Econometric theory and methods, Russell Davidson - Chapter 13 potx

... 1999, Russell Davidson and James G. MacKinnon Chapter 13 Methods for StationaryTime-Series Data 13. 1 IntroductionTime-series data have special features that often require the use of special-ized ... a wayCopyrightc 1999, Russell Davidson and James G. MacKinnon 547 13. 3 Estimating AR, MA, and ARMA Models 563limit and the factor of n−1in expression (13. 47) and replace Ω by a suitableestimate, ... denotes the standard normal density. The ﬁrst factor in (13. 85) isCopyrightc 1999, Russell Davidson and James G. MacKinnon 13. 2 Autoregressive and Moving Average Processes 555Equation (13. 25) provides...

Econometric theory and methods, Russell Davidson - Chapter 9 potx

... moments and the inverse of the matrix WΩ0W. Equivalently, it is aquadratic form in n−1/2W(y − Xβ) and the inverse of n−1WΩ0W, sinceCopyrightc 1999, Russell Davidson and James ... the Newey-West esti-mator, and shows that, in some circumstances, they may perform better thanit does in ﬁnite samples. A diﬀerent approach to HAC estimation is suggestedby Andrews and Monahan ... elements ht(yt) and m∗t(u∗t, θ), respectively. We see that the covariance matrix Ω has two com-ponents, one due to the randomness of the data and the other due to therandomness of the...

Econometric theory and methods, Russell Davidson - Chapter 1 docx

... horizontally.Similarly, X11 and X21have the same number of columns, and also X12 and X22, as required for the submatrices to ﬁt together vertically as well.Copyrightc 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 independent values utof the ... of computer-generated random numbers as pseudo-random.However, for the purposes of simulations, the numbers computers provide haveall the prop erties of random numbers that we need, and so we...

Econometric theory and methods, Russell Davidson - Chapter 2 doc

... OC.Copyrightc 1999, Russell Davidson and James G. MacKinnon2.4 The Frisch-Waugh-Lovell Theorem 69by looking again at Figure 2 .13, in which the constant ι plays the role of X1, and the centered ... least squares esti-mates, which we will refer to as the Frisch-Waugh-Lovell Theorem, or FWLTheorem for short. It was introduced to econometricians by Frisch and Waugh(1933), and then reintroduced ... 2.8, and imagine that the angle θbetween x1 and x2tends to zero. If θ = 0, then x1 and x2are parallel, and wecan write x1= αx2, for some scalar α. But this means that x1−αx2= 0, and so...

Econometric theory and methods, Russell Davidson - Chapter 3 ppt

... regressors and their cross-products. Thus there should not be too muchdependence between XtiXtj and XsiXsjfor s = t, and the variances of thesequantities should not differ too much as t and ... (3.19)Copyrightc 1999, Russell Davidson and James G. MacKinnon3.6 Residuals and Error Terms 109The consistency ofˆβ implies thatû → u as n → ∞, but the finite-sampleproperties ofû ... aboutˆβ is that it is now, in general, biased. Sub-stituting the right-hand side of (3.59) for y in (3.04), and taking expectationsconditional on X and Z, we find thatE(ˆβ) = E(XX)−1X(Xβ0+...

Econometric theory and methods, Russell Davidson - Chapter 4 ppt

... theCopyrightc 1999, Russell Davidson and James G. MacKinnon4.3 Some Common Distributions 131 the rest of this section, we therefore use lower-case letters to denote bothrandom variables and the arguments ... nopossible confusion.Copyrightc 1999, Russell Davidson and James G. MacKinnon4.3 Some Common Distributions 133 where z1, z2, and z3are mutually independent standard normal variables, thenb1z1+b2z2is ... the sum of m independent, squared, standardnormal random variables. From the deﬁnition of the chi-squared distribution,Copyrightc 1999, Russell Davidson and James G. MacKinnon4.4 Exact Tests...

Econometric theory and methods, Russell Davidson - Chapter 5 ppsx

... factor on the right-hand side tends to S−1XXas n → ∞, and the second factor, which is just v, tends to a random vector distributed asCopyrightc 1999, Russell Davidson and James G. MacKinnon5.3 ... 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 makes perfect sense, ... definition. Any τ greater than themedian is in the right-hand tail of the distribution, and any τ less than themedian is in the left-hand tail.Exact Confidence Intervals for Regression CoefficientsIn...

Econometric theory and methods, Russell Davidson - Chapter 6 docx

... 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 assumptionin (6.02) is enough to allow us to apply a law of large numbers to that sum. Itfollows that the right-hand side, and therefore also the left-hand side, of ... 5.5,ˆΩ can, and probably should, be replaced by amodiﬁed version with better ﬁnite-sample properties.Copyrightc 1999, Russell Davidson and James G. MacKinnon6.5 The Gauss-Newton Regression...

Econometric theory and methods, Russell Davidson - Chapter 7 doc

... matrix-weighted averages of the within-groups, or fixed-effects, estimator (7.85) and Copyrightc 1999, Russell Davidson and James G. MacKinnon Chapter 7Generalized Least Squares and Related Topics7.1 IntroductionIf ... the2See Dufour, Gaudry, and Liem (1980) and Betancourt and Kelejian (1981).Copyrightc 1999, Russell Davidson and James G. MacKinnon300 Generalized Least Squares and Related Topicsof the ... discuss here; see Arellano and Bond (1991) and Arellano and Bover (1995).Fixed-Effects EstimationThe model that underlies fixed-effects estimation, based on equation (7.82) and the simplified version...

Econometric theory and methods, Russell Davidson - Chapter 8 pot

... terms.Copyrightc 1999, Russell Davidson and James G. MacKinnon8.3 Instrumental Variables Estimation 313 It can be seen from this solution that pt and qtwill depend on both udt and ust, and on every ... (1999), Donald and Newey(2001), Hahn and Hausman (2002), Kleibergen (2002), and Stock, Wright, and Yogo (2002). There remain many unsolved problems.Copyrightc 1999, Russell Davidson and James ... (1994),Bound, Jaeger, and Baker (1995), Dufour (1997), Staiger and Stock (1997),Wang and Zivot (1998), Zivot, Startz, and Nelson (1998), Angrist, Imbens, and Krueger (1999), Blomquist and Dahlberg (1999),...

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