Dear Statalisters,

I want to know whether I can estimate a long-difference regression using PPML.

I am estimating: ln(Commuters_i,j,2000) - ln(Commuters_i,j,1990) = β * (TravelTime_i,j,2000 - TravelTime_i,j,1990) + Controls + Errors, where the left-hand side (LHS) is the 1990-2000 log change in the number of commuters from i to j, and the main right-hand side (RHS) variable is the 1990-2000 change in the travel time from i to j.

I have some instrumental variables (IVs) for the main RHS variable. I have to run the above long-difference regression, instead of a usual panel regression, because my IVs are time-invariant. My advisor suggested me to run the long-difference regression using PPML, because commuting flows are like trade flows and the above regression can indeed be motivated by a gravity model. However, I am confused becasue by differencing, the LHS can be negative and PPML seems to deal with only positive LHS variables.

Can you help me with this? Many thanks!

Best,
Xavier