Eyit|wi, ci0, ci1 Eyit0|ci0 twit.
If we assume
Eyit0|ci0 t0 ci0,
Eyit|wi, ci0, ci1 t0 ci0 twit,
an estimating equation that leads to FE or FD (often with t . ∙ If add strictly exogenous covariates, and assume linearity of conditional expectations, and allow the gain from treatment to depend on xit and an additive unobserved effect ai, get
Eyit|wi, xi, ci0, ai t0 twit xit0
witxit−t ci0 aiwit,
a correlated random coefficient model because the 21