Dear all,

I'm estimating system gmm on a panel of 249 individuals across three waves. I wanted to look at how once-lagged expenditures will impact on a categorical health outcome and my control variable include once lagged health outcome. I used xtabond2 and Stata15.1.

I could not get ar (1) and (2) tests, I noticed similar issues/posts on this and the explanation was there was no 3rd lag in levels. But I'm still wondering:
1. In this case, would the result still valid?
2. How many waves needed at least to run system GMM?

My codes and results are the following


Code:
xtabond2 health L(1/1).i.health L(1/1).exp L(1/1).age L(1/1).female, robust small gmm(L(1/1).i.health) ivstyle(L(1/1).exp L(1/1).age L(1/1).gender, equation(level))
Code:
Group variable: pid    Number of obs    =    469
Time variable : Year    Number of groups    =    248
Number of instruments = 15    Obs per group: min    =    1
F(13, 247)    =      3.70    avg    =    1.89
Prob > F      =     0.000    max    =    2
Code:
Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/2).(1bL.health 2L.health 3L.health)
Instruments for levels equation
Standard
L.exp L.age L.gender _cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
D.(1bL.health 2L.health 3L.health)

Arellano-Bond test for AR(1) in first differences: z =      .  Pr > z =      .
Arellano-Bond test for AR(2) in first differences: z =      .  Pr > z =      .

Sargan test of overid. restrictions: chi2(1)    =  28.61  Prob > chi2 =  0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(1)    =   8.96  Prob > chi2 =  0.003
(Robust, but weakened by many instruments.)

Many many thanks in advance.


Cheers,
Tianxin