Dear Statalisters,
I am new to Stata Forum. I am not much familiar with GMM estimation using xtabond2 however, tried it using different options such as collapse, robust, year dummies and sector dummies.
Recently, i read and came to know that for estimating GMM, we should be sure about the existence of endogenity among the variables in model which can be confirmed through literature.
However, I observed that in my field, researchers are generally estimating GMM directly in their articles without mentioning about the endogenity issues.
I searched and found that we can test endogenity among the variables using ivregress 2sls command. I found 2 ways but do not know which one is correct. Therefore, I need help.


I am using below variables;
Dependent variables - ROA
Independent variables - ACP, ICP, APP ONWC
Control variables, FS, DR

I assume that ACP is independent variable, ICP is my endogenous variable and APP, ONWC, FS and TDTA are my instrumental variables

Estimation Procedure;
First, i run the command
ivregress 2sls
using DV, IV and Instrumental variables
Second,
estat endogentiy
Third, Check Instrumental Variables through
estat firststage
Results;
Code:
. ivregress 2sls ROA ACP (ICP = APP ONWC FS TDTA)

Instrumental variables (2SLS) regression               Number of obs =    1040
                                                       Wald chi2(2)  =   75.04
                                                       Prob > chi2   =  0.0000
                                                       R-squared     =       .
                                                       Root MSE      =  .13991

------------------------------------------------------------------------------
         ROA |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         ICP |   .0007183   .0000992     7.24   0.000      .000524    .0009127
         ACP |  -.0004456   .0000555    -8.03   0.000    -.0005544   -.0003368
       _cons |   .0132083    .010531     1.25   0.210     -.007432    .0338487
------------------------------------------------------------------------------
Instrumented:  ICP
Instruments:   ACP APP ONWC FS TDTA

. estat endog

  Tests of endogeneity
  Ho: variables are exogenous

  Durbin (score) chi2(1)          =  93.2008  (p = 0.0000)
  Wu-Hausman F(1,1036)            =  101.982  (p = 0.0000)

. estat firststage

  First-stage regression summary statistics
  --------------------------------------------------------------------------
               |            Adjusted      Partial
      Variable |   R-sq.       R-sq.        R-sq.     F(4,1034)   Prob > F
  -------------+------------------------------------------------------------
           ICP |  0.1889      0.1850       0.1361         40.71    0.0000
  --------------------------------------------------------------------------


  Minimum eigenvalue statistic = 40.71       

  Critical Values                      # of endogenous regressors:    1
  Ho: Instruments are weak             # of excluded instruments:     4
  ---------------------------------------------------------------------
                                     |    5%     10%     20%     30%
  2SLS relative bias                 |  16.85   10.27    6.71    5.34
  -----------------------------------+---------------------------------
                                     |   10%     15%     20%     25%
  2SLS Size of nominal 5% Wald test  |  24.58   13.96   10.26    8.31
  LIML Size of nominal 5% Wald test  |   5.44    3.87    3.30    2.98
  ---------------------------------------------------------------------
The above method confirms existence of endogenity for ICP

However, in another method, by using lags of ICP, results are different

Code
Code:
. ivregress 2sls ROA ACP APP ONWC FS TDTA (ICP = ICP_01)

Instrumental variables (2SLS) regression               Number of obs =    1039
                                                       Wald chi2(6)  =  241.39
                                                       Prob > chi2   =  0.0000
                                                       R-squared     =  0.1904
                                                       Root MSE      =  .10224

------------------------------------------------------------------------------
         ROA |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         ICP |  -.0001331   .0000441    -3.02   0.003    -.0002195   -.0000466
         ACP |  -.0000327   .0000429    -0.76   0.445    -.0001168    .0000513
         APP |  -.0001001   .0000495    -2.02   0.043    -.0001972   -3.03e-06
        ONWC |   .2484759   .0238135    10.43   0.000     .2018023    .2951495
          FS |   .0154282    .002339     6.60   0.000     .0108438    .0200125
        TDTA |   .0131924   .0246532     0.54   0.593     -.035127    .0615117
       _cons |  -.1584281   .0315125    -5.03   0.000    -.2201915   -.0966646
------------------------------------------------------------------------------
Instrumented:  ICP
Instruments:   ACP APP ONWC FS TDTA ICP_01

. estat endog

  Tests of endogeneity
  Ho: variables are exogenous

  Durbin (score) chi2(1)          =  .744985  (p = 0.3881)
  Wu-Hausman F(1,1031)            =  .739779  (p = 0.3899)

. estat firststage

  First-stage regression summary statistics
  --------------------------------------------------------------------------
               |            Adjusted      Partial
      Variable |   R-sq.       R-sq.        R-sq.     F(1,1032)   Prob > F
  -------------+------------------------------------------------------------
           ICP |  0.5358      0.5331       0.4264       767.013    0.0000
  --------------------------------------------------------------------------


  Minimum eigenvalue statistic = 767.013     

  Critical Values                      # of endogenous regressors:    1
  Ho: Instruments are weak             # of excluded instruments:     1
  ---------------------------------------------------------------------
                                     |    5%     10%     20%     30%
  2SLS relative bias                 |         (not available)
  -----------------------------------+---------------------------------
                                     |   10%     15%     20%     25%
  2SLS Size of nominal 5% Wald test  |  16.38    8.96    6.66    5.53
  LIML Size of nominal 5% Wald test  |  16.38    8.96    6.66    5.53
  ---------------------------------------------------------------------
The second method using lags of ICP is giving opposite result meaning that ICP is not endogenous

Please help with the below questions;

1. Which method is correct ?
2. If one is correct from above, is it sufficient to check the endogenity of all IVs one by one and run xtabond2 (difference/system) ?

Thank you