''Gravity model of trade - Correctness of specification tests and syntax -Two step system GMM''

[PANOS TSITSOGLOU]

Dear experts,

I use gravity model of trade in a panel of 67 and 73 countries respectively for time period 2003-2022.

I would appreciate if you check my models below whether the syntax is correct and specification tests are satisfying.

Difference in Hansen test of exogeneity is missing. Is that ok;

I think AR(1), AR(2), Hansen and Sargan tests are ok, but I would appreciate a second opinion.

Thank you in advance!

MODEL1

 xtabond2 lrcaresc l.lrcaresc LGDP LDIS presence_consulate land lpolresc EU ,
gmm (l.lrcaresc, lag(1 5) eq (level) collapse)
iv (LDIS presence_consulate lpolresc land LGDP EU) twostep robust small

 Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: unit_id                         Number of obs      =      1272
Time variable : time                            Number of groups   =        67
Number of instruments = 12                      Obs per group: min =        18
F(7, 66)      =    222.33                                      avg =     18.99
Prob > F      =     0.000                                      max =        19
------------------------------------------------------------------------------------
                   |              Corrected
          lrcaresc | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------+----------------------------------------------------------------
          lrcaresc |
               L1. |   .5934694   .0886236     6.70   0.000     .4165267     .770412
                   |
              LGDP |  -.0920508   .0261888    -3.51   0.001    -.1443385   -.0397632
              LDIS |  -.2340949   .0657415    -3.56   0.001     -.365352   -.1028378
presence_consulate |   .1270339   .0544398     2.33   0.023     .0183414    .2357264
              land |   -.247983   .0881701    -2.81   0.006    -.4240202   -.0719457
          lpolresc |   .0348376     .03577     0.97   0.334    -.0365794    .1062547
                EU |  -.0548825   .0749537    -0.73   0.467    -.2045325    .0947675
             _cons |   4.468997   1.156137     3.87   0.000     2.160694    6.777299
------------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(LDIS presence_consulate lpolresc land LGDP EU)
Instruments for levels equation
  Standard
    LDIS presence_consulate lpolresc land LGDP EU
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL(1/5).L.lrcaresc collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -3.11  Pr > z =  0.002
Arellano-Bond test for AR(2) in first differences: z =   0.30  Pr > z =  0.768
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(4)    =   3.07  Prob > chi2 =  0.547
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(4)    =   1.58  Prob > chi2 =  0.812
  (Robust, but weakened by many instruments.)

MODEL 2

  xtabond2 ln_exports_Gr l.ln_exports_Gr ln_impop ln_dis EU landlocked Total_Repres lpol_rescale,
gmm (l.ln_exports_Gr, lag(1 3) eq (level) collapse)
iv( ln_impop ln_dis EU Total_Repres lpol_rescale landlocked ) twostep robust small

 Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: unit_id                         Number of obs      =      1387
Time variable : YEAR                            Number of groups   =        73
Number of instruments = 10                      Obs per group: min =        19
F(7, 72)      =  42147.03                                      avg =     19.00
Prob > F      =     0.000                                      max =        19
-------------------------------------------------------------------------------
              |              Corrected
ln_exports_Gr | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------
ln_exports_Gr |
          L1. |   .7145964   .0723301     9.88   0.000     .5704089    .8587839
              |
     ln_impop |   .0634149   .0420344     1.51   0.136    -.0203793     .147209
       ln_dis |  -.2702084   .0894006    -3.02   0.003    -.4484253   -.0919915
           EU |    .155858    .087484     1.78   0.079    -.0185382    .3302542
   landlocked |  -.3406717   .1187126    -2.87   0.005    -.5773209   -.1040225
 Total_Repres |   .0795261   .0249087     3.19   0.002     .0298716    .1291807
 lpol_rescale |   .2779777   .1110468     2.50   0.015       .05661    .4993454
        _cons |   3.231109   .9613727     3.36   0.001     1.314647     5.14757
-------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(ln_impop ln_dis EU Total_Repres lpol_rescale landlocked)
Instruments for levels equation
  Standard
    ln_impop ln_dis EU Total_Repres lpol_rescale landlocked
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL(1/3).L.ln_exports_Gr collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -4.03  Pr > z =  0.000
Arellano-Bond test for AR(2) in first differences: z =   0.65  Pr > z =  0.518
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(2)    =   3.71  Prob > chi2 =  0.156
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(2)    =   1.96  Prob > chi2 =  0.376
  (Robust, but weakened by many instruments.)

[Joao Santos Silva]

Are you sure you want to estimate a dynamic linear model?

[PANOS TSITSOGLOU]

Yes. P-value of the first lag of the dependent variable is significant and the respective coefficient is between 0-1, while there is endogeneity.
Furthermore, I have 67 and 73 countries respectively (N>25) and T=20 (T<25), that's why I apply GMM. Are my specification tests valid;

[Joao Santos Silva]

The fact that the first lag is significant does not imply that you should estimate a dynamic model. All depends on what you want to use the model for. A danger of using a dynamic model is that you may conclude that two countries trade a lot this year because they traded a lot last year, but you will not know why they traded that much last year.

[PANOS TSITSOGLOU]

Thank you for your useful remarks, but I would appreciate if you answer my question about the validity of the specification tests or the correctness of the syntax.

[Joao Santos Silva]

I am afraid I cannot advise on that. I would be able to advise if you were estimating a standard gravity equation as described here.

[PANOS TSITSOGLOU]

 Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: unit_id                         Number of obs      =      1272
Time variable : time                            Number of groups   =        67
Number of instruments = 12                      Obs per group: min =        18
F(7, 66)      =    493.13                                      avg =     18.99
Prob > F      =     0.000                                      max =        19
------------------------------------------------------------------------------------
                   |              Corrected
          lrcaresc | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------+----------------------------------------------------------------
          lrcaresc |
               L1. |     .62465   .0818597     7.63   0.000     .4612117    .7880882
                   |
              LGDP |  -.0868544   .0225589    -3.85   0.000    -.1318948    -.041814
              LDIS |  -.1552797   .0395584    -3.93   0.000    -.2342607   -.0762987
presence_consulate |   .0982549   .0364754     2.69   0.009     .0254294    .1710803
              land |  -.2152751   .0670996    -3.21   0.002    -.3492437   -.0813066
       COMCURRENCY |   .0466412   .0603081     0.77   0.442    -.0737679    .1670502
         COMBORDER |   .3903893    .136391     2.86   0.006      .118076    .6627026
             _cons |   3.773131   .9206656     4.10   0.000     1.934963    5.611299
------------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(LDIS presence_consulate land LGDP COMCURRENCY COMBORDER)
Instruments for levels equation
  Standard
    LDIS presence_consulate land LGDP COMCURRENCY COMBORDER
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL(1/5).L.lrcaresc collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -3.20  Pr > z =  0.001
Arellano-Bond test for AR(2) in first differences: z =   0.32  Pr > z =  0.748
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(4)    =   3.32  Prob > chi2 =  0.506
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(4)    =   1.22  Prob > chi2 =  0.875
  (Robust, but weakened by many instruments.)

.