacher per student: irrelevant to the argument. A graduation rate is a graduation rate is a graduation rate. If graduation rate is your measure of success then whether you spend the money on more teachers to reduce class size, more computers, better music education, more field trips, or increased janitorial staff does not enter into the argument so long as increased spending improves the graduation rate.

    Spending money now vs. graduation rates in the future: I can't speak to this. I did not investigate the data beyond what was presented in the graphic, so I don't know if the dollars were for a single year or averaged over a period of time. Clearly the data would be clearer if the dollars were averaged over the usual 13 years of primary and secondary education.

    Knowledge being path dependent: yes it is. However, while some kids will be inspired by a teacher, most will likely take their educational cues from their parents, just as they take their political and religious cues from them. I suspect that parental attitudes are a huge factor in high school graduation rates - and one that additional funding will not affect at all.

    Criticizing government strategy: I do not intend to criticize any strategy. My interest is simply in understanding the data presented. Certainly there needs to be investment in education, but like any other investment, there are diminishing returns and it may simply be that we have hit that point as far as gross dollars being invested in education. We have plucked the low-hanging fruit. If that is the case then to improve education it is necessary to target specific factors that not only correlate to improved graduation rates, but are in fact causal factors in the improvement.

    Two things to keep in mind, though. First, the federal government really only has one tool at its disposal: money. As the saying goes, when the only tool you have is a hammer, everything looks like a nail, by which I mean it is difficult for the federal government to solve a problem that cannot be fixed by additional funding.

    Second, not all factors will be affected by money. If parental influence were to be the largest factor in high school graduation rates, then all the money in the world would not change the outcome.

    One other thing to consider: maybe the least expensive solution is simply for the federal government to pay X thousand dollars to each student on graduation. It sounds crass, doesn't it? But having an explicit, tangible goal might encourage a higher graduation rate than anything else the federal government could do. How motivated would a kid be to get $13,000 on graduation, no strings attached? And that's just a thousand dollars per year per kid. Just a thought. A heretical thought to be sure, but if you're only looking at the dollars spent versus graduation rates then it is a viable solution.