Dangling epsilons

Whenever I look at an estimation equation like this:
from this paper, I wonder what’s in that dangling epsilon term. In this equation we have Y’s on the left hand side. And I think to myself, “what kinds of things produce Y’s (or changes in Y’s)”. Now, Y is GDP and from my intro macro class I remember things like K’s and L’s produce Y’s. So given there’s no L’s and K’s in the equation, they must be in the dangling epsilon.

Changes in labor and capital are in the error term, but this is only a problem if changes in these factors of production are correlated with the other variables on the right hand side that aren’t in the error term.


It seems to me changes in labor and capital are correlated with changes in government expenditures (and military expenditures in particular… after all, the military is the worlds biggest employer). So while this paper claims to show the effect of military expenditures on output, it really shows that military expenditures create jobs and attract capital (they have an IV but as far as I can tell it doesn’t address this issue).

But can we salvage the overall message of the paper? Isn’t creating jobs and attracting capital exactly what we’re trying to do with fiscal stimulus? Yes, but not if it means that labor and capital is coming from other States. GDP is increasing in the States that have more military expenditures but is necessarily decreasing in the States that are losing workers and capital. Because these two effects cancel each other out, the “true” fiscal multiplier is less than the 1.5 estimated by this paper.

New course in social psychology

As I, fingers crossed, wind down my graduate work in economics, I am looking for new hobbies. I was thinking about getting back into baseball. I loved baseball when I was a kid and now, thanks to Moneyball and Baseball Prospectus, there is a “scientific” sub-culture where I would fit nicely. Plus, I’d finally have a reason to get cable.

Or maybe the stock market. Lots of easily accessible data. Check. Interesting theory. Check. Lots of amateurish dabbling. Double check. The only problem is I can’t get excited about trading stocks. The data crunching has moved analysis so far away from the fundamentals that unless you think winning at zero-sum games is fun it’s hard to maintain excitement about it. I’ll probably dabble.

Then there’s social psychology. There’s some data and amateurs abound. Methodologically, the field is familiar to economists but they have done what economists are only starting to do; they’ve dropped the assumption of context independent behavior. The field is young enough that it still has a multi-disciplinary feel and every new finding seems revolutionary. Will Wilkinson is teaching an introductory course in it at his new blog (partial syllabus here). I’ve signed up.

The most subversive sentence I’ve ever written

In a paper on the “selection” of Mexican immigrants where we find that Mexican immigrants to the US are about the same as non-migrant Mexicans in terms of observable skills like education and age but, as it turns out, they have lower unobserved skills:

It may be the case that because many border crossings occur without documentation, there may be selection on certain unobserved characteristics (e.g. risk-taking, underestimating dangers, low respect for authority) that may have a negative correlation with productivity.

Man, I feel like running down the street with a black bandanna covering my face, breaking windows and burning cars!

R: solving a small system of equations fast

My google-fu failed me on this one, so for the next person googling “stupid fast library for solving a system of equations in R such that the trade off between speed and ‘robustness’ is way on the speed side”, you’re welcome.

I’m on the final leg of my dissertation and I have some code that loops through a discreet state-space with about 300k points. Each of these iterations requires a two-equation non-linear system to be solved. Because all of this is contained in a loop that is (supposed to be) converging on a pair of value functions, its not super critical that the solutions to this system are “correct” every time. I want speed, baby.

Here’s the R libraries I tried:

  • nleqslv with the functions written to have a high penalty: each iteration took 0.020 seconds with a standard deviation of 0.007 seconds
  • optim using the “make the system a single quadratic” trick and having a high penalty: mean 0.253 seconds with a standard deviation of 0.130 seconds
  • optim using the “make the system a single quadratic” trick and using the “L-BFGS-B” algorithm to deal with boundedness: mean 0.014 seconds with a standard deviation of 0.032 seconds
  • pso (partical swarm optimization) with bounds: mean 20 seconds!

I was kind of excited about particle swarm optimization but it was waaaaaay slow (at least with the default settings). The best was optim (available with the R core installation) using the quadratic trick. The quadratic trick is just defining all your functions in the system with the right hand side equal to zero and then having the algorithm minimize the sum of squares of those equations. Interestingly the nleqslv library, which is built for solving “medium-sized” systems, did almost as well on average but had had a much better variance. I’m not sure if this is because nleqslv gives up earlier or if it does a better job staying out of pathological parts of the parameter space relative to optim.

Anyway, there you go. If you find your self solving a small system of equations lots and lots of times over and over again, optim should do the trick for you in terms of speed.

PS – R seems to be the wrong environment for this task. Fortran code that does a very similar thing runs about 10 times faster.

Help, Help! I’m being repressed!

I’m watching the re-re-renewed debate about academic bias against conservatives with a little more skin in the game this time around. Two facts about me: for some strange reason I’m considered conservative by my academic friends, especially by non-economists, and I have decided to take a job outside of academics. So clearly there’s bias in the academy! (Where do I pick up my check.)

Megan McArdle has a great post up where she makes the standard analogy between racial and political bias and she points out that, in true fashion for partisans, the table and arguments used have done a 180. Conservatives are arguing against subtle biases inherent in the the system and liberals are calling the game because there’s no explicit rules against hiring conservatives in the academy or they are otherwise blaming the out-group.

The analogy may be apt but you would be upset with me if I said so and I also said, “who cares”! So, I’ll do just that. The academy and places of employment, say, are free associations of individual people. If these places want to exclude interesting people because of arbitrary differences, then its their loss. In the long-run Beckerian forces prevail and the non-discriminating universities and firms win.

Well, except, I care. The long-run could be a very long time! Life consists of the transitions between steady states. Without a model of how fast those transitions are and, importantly, what shapes they take, analyses of the properties of steady states is next to useless. I want to help progress along a little even to just make it visible within my lifetime. I’m selfish like that.

But there are also standard externality arguments. The academy produces non-rival and non-excludable ideas that are used to produce innovations that drive economic growth. By excluding conservatives, the academy makes the idea generating process less efficient and we all lose out. We need to subsidize Rush!

What’s upsetting about these reasons to care about discrimination is that they don’t apply to racial discrimination or other types of discrimination that I care about much more than bias in the academy. First, I’m not creative enough to make the externality argument for blacks or women. Why does discrimination against them harm me, a white male?

Second: of course the long-run is undetermined with regards to racial discrimination too, but it is not clear that the long-run transition to equality is being driven by the dynamics of discrimination. While there’s significant evidence that anti-discrimination laws had an effect on closing wage gaps, there’s much less certainty about the size of that effect. One estimate has the black-white male wage gap in the South BEFORE the CRA halving every generation or so. The CRA sped up this transition, but only in the South and only for a decade or so. The half-life reduced to about one half a generation in the decade or so after the CRA but there has been no improvement in the black-white southern male wage gap since. This sweeping legislation appears to have had minimal long-run effects, at least with regards to wage gaps. (PS – these stats are from memory, look up the . Donahue and Heckman paper if you don’t believe me)

One option, at this point, is to throw up my arms and to insist discrimination is no big deal. It will fix itself in the long-run and there doesn’t appear to be anything that we can do to speed up the transition to that long-run. But there’s a larger argument about externalities, ones at the foundational level of institutions and the structure of rules.

Tyler Cowen linked to a new paper from Buchanan that points out that the “rules of the game” are endogenous, they are not given, and more importantly non-rival and non-excludable. There is a “market” failure in the production of rules. The rules of the game are inefficiently produced; there is some marginal change to the set of rules that could make everyone better off and there needs to be some meta process that ensures these Pareto improvements can be made (Buchanan cites Coasean political entrepreneurs). The argument against discrimination: if the rules of the game are arbitrarily deficient for some large group of people then its possible they could evolve to be arbitrarily deficient for a group of people that I belong to. I have interest in making sure there exists a process that removes these sorts of deficiencies.

Does the Welfare State screw the poor?

Milton Friedman’s complaints about rent control and the minimum wage are cliche. These programs hurt the people they’re intended to help. Unintended negative consequences are the first things I look for when I think about a policy intended to help the poor. I just took their existence as an empirical fact.

But I never really thought about the structure of these unintended consequences. So I second Karl Smith’s recommendation to read Beaulier and Caplan’s paper on the subject.

Poverty policy might hurt the poor because:

  1. Poor people pay more for it than they get. E.g. poor people live shorter lives suggesting they get less social security benefits and social security taxes are regressive.
  2. There may be inter- or intra- family externalities. E.g. a welfare program may make a dad better off by leaving his family but his absence may make the rest of the family worse off.
  3. Poor folks are lead to make bad decisions (where bad is relative to a neoclassical norm) for themselves because of the program. E.g. affirmative action leads minority students to choose “higher ranked” schools whereas they would have had better outcomes if they choose less prestigious schools.

The point of the paper is to show that the third possibility is untenable in the neoclassical framework (where expanding a person’s choice set can only make them better off) but it becomes tenable if results from behavioral economics are taken seriously. Plus, deviations from rational expectations may be especially pronounced among the poor.

23andMe data are in…

… and I’m boring. There’s no traces of Indian in me (a now debunked family story) and the white in me isn’t that interesting either:

This chart was produced using EURO-DNA-CALC (h/t Volokh). I’m 1/4 Italian-Swiss (hence the name) and the rest Anglo-French mix so the tool did a pretty good job pin-pointing my genetic origins.

Next, I think, I’ll do this. I have no clue why one would want to phase one’s genes but, you know, “because it’s there”.

UPDATE: Here’s one reason why you’d want to phase your genome… Did mom or dad give you your Neanderthal genes?