A MONOTONIC PROPERTY FOR ITERATIVE GLS IN THE 2-WAY RANDOM EFFECTS MODEL
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This paper shows that maximum likelihood estimation for the two-way random effects model can be obtained as an iterated GLS procedure based on two subsets of the parameters: The first subset contains the regression coefficients , and the second subset contains two variance components ratios, 1 and 2. Fixing i (i=1, 2) and iterating between and j (j=1, 2 and ji), the sequence of j's generated by this algorithm form a monotonic sequence. This result is an extension of Breusch's (1987) 'remarkable property' for iterative GLS from the one-way to the two-way model. Since the i's are both between zero and one, a search over i while iterating on the other j and will guard against the possibility of multiple local maxima of the likelihood function. However, such a search procedure can be relatively costly. This paper suggests an alternative computationally more efficient algorithm which makes use of Deaton's (1975) ridge-walking algorithm and Breusch's (1987) monotonic property. The proposed algorithm is shown to converge rapidly for the investment equation considered by Grunfeld (1958). 1992.
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