# Perfect multicollinearity when estimating a gravity model

everyone!

I am estimating a gravity model in order to analyze the impacts of tighter environmental regulations on international trade. More specifically, I am analyzing Brazil's trade flow.

My (linearized) model is as follows:

$$\ln(EXP) = \ln(GDP_O) + \ln(GDP_D) + \ln(POP_O) + \ln(POP_D) + \dots$$

In other words, the exports from Brazil (origin) to a country D (destination) depend on both countries GDPs,Populations, Total Area and another couple of variables.

My problem is: because Brazil is the origin for the exports to all other countries, GDP_O, POP_O and any other variables representing Brazilian data will be equal for all observations and as such there will be perfect multicollinearity.

How do I circumvent this? Every gravity model uses both the exporter and importer variables in order to explain the bilateral trade flow.

EDIT: See for instance the estimation carried out here: https://drive.google.com/file/d/1DczfoFI_mkI8Tm4H0WcaVZTz9ZXLGb2K/view?usp=drivesdk

EDIT2: Specifically, here:

[Regression table] (https://i.stack.imgur.com/TQDA3.png)

I appreciate any help!

Kind regards, Pedro!

They will simply be sucked up into one variable. To "fix" this, you could simply drop all of Brazil's characteristics and leave a constant in: $$\ln(EXP_D) = c + \beta_1 \ln(GDP_D) + \beta_2 \ln(POP_D) + \ldots$$

## Edit

Just understood the question from the comments below.

If you have only a cross-sectional data, you cannot distinguish the effects of GDP, population, etc. of the origin country (Brazil) on its exports.

One way you could do this is to run a panel regression... then you'll have variation in GDP, population, exports, etc.

In order to do this, you need to assume that the relationship remains the same throughout your sample period. If, for example, you have a change in government, then you might need to control for that, etc.

• That's what I did, but I think it's wrong. Because if I want, for instance, to see the impact of Brazil's GDP on exports I won't be able to. – Pedro Cunha Oct 19 at 4:28
• You mean you want to see impact of Brazil's GDP on export to each destination? – Art Oct 19 at 6:01
• No. I want to regress exports as a function of, among other things, Brazil's GDP. As such, I want to see the effect of GDP on Brazil's exports and not the effect of GDP on exports to each country – Pedro Cunha Oct 19 at 10:20
• Got it. Please see if the edit makes sense. – Art Oct 19 at 10:25
• It does make sense to me, it is what I think. However, I refer you once again to the article I linked, on which the authors estimated all these coefficients in a cross sectional regression. EDIT: please look at the table I've annexed in my original post. – Pedro Cunha Oct 19 at 10:52