Milton Friedman Meets Robert Klitgaard

I encountered the writings of Robert Klitgaard twice.

I read “Tropical Gangsters” an excellent book on his experience working for The World Bank in Ecuatorial Guinea which is not to be confused with the epymenus epyminus (oh hell I’ll never guess the spelling of that word ) CD by King Creole and the Coconuts.

Years earlier, when I was a freshman I think, I saw students protesting “The Klitgaard Report” to the president of Harvard, in which he noted the fact (it’s a simple calculation) that African American students at Harvard had a lower GPA* than would be expected conditional on SAT scores. Brad DeLong, who actually read the report, says he detected no sign of racism in it.

Now obviously we all knew that average SAT scores of African Americans are lower than those of Euro-Americans so the SAT was presumably biased against African Americans (I mean if interpreted as a measure of smarts not assimilation in the dominant US cultural tradition). A justification for affirmative action which I personally liked a lot was that a reasonable prediction of performance would be standard measures (like the SAT) corrected for disadvantage. Thus I was most distressed by the Klitgaard report (not enough to go to the protest where Derek Bok talked to angry students as he often did because I mean he just did a simple calculation and the data ambushed him).

Now I understand. First lets assume that the cultural bias in Harvard grading is the same as the cultural bias in the SAT so race has the same effect on the expected value of the Harvard GPA as on the SAT score. Now note that an SAT score is the sum of the expected SAT score for that individual and a disturbance term which is specific to that test that day. The disturbance term includes did the student have a cold that day etc and also, if the student guessed on questions, did the student guess right. Fact is, if someone takes the SAT twice he or she will get different scores.

Given the fact that the distribution of SAT scores of African Americans is lower than that of Whites (first order stochastic dominance) if one has an African American and a White American with the same SAT score, one can rationally (and illegally) infer that the African American probably had a good day that day and the White American a bad day, that is that the expected value of the day specific disturbance is higher for the African American than for the White American.

Already this implies the Klitgaard effect even if the effect of race on expected SAT score and expected GPA is the same. The explanation of the Klitgaard effect is the same as Milton Friedman’s explanation of the fact that African Americans save more than White Americans with the same income (this is a fact). The same current income implies a lower expected value for permanent income just as the same success at demonstrating acculturation of whatever on a given day corresponds to lower expected level of acculturation to White America.

This is a general issue. There are many many empirical results which I found disturbing in which African Americans have outcomes like White Americans with lower incomes. All of this makes sense of important outcomes depend on permanent non current income. Of course they do. A huge amount of social science research on race and income was rendered obsolete by the permanent income hypothesis decades ago.

Of course that’s not the half of it. Even without colds and lucky guesses and such, the SAT is correlated with GPA but they are not measuring the same thing (whatever it is and whether or not either has anything to do with one’s real ability to contribute to the growth of human knowledge and the fullest flowering of humanity which they might because, hell, anything is possible). For example, in the SAT they gave us tiny little passages to read and it was wise to read every word. At Harvard professors don’t bother to winnow their reading lists so you have to quickly decide what to skip and what to actually read (unless you are Brad DeLong and read 1000 words a minute and never learned that skill and is suffering from that lack now). So for the same SAT score, one would guess that the African American student has more ability to read every word and understand compared to his or her ability to decide what to read when he or she doesn’t have time to read every word.

Ergo** Klitgaard effect.

Now even if the SAT has a particularly strong cultural bias so race has a bigger effect on expected SAT score than on expected GPA, the measurement error statistical discrimination bit can imply Klitgaard’s result if it outweighs the SAT is biased effect.

OK now sticking with GPA as our end point, I note that even if 11% of people who would get a harvard GPA over 3.9 (Harvard is different 4 is the max) are African American, this won’t be true of people admitted to Harvard if 11% of admitted students are African American. It’s that disadvantage and cultural difference and stuff makes the predictors of performance less accurate. Getting a student with an over 3.9 GPA requires that there be such a student and that one detects him or her and that you don’t have to choose between him or her and the son of a super rich alumnus who will give tons of money if you admit his son but it is neither gross class bias or bribery because Harvard is different and superior and you don’t understand and an institution struggling to get by with an endowment of only I don’t know how much more than $ 40 billion*** has to make some compromises.

*Harvard called it something else like a “cube” because Harvard is superior and so it has a superior measure of grades)

** I never heard a Harvard student use that word except when denouncing “Ergo” a really dumb libertarian student magazine published by people who claimed some affiliation to MIT.

*** I note that the person who will start managing all that money in one week, Jane Mendillo seems to be neither male nor anglo. Another glass ceiling broken. Now she can decide whether to bail out a firm run into the ground by Jenna Bush like a predecessor of hers did for Harken energy (high treason since Bush is a Yalie).

update: This post was more than usually incomprehensible. I try to explain in comments and here (same text cut and pasted)

Sorry my post was incomprehensible. The permanent income hypothesis is unusual in economics because it explains facts which seem very odd at first glance. It is not true (has been rejected by the data) but, in this case, the glass is half full (in others it is totally empty).

One fact which it explains is that, when one regresses log consumption on log current income, one gets a coefficient less than one, yet over time, aggregate consumption grows at the same rate as aggregate income. Another is that Blacks consume less compared to Whites than one would predict given their current income.

Both can be explained if consumption depends on income averaged over a long period (as it does according to the PIH) so current income is equal to this average plus a disturbance term.

Now the bit on SATs and GPAs has nothing to do with bias in the SAT. “Biased” is a statement about the expected value of a statistic.

Let’s say there is something call it ESATGPA which causes high expected SATs and GPAs so SAT score is ESATGPA plus a mean zero disturbance and GPA s a function of ESATGPA plus another uncorrelated mean zero disturbance. Thus the SAT is, by assumption an unbiased measure of something to do with the GPA.

Now consider a group with lower than average ESATGPA. To avoid race, consider people whose first language is not English (hugely correlated with low SAT). Note I am assuming ENFL (English not first language) has the same effect on SAT and GPA so the SAT remains unbiased even if some people didn’t learn English as babies. However, given the disturbance to SAT, the best estimate of ESATGPA has a positive coefficient on SAT and a negative coefficient on ENFL (this follows mathematically from my assumptions). Thus people with ENFL will have lower expected GPAs than people with the same SAT scores and English as a first language.

Or forget GPA. Let’s say we are trying to use SAT scores from one day to predict SAT scores on a second sitting of the SAT. The SAT is certainly not a biased measurement of expected score on the SAT. However, Thus people with ENFL will have lower expected new SAT scores than people with the same SAT scores and English as a first language.

I assure the irritated reader that this is simple statistics. It also explains away a huge number of apparently interesting results in social science.

Comments (0) | |