Econometric theory and methods, Russell Davidson - Chapter 15 docx

... (15. 13) can be based on the following Gauss-Newton regression: u t ( ˆ β) = X t ( ˆ β)b + cz t ( ˆ β) + residual, (15. 20) Copyright c  1999, Russell Davidson and James G. MacKinnon Chapter 15 Testing ... elements of r, and Z t and r t are, respectively, the t th row and t th element of Z and r. Copyright c  1999, Russell Davidson and James G. MacKinnon 664 Testing...

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... horizontally. Similarly, X 11 and X 21 have the same number of columns, and also X 12 and X 22 , as required for the submatrices to fit together vertically as well. Copyright c  1999, Russell Davidson and James ... of the error terms, if necessary spec- ifying parameters such as its mean and variance; • Use a random-number generator to generate the n successive and mutu- ally...

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... include Bard (1974), Gill, Murray, and Wright (1981), Quandt (1983), Bates and Watts (1988), Seber and Wild (1989, Chapter 14), and Press et al. (1992a, 1992b, Chapter 10). There are many algorithms ... has mean 0, and the IID assumption in (6.02) is enough to allow us to apply a law of large numbers to that sum. It follows that the right-hand side, and therefore also the left...

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... OC. Copyright c  1999, Russell Davidson and James G. MacKinnon 2.4 The Frisch-Waugh-Lovell Theorem 69 by looking again at Figure 2.13, in which the constant ι plays the role of X 1 , and the centered ... least squares esti- mates, which we will refer to as the Frisch-Waugh-Lovell Theorem, or FWL Theorem for short. It was introduced to econometricians by Frisch and Waugh (1933), an...

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... regressors and their cross-products. Thus there should not be too much dependence between X ti X tj and X si X sj for s = t, and the variances of these quantities should not differ too much as t and ... (3.19) Copyright c  1999, Russell Davidson and James G. MacKinnon 3.6 Residuals and Error Terms 109 The consistency of ˆ β implies that ˆ u → u as n → ∞, but the finite-sample...

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... provided in Davidson and MacKinnon (1993). How- ever, it is impossible to understand large parts of econometrics without having some idea of how asymptotic theory works and what we can learn ... the sum of m independent, squared, standard normal random variables. From the definition of the chi-squared distribution, Copyright c  1999, Russell Davidson and James G. MacKinnon 4.4 E...

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... factor on the right-hand side tends to S −1 X  X as n → ∞, and the second factor, which is just v, tends to a random vector distributed as Copyright c  1999, Russell Davidson and James G. MacKinnon 5.3 ... may still seem strange that the lower and upper limits of (5.13) depend, respectively, on the upper-tail and lower-tail quantiles of the t(n − k) distri- bution. This actually...

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... matrix- weighted averages of the within-groups, or fixed-effects, estimator (7.85) and Copyright c  1999, Russell Davidson and James G. MacKinnon Chapter 7 Generalized Least Squares and Related Topics 7.1 Introduction If ... the 2 See Dufour, Gaudry, and Liem (1980) and Betancourt and Kelejian (1981). Copyright c  1999, Russell Davidson and James G. MacKinnon 300 Gener...

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... (1999), Donald and Newey (2001), Hahn and Hausman (2002), Kleibergen (2002), and Stock, Wright, and Yogo (2002). There remain many unsolved problems. Copyright c  1999, Russell Davidson and James ... terms. Copyright c  1999, Russell Davidson and James G. MacKinnon 8.3 Instrumental Variables Estimation 313 It can be seen from this solution that p t and q t will depend...

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... moments and the inverse of the matrix W  Ω 0 W. Equivalently, it is a quadratic form in n −1/2 W  (y − Xβ) and the inverse of n −1 W  Ω 0 W, since Copyright c  1999, Russell Davidson and James ... the Newey-West esti- mator, and shows that, in some circumstances, they may perform better than it does in finite samples. A different approach to HAC estimation is suggested by Andrew...

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