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```I would really appreciate any comments, thank you in advance.
Evan M.
My estimation is below:

xtabond2 oss l.oss realyldglp OE2assets TE2assets glp2assets
costperloan iyear lindi lsolid lvillage, gmm(oss lindi lsolid
lvillage) iv(iyear l2.pm) two robust small orthogonal
Favoring space over speed. To switch, type or click on mata: mata set
matafavor speed, perm.
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate optimal weighting matrix
for two-step estimation.
Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: mfiid                           Number of obs      =       379
Time variable : year                            Number of groups   =       233
Number of instruments = 42                      Obs per group: min =         0
F(10, 232)    =     11.06                                      avg =      1.63
Prob > F      =     0.000                                      max =         3
------------------------------------------------------------------------------
|              Corrected
oss |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
oss |
L1. |  -.2034418   .1627875    -1.25   0.213    -.5241726    .1172889
|
realyldglp |   1.554736   1.142141     1.36   0.175    -.6955579    3.805029
OE2assets |   .6808866    3.31698     0.21   0.838    -5.854367     7.21614
TE2assets |  -3.917173   2.493656    -1.57   0.118    -8.830279    .9959336
glp2assets |   2.215048    1.15665     1.92   0.057    -.0638324    4.493929
costperloan |  -.0002647   .0025206    -0.11   0.916     -.005231    .0047015
iyear |   .0948036   .0881907     1.07   0.283    -.0789535    .2685606
lindi |  -.0716274   .2376581    -0.30   0.763    -.5398714    .3966167
lsolid |   .0086089   .0974341     0.09   0.930    -.1833599    .2005777
lvillage |  -.0022004   .0250286    -0.09   0.930    -.0515128    .0471119
_cons |   .6784071   4.190431     0.16   0.872    -7.577756     8.93457
------------------------------------------------------------------------------
Instruments for orthogonal deviations equation
Standard
FOD.(iyear L2.pm)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/5).(oss lindi lsolid lvillage)
Instruments for levels equation
Standard
iyear L2.pm
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
D.(oss lindi lsolid lvillage)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.00  Pr > z =  0.315
Arellano-Bond test for AR(2) in first differences: z =   0.10  Pr > z =  0.917
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(31)   =  87.67  Prob > chi2 =  0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(31)   =  19.86  Prob > chi2 =  0.939
(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group:     chi2(19)   =  12.54  Prob > chi2 =  0.861
Difference (null H = exogenous): chi2(12)   =   7.32  Prob > chi2 =  0.836
iv(iyear L2.pm)
Hansen test excluding group:     chi2(29)   =  16.57  Prob > chi2 =  0.968
Difference (null H = exogenous): chi2(2)    =   3.29  Prob > chi2 =  0.193

On Wed, Apr 24, 2013 at 5:52 PM, Evan Markel <markelev@gmail.com> wrote:
> Dear listservers,
>
> I am estimating an xtabond2 model using a panel where N=434
> microfinance institutions (MFI's) and where T=5. After executing
> xtabond2 system GMM this reduces to N=233 and T=3.
>
> My primary concern right now is the implication of failing to reject
> the null hypothesis of no autocorrelation in the Arellano-Bond test
> for AR(1). I have read Roodman 2006 and understand that negative first
> order serial correlation is to be expected in AR(1) because of the
> mathematical relation between the first difference and the first lag
> of difference.
>
> Specifically (eit)-(eit-1) is related to (eit-1)-(eit-2). But what
> does this mean when I fail to reject the null. Does it give evidence
> of a random walk? I have found several examples and discussions
> stating why first order serial correlation is expected in AR(1), but
> have not found a discussion on the implications of the contrary.
>
>  Below is an extract from my xtabond2 output.
>
> Instruments for orthogonal deviations equation
>   Standard
>     FOD.(iyear L2.pm)
>   GMM-type (missing=0, separate instruments for each period unless collapsed)
>     L(1/5).(oss lindi lsolid lvillage)
> Instruments for levels equation
>   Standard
>     iyear L2.pm
>     _cons
>   GMM-type (missing=0, separate instruments for each period unless collapsed)
>     D.(oss lindi lsolid lvillage)
> ------------------------------------------------------------------------------
> Arellano-Bond test for AR(1) in first differences: z =  -1.00  Pr > z =  0.315
> Arellano-Bond test for AR(2) in first differences: z =   0.10  Pr > z =  0.917
> ------------------------------------------------------------------------------
> Sargan test of overid. restrictions: chi2(31)   =  87.67  Prob > chi2 =  0.000
>   (Not robust, but not weakened by many instruments.)
> Hansen test of overid. restrictions: chi2(31)   =  19.86  Prob > chi2 =  0.939
>   (Robust, but weakened by many instruments.)
>
> Difference-in-Hansen tests of exogeneity of instrument subsets:
>   GMM instruments for levels
>     Hansen test excluding group:     chi2(19)   =  12.54  Prob > chi2 =  0.861
>     Difference (null H = exogenous): chi2(12)   =   7.32  Prob > chi2 =  0.836
>   iv(iyear L2.pm)
>     Hansen test excluding group:     chi2(29)   =  16.57  Prob > chi2 =  0.968
>     Difference (null H = exogenous): chi2(2)    =   3.29  Prob > chi2 =  0.193
>
> My variable of interest is Operational Self-sufficiency (OSS).
> Following Roodman 2009 I regress OSS on the lagged level of OSS which
> yields a low R^2 of .117 possibly signally lag 1.oss is a weak
> instrument. Maybe this is a source of my failure to reject AR(1)?
>
> regress oss l.oss
>
>       Source |       SS                df            MS
>                   Number of obs =     784
> -------------+------------------------------
>                            F(  1,   782) =  103.65
>        Model |    19.0811599        1      19.0811599
>            Prob > F      =  0.0000
>     Residual |   143.966445       782   .184100313
>         R-squared     =  0.1170
> -------------+------------------------------
>        Total |      163.047605       783     .208234489
>            Root MSE      =  .42907
>
> ------------------------------------------------------------------------------
>          oss |      Coef.           Std. Err.      t    P>|t|     [95%
> Conf. Interval]
> -------------+----------------------------------------------------------------
>          oss |
>          L1. |     .3328396   .0326934    10.18   0.000     .2686624    .3970168
>              |
>        _cons |   .7341655   .0399425    18.38   0.000     .6557582    .8125727
>
>
>
> Evan M.
> *
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```