foundations of econometrics phần 7 docx

... (10. 67) In Exercise 7. 11, expressions were developed for the blocks of the inverses of partitioned matrices. It is easy to see from those expressions that the inverse of (10. 67) is the 22 block of ... −I −1 11 s 1 . (10 .77 ) Here I 11 and s 1 denote, respectively, the (k − r) ×(k − r) block of I and the subvector of s that correspond to θ 1 . We rewrite the last expression i...

Ngày tải lên: 14/08/2014, 22:21

... through numbers: “The five steps in the process are,” “There are two kinds of family,” or “The three basic causes of the revolution were.” o Listen for verbal “summing-up” clues such as “in ... class adequate for passing the test? What kind of material was emphasized on the test (researchers, theories, straight facts, etc.). The kind of material emphasized on the first test will...

Ngày tải lên: 22/07/2014, 22:20

... with that of poly(vinyl alcohol)–[CH 2 –CHOH] n − , whose T g is +70 ◦ C, gives an idea of the importance of interactions. The effect of main chain substituents is more complex. The size of certain atoms ... mas- tication of certain polymers in the molten state, in particular of natural rubber before addition of stabilizing additives, may cause a drastic reduction of their...

Ngày tải lên: 14/08/2014, 10:20

... ij th element of the result is equal to the inner product of the i th row of the first matrix with the j th column of the second matrix. Thus, if C = AB, C ij = m  k=1 A ik B kj . (1. 27) For (1. 27) to ... horizontal limits of the circle of B are allowed. If one computes the area of the part of the circle to the left of a given vertical line, then for each event a ≡ (X ≤ x...

Ngày tải lên: 14/08/2014, 22:21

... 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 ) of the previous ... columns of X are linearly dependent. Copyright c  1999, Russell Davidson and James G. MacKinnon 3.8 Measures of Goodness of Fit 1 17 One possibility might be to use s,...

Ngày tải lên: 14/08/2014, 22:21

... (unre- stricted) estimate of σ 2 and can be thought of as a measure of the scale of the random noise. Since u ∼ N(0, σ 2 I), every element of u has the same variance, and so every component of (4. 37) , if centered ... sample will contain some of the residuals exactly once, some of them more than once, and some of them not at all. Therefore, the value of each drawing must...

Ngày tải lên: 14/08/2014, 22:21

... proportional to the inverse of the variance of its error term. Efficiency of the GLS Estimator The GLS estimator ˆ β GLS defined in (7. 04) is also the solution of the set of moment conditions X  Ω −1 (y ... model (7. 01) is defined in terms of an n × k matrix of exogenous variables W, where k is the dimension of β, by the equations W  (y − Xβ) = 0. (7. 08) These equations are a...

Ngày tải lên: 14/08/2014, 22:21

... β 5 . We see that (7. 78) has only 7 identifiable parameters: β 2 , γ 4 , γ 5 , δ 1 , δ 2 , δ 3 , and δ 4 , instead of the 11 parameters, many of them not identifiable, of expression (7. 77) . In contrast, ... the test statistic for H 0 against H 2 . The result (7. 81) is not particularly useful in the case of (7. 71), (7. 72), and (7. 73), where all of the test statistics are quit...

Ngày tải lên: 14/08/2014, 22:21

... (9. 07) . We may reasonably expect that, with such a choice of J, the covariance matrix will no longer have the form of a sandwich. The simplest choice of J that eliminates the sandwich in (9. 07) ... asymptotic covariance matrix of n 1/2 ( ˆ θ − θ 0 ) when ¯ F is used in place of Z and the covariance matrix of f (θ) is σ 2 I, we start from expression (9. 67) . Using (9 .73 ), we...

Ngày tải lên: 14/08/2014, 22:21

... the determinant of the inverse of a matrix is the reciprocal of the determinant of the matrix itself, we have − log |Σ| = log |Σ −1 |, so that we can readily express all of (12.33) in terms of Σ −1 rather ... first equation of (12.88) is the transpose of ˆ X • , of which the typical diagonal block is, from (12. 57) , [ Z i P W Y i ]. In both cases, the matrix is an estimate...

Ngày tải lên: 14/08/2014, 22:21