Mostly Harmless Econometrics » Corrections

How many df in that?!

josh — Sun, 02 May 2010 02:44:37 +0000

Reading pp 298-299 with somewhat more care than they were written,
Tobias Wuergler from Zurich writes:

In order to demonstrate that robust standard errors are likely to
be more biased than non-robust under homoskedasticity, you use a
bivariate example, where the single regressor is assumed to be in
deviations-from-means form. Wouldn't one need, strictly speaking,
the regressand "y" to be in deviations-from-means form, too, in
order to partial out the constant? If so, the appropriate
degree-of-freedom correction should be (1-2/N) since the residual
maker in a demeaned regression is M(x)M(1), where M(1) is the
annihilator associated with the vector of ones (which one needs to
demean). The square of this residual maker is (M(1)-H(x)), hence
E(e(hat)²)=sigma²*(m(ii,1)-h(ii,x)), and the sum of
(m(ii,1)-h(ii,x)) is equal to (N-1-1) since m(ii,1)=(1-1/N).
Intuitively, a demeaned simple regression (with the original model
having a constant) still needs a degree of freedom correction of 2
as an average needs to be estimated apart from the single beta. Or
am I misunderstanding your example?
(In order to circumvent this complication one could assume a simple
regression through the origin, which would not require x (nor y) to
be demeaned.)

Good catch Toby - partialing out the constant does not change the
underlying df in the estimated residual; you can't fool mother
nature.  So the df should be 2 and not 1. The argument about
relative bias of robust and conventional standard errors still
goes through, but to get the details right, change 1-1/N to 1-2/N
and make sure the leverage adds up to 2 and not 1.

42 clusters references swap

josh — Thu, 18 Mar 2010 19:43:25 +0000

The references to Hansen (2007a) and Hansen (2007b) on page 322-323 are swapped. On page 322, it should be Hansen (2007b) referenced as discussing bias-correction of serial correlation parameters and on page 323, it should be Hansen (2007a) referenced as showing pretty good results for state clustering with modest numbers of states.

Steve must have been dozin’ on his galleys by this point.

Typo on p. 136

josh — Sat, 26 Dec 2009 15:24:07 +0000

Careful reader Christian Perez notes that on page 136 the parameter to be estimated in equation 4.1.15 is \rho and not \e as stated in the text. Thanks Chris!

Multivariate first stage F . . . NOT

josh — Fri, 30 Oct 2009 16:55:51 +0000

This just in from the ivreg2 team (Chris Baum, Mark Schaffer, and Steve Stillman):

How should you construct a first stage F stat to measure instrument strength when you have more than one endogenous variable? Not by following the instructions we gave at the bottom of page 218. Althought the theoretical expressions that motivate the p. 218 procedure are right, the computational algorithm we gave is not.

Specifically, where it says:

“regress the first-stage fitted values (for x_2) on the other first-stage fitted values and any exogenous covs . . .”

it should read:

“regress x_2 on the other first stage fitted values and any exogenous covs . . .”

If you do what we originally wrote, you’ll get an R2 of one, always a cause for concern.

Thanks guys for cleaning this up!

Bbbbb . . . bivariate probit!

josh — Fri, 30 Oct 2009 13:58:44 +0000

Raphael Studer from Switzerland noticed that the bivariate probit likelihood on page 199 looks suspiciously like the likelihood for old fashioned monaural probit.

Thanks Raphael – this is indeed the wrong likelihood, so don’t try to maximize that at home, folks. It works only if you don’t have an endogenous regressor in the first place. For the correct biprobit likelihood, see, e.g., pp. 849-851 in Greene (2007) or better yet, just do it in stata using biprobit (if you must).

This of course raises the question of how we came to make such a mistake. Is it because Angrist has such a strong aversion to latent-index models that he couldn’t stand the sight of the full likelihood? Or is it just another silly mistake Steve missed in galleys?

Typo on page 130

josh — Fri, 04 Sep 2009 21:40:41 +0000

Well, we like the occasional casual relationship as much as the next guy, but on page 130 the relationship between draft-eligibility and earnings is meant to be causal . . .

Thanks to Peter Dizikes for pointing this out!

Typo on page 174

josh — Tue, 01 Sep 2009 13:13:47 +0000

Hendrik Juerges from the University of Mannheim caught this one:
Bottom of page 174
– should read: “where rho_1 is LATE using …”
– not: “where psi_1 is LATE using …”

many thanks Hendrik!

Just-identified IV

admin — Fri, 08 May 2009 16:58:56 +0000

Gary Solon of Michigan State University pointed out to us that our claim on p. 209 that “just identified 2SLS is median unbiased” is not quite correct and that the claim should be qualified. Gary notes that if the first stage is really zero, the just identified IV estimator is centered at the same point as the biased OLS estimator. Similarly, just identified IV is biased for instruments that are extremely weak, as has been shown in the literature.

Gary is right, of course, and we thank him for pointing this out. Just-identified IV is approximatelyly median unbiased, but if the instruments are weak enough you’ll certainly have bias. On the other hand, if a single instrument is really that weak, you’re unlikely to want to use it since a very low t-stat and high 2nd stage standard errors will warn you away. See the attached note for details.

Typos and mistakes on pages 177 and 183

admin — Fri, 08 May 2009 16:56:41 +0000

Careful reader Ian Gow from Stanford caught the following two typos/mistakes:

Assumption CA1 on p. 177 should read just like assumption A1 on p. 155, except conditional on X_i (the subscript 0 on Y_0i is incorrect).

On p. 183, the para beginning “The size of the group of compliers i given by . . .” First, the statement that P(S_1i=>s=>S_0i) is non-negative by virtue of monotonicity is silly: of course this non-negative, since its a probability! Monotonicity is needed, however, for this to be equal to the difference in the CDFs of S0_i and S1_i (as the sentence following should read).

Thanks Ian!

Mistake on page 74

admin — Fri, 08 May 2009 16:55:28 +0000

Careful reader Israel Arroyo caught this mistake:

Sir,

I’m reading the amazing “Mostly Harmless” and I’ve found what I believe to be a typo-though maybe is not and I’m just getting dumber- In Chapter 3, p.74, about the end of 2nd paragraph, it says “[...] regression of Yi on Di and Xi is the same as the regression of Yi on E[Yi|Di,Xi]” shouldn’t it say “the same as the regression of E[Yi|Di,Xi] on Di and Xi”?

Thank you very much for your patience and once again for a fantastic book,
Israel Arroyo

Indeed it should! Thank you Israel