Last week I posted an analysis of the ABA employment data that ranked law schools by collapsing all the employment data (109 pieces of information) down to a single dimension. I posted this in response to The Faculty Lounge blog's post by Dan Filler that had some strange results, such as Kentucky Law being tied for #2 ahead of Harvard, Stanford, NYU, Chicago, etc. and Georgetown Law being tied for #78, below multiple schools that are unranked in US News.
The ranking created by Professor Filler was obviously methodologically flawed, but my prior post didn't explain why. In this post, I create a two-dimensional version of the prior ranking that shows where things went wrong with the Filler ranking. In the plot below, I show a two-dimensional representation of the ABA employment data, based on a principal components analysis and rotated π/4 radians counterclockwise.
Enlarge the picture by clicking on it. Analysis follows below...
As you move from left to right, schools tend to have better employment numbers where any type of employment counts, independently of the "quality" or prestige of the employment. Thus, schools like Kentucky and Seton Hall, which ranked in the top ten in Professor Filler's ranking, are on the right-hand side along Chicago, Duke, Penn, etc. Many schools that are not necessarily "elite" national schools rank very high, in some cases even higher than elite schools. This is the dimension that Filler captured in his ranking. Note that Georgetown does not look particularly elite, with a worse score than University of New Mexico.
As you move from the bottom to the top, however, you see that there is another dimension that Filler's analysis missed. This dimension represents mostly Biglaw jobs and federal clerkships, and here there is a clear separation between the elite schools and other schools. Even schools that have very good overall employment numbers, such as Kentucky, do not rise very high on this second dimension of employment outcomes. Not all employment is equal in the eyes of law students, and this two-dimensional plot teases out different types of employment success.
Where one schools is higher than another school on both dimensions, the first school has better employment outcomes than the second (assuming away statistical error, other meaningful dimensions, and the like). But where one school is higher on one dimension and another school is higher on another dimension, the decision depends on an individual student's preferences (indifference curves). A student who is focused on prestige would take the vertical dimension into account more than the horizontal (a more horizontal indifference curve). A student who is focused on employment but doesn't care as much about prestige would focus on the horizontal dimension (a more vertical indifference curve).
The ranking published in my prior post blends these two dimensions, which means that schools have higher employment rankings as one moves toward the upper-right side of the plot. That is why Chicago came out on top even though Columbia appears to have slightly more "prestige" placements and Cornell appears to have slightly more placements overall. Chicago had the best blend of prestige and overall placement.
Why Harvard and Yale aren't dominant on either dimension is a bit of a mystery. Most likely the reason is because they have higher levels of placement in ambiguous categories, such as academic, government, or JD advantage jobs, which are present in both elite schools and lower-ranked schools, but mean very different things at elite schools and lower-ranked schools.