I estimate an instrumental variables fixed effects regression. The details of my estimation can be found in the thread https://www.statalist.org/forums/for...iable-strategy I do not have get into the details of my estimation further and the following information should be enough to ask my questions. I have six instruments and two endogenous variables. The concern is whether the instruments provide independent sources of exogenous variation for each endogenous regressor. This is a concern in my setting because the instruments could speak to both endogenous regressors economically and I need to convince the referees of a journal that the instruments provide independent sources of exogenous variation.
To this purpose, I consider tests of weak identification. First, I consider the Sanderson-Windmeijer first stage F statistic. The statistic takes the values 10.379 and 25.645 for the two endogenous regressors which both have p values 0.000. I take this as evidence that the instruments provide independent sources of exogenous variation for each endogenous regressor and therefore their effects are identified in the second stage.
Now a referee complains that this is not the right statistic and that I should consider the Kleibergen and Paap statistic. I do not agree with the referee that it is not the right test, but I do not object to conduct the additional Cragg and Donald test or the robust version of it, which is the Kleibergen and Paap F test. I have two questions about this second test.
1. The Cragg and Donald test is valid under i.i.d. errors. The critical values tabulated by Stock and Yogo are also valid under i.i.d. errors. But in my regression I allow the errors to be not i.i.d. as I use the cluster(panelid) option. Some papers present the robust version of the Cragg and Donald test which is the Kleibergen and Paap Wald Rank F test that does not assume i.i.d. errors, and compare the value of the test with Stock and Yogo critical values which are valid under i.i.d. errors, and acknowledge that this is not entirely correct and research on this is still going on. I am more critical. To me this does not make sense. What is the point of comparing the value of a robust statistic with critical values that are not robust?
Therefore, I do the following in my paper. I explain that I estimate the model assuming i.i.d errors (so no robust option is used), although the baseline model does not assume this, and present the result of the Cragg and Donald test and the Stock and Yogo critical values just to give an indication of whether weak identification could be a problem. In particular I write the following:
"Cragg and Donald (1993) introduced the second-stage F statistic to test for weak identification. Stock and Yogo (2005) tabulated critical values for two particular consequences of weak instruments: bias of the instrumental variable estimator relative to the bias of the least squares estimator, and distortion of the test size. However, the test and the critical values of the test are valid under the assumption that the errors of the regression equation are independently and identically distributed. Therefore, we conduct the test based on the regression where we assume that errors are independently and identically distributed. The value of the test is 18.259 and exceeds the critical value of 15.72 for 5 percent maximum relative bias, and it exceeds the critical value of 12.33 for 15 percent maximum size distortion, but not the critical value of 21.68 for 10 percent maximum size distortion. This suggests that there is no evidence to suspect that our model is heavily affected by the problem of weak instruments."
Does my approach make sense?
2. Some papers mention about critical values (of Stock and Yogo) regarding the relative bias, and totally ignore the critical values regarding the size distortion. As I interpret it, this is because relative bias regards the empirical analysis being conducted in these papers, whereas size distortion is about the test itself which does not say anything about whether there is weak identification. Is my interpretation correct?
To this purpose, I consider tests of weak identification. First, I consider the Sanderson-Windmeijer first stage F statistic. The statistic takes the values 10.379 and 25.645 for the two endogenous regressors which both have p values 0.000. I take this as evidence that the instruments provide independent sources of exogenous variation for each endogenous regressor and therefore their effects are identified in the second stage.
Now a referee complains that this is not the right statistic and that I should consider the Kleibergen and Paap statistic. I do not agree with the referee that it is not the right test, but I do not object to conduct the additional Cragg and Donald test or the robust version of it, which is the Kleibergen and Paap F test. I have two questions about this second test.
1. The Cragg and Donald test is valid under i.i.d. errors. The critical values tabulated by Stock and Yogo are also valid under i.i.d. errors. But in my regression I allow the errors to be not i.i.d. as I use the cluster(panelid) option. Some papers present the robust version of the Cragg and Donald test which is the Kleibergen and Paap Wald Rank F test that does not assume i.i.d. errors, and compare the value of the test with Stock and Yogo critical values which are valid under i.i.d. errors, and acknowledge that this is not entirely correct and research on this is still going on. I am more critical. To me this does not make sense. What is the point of comparing the value of a robust statistic with critical values that are not robust?
Therefore, I do the following in my paper. I explain that I estimate the model assuming i.i.d errors (so no robust option is used), although the baseline model does not assume this, and present the result of the Cragg and Donald test and the Stock and Yogo critical values just to give an indication of whether weak identification could be a problem. In particular I write the following:
"Cragg and Donald (1993) introduced the second-stage F statistic to test for weak identification. Stock and Yogo (2005) tabulated critical values for two particular consequences of weak instruments: bias of the instrumental variable estimator relative to the bias of the least squares estimator, and distortion of the test size. However, the test and the critical values of the test are valid under the assumption that the errors of the regression equation are independently and identically distributed. Therefore, we conduct the test based on the regression where we assume that errors are independently and identically distributed. The value of the test is 18.259 and exceeds the critical value of 15.72 for 5 percent maximum relative bias, and it exceeds the critical value of 12.33 for 15 percent maximum size distortion, but not the critical value of 21.68 for 10 percent maximum size distortion. This suggests that there is no evidence to suspect that our model is heavily affected by the problem of weak instruments."
Does my approach make sense?
2. Some papers mention about critical values (of Stock and Yogo) regarding the relative bias, and totally ignore the critical values regarding the size distortion. As I interpret it, this is because relative bias regards the empirical analysis being conducted in these papers, whereas size distortion is about the test itself which does not say anything about whether there is weak identification. Is my interpretation correct?
