Econometric theory and methods, Russell Davidson - Chapter 14 pot

... hypothesis. Dickey-Fuller tests of the null hypothesis that there is a unit root may be based on any of regressions (14. 15), (14. 18), (14. 21), or (14. 22). In practice, regressions (14. 18) and ... dr, Copyright c  1999, Russell Davidson and James G. MacKinnon Chapter 14 Unit Roots and Cointegration 14. 1 Introduction In this chapter, we turn our attention to models for a...

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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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... particular, Lee and King (1993) and Demos and Sentana (1998) have proposed various tests which take into account the fact that the alter- native hypothesis is one-sided. These one-sided tests have ... set- ting up the complicated loglikelihood. The estimates are not equal to ML es- timates, and are in general less efficient, although in some cases they are Copyright c  1999, Russell...

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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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... 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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... in the Copyright c  1999, Russell Davidson and James G. MacKinnon 4.5 Large-Sample Tests in Linear Regression Models 147 regressions on the two subsamples. If SSR 1 and SSR 2 denote the sums ... 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...

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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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... 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 ... are Copyright c  1999, Russell Davidson and James G. MacKinnon 6.7 Hypothesis Testing 241 6.7 Hypothesis Testing Hypotheses about the parameters of nonlinear regression mo...

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