Dear all,

I am currenlty working on the causal relationship between the informal care decision and the life satisfaction of potential caregivers. As I suspect my first approach, OLS with fixed effect, to biaised due to several sources of endogeneity, I finally use two-step GMM-system estimator. My main specification is the following:


xtabond2 Lifesat lagLS Informal Gender i.Agecat Obj_health i.Marital i.Educ i.Occupation_cat Children Whours ln_st_Hninc i.Urban i.year if RC==2 & gmm_sample==1, h(1) gmm(lagLS, lag(2 3)) gmm(Informal Obj_health i.Marital i.Educ i.Occupation_cat Children Whours ln_st_Hninc i.Urban, lag(1 2)) iv(Gender i.Agecat) iv(i.year, eq(level)) small twostep



Dynamic panel-data estimation, two-step system GMM
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Group variable: nomem_encr Number of obs = 9180
Time variable : year Number of groups = 1188
Number of instruments = 470 Obs per group: min = 1
F(38, 1187) = 3439.01 avg = 7.73
Prob > F = 0.000 max = 9
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Lifesat | Coef. Std. Err. t P>|t| [95% Conf. Interval]
--------------+----------------------------------------------------------------
lagLS | .0661194 .0113218 5.84 0.000 .0439063 .0883324
Informal | -.0857742 .0248276 -3.45 0.001 -.1344851 -.0370632
Gender | -.0503902 .033579 -1.50 0.134 -.1162711 .0154907
_IAgecat_3 | .2282389 .0517332 4.41 0.000 .1267403 .3297376
_IAgecat_4 | .103332 .0522224 1.98 0.048 .0008735 .2057905
_IAgecat_5 | .1005478 .0544976 1.84 0.065 -.0063747 .2074702
_IAgecat_6 | .1969415 .0631799 3.12 0.002 .0729848 .3208982
_IAgecat_7 | .1364177 .0751936 1.81 0.070 -.0111095 .2839449
Obj_health | .1210188 .0424115 2.85 0.004 .037809 .2042286
_IMarital_2 | .2705168 .0652681 4.14 0.000 .1424632 .3985705
_IMarital_3 | .2307198 .0908654 2.54 0.011 .0524452 .4089944
_IMarital_4 | -.472043 .0989332 -4.77 0.000 -.6661464 -.2779397
_IMarital_5 | -.3583853 .0896283 -4.00 0.000 -.5342329 -.1825377
_IEduc_2 | -.2848591 .0605002 -4.71 0.000 -.4035583 -.1661599
_IEduc_3 | -.3615773 .0881303 -4.10 0.000 -.5344858 -.1886688
_IEduc_4 | -.2729954 .0961199 -2.84 0.005 -.4615792 -.0844117
_IEduc_5 | .0225658 .0814172 0.28 0.782 -.1371717 .1823034
_IEduc_6 | .0387999 .0951248 0.41 0.683 -.1478316 .2254314
_IEduc_7 | -.6792458 .0951736 -7.14 0.000 -.8659731 -.4925185
_IEduc_8 | -.2539277 .1004043 -2.53 0.012 -.4509174 -.0569379
_IEduc_9 | -1.15633 .2521884 -4.59 0.000 -1.651115 -.6615454
_IOccupatio_1 | -.2841957 .0604651 -4.70 0.000 -.4028262 -.1655653
_IOccupatio_2 | .1725232 .0570797 3.02 0.003 .0605349 .2845116
Children | .0130852 .0393558 0.33 0.740 -.0641294 .0902998
Whours | -.0043842 .0010849 -4.04 0.000 -.0065128 -.0022556
ln_st_Hninc | -.0886799 .019323 -4.59 0.000 -.1265909 -.0507689
_IUrban_2 | -.1629436 .0972537 -1.68 0.094 -.3537519 .0278647
_IUrban_3 | .425273 .0910808 4.67 0.000 .2465756 .6039704
_IUrban_4 | -.1455187 .0927251 -1.57 0.117 -.327442 .0364046
_IUrban_5 | .5804202 .0825634 7.03 0.000 .4184337 .7424066
_Iyear_2009 | .0304288 .0190255 1.60 0.110 -.0068986 .0677562
_Iyear_2010 | .0105775 .0137473 0.77 0.442 -.0163942 .0375492
_Iyear_2012 | -.0914997 .0176903 -5.17 0.000 -.1262075 -.0567919
_Iyear_2013 | -.0035593 .0195913 -0.18 0.856 -.0419967 .0348781
_Iyear_2014 | -.1069861 .0215754 -4.96 0.000 -.1493162 -.064656
_Iyear_2015 | -.0067729 .0223089 -0.30 0.761 -.0505421 .0369963
_Iyear_2017 | -.0604441 .0254589 -2.37 0.018 -.1103936 -.0104947
_Iyear_2018 | -.1204303 .025664 -4.69 0.000 -.1707822 -.0700784
_cons | 7.48364 .2047738 36.55 0.000 7.081881 7.885399
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Warning: Uncorrected two-step standard errors are unreliable.

Instruments for first differences equation
Standard
D.(Gender _IAgecat_3 _IAgecat_4 _IAgecat_5 _IAgecat_6 _IAgecat_7)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/2).(Informal Obj_health _IMarital_2 _IMarital_3 _IMarital_4
_IMarital_5 _IEduc_2 _IEduc_3 _IEduc_4 _IEduc_5 _IEduc_6 _IEduc_7 _IEduc_8
_IEduc_9 _IOccupatio_1 _IOccupatio_2 Children Whours ln_st_Hninc _IUrban_2
_IUrban_3 _IUrban_4 _IUrban_5)
L(2/3).lagLS
Instruments for levels equation
Standard
_Iyear_2009 _Iyear_2010 _Iyear_2011 _Iyear_2012 _Iyear_2013 _Iyear_2014
_Iyear_2015 _Iyear_2017 _Iyear_2018
Gender _IAgecat_3 _IAgecat_4 _IAgecat_5 _IAgecat_6 _IAgecat_7
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
D.(Informal Obj_health _IMarital_2 _IMarital_3 _IMarital_4 _IMarital_5
_IEduc_2 _IEduc_3 _IEduc_4 _IEduc_5 _IEduc_6 _IEduc_7 _IEduc_8 _IEduc_9
_IOccupatio_1 _IOccupatio_2 Children Whours ln_st_Hninc _IUrban_2
_IUrban_3 _IUrban_4 _IUrban_5)
DL.lagLS
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Arellano-Bond test for AR(1) in first differences: z = -11.20 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = 1.51 Pr > z = 0.131
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Sargan test of overid. restrictions: chi2(431) = 451.36 Prob > chi2 = 0.240
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(431) = 429.72 Prob > chi2 = 0.508
(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(261) = 259.75 Prob > chi2 = 0.510
Difference (null H = exogenous): chi2(170) = 169.97 Prob > chi2 = 0.486
gmm(lagLS, lag(2 3))
Hansen test excluding group: chi2(416) = 393.68 Prob > chi2 = 0.778
Difference (null H = exogenous): chi2(15) = 36.04 Prob > chi2 = 0.002
iv(Gender _IAgecat_3 _IAgecat_4 _IAgecat_5 _IAgecat_6 _IAgecat_7)
Hansen test excluding group: chi2(425) = 418.60 Prob > chi2 = 0.578
Difference (null H = exogenous): chi2(6) = 11.12 Prob > chi2 = 0.085
iv(_Iyear_2009 _Iyear_2010 _Iyear_2011 _Iyear_2012 _Iyear_2013 _Iyear_2014 _Iyear_2015 _Iyear_2017 _Iyear_2018, eq(level))
Hansen test excluding group: chi2(422) = 420.59 Prob > chi2 = 0.510
Difference (null H = exogenous): chi2(9) = 9.13 Prob > chi2 = 0.426




My question is about the number of instruments and whether should I be worried. I have 470 instruments and 1188 units of individuals meaning that the arbitrary rule-of-thumb mentioned by Roodman (2009) is respected: the number of instruments should not outnumber the number of units of individuals. However, Roodman (2009) also says that a too high number of instruments might weaken the Hansen test, which my case, is higher than 0.25 (and it might be a sign of trouble). I have also used the command collapse. The number of instruments has slighlty decreased (roughly 450) but the Hansen test is still above 0.25.

Overall, should I be worried about the results I post here, especially the number of instruments (470) or could I consider that 470 is too low compared with the size sample and the number of units ?

I hope my explanation is clear and I thank you in advance for your time and consideration,

Marie