[George Ford]

Yes. The first-differencing deals with firm FE (0's the means).

Year FE will 0 mean the variables for each year.

I think the "td" option may do the time fixed effects.

[Jesse Nooijen]

Interesting, I think you are correct. After specifying td in my model, it leads to the following results;

. pvar FP stdCSR stdCSI, lags(2) exog(FS FL ROA AI RDI) td instlags(1/3) overid

Panel vector autoregresssion



GMM Estimation

Final GMM Criterion Q(b) =    .00347
Initial weight matrix: Identity
GMM weight matrix:     Robust
                                                   No. of obs      =      3898
                                                   No. of panels   =       997
                                                   Ave. no. of T   =     3.910


------------------------------------------------------------------------------
             | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
FP           |
          FP |
         L1. |   .2596992   .1701477     1.53   0.127    -.0737841    .5931826
         L2. |  -.0177389   .0474393    -0.37   0.708    -.1107183    .0752404
             |
      stdCSR |
         L1. |    -.09184   .0539606    -1.70   0.089    -.1976008    .0139208
         L2. |  -.0621837   .0301958    -2.06   0.039    -.1213665    -.003001
             |
      stdCSI |
         L1. |     .06457   .0473411     1.36   0.173    -.0282168    .1573567
         L2. |   .0183179    .023301     0.79   0.432    -.0273513    .0639871
             |
          FS |   -1.20848   .8741295    -1.38   0.167    -2.921742    .5047827
          FL |  -.1987473   1.006738    -0.20   0.844    -2.171918    1.774423
         ROA |  -1.582318   .6832335    -2.32   0.021    -2.921431   -.2432054
          AI |   1.009488   .5874366     1.72   0.086    -.1418668    2.160842
         RDI |  -.0186685   .0142599    -1.31   0.190    -.0466173    .0092804
-------------+----------------------------------------------------------------
stdCSR       |
          FP |
         L1. |   .0031596   .0581674     0.05   0.957    -.1108464    .1171656
         L2. |  -.0123654   .0172323    -0.72   0.473    -.0461402    .0214093
             |
      stdCSR |
         L1. |   .5791404   .0605278     9.57   0.000      .460508    .6977727
         L2. |   .1529949   .0491522     3.11   0.002     .0566584    .2493315
             |
      stdCSI |
         L1. |  -.1107846    .057075    -1.94   0.052    -.2226496    .0010804
         L2. |   .0561206   .0326719     1.72   0.086    -.0079151    .1201563
             |
          FS |  -.2674409   .3376316    -0.79   0.428    -.9291867    .3943048
          FL |  -.2290882   .7379384    -0.31   0.756    -1.675421    1.217244
         ROA |   .2910557   .2420082     1.20   0.229    -.1832717    .7653831
          AI |  -.6433749   .2910268    -2.21   0.027    -1.213777   -.0729728
         RDI |   .0131324   .0066843     1.96   0.049     .0000313    .0262334
-------------+----------------------------------------------------------------
stdCSI       |
          FP |
         L1. |   .0846545   .0757073     1.12   0.263    -.0637292    .2330382
         L2. |   .0006962   .0228989     0.03   0.976    -.0441847    .0455772
             |
      stdCSR |
         L1. |   .0045206   .0491892     0.09   0.927    -.0918884    .1009296
         L2. |   .0050363   .0407154     0.12   0.902    -.0747644    .0848371
             |
      stdCSI |
         L1. |   .3250604   .1151785     2.82   0.005     .0993146    .5508062
         L2. |   .1818229   .0672496     2.70   0.007     .0500161    .3136297
             |
          FS |   .0829144    .398459     0.21   0.835    -.6980508    .8638796
          FL |   .7134196   .8530795     0.84   0.403    -.9585856    2.385425
         ROA |   .2815334       .254     1.11   0.268    -.2162974    .7793643
          AI |  -.2938101   .3433918    -0.86   0.392    -.9668457    .3792255
         RDI |   .0071632   .0078401     0.91   0.361     -.008203    .0225294
------------------------------------------------------------------------------
Instruments : l(1/3).(FP stdCSR stdCSI) FS FL ROA AI RDI



Test of overidentifying restriction: 
  Hansen's J chi2(9) = 13.519271 (p = 0.140)

. estimates store PVARmodel 

. pvarstable

   Eigenvalue stability condition

  +----------------------------------+
  |      Eigenvalue      |           |
  |   Real     Imaginary |  Modulus  |
  |----------------------+-----------|
  |  .7819005          0 |  .7819005 |
  |  .6301147          0 |  .6301147 |
  | -.3012884          0 |  .3012884 |
  | -.1923009          0 |  .1923009 |
  |   .122737  -.0844876 |  .1490052 |
  |   .122737   .0844876 |  .1490052 |
  +----------------------------------+

   All the eigenvalues lie inside the unit circle.
   pVAR satisfies stability condition.

. pvargranger

  panel VAR-Granger causality Wald test
    Ho: Excluded variable does not Granger-cause Equation variable
    Ha: Excluded variable Granger-causes Equation variable

  +------------------------------------------------------+
  |  Equation \ Excluded |    chi2     df   Prob > chi2  |
  |----------------------+-------------------------------|
  |FP                    |                               |
  |               stdCSR |      5.216    2        0.074  |
  |               stdCSI |      2.029    2        0.362  |
  |                  ALL |      5.448    4        0.244  |
  |----------------------+-------------------------------|
  |stdCSR                |                               |
  |                   FP |      0.961    2        0.618  |
  |               stdCSI |      9.568    2        0.008  |
  |                  ALL |      9.924    4        0.042  |
  |----------------------+-------------------------------|
  |stdCSI                |                               |
  |                   FP |      2.222    2        0.329  |
  |               stdCSR |      0.018    2        0.991  |
  |                  ALL |      2.233    4        0.693  |
  +------------------------------------------------------+

While not all predicted relations appear significant (which is fine), it has a satisfactory J p-value and is stable. I believe this is the model I need to report on.

I want to thank you so much for your help these past weeks, I highly appreciate it!

[George Ford]

You've got a little love between CSR and FP. Looks good.

[Jesse Nooijen]

You've got a little love between CSR and FP. Looks good.

I continued to use the model as is above, so thanks once again. I do have one last question, how do I figure out the total number of observations I lose due to lagging and instrumenting GMM? My dataset observation count using the count command is 34,966. I know one of my variables (Advertising Intensity) only has 13,143 observations but my final PVAR model has 3,989 observations. I want to include this in my paper for transparency. Does that mean I lose 31,068 observations due to lagging and instrumenting, or do I already lose observations due to this variable? I'm unsure how to approach this, do you have any insights?