The method of elimination and substitution in the GMM estimation of mixed regressive, spatial autoregressive models

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GMM estimation of social interaction models with centrality (2010, methodology): “Based on a transformed model that has the group dummies eliminated, Lee et al. (2009) has generalized the ML estimation approach in Lee (2007b) to the network model with a sociomatrix having constant row sums (including the special case of a row-normalized sociomatrix).4 However, when the…”
EFFICIENT GMM ESTIMATION OF HIGH ORDER SPATIAL AUTOREGRESSIVE MODELS WITH AUTOREGRESSIVE DISTURBANCES (2009, methodology): “It follows from Lee (2007a) that n = ( 0kIV×kIV μ3 Q′nωnm μ3ω ′ nm Qn (μ4 −3σ 40 )ω′nmωnm ) + Vn, (9) with ωnm = [vecD(P1n), . . . ,vecD(Pmn)], and Vn = σ 40 ⎛⎜⎜⎜⎜⎝ 1 σ 20 Q′n Qn 0kIV×1 · · · 0kIV×1 01×kIV tr(Ps1n P1n) · · · tr(Ps1n Pmn) ... ... . . . ... 01×kIV tr(Psmn P1n) · · · tr(Psmn…”
Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances (2010, unknown): “It is not difficult to see that this linear independence condition is an analog to the identification conditions postulated in Lee (2007b), Assumption 5(b), relating to quadratic forms under homoskedasticity.”