weakivtest in case of just identified case

[Tariq Abdullah]

According to my weakivtest my effective F-test statitic is less than critical value of tau being 10%. So, can't reject the null hypothesis that my isntrument is weak. However, according to all other weak instrument test automatically generated with ivreg2 command suggests that my isntrument is strong. Kleibergen-Paap Wald rk F statistic is greater than the critical value Stock-Yogo weak ID test critical values for K1=1 and L1=1.

According to the confidence interval of Anderson-rubin wald test I cab reject the null hypothesis of Ho: B1=0 and orthogonality conditions are valid.

http://economics.mit.edu/files/15326
From what I understand regardless of the strength of the instrument, it is recommended to report Anderson Rubin as it is robust to weak instruments.

"Specifically, in the leading case with a single endogenous regressor, we recommend that researchers judge instrument strength based on the effective F-statistic of Montiel Olea & Pflueger (2013). If there is only a single instrument, we recommend reporting identification-robust Anderson-Rubin confidence intervals. These are efficient regardless of the strength of the instruments, and so should be reported regardless of the value of the first stage F."

Now I am not sure which is this AR Statistic they refer to, the one automatically reported by ivreg2? or the one reported by weakiv command after ivreg2.

 weakivtest, level(0.05)
(obs=1,954,820)

Montiel-Pflueger robust weak instrument test
--------------------------------------------
Effective F statistic:       19.810
Confidence level alpha:          5%
--------------------------------------------

--------------------------------------------
Critical Values             TSLS      LIML
--------------------------------------------
% of Worst Case Bias
tau=5%                    37.105    37.105
tau=10%                   23.109    23..109
tau=20%                   15.374    15.374
tau=30%                    9.650     9.650
--------------------------------------------

According to this http://economics.mit.edu/files/15326 "If there is only a single instrument, we recommend reporting identification-robust Anderson-Rubin confidence intervals."

Is the following Anderson-Rubin Wald test give me the Anderson-Rubin confidence intervals ?

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)=5.07     P-val=0.0243

Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic                                    2.1e+05
Kleibergen-Paap Wald rk F statistic                                19.81

Stock-Yogo weak ID test critical values for K1=1 and L1=1:
                                   10% maximal IV size             16.38
                                   15% maximal IV size              8.96
                                   20% maximal IV size              6.66
                                   25% maximal IV size              5.53
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(1,405)=      37.36     P-val=0.0000
Anderson-Rubin Wald test           Chi-sq(1)=     37.38     P-val=0.0000
Stock-Wright LM S statistic        Chi-sq(1)=         .     P-val=     .

[Joro Kolev]

Yes, what they are referring to in the text you highlighted in your quote, is at the end of your output:

 
 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(1,405)=      37.36     P-val=0.0000 Anderson-Rubin Wald test           Chi-sq(1)=     37.38     P-val=0.0000 Stock-Wright LM S statistic        Chi-sq(1)=         .     P-val=     .

[Tariq Abdullah]

According to Andrews et. al(2019), regardless of the strength of IV one should report the AR confidence interval which I did in my other post. Though my Montiel Olea and Pflueger (2013) effective F-stat indicates my instrument is weak but the AR confidence interval provided by weakiv package says my endogenous regressor is significant.

So, as long as my endogenous regressor is significant, I'm good regardless of the strength of IV - this is what it says in Andrews et. al(2019) https://scholar.harvard.edu/files/wi...orrected_0.pdf - here they analyzed all the IV papers published in AER ( American Economic Review ) from 2013-2018.

"Specifically, in the leading case with a single endogenous regressor, we recommend that researchers judge instrument strength based on the effective F-statistic of Montiel Olea & Pflueger (2013). If there is only a single instrument, we recommend reporting identification-robust Anderson-Rubin confidence intervals. These are efficient regardless of the strength of the instruments, and so should be reported regardless of the value of the first stage F."

Though I'll keep working to make my IV stronger, at least it's good to know whatever I have at hand right now is also good enough to go according to the most recent development in IV literature.

[Tariq Abdullah]

Thanks so much for your kind feedback! Learned a lot from your previous posts where you explained everything related to IV issues other people had. Reading all those posts was very helpful to come to the stage where I'm at now despite not having such a strong conceptual understanding of IV.

[Tariq Abdullah]

Mr. Kolev,

I'm using ivreg2 for my regression.

However, I've a binary dependent variable and a binary endogenous regressor, and a continuous instrumental variable. In this setup, do I need to use biprobit after using ivregress or just using ivreg2 is going to be fine?

I got the idea of running first ivregress and then using biprobit from this post

https://www.statalist.org/forums/for...ary-instrument

[Mustafa Coban]

Hi Tariq,

since you want to fit a recursive bivariate probit model, I would recommend to switch to the rbiprobit package; available on SSC by

ssc install rbiprobit

This package accounts for recursive nature of your model, gives correct predictions and enables the estimation of various treatment effects. Here, a short example for the estmation of the average treatment effect

rbiprobit y1 = x1 x2 x3, endog(y2 = x1 x2 x4 x5)
rbiprobit tmeffects, tmeffect(ate)

For more background:

Check out the repo of the package on GitHub and the current presentation slides from the Italian Stata Conference.

I know it's quote common to use ivreg2 and to neglect the fact that the outcome variable is binary and not continuous. But still, I would recommend to use rbiprobit for estimation and to check the strength of your IV using ivreg2.