Whether you should go to college, that’s what. At least, whether you should do so as a financial matter. Who knows if she’s qualified to provide advice with regards to any other basis of evaluation, but I’m confident she’s very competent at finance, and more to the point, she’s going to be setting nominal interest rates pretty soon, and that’s what really matters.
Now, we neoreactionaries are keen on trying to understand human nature which we assert is highly heritable, variable between diverse human population groups, and robust to efforts to neutralize and replace it through social engineering.
Here’s human nature – I write a giant post demonstrating mathematically how unskilled immigration can increase inequality and depress wages for your existing working class citizens (absent some semi-preposterous assumptions) – a subject of imminent political import – and I get zero feedback on the merits of the argument. That’s to be expected. Nobody likes math modelling. Not Vladimir, and I’m not quite sure about zhai2nan2 over at vulture of critique.
On the other hand, since I’m a social, friendly guy who believes in building community, I would like all the bloggers and commenters towards which I feel affinities to also try to get along better and be friendlier with each other and to see me as an ally instead of an adversary. Also I thought it might get his attention and nudge Nick B. Steves to come out of hibernation (mission accomplished!). So I tried to smooth things over with Charlton by inviting him and other to talk about religion a little and Bam, I start getting bombarded, including multiple hits from freakin’ Kyrgyzstan. How’s Manas doing boys?
The point is, that’s what people want to talk about, arguing about religion and such, the universal past-time, and that’s human nature. They certainly don’t want to engage with equations. As Derb points out, it’s a bizarre minority taste.
I get it. But, you know what? My blog, my rules, my math.
Vladimir is skeptical of mathematical presentations claiming to model reality but without solid epistemological foundations. That’s fine with me. But you know what everyone agrees we should use math to do? Accounting. So let’s do some college accounting.
Why? Well, there’s a constant stream of chaotic and unorganized higher-education chatter in the econoblogosphere these days. Is it just signalling or acquisition of useful, valuable skills? For example, Arnold Kling supports ‘The Null Hypothesis‘ while Caplan makes the case for signalling.
The answer to these questions depends a lot, I think, on what kind of person we’re talking about. College is just an enjoyably social, but time-and-money wasting hoop to jump through for a lot of people on their way to adult working life. They wouldn’t do it if it wasn’t essential to getting a good job and having higher social status. They never cared about what was being taught, and they rarely retain more than scant amounts of the content.
Only the other hand, the above benefits are merely perks and icing-on-the-knowledge-cake for others, who have talent and motivation and derive a lot of personal and professional value from their college experience.
The backdrop for all these concerns is the explosion in tuition costs over the past generation. WaPo just did a 10-part series on it. Glenn Reynolds wrote a whole book about it. It’s starting to bite, and so people are noodling on the whole subject. It’s interesting to me how little good practical advice is available for teenagers and parents. But I’m from the government and I’m here to help, so let’s get started.
Our finance-obsessed teenager is a hard-core Friedman fan and loves him some Consumption Smoothing. In fact, at 18, all he cares about regarding the decision of whether to attend university or begin working is which path will give him the highest smoothed consumption level over his lifetime. He starts out with zero savings.
If he starts work, he sets out on a non-college income path, finances some of his consumption with debt early in life, but gradually breaks even and accumulates equity until retirement, which he then spends into nothing at the moment of his death.
If, instead, he goes to college, he has to borrow a lot of money to pay the hefty tuition and also forgo the opportunity to work for four years. But then he has the opportunity to work on a higher income path. It’s kind of like the decision to go into the military as an enlistedman or an officer, but without the education and pension benefits. But will he be able to come out ahead?
He goes to his gypsy psychic and government statistics parser high school guidance counselor and she looks in her crystal ball and tells him the two income paths for High School graduate () and College Graduate (), as well as Tuition (T):
Which combined with college tuition should look something like this:
With equity over time looking something like this if you retire at 65 and die at 80 (the numbers aren’t important at this point, just the relative shapes of the curves):
Now, the first thing we’re going to need is a way to transform the start points and income paths into equity and an unknown smoothed consumption level given continuous interest operating on a arithmetic annuity. Thankfully, we can do this with a basic first order linear differential equation solution technique. (Who knows if education is useless or not for people in general, but I learned techniques like this in high school, have never used it in my work in my whole life and it’s never been part of my compensation, and yet really value knowing how to do it. I don’t know if I would have ever learned it on my own if left to my own devices.)
Well, after a little manipulation, we get an equity equation over time, where C is the smoothed consumption level, i is the interest rate, and F is the annual raise our youngster can expect to receive:
For the High School case, you start at equity 0, sove for E(R), where R is retirement age, and then solve for the level of consumption that brings equity down to zero at death age, D.
Now, wait a minute. It’s one thing to estimate one’s retirement age. It’s another to know how long you’re going to live. The huge uncertainty involved is why we have things like Social Security. What is this, some Greek Mythology Existential Crisis?
Well, fortunately, and logically if you assume you’ll retire at the same age and live just as long in both paths, all that really matters to is the amount of savings you have at retirement. We only have to solve for zero at death as an intermediate step, but it must somehow cancel away later. is his starting salary and is his annual raise.
What we get is a mouthful:
We do the same thing for the College Graduate path (, starting salary, , annual raise, , tuition) but in three steps. Down for four years, up for working career, then down again from Retirement (R) until Death (D). An slightly bigger morsel to chew on.
And now we’re going to combine them into a real mouth stuffer: Let
Whew! We’re going to set because that will help us determine the conditions of our decision-change point. Since the prices are nominally arbitrary, we’ll scale them all to using and
Now we can define which is the minimum ratio between the High School Graduate starting wage and the College Graduate starting wage needed to financially justify picking the college path. Stretch your esophagus and throat muscles for this one:
Now for a few slights-of-hand, er, I mean, ‘reasonable assumptions for simplification’.
Let’s assume the scaled annual raises are both small compared to total wages (on the order of the interest rate) and close to each other. That should make the and terms above nearly cancel out. Exemplary justification: If and then if the raises are close the remainder is only . Remember that is scaled in terms of , so it’s probably less than 0.1 and the remainder error in Z is probably less than 0.02. Even if bigger, it’s still small enough to ignore, and there’s always the wage compression phenomenon to help us out.
Much more manageable! Now, let’s set Retirement at 65 years old. And lets express the interest rate in terms of x% instead of . A good approximation is:
Voila! Goodness, only the interest rate is left.
Assuming all the reasonable things we assumed, even if the interest rate is zero, a college graduate starting salary must be at least 20% greater than a high school graduate starting salary. As the interest rate rises, so does Z, but not too fast. At about 6% it means a minimum 50% premium for financial justification.
Even if you can’t do all this symbolic manipulation nonsense, it’s ridiculously easy to simulate all of this in any spreadsheet. I imagine one could write a Java app that did it, and maybe even pulled in the latest interest rate and some government statistics on tuition, employment, and income vs. SAT scores. An advice machine. Why doesn’t this exist already? Why isn’t junior being advised in this very practical manner?
Anyway, you may make the mild objection that it is Congress that now sets the interest rates on student loans, and that, under present law, these have nothing to do with either market rates or the Federal Reserve’s discount rate. Furthermore, while there may be some impact in the short run, over the long run Monetary Policy is not thought to influence the real interest rate.
Yes, but. The model assumed the same average interest rate, both for debt and savings, throughout the whole period. That’s a reasonable-enough assumption for the high-school graduate, who accumulates his debts and savings slowly and over a long period of time.
It’s not reasonable for the college graduate, who accumulates a lot of debt over at the very beginning and in a short time frame. The interest rate on those loans are fixed (assuming Congress doesn’t allow ‘refinancing’) and the nominal price of servicing them is thus sticky. His early attempts at savings are mostly trying to fight the compound interest on that nominal debt.
Enter the Federal Reserve. If average nominal interest rates over your life are higher than when you took out your fixed-rate loans, then it acts like inflation-induced debt-forgiveness and you sign praises to the keepers of the secrets of the temple. It also means, if you anticipate this will happen, you can financially justify going to college at a lower wage premium.
On the other hand, if interest rates were high when you took out your loans (which you can’t refinance without a penalty that would nullify the effort anyway), and lower for the rest of your life, then you needed a much bigger premium to justify college. In fact, if soon after college, you were surprised with pegged-to-zero risk-free rates and rampant under/malemployment for college graduates, then … oh snap. Does any of this sound familiar?
That’s bound to make a lot of the younger victims of that process angry and frustrated. But if they can’t understand what happened, they’re bound to make a lot of random, incoherent complains at whatever their ideological preferences tell them should be thought of as ‘the bad guys’. OWS, anyone?
Where were their guidance counselors? Down at the group-think lounge, eating up that pretty-lie cake: ‘everyone should go to college, even below-average kids‘.
Next time, go ask Janet.