# If I had a million dollars

The legal internets are atwitter with talk of a new paper which suggests that a law degree is worth a million dollars. It’s an interesting exercise in econometric advocacy, and I’m going to spend some time analyzing the authors’ claims.

I’m going to proceed in two parts. First, I’m going to assume for the purposes of argument that the paper’s interpretation of its data is correct in regard to the value of law degrees acquired in the past, and that, as they argue, there is no good reason to assume this value will not be maintained in regard to law degrees acquired in the future. Then I’ll critique those assumptions.

Simkovic and McIntyre estimate “the mean pre-tax lifetime value of a law degree as approximately $1,000,000.” Wary readers will have their suspicions triggered by the words “mean” and “pre-tax.” And indeed the authors’ impressive-sounding conclusion is watered down considerably by looking at their data in terms of median post-tax outcomes. (Taxes are of course an extremely relevant consideration in this sort of analysis, since a law degree must be paid for in post-tax dollars, to service a debt incurred at what under current conditions is a very high interest rate).

The authors estimate that the median post-tax value of a law degree is (or has been, which they treat as the same thing) $420,000. Since they assume a working life of 42 years, they are in fact estimating that for the median graduate a law degree generates a $10,000 annual income premium (in 2012 dollars) over what an otherwise similar college graduates who choose not to go to law school could expect to earn over the course of their lifetimes.

That still sounds like a pretty good outcome, even if it’s not nearly as spectacular-sounding as the headline-grabbing million-dollar claim.

Yet the wary reader will have noticed a striking omission from the argument so far: *how much is it going to cost a law graduate to generate this premium?* It’s no exaggeration to say that the authors are doing the equivalent of arguing that buying a house is an excellent investment, without factoring into their analysis the fact that acquiring a house usually costs money, and that most of this money is usually borrowed, and then paid back over time.

The authors do try to estimate how much law students are currently paying in tuition, and conclude rather vaguely that law school tuition is a whole lot less than a million dollars. Thus they elect not to include the cost of a law degree in their estimate of its net present value, since “for most law graduates, the net present value of a law degree typically exceeds its cost by hundreds of thousands of dollars.”

A wise man once noted that we are all interested in the future, because that is where you and I (and prospective law students) are going to spend the rest of our lives. And indeed Simkovic’s and McIntyre’s argument is expressly prospective: they claim that going to law school will continue to be a good to excellent investment for the typical law graduate, although not of course for every single person who chooses to go to law school.

To evaluate this claim, we need to know how much getting a law degree is going to cost the typical law graduate who enrolls in law school now. This requires a bit of extrapolation, although to a far more modest degree than the authors’ attempt to extrapolate the lifetime earnings of current prospective law students. The vast majority of law students borrow the vast majority of the cost of attending law school. For the purposes of this analysis I’m going to treat graduate debt at repayment as a proxy for the cost of attending law school, although this is in fact a significant understatement of that cost, since it excludes costs paid out of pocket, and opportunity costs.

The typical law school matriculant who enrolls in law school this fall will have about $200,000 in education-related debt at repayment, six months after graduation. I emphasize that this is a conservative estimate. (For one thing, it assumes that the amount law students borrow will increase by only 3% per year over the next three years, even though in recent years that figure has increased by 5% to 6% per year).

That figure is derived as follows: About 80% of law students are either attending private law schools, or paying quasi-private law school tuition. (Quasi-private law school tuition includes in-state tuition at the several large public law schools where in-state tuition is now as much or more as average private law school tuition – for example in-state tuition at UC-Berkeley is now $51,000 per year — and students paying out of state tuition at public law schools).

If we assume the average amount borrowed by these students will increase by 3% per year, they will borrow a total of around $140,000 during law school. Most of this money will be borrowed at 7.9%, while the rest will be borrowed at 6.8%. Interest will accrue on these loans as soon as they are issued, so total law school debt at repayment six months after graduation will be around $167,000. In addition, people now graduating from college who have debt (70% of all graduates) are carrying an average of about $35,000 in college-related debt.

So the typical law school student who enrolls this fall will have around $200,000 in educational debt, the vast majority of it carrying an interest rate of around 7.5%.

Recall that the authors estimate the median post-tax value of a law degree as $420,000. How much will the typical law student end up paying, in principal and interest, in order to make this investment?

The answer is $444,150 (This assumes graduates will use the “extended” 25-year repayment plan, since at these levels of debt service what used to be called the “standard” ten-year repayment plan will be out of the question for all but a small percentage of very high earners).

Does this mean that, even assuming the authors’ claims about the income premium generated by a law degree are actually correct, a law degree will have negative net present value for the typical matriculant in the class of 2013? Not quite. This is because the authors discount the hypothetical future earnings of current law students to present value. So – again, granting the accuracy of all of their data and methods – the present value of a law degree for people now enrolling in law school would be the difference between $420,000 and the negative net present value of a legal obligation to amortize $200,000 of debt at 7.5% interest over the next 25 years.

What this latter figure is depends on various assumptions about future rates of inflation and the like, but, given recent historical trends (inflation has been considerably less than half of the interest rate law students must pay on their debt), it’s reasonable to assume that the negative net present value of this obligation is somewhere around halfway between the present payoff cost of the debt and the total future income stream necessary to amortize it under its terms. (The authors use a real discount rate of 3%, which is congruent with this assumption).

In other words, if we give the authors’ analysis every possible benefit of the doubt, we would conclude that, after including the cost of the investment in the analysis, the typical pecuniary premium generated by a law degree acquired by matriculants in the class of 2013 will be about $109,000. $109K thus represents the median net present value, if we accept the authors’ calculations, of a law degree, after subtracting both taxes and the net present negative value of the investment cost, discounted at the same rate as the higher earnings.

In part two, I will critique the authors’ data and methods.