Dealing with AR2 significant in xtabond2 and Hansen test greater than 0.25

[Marco Astori]

Dear statalists, I'm trying to obtain some resuts with xtabond2 but, when I don't use the collapse suboption I get AR2 significant test. Is it correct to use further lags in order to solve this problem from a specification point of view?

This is one of my results

 xtabond2 LSECI L.LSECI  LRR1   LSFI1 LPA LHC    i.year , gmm(L.LSECI, lag(2 3) ) gmm(LRR1, lag(1 2)) iv( LSFI1 LPA LHC i.year) 
>    twostep robust
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
2002b.year dropped due to collinearity
2017.year dropped due to collinearity
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: Code                            Number of obs      =      1369
Time variable : year                            Number of groups   =       106
Number of instruments = 106                     Obs per group: min =         1
Wald chi2(20) =   7134.64                                      avg =     12.92
Prob > chi2   =     0.000                                      max =        16
------------------------------------------------------------------------------
             |              Corrected
       LSECI | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       LSECI |
         L1. |   .6976077   .1281166     5.45   0.000     .4465037    .9487117
             |
        LRR1 |   .0064297   .0066735     0.96   0.335    -.0066501    .0195096
       LSFI1 |  -.0960979   .0449557    -2.14   0.033    -.1842093   -.0079864
         LPA |   .0203076   .0153201     1.33   0.185    -.0097193    .0503345
         LHC |   .1835515   .0900324     2.04   0.041     .0070912    .3600118
             |
        year |
       2003  |   .0168603   .0426234     0.40   0.692      -.06668    .1004006
       2004  |  -.0424606   .0410275    -1.03   0.301     -.122873    .0379518
       2005  |   .0705754   .0527377     1.34   0.181    -.0327886    .1739395
       2006  |   .0161151   .0387876     0.42   0.678    -.0599073    .0921375
       2007  |   .0092724   .0382754     0.24   0.809     -.065746    .0842909
       2008  |  -.0378717   .0531334    -0.71   0.476    -.1420114    .0662679
       2009  |  -.0177835   .0446723    -0.40   0.691    -.1053397    .0697726
       2010  |   .0131428   .0431673     0.30   0.761    -.0714636    .0977492
       2011  |   -.021425   .0428425    -0.50   0.617    -.1053948    .0625449
       2012  |  -.0091968    .040068    -0.23   0.818    -.0877285     .069335
       2013  |   .0069627   .0424752     0.16   0.870    -.0762872    .0902126
       2014  |  -.0251427   .0358895    -0.70   0.484    -.0954848    .0451993
       2015  |   .0025728   .0341697     0.08   0.940    -.0643986    .0695443
       2016  |  -.0532734   .0483048    -1.10   0.270    -.1479491    .0414023
       2018  |  -.0106388   .0373712    -0.28   0.776    -.0838851    .0626075
             |
       _cons |  -.1478692   .1113342    -1.33   0.184    -.3660802    .0703417
------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(LSFI1 LPA LHC 2002b.year 2003.year 2004.year 2005.year 2006.year
    2007.year 2008.year 2009.year 2010.year 2011.year 2012.year 2013.year
    2014.year 2015.year 2016.year 2017.year 2018.year)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(1/2).LRR1
    L(2/3).L.LSECI
Instruments for levels equation
  Standard
    LSFI1 LPA LHC 2002b.year 2003.year 2004.year 2005.year 2006.year 2007.year
    2008.year 2009.year 2010.year 2011.year 2012.year 2013.year 2014.year
    2015.year 2016.year 2017.year 2018.year
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    D.LRR1
    DL.L.LSECI
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -4.09  Pr > z =  0.000
Arellano-Bond test for AR(2) in first differences: z =   2.54  Pr > z =  0.011
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(85)   =  93.31  Prob > chi2 =  0.252
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(85)   =  87.53  Prob > chi2 =  0.404
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(55)   =  57.75  Prob > chi2 =  0.374
    Difference (null H = exogenous): chi2(30)   =  29.79  Prob > chi2 =  0.477
  gmm(L.LSECI, lag(2 3))
    Hansen test excluding group:     chi2(44)   =  38.60  Prob > chi2 =  0.702
    Difference (null H = exogenous): chi2(41)   =  48.93  Prob > chi2 =  0.185
  gmm(LRR1, lag(1 2))
    Hansen test excluding group:     chi2(39)   =  35.11  Prob > chi2 =  0.648
    Difference (null H = exogenous): chi2(46)   =  52.42  Prob > chi2 =  0.239
  iv(LSFI1 LPA LHC 2002b.year 2003.year 2004.year 2005.year 2006.year 2007.year 2008.year 2009.year 2010.year 2011.year 2012.year
>  2013.year 2014.year 2015.year 2016.year 2017.year 2018.year)
    Hansen test excluding group:     chi2(67)   =  69.66  Prob > chi2 =  0.388
    Difference (null H = exogenous): chi2(18)   =  17.88  Prob > chi2 =  0.464

with L.LSECI considered as endogenous I thought that it would be necessary the third lag as first. The other problem is the relatively high value fo the Hansen test: could it be too much high?

How fast does the p-value of the test increase, when there are many instruments?

[David Roodman]

The Hansen p doesn't look high to me. A sign of degenerate behavior is this p value going to 1. Nevertheless, 106 instruments for 1369 observations seems like a lot to me, so I'd definitely try to reduce the instrument count.
--David

[Marco Astori]

The Hansen p doesn't look high to me. A sign of degenerate behavior is this p value going to 1. Nevertheless, 106 instruments for 1369 observations seems like a lot to me, so I'd definitely try to reduce the instrument count.
--David

Thank you very much David Roodman I'll try to reduce instruments. The AR2 significant is treated in the right way? I used third lag for endogenous variable and first lag for predetermined

[Marco Astori]

Anyone can answer to the question? I think it is simple: in my results I have second order autocorrelation so \[ v_{it}=\alpha v_{i,t-1}+\beta v_{i,t-2}\]. In the Roodman article it is specified the endogeneity of the second lag for the endogenous variables with first order autocorrelation, so in this case I think I should start with the fourth lag: \[v_{i,t-1}=\delta v_{i,t-2}+\gamma v_{i,t-3}\] and for predetermined variables it depends on what is the degree of certainty related to the correlation between the past error term and the predetermined variable: if I'm sure, then with 2nd order autocorrelation I've to start with the second lag which is correlated with the third lag of the error but this is not correlated with the first lag of first differences; if I'm not sure I can start with the first lag. Is it correct? I looked for this on the forum and on the Internet but I couldn't find anything.

[Sebastian Kripfganz]

A significant AR(2) test indicates that there might be second-order serial correlation in the first-differenced errors. This corresponds to first-order serial correlation in the level errors.

Assuming that there is no higher-order serial correlation, you could then use the 3rd lag of an endogenous variable as an instrument in the first-differenced model, and the 2nd lag of a predetermined variable. With a system GMM estimator, you also need to shift the lag orders for the instruments in the level model: 2nd lag for an endogenous variable, 1st lag for a predetermined variable.

While this can generally lead to valid instruments, it may not necessarily be the best approach, because deeper lags tend to be weaker instruments. An alternative could be to add further lags of the dependent variable and/or independent variables directly as regressors to the model. This would aim at obtaining a dynamically complete model, in which the errors are serially uncorrelated.

[Marco Astori]

Thank you very much Sebastian Kripfganz

you also need to shift the lag orders for the instruments in the level model: 2nd lag for an endogenous variable, 1st lag for a predetermined variable.

Does Stata do it automatically?