Good afternoon! I am estimating a PPML gravity model of trade adding an index of ethnic fractionalisation for each country as independent variables. Ethnic fractionalisation is a continuous variable from 0 to 1 which is a probability that two random individuals in a country are from different ethnic groups.

I had two basic questions regarding the model. First, should I log-transform ethnic fractionalisation or keep it in the standard form (all other variables besides dependent variable and dummies are logged)? Second, If I want to study the interaction between ethnic diversities in two countries, can I add ethnic1 * ethnic2 in the model or it may bias the estimates? Thank you for your help!