Sargan-Hansen test of the overidentifying restrictions problem

[Amelia Azjahra]

Dear Statalist,

I am currently facing problems with the overidentification test results in my GMM estimation using the `xtdpdgmm’ syntax. My research focuses on estimating the effect of servicification on firm productivity, proxied by TFP (Levinsohn-Petrin) and labor productivity, using annual firm-level survey data. I suspect that the TFP variable may be endogenous, so I have applied various GMM methods within `xtdpdgmm’, including Arellano-Bond, Ahn-Schmidt, blundell-Bond, and Hayakawa. However, all these methods yield similar outcomes, where the Sargan-Hansen test rejects the null hypothesis.

Could anyone provide guidance or insights on how to address this issue? I attach the Blundell-Bond estimation results for reference.

 // Blundell-Bond two-step, iterated, and continuously-updating GMM estimators
.         
.         xtdpdgmm L(0/1).ltfp2 s_exp gvc2 lska size own kl, ///
>         gmm(L.ltfp2 s_exp gvc2 lska size own kl, l(1 4) m(d)) /// 
>         iv(L.ltfp2 s_exp gvc2 lska size own kl, d) c two vce(r)

Generalized method of moments estimation

Fitting full model:
Step 1         f(b) =   .0737233
Step 2         f(b) =  .07064255

Group variable: psid                         Number of obs         =    109580
Time variable: year                          Number of groups      =     22323

Moment conditions:     linear =      36      Obs per group:    min =         1
                    nonlinear =       0                        avg =  4.908838
                        total =      36                        max =        10

                              (Std. err. adjusted for 22,323 clusters in psid)
------------------------------------------------------------------------------
             |              WC-Robust
       ltfp2 | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       ltfp2 |
         L1. |   .2096717   .0084163    24.91   0.000     .1931761    .2261673
             |
       s_exp |   .0151812   .0012905    11.76   0.000     .0126519    .0177105
        gvc2 |  -.1196046   .0355005    -3.37   0.001    -.1891843   -.0500248
        lska |   .1386593   .0059761    23.20   0.000     .1269462    .1503723
        size |   .0591107   .0463177     1.28   0.202    -.0316703    .1498916
         own |    .394086   .0691181     5.70   0.000     .2586171    .5295548
          kl |  -.6497143    .009554   -68.00   0.000    -.6684397   -.6309889
       _cons |   10.11826   .1385742    73.02   0.000     9.846661    10.38986
------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(diff):
   L1.L.ltfp2 L2.L.ltfp2 L3.L.ltfp2 L4.L.ltfp2 L1.s_exp L2.s_exp L3.s_exp
   L4.s_exp L1.gvc2 L2.gvc2 L3.gvc2 L4.gvc2 L1.lska L2.lska L3.lska L4.lska
   L1.size L2.size L3.size L4.size L1.own L2.own L3.own L4.own L1.kl L2.kl
   L3.kl L4.kl
 2, model(level):
   D.L.ltfp2 D.s_exp D.gvc2 D.lska D.size D.own D.kl
 3, model(level):
   _cons
.         
.         estat overid

Sargan-Hansen test of the overidentifying restrictions
H0: overidentifying restrictions are valid

2-step moment functions, 2-step weighting matrix       chi2(28)    = 1576.9536
                                                       Prob > chi2 =    0.0000

2-step moment functions, 3-step weighting matrix       chi2(28)    = 1609.4307
                                                       Prob > chi2 =    0.0000
.         
.         estat serial

Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1      z =  -47.4769   Prob > |z|  =    0.0000
H0: no autocorrelation of order 2      z =   -0.5511   Prob > |z|  =    0.5816

Regards,
Amelia

[Sebastian Kripfganz]

With your very large sample size, N=22323, the overidentification test can pick up already relatively minor model misspecifications. It can therefore sometimes be difficult to find a specification that is not rejected.

Currently, you have classified all variables as predetermined (rather than endogenous). For endogenous variables, you need to start with the second lag for the instruments; i.e., lag(2 4) instead of lag(1 4). Please also see the section on Model Selection in the following presentation:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.