Hey everyone,

I have the following equation:

y=aX1+bX2+cX3+dX4+e

I am instrumenting Z1 for X1 and Z2 for X2.

ivreg2 y (X1 X2= Z1 Z2) X3 X4, cluster(x5) first

I am getting back this:


Underidentification test
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
Kleibergen-Paap rk LM statistic Chi-sq(1)=3.40 P-val=0.0651

Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic 25.78
Kleibergen-Paap Wald rk F statistic 6.48

Stock-Yogo weak ID test critical values for K1=2 and L1=2:
10% maximal IV size 7.03
15% maximal IV size 4.58
20% maximal IV size 3.95
25% maximal IV size 3.63
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

Weak-instrument-robust inference
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
Anderson-Rubin Wald test F(2,10)= 1.30 P-val=0.3161
Anderson-Rubin Wald test Chi-sq(2)= 3.21 P-val=0.2007
Stock-Wright LM S statistic Chi-sq(2)= . P-val= .

I am interested if

1. underidentification is relevant when I have instruments for 2 variables?
2. Is Stock - Yogo test relevant in this case? My first stage F statistics are 28.84 and 376.22
3. What tests are important in case of multiple instruments?

Thank you for your help.