I am doing a panel regression in which time relative towards an event (migration) is included. this is done by the sum of dummies modelling k, which signifies the effects of being a migrant start at T0 and ending in T1. For example, k=-1signifies the effects of one year before migrating, and k=1 are the effects of 1 year after migration. This is modelled by a series of dummies from k=-4 to k=6. this is modelled in the attached paper as well in a fixed-effects model. I intend to use a Mundlak specified random-effects model, to include time-invariant variables.

In a Mundlak specification, the group mean is included in the model to specifically model the between effects. However, with dummies, it seems a bit nonsensical to create a group mean which will only be equal to one at one point in the entire model. Does anyone know how to include this or have suggestions for a different approach around the dummies?