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Mikkel, Solvsten ; Raffaele, Saggio ; Raffaele, Saggio ; Patrick, Kline ; Mikkel, Sølvsten. (2019) Leave-out estimation of variance components.
In: Papers. RePEc:arx:papers:1806.01494.
Full description at Econpapers
cites:
Fast computation of these scores is an active area of research in computer science (see, e.g., the discussion in Drineas et al., 2012). We use recent advances in this area to illustrate how these scores can be computed efficiently in two-way fixed effects models. Without loss of generality, we can write the model of Section 7.2 as yi = x0 iβ + εi where xi = (d0 i, − ˙ f0 i)0 , ˙ fi = (1j(g,t)=0, . . . , 1j(g,t)=J )0 , β = (α0 , −È0 )0 and È = (È0, . . . , ÈJ ). It is easy to verify that in this case Sxx = L̇ where L̇ is the weighted Laplacian associated with the bipartite graph G formed by workers and firms. This implies that: Pii = x0 iS†xxxi = L̇†g,g + L̇†N+j(g,t),N+j(g,t) − 2L̇†g,N+j(g,t) = (eg − eN+j(g,t)) 0 L̇†(eg − eN+j(g,t)) = (eg − eN+j(g,t)) 0
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