Andrews and Lu's (2001) test in dynamic panel data model (xtabond2)

[Cooper Felix]

Andrews, Donald WK, and Biao Lu. "Consistent model and moment selection procedures for GMM estimation with application to dynamic panel data models." Journal of Econometrics 101.1 (2001): 123-164.

I'm interested in testing how many lags of the dependent variable are needed in my dynamic panel data model, the paper by Andrews and Lu (2001) seems to offer some statistics that could get the job done. Is there any existing routine related to the above paper? Currently my go-to routine is xtabond2 written by Roodman (2009), but from his Stata journal paper, I don't see he mentioned any procedures to determine the number of lags.

[Cooper Felix]

Any suggestions?

[Sebastian Kripfganz]

To my knowledge, this is not implemented in any Stata package to date. (It is actually a good idea and I will put it on my todo list for my xtdpdgmm command.) However, it is relatively easy to obtain these statistics after having estimated a model with xtabond2, e.g. the MMSC-BIC criterion(page 136 of the referenced article):

. webuse abdata

. xtabond2 n L.n w k, twostep robust gmm(n, lag(2 3)) iv(w k) noleveleq nodiff
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.

Dynamic panel-data estimation, two-step difference GMM
------------------------------------------------------------------------------
Group variable: id                              Number of obs      =       751
Time variable : year                            Number of groups   =       140
Number of instruments = 15                      Obs per group: min =         5
Wald chi2(3)  =    257.86                                      avg =      5.36
Prob > chi2   =     0.000                                      max =         7
------------------------------------------------------------------------------
             |              Corrected
           n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           n |
         L1. |   .4325934   .1361518     3.18   0.001     .1657407     .699446
             |
           w |  -.5628457   .1083476    -5.19   0.000     -.775203   -.3504884
           k |   .3591999   .0570292     6.30   0.000     .2474246    .4709752
------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(w k)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/3).n
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.90  Pr > z =  0.058
Arellano-Bond test for AR(2) in first differences: z =  -0.53  Pr > z =  0.595
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(12)   = 114.32  Prob > chi2 =  0.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(12)   =  40.41  Prob > chi2 =  0.000
  (Robust, but weakened by many instruments.)


. display "MMSC-BIC = " e(hansen) - e(hansen_df) * ln(e(N_g))
MMSC-BIC = -18.893466

[Cooper Felix]

To my knowledge, this is not implemented in any Stata package to date. (It is actually a good idea and I will put it on my todo list for my xtdpdgmm command.) However, it is relatively easy to obtain these statistics after having estimated a model with xtabond2, e.g. the MMSC-BIC criterion(page 136 of the referenced article):

. webuse abdata

. xtabond2 n L.n w k, twostep robust gmm(n, lag(2 3)) iv(w k) noleveleq nodiff
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.

Dynamic panel-data estimation, two-step difference GMM
------------------------------------------------------------------------------
Group variable: id Number of obs = 751
Time variable : year Number of groups = 140
Number of instruments = 15 Obs per group: min = 5
Wald chi2(3) = 257.86 avg = 5.36
Prob > chi2 = 0.000 max = 7
------------------------------------------------------------------------------
| Corrected
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
n |
L1. | .4325934 .1361518 3.18 0.001 .1657407 .699446
|
w | -.5628457 .1083476 -5.19 0.000 -.775203 -.3504884
k | .3591999 .0570292 6.30 0.000 .2474246 .4709752
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(w k)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(2/3).n
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -1.90 Pr > z = 0.058
Arellano-Bond test for AR(2) in first differences: z = -0.53 Pr > z = 0.595
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(12) = 114.32 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(12) = 40.41 Prob > chi2 = 0.000
(Robust, but weakened by many instruments.)


. display "MMSC-BIC = " e(hansen) - e(hansen_df) * ln(e(N_g))
MMSC-BIC = -18.893466

Thanks for your response, I appreciate that.

[Cooper Felix]

]

By the way, I benefited a lot from reading your other posts, thanks for your contribution to the Stata community!

[Sebastian Kripfganz]

Cooper Felix
Thanks again for this idea. I have now implemented the Andrews-Lu model and moment selection criteria as a postestimation command for my xtdpdgmm package:
XTDPDGMM: new Stata command for efficient GMM estimation of linear (dynamic) panel models with nonlinear moment conditions