Estimating effects of perfectly collinear regressors in PPML gravity model

[Robert Pham]

Dear Joao Santos Silva and others,

I am currently trying to estimate a sectoral augmented gravity model using panel data, with standard trade cost proxies (distance, contiguity, common language, colonial ties) augmented with an additional variable that is varying at the destination-year level. When I try to estimate the gravity equation with

ppml_panel_sg

, unfortunately this variable gets omitted due to collinearity, which is unfortunate because it is my main variable of interest.

My question: Is there a way to work around this issue (by for example transforming the variable somehow or using other estimation techniques)?

Thank you in advance,
RP

[Maxence Morlet]

Can you type up your equation? If you include destination year fixed effects, as is standard in the gravity literature, then your variable will be collinear with the fixed effects and dropped. No transformation will fix that. It must vary within the fixed effects.

[Robert Pham]

Thank you for your answer. As I am doing industry level gravity analysis, I include origin-industry-time, and destination-industry-time fixed effects along with origin-destination-industry effects. My variable of interest is destination-year specific.

[Maxence Morlet]

Your variable of interest is collinear with destination-industry-time fixed effects.