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and then

Eyit|wi, ci0, ci1Eyit0|ci0twit.

If we assume

Eyit0|ci0t0 ci0,

then

Eyit|wi, ci0, ci1t0 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, ait0 twit xit0

  • witxittci0 aiwit,

a correlated random coefficient model because the 21

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