2SLS-Interpreting Cragg-Donald Wald F statistic

[MARIA CHRISTOFIDOU]

After running first and second stage regression I get the below result - I want help on how to interpret the results especially in relation to the Cragg-Donald Wald F and Stock-Yogo weak ID values.
Is my IV good? Are my results robust? Thank you

	(1)	(2)	(3)
VARIABLES	First stage	Second stage	2SLS
PR2	0.521***
	(0.027)
ESGCom	0.014	-0.185	-0.185
	(0.033)	(1.415)	(1.379)
NZBA	0.098**	3.284*	3.284*
	(0.043)	(1.851)	(1.804)
PCAF	0.072**	3.290**	3.290**
	(0.033)	(1.396)	(1.361)
WOMB	-0.037	1.176	1.176
	(0.061)	(2.603)	(2.537)
WOME	0.034	-3.896	-3.896
	(0.070)	(2.990)	(2.914)
SIZE	-0.005	-0.171	-0.171
	(0.013)	(0.539)	(0.525)
LEV	-0.007*	0.022	0.022
	(0.004)	(0.157)	(0.153)
ROAA	-0.005	0.708*	0.708*
	(0.010)	(0.420)	(0.410)
REMHat		14.588***
		(2.167)
REM			14.588***
			(2.113)
Constant	0.031	8.628	8.628
	(0.219)	(9.314)	(9.078)
Observations	176	176	176
R-squared	0.863	0.722	0.661

Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1

. ivreg2 GERQS (REM=PR2) ESGCom NZBA PCAF WOMB WOME SIZE LEV ROAA i.CCODE

IV (2SLS) estimation

----------------------------------------------------------------------------
Underidentification test (Anderson canon. corr. LM statistic): 129.886
Chi-sq(1) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 385.875
Stock-Yogo weak ID test critical values: 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.
------------------------------------------------------------------------------
Sargan statistic (overidentification test of all instruments): 0.000
(equation exactly identified)
------------------------------------------------------------------------------

[Carlo Lazzaro]

Maria:
given your just identified model, Anderson and Sargan statistics are not informative.
CDW F-statistic tells you that your instrumenti is not weak.
If a just identified model is the way to go in your case, I cannot say though.

[Josh Zweig]

Hi Maria,

Here's a brief summary and clarification regarding the diagnostics from your IV model.

You've estimated a just-identified model, instrumenting REM with PR2. In this context:

• The Cragg-Donald Wald F-statistic (F = 385.875) is the key result to focus on. This value is well above all Stock-Yogo critical thresholds, meaning your instrument is not weak — a very positive sign.
• The Anderson LM test technically confirms model identification, but in a just-identified setting, this test adds little beyond confirming what the first stage already shows.
• The Sargan test, on the other hand, is not applicable in your model — it requires overidentification (i.e., more instruments than endogenous regressors), which you don’t currently have.

Carlo Lazzaro is absolutely right in pointing out that the Anderson and Sargan statistics are not informative in your case. The Cragg-Donald test is the relevant diagnostic, and its result strongly supports your instrument’s strength.

Finally, whether a just-identified specification is appropriate depends on how confident you are that PR2 satisfies the exclusion restriction, this is, it affects GERQS only through REM. If you have additional valid instruments, it could be worth estimating an overidentified model to allow formal testing of instrument validity.

Best regards,
Josh Zweig - Estima