Sunday, March 06, 2011

Simpson's Paradox

Last week, Paul Krugman argued that kids in Wisconsin outperform kids in Texas, which to him implied this was due to the collective bargaining rights of Wisconsin educators (Texas does not have those).

IowaHawk noted this finding isn't what it appears. As he notes:
white students in Texas perform better than white students in Wisconsin,black students in Texas perform better than black students in Wisconsin,Hispanic students in Texas perform better than Hispanic students in Wisconsin.

So, on average Wisconsin outperforms Texas, but within each ethnicity, Texas outperforms Wisconsin. As ethnic performance varies predictably across all states, ignoring the ethnic composition of states is really misleading, and is why my state, Minnesota, appears to do so well on these simple measures.

It's the old Simpson's Paradox! It's a really fun issue that pops up often, and good to be aware of because it's one of those cases where an omitted variables bias is at work. That is, the effect of x on y shows a significant coefficient, but when you include another variable, the coefficient on x goes to zero or even changes sign. This usually shows up in a simple cross-tabulation, and it's good practice to always be looking for other variables that could affect your findings, because if you are trying to make money like I am, it's good to know the truth (if your a partisan shill it's a minor annoyance).

Here's my application of Simpson's Paradox to the CAPM, something I go over in Finding Alpha (this is from Chapter 1 of my videos):


One could also adjust for price and also find this gets rid of the positive relation between beta and average returns. Much of the apparent relation between price or size and returns, meanwhile, is the result of measurement errors such as the delisting bias and the problems of geometric averaging (I know CRSP says they got rid of the delisting bias, but there's still a huge low-price premium in their data, and that's obviously not obtainable, as evidenced by the failure of low-priced funds that were popular in the late 80's--now gone).

10 comments:

Patrick R. Sullivan said...

Another Dick Cavett Moment--he once admitted on his national television show that he lived in fear of saying something so stupid he'd be too embarrassed to come out of his house for a year--for Krugman. Right up there with swallowing Jason Leopold's nonsense about Army Sec'y Thomas White, or that Fannie and Freddie were prohibited by law from being involved with subprime mortgages.

Could you even find one Princeton undergrad who wouldn't have thought, 'Well, Texas shares a border with Mexico....' Raghu Rajan must be laughing his ass off.

Anonymous said...

"Last week, Paul Krugman argued that kids in Wisconsin outperform kids in Texas, which to him implied this was due to the collective bargaining rights of Wisconsin educators (Texas does not have those). "

Krugman doesn't mention Wisconsin in the op-ed that is linked from the post above. The op-ed is only about Texas. Says nothing about collective bargaining either.

Patrick R. Sullivan said...

Well, Anon, when Krugman says:

'By the way, given the current efforts to blame public-sector unions for state fiscal problems....'

what state did you think Krugman had in mind?

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Anonymous said...

The full sentence in Krugman's op-ed is: "By the way, given the current efforts to blame public-sector unions for state fiscal problems, it’s worth noting that the mess in Texas was achieved with an overwhelmingly nonunion work force.)"

He is saying that the state fiscal problems are being blamed on unions.

Saying "Paul Krugman argued that kids in Wisconsin outperform kids in Texas, which to him implied this was due to the collective bargaining rights of Wisconsin educators" is a gross mischaracterization of what that op-ed says.

Patrick R. Sullivan said...

You forgot to answer my question, Anon. What state do you think Krugman had in mind?

Anonymous said...

Patrick Sullivan is going on a decade now with his insane rant. This is a guy who should be committed. You're an obsessed freak, Patrick. A sick, sick man.

matal said...

Ok, too many anon's - i am the first two anonymous comments above, not the last one that is an ad hominem on Patrick.

To respond to Patrick - yes, I would guess that Krugman had Wisconsin in mind. So what?

Patrick R. Sullivan said...

Obviously, that Krugman had Wisconsin in mind invalidates your initial comment:

'Krugman doesn't mention Wisconsin in the op-ed that is linked from the post above. The op-ed is only about Texas.'

matal said...

Patrick -

Obviously our readings of the op-ed are very different. I don't think Krugman makes a connection between collective bargaining and relative performance of students.

I am not sure it's worth continuing this fairly tangential point. Let's stop.

matal