Help: xtabond and sargan test

[Amit Kumar]

Hello! I am new to Stata list and need some guidance.
I ran the xtreg, fe model to test the effect of my IV on the DV. I realized the data had autocorrelation (Wooldridge test). So, I conducted xtabond. The artests(2) (estat xtabond) were correct (order 1: significant and order 2: non-significant) only if I take lags(2). Hence, I took 2 lags. I followed it with the Sargan test (estat sargan). The result was significant.

xtabond equation:
xtabond std_f_sh_first_msa10_mc std_lag_2index_nsa std_ln_nsize_1yr std_outward_orientation std_hhi_n_pat_mainclass std_degree_centralization std_ln_emp_hightech std_pc_annual_payment_hightech y_1-y_17, lags(1) artests(2)


Arellano–Bond dynamic panel-data estimation Number of obs = 4,581
Group variable: MSAstate Number of groups = 424
Time variable: year
Obs per group:
min = 1
avg = 10.80425
max = 13

Number of instruments = 125 Wald chi2(22) = 610.54
Prob > chi2 = 0.0000
One-step results
------------------------------------------------------------------------------------------------
std_f_sh_first_msa10_mc | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------------------------+----------------------------------------------------------------
std_f_sh_first_msa10_mc |
L1. | .1652581 .0226839 7.29 0.000 .1207984 .2097177
L2. | .1705293 .0191928 8.89 0.000 .1329122 .2081464
|
std_lag_2index_nsa | -.0657571 .020347 -3.23 0.001 -.1056365 -.0258777
std_ln_nsize_1yr | .0924772 .0782206 1.18 0.237 -.0608324 .2457867
std_outward_orientation | .0244185 .009956 2.45 0.014 .0049052 .0439319
std_hhi_n_pat_mainclass | .0183985 .0151115 1.22 0.223 -.0112195 .0480165
std_degree_centralization | .0376602 .0198398 1.90 0.058 -.001225 .0765455
std_ln_emp_hightech | .0339718 .0421255 0.81 0.420 -.0485926 .1165363
std_pc_annual_payment_hightech | .0476782 .0289956 1.64 0.100 -.0091521 .1045086
y_3 | .2831649 .0694936 4.07 0.000 .14696 .4193698
y_4 | .2823377 .0649208 4.35 0.000 .1550952 .4095802
y_5 | .2957124 .0609644 4.85 0.000 .1762243 .4152004
y_6 | .3263206 .0574517 5.68 0.000 .2137173 .4389239
y_7 | .3015834 .0536802 5.62 0.000 .1963721 .4067946
y_8 | .3749698 .050919 7.36 0.000 .2751703 .4747693
y_9 | .386725 .0511317 7.56 0.000 .2865087 .4869414
y_10 | .3402882 .0511256 6.66 0.000 .2400839 .4404926
y_11 | .2469398 .0488287 5.06 0.000 .1512373 .3426422
y_12 | .1356522 .0466845 2.91 0.004 .0441523 .2271522
y_13 | .0971989 .0462503 2.10 0.036 .00655 .1878479
y_14 | -.0041391 .0449296 -0.09 0.927 -.0921994 .0839212
y_15 | -.0111178 .0377203 -0.29 0.768 -.0850483 .0628127
_cons | -.3968184 .0417313 -9.51 0.000 -.4786103 -.3150266
------------------------------------------------------------------------------------------------
Instruments for differenced equation
GMM-type: L(2/.).std_f_sh_first_msa10_mc
Standard: D.std_lag_2index_nsa D.std_ln_nsize_1yr D.std_outward_orientation
D.std_hhi_n_pat_mainclass D.std_degree_centralization D.std_ln_emp_hightech
D.std_pc_annual_payment_hightech D.y_3 D.y_4 D.y_5 D.y_6 D.y_7 D.y_8 D.y_9
D.y_10 D.y_11 D.y_12 D.y_13 D.y_14 D.y_15
Instruments for level equation
Standard: _cons

Sargan test
estat sargan
Sargan test of overidentifying restrictions
H0: Overidentifying restrictions are valid

chi2(102) = 862.8817
Prob > chi2 = 0.0000

Please help:
1. The Sargan test is significant. Does it mean the instrument is invalid? What can I do to fix this issue? I learned that it may be solved if I reduce the number of instruments or collapse them (not sure how). The analysis shows that the number of instruments is 125 - I am not sure how STATA creates them, so, I don't know how to reduce their number. Even if I remove all controls and year dummy, the number of instruments was 107 and the Sargan test was significant.

xtabond std_f_sh_first_msa10_mc std_lag_2index_nsa, lags(1) artests(2)

Arellano–Bond dynamic panel-data estimation Number of obs = 5,717
Group variable: MSAstate Number of groups = 439
Time variable: year
Obs per group:
min = 3
avg = 13.02278
max = 14

Number of instruments = 107 Wald chi2(2) = 498.65
Prob > chi2 = 0.0000
One-step results
-----------------------------------------------------------------------------------------
std_f_sh_first_msa10_mc | Coefficient Std. err. z P>|z| [95% conf. interval]
------------------------+----------------------------------------------------------------
std_f_sh_first_msa10_mc |
L1. | .3600455 .0166373 21.64 0.000 .327437 .3926541
|
std_lag_2index_nsa | -.0562578 .0177317 -3.17 0.002 -.0910113 -.0215044
_cons | -.0520827 .0081361 -6.40 0.000 -.0680291 -.0361363
-----------------------------------------------------------------------------------------
Instruments for differenced equation
GMM-type: L(2/.).std_f_sh_first_msa10_mc
Standard: D.std_lag_2index_nsa
Instruments for level equation
Standard: _cons

. estat sargan
Sargan test of overidentifying restrictions
H0: Overidentifying restrictions are valid

chi2(104) = 1281.709
Prob > chi2 = 0.0000


2. I ran other equations (with 2 lags of DV) for reliable estimation and addressing autocorrelation (if the xtabond is insufficient as the Sargan test is significant).

• FE panel regression with Driscoll-Kraay standard errors: xtscc std_f_sh_first_msa10_mc l.std_f_sh_first_msa10_mc l2.std_f_sh_first_msa10_mc std_lag_2index_nsa std_ln_nsize_1yr std_outward_orientation std_hhi_n_pat_mainclass std_degree_centralization std_ln_emp_hightech std_pc_annual_payment_hightech i.year, fe
• System GMM/Blundell-Bond estimator: xtdpdsys std_f_sh_first_msa10_mc std_lag_2index_nsa std_ln_nsize_1yr std_outward_orientation std_hhi_n_pat_mainclass std_degree_centralization std_ln_emp_hightech std_pc_annual_payment_hightech y_1 y_2 y_3 y_4 y_5 y_6 y_7 y_8 y_9 y_10 y_11 y_12 y_13 y_14 y_15 y_16 y_17, lags(2) artests(2)

The Sargan test is still significant.

• FE panel regression with autoregressive errors: xtregar std_f_sh_first_msa10_mc l(1/2).std_f_sh_first_msa10_mc std_lag_2index_nsa std_ln_nsize_1yr std_outward_orientation std_hhi_n_pat_mainclass std_degree_centralization std_ln_emp_hightech std_pc_annual_payment_hightech y_1-y_17, fe

Are these methods correct and sufficient to deal with the problem of autocorrelation (temporal dependence)? Results in all these analyses support my hypotheses.

Thank you very much for your kind help!

[Sebastian Kripfganz]

I recommend that you try to understand the estimators a bit better before continuing with your analysis. It is difficult to give helpful answers at this stage. The following presentation and the references therein might be of help:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.

[Amit Kumar]

Thank you, Sebastian!