A Note on Private Law School Tuition Projections Methodology

Diligent readers may know that as of right now I’ve updated about 60 percent of the law schools on the tuition page, which includes tuition projections for private law schools. However, the tuition projections page itself has not been updated. That’s where I am. I’ve decided that before I get to that page specifically, it’s worthwhile to discuss/digress on the methodology I’ve chosen for projecting private law schools’ tuition individually. The reason I’m doing this is that both the tuition page and the projection page have been cited by researchers and academics (the latter page even making an appearance in Chapter 9 of Brian Tamanaha’s Failing Law Schools (FYI: Yale’s projection is actually one of the most accurate ones)), and these types of people might want more detail on the numbers. I think they’re entitled to it, but I also think that casual readers won’t be so interested (you should be), so I’m creating this post separately.

As of fall 2012, there are 117 private law schools outside of Puerto Rico whose tuition the Official Guide tracks. I exclude the two private Puerto Rico law schools for two reasons: one, the dollar’s purchasing power is lower there so including them slightly distorts any averages; and two, neither behaves like stateside law schools in terms of tuition increases. Why do I not include public law schools in the projections at all? Because they are (usually) subsidized by state governments, and the goal of the tuition projections is to see where tuition inflation due to increased spending (including cross-subsidizing students) will go, not tuition inflation due to decreased subsidies. As of right now, I’m also excluding public law schools that are clearly not subsidized by their state governments, even though I sometimes include them in my synthetic, “Adjusted Private Law School” category in other discussions. That may change in future methodological analyses.

This post analyzes the projections methodology by testing it on the last year for which precise data are available: 2011. The results, incidentally, are an interesting lesson in measurement accuracy and precision. The projections are all characterized in nominal dollars to avoid the need for projecting future inflation as well. Arguably, inflation is a minor factor in law school tuition increases, but I’ll not ponder that today.

The Methodologies

There are three potential methodologies I can think of for projecting private law school tuition.

(1)  The current methodology merely extends the linear regression for each law school’s tuition individually into the future based on its Official Guide tuition data going back to 2004 or whenever it was first available. The basis is that past tuition increases are a guide for future ones.

(2)  If one believes that various factors distort individual law schools’ tuition trends, an alternative is to take the annualized rate of average private law school tuition increases and apply it to private law schools individually, an “ecological” methodology.

(3)  Finally, one can try to accommodate both methodologies by calculating the annualized rate for each law school individually and using that rate into the future. In fact, this methodology takes the worst qualities of both: it makes any distortions exponential rather than linear.

The Facts: What Do We Know about Law School Tuition

Before jumping into the analysis, it’s necessary to discuss a few empirical findings from what’s available in the Official Guide from 2004 to 2011 and elsewhere.

  • One would think that law school tuition grows exponentially, but in reality it’s better characterized as linear growth because the R­2­­ statistic (shown below) is closer to one for linear regression than exponential regression. This is why I chose the linear regression methodology in the first place.

  • Even so, the rate of nominal tuition increases has dropped recently, and we know it’s below five percent in 2012 as well. Unfortunately, even the linear regression model doesn’t capture this for 2011. It’s about 16 percent higher than what actually happened.

Comparing the average growth rate from 2004-2009 (5.74 percent) to the average growth rate in 2010-2011 (4.27 percent), the rate dropped by about a quarter, and it stayed at about that level in 2012, according to the National Law Journal.

  • Speaking of distortions, a handful of law schools saw rapid tuition growth between 2004 and 2011. The furthest outlier is Faulkner University, which after obtaining ABA accreditation went from charging $15,000 per year in 2006 to $32,200 in 2011, a 14 percent annualized increase that dwarfs all other private law schools. Six others increased their tuition by more than a 4.9 percent annualized rate, placing them in the third average deviation or higher of tuition increases (the mean is 3.1 percent annualized). These law schools frustrate tuition projections for a few reasons:
    • (1) The first and third methodologies above, which use individualized rates, are certain to overstate these schools’ tuition in the future. Faulkner in particular is way, way out there.
    • (2) Given the drop in applications, I doubt private law schools will go on building sprees as they did in the past. Then again, there appears to be an endless supply of wealthy alumni who are willing to finance new buildings, so I could be terribly wrong.

  • As stated above, it’s very unlikely law school tuition will increase at a high rate again. Although I don’t expect the average nominal price to drop (the prices are very sticky downwards), I also don’t expect them to go above five percent ever again.

The Test

For 2011, all three methodologies produce average private law school tuition figures ranging from $40,100 (linear regression) to $40,300 (individual annualized rate), all high as the actual rate was about $39,700. However, comparing the absolute values of the variances between the projected tuition and the actual tuition provides a clearer finding: the average annualized rate is the most accurate but also the most dispersed.

Linear Regression Average Annualized Rate (5.51%) Individual Annualized Rate
Average Variance 2.2% 1.6% 2.0%
Avg. Deviation % of Variance 27.7% 37.6% 31.3%

However, since we know that law school tuition is not likely to grow as quickly as it did in the past, we’d want to know the actual variances, not their absolute values, because law schools that come in below the projected average will probably be more accurate in the long run than those actually at the average. When we do this, we find just how poorly the methodology I’ve chosen performs in terms of precision (had to say it).

Linear Regression Average Annualized Rate (5.51%) Individual Annualized Rate
Average Variance 1.2% 1.1% 1.6%
Avg. Deviation % of Variance 78.87% 3.3% 2.3%

Here’s what it looks like. To clarify, I counted these using the “FREQUENCY” function, meaning the tick marks on the x-axis mean that the result is greater than the previous tick mark but less than or equal to the current one, so on the red line, 36 private law schools’ projected tuitions were greater than one percent but less than or equal to two percent above what their actual tuitions were, a very precise yet mildly inaccurate finding that would rapidly compound over time.

That blue bump on the far right is, of course, Faulkner, but the blue bump on the far left is Cooley, which raised its tuition by much more than we’d expect based on a linear regression of its previous costs going back to 2004. Here’s a simpler chart to make things clearer, same >x­­≥% rule.

It’s obvious that the individual annualized rate is the worst of both worlds; it’s less accurate and less precise than the average annualized rate. I’m eliminating it as a viable alternative to individual linear regression.

But there you have it: An unpleasant tradeoff. Either I switch to a methodology that precisely predicts tuition will be higher than it will be (though it “rescues” Faulkner and predicts its tuition much more accurately), or I stay with the original methodology that is more accurate on average but more imprecise overall.

Conclusion

Of the three methodologies I’ve tested, none really gives me the results I want, but then again, I have a perfectionist streak. I may run this variance test again when the 2012 tuition numbers come out in official form (U.S. News is close, but … perfectionism), but trying to find a one-size-fits-all formula for projecting private law school tuition increases might not be possible. I have other ideas up my sleeve, like basing the trend on the last three years’ tuition, excluding more recently accredited law schools entirely, or listing the law schools’ annualized tuition growth rates and/or R‘s and highlighting those that are unusually high or low.

In the meantime, though, I’ll stay the course for at least three reasons: (1) I think linear regression provides a reasonably accurate assessment for average private law school tuition overall (half the R2‘s are greater than .993), (2) the numbers aren’t outrageously wrong even 10 years out, which is more than enough, and (3) my original motivations for publishing the tuition projections remain valid. Law school tuition will continue to increase, though not as high as in the past, I think, and it’s important for anyone who cares about the issue to see that. I particularly hope that any potential applicants who see either the tuition page or the projections will see law schools’ Janus-faced behavior, how they can speak solemnities about lawyers’ important roles and responsibilities in society while at the same time collecting rents from taxpayers and showing contempt for their students’ futures.

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One Response

  1. […] years from now. This requires a note (or digression) on the methodology I use. Last year, I went to great lengths to justify my decision to use law schools’ tuition data in individual linear regressions for […]

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