System GMM xtdpdgmm command

[Zeenat Murtaza]

Dear Sebastian,

Hope you are doing well. Sir, I need your expert advise on the matter of insignificant p-values of constant and time effects while applying system gmm on the data.

My panel data sample consists of N=1880; T=25 observations. The independent variables included in the dynamic panel data model are lag of dependent financial variable; MTB (a ratio of financial variables); S (difference between financial variable in time t and t-1); other financial variables and lags of these variables (CCH CF, STI, DEI); age, size and a dummy for 2 firm categories i.e. 0 for widely held firms and 1 for family firms. According to literature, all independent financial variables are treated as endogenous so I lagged them accordingly. Dummy for firm categories is treated as predetermined as firm category has an effect on dependent variable and also independent variable. Is it correct to treat it predetermined???
I use following code (main interest is family firm)

xtdpdgmm L(0/1).Y Y^2 CCH CCH_L1 CF CF_L1 STI STI_L1 DEI DEI_L1 MTB S FIRM DUMMY c.CCH#1.FIRM DUMMY AGE SIZE, model(diff) collapse gmm(Y_L1 CCH CF STI DEI MTB S , lag(2 6)) gmm(FIRM DUMMY , lag(1 6)) gmm(Y_L1 CCH CF STI DEI MTB S, lag(1 2) diff model(level)) gmm(FIRM DUMMY, lag(0 1) diff model(level)) two vce(r)

Following literature, i used 6 lags as instruments for model in difference while 2 lags for model in levels. I tried teffects command for time dummy but the results become spurious or invalid; not supported by literature for some of the variables. So I ran command without teffects but still the value of constant is insignificant in both cases:

Generalized method of moments estimation
Fitting full model:
Step 1 f(b) = .0021157
Step 2 f(b) = .37936926
Group variable: isin_code Number of obs = 1705
Time variable: year Number of groups = 123
Moment conditions: linear = 59 Obs per group: min = 2
nonlinear = 0 avg = 13.86179
total = 59 max = 24
( Std. err. adjusted for 123 clusters in isin_code)

			WC-Robust
Y	Coefficient	std. err.		z	P>z	95%		confidence interval
Y_L1.	0.660	0.160		4.120	0.000	0.346		0.974
Y^2	-0.261	0.151		-1.720	0.085	-0.557		0.036
CCH	-0.048	0.062		-0.780	0.438	-0.169		0.073
CCH_L1	-0.075	0.041		-1.830	0.067	-0.155		0.005
CF_ta	0.077	0.071		1.080	0.280	-0.062		0.216
CF_L1	-0.053	0.029		-1.830	0.068	-0.110		0.004
STI	0.238	0.059		4.040	0.000	0.123		0.354
STI_L1	-0.014	0.032		-0.430	0.664	-0.078		0.049
DEI	-0.139	0.807		-0.170	0.864	-1.721		1.443
DEI_L1	-0.004	0.032		-0.110	0.911	-0.066		0.059
MTB	0.000	0.003		0.170	0.869	-0.005		0.006
S	-0.001	0.002		-0.810	0.421	-0.005		0.002
1.firm_DUMMY	-0.040	0.023		-1.690	0.090	-0.085		0.006
c.FIRM DUMMY#c.CCH_L1	0.086	0.043		2.030	0.042	0.003		0.170
AGE	-0.001	0.001		-0.720	0.473	-0.004		0.002
SIZE	-0.000	0.004		-0.030	0.977	-0.008		0.007
_cons	0.079	0.060		1.320	0.187	-0.038		0.197

Diagnostic testing Results are as follows:

Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1 z = -3.8241 Prob > |z| = 0.0001
H0: no autocorrelation of order 2 z = 0.4675 Prob > |z| = 0.6401
H0: no autocorrelation of order 3 z = -0.6046 Prob > |z| = 0.5454


Sargan-Hansen test of the overidentifying restrictions
H0: overidentifying restrictions are valid

2-step moment functions, 2-step weighting matrix chi2(42) = 46.6624
Prob > chi2 = 0.2867

2-step moment functions, 3-step weighting matrix chi2(42) = 55.8996
Prob > chi2 = 0.0740


With t-effects, the results are:

Generalized method of moments estimation
Fitting full model:
Step 1 f(b) = .00201183
Step 2 f(b) = .36048898
Group variable: isin_code Number of obs = 1705
Time variable: year Number of groups = 123
Moment conditions: linear = 82 Obs per group: min = 2
nonlinear = 0 avg = 13.86179
total = 82 max = 24
(Std. err. adjusted for 123 clusters in isin_code)

			WC-Robust
Y	Coefficient	std.err		z	P>z	95%		CONFIDENCE INTERVAL
Y_L1.	0.646	0.190		3.400	0.001	0.274		1.019
Y^2	-0.279	0.174		-1.600	0.109	-0.620		0.062
CCH	-0.084	0.083		-1.020	0.307	-0.246		0.078
CCH_L1	-0.070	0.048		-1.450	0.146	-0.164		0.024
CF	0.100	0.073		1.370	0.171	-0.043		0.244
CF_L1	-0.057	0.036		-1.570	0.116	-0.128		0.014
STI	0.275	0.074		3.720	0.000	0.130		0.420
STI_L1	-0.012	0.034		-0.370	0.714	-0.079		0.054
DEI	-0.127	1.092		-0.120	0.907	-2.267		2.013
DEI_L1	0.002	0.042		0.040	0.967	-0.081		0.085
MTB	0.000	0.003		0.100	0.918	-0.005		0.006
S	-0.000	0.002		-0.120	0.907	-0.004		0.004
1.FIRM DUMMY	-0.030	0.021		-1.440	0.151	-0.071		0.011
C.FIRM DUMMY #CCH	0.084	0.049		1.720	0.086	-0.012		0.180
AGE	-0.001	0.001		-0.560	0.576	-0.002		0.001
SIZE	0.000	0.005		0.050	0.963	-0.010		0.010
year
1999	-0.020	0.053		-0.380	0.701	-0.124		0.083
2000	-0.021	0.051		-0.410	0.685	-0.120		0.079
2001	-0.026	0.053		-0.500	0.618	-0.130		0.077
2002	-0.007	0.048		-0.140	0.885	-0.101		0.087
2003	-0.014	0.050		-0.270	0.786	-0.111		0.084
2004	-0.016	0.050		-0.330	0.743	-0.114		0.081
2005	-0.034	0.052		-0.650	0.516	-0.135		0.068
2006	-0.021	0.050		-0.420	0.673	-0.118		0.076
2007	-0.019	0.049		-0.380	0.704	-0.115		0.078
2008	-0.012	0.048		-0.250	0.804	-0.106		0.082
2009	-0.011	0.049		-0.230	0.819	-0.108		0.085
2010	-0.011	0.048		-0.230	0.818	-0.106		0.083
2011	-0.009	0.048		-0.200	0.844	-0.103		0.084
2012	-0.013	0.048		-0.270	0.787	-0.106		0.080
2013	-0.008	0.049		-0.150	0.877	-0.103		0.088
2014	-0.018	0.048		-0.370	0.712	-0.111		0.076
2015	-0.014	0.050		-0.290	0.770	-0.112		0.083
2016	-0.019	0.051		-0.370	0.711	-0.118		0.081
2017	-0.016	0.047		-0.330	0.743	-0.108		0.077
2018	-0.010	0.049		-0.210	0.830	-0.106		0.085
2019	-0.009	0.047		-0.200	0.843	-0.101		0.082
2020	-0.006	0.049		-0.130	0.897	-0.102		0.090
2021	-0.016	0.049		-0.340	0.734	-0.112		0.079
_cons	0.064	0.056		1.140	0.256	-0.047		0.175

Instruments corresponding to the linear moment conditions:

Please advise where i am doing the mistake and how can i correct it?

Thanks in anticipation.

[Sebastian Kripfganz]

I cannot tell you whether it is correct to treat firm categories as predetermined. This is application specific. If there is no delayed feedback from the dependent variable on the firm categories and neither current nor past shocks are correlated with firm categories, then it would be exogenous.

Following literature, i used 6 lags as instruments for model in difference while 2 lags for model in levels.

I am surprised that this is done in your literature, but if that's the case, then I won't interfere.

Why do you worry about the statistical significance of the constant term? That's not usually a reason for concern.

Finally, you would not normally treat the lagged dependent variable Y_L1 as endogenous, but as predetermined instead.

[Zeenat Murtaza]

I extend infinte thanks and gratitude for your valuable response and time. Regarding the statistical significance of constant term, I was worried as I kept family as dummy 1 while o as non-family so when constant is insignificant , doesnt it exhibit that non-family firms impact on dependent variable is insignificant when other independent variables are assumed to be 0. However, literature shows non-family firms to have a greater impact than family firms. Further, firm specifities have been shown to determine the firm's investment in dependent variable. if a firm is family, it invests less while if it is non-family it may invest more. Over time, it is likely firm status change from family to non-family so it could have an impact accordingly. Thats why i treated it predetermined. Using interaction terms of family firms further categories and another independent variable however is influencing the results. Can you please comment on it?

[Sebastian Kripfganz]

The impact of being a family/non-family firm is given by the coefficient of the family dummy. You are normally just interested in a relative effect: being a family firm as opposed to a non-family firm. The constant term gives you an average of the dependent variable if all regressors were evaluated at zero (which includes being a non-family firm), which may or may not be meaningful in your application.

If the dependent variable affects the probability for family firms to become non-family firms in the future, then this would make the family dummy predetermined.

[Zeenat Murtaza]

Thank you so much sir. It was really helpful.

[Zeenat Murtaza]

Dear Sebastian,

Hope you are doing well. Sir, I need to test crisis effects and sectoral differences while applying system gmm approach in stata.

My panel data sample consists of N=3094; T=25 observations. The independent variables included in the dynamic panel data model are lag of dependent financial variable; Tobin Q (a ratio of financial variables); Sales Growth; and other financial variables in time t and their lags (Liquidity, Cash flow, Stock & debt); age and a dummy for 2 firm categories i.e. 0 for widely held firms and 1 for family firms. In order to run crises effects, I used 4 dummies i.e. 0 as reference, 1 for financial crises, 2 for debt crises, 3 for covid crisis. Can you please help with the code as the inbuilt gmm command in stata gives by and sort option for Arellano & Bond gmm but I am not sure whether this approach is appropriate or is it more reasonable to simply input i.crisis in xtdpdgmm command to see the effects of all periods simultaneously? Results show a drastic change in significance levels when i adopted the latter approach. Please advise.

[Sebastian Kripfganz]

Including dummy variables i.crisis accounts for different intercept in different crisis periods. If you want the slope coefficients of the other regressors to be potentially different across crisis periods, you could either interact all of these regressors with the crisis dummies, or you could restrict the estimation sample with the if qualifier to a particular subsample.

[Zeenat Murtaza]

Thank you Sebastian.