Gravity Model PPML estimator with zero value on independent variable

[NY ATYKUNN]

Dear Statalist,

I am doing my MSc dissertation and working on the gravity model to study the effect of the EU's EBA scheme on Cambodia's exports. My dependent variable is Cambodia's exports to EU countries. My independent variables include the basic variables of the gravity model, the dummy variable of EBA representing the effect of EBA on Cambodia's exports, and the variable ODA, representing the amount of ODA granted by EU member countries in year t to Cambodia as well interaction term between EBA and ODA. The rationale is to understand whether granting ODA complements the LDC to be competitive and able to utilize EBA for export.

I have two questions. (1) As Cambodia is the only exporter of interest, should I use only the exporter-time fixed effect?

(2) While I understand the PPML deals with zero trade value in the dependent variable, which is exactly my case. I also encounter zero ODA value in the independent variable, which after doing the log-linear form, a substantial amount of observations are dropped. I have read previous discussions on the use of PPML in the Log of Gravity by Silva and Tenreyro (2006) and An Advanced Guide to Trade Policy Analysis: The Structural Gravity Model by Yotov, et al., (2016) and seem to understand that by using PPML, I should not take log of the dependent variable, but how about the case where independent variable is zero like my case, should I or should I not take log of independent variable ODA and interaction?

My Stata command for PPML estimation if I do not take log of the ODA independent variable:

ppml camexport EXPORTER_TIME_FE* logcamgdp logeugdp logdistance logeupop loginland landlocked eba oda odainteba, cluster(pair_id)

Thanks in advance for any input.

[Joao Santos Silva]

Dear NY ATYKUNN,

1) No.

2) Indeed you should not log the dependent variable. As for ODA, my suggestion would be that you log it, replace the missing values with zeros, and add to the model a dummy that identifies those observations.

Best wishes,

Joao

[NY ATYKUNN]

Dear Prof Joao Santos Silva,

Thanks for your input and kind suggestion. This along with your other works and contributions in the topic are very helpful.

Best regards,
Atykunn

[NY ATYKUNN]

Dear Prof Joao Santos Silva

Following your kind suggestion, I have regressed the PPML and have every missing value in logODA of the independent variables replaced with zeros. In doing so, I added a dummy variable of those replaced observations. However, can you give your thoughts on how I should interpret that dummy variable of the replaced values, i.e. odazerodummy.

Best regards,
Atykunn
Following you suggestion, I have

[Joao Santos Silva]

Dear NY ATYKUNN,

Suppose ODA is large and positive, and it drops by 1%; the expectation drops by 0.13%. This is true until ODA drops to zero, in which case the expectation drops by exp(0.18) - 1 = 19.7%. Does this make sense?

Best wishes,

Joao

[NY ATYKUNN]

Thanks Prof Joao Santos Silva

This is clear to me. Thanks for enlightening me on this aspect. However, I would like to ask another question. On the logODA which is not statistically significant, should I, in this case, attempt to interpret it which in that case would include interpretation of the zerodummy variable? Please do not mind me, if this sounds rather a clumsy question.

Overall, I am really grateful for your kind contributions to my inquiry, especially considering your massive and significant contribution to the gravity model and international trade. Thanks, Prof.

Best regards,
Atykunn

[Joao Santos Silva]

Dear NY ATYKUNN,

Indeed, I commented on the interpretation but not on the significance. Statistical and economic significance are subtle issues, but here is something that can help. Your sample is relatively small and, assuming that you are clustering standard errors, the number of clusters will be smaller. Therefore we need to be cautious when interpreting statistical significance. As you say, logoad is not significant at the 5% level, but in this case I would say that is OK to take the 10% level as the reference, in which case the estimate is very close to being significant, and it appears to be economically significant. So, I think it is worth interpreting the results. The case of the dummy is different because it is much less significant. This, however, can just be the result of the variable having few values equal to 1. So, I would interpret the estimate, but be cautious about its possible statistical significance.

Best wishes,

Joao

[NY ATYKUNN]

Dear Prof. Joao Santos Silva

Thanks once again for your insightful support of my inquiry. This is really helpful and I will try to follow your suggestion.

Best regards,
Atykunn