[Romano Piras]

Hi Tom
yes I'm using Stata 12 (actually 12.1). Is it a problem? Can't the estimate with ppmlhdfe be done with Stata 12? If it cannot be done, is there any other way to circumvent the problem? I mean:
1) is there any other way to use the ppmlhdfe command with Stata 12? or
2) is there any other way to use the ppml command to do the same estimate that can be done with the ppmlhdfe command?

Furthermore I add another question. I know (Santos Silva has written this in many posts in this list) that the ppml command requires that the dependent variable (be it trade, migration, FDI and so on) should NOT be logged. But what about the ppmlhdfe command? Is the raccomandation of Santos Silva also valid for the ppmlhdfe command?

Regards
Romano

[Long Nguyenn]

Dear Tom Zylkin,

I am following your instructions on how to use ppml and ppmlhdfe command on this thread and many other threads. I am currently working with my sample data which consists of three countries with multilateral trade (from 1998 to 2018) and I only include exporter GDP, importer GDP, and distance as my independent variables and I want to figure out how these variables affect export volume.

After reading this thread, to my understanding, the ppml command

ppml lnvol lndist lnGDPimp lnGDPexp exporter_* importer_* year_*

and ppmlhdfe command

ppmlhdfe lnvol lndist lnGDPimp lnGDPexp, a(importer exporter year) vce(robust)

should give me the same results. However this is not the case.

. ppml lnvol lndist lnGDPimp lnGDPexp exporter_* importer_* year_*

note: checking the existence of the estimates

Number of regressors excluded to ensure that the estimates exist: 4
Excluded regressors:  exporter_1 exporter_2 importer_2 year_21
Number of observations excluded: 0

note: starting ppml estimation
note: lnvol has noninteger values

Iteration 1:   deviance =  4.493896
Iteration 2:   deviance =  4.420987
Iteration 3:   deviance =  4.420984
Iteration 4:   deviance =  4.420984

Number of parameters: 27
Number of observations: 126
Pseudo log-likelihood: -260.46453
R-squared: .92118197
Option strict is: off
------------------------------------------------------------------------------
             |               Robust
       lnvol |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      lndist |  -.1561562   .0309894    -5.04   0.000    -.2168942   -.0954182
    lnGDPimp |    .109938    .041569     2.64   0.008     .0284643    .1914116
    lnGDPexp |   .0555364   .0383281     1.45   0.147    -.0195854    .1306582
  exporter_3 |  -.1191625   .1528654    -0.78   0.436    -.4187731    .1804482
  importer_1 |  -.0974729   .0498772    -1.95   0.051    -.1952305    .0002847
  importer_3 |   .0270576    .201956     0.13   0.893    -.3687689    .4228841
      year_1 |  -.2258452   .0935905    -2.41   0.016    -.4092792   -.0424112
      year_2 |  -.2105067   .0929665    -2.26   0.024    -.3927178   -.0282957
      year_3 |   -.169045   .0887337    -1.91   0.057    -.3429598    .0048697
      year_4 |  -.1605192   .0825138    -1.95   0.052    -.3222432    .0012048
      year_5 |  -.1382407   .0744673    -1.86   0.063     -.284194    .0077125
      year_6 |   -.098291   .0650511    -1.51   0.131    -.2257887    .0292068
      year_7 |  -.0801831    .061846    -1.30   0.195    -.2013991    .0410329
      year_8 |  -.0822553   .0601515    -1.37   0.171    -.2001501    .0356395
      year_9 |  -.0772801   .0564199    -1.37   0.171     -.187861    .0333008
     year_10 |  -.0575561   .0509048    -1.13   0.258    -.1573278    .0422155
     year_11 |  -.0422892   .0481685    -0.88   0.380    -.1366976    .0521193
     year_12 |  -.0486424    .046542    -1.05   0.296    -.1398631    .0425783
     year_13 |  -.0343536   .0433686    -0.79   0.428    -.1193546    .0506473
     year_14 |  -.0248547    .041068    -0.61   0.545    -.1053465    .0556371
     year_15 |  -.0188818    .039707    -0.48   0.634    -.0967062    .0589426
     year_16 |  -.0153306   .0391906    -0.39   0.696    -.0921427    .0614815
     year_17 |  -.0105907   .0387608    -0.27   0.785    -.0865605    .0653791
     year_18 |  -.0085547   .0389603    -0.22   0.826    -.0849155    .0678061
     year_19 |  -.0075817   .0398676    -0.19   0.849    -.0857207    .0705573
     year_20 |  -.0030358   .0400476    -0.08   0.940    -.0815278    .0754561
       _cons |   2.462663   .4698884     5.24   0.000     1.541698    3.383627
------------------------------------------------------------------------------

. ppmlhdfe lnvol lndist lnGDPimp lnGDPexp, a(importer exporter year) vce(robust)
note: 1 variable omitted because of collinearity: lndist
Iteration 1:   deviance = 4.4939e+00  eps = .         iters = 4    tol = 1.0e-04
>   min(eta) =   1.10  P   
Iteration 2:   deviance = 4.4210e+00  eps = 1.65e-02  iters = 4    tol = 1.0e-04
>   min(eta) =   1.09      
Iteration 3:   deviance = 4.4210e+00  eps = 6.85e-07  iters = 3    tol = 1.0e-04
>   min(eta) =   1.09      
Iteration 4:   deviance = 4.4210e+00  eps = 3.93e-15  iters = 2    tol = 1.0e-05
>   min(eta) =   1.09      
Iteration 5:   deviance = 4.4210e+00  eps = 1.04e-15  iters = 2    tol = 1.0e-08
>   min(eta) =   1.09   S O
--------------------------------------------------------------------------------
> ----------------------------
(legend: p: exact partial-out   s: exact solver   h: step-halving   o: epsilon b
> elow tolerance)
Converged in 5 iterations and 15 HDFE sub-iterations (tol = 1.0e-08)

HDFE PPML regression                              No. of obs      =        126
Absorbing 3 HDFE groups                           Residual df     =         99
                                                  Wald chi2(2)    =       7.52
Deviance             =  4.420984129               Prob > chi2     =     0.0233
Log pseudolikelihood = -260.4645284               Pseudo R2       =     0.0909
------------------------------------------------------------------------------
             |               Robust
       lnvol |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      lndist |          0  (omitted)
    lnGDPimp |    .109938    .041569     2.64   0.008     .0284643    .1914116
    lnGDPexp |   .0555364   .0383281     1.45   0.147    -.0195854    .1306582
       _cons |   1.002081   .4973192     2.01   0.044     .0273532    1.976809
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
    importer |         3           0           3     |
    exporter |         3           1           2     |
        year |        21           1          20    ?|
-----------------------------------------------------+
? = number of redundant parameters may be higher

Essentially, as I said above, I want to figure out how GDP and distance affect export volume. Can you help me explain what was going wrong with my data and give me any recommendations?

[Tom Zylkin]

Hi Long Nguyenn,

I believe if you move your fixed effects to the left in your use of the ppml command you will get the same result. Try the following:

ppml exporter_* importer_* year_* lnvol lndist lnGDPimp lnGDPexp

Regards,
Tom

Dear Tom Zylkin,

I am following your instructions on how to use ppml and ppmlhdfe command on this thread and many other threads. I am currently working with my sample data which consists of three countries with multilateral trade (from 1998 to 2018) and I only include exporter GDP, importer GDP, and distance as my independent variables and I want to figure out how these variables affect export volume.

After reading this thread, to my understanding, the ppml command

ppml lnvol lndist lnGDPimp lnGDPexp exporter_* importer_* year_*

and ppmlhdfe command

ppmlhdfe lnvol lndist lnGDPimp lnGDPexp, a(importer exporter year) vce(robust)

should give me the same results. However this is not the case.

. ppml lnvol lndist lnGDPimp lnGDPexp exporter_* importer_* year_*

note: checking the existence of the estimates

Number of regressors excluded to ensure that the estimates exist: 4
Excluded regressors: exporter_1 exporter_2 importer_2 year_21
Number of observations excluded: 0

note: starting ppml estimation
note: lnvol has noninteger values

Iteration 1: deviance = 4.493896
Iteration 2: deviance = 4.420987
Iteration 3: deviance = 4.420984
Iteration 4: deviance = 4.420984

Number of parameters: 27
Number of observations: 126
Pseudo log-likelihood: -260.46453
R-squared: .92118197
Option strict is: off
------------------------------------------------------------------------------
| Robust
lnvol | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lndist | -.1561562 .0309894 -5.04 0.000 -.2168942 -.0954182
lnGDPimp | .109938 .041569 2.64 0.008 .0284643 .1914116
lnGDPexp | .0555364 .0383281 1.45 0.147 -.0195854 .1306582
exporter_3 | -.1191625 .1528654 -0.78 0.436 -.4187731 .1804482
importer_1 | -.0974729 .0498772 -1.95 0.051 -.1952305 .0002847
importer_3 | .0270576 .201956 0.13 0.893 -.3687689 .4228841
year_1 | -.2258452 .0935905 -2.41 0.016 -.4092792 -.0424112
year_2 | -.2105067 .0929665 -2.26 0.024 -.3927178 -.0282957
year_3 | -.169045 .0887337 -1.91 0.057 -.3429598 .0048697
year_4 | -.1605192 .0825138 -1.95 0.052 -.3222432 .0012048
year_5 | -.1382407 .0744673 -1.86 0.063 -.284194 .0077125
year_6 | -.098291 .0650511 -1.51 0.131 -.2257887 .0292068
year_7 | -.0801831 .061846 -1.30 0.195 -.2013991 .0410329
year_8 | -.0822553 .0601515 -1.37 0.171 -.2001501 .0356395
year_9 | -.0772801 .0564199 -1.37 0.171 -.187861 .0333008
year_10 | -.0575561 .0509048 -1.13 0.258 -.1573278 .0422155
year_11 | -.0422892 .0481685 -0.88 0.380 -.1366976 .0521193
year_12 | -.0486424 .046542 -1.05 0.296 -.1398631 .0425783
year_13 | -.0343536 .0433686 -0.79 0.428 -.1193546 .0506473
year_14 | -.0248547 .041068 -0.61 0.545 -.1053465 .0556371
year_15 | -.0188818 .039707 -0.48 0.634 -.0967062 .0589426
year_16 | -.0153306 .0391906 -0.39 0.696 -.0921427 .0614815
year_17 | -.0105907 .0387608 -0.27 0.785 -.0865605 .0653791
year_18 | -.0085547 .0389603 -0.22 0.826 -.0849155 .0678061
year_19 | -.0075817 .0398676 -0.19 0.849 -.0857207 .0705573
year_20 | -.0030358 .0400476 -0.08 0.940 -.0815278 .0754561
_cons | 2.462663 .4698884 5.24 0.000 1.541698 3.383627
------------------------------------------------------------------------------

. ppmlhdfe lnvol lndist lnGDPimp lnGDPexp, a(importer exporter year) vce(robust)
note: 1 variable omitted because of collinearity: lndist
Iteration 1: deviance = 4.4939e+00 eps = . iters = 4 tol = 1.0e-04
> min(eta) = 1.10 P
Iteration 2: deviance = 4.4210e+00 eps = 1.65e-02 iters = 4 tol = 1.0e-04
> min(eta) = 1.09
Iteration 3: deviance = 4.4210e+00 eps = 6.85e-07 iters = 3 tol = 1.0e-04
> min(eta) = 1.09
Iteration 4: deviance = 4.4210e+00 eps = 3.93e-15 iters = 2 tol = 1.0e-05
> min(eta) = 1.09
Iteration 5: deviance = 4.4210e+00 eps = 1.04e-15 iters = 2 tol = 1.0e-08
> min(eta) = 1.09 S O
--------------------------------------------------------------------------------
> ----------------------------
(legend: p: exact partial-out s: exact solver h: step-halving o: epsilon b
> elow tolerance)
Converged in 5 iterations and 15 HDFE sub-iterations (tol = 1.0e-08)

HDFE PPML regression No. of obs = 126
Absorbing 3 HDFE groups Residual df = 99
Wald chi2(2) = 7.52
Deviance = 4.420984129 Prob > chi2 = 0.0233
Log pseudolikelihood = -260.4645284 Pseudo R2 = 0.0909
------------------------------------------------------------------------------
| Robust
lnvol | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lndist | 0 (omitted)
lnGDPimp | .109938 .041569 2.64 0.008 .0284643 .1914116
lnGDPexp | .0555364 .0383281 1.45 0.147 -.0195854 .1306582
_cons | 1.002081 .4973192 2.01 0.044 .0273532 1.976809
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
Absorbed FE | Categories - Redundant = Num. Coefs |
-------------+---------------------------------------|
importer | 3 0 3 |
exporter | 3 1 2 |
year | 21 1 20 ?|
-----------------------------------------------------+
? = number of redundant parameters may be higher

Essentially, as I said above, I want to figure out how GDP and distance affect export volume. Can you help me explain what was going wrong with my data and give me any recommendations?

[Long Nguyenn]

Dear Tom Zylkin,

Thank you very much for your fast reply. However, I follow your code and it did not work.

ppml exporter_* importer_* year_* lnvol lndist lnGDPimp lnGDPexp

note: checking the existence of the estimates

Number of regressors excluded to ensure that the estimates exist: 3
Excluded regressors:  exporter_2 exporter_3 importer_1
Number of observations excluded: 84

note: importer_2 omitted because of collinearity
note: importer_3 omitted because of collinearity
note: year_1 omitted because of collinearity
note: year_21 omitted because of collinearity

note: starting ppml estimation

Iteration 1:   deviance =         0
Iteration 2:   deviance =         0

Number of parameters: 24
Number of observations: 42
Pseudo log-likelihood: -42
R-squared: .
Option strict is: off
------------------------------------------------------------------------------
             |               Robust
  exporter_1 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      year_2 |          0  (omitted)
      year_3 |          0  (omitted)
      year_4 |          0  (omitted)
      year_5 |          0  (omitted)
      year_6 |          0  (omitted)
      year_7 |          0  (omitted)
      year_8 |          0  (omitted)
      year_9 |          0  (omitted)
     year_10 |          0  (omitted)
     year_11 |          0  (omitted)
     year_12 |          0  (omitted)
     year_13 |          0  (omitted)
     year_14 |          0  (omitted)
     year_15 |          0  (omitted)
     year_16 |          0  (omitted)
     year_17 |          0  (omitted)
     year_18 |          0  (omitted)
     year_19 |          0  (omitted)
     year_20 |          0  (omitted)
       lnvol |          0  (omitted)
      lndist |          0  (omitted)
    lnGDPimp |          0  (omitted)
    lnGDPexp |          0  (omitted)
       _cons |          0  (omitted)
------------------------------------------------------------------------------

This result in it trying to predict export dummy variable. I am assuming you might have missed the trade volume (lnvol) as the dependent variable in your recommendation so I tried the following

. ppml lnvol exporter_* importer_* year_* lndist lnGDPimp lnGDPexp

:

The result from this is exactly the same as putting those fixed effects dummy variables to the back of the code.

------------------------------------------------------------------------------
             |               Robust
       lnvol |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  exporter_3 |  -.1191625   .1528654    -0.78   0.436    -.4187731    .1804482
  importer_1 |  -.0974729   .0498772    -1.95   0.051    -.1952305    .0002847
  importer_3 |   .0270576    .201956     0.13   0.893    -.3687689    .4228841
      year_1 |  -.2258452   .0935905    -2.41   0.016    -.4092792   -.0424112
      year_2 |  -.2105067   .0929665    -2.26   0.024    -.3927178   -.0282957
      year_3 |   -.169045   .0887337    -1.91   0.057    -.3429598    .0048697
      year_4 |  -.1605192   .0825138    -1.95   0.052    -.3222432    .0012048
      year_5 |  -.1382407   .0744673    -1.86   0.063     -.284194    .0077125
      year_6 |   -.098291   .0650511    -1.51   0.131    -.2257887    .0292068
      year_7 |  -.0801831    .061846    -1.30   0.195    -.2013991    .0410329
      year_8 |  -.0822553   .0601515    -1.37   0.171    -.2001501    .0356395
      year_9 |  -.0772801   .0564199    -1.37   0.171     -.187861    .0333008
     year_10 |  -.0575561   .0509048    -1.13   0.258    -.1573278    .0422155
     year_11 |  -.0422892   .0481685    -0.88   0.380    -.1366976    .0521193
     year_12 |  -.0486424    .046542    -1.05   0.296    -.1398631    .0425783
     year_13 |  -.0343536   .0433686    -0.79   0.428    -.1193546    .0506473
     year_14 |  -.0248547    .041068    -0.61   0.545    -.1053465    .0556371
     year_15 |  -.0188818    .039707    -0.48   0.634    -.0967062    .0589426
     year_16 |  -.0153306   .0391906    -0.39   0.696    -.0921427    .0614815
     year_17 |  -.0105907   .0387608    -0.27   0.785    -.0865605    .0653791
     year_18 |  -.0085547   .0389603    -0.22   0.826    -.0849155    .0678061
     year_19 |  -.0075817   .0398676    -0.19   0.849    -.0857207    .0705573
     year_20 |  -.0030358   .0400476    -0.08   0.940    -.0815278    .0754561
      lndist |  -.1561562   .0309894    -5.04   0.000    -.2168942   -.0954182
    lnGDPimp |    .109938    .041569     2.64   0.008     .0284643    .1914116
    lnGDPexp |   .0555364   .0383281     1.45   0.147    -.0195854    .1306582
       _cons |   2.462663   .4698884     5.24   0.000     1.541698    3.383627
------------------------------------------------------------------------------

Also, I want to ask you if there is an option in the ppmlhdfe command that could help me produce the coefficient for the distance variable since it is one important variable in the gravity model. I do understand that distance is directly correlated to the fixed effects such as importer, exporter, or country-pair but the ppml command with dummy variables showed a negative coefficient for distance, which is good even though it is not as high as I would hope. However, I expect this might only be due to my sample being too small.

Thank you very much and I apologize for the long reply.

[Tom Zylkin]

Hi Long Nguyenn,

Yes sorry that was my mistake. My point was that Stata drops collinear regressors from right to left. It looks to me that ln_dist is perfectly collinear with your fixed effects, but ppml is failing to detect it for some reason. You can tell that the two sets of results are actually the same; look at the estimates for all the other coefficients and look at the deviance. Here is one way to test this: run

reghdfe lndist, a(importer exporter year)

If I am right, the R^2 from this regression should be 1. That would confirm that lndist is perfectly predicted by your fixed effects.

Actually now that you mention the dependent variable, is that that *log* of the variable "volume" you are using? If so, that would be incorrect. To use ppml, you should estimate the dependent variables in levels, not in logs.

Sorry again about the confusion. Let me know if the above clarifies.

Regards,
Tom

[Long Nguyenn]

Dear Tom Zylkin,

You are right, the R2 from the reghdfe command is exactly 1. Thank you for your clarification. I really appreciate your help here and from all the threads that I follow.

On another note, I have tried ppmlhdfe command again with levels of volume instead of logs and produced these following results:

ppmlhdfe volume lndist lnGDPimp lnGDPexp, a(importer exporter year) cluster(lndist)

note: 1 variable omitted because of collinearity: lndist
HDFE PPML regression                              No. of obs      =        126
Absorbing 3 HDFE groups                           Residual df     =          2
Statistics robust to heteroskedasticity           Wald chi2(2)    =      10.62
Deviance             =   284791.733               Prob > chi2     =     0.0049
Log pseudolikelihood = -143119.9672               Pseudo R2       =     0.9850

Number of clusters (lndist) =          3
                                 (Std. Err. adjusted for 3 clusters in lndist)
------------------------------------------------------------------------------
             |               Robust
      volume |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      lndist |          0  (omitted)
    lnGDPimp |   1.700467   1.637339     1.04   0.299    -1.508658    4.909592
    lnGDPexp |   1.137436   1.678489     0.68   0.498    -2.152341    4.427214
       _cons |  -13.31204    29.5915    -0.45   0.653    -71.31033    44.68624
------------------------------------------------------------------------------

. ppmlhdfe volume lndist lnGDPimp lnGDPexp, a(importer exporter year) cluster(pairid)

HDFE PPML regression                              No. of obs      =        126
Absorbing 3 HDFE groups                           Residual df     =          5
Statistics robust to heteroskedasticity           Wald chi2(2)    =       5.16
Deviance             =   284791.733               Prob > chi2     =     0.0759
Log pseudolikelihood = -143119.9672               Pseudo R2       =     0.9850

Number of clusters (pairid) =          6
                                 (Std. Err. adjusted for 6 clusters in pairid)
------------------------------------------------------------------------------
             |               Robust
      volume |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      lndist |          0  (omitted)
    lnGDPimp |   1.700467   1.180878     1.44   0.150     -.614011    4.014945
    lnGDPexp |   1.137436   1.198446     0.95   0.343    -1.211474    3.486346
       _cons |  -13.31204   21.10152    -0.63   0.528    -54.67026    28.04617
------------------------------------------------------------------------------

ppmlhdfe volume lndist lnGDPimp lnGDPexp, a(importer exporter year) vce(robust)

HDFE PPML regression                              No. of obs      =        126
Absorbing 3 HDFE groups                           Residual df     =         99
                                                  Wald chi2(2)    =      57.50
Deviance             =   284791.733               Prob > chi2     =     0.0000
Log pseudolikelihood = -143119.9672               Pseudo R2       =     0.9850
------------------------------------------------------------------------------
             |               Robust
      volume |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      lndist |          0  (omitted)
    lnGDPimp |   1.700467   .3190902     5.33   0.000     1.075062    2.325872
    lnGDPexp |   1.137436   .3222978     3.53   0.000     .5057441    1.769128
       _cons |  -13.31204   5.673695    -2.35   0.019    -24.43228   -2.191806
------------------------------------------------------------------------------

To my understanding, vce(robust) should give me the same result as cluster(panel variables) as this is stated from the xtreg help files. However, even though my coefficients the same, the SEs are not quite.

Could you help me explain what caused these differences and recommend which one should I used?

[Tom Zylkin]

Hi Long Nguyenn,

The help file for xtreg only applies to that command. vce(robust) should give you the same standard errors as ppml using the "robust" command. You can confirm from one of your earlier posts that this is indeed the case.

To give a more thorough answer, vce(robust) assumes the errors for all observations are heteroscedastic but uncorrelated with one another. Cluster(pair_id) assumes that they are instead correlated (or "clustered") within observations that share the same pair_id.

Edited to add: in answer to your last question, since you have multiple years clustering by pair makes more sense here.

I hope that helps!

Regards,
Tom

[Long Nguyenn]

Dear Tom Zylkin,

Your explanation is perfect! Thank you for your help.

Best,
Long

[Long Nguyenn]

Dear Tom Zylkin,

If you have time, I would like to ask you some more questions.

I am working on a dataset that consists of one country export to 15 other countries from 1998 to 2018. My general code is the following:

ppmlhdfe export lnimpgdp lnexpgdp lnexrate lnimpopen lnexpopen, a(pairid) cluster(pairid)

however, I am a little confused about how to use the absorb option effectively. Since I am working with a 1xN dataset, should I also be absorbing exporter fixed effects as well as year? My intuition is that since I only have one exporter, variables such as exporter gdp and exporter trade openness might be explained by the exporter fixed effects and therefore be omitted. However, these variables are time-varying so I am not sure. Could you give me a general rule of thumbs of when to use exporter fixed effects, country/time fixed effects?

Thank you very much

[Tom Zylkin]

Hi Long Nguyen,

If you only have 1 exporter, there are a couple things to keep in mind wrt to the fixed effects:
- there is no need to have an exporter fixed effect. The dummy associated with this fixed effect would be equal to 1 for all observations. In other words, it's just a constant.
- the importer fixed effect is the same thing as a pair fixed effect, since the importer is the only thing that is different for each pair.
- If a variable varies by both country and time, it will not be absorbed by a country fixed effect. It will, however, be absorbed by a country-time fixed effect.
- In general, say you want to estimate a variable that varies by i and t. It would make sense to have (separate) i and t fixed effects. Alternatively, you might have data that varies by i, j, t, as in trade data (exporter, importer, and time). In that case, it makes sense to have it, jt, and ij fixed effects, though less strict approaches could instead have i, j, and t fixed effects, it and jt fixed effects, ij and t fixed effects, and so on. Choosing between these alternatives often depends on what variable you are trying to identify, as explained in the previous point.

In your case, it is most useful to think of your data as varying by importer and time (forget exporter). Therefore, use two fixed effects: importer and time.

Regards,
Tom

[Long Nguyenn]

Dear Tom Zylkin,

Thank you for your recommendation. I followed and get this result:

ppmlhdfe export lnIMPgdp lnExrate lnIMPopen, a(importer_* year_*) vce(cluster pairid)

HDFE PPML regression                              No. of obs      =        315
Absorbing 36 HDFE groups                          Residual df     =         14
Statistics robust to heteroskedasticity           Wald chi2(3)    =       6.92
Deviance             =  64242.15402               Prob > chi2     =     0.0746
Log pseudolikelihood =  -33538.1381               Pseudo R2       =     0.9675

Number of clusters (pairid) =         15
                                (Std. Err. adjusted for 15 clusters in pairid)
------------------------------------------------------------------------------
             |               Robust
      export |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    lnIMPgdp |   .4813494   .3541968     1.36   0.174    -.2128636    1.175562
    lnExrate |  -.1700355   .1213745    -1.40   0.161    -.4079251    .0678541
   lnIMPopen |   .0531632   .6839801     0.08   0.938    -1.287413     1.39374
       _cons |   6.296457   5.834532     1.08   0.281    -5.139015    17.73193
------------------------------------------------------------------------------

I also tried some other fixed effects such as

ppmlhdfe export lnIMPgdp lnExrate lnIMPopen, a(importer_*#year_*) vce(cluster pairid)

HDFE PPML regression                              No. of obs      =        314
Absorbing 35 HDFE groups                          Residual df     =         14
Statistics robust to heteroskedasticity           Wald chi2(3)    =       6.20
Deviance             =  63270.63511               Prob > chi2     =     0.1024
Log pseudolikelihood = -33048.38428               Pseudo R2       =     0.9679

Number of clusters (pairid) =         15
                                (Std. Err. adjusted for 15 clusters in pairid)
------------------------------------------------------------------------------
             |               Robust
      export |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    lnIMPgdp |   .5002167   .3477729     1.44   0.150    -.1814057    1.181839
    lnExrate |  -.1299062   .1181805    -1.10   0.272    -.3615357    .1017232
   lnIMPopen |   .1091948     .66577     0.16   0.870     -1.19569     1.41408
       _cons |   5.604361   5.706363     0.98   0.326    -5.579904    16.78863
------------------------------------------------------------------------------

ppmlhdfe export lnIMPgdp lnExrate lnIMPopen, a(importer_*#year) vce(cluster pairid)

HDFE PPML regression                              No. of obs      =        294
Absorbing 15 HDFE groups                          Residual df     =         13
Statistics robust to heteroskedasticity           Wald chi2(3)    =       6.08
Deviance             =  55401.08588               Prob > chi2     =     0.1077
Log pseudolikelihood = -29004.27896               Pseudo R2       =     0.9555

Number of clusters (pairid) =         14
                                (Std. Err. adjusted for 14 clusters in pairid)
------------------------------------------------------------------------------
             |               Robust
      export |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    lnIMPgdp |   .6151594   .3405068     1.81   0.071    -.0522216     1.28254
    lnExrate |   -.091259   .1112315    -0.82   0.412    -.3092687    .1267508
   lnIMPopen |   .3786789   .6052406     0.63   0.532    -.8075708    1.564929
       _cons |    3.12602   5.274238     0.59   0.553    -7.211297    13.46334
------------------------------------------------------------------------------

These are two very different results from my first ppmlhdfe command and there is only one coefficient that is statistically significant. As the trade volume varies by both the importer countries and time, my intuition is that a(importer_* year_*), a(importer_*#year), and a(importer_*#year_*) should all give me the same results. However, this is not true as seen above. Could you help me explain what is going on wrong? I truly appreciate your help!

[Tom Zylkin]

Hi Long Nguyenn,

You are not using the absorb option correctly in these examples. You were using it correctly before. Check some of your earlier posts.

Regards,
Tom

[Long Nguyenn]

Dear Tom Zylkin,

Thank you very much!

[Long Nguyenn]

Dear Tom Zylkin,

Sorry to bother you again but I ran into some more problems. I would very much appreciate it if you could help me.

I am working with a sample consists of 1 exporter country (Vietnam) and 30 importer countries from 1998 to 2018. My independent variables are exporter's and importer's GDPs, exporter's and importer's trade openness (% of GDP), and real effective exchange rate (data from https://www.bruegel.org/publications...-new-database/.)

My code is as follow:

ppmlhdfe exportvolume lnExrate lnEXPgdp lnIMPgdp lnEXPopen lnIMPopen, a(importer year) vce(cluster pairid)

note: 2 variables omitted because of collinearity: lnEXPgdp lnEXPopen
HDFE PPML regression                              No. of obs      =        609
Absorbing 2 HDFE groups                           Residual df     =         28
Statistics robust to heteroskedasticity           Wald chi2(3)    =       9.51
Deviance             =  118024.1806               Prob > chi2     =     0.0232
Log pseudolikelihood = -61627.18238               Pseudo R2       =     0.9566

Number of clusters (pairid) =         29
                                (Std. Err. adjusted for 29 clusters in pairid)
------------------------------------------------------------------------------
             |               Robust
exportvolume |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    lnExrate |  -.8901078   .3309642    -2.69   0.007    -1.538786   -.2414299
    lnEXPgdp |          0  (omitted)
    lnIMPgdp |   .3200044   .2898905     1.10   0.270    -.2481706    .8881794
   lnEXPopen |          0  (omitted)
   lnIMPopen |   .4969847   .3851513     1.29   0.197    -.2578979    1.251867
       _cons |   2.171014    4.67038     0.46   0.642    -6.982762    11.32479
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
    importer |        29          29           0    *|
        year |        21           0          21     |
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

My questions are:

1) The variables that are related to my exporter country are omitted. Is there a way for me to show these variables? I understand that this is due to the fixed effects as these variables are the same across country-pair. However, I do want to use it to explain the trade activity of a specific exporter.

2) Can you help me check my real effective exchange rate variable? This is an index number calculated as the cpi-based weighted average of a currency against a basket of currency. I was thinking I could incorporate this variable as the exchange rate does has an impact on trade. I calculate the REER by dividing the REER index number of Vietnam by the REER index number of a partner country. For example, in 2017 the REER for Vietnam is 104 and for Austria is 108, I would calculate the REER of Vietnam/Austria by 104/108 = 0.96.

I suspect the REER to have a positive impact on export volume because of how the depreciation of a currency, which means the REER rises, will result in export being cheaper, thus export will rise as well. However, the coefficient for REER in my model is significantly negative.

3) For those variables that did have coefficients, they are not statistically significant even though I have increased the sample size from last time. Do you think my sample is still too small to produce a significant result? If not then what seems to be the reason and how may I improve it?

[Tom Zylkin]

Hi Long Nguyenn,

1) Because you only have one exporter, any exporter-year effects are absorbed by the year fixed effect. You could drop the year fixed effect but then you would not be accounting for omitted factors that vary by year. An important example is the value of the units your dependent variable is measured in. Assuming there is inflation over time, you will always have more trade in nominal terms in later periods than in earlier ones. A time fixed effect takes care of this. If you don't have a time fixed effect, at minimum you need to make sure your dependent variable is measured in real terms rather than in nominal terms. Likely you would need to deflate it.

I do have a question I would ask at this point, though. What is the sense in regressing Vietnam's exports on its openness to trade? Unless you are only using exports from a particular sector that you are focusing on, it seems to me the two things are related mechanically. I can understand why you do it for the importer because you can't use importer-year fixed effects. But there it seems like it should function as a control rather than as a variable of interest.

2) Sorry, your explanation of how you calculated the RER variable is a bit confusing. I agree that if Austria's RER depreciates, one would expect its imports from Vietnam to go down. Are your results implying the opposite? One does not often see the RER included as a variable in this context. Thus I can only offer limited advice. One thing to be aware of is that the RER is potentially endogenous to trade. If Austria's RER depreciates because of higher relative demand for Vietnamese-produced goods, one would observe the opposite of the expected sign.

3) Yes sample size could be an issue. You only have 28 clusters, which is relatively small.

Regards,
Tom