Fixed effect with trade flow Gravity Model PPML

[zeinab Mamdouh]

I am running model to see the impact of RTA in africa specifically AFCFTA and COMESA as well as logistics performance index score on the trade trade flow between egypt (as exporter) vs the african countries (as importer) using gravity PPML model.
this is my model over period (2007-2021). the results are compliant with the economic theory without using fixed effect. as follows:

ppmlhdfe tradeflow_baci ln_dist ln_gdpcap_o ln_gdpcap_d contig comlang_off RTA LPI score , cluster (dist)

warning: dependent variable takes very low values after standardizing (3.1139e-07)
Iteration 1: deviance = 5.0031e+07 eps = . iters = 1 tol = 1.0e-04 min(eta) = -2.89 P
Iteration 2: deviance = 4.4879e+07 eps = 1.15e-01 iters = 1 tol = 1.0e-04 min(eta) = -3.27
Iteration 3: deviance = 4.4784e+07 eps = 2.13e-03 iters = 1 tol = 1.0e-04 min(eta) = -3.37
Iteration 4: deviance = 4.4784e+07 eps = 1.43e-06 iters = 1 tol = 1.0e-04 min(eta) = -3.37
Iteration 5: deviance = 4.4784e+07 eps = 9.39e-13 iters = 1 tol = 1.0e-05 min(eta) = -3.37 S O
------------------------------------------------------------------------------------------------------------
(legend: p: exact partial-out s: exact solver h: step-halving o: epsilon below tolerance)
Converged in 5 iterations and 5 HDFE sub-iterations (tol = 1.0e-08)

PPML regression No. of obs = 704
Residual df = 53
Statistics robust to heteroskedasticity Wald chi2(7) = 329.82
Deviance = 44783540.23 Prob > chi2 = 0.0000
Log pseudolikelihood = -22395861.37 Pseudo R2 = 0.7132

Number of clusters (dist) = 54
(Std. err. adjusted for 54 clusters in dist)
-------------------------------------------------------------------------------
| Robust
tradeflow_b~i | Coefficient std. err. z P>|z| [95% conf. interval]
--------------+----------------------------------------------------------------
ln_dist | -1.11157 .6438715 -1.73 0.084 -2.373535 .1503952
ln_gdpcap_o | .4029311 .1822195 2.21 0.027 .0457873 .7600748
ln_gdpcap_d | .3325304 .088916 3.74 0.000 .1582583 .5068026
contig | .5806069 .4121333 1.41 0.159 -.2271595 1.388373
comlang_off | .4441243 .5074212 0.88 0.381 -.5504031 1.438652
RTA | .9452284 .2998859 3.15 0.002 .3574629 1.532994
LPI score | .0458755 .0114115 4.02 0.000 .0235094 .0682415
_cons | 16.91456 5.332249 3.17 0.002 6.463544 27.36558
-------------------------------------------------------------------------------

however when using fixed effect as follows
egen exporter = group(iso3_o)
egen importer = group(iso3_d)
tabulate exporters, generate(EXP_TIME_FE)
tabulate importers, generate(IMP_TIME_FE)


results are not compliant with the theory and also many warnings:
ppmlhdfe tradeflow_baci ln_dist ln_gdpcap_o ln_gdpcap_d contig comlang_off fta_wto LPIpercentile IMP_TIME_FE* , cluster (dist)
warning: dependent variable takes very low values after standardizing (3.1139e-07)
note: 39 variables omitted because of collinearity: IMP_TIME_FE121 IMP_TIME_FE151 IMP_TIME_FE166 IMP_TIME_FE196 IMP_TIME_FE286 IMP_TIME_FE30
> 1 IMP_TIME_FE302 IMP_TIME_FE303 IMP_TIME_FE306 IMP_TIME_FE307 IMP_TIME_FE308 IMP_TIME_FE309 IMP_TIME_FE310 IMP_TIME_FE311 IMP_TIME_FE312 I
> MP_TIME_FE313 IMP_TIME_FE314 IMP_TIME_FE331 IMP_TIME_FE361 IMP_TIME_FE362 IMP_TIME_FE365 IMP_TIME_FE368 IMP_TIME_FE371 IMP_TIME_FE372 IMP_
> TIME_FE555 IMP_TIME_FE571 IMP_TIME_FE586 IMP_TIME_FE603 IMP_TIME_FE604 IMP_TIME_FE608 IMP_TIME_FE609 IMP_TIME_FE616 IMP_TIME_FE660 IMP_TIM
> E_FE705 IMP_TIME_FE720 IMP_TIME_FE732 IMP_TIME_FE733 IMP_TIME_FE734 IMP_TIME_FE735
Iteration 1: deviance = 7.8255e+06 eps = . iters = 1 tol = 1.0e-04 min(eta) = -2.37 P
Iteration 2: deviance = 1.4226e+06 eps = 4.50e+00 iters = 1 tol = 1.0e-04 min(eta) = -3.37
Iteration 3: deviance = 3.2747e+05 eps = 3.34e+00 iters = 1 tol = 1.0e-04 min(eta) = -4.37
Iteration 4: deviance = 7.6732e+04 eps = 3.27e+00 iters = 1 tol = 1.0e-04 min(eta) = -5.37
Iteration 5: deviance = 1.7213e+04 eps = 3.09e+00 iters = 1 tol = 1.0e-04 min(eta) = -6.37
Iteration 6: deviance = 3.8433e+03 eps = 6.94e-01 iters = 1 tol = 1.0e-04 min(eta) = -7.37
Iteration 7: deviance = 9.2689e+02 eps = 1.51e-01 iters = 1 tol = 1.0e-04 min(eta) = -8.37
Iteration 8: deviance = 2.3514e+02 eps = 3.59e-02 iters = 1 tol = 1.0e-04 min(eta) = -9.37
Iteration 9: deviance = 5.9640e+01 eps = 9.11e-03 iters = 1 tol = 1.0e-04 min(eta) = -10.36
Iteration 10: deviance = 1.4763e+01 eps = 2.33e-03 iters = 1 tol = 1.0e-04 min(eta) = -11.35
Iteration 11: deviance = 3.3722e+00 eps = 5.91e-04 iters = 1 tol = 1.0e-04 min(eta) = -12.33
Iteration 12: deviance = 6.7566e-01 eps = 1.40e-04 iters = 1 tol = 1.0e-04 min(eta) = -13.26
Iteration 13: deviance = 9.3903e-02 eps = 3.02e-05 iters = 1 tol = 1.0e-04 min(eta) = -14.08
Iteration 14: deviance = 6.7081e-03 eps = 3.48e-07 iters = 1 tol = 1.0e-05 min(eta) = -14.67
Iteration 15: deviance = 1.1391e-04 eps = 5.91e-09 iters = 1 tol = 1.0e-06 min(eta) = -14.94 S O
------------------------------------------------------------------------------------------------------------
(legend: p: exact partial-out s: exact solver h: step-halving o: epsilon below tolerance)
Converged in 15 iterations and 15 HDFE sub-iterations (tol = 1.0e-08)
warning: missing F statistic; dropped variables due to collinearity or too few clusters
Warning: Variance matrix is nonsymmetric or highly singular.

PPML regression No. of obs = 704
Residual df = 0
Statistics robust to heteroskedasticity Wald chi2(703) = .
Deviance = .0001139068 Prob > chi2 = .
Log pseudolikelihood = -4091.25808 Pseudo R2 = 0.9999

Number of clusters (dist) = 54
(Std. err. adjusted for 54 clusters in dist)
--------------------------------------------------------------------------------
| Robust
tradeflow_baci | Coefficient std. err. z P>|z| [95% conf. interval]
---------------+----------------------------------------------------------------
ln_dist | -338.9417 . . . . .
ln_gdpcap_o | 3.801462 . . . . .
ln_gdpcap_d | 3.782563 . . . . .
contig | -91.06106 . . . . .
comlang_off | -294.6057 . . . . .
fta_wto | -117.9866 . . . . .
LPIpercentile | -1.584949 . . . . .
IMP_TIME_FE1 | -142.6369 . . . . .
IMP_TIME_FE2 | -148.6913 . . . . .
IMP_TIME_FE3 | -147.7366 . . . . .
IMP_TIME_FE4 | -154.2487 . . . . .
IMP_TIME_FE5 | -154.5188 . . . . .
IMP_TIME_FE6 | -154.1491 . . . . .
IMP_TIME_FE7 | -147.921 . . . . .
IMP_TIME_FE8 | -139.6954 . . . . .
IMP_TIME_FE9 | -148.0377 . . . . .
IMP_TIME_FE10 | -156.4992 .
_cons | 3085.444 . . . . .
--------------------------------------------------------------------------------

NB: I remove the rest o the fixed effect result due to limitation in posting for the number of characters allowed. howerver all the fixed (more than 700) do apprears in the results


I also use the command absorb ( improters) to try to solve the problems, yields either all coefficients except GDP cap become zero or no results at all as floows:

ppmlhdfe tradeflow_baci ln_dist ln_gdpcap_o ln_gdpcap_d contig comlang_off comcol col45 fta_wto, absorb ( importer) cluster (dist)
warning: dependent variable takes very low values after standardizing (3.1863e-07)
note: 5 variables omitted because of collinearity: contig comlang_off comcol col45 fta_wto
note: ln_dist is probably collinear with the fixed effects (all partialled-out values are close to zero; tol = 1.0e-06)
Iteration 1: deviance = 1.8259e+07 eps = . iters = 1 tol = 1.0e-04 min(eta) = -2.78 P
Iteration 2: deviance = 1.1329e+07 eps = 6.12e-01 iters = 1 tol = 1.0e-04 min(eta) = -3.85
Iteration 3: deviance = 1.0400e+07 eps = 8.93e-02 iters = 1 tol = 1.0e-04 min(eta) = -4.83
Iteration 4: deviance = 1.0227e+07 eps = 1.69e-02 iters = 1 tol = 1.0e-04 min(eta) = -5.74
Iteration 5: deviance = 1.0193e+07 eps = 3.34e-03 iters = 1 tol = 1.0e-04 min(eta) = -6.52
Iteration 6: deviance = 1.0187e+07 eps = 6.12e-04 iters = 1 tol = 1.0e-04 min(eta) = -7.34
Iteration 7: deviance = 1.0186e+07 eps = 8.02e-05 iters = 1 tol = 1.0e-04 min(eta) = -7.95
Iteration 8: deviance = 1.0186e+07 eps = 6.17e-06 iters = 1 tol = 1.0e-05 min(eta) = -8.22
Iteration 9: deviance = 1.0186e+07 eps = 1.15e-07 iters = 1 tol = 1.0e-06 min(eta) = -8.26 S
Iteration 10: deviance = 1.0186e+07 eps = 5.78e-11 iters = 1 tol = 1.0e-07 min(eta) = -8.26 S O
------------------------------------------------------------------------------------------------------------
(legend: p: exact partial-out s: exact solver h: step-halving o: epsilon below tolerance)
Converged in 10 iterations and 10 HDFE sub-iterations (tol = 1.0e-08)

HDFE PPML regression No. of obs = 747
Absorbing 1 HDFE group Residual df = 56
Statistics robust to heteroskedasticity Wald chi2(2) = 17.00
Deviance = 10186142.46 Prob > chi2 = 0.0002
Log pseudolikelihood = -5097373.499 Pseudo R2 = 0.9374

Number of clusters (dist) = 57
(Std. err. adjusted for 57 clusters in dist)
------------------------------------------------------------------------------
| Robust
tradeflow_~i | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
ln_dist | 0 (omitted)
ln_gdpcap_o | .5488741 .134331 4.09 0.000 .2855902 .812158
ln_gdpcap_d | .3496276 .140808 2.48 0.013 .073649 .6256063
contig | 0 (omitted)
comlang_off | 0 (omitted)
comcol | 0 (omitted)
col45 | 0 (omitted)
fta_wto | 0 (omitted)
_cons | 11.59021 .2481093 46.71 0.000 11.10392 12.07649
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
Absorbed FE | Categories - Redundant = Num. Coefs |
-------------+---------------------------------------|
importer | 52 0 52 |
-----------------------------------------------------+



or ppmlhdfe tradeflow_baci ln_dist ln_gdpcap_o ln_gdpcap_d contig comlang_off fta_wto LPIpercentile , absorb( importers) cluster (dist)
(dropped 704 observations that are either singletons or separated by a fixed effect)
insufficient observations
r(2001);


The observations are 55 african countries * time series (15 years)
I control only for improters as there is only one exporter (egypt) vs african coutries that I am interets on the impact on its trade flow

Questtions:

1) is the fixed effect is a must and if yes how to solve this?
2) is using GDP per cap is good or use GDP and pop separatly,
3) what test should be done after running the model to test it and its significance?
4) ehat is the min value of R2 that is accepted?

[Joao Santos Silva]

Dear zeinab Mamdouh,

1) it appears to me that if you include the standard country-time fixed effects, all your variables will be wiped out. So, you may have to think again about what you want to do. In any case, you should always absorb the fixed effects.
2) I have no strong preference on this.
3) Maybe try the RESET test?
4) Ignore the value of the pseudo R2 reported by ppmlhdfe; see here.

Best wishes,

Joao

[zeinab Mamdouh]

please explain more what do you mean by think about what you want to do? do yuo see some thing worng in specification. I an checking the impact of these dependant variables on trade flow to asses the most factor affect trade flow and if member states in comesa has an inpact on trade flow and the LPI score of partner country affect?
I already used absorb in Fixed effct abd reuslted the following /: or ppmlhdfe tradeflow_baci ln_dist ln_gdpcap_o ln_gdpcap_d contig comlang_off fta_wto LPIpercentile , absorb( importers) cluster (dist)
(dropped 704 observations that are either singletons or separated by a fixed effect)
insufficient observations
r(2001);

[Joao Santos Silva]

Dear zeinab Mamdouh

Is this for an undergrad project, a master's dissertation, PhD thesis, part of your job, or maybe something else?

Best wishes,

Joao

[zeinab Mamdouh]

It is my PhD thesis . thank you for all your support. however im still trapped in the fixed effect for gravity model usign ppmlfe, or hdppmlfe.
I am running model to see the impact on egypt trade from joining comesa as well as the impact of logistics performance index score on the trade flow between egypt (as exporter) vs the comesa (as importer) using gravity PPML model.
this is my model over period (2007-2021) and sampel of all africa countries to give comesa member state RTA comesa dummy 1 and be zrro if africa non comesa


egen exporters = group ( iso3_o year)
egen importers = group ( iso3_d year)
tabulate exporters, generate(EXP_TIME_FE)
tabulate importers, generate(IMP_TIME_FE)

here i use improter onlu dummy and time not exporter because it is noly one exporters (egypt) vs all other importers
ppmlhdfe tradeflow_baci ln_dist ln_gdpcap_o ln_gdpcap_d contig comlang_off comcol col45 fta_wto IMP_TIME_FE_* , cluster (dist)

a lot of dummy around (17 years * 49 bosrvations ~800 dummy have been created) and a message appear insufficient observations.

ppmlhdfe tradeflow_baci ln_dist ln_gdpcap_o ln_gdpcap_d contig RTAcomesa LPI score , cluster (dist)

when i use absorb to avoid create a lot of dummy variables it absort the time invariate variable that are the most imprrtatnt my model namely RTAcomesa , dist , contig , so inedd tokeep them .
ppmlhdfe Exports_baci ln_dist ln_gdpcap_o ln_gdpcap_d contig FTA LPIpercentile , absorb (importer year) cluster (dist)
(Std. Err. adjusted for 54 clusters in dist)
-------------------------------------------------------------------------------
| Robust
Exports_baci | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
ln_dist | 0 (omitted)
ln_gdpcap_o | .7135059 .1437883 4.96 0.000 .431686 .9953258
ln_gdpcap_d | .260147 .1162747 2.24 0.025 .0322527 .4880413
contig | 0 (omitted)
FTA | 0 (omitted)
LPIpercentile | .0046897 .0040275 1.16 0.244 -.0032041 .0125835
_cons | 11.31256 .281835 40.14 0.000 10.76017 11.86494
-------------------------------------------------------------------------------

although i found many studies use ppml to estiate gravity for efefct of RTA on trade and the term of RTA is still there not omitted. what shoudl i do to avoid ommitted improtant variable?

[Joao Santos Silva]

Dear zeinab Mamdouh,

Thank you for the additional information. You need to use the absorb option, but you are not doing it correctly. you need either to absorb exporters (as created in the code above) or importer##year (not just importer and year). With this specification, some variables will be omitted, which means that their effect cannot be identified. To be able to estimate the effect, say, of FTA you need to have observations from the period before the agreement started and also observations for partners that are not part of the agreement.

Best wishes,

Joao