Testing weakness of instrumental variables

[Janet Lewis]

Hi there!
I am running regressions using xtivreg2. I am wondering which tests I need to be looking at to test the validity of the instruments. I have two instrumental variables in my equation.
The reason for my confusion is that, some papers will report the Cragg-Donald Wald F statistic and use a rule of thumb as an F statistic over 10 shows all instruments are not weak. Though in some papers I notice people reporting separate F stats on all the instruments. I am unsure of what is 'correct'.
Thanks!

[Joro Kolev]

James Stock:

Do: o Use the Montiel Olea-Pflueger (2013) effective first-stage F statistic F Eff = F N × correction factor for non-homoskedasticity o Report F Eff o Compare F Eff to MOP critical values (weakivtest.ado), or to 10. o If F Eff ≥ MOP critical value, or ≥ 10 for rule-of-thumb method, use TSLS inference; else use weak-instrument robust inference.

https://scholar.harvard.edu/files/st...akiv1-2_v4.pdf

[Janet Lewis]

Thanks Joro. I assumed these tests were inbuilt using ivreg2

[Jeff Wooldridge]

Janet: I use weakivtest after the Stata built-in command ivregress 2sls. You will get the effective F statistic and critical values. In my experience, the 5% critical value is often well above 10.

This literature seems to still be in flux. Andrews, Stock, and Sun (2019, Annual Review of Economics) suggest computing the effective F statistic but using the usual Stock-Yogo critical value of about 10. Of course, that is appealing because it makes it more likely the IV will pass.

[Joro Kolev]

The user written -weakivtest- that Professor Wooldridge mentions "implements the weak instrument test of Montiel Olea and Pflueger (2013). It is a postestimation command for ivreg2 and ivregress."

The presentation by James Stock that I attached is based on, or is the working paper version of Andrews, Stock, and Sun (2019, Annual Review of Economics).

[Eric de Souza]

If I remember well, weakivtest will hang if you forget the robust option. I have in my notes: "estimation command for model has to be run with robust option (or any other option specifying heteroscedasticity or serially correlation)"
For those interested there is a very recent paper by Lee, Moreira, McCray and Porter entitled "Valid t-ratio Inference for IV" with the date 15 October 2020. I don't have a link but in the margin is written "arXiv:2010.05058v1 [econ.EM] 10 Oct 2020"

[Sebastian Kripfganz]

For weak-instruments tests and weak-instruments robust inference, the following community-contributed packages can be useful:

• ivreg2 (Baum et al. 2003, 2007)
• condivreg (Moreira and Poi 2003; Mikusheva and Poi 2006)
• rivtest (Finlay and Magnusson 2009)
• weakivtest (Pflueger and Wang 2015)
• twostepweakiv (Sun 2018)
• boottest (Roodman et al. 2019)

All references refer to Stata Journal articles.

[Janet Lewis]

Thank you all for your responses. Unfortunately, Weakivtest does not work after xtivreg2. I will have a look at the other commands Sebastian recommended and see how I go.

[Eric de Souza]

rivtest has been "incorporated" into weakiv by Finaly, Magnusson and Schaffer (ssc install weakiv). As the help file states "weakiv builds on and extends the command rivest by Finlay and Magnusson (2009)"

[Eric de Souza]

rivtest has been "incorporated" into weakiv by Finaly, Magnusson and Schaffer (ssc install weakiv). As the help file states "weakiv builds on and extends the command rivest by Finlay and Magnusson (2009)"

weakiv does

On Edit : please ignore this post. Replaced by #11

[Eric de Souza]

Thank you all for your responses. Unfortunately, Weakivtest does not work after xtivreg2. I will have a look at the other commands Sebastian recommended and see how I go.

weakiv does

[Janet Lewis]

Thanks Eric de Souza This seemed to work. Though I am struggling a little with the interpretation. I got this output:

Test        Statistic         p-value

AR  chi2(2)   =     8.54     0.0140

Wald  chi2(2)   =     8.24     0.0162

Number of obs N = 12708.  Number of groups = 1989; avg obs    per    group = 6.4.    Warning    - singleton groups    detected.    369
observation(s) not used.
Method = lagrange multiplier (LM).
Tests robust to heteroskedasticity.
Wald statistic in last row is based on xtivreg2 estimation    and    is not robust    to weak    instruments.

I have read the help file which includes the interpretation though, I am unclear about the last comment: Wald statistic in last row is based on xtivreg2 estimation and is not robust to weak instruments.

[Eric de Souza]

The help file states that "The null hypothesis is H0:beta=b0. Identification of beta in the IV estimation is assumed to be strong". In other words, it is only valid when the instruments are strong

[Janet Lewis]

Thanks!

[Nishant Kathuria]

Hello everyone,

Sorry for a basic question. In the above result shared by Janet Lewis ,
"Test Statistic p-value AR chi2(2) = 8.54 0.0140 Wald chi2(2) = 8.24 0.0162 Number of obs N = 12708. Number of groups = 1989; avg obs per group = 6.4. Warning - singleton groups detected. 369 observation(s) not used. Method = lagrange multiplier (LM). Tests robust to heteroskedasticity. Wald statistic in last row is based on xtivreg2 estimation and is not robust to weak instruments. "

Would it be correct to say that AR chi2(2) show that H0 is rejected at p<0.05, therefore the instrument is likely relevant and exogenous (lack of evidence that the instrument is weak), specially if the range of the confidence interval for Wald stats is similar to the range of confidence interval for AR? Thank you so much in advance.

Nishant