foundations of econometrics phần 2 ppsx

... MacKinnon 2. 8 Exercises 85 P X y = X 2 β 2 + u;e) M 1 y = X 2 β 2 + u;f) M 1 y = M 1 X 2 β 2 + u;g) M 1 y = X 1 β 1 + M 1 X 2 β 2 + u;h) M 1 y = M 1 X 1 β 1 + M 1 X 2 β 2 + u;i) P X y = M 1 X 2 β 2 + ... the different definitions of R 2 would no longer be the same: 1 − y − X ˜ β 2 y 2 = X ˜ β 2 y 2 . If we chose to define R 2 in terms of the res...

Ngày tải lên: 14/08/2014, 22:21

... James G. MacKinnon 8 .2 Correlation Between Error Terms and Regressors 311 where u t ≡ u ◦ t + v 2t − β 2 v 1t . Thus Var(u t ) is equal to σ 2 + ω 2 2 + β 2 2 ω 2 1 . The effect of the measurement ... ( ˆ β 2 − β 20 )    Var( ˆ β 2 )  −1 ( ˆ β 2 − β 20 ), (8.48) where  Var( ˆ β 2 ) is the submatrix of (8.34) that corresponds to the vector β 2 . This Wald stat...

Ngày tải lên: 14/08/2014, 22:21

Ngày tải lên: 24/07/2014, 08:20

... valuations, and soar- ing layoffs. Others have a sense of the association and are trying to see their way clear. Not all of the economic malaise of the years 20 00 to 20 02 is due to these two developments, ... and operation of a business? As individuals, all of us have thousands of needs and wants, ranging from the essentials of life, such as safety and security, to 20 Part...

Ngày tải lên: 10/08/2014, 11:20

... Properties Property Description onreadystatechange The event handler that fires at every state change. readyState The state of the request: 0 = uninitialized, 1 = loading, 2 = loaded, 3 = interactive, 4 = complete responseText The response from ... server. statusText The text version of the HTTP status code. Sample Code function createXMLHttpRequest() { if (window.ActiveXObject) {...

Ngày tải lên: 12/08/2014, 17:20

... A 12 B 21 A 11 B 12 + A 12 B 22 A 21 B 11 + A 22 B 21 A 21 B 12 + A 22 B 22  . Check all the expressions on the right-hand side, verifying that all products are well defined and that all sums are of ... inverse of the product of an arbitrary number of factors. 1.17 Consider the following example of multiplying partitioned matrices:  A 11 A 12 A 21 A 22...

Ngày tải lên: 14/08/2014, 22:21

... be σ 2 0 [ −S 21 S −1 11 1 ]  S 11 S 12 S 21 S 22  −S −1 11 S 12 1  = σ 2 0  S 22 − S 21 S −1 11 S 12  . (4.57) Copyright c  1999, Russell Davidson and James G. MacKinnon 4.7 The Power of ... 155 The denominator of (4.51) is, thankfully, easier to analyze. The square of the second factor is n −1 x 2  M 1 x 2 = n −1 x 2  x 2 − n −1 x 2  P 1 x 2 =...

Ngày tải lên: 14/08/2014, 22:21

... rewritten as n 1 /2 ˆ β 2   n  Var( ˆ β 2 )  −1 n 1 /2 ˆ β 2 . (6.77) This is asymptotically equivalent to the statistic 1 ´σ 2 n 1 /2 ´ b 2  (n −1 ´ X 2  M ´ X 1 ´ X 2 )n 1 /2 ´ b 2 , (6.78) which ... which projects on to a space of dimension k − k 1 = k 2 . Thus the numerator of (6.70) is σ 2 0 times a χ 2 variable with k 2 degrees of freedom, divided...

Ngày tải lên: 14/08/2014, 22:21

... + 1 2 σ 2 ). (9.1 02) The derivatives of these functions with respect to the parameters are ∂f t1 ∂µ = −1; ∂f t1 ∂σ 2 = 0; ∂f t2 ∂µ = −e µ+σ 2 /2 ; ∂f t2 ∂σ 2 = − 1 − 2 e µ+σ 2 /2 . (9.103) These ... The 2n vector f(µ, σ 2 ) of the full set of elementary zero functions, and the 2n × 2 matrix F (µ, σ 2 ) of the derivatives with respect to the parameters, can thus...

Ngày tải lên: 14/08/2014, 22:21

... n −1 /2 g 2  ( ˜ θ)( ˜ I −1 ) 22 n −1 /2 g 2 ( ˜ θ) = g 2  ( ˜ θ)( ˜ I −1 ) 22 g 2 ( ˜ θ), (10.68) in which ˜ I = n −1 I( ˜ θ), and the notations ( ˜ I −1 ) 22 and ( ˜ I −1 ) 22 signify the 22 blocks of the inverses of ˜ I ... V 22 / ˆ β 4 2 . If instead the restriction is written in the form of r 2 , then R(β 1 , β 2 ) = [1/β 2 1 1], and the Wald statisti...

Ngày tải lên: 14/08/2014, 22:21