Gravity Model with Intranational (Domestic) Flows

[Adarsh Nayak]

Hi,

For my undergrad dissertation I am looking to estimate a gravity model of bilateral M&A flows for countries in Europe from 2000-2012. I have read much of the literature on gravity models for trade and they recommend to include intranational, or domestic, trade flows in the estimation, calculating them by DomTrade = IndustrialProduction - Exports, or something similar to this. For me, as I am looking at M&A deals, it would just be the number of domestic M&A deals for each country. This is something I definitely want to include, as my aim is to measure the extent of home bias in M&A.

My question was regarding the formulation of the model when intranational trade flows are included. When they are excluded a simple cross-sectional specification is:

lnTradeij = a(lnXi) + b(lnXj) + c(lnZij) + eij for i=/=j

where last term is just the error. i is for importer , j is for exporter.
Xi is vector of importer-specific variables (like GDP), Xj is vector of exporter-specific variables (GDP), Zij is vector of pair-specific bilateral variables (distance).
I understand usually there will be importer and exporter FE but just abstracting from that for now.

When intranational trade flows are included, we can have i = j.

1. For the unilateral variables, they now appear twice for these observations - Xi = Xj e.g. GDPi = GDPj. If we include fixed effects for importer and exporter we get the same thing I think - the fixed effects are equal for the domestic observations

Is this an issue - and should this be solved by interacting all the exporter-specific variables Xj with a dummy = 1 when i=/=j? So replacing Xj with (INTERij * Xj) where INTERij = 1 when i=/=j

The idea being that monodic variables should not enter twice if i = j.

2. For the dyadic (bilateral) variables Zij like distance, I collected them from the CEPII database and some are counterintuitively coded e.g. (ComLangij, a dummy for whether i and j share same official language, is 0 when i=j). The interpretation for some of them is also a bit ambiguous when i=j e.g. FTAij, a dummy that equals 1 when countries share a free trade agreement.
Would these need to be recoded by me to make intuitive sense, or does their value for domestic trade flows not matter when a HOMEij dummy is also included as a regressor.

In other words, putting 1 and 2 together, is the below a suitable specification to run in the presence of domestic trade flows:

lnTradeij = k(HOMEij) + a(lnXi) + b(lnXj * INTERij) + c(lnYij) + eij for all i,j

where HOMEij = 1 when i = j
and INTERij = 1 when i=/=j (so they are just opposites)


Apologies if this question is not Stata-focused enough and more metrics-focused.

If anyone could help out or point me in the right direction for the correct way to include intranational flows in the gravity model, I would be very grateful.

Thank you!

[Joao Santos Silva]

Dear Adarsh Nayak,

On 1, do not worry about it. The standard approach is just to include the fixed effects and the home dummy, often interacted with time.
On 2, again the standard is to let variables like FTA to be zero when i=j, but include also the pair fixed effect.
Finally, do not log the dependent variable and estimate the model by Poisson regression using the command ppmlhdfe. See more here.

Best wishes,

Joao

[Adarsh Nayak]

Dear Professor Santos Silva,

Thank you so much for the advice! It is very helpful. I have in fact been using the PPML estimator with the ppmlhdfe command to obtain my results (keeping the dependent variable in levels), having discovered your work in this area

For question 2:

From what I understand, the coefficient on the home dummy (and other bilateral time-invariant variables like distance) can be estimated in the presence of importer-time and exporter-time fixed effects, but not once a pair fixed effect is included as it absorbs them. I understand that by interacting the home dummy with time we would still be able to see how home bias changes over time even in the presence of the pair fixed effects, which would be interesting.

However, if I wanted to estimate the actual level (not change over time) of the coefficient on the home dummy, I would need to drop the pair fixed effect (and include control variables like SameLanguage, Contiguity etc.). This is something I am looking to do, as I first need to establish that there is indeed evidence of home bias. Given this,

a) Without the pair FE, would it still be the standard to let bilateral variables be zero when i=j? (I guess this is equivalent to multiplying them by an INTERNATIONAL dummy). Internal distance usually seems to be defined as some function of each country's surface area and not 0, as an example.

b) If we do zero the bilateral variables when i=j, can the coefficient on HOME still be interpreted as the home bias - how much more country i trades with itself, when compared to trade with an international trading partner, otherwise identical to country i?


[For transparency and to help anyone with similar questions, I initially cross-posted this query here: https://stats.stackexchange.com/ques...c-trade-flows]

Best wishes,
Adarsh

[Joao Santos Silva]

Dear Adarsh Nayak,

I suggest you discuss these issues with your supervisor because I do not know enough about what you are doing and therefore can give you incorrect advice.

Best of luck,

Joao

[Adarsh Nayak]

Dear Professor Santos Silva,

Yes I will definitely do so - thank you for your help.

For the benefit of anyone who comes across this post, I found a useful paper that explicitly addresses the question of how bilateral (binary) variables should be defined for intranational (domestic) trade flows: 'National Borders, Trade and Migration' (Helliwell, 1997). In the paper it is explained on pg9 that setting these variables (e.g. common language) to 0 or 1 when i=j is a matter of how you define the home bias you are trying to estimate. Setting them equal to 0 will lead to a greater home bias estimate that also absorbs the effect of the bilateral variable. The choice simply depends on what counterfactual you are measuring your home bias against - different papers take different approaches because the specific quantity representing home bias does not have a consistent definition in the literature.