Dynamic panel model where the independent variables are interactions of endogenous variables and dummies

[Rim Achour]

Hi,

I am a beginner to STATA and to Dynamic Panel Regression and I am facing the following problem,

I am running a dynamic panel regression, I am dealing with a finance data where my dependent variable is profitability measure and independent variables are variables of the Balance sheet. Therefore all of them affect my return on equity. It is dynamic because profitability depends on the lagged variables.

I am selecting endogenous variables that are theoretically justified. I am considering the time and lagged variables as instrument variables. All my regressors are formed from an interaction of endogenous variables with the correspondent dummy variable (Negw or Posw),

Here are the regressors:
ocNegw: operating expenses (oc) of the firm multiplied by a dummy variable that equals to 1 if a firm has low profitability and zero otherwise. i.e with ROE<median ROE of peers.
i.e. ocNegw = oc*Negw. This applies to all the regressors.
ocPosw: operating expenses (oc) of the firm multiplied by 1- dummy variable that equals to 1 if a firm has low profitability and zero otherwise. i.e with ROE>median ROE of peers
LConNegavgw: liquidity creation (on balance sheet activities) for firm with ROE<median ROE of peers
LConPosavgw: liquidity creation (on balance sheet activities) for firm with ROE> or equal to median ROE of peers.
LCoffNegavgw: liquidity creation (off balance sheet activities) for firm with ROE<median ROE of peers.
LCoffPosavgw: liquidity creation (off balance sheet activities) for firm with ROE> or equal to median ROE of peers.
CARNegw: car with ROE<median ROE of peers
CARPosw: car with ROE> or equal to median ROE of peers.
DLLNegw: Discretionary loan loss provisions for firm with ROE<median ROE of peers.
DLLPosw: Discretionary loan loss provisions for firm with ROE>=median ROE of peers.


I am using xtabond2 and my code is as the following:
[xtabond2 roeavgw L.roeavgw LConNegavgw LConPosavgw LCoffNegavgw LCoffPosavgw CARNegw CARPosw DLLNegw DLLPosw ocNegw ocPosw i.year gdpg hh if sz_large == 1, gmm(roeavgw LConNegavgw LConPosavgw LCoffNegavgw LCoffPosavgw CARNegw CARPosw DLLNegw DLLPosw ocNegw ocPosw ,lag(1 1) collapse) iv(i.year) robust twostep small][/CODE]

My output:

. xi: xtabond2 roeavgw L.roeavgw LConNegavgw LConPosavgw LCoffNegavgw LCoffPosavgw CARNegw CARPosw DLLNegw DLLPosw ocNegw ocPosw
> i.year gdpg hh if sz_large == 1, gmm(roeavgw LConNegavgw LConPosavgw LCoffNegavgw LCoffPosavgw CARNegw CARPosw DLLNegw DLLPosw
> ocNegw ocPosw ,lag(3 4) collapse) iv(i.year) robust twostep small
i.year _Iyear_1995-2014 (naturally coded; _Iyear_1995 omitted)
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate optimal weighting matrix for two-step estimation.
Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: rssd9001 Number of obs = 3290
Time variable : q_date Number of groups = 273
Number of instruments = 46 Obs per group: min = 1
F(32, 272) = 10.89 avg = 12.05
Prob > F = 0.000 max = 48
------------------------------------------------------------------------------
| Corrected
roeavgw | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
roeavgw |
L1. | .3887444 .0864462 4.50 0.000 .2185557 .5589331
|
LConNegavgw | .1307191 .0596548 2.19 0.029 .0132752 .248163
LConPosavgw | .0169042 .1426191 0.12 0.906 -.2638734 .2976819
LCoffNegavgw | -.0262093 .1746486 -0.15 0.881 -.3700442 .3176256
LCoffPosavgw | -.6096021 .4487993 -1.36 0.175 -1.493164 .2739598
CARNegw | .0010304 .0014068 0.73 0.465 -.0017392 .0038
CARPosw | -.000301 .0014241 -0.21 0.833 -.0031048 .0025027
DLLNegw | -.0678939 .0419485 -1.62 0.107 -.1504789 .0146911
DLLPosw | .0153792 .1075936 0.14 0.886 -.196443 .2272013
ocNegw | 1.12e-06 1.95e-07 5.74 0.000 7.34e-07 1.50e-06
ocPosw | 2.99e-06 5.75e-07 5.19 0.000 1.85e-06 4.12e-06
_Iyear_1996 | 0 (omitted)
_Iyear_1997 | 0 (omitted)
_Iyear_1998 | 0 (omitted)
_Iyear_1999 | 0 (omitted)
_Iyear_2000 | 0 (omitted)
_Iyear_2001 | .1204523 .0223787 5.38 0.000 .0763948 .1645099
_Iyear_2002 | .1445693 .0301783 4.79 0.000 .0851566 .203982
_Iyear_2003 | .1757185 .0427176 4.11 0.000 .0916193 .2598178
_Iyear_2004 | .1339142 .0326646 4.10 0.000 .0696066 .1982217
_Iyear_2005 | .1495176 .032283 4.63 0.000 .0859612 .213074
_Iyear_2006 | .1565908 .03446 4.54 0.000 .0887487 .224433
_Iyear_2007 | .1082364 .0242808 4.46 0.000 .0604342 .1560387
_Iyear_2008 | 0 (omitted)
_Iyear_2009 | .0519521 .0338198 1.54 0.126 -.0146298 .1185339
_Iyear_2010 | .0928315 .0435762 2.13 0.034 .007042 .178621
_Iyear_2011 | .0991386 .0349756 2.83 0.005 .0302812 .1679959
_Iyear_2012 | .0886473 .0309433 2.86 0.004 .0277286 .149566
_Iyear_2013 | .1094711 .0396191 2.76 0.006 .0314721 .1874701
_Iyear_2014 | 0 (omitted)
gdpg | -.0140521 .0057617 -2.44 0.015 -.0253953 -.0027088
hh | -.0000207 .0000147 -1.41 0.158 -.0000496 8.12e-06
_cons | -.1408473 .0454064 -3.10 0.002 -.23024 -.0514545
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(_Iyear_1996 _Iyear_1997 _Iyear_1998 _Iyear_1999 _Iyear_2000 _Iyear_2001
_Iyear_2002 _Iyear_2003 _Iyear_2004 _Iyear_2005 _Iyear_2006 _Iyear_2007
_Iyear_2008 _Iyear_2009 _Iyear_2010 _Iyear_2011 _Iyear_2012 _Iyear_2013
_Iyear_2014)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(3/4).(roeavgw LConNegavgw LConPosavgw LCoffNegavgw LCoffPosavgw CARNegw
CARPosw DLLNegw DLLPosw ocNegw ocPosw) collapsed
Instruments for levels equation
Standard
_Iyear_1996 _Iyear_1997 _Iyear_1998 _Iyear_1999 _Iyear_2000 _Iyear_2001
_Iyear_2002 _Iyear_2003 _Iyear_2004 _Iyear_2005 _Iyear_2006 _Iyear_2007
_Iyear_2008 _Iyear_2009 _Iyear_2010 _Iyear_2011 _Iyear_2012 _Iyear_2013
_Iyear_2014
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL2.(roeavgw LConNegavgw LConPosavgw LCoffNegavgw LCoffPosavgw CARNegw
CARPosw DLLNegw DLLPosw ocNegw ocPosw) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -5.30 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = -3.39 Pr > z = 0.001
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(13) = 70.76 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(13) = 30.79 Prob > chi2 = 0.004
(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(2) = 10.25 Prob > chi2 = 0.006
Difference (null H = exogenous): chi2(11) = 20.55 Prob > chi2 = 0.038
iv(_Iyear_1996 _Iyear_1997 _Iyear_1998 _Iyear_1999 _Iyear_2000 _Iyear_2001 _Iyear_2002 _Iyear_2003 _Iyear_2004 _Iyear_2005 _Iye
> ar_2006 _Iyear_2007 _Iyear_2008 _Iyear_2009 _Iyear_2010 _Iyear_2011 _Iyear_2012 _Iyear_2013 _Iyear_2014)
Hansen test excluding group: chi2(1) = 13.17 Prob > chi2 = 0.000
Difference (null H = exogenous): chi2(12) = 17.63 Prob > chi2 = 0.128


The tests are suggesting that the instruments are wrong.
Q1- How can I improve my model and choose the correct instrument?
Q2- what are the choices that I have?
Q3- what is the instrument to take when I have interaction variables of this kind?

I highly appreciate your help,

Thanks,

[Sebastian Kripfganz]

Serial correlation appears to be a problem because the Arellano-Bond AR(2) test rejects the null hypothesis of no second-order serial correlation in the first differenced errors. Adding a second lag of the dependent variable to the list of regressors might help.

Using only lags 3 and 4 of the regressors is likely to create a weak instruments problem because variables distant in the past are only weakly correlated with current observations.

Please see my comment in the Statalist topic on xtabond2 and deeper lags and the links therein for some remarks on the use of time dummies.

[Rim Achour]

Dear Kripfganz,

Thank you for your help,

Following your advice, I ran the following regression, however, AR(1) and AR(2) are giving me the same results

here is my code:
[xi: xtabond2 roeavgw L.roeavgw LConNegavgw LConPosavgw LCoffNegavgw LCoffPosavgw DLLNegw DLLPosw ocNegw ocPosw i.year gdpg hh if sz_large == 1, gmm(roeavgw, lag(4 5) collapse) gmm(LConNegavgw LConPosavgw LCoffNegavgw LCoffPosavgw DLLNegw DLLPosw ocNegw ocPosw ,lag(4 5) collapse) iv(i.year, eq(level)) robust twostep artests(3)
]

my output:


. xi: xtabond2 roeavgw L.roeavgw LConNegavgw LConPosavgw LCoffNegavgw LCoffPosavgw DLLNegw DLLPosw ocNegw ocPosw i.year gdp
> g hh if sz_large == 1, gmm(roeavgw, lag(4 5) collapse) gmm(LConNegavgw LConPosavgw LCoffNegavgw LCoffPosavgw DLLNegw DLLP
> osw ocNegw ocPosw ,lag(4 5) collapse) iv(i.year, eq(level)) robust twostep artests(3)
i.year _Iyear_1995-2014 (naturally coded; _Iyear_1995 omitted)
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate optimal weighting matrix for two-step estimation.
Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: rssd9001 Number of obs = 6112
Time variable : q_date Number of groups = 451
Number of instruments = 45 Obs per group: min = 1
Wald chi2(30) = 304.75 avg = 13.55
Prob > chi2 = 0.000 max = 60
------------------------------------------------------------------------------
| Corrected
roeavgw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
roeavgw |
L1. | -.0052015 .0916993 -0.06 0.955 -.184929 .1745259
|
LConNegavgw | -.1191484 .1068889 -1.11 0.265 -.3286469 .09035
LConPosavgw | .3645762 .2915927 1.25 0.211 -.206935 .9360873
LCoffNegavgw | .3631361 .201528 1.80 0.072 -.0318516 .7581238
LCoffPosavgw | -.3883363 .6292539 -0.62 0.537 -1.621651 .8449788
DLLNegw | -.000328 .0633174 -0.01 0.996 -.1244277 .1237718
DLLPosw | .8980324 .1809226 4.96 0.000 .5434307 1.252634
ocNegw | 5.94e-07 2.78e-07 2.14 0.033 4.89e-08 1.14e-06
ocPosw | -4.63e-07 7.36e-07 -0.63 0.529 -1.90e-06 9.79e-07
_Iyear_1996 | -.0307084 .0701683 -0.44 0.662 -.1682358 .1068189
_Iyear_1997 | -.046738 .0719881 -0.65 0.516 -.187832 .094356
_Iyear_1998 | -.045057 .075301 -0.60 0.550 -.1926443 .1025302
_Iyear_1999 | -.0232398 .0738905 -0.31 0.753 -.1680626 .1215829
_Iyear_2000 | -.0077236 .0564889 -0.14 0.891 -.1184398 .1029926
_Iyear_2001 | .0419377 .0319804 1.31 0.190 -.0207427 .104618
_Iyear_2002 | .0042315 .0470665 0.09 0.928 -.088017 .0964801
_Iyear_2003 | -.0131511 .0668679 -0.20 0.844 -.1442099 .1179076
_Iyear_2004 | -.0026654 .0567368 -0.05 0.963 -.1138675 .1085367
_Iyear_2005 | .0213983 .0546436 0.39 0.695 -.0857012 .1284978
_Iyear_2006 | .0355879 .0504077 0.71 0.480 -.0632094 .1343852
_Iyear_2007 | .0118378 .044704 0.26 0.791 -.0757803 .099456
_Iyear_2008 | 0 (omitted)
_Iyear_2009 | -.1241165 .0289991 -4.28 0.000 -.1809537 -.0672794
_Iyear_2010 | -.0959561 .0471027 -2.04 0.042 -.1882758 -.0036365
_Iyear_2011 | -.0325388 .0395346 -0.82 0.410 -.1100253 .0449476
_Iyear_2012 | -.0005885 .0374281 -0.02 0.987 -.0739462 .0727693
_Iyear_2013 | -.0068789 .0487196 -0.14 0.888 -.1023676 .0886098
_Iyear_2014 | 0 (omitted)
gdpg | .0128689 .0086965 1.48 0.139 -.0041759 .0299138
hh | -.0000501 .0000175 -2.86 0.004 -.0000845 -.0000157
_cons | .0694473 .0668606 1.04 0.299 -.061597 .2004916
------------------------------------------------------------------------------
Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(4/5).(LConNegavgw LConPosavgw LCoffNegavgw LCoffPosavgw DLLNegw DLLPosw
ocNegw ocPosw) collapsed
L(4/5).roeavgw collapsed
Instruments for levels equation
Standard
_Iyear_1996 _Iyear_1997 _Iyear_1998 _Iyear_1999 _Iyear_2000 _Iyear_2001
_Iyear_2002 _Iyear_2003 _Iyear_2004 _Iyear_2005 _Iyear_2006 _Iyear_2007
_Iyear_2008 _Iyear_2009 _Iyear_2010 _Iyear_2011 _Iyear_2012 _Iyear_2013
_Iyear_2014
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL3.(LConNegavgw LConPosavgw LCoffNegavgw LCoffPosavgw DLLNegw DLLPosw
ocNegw ocPosw) collapsed
DL3.roeavgw collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -3.90 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = -3.44 Pr > z = 0.001
Arellano-Bond test for AR(3) in first differences: z = -2.55 Pr > z = 0.011
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(14) = 169.70 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(14) = 48.50 Prob > chi2 = 0.000
(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(5) = 16.46 Prob > chi2 = 0.006
Difference (null H = exogenous): chi2(9) = 32.04 Prob > chi2 = 0.000
gmm(roeavgw, collapse lag(4 5))
Hansen test excluding group: chi2(11) = 23.80 Prob > chi2 = 0.014
Difference (null H = exogenous): chi2(3) = 24.70 Prob > chi2 = 0.000


Kindly note that I am using the interactions as instrument variables. i.e ocNegw = oc*Negw.

Should I use oc (endogenous variable) in place of its interaction with a dummy ocNegw??

Thank you in advance