policies can switch on and off over time. ∙ With large G and small T, one can estimate an unstricted variance matrix _{g }and proceed with GLS – this is the approach suggested by Kiefer (1980) and studied more recently by Hausman and Kuersteiner (2003). Works pretty well with G 50 and T 10, but get substantial size distortions for G 50 and T 20. ∙ If the M_{gt }are not large, might worry about

̂ ignoring the estimation error in the _{gt}. Can instead

aggregate the equations over individuals, giving

ȳ_{gt } _{t } _{g } x_{gt} z̄_{gt} v_{gt } ū_{gt}, t 1, . . , T, g 1, . . . , G.

Can estimate this by FE and use fully robust inference because the composite error,

r

_{gt }≡ v_{gt } ū_{gt}, is weakly dependent.

16

(10)