ARE213, Section 7, Hendrik Wolff Advantage Disadvantage Scale Variance Estimates Needed Boundary Comments LR= 2(L u (b u )-L u (b r )) - None of the 6 (4) choices to made for estimating Info - Don’t need to estimate Info: Advantage, because of Info often is difficult or inaccurate - need both, restricted and unrestricted estimates LR is scale invariant to reparametrizations of conditional density b u and b r True parameter must be in the interior of parameter space (because the derivation of LR makes use of the Central Limit Theorem 2 comes from the second derivatives of Taylor Series Expansion Wald= N (b u0 -b r0 ) T Info0 0-1 (b u - b r ) Wald= N c(b u ) T c ’T Info c ’ c(b u ) - In simplest case: We only need to estimate the model once unrestrictedly. Sometimes b u is easier than b r , e.g. imposing symmetry conditions on Slutzky in demand system Scale variant True parameter must be in interior of the parameter space Scale variant !
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