Econometric theory and methods, Russell Davidson - Chapter 3 ppt

... first-difference model (3. 71), and then, without using the results of (3. 70), rederive the estimates of α, β, γ 0 , and γ 1 solely on the basis of your results from (3. 71). 3. 23 Simulate model (3. 70) ... w  Var( ˆ β)w, and similarly for Var(˜γ). Therefore, the difference between Var(˜γ) and Var(ˆγ) is w  Var( ˜ β)w − w  Var( ˆ β)w = w   Var( ˜ β) − Var( ˆ β)  w. (3. 36) The...

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... no possible confusion. Copyright c  1999, Russell Davidson and James G. MacKinnon 4 .3 Some Common Distributions 133 where z 1 , z 2 , and z 3 are mutually independent standard normal variables, then b 1 z 1 +b 2 z 2 is ... independent Copyright c  1999, Russell Davidson and James G. MacKinnon 4.5 Large-Sample Tests in Linear Regression Models 151 −4 3 −2 −1 0 1 2 3 4 0...

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... models? Copyright c  1999, Russell Davidson and James G. MacKinnon 484 Discrete and Limited Dependent Variables 0 1 2 3 4 5 6 7 8 9 10 0.0 0.5 1.0 1.5 2.0 2.5 3. 0 3. 5 4.0 4.5 5.0 Exponential, ... (11. 83) we see that the hazard and survivor functions for observation i are α exp(αX i β)t α−1 and exp  −t α exp(αX i β)  , Copyright c  1999, Russell Davidson and Jame...

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... defined by the equations ˆ X •  ( ˆ Σ −1 3SLS ⊗ I n )(y • − X • ˆ β 3SLS • ) = 0, and ˆ Σ 3SLS = 1 − n (Y ˆ Γ 3SLS − W ˆ B 3SLS )  (Y ˆ Γ 3SLS − W ˆ B 3SLS ). (12.88) The second of these equations ... Here it is the equation-by-equation IV estimator that takes the place of the equation-by-equation OLS estimator. Copyright c  1999, Russell Davidson and James G. MacKinnon 532 Multiva...

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... software packages, and we know better than to try to upset such preferences. Copyright c  1999, Russell Davidson and James G. MacKinnon 1.4 Matrix Algebra 31 If two matrices A and B of the same ... 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 ...

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... 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 (1 933 ), and then reintroduced ... 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...

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... then we already know how to cal- culate Var(ˆγ); recall the result (3. 33) . The idea of the delta method is to find a linear approximation to g(θ) and then apply (3. 33) to this approximation. Taylor’s ... 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. Mac...

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... include Bard (1974), Gill, Murray, and Wright (1981), Quandt (19 83) , Bates and Watts (1988), Seber and Wild (1989, Chapter 14), and Press et al. (1992a, 1992b, Chapter 10). There are many algorithms ... between the parameters δ 0 , δ 1 , and ρ of this model and the parameters α, β, γ 0 , and γ 1 of (6.94). How Copyright c  1999, Russell Davidson and James G. MacKinn...

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... the 2 See Dufour, Gaudry, and Liem (1980) and Betancourt and Kelejian (1981). Copyright c  1999, Russell Davidson and James G. MacKinnon 30 0 Generalized Least Squares and Related Topics of the ... 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 Leas...

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... terms. Copyright c  1999, Russell Davidson and James G. MacKinnon 8 .3 Instrumental Variables Estimation 31 3 It can be seen from this solution that p t and q t will depend on both u d t and u s t , and on every ... of nonlinear regression models is dealt Copyright c  1999, Russell Davidson and James G. MacKinnon 30 9 8.7 Durbin-Wu-Hausman Tests 33 9 Tests Based on Vec...

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