By Thomas S. Ferguson
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Additional resources for Mathematical Statistics. A Decision Theoretic Approach
To do this, we select a GLS estimator. The GLS estimator is as follows: Page 34 Given where unt = lt + µn + xnt and lt are random over time and distributed N (0, s2lj) µn are random over cross sections and distributed N (0, s2my) and xnt are random over space and time and distributed N (0, s2ls2ny). At this point, we do not assume lt = rlt1 + nt and s2l = r2n/1r2. 15 This is an ARMA variation of the GLS model we take up in the next section. The joint distribution now looks like: jii = s2l + s2m + s2n and the covariance between disturbances for two different cross-sections is: jij = s2l.
1 and rewriting as follows: where unt = lt + µn + xnt Therefore: for n = (1 N) cross sections and t = (1 T) time series. The lt and mn are assumed to be "fixed" conditionally in the intercept while xnt is assumed to be random. The LSDV model should be used with some caution as it could be less efficient than other estimators and information could be lost when the X vector contains time invariant variables. 11 Earlier in this discussion, it was claimed that the difference between fixed or random effects was not worth pursuing too vehemently, but when an intercept is introduced this issue must be given more scrutiny.
Since the coefficient of interest, however, is no longer neatly interpretable as the change in the level of international conflict for a one-unit change in internal conflict, it is preferable to retain the unscored data but adjust the coefficient to reflect nonconstant variance. This adjustment can be derived in many ways, but only four general ways are discussed here. 129 als? Let us begin to answer this question with the constant coefficients model. Page 19 3. The Constant Coefficients ModelA In the constant coefficients model, we assume that all the coefficients are the same for each cross-section in the pool.
Mathematical Statistics. A Decision Theoretic Approach by Thomas S. Ferguson