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# st: Cragg-Donald statistic test for weak instruments

 From "Lim, Elizabeth" To "'statalist@hsphsun2.harvard.edu'" Subject st: Cragg-Donald statistic test for weak instruments Date Fri, 25 Nov 2011 17:46:08 +0000

```Hello,

I've read the postings in the archives on the subject of Cragg-Donald statistic for multiple endogenous regressors but would like to seek further clarifications.  According to the Baum, Schaffer, and Stillman (2007) paper on page 23, the Cragg and Donald (1993) statistic is [(N-L)/L2)(r2k1/1-r2k1].  I currently have the following info:-

Number of observations N=542
Number of regressors K=30
Number of instruments L=36
Number of excluded instruments L1=8
Number of endogenous regressors K1 =2

I'm interested in finding out more about the following issues:

(1) How to compute Cragg-Donald statistic manually?  Looking at the formula provided by Baum et al (2007), I know I have a few pieces of the info (N and L) required to plug into the formula, but how and where do I get the rest of the info to successfully compute the C-D?  Or is there an alternative way to get the C-D statistic based on the existing pieces of info I've provided above?

(2) When to reject the null hypothesis of weak instruments using the Cragg-Donald statistic?  I know I should compare the Cragg-Donald statistic with the Stock and Yogo's (2005) range of critical values for maximal IV relative bias (5%, 10%, 20%, 30%) and maximal IV size (10%, 15%, 20%, 25%), but at what point do I know I have weak instruments? Other statistics use a single p-value so it's easy to know that the null hypothesis will  be rejected when p<0.05, but with a range of critical values, what is the threshold for rejection of the null (within these range of critical values)?  For example, if my C-D statistic falls between a maximal IV relative bias of 20% and 30% or if I have a maximal IV size of >25% maximal IV size, etc, does it mean that I've got weak instruments?

(3) Since there are two sets of S-Y critical values, which one should I use to reject my null?  Will I always get the same conclusion (i.e., reject null or not) regardless of whether I use the critical values for "maximal IV relative bias" or "maximal IV size"?

Sorry if my questions sounded fundamental, but this is a new topic for me, and I'm still trying to grasp the logic behind the statistics.

Best,
Elizabeth

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