Hello,
I have a panel dataset with 21 countries and about 30 years of data for each country. I am using an IV for one of my endogenous variables, which in my context is subject to simultaneity. So I have one endogenous variable and one IV (exactly-identified). I am running a regression using
ivreg2 depvar l.depvar othercontrols yy* cc* (endogenousvar=iv variable) if subsample==1 , cluster(countryn) first partial(yy* cc* othercontrols)
Now I would like to see whether my IV is weak or not. I know that I can look at "Kleibergen-Paap rk Wald F statistic" and compare it with Stock-Yogo weak ID test critical values with caution of course as the assumption underlying these critical values is that errors are iid and in my case, they are not. What I get is F of larger than 20 and it is greater than all the critical values listed by STATA for one of my subsamples. For the other subsample, the F is low ( about 5) and less than all critical values listed. Before dismissing the results I came across this paper:
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 rivtest after ivreg2 or the one reported by weakiv command after ivreg2. I get very different answers with each of these. For the sub-sample with low F,
The AR reported automatically with ivreg2 is :
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(1,15)= 53.87 P-val=0.0000
Anderson-Rubin Wald test Chi-sq(1)= 63.87 P-val=0.0000
The AR reported with weakiv:
Weak instrument robust tests and confidence sets for linear IV
H0: beta[b1:shock] = 0
------------------------------------------------------------------------------
Test | Statistic p-value | Conf. level Conf. Set
------+---------------------------------+-------------------------------------
AR | chi2(1) = 8.16 0.0043 | 95% [ ... ,-.902798]
------+---------------------------------+-------------------------------------
Wald | chi2(1) = 6.93 0.0085 | 95% [-3.12553,-.458251]
------------------------------------------------------------------------------
Confidence sets estimated for 100 points in [-4.45917, .875389].
Number of obs N = 499.
Method = lagrange multiplier (LM).
Tests robust to heteroskedasticity and clustering on countryn (N_clust=16).
Wald statistic in last row is based on ivreg2 estimation and is not robust to weak
instruments.
The AR reported with rivtest:
Weak instrument robust tests and confidence sets for linear IV with cluster VCE
H0: beta[b1:shock] = 0
-------------------------------------------------------------------------------------------
Test | Statistic p-value 95% Confidence Set
------+------------------------------------------------------------------------------------
AR | chi2(1) = 63.87 Prob > chi2 = 0.0000 [-4.45917,-1.01057]
------+------------------------------------------------------------------------------------
Wald | chi2(1) = 6.93 Prob > chi2 = 0.0085 [-3.12553,-.458251]
-------------------------------------------------------------------------------------------
Note: Wald test not robust to weak instruments. Confidence sets estimated for 100 points in
[-4.45917, .875389].
Now here are my questions:
(1) Which AR should I look at to test the weakness of my instrument?
(2) Why the confidence interval reported with weakiv has an open-end? It is not clear to me what the interpretation of these confidence bands is. The help file explanation did not help either:
"Disjoint confidence intervals arise when the plot of the rejection probability dips below L% in more than one range; an example is when the
K statistic has inflection points or local minima that cause spurious power losses (inspection of a graph of the K
rejection probability is a way of detecting this). "
(3) What is really the difference between weakiv command and rivtest command? It seemed that weakiv is the extension of the rivtest, but I am not sure why they yield different results.
Appreciate any help!
I have a panel dataset with 21 countries and about 30 years of data for each country. I am using an IV for one of my endogenous variables, which in my context is subject to simultaneity. So I have one endogenous variable and one IV (exactly-identified). I am running a regression using
ivreg2 depvar l.depvar othercontrols yy* cc* (endogenousvar=iv variable) if subsample==1 , cluster(countryn) first partial(yy* cc* othercontrols)
Now I would like to see whether my IV is weak or not. I know that I can look at "Kleibergen-Paap rk Wald F statistic" and compare it with Stock-Yogo weak ID test critical values with caution of course as the assumption underlying these critical values is that errors are iid and in my case, they are not. What I get is F of larger than 20 and it is greater than all the critical values listed by STATA for one of my subsamples. For the other subsample, the F is low ( about 5) and less than all critical values listed. Before dismissing the results I came across this paper:
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 rivtest after ivreg2 or the one reported by weakiv command after ivreg2. I get very different answers with each of these. For the sub-sample with low F,
The AR reported automatically with ivreg2 is :
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(1,15)= 53.87 P-val=0.0000
Anderson-Rubin Wald test Chi-sq(1)= 63.87 P-val=0.0000
The AR reported with weakiv:
Weak instrument robust tests and confidence sets for linear IV
H0: beta[b1:shock] = 0
------------------------------------------------------------------------------
Test | Statistic p-value | Conf. level Conf. Set
------+---------------------------------+-------------------------------------
AR | chi2(1) = 8.16 0.0043 | 95% [ ... ,-.902798]
------+---------------------------------+-------------------------------------
Wald | chi2(1) = 6.93 0.0085 | 95% [-3.12553,-.458251]
------------------------------------------------------------------------------
Confidence sets estimated for 100 points in [-4.45917, .875389].
Number of obs N = 499.
Method = lagrange multiplier (LM).
Tests robust to heteroskedasticity and clustering on countryn (N_clust=16).
Wald statistic in last row is based on ivreg2 estimation and is not robust to weak
instruments.
The AR reported with rivtest:
Weak instrument robust tests and confidence sets for linear IV with cluster VCE
H0: beta[b1:shock] = 0
-------------------------------------------------------------------------------------------
Test | Statistic p-value 95% Confidence Set
------+------------------------------------------------------------------------------------
AR | chi2(1) = 63.87 Prob > chi2 = 0.0000 [-4.45917,-1.01057]
------+------------------------------------------------------------------------------------
Wald | chi2(1) = 6.93 Prob > chi2 = 0.0085 [-3.12553,-.458251]
-------------------------------------------------------------------------------------------
Note: Wald test not robust to weak instruments. Confidence sets estimated for 100 points in
[-4.45917, .875389].
Now here are my questions:
(1) Which AR should I look at to test the weakness of my instrument?
(2) Why the confidence interval reported with weakiv has an open-end? It is not clear to me what the interpretation of these confidence bands is. The help file explanation did not help either:
"Disjoint confidence intervals arise when the plot of the rejection probability dips below L% in more than one range; an example is when the
K statistic has inflection points or local minima that cause spurious power losses (inspection of a graph of the K
rejection probability is a way of detecting this). "
(3) What is really the difference between weakiv command and rivtest command? It seemed that weakiv is the extension of the rivtest, but I am not sure why they yield different results.
Appreciate any help!
