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 Mgt are not large, might worry about
̂ ignoring the estimation error in the gt. Can instead
aggregate the equations over individuals, giving
ȳgt t g xgt z̄gt vgt ūgt, t 1, . . , T, g 1, . . . , G.
Can estimate this by FE and use fully robust inference because the composite error,
rgt ≡ vgt ūgt, is weakly dependent.