Problems with RESET test p-value for PPML estimators

[Karen Chan]

Dear Statalist,

Using a gravity model, I am estimating the impact of ASEAN-China Free Trade Agreement on trade creation and trade diversion using a panel of 21 countries (China, 10 ASEAN countries, and top 10 China's trading partners) spanning from 2000 to 2015 and generates 6720 obs with around 100 zeros in my dependent variable (export).

I have read through the forum and decided to use PPML to estimate my model with different FEs, but when I tried to perform RESET test I obtained very low p-value, which suggests that PPML does not pass the RESET test, which is confusing since the paper from Santo Silva and Tenreyro (2006) suggest that PPML should be the best method given the presence of zeros.


TIME AND COUNTRY-PAIR FIXED EFFECT ESTIMATION
I used the code:

ppml ex lgdp1 lgdp2 lgdpc1 lgdpc2 ldis adj lang lpop1 lpop2 FTA_1 FTA_2 FTA_3 id_* time_*, cluster(id)

I followed the approach from the "Log of Gravity" website and perform the RESET test using the following code:

predict fit, xb
gen fit2=fit^2
ppml ex lgdp1 lgdp2 lgdpc1 lgdpc2 ldis adj lang lpop1 lpop2 FTA_1 FTA_2 FTA_3 id_* time_* fit2, cluster(id)
test fit2=0

The test p-value is as following:

( 1) fit2 = 0

chi2( 1) = 13.38
Prob > chi2 = 0.0003

If I am not wrong, the p-value suggests the above specification is not in correct functional form i.e. PPML is not a good estimator. I would like to ask why is this the case and is there any solutions to that?

COUNTRY-TIME AND COUNTRY-PAIR FIXED EFFECT ESTIMATION
I used the code:

egen impyear_=group(impid time)
qui tab impyear_, gen(impyear_)
egen expyear_=group(expid time)
qui tab expyear_, gen(expyear_)

ppml ex FTA_1 FTA_2 FTA_3 expyear_* impyear_* id_*

I run the RESET test using the above approach. However after running the regression that includes the fit2 value, I received a warning saying variance matrix is nonsymmetric or highly singular after Iteration 34. All SE and p-value etc is missing so I cannot run the test for fit2.

I don't quite understand how this happened and is there any solutions to that?

On a side note, I tried to estimate the second FE estimation using other commands but in no luck:

When I run ppml_panel_sg with the following code, only coefficient of FTA_1 can be estimated - is it possible to estimate all FTA coefficients using this command?

ppml_panel_sg ex FTA_1 FTA_2 FTA_3, ex(expid) im(impid) y(time)

PS: FTA_1 takes a value of 1 if both countries belong to the RTA; FTA_2 takes a value of 1 if country i belongs to the RTA but country j doesn't; FTA_3 takes a value of 1 if country j belongs to the RTA and country i doesn't.

Thank you very much in advance and really really appreciate your help!

Best Regards
Karen

[Joao Santos Silva]

Dear Karen,

About your first question, the problem is not that PPML is not the right estimator for the model but that your model is not right for the data. I suggest that you try to improve the model specification.

On the second question, I believe that your model only contains dummies (some of them perfectly collinear). It is likely that in this case fit2 will be also collinear.

Finally, in that model only FTA_1 is identified; you cannot estimate any of the other FTA variables, whatever method you use.

Best wishes,

Joao

[Karen Chan]

Dear Joao,

Thank you very much for the suggestion and I will re-specify my model with extra variables.

Best Regards
Karen

[Emrah Eray Akca]

Dear Professor Joao, i hope you are doing very well, i am analyzing trade flows between Turkey and its 30 main partners. For this, I follow hierarchical regression analysis, namely, first I estimate the basic gravity model with 3 variables, then I add other geographical variables, then institutional variables, and lastly policy variables. I considered exporter and importer fixed effects and PPML estimator. i completed the analysis, but ı realized that in your seminal paper the RESET test is necessary to see whether there is any model specification error. So, I applied the RESET test for all alternative model specifications. The results are confusing for me. The first three models are significant statistically, as far as I understand in this case there is model specification error. But when I augmented the model with institutional and policy variables which is my most comprehensive model, the RESET test is not significant, which means no model specification error. How should I interpret these results, good or bad? Very thanks for your interest. Best regards.

[Joao Santos Silva]

Dear Emrah Eray Akca,

It is natural that not all specifications pass the test, but it is good to know that your preferred specification passes it. So, nothing t worry about.

Best wishes,

Joao

[Emrah Eray Akca]

Dear Joao Santos Silva, i am happy to see your reply,

Do Wald test statistics matter for the estimation results of PPML?

Best regards

[Joao Santos Silva]

Sorry, I do not understand the question...

[Emrah Eray Akca]

I read some papers which mention the Wald test of which results show whether the model is statistically significant or not. I asked you for this.

[Joao Santos Silva]

Sorry, still do not get it, but as long as you use the correct standard errors you can use Wald tests just like in OLS.

[Emrah Eray Akca]

Dear Joao Santos Silva

I mean that one paper using PPML estimator gave place to Wald test statistic of which hypothesis is that all the coefficients are equal the zero. When the hypothesis rejected, the model is found statistically significant, according to the paper.

Very thanks for your interest,
Best regards,

[Joao Santos Silva]

Ah! That is clear now. I would ignore that test; you will always reject the null.

Best wishes,

Joao

[Emrah Eray Akca]

Ok sir, so i will ignore it as well
Best regards

[Emrah Eray Akca]

Dear Joao Santos Silva

Hello again,
Even if we would use the PPML estimator, yet is it really necessary to prove that the distribution of the log model is heteroscedastic, or can we assume it?
Because I am striving to save space in my paper.
Best regards,

[Joao Santos Silva]

It is safe to assume that the data is heteroskedastic, and PPML will do fine even if that is not the case.

[Emrah Eray Akca]

Thank you, sir.