Eric Rasmusen’s Weblog

I just realized something about censoring in econometrics: it has two varieties,
one like a corner solution and one like a narrow window of observation. (more…)

I will here talk about three topics in econometrics: 1. Why OLS is biased when Y cannot exceed 10. 2. Why the Heckman correction corrects for that. 3. Why OLS is biased when Y cannot exceed X. This complements my earlier post on topic 1. (more…)

I’ve written up some notes on how to interpret “marginal effects” in tobit regressions when the variable is a dummy, so the change is discrete (something one gets out of the STATA 6-and-later “mfx” command). I resorted to empiricism. I ran a test regression on some data I have on Japanese executives— the meaning of the variables doesn’t matter for present purposes. The mean of lntax04tb, the log of tax04tb, is 9.43 for nonpresidents and 9.57 for presidents. (more…)

I’ve run into a censoring problem in econometrics (”censoring” in a technical math sense, not in a political or moral sense, so this post will be uninteresting for most people). Suppose you are regressing a person’s consumption C in a year on his income Y for that year, trying to find the marginal propensity to consume, and you have data on 1,000 people for one year. Can you use OLS? I’m not thinking of measurement error or the permanent income hypothesis or heteroskedasticity or serial correlation, but of a different problem: consumption cannot exceed income (we’ll define income as including gifts, government handouts, etc.). (more…)

Dubner and Levitt’s Freakonomics was on my Dozen Best list for 2005, but I also enjoy the caustic rough translation of Ariel Rubinstein’s review of it, a review similar in style to Ed Leamer’s review of Thomas Friedman’s The World Is Flat. Both reviews make fun of the books, while also noting their good points, and both reviews have penetrating main ideas that I was embarassed not to have thought of myself. (That, by the way, is a good test for a brilliant idea. George Stigler was a master at that— at the short, simple, seminar question which totally derailed the paper being presented.) Leamer’s idea is “Friedman’s metaphor of the flat world is not wrong, but simply meaningless,” and Rubinstein’s idea is “Most of Levitt’s Freakonomics isn’t economics at all, just smart thinking.” (more…)

Dan Seligman has a good article in Commentary on Betty Friedan, “The Friedan Mystique,” which shows how intellectually empty, naive, and pretentious was the best-known book of this fellow-traveller of the Communists, so representative of 1950’s liberalism and 1960’s protest about how unfair life was for the suburban elite: (more…)

At a Pizza Parlor I observed a man ordering a small pizza to go. He appeared to be alone and the cook asked him if he would like it cut into 4 pieces or 6. He though about it for some time before responding. “Just cut it into 4 pieces; I don’t think I’m hungry enough to eat 6.”

1 + 2 = 4,

for sufficiently large values of one.

(or sufficiently small values of 4)

1. Teaching Math In 1960
A logger sells a truckload of lumber for $100. His cost of
production is 4/5 of the price. What is his profit?

2. Teaching Math in 1970
A logger sells a truckload of lumber for $100. His cost
of production is 4/5 of the price, or $80. What is his profit?

3. Teaching Math In 1980
A logger sells a truckload of lumber for $100. His cost
of production is $80. Did he make a profit?

4. Teaching Math In 1990
A logger sells a truckload of lumber for $100. His cost of
production is $80 and his profit is $20. Your assignment: Underline the
number 20.

5. Teaching Math In 2000
A logger cuts down a beautiful forest because he is selfish
and inconsiderate and cares nothing for the habitat of animals or the
preservation of our woodlands. He does this so he can make a profit of
$20. What do you think of this way of making a living?

6. Teaching Math In 2010
Un hachero vende una carretada de maderapara $100. El
costo de la produccion es $80.

I had a good dinner conversation about intelligent design a couple of nights ago which inspired me to think about it in terms of frequentist (classical) versus Bayesian statistics and to contrast its application to physics with its application to biology. My notes follow.

(1) How do we do a classical (or frequentist) test here?

Null: Randomness, according to some distribution.

Alternative: Non-Random,

Test: Are the parameters in confidence region R?

(2) A simple example Let possible values of X be in {0,1,2,…1000}. Only X=1000 permits life. (more…)

Eugene Volokh had a post today on whether something can be “nearly infinite”. I think it can— but only if it actually is infinite. First, here’s what he says: (more…)

Wikipedia describes Simpson’s Paradox in statistics.

One the best known real life examples of Simpson’s paradox occurred when U. C. Berkeley was sued for bias against women applying to grad school. The admission figures showed that men applying were more likely than women to be admitted, and the difference was so large that it was unlikely to be due to chance. However when examining the individual departments, it was found that no department was significantly biased against women; in fact, most departments had a small (and not very significant) bias against men.

The explanation turned out to be that women tended to apply to departments with low rates of admission, while men tended to apply to departments with high rates of admission.

Professor Jeff Conner-Linton has a good explanation of the Chi-Squared frequency test up on the web. This test is used for seeing whether the entries in a table of observed frequencies are equal to each other or not. I see that if any frequency is 0, though, the test cannot be used at all (division by zero occurs) and for low frequencies, it can be of dubious value because it is an approximate test, which relies on the idea that sample frequencies are normally distributed around the population value. He says that the test is reliable for large tables (bigger than 2×4 or 3×3) if all but one entry has a frequency of more than 5, even if one entry is 1.

I couldn’t sleep on account of a cold, so I got up and read a bit of math.
“Measure” is an extension of the idea of “length” or “size” to apply to sets of
points that aren’t made up just of intervals. An example of an interval is

A= “All the points from 0 to 1, inclusive, plus all the points from 2 to 4, not
including 2 and 4″ (more…)

I have always been careless about the use of the terms “significance level” and “confidence level”, in the sense of whether I say I am using a 5% significance level or a 5% confidence level in a statistical test. (more…)

Here are how to calculate elasticities from regression coefficients, a note possibly useful to economists who like me keep having to rederive this basic method: (more…)

Using Google’s useful command “define: mathematized” and
“define: mathematicized”, I was surprised to find no results for either word. I wanted to use it in: (more…)

I’ve been trying to connect the Hausman Test to the Wald, Likelihood Ratio (LR) and Lagrange-Multiplier (LM) statistics. Here are my notes, which will interest only people who know quite a bit of statistics. Don’t trust them too far– these are the possibly confused ideas of a non-expert. But they might be helpful. (more…)

If you do maximum likelihood regressions, your computer regression package will usually give you something called the Pseudo-R2 to help gauge how well your estimates capture the variability in the data, in analogy to the R2 of OLS. But I have decided the Pseudo-R2 is too misleading to use. (more…)

6 How do you measure distance between two people? Here are some ways:

1. The shortest distance between them.
2. The longest straight line between them.
3. The longest straight line between them that does not pass through their bodies.
4. The average shortest distance between them.
5. The shortest radius of the convex bubble that contains them both.
6. The longest radius of the convex bubble that contains them both.