International trade gravity model

[Bhishma Raj Dahal]

Hello everyone! I hope you're well. Firstly, I apologize for posting a perhaps simplistic question. I'm working on trade analysis using the gravity model, specifically sectoral analysis, focusing on a particular commodity (let's call it X). At the same time, I have some understanding of the significance of intra-national trade within the structural gravity model. My confusion arises from the fact that, since I am analyzing only one commodity, some countries, although involved in export/import, may not have domestic production. In this context, my question is whether a country's ability to engage in domestic trade (intranational trade: A to A) should be considered zero or if the country pair (with itself) should be excluded. I appreciate your time! Thank you!

[Bhishma Raj Dahal]

Dear Joao Santos Silva , Jeff Wooldridge , and Tom Zylkin I would be grateful for your insights on the above question. Please help me!

[Tom Zylkin]

Hi Bhishma,
I agree it is possible for a country's intra-national trade for a particular commodity could be 0, in which case it should be fine to record it as a 0. However, if you are not sure that the value is indeed 0, you can instead treat it as missing.
Regards,
Tom

[Bhishma Raj Dahal]

Tom Zylkin Thank you for your kind reply. So, if it's not a true zero and I treat it as missing, in that case, I may have an unbalanced panel. So, it will not be a true structural gravity model, right? Therefore, can you please tell me what kind of analysis will be restricted (Welfare analysis or more) if I have an unbalanced panel in the context of gravity (structural) model? Is there anything that I need to know and consider while performing analysis and more? Thank you!

[Tom Zylkin]

Tom Zylkin Thank you for your kind reply. So, if it's not a true zero and I treat it as missing, in that case, I may have an unbalanced panel. So, it will not be a true structural gravity model, right? Therefore, can you please tell me what kind of analysis will be restricted (Welfare analysis or more) if I have an unbalanced panel in the context of gravity (structural) model? Is there anything that I need to know and consider while performing analysis and more? Thank you!

Hi Bhishma,
Technically I would not agree you no longer have have a structural gravity model if you have an unbalanced panel, at least not for estimation purposes. The model is what you write down on paper to describe the data (actually the "population" or "data generating process" behind the data). The sample data you have is what you use to estimate the parameters of the model. We just need to make sure the model is well specified (not missing anything important) and that you have enough information on each of the key parameters to be estimated. Only the former consideration is a matter of modelling; the latter is strictly a matter of econometrics.

That said, yes if you want to do a general equilibrium welfare analysis based on the estimated parameters, the missing values are a problem there. The standard practice in that case would be to impute the missing values before computing the model results. For missing internal trade values for a particular commodity, you could impute them based on the domestic sales shares for other similar commodities I suppose.

Hope this makes sense and is helpful!

Regards,
Tom

[Bhishma Raj Dahal]

Tom Zylkin Thank you for your kind response. I have an additional question, and I apologize for bothering you. If the objective is to conduct a general equilibrium welfare analysis based on the estimated parameters, and there are multiple products, and I want to use an importer-exporter-product-year fixed effect, do I need to have a balanced panel of both inter and intra-national trade for each product?

[Tom Zylkin]

Tom Zylkin Thank you for your kind response. I have an additional question, and I apologize for bothering you. If the objective is to conduct a general equilibrium welfare analysis based on the estimated parameters, and there are multiple products, and I want to use an importer-exporter-product-year fixed effect, do I need to have a balanced panel of both inter and intra-national trade for each product?

For the welfare analysis, you need at least one year of data with a complete network of trade flows that can serve as your "baseline". Then you can compute the change in equilibrium relative to that baseline of a change in the parameter values or of a change in policies. For the estimation of the parameters, it should not affect the validity of the estimates if you have an unbalanced panel so long as the model is correctly specified and you have enough data.