st: IV-GMM

[Bond Tiger <bond0910@ymail.com>]

Dear all,

I am trying to estimate a simultaneous equations model (involving 2 equations) 
and trying to estimate both the equations simultaneously (i.e. SYSTEM EQUATIONS 
ESTIMATION and NOT SINGLE EQUATION ESTIMATION). Following are my two equations:

Y1=a0+a1*Y2+a2*L+e1...................(1)
Y2=b0+b1*Y1+b2*K+e2..................(2)

Variable Y1 is a continuous variable and Y2 is a dummy variable (with values 0 & 

1), L & K are sets of other exogenous variables. Both L & K may have some common 

variables also. e1 & e2 are independent error terms.

By model specification, I have assumed Y1 to be the endogenous in Eqn. (2) and 
Y2 to be endogenous in Eqn. (1). I have also tested for heteroskedasticity of 
disturbances and could detect presence of heteroskedasticity in my model. So I 
am trying to use Instrumental variable GMM estimation technique to estimate my 
model. I have considered different sets of instruments for Y1 & Y2. All my 
instruments are dummy variables (with 0 & 1 values). Now my questions are,

(1) Since, all the instruments in my model are dummy variables (with values 1 & 
0), can there be any efficiency loss due to use of dummy instrumental variables 
in estimation?
  
Taking single equation setup to test my instruments, the instruments are all 
satisfying overidentifying restriction tests, however, they are appearing to be 
weak instruments in eqn. (1) with Y2 as endogenous regressor. For your 
information, I have tested weak instruments using Kleibergen-Paap (K-P) rk Wald 
F statistics and Stock-Yogo weak IV test critical values. 

(2) My K-P rk Wald F stat is < the Stock-Yogo critical values and therefore, the 

IVs are weak. Is this correct inference?

(3) Do you think, since my instruments for the dummy regressor Y2 are also dummy 

variables (with values 0 & 1 and frequencies of 0s are more than 1s), therefore 
this weak instrument problem is arising?

(4) How important is the Anderson-Rubin Wald test and Stock-Wright LM test 
statistics, to test significance of the endogenous regressors in the 
structural equation? In these tests, do rejection of H0 implies that the 
endogenous regressors are significant?

Also do you have any idea about cluster robust estimates when there is 
within-cluster correlation? In my retirement savings analysis for workers in 
different firms, I have two 

data sets containing same variables. The only difference between the two data 
sets is that one data set (Say, data set 'A') contains duplicate Firm IDs (ID of 

different firms) and the other data set (data set 'B') contains no duplicate 
Firm IDs.

Data set 'A' looks as following: (Firm IDs are 001, 002 & 003 and corresponding 
worker IDs are 001i, (i=1,....n) for each firm)

FirmID   WorkerID     Wage 
001          0011            $1000
001          0012            $2000
001          0013            $500
002          0021            $300
002          0022            $3000
002          0023            $500
003          0031            $600
003          0032            $1500
etc.

and Data set 'B' looks as following (by deleting duplicate FirmID 
randomly): (Firm IDs are 001, 002 & 003 and corresponding worker IDs are 001i, 
(i=1,....n) for each firm)

FirmID   WorkerID     Wage 
001          0011            $1000
002          0023            $500
003          0032            $1500
etc.               

(5) With which data set should I use cluster() option?  
 
Any suggestions are highly welcome. I will greatly appreciate your kind help.

Please, Please help me if possible.

Regards,

Bond



      

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