By George G. Judge, William Griffith, Helmut Lütkepohl, Tsoung-Chao Lee, Helmut Lutkepohl
A working laptop or computer instruction manual to accompany "Introduction to the idea and perform of Econometrics" (Second edition).
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Extra resources for Learning Econometrics Using GAUSS
When W T by Newey and West, it is guaranteed to be positive deÞnite which is a good thing since you need to invert it to do GMM. 9 You might try values such as m = T 1/4 . To test 8 Alternatively, you may be interested in a multiple equation system in which the theory imposes parameter restrictions across equations so not only may the model be nonlinear, ²t could be a vector of error terms. 9 Andrews  and Newey and West  oﬀer recommendations for letting the data determine m. 38 CHAPTER 2.
S11 s12 where S = . 5) to get qt = ∞ X j=0 (11) (eq. 6) j=0 where Bj ≡ Dj S = Cj Λ−1 S and ηt ≡ S−1 vt , is the 2 × 1 vector of zeromean orthogonalized innovations with covariance matrix E(ηt η 0t = I). Note that S−1 is also upper triangular. 7) b22,j η2,t−j . 1. UNRESTRICTED VECTOR AUTOREGRESSIONS 29 The eﬀect on q1t at time k of a one standard deviation orthogonalized innovation in η1 at time 0, is b11,k . Similarly, the eﬀect on q2k is b21,k . Graphing the transformed moving-average coeﬃcients is an eﬃcient method to examine the impulse responses.
For now, we will proceed with the transformed observations. The resulting test equations are ∆˜ qit = αi + δi t + βi q˜it−1 + ki X φij ∆˜ qit−j + ²it . 72) j=1 The slope coeﬃcient on q˜it−1 is constrained to be equal across individuals, but no such homogeneity is imposed on the coeﬃcients on the lagged diﬀerences nor on the number of lags ki . To allow for this speciÞcation in estimation, regress ∆˜ qit and q˜it−1 on a constant (and possibly 54 CHAPTER 2. 74) j=1 where eˆit and vˆit are OLS residuals.