Econometric theory and methods, Russell Davidson - Chapter 1 docx
... factors. 1. 17 Consider the following example of multiplying partitioned matrices: A 11 A 12 A 21 A 22 B 11 B 12 B 21 B 22 = A 11 B 11 + A 12 B 21 A 11 B 12 + A 12 B 22 A 21 B 11 + A 22 B 21 A 21 B 12 + ... = k 1 k 2 X 11 X 12 n 1 X 21 X 22 n 2 with the submatrix X 11 of dimensions n 1 × k 1 , X 12 of dimensions n 1 × k 2 ,...
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... include Bard (19 74), Gill, Murray, and Wright (19 81) , Quandt (19 83), Bates and Watts (19 88), Seber and Wild (19 89, Chapter 14 ), and Press et al. (19 92a, 19 92b, Chapter 10 ). There are many algorithms ... (6 .12 ), we obtain α(β 1 , β 2 ) = plim n→∞ n 1 n t =1 (β 0 1 − β 1 ) + 1 / t (β 0 2 − β 2 ) + u t n 1 n t =1 1 / t (β 0 1 − β 1 ) +...
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... vari- ables 1 , 2 , 2 , 3 , and 4 . Consider the nonnested linear regression models H 1 : = α 1 + β 1 1 + β 2 2 + , and H 2 : = α 2 + γ 1 1 + γ 2 2 + γ 3 3 + γ 4 4 + . Copyright c 19 99, Russell Davidson ... (15 .12 ) by the somewhat weaker condition plim n→∞ µ 1 − n n t =1 m t (y t , θ) = 0. (15 .13 ) The empirical counterpart of the left-hand side of condition (15...
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Econometric theory and methods, Russell Davidson - Chapter 2 doc
... show that P X P 1 = P 1 , we proceed as follows: P X P 1 = P X X 1 (X 1 X 1 ) 1 X 1 = X 1 (X 1 X 1 ) 1 X 1 = P 1 . The middle equality follows by noting that P X X 1 = X 1 , because all ... matrix, which is 5 × 3: 1 0 1 1 4 0 1 0 1 1 4 0 1 0 1 . (2 .16 ) Copyright c 19 99, Russell Davidson and James G. MacKinnon...
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Econometric theory and methods, Russell Davidson - Chapter 3 ppt
... is ˆ β 1 = x 1 M 2 y x 1 M 2 x 1 , and, by a calculation similar to that leading to (3.28), its variance is σ 2 0 x 1 M 2 x 1 1 = σ 2 0 x 1 M 2 x 1 . (3. 31) Thus Var( ˆ β 1 ) is ... sensible estimators are the following: ˆµ 1 = 1 n + 1 n t =1 y t , ˆµ 2 = 1. 01 n n t =1 y t , and ˆµ 3 = 0.01y 1 + 0.99 n 1 n t=2 y t . The first of these es...
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Econometric theory and methods, Russell Davidson - Chapter 4 ppt
... that E(w |z 1 ) = b 1 z 1 + b 2 E(z 2 |z 1 ) = b 1 z 1 + b 2 E(z 2 ) = b 1 z 1 . The first equality follows because b 1 z 1 is a deterministic function of the condi- tioning variable z 1 , and so can ... ≡ X 1 X 2 , where y 1 and y 2 are, respectively, an n 1 vector and an n 2 vector, while X 1 and X 2 are n 1 × k and n 2 × k matrices. Even if we...
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Econometric theory and methods, Russell Davidson - Chapter 5 ppsx
... (5.20) as n 1/ 2 ( ˆ β − β 0 ) = 1 − n X X 1 n 1/ 2 X u, then the first 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 ... so Pr t α/2 ≤ ˆ β 2 − β 20 s 2 ≤ t 1 (α/2) = 1 − α, (5 .12 ) where t α/2 and t 1 (α/2) denote the α/2 and 1 − (α/2) quantiles of the t(n − k) distribution. We can use equa...
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Econometric theory and methods, Russell Davidson - Chapter 7 doc
... ˜u t 1 ) 2 n t =1 ˜u 2 t = n 1 ˜ u ˜ u + n 1 ˜ u 1 ˜ u 1 n 1 ˜ u ˜ u − n 1 ˜u 2 1 + 2n 1 ˜ u ˜ u 1 n 1 ˜ u ˜ u . (7.53) If we ignore the difference between n 1 ˜ u ˜ u and n 1 ˜ u 1 ˜ u 1 , ... n 1 ˆ u 1 ˆ u 1 tends to σ 2 ε / (1 − ρ 2 0 ). The limit of n 1 (X − ˆρX 1 ) ˆ u 1 is the 2 See Dufour, Gaudry, and Liem (19 80) and...
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Econometric theory and methods, Russell Davidson - Chapter 8 pot
... vector y − X 1 ´ β 1 and the projection matrices M P W X 1 and M P W X , respectively. Thus SSR 0 − SSR 1 = (y − X 1 ´ β 1 ) (M P W X 1 − M P W X )(y − X 1 ´ β 1 ) = (y − X 1 ´ β 1 ) (P P W X − ... Buse (19 92), Bekker (19 94), Bound, Jaeger, and Baker (19 95), Dufour (19 97), Staiger and Stock (19 97), Wang and Zivot (19 98), Zivot, Startz, and Nelson (1...
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Econometric theory and methods, Russell Davidson - Chapter 9 potx
... a sandwich estimator of the form A 1 BA 1 , and we find that A = plim n→∞ (n 1 F ∗ 0 W ) ˆ Σ 1 (n 1 W F ∗ 0 ), and B = plim n→∞ (n 1 F ∗ 0 W ) ˆ Σ 1 (n 1 W Ω W ) ˆ Σ 1 (n 1 W F ∗ 0 ), (9.98) where ... as ¯m 1 (µ, σ 2 ) = ¯z and ¯m 2 (µ, σ 2 ) = ¯y, (9 .11 1) where ¯z and ¯y are the sample averages of the z t and the y t , respectively, and ¯m i (µ, σ...
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