PPML Method

[Murry Siyasiya]

Dear colleagues,

I am estimating trade potential in Africa and I happen to use the PPML method to estimate the gravity equation of trade and using cross section data. Here are my questions (seeking clarifications in case I may be doing something wrong):
1) What problems must I anticipate and therefore keep an eye on?
2) What formal tests should I conduct?
3) Does the PPML method automatically correct for heteroskedasticity, autocorrelation (?? since its cross section data), model misspecification etc.?

Your insights will be highly appreciated (I will also appreciate if you post with references where possible).

[Joao Santos Silva]

Dear Murry Siyasiya,

I suggest you have a look at this paper. In response to your questions:
1) The main thing is to get good data and then follow the standard approach, as explained here. There are several commands that implement the PPML estimator, but I recommend you use ppmlhdfe.
2) No tests are essential, but it is useful to perform a RESET.
3) Heteroskedasticity and correlation are not a problem if you cluster the standard errors (or use robust in a cross section).

Best wishes,

Joao

[Murry Siyasiya]

Dear Joao Santos Silva,

Thanks for your response. It has helped me a great deal!

Good times.

[Maadouhan Konare]

Dear Joao Santos Silva,

I need clarifications concerning the estimation of the gravity model of trade.

In the paper you suggested to have a look "An Advanced Guide to Trade Policy Analysis", I encountered some difficulties to understand something about the introduction of fixed effects.

At the page 44, they state that "No constant term is included in the presence of the fixed effects". What can be the reason for excluding the constant term from the model ? Does the PPML method care about that fact ?

I appreciate your thoughts on ths.

Kind regards

[Joao Santos Silva]

Dear Maadouhan Konare,

The including fixed effects is the same as including a different constant for each group, so there is no overall constant because it would be collinear with the fixed effects. This is not just with PPML but with any estimator.

Best wishes,

Joao

[Maadouhan Konare]

Thank you very much Dear Joao for your quick response.

I understand better now. However I still don't get the reason why after running the ppml command in order to estimate my model, the result show a constant term.

I'm trying to calculate trade potential for Senegal towards its african partners. And to do so, I first need to estimate the gravity model.

For that, I run the following syntax :

ppml Trade ln_PIB_i ln_PIB_j ln_Dist_ij F_ij L_ij C_ij CEDEAO_j dimp* dyear*, cluster(pairid)

Where PIB_i PIB_j stand for the exporter's and import's GDPs.

Dist_ij is the distance between Senegal and its african partners

F_ij L_ij C_ij are dummies variables for common border, common language and contiguity

CEDEAO_j is our trade policy variable which equal 1 if the importer belong to ECOWAS and 0 else.

As I said early, the result come with a constant term. Am I doing something wrong ?

[Maadouhan Konare]

*Dear Joao Santos Silva

[Joao Santos Silva]

Dear Maadouhan Konare,

The constant is reported because one of the fixed effects is dropped, but its coefficient has no meaning (it is actually the coefficient on the dropped FE). You can estimate the model with the noconstant option and you will see that the results are the same but no FE is dropped.

Best wishes,

Joao

[Maadouhan Konare]

Thank you very much Dear Joao Santos Silva for your prompt answers.

You can't imagine how much you helped me.

Best wishes.

[Maadouhan Konare]

Hello Dear Joao Santos Silva !

First of all I sincerely thank you for your replies of the last time. It has helped me a great deal.

I'm back again with a concern about one of your posts with which I need further explanations if possible.

You said "In the contxt of non-linear models such as the one estimated by PPML, the random effect estimators are not interesting because they depend on very strong assumptions".

May I ask which "strong assumptions" are you refering to ? Can you shed more light about that please ?

Kind regards.

[Maxence Morlet]

Dear Maadouhan Konare, random effects methodology assumes that regressors are uncorrelated with the time-invariant unobserved heterogeneity (aka unit fixed-effects). This assumption is generally tested using a Mundlak (1978) or Hausman test, but is pretty much always implausible because much too stringent.

[Joao Santos Silva]

Dear Maadouhan Konare,

In addition to Maxence helpful reply, in non-linear models we need to specify the distribution of the random effects and integrate them out either numerically or analytically. In general, if we do not specify the distribution of the RE correctly, the estimator is inconsistent. That means that in non-linear models, the consistence of the RE estimator generally depends on the validity of the assumptions made about the distribution of the RE. In contrast, the validity of the Poisson regression with fixed effects does not depend on any specific assumptions about the distributions (check out Jeff Wooldridge's 1999 paper on this).

Best wishes,

Joao

[SALSABILA DYAN PRATIWI]

Dear Professor Joao Santos Silva,

I have a question regarding the use of PPML for a gravity model. I am working with a dataset containing 240 observations, consisting of 10 exporters, 1 importer (Indonesia), 6 HS6 products, and 4 years (2021–2024). My main concern is whether PPML can be appropriately applied to this data structure and whether the estimation results can still be considered valid with only one importer. In this case, I am also unsure about the appropriate fixed-effects specification. Should I use exporter and importer fixed effects, as commonly used in bilateral gravity models, or would year fixed effects be sufficient given that there is only one importer? This is particularly important for my study because I need to estimate the distance coefficient separately for CIF and FOB trade flows. I would greatly appreciate your advice on whether this specification is appropriate and how you would recommend setting up the fixed effects in this case.

Thank you very much for your time and guidance.

Kind regards,
Salsabila Dyan Pratiwi

[Joao Santos Silva]

Dear SALSABILA DYAN PRATIWI,

Your dataset is rather small, but you can still use PPML. About fixed effects, the standard is to use importer-year and exporter-year FE, but with a single importer (if I am not mistaken) this reduces to exporter-year and year fixed effects. Anyway, if you use ppmlhdfe, you can specify importer-year and exporter-year FE as usual and let the command drop what is not needed.

Best wishes,

Joao

[SALSABILA DYAN PRATIWI]

Dear Professor Joao Santos Silva

Thank you very much for your previous clarification.

I have another question regarding the fixed effects specification. In my estimation, I use weighted average distance as the main variable to estimate the distance coefficient for trade under-invoicing analysis. I also include RTA, contiguity, population, GDP, and common language as explanatory variables. However, the weighted average distance variable is time-invariant in my dataset. Therefore, when I include exporter-year fixed effects as suggested, ppmlhdfe drops the weighted average distance variable due to collinearity. In this case, would it be acceptable to estimate the model using only year fixed effects, so that the distance coefficient can still be identified? Or would this create an important econometric issue because exporter-specific characteristics are no longer absorbed by fixed effects? I would greatly appreciate your advice on the appropriate specification for this case.

Thank you very much for your time and guidance.

Kind regards,
Salsabila Dyan Pratiwi