**Doug Staiger and James Stock** (1997): *Instrumental Variables Regression with Weak Instruments*

**Five Questions:**

- What is the "weak instruments" problem?
- How many studies with weird instruments--latitude, military spending--are affected by the weak instruments problem?
- How does the weak instruments problem interact with the desk-drawer problem?
- They say that your first stage F statistic needs to be greater than 10 for you not to worry. On what considerations do they base this rule of thumb?
- They say their paper is valid for "10 to 20" (or more) "observations per instrument". What, in this context, is an "observation", really?

Cf: <http://econ.lse.ac.uk/staff/spischke/ec533/Weak%20IV.pdf> <http://econweb.ucsd.edu/~elib/250A/Instrumental%20Variables2.pdf>

**Doug Staiger and James Stock** (1997): *Instrumental Variables Regression with Weak Instruments*: "This paper develops asymptotic distribution theory for single-equation instrumental variables regression when the partial correlations between the instruments and the endogenous variables are weak...

here modeled aslocal to zero. Asymptotic representations are provided for various statistics, including two-stage least squares (TSLS) and limited information maximum likelihood (LIML) estimators, Wald statistics, and statistics testing overidentification and endogeneity. The asymptotic distributions are found to provide good approximationt to sampling distributions with 10-20 observations per instrument. The theory suggests concrete guidelines for applied work, including using nonstandard methods for construction of confidence regions. These results are used to interpret Angrist and Krueger's (1991) estimates of the returns to education: whereas TSLS estimates with many instruments approach the OLS estimate of 6%, the more reliable LIML estimates with fewer instruments fall between 8% and 10%, with a typical95% confidence interval of (5%,15%)...