Which Anderson-Rubin test statistic to read — for weak IV robust inference with cluster-robust standard errors

[Adam Siklosi]

Hi everyone!

I am quite novice in the theoretics of statistics, so please excuse me if my question is dumb.

I am running an IV regression, and trying to see the AR test statistic to make sure my borderline instrument strength is not causing false positives. As per this paper: https://www.annualreviews.org/conten...-092123-111021

I am unsure, however, which statistic I should read, in the case of clustered macro panel data (heteroscedastic):

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(1,24)= 3.98 P-val=0.0575
Anderson-Rubin Wald test Chi-sq(1)= 4.36 P-val=0.0368


Thank you for your time!!

[Andrew Musau]

The distinction between the F-statistic version and the Chi-squared version of the Anderson-Rubin test is discussed in the documentation for ivreg2 from SSC. Most authors report the Chi-squared version. Both are Wald tests, and their validity is preserved regardless of whether standard errors are clustered or heteroscedasticity-robust. Therefore, the presence of heteroscedasticity or the use of clustered standard errors does not invalidate the Anderson-Rubin Wald test. The following is from

help ivreg2

The first-stage output also includes two statistics that provide weak-instrument robust
inference for testing the significance of the endogenous regressors in the structural
equation being estimated. The first statistic is the Anderson-Rubin (1949) test (not to be
confused with the Anderson-Rubin overidentification test for LIML estimation; see above).
The second is the closely related Stock-Wright (2000) S statistic. The null hypothesis
tested in both cases is that the coefficients of the endogenous regressors in the structural
equation are jointly equal to zero, and, in addition, that the overidentifying restrictions
are valid. Both tests are robust to the presence of weak instruments. The tests are
equivalent to estimating the reduced form of the equation (with the full set of instruments
as regressors) and testing that the coefficients of the excluded instruments are jointly
equal to zero. In the form reported by ivreg2,the Anderson-Rubin statistic is a Wald test
and the Stock-Wright S statistic is an LM test. Both statistics are distributed as
chi-squared with L1 degrees of freedom, where L1=number of excluded instruments. The
traditional F-stat version of the Anderson-Rubin test is also reported. See Stock and Watson
(2000), Dufour (2003), Chernozhukov and Hansen (2005) and Kleibergen (2007) for further
discussion. For related alternative test statistics that are also robust to weak
instruments, see condivreg and weakiv, and the corresponding discussions in Moreira and Poi
(2003) and Mikusheva and Poi (2006), and in Finlay and Magnusson (2009), respectively.