I'm trying to estimate this model on immigration levels I found in a paper and I'm not sure if they used OLS or fixed effects, it says that its a simple OLS but then mentions adding the country fixed effects. can someone help?
$\gamma_c$ is the country fixed effect, so this is a fixed effect model.
It's a little misnomer to call a linear regression model without any fixed effect OLS, and one with fixed effect FE. They can both be estimated using an OLS estimator, as long as you have the right variables included (or excluded). But there are more efficient estimator, such as
felm to deal with fixed effect models more efficiently.