Specification and instruments in xtabond2

[Anna Bracci]

Dear all,
I am carrying out a panel GMM estimator to analyse the causal effect of bad jobs on mental disorder. My panel data consist of 13 years and 16’000 obs. Panel is unbalanced.

Below my syntax for an AR(2) model, where I consider as endogenous the bad job score for reversed causality with my DV and some covariates (household disposable income, health impediment, family conflict and sleeping problems):

xtabond2 l(0/2).(mental_dis) score_JQ women $covariate d_year4-d_year13 lambda, ///
gmm(mental_dis, lag (3 3) eq(level)) ///
gmm(mental_dis, lag (3 3) eq(diff)) ///
gmm(score_JQ, lag (2 2) eq(level)) ///
gmm(score_JQ, lag (2 3) eq(diff)) ///
gmm(disposable_income impediment conflict sleeping, lag (2 2) eq(level)) ///
gmm(disposable_income impediment conflict sleeping, lag (2 3) eq(diff)) ///
iv(women age swiss education_D2 education_D3 illness past_experience couple kids age_kidsD2 age_kidsD3, eq(level)) ///
iv(self_employed ISCO_D2 ISCO_D3 ISCO_D4 public size_D2 size_D3, eq(level)) ///
iv(NOGA_D1 NOGA_D3 NOGA_D4 NOGA_D5 NOGA_D6 NOGA_D7 NOGA_D8 NOGA_D9 NOGA_D10, eq(level)) ///
iv(regionD1 regionD2 regionD4 regionD5 regionD6 regionD7 unemp_rate_m unemp_rate_f, eq(level)) ///
iv(d_year4-d_year13 lambda, eq(level)) ///
h(2) ar(3) two cluster(idpers)

Below my results:

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: idpers Number of obs = 15843
Time variable : year Number of groups = 4392
Number of instruments = 216 Obs per group: min = 1
Wald chi2(53) = 852.09 avg = 3.61
Prob > chi2 = 0.000 max = 11

……………

Arellano-Bond test for AR(1) in first differences: z = -6.89 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = 0.73 Pr > z = 0.465
Arellano-Bond test for AR(3) in first differences: z = 0.41 Pr > z = 0.680
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(162) = 216.29 Prob > chi2 = 0.003
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(162) = 147.97 Prob > chi2 = 0.778
(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(103) = 79.84 Prob > chi2 = 0.956
Difference (null H = exogenous): chi2(59) = 68.13 Prob > chi2 = 0.195
gmm(mental_disorder, eq(level) lag(3 3))
Hansen test excluding group: chi2(153) = 136.96 Prob > chi2 = 0.819
Difference (null H = exogenous): chi2(9) = 11.00 Prob > chi2 = 0.275
gmm(mental_disorder, eq(diff) lag(3 3))
Hansen test excluding group: chi2(152) = 131.26 Prob > chi2 = 0.887
Difference (null H = exogenous): chi2(10) = 16.71 Prob > chi2 = 0.081
gmm(score_JQ, eq(level) lag(2 2))
Hansen test excluding group: chi2(152) = 139.03 Prob > chi2 = 0.767
Difference (null H = exogenous): chi2(10) = 8.94 Prob > chi2 = 0.538
gmm(score_JQ, eq(diff) lag(2 3))
Hansen test excluding group: chi2(142) = 132.76 Prob > chi2 = 0.699
Difference (null H = exogenous): chi2(20) = 15.21 Prob > chi2 = 0.764
gmm(disposable_income impediment conflict sleeping_problem, eq(level) lag(2 2))
Hansen test excluding group: chi2(122) = 112.41 Prob > chi2 = 0.722
Difference (null H = exogenous): chi2(40) = 35.56 Prob > chi2 = 0.670
gmm(disposable_income impediment conflict sleeping_problem, eq(diff) lag(2 3))
Hansen test excluding group: chi2(82) = 75.62 Prob > chi2 = 0.677
Difference (null H = exogenous): chi2(80) = 72.35 Prob > chi2 = 0.716
iv(women age swiss education_D2 education_D3 illness past_experience couple kids age_kidsD2 age_kidsD3, eq(level))
Hansen test excluding group: chi2(151) = 138.02 Prob > chi2 = 0.768
Difference (null H = exogenous): chi2(11) = 9.95 Prob > chi2 = 0.535
iv(self_employed ISCO_D2 ISCO_D3 ISCO_D4 public size_D2 size_D3, eq(level))
Hansen test excluding group: chi2(155) = 140.30 Prob > chi2 = 0.795
Difference (null H = exogenous): chi2(7) = 7.67 Prob > chi2 = 0.363
iv(NOGA_D1 NOGA_D3 NOGA_D4 NOGA_D5 NOGA_D6 NOGA_D7 NOGA_D8 NOGA_D9 NOGA_D10, eq(level))
Hansen test excluding group: chi2(153) = 143.00 Prob > chi2 = 0.708
Difference (null H = exogenous): chi2(9) = 4.97 Prob > chi2 = 0.837
iv(regionD1 regionD2 regionD4 regionD5 regionD6 regionD7 unemp_rate_m unemp_rate_f, eq(level))
Hansen test excluding group: chi2(154) = 144.09 Prob > chi2 = 0.705
Difference (null H = exogenous): chi2(8) = 3.88 Prob > chi2 = 0.868
iv(d_year4 d_year5 d_year6 d_year7 d_year8 d_year9 d_year10 d_year11 d_year12 d_year13 lambda, eq(level))
Hansen test excluding group: chi2(151) = 141.75 Prob > chi2 = 0.693
Difference (null H = exogenous): chi2(11) = 6.22 Prob > chi2 = 0.858

In particular, my doubts concern:

1. Although the results pass the main tests, they are quite sensitive to the specification choices. Do you have any idea about the cause of this?
2. Is it a problem a quite high p-value in the Hansen test?
3. The Diff-in-Hansen test referring to the lagged mental disorder (in bold) does not improve despite I specify different lag orders (and use collapse).
4. How can I chose endogenous variables if they are valid in both the IV- and the GMM-style?
5. In a system-GMM does it make sense to consider transitions as variables (e.g. life events or job loss)?
6. When a variable can be considered predetermined instead of endogenous in my sample?

Many thanks for your help!