Xtabond2, why including and excluding one variable in the gmmstyle option, the results are so different

[zhuxiaozhu918]

Basically , the qustion is: why sargan test statistic changes a lot by including and excluding one variable in gmmstyle option.


In my regression, tobin_q in the main explanatory variable, and could be influenced by past dependent variable. So, it should be included in the gmmstyle option, right? However, I find the results are very different by including and excluding it in the gmmstyle option. I do not know why?

I checked Roodman's paper, but I did not find a clear cut answer. On page 38 of Roodman (2008) paper, I find "As a result, most regressors appear twice in a command line, once before the comma for inclusion in X, once after as a source of IV- or GMM-style instruments."

Does this mean it is okay to leave tobin_q out of the gmmstyle option?

Thank you very much.




1. excluding the tobin_q from the gmm option
xi: xtabond2 ownershipratiosum l.ownershipratiosum l2.ownershipratiosum ///
L(0/2).(tobin_q logsales sigma divratio) ///
logfirmage i.calyear , ///
gmm(ownershipratiosum logsales sigma divratio, lag(3 .) collapse ) iv(i.calyear logfirmage ) ///
ar(5) twostep robust small


results:

Arellano-Bond test for AR(1) in first differences: z = -3.54 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = -0.03 Pr > z = 0.979
Arellano-Bond test for AR(3) in first differences: z = -0.13 Pr > z = 0.900
Arellano-Bond test for AR(4) in first differences: z = 1.27 Pr > z = 0.203
Arellano-Bond test for AR(5) in first differences: z = -0.84 Pr > z = 0.402
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(54) = 66.72 Prob > chi2 = 0.115
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(54) = 62.80 Prob > chi2 = 0.193
(Robust, but can be weakened by many instruments.)




2. including the tobin_q in the gmmoption
xi: xtabond2 ownershipratiosum l.ownershipratiosum l2.ownershipratiosum ///
L(0/2).(tobin_q logsales sigma divratio) ///
logfirmage i.calyear , ///
gmm(ownershipratiosum tobin_q logsales sigma divratio, lag(3 .) collapse ) iv(i.calyear logfirmage ) ///
ar(5) twostep robust small

results:

Arellano-Bond test for AR(1) in first differences: z = -4.35 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = 0.93 Pr > z = 0.353
Arellano-Bond test for AR(3) in first differences: z = -1.28 Pr > z = 0.201
Arellano-Bond test for AR(4) in first differences: z = 1.45 Pr > z = 0.146
Arellano-Bond test for AR(5) in first differences: z = -1.17 Pr > z = 0.242
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(71) = 135.92 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(71) = 98.38 Prob > chi2 = 0.017
(Robust, but can be weakened by many instruments.)

[Sebastian Kripfganz]

Think about it as an instrumental variable procedure. You are specifying the instruments with the gmm() and iv() options. It is clear that it makes a big difference for the results whether you instrument tobin_q by itself (its own lags) or rely on other variables as instruments that have potentially a relatively low correlation with tobin_q.

[zhuxiaozhu918]

Thanks, Sebastian. It is clearer now. One more question: does the Sargan/Hansen statistics suggest that tobin_q and its own lags are not a good instrumental variable on its own, and should be left out from the gmm or iv option?

Thanks.

[Sebastian Kripfganz]

Without further analysis, the results seem indeed to be indicative that the lags of tobin_q may not be valid instruments. A better way to analysis it is an appropriate difference-in-Sargan test that xtabond2 can also report. To get this test statistic for tobin_q in your case, specify gmm(ownershipratiosum logsales sigma divratio, lag(3 .) collapse) and gmm(tobin_q, lag(3 .) collapse) separately. (You can specifiy as many gmm() options as you like. That does not affect the estimation if you use the same lags and collapse in both cases but creates additional difference-in-Sargan tests for all subsets of instruments.)

[zhuxiaozhu918]

Thank you very much, Sebastian. I really appreciate it.

The test statistics are a little bit strange to me.

Difference-in-Hansen test statistics seems more or less similar to two instrumental subsets which are indicated by gmm(ownershipratiosum logsales sigma, collapse lag(3 .)) and gmm(tobin_q, collapse lag(3 .)), respectively.

However, when tobin_q is removed, the statistics indicate that the remaining instrument variables perform fine.

I expected to see by excluding tobin_q the difference-in-Sargan test statistics will be more powerful, but I did not. I am still not sure how to interpret it.



1. Including tobin_q in the GMM option separately

xi: xtabond2 ownershipratiosum l.ownershipratiosum l2.ownershipratiosum ///
L(0/2).(tobin_q logsales sigma ) L(0/2).divratio ///
logfirmage i.calyear , ///
gmm(ownershipratiosum logsales sigma, lag(3 .) collapse ) gmm(tobin_q, lag(3 .) collapse) iv(i.calyear logfirmage ) ///
ar(5) twostep robust small



Arellano-Bond test for AR(1) in first differences: z = -4.25 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = 1.17 Pr > z = 0.240
Arellano-Bond test for AR(3) in first differences: z = -1.51 Pr > z = 0.132
Arellano-Bond test for AR(4) in first differences: z = 1.65 Pr > z = 0.099
Arellano-Bond test for AR(5) in first differences: z = -1.33 Pr > z = 0.182
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(54) = 99.83 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(54) = 71.23 Prob > chi2 = 0.058
(Robust, but can be weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(50) = 62.45 Prob > chi2 = 0.111
Difference (null H = exogenous): chi2(4) = 8.78 Prob > chi2 = 0.067
gmm(ownershipratiosum logsales sigma, collapse lag(3 .))
Hansen test excluding group: chi2(3) = 5.75 Prob > chi2 = 0.125
Difference (null H = exogenous): chi2(51) = 65.49 Prob > chi2 = 0.083
gmm(tobin_q, collapse lag(3 .))
Hansen test excluding group: chi2(37) = 49.54 Prob > chi2 = 0.081
Difference (null H = exogenous): chi2(17) = 21.69 Prob > chi2 = 0.197
iv(_Icalyear_1995 _Icalyear_1996 _Icalyear_1997 _Icalyear_1998 _Icalyear_1999 _Icalyear_2000 _Icalyear_2001 _Icalye
> ar_2002 _Icalyear_2003 _Icalyear_2004 _Icalyear_2005 _Icalyear_2006 _Icalyear_2007 _Icalyear_2008 _Icalyear_2009 _I
> calyear_2010 _Icalyear_2011 _Icalyear_2012 logfirmage)
Hansen test excluding group: chi2(36) = 47.88 Prob > chi2 = 0.089
Difference (null H = exogenous): chi2(18) = 23.35 Prob > chi2 = 0.177



2. Excluding tobin_q from GMM, the test results seem ok.

xi: xtabond2 ownershipratiosum l.ownershipratiosum l2.ownershipratiosum ///
L(0/2).(tobin_q logsales sigma ) L(0/2).divratio ///
logfirmage i.calyear , ///
gmm(ownershipratiosum logsales sigma, lag(3 .) collapse ) iv(i.calyear logfirmage ) ///
ar(5) twostep robust small


Arellano-Bond test for AR(1) in first differences: z = -3.54 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = -0.26 Pr > z = 0.794
Arellano-Bond test for AR(3) in first differences: z = 0.58 Pr > z = 0.560
Arellano-Bond test for AR(4) in first differences: z = 1.06 Pr > z = 0.290
Arellano-Bond test for AR(5) in first differences: z = -0.77 Pr > z = 0.441
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(37) = 37.91 Prob > chi2 = 0.428
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(37) = 35.47 Prob > chi2 = 0.541
(Robust, but can be weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(34) = 29.42 Prob > chi2 = 0.692
Difference (null H = exogenous): chi2(3) = 6.04 Prob > chi2 = 0.110
iv(_Icalyear_1995 _Icalyear_1996 _Icalyear_1997 _Icalyear_1998 _Icalyear_1999 _Icalyear_2000 _Icalyear_2001 _Icalye
> ar_2002 _Icalyear_2003 _Icalyear_2004 _Icalyear_2005 _Icalyear_2006 _Icalyear_2007 _Icalyear_2008 _Icalyear_2009 _I
> calyear_2010 _Icalyear_2011 _Icalyear_2012 logfirmage)
Hansen test excluding group: chi2(19) = 15.93 Prob > chi2 = 0.662
Difference (null H = exogenous): chi2(18) = 19.54 Prob > chi2 = 0.359