Theory and practice of counseling and psychotherapy 10th corey chapter 06

Econometric theory and methods, Russell Davidson - Chapter 1 docx

... number of factors 1. 17 Consider the following example of multiplying partitioned matrices: A 11 A 21 A12 A22 B 11 B 21 B12 B22 = A 11 B 11 + A12 B 21 A 21 B 11 + A22 B 21 A 11 B12 + A12 B22 A 21 B12 + A22 B22 ... have k1 X= k2 X 11 X 21 X12 X22 n1 n2 with the submatrix X 11 of dimensions n1 × k1 , X12 of dimensions n1 × k2 , X 21 of dimensions n2 × k1 , and X22 of dimensions n2 × k2 , with n1 + n2 = n and k1 ... product of X1 and an independent random variable Z, which equals with probability 1/ 2 and 1 with probability 1/ 2 Copyright c 19 99, Russell Davidson and James G MacKinnon 1. 7 Exercises 41 What is...

Econometric theory and methods, Russell Davidson - Chapter 2 doc

... = X1 β1 + X2 2 + MX y (2. 43) Premultiplying the leftmost and rightmost expressions in (2. 43) by X2 M1 , we obtain ˆ X2 M1 y = X2 M1 X2 2 (2. 44) Copyright c 1999, Russell Davidson and James ... 2 + u; c) P1 y = P1 X2 2 + u; d) PX y = X1 β1 + X2 2 + u; Copyright c 1999, Russell Davidson and James G MacKinnon 2. 8 Exercises 85 e) PX y = X2 2 + u; f) M1 y = X2 2 + u; g) M1 y = M1 X2 ... = β1 x1 + 2 x2 + β3 x3 + u, and y = α1 z1 + 2 z2 + α3 z3 + u, where z1 = x1 − 2x2 , z2 = x2 + 4x3 , and z3 = 2x1 − 3x2 + 5x3 Let X = [x1 x2 x3 ] and Z = [z1 z2 z3 ] Show that the columns of...

Econometric theory and methods, Russell Davidson - Chapter 3 ppt

... β2 ∆yt + 3 ∆yt−1 + β4 ∆yt−2 + β5 ∆yt 3 + β6 ∆yt−4 (3. 69) Let γ = ˆ i=2 βi Calculate γ and its standard error in two different ways One method should explicitly use the result (3. 33) , and the ... first-difference model (3. 71), and then, without using the results of (3. 70), rederive the estimates of α, β, γ0 , and γ1 solely on the basis of your results from (3. 71) 3. 23 Simulate model (3. 70) ... using (3. 43) , prove that, if E(u2 ) = σ0 and E(us ut ) = for all s = t, t then Var(ˆt ) = (1 − ht )σ0 This is the result (3. 44) u 3. 13 Use the result (3. 44) to show that the MM estimator σ of (3. 46)...

Econometric theory and methods, Russell Davidson - Chapter 4 ppt

... values less than 0, and there is a very long right-hand tail For n = Copyright c 1999, Russell Davidson and James G MacKinnon 4. 5 Large-Sample Tests in Linear Regression Models 0 .40 151 f (z) ... Copyright c 1999, Russell Davidson and James G MacKinnon 4. 5 Large-Sample Tests in Linear Regression Models 153 are generated by (4. 47) with β2 = 0, we have that M1 y = M1 u, and so (4. 50) is asymptotically ... c 1999, Russell Davidson and James G MacKinnon 4. 4 Exact Tests in the Classical Normal Linear Model 139 4. 4 Exact Tests in the Classical Normal Linear Model In the example of Section 4. 2, we...

Econometric theory and methods, Russell Davidson - Chapter 5 ppsx

... (5. 54) As readers are asked to check in Exercise 5. 16, the intervals (5. 53) and (5. 54) are not the same The Vector Case The result (5. 49) can easily be extended to the case in which both θ and ... converges to (5. 35) The above argument shows that (5. 37) tends in probability to (5. 35) Because (5. 37) is asymptotically equivalent to (5. 36), the latter also tends in probability to (5. 35) Consequently, ... version of (5. 46) is a ˆ ˆ n1/2 (θ − θ0 ) ∼ N 0, V ∞ (θ) , (5. 55) ˆ ˆ where V ∞ (θ) is the asymptotic covariance matrix of the vector n1/2 (θ − θ0 ) Using the result (5. 55) and a ﬁrst-order Taylor...

Econometric theory and methods, Russell Davidson - Chapter 6 docx

... just (6. 06) Thus the model (6. 06) is a special case of the model (6. 66) Therefore, if (6. 06) is a correctly specified model, that is, if the true DGP is a special case of (6. 06) , then (6. 66) must ... correctly specified model as well, because every DGP in (6. 06) automatically belongs to (6. 66) Since (6. 66) is correctly specified, the standard theory of the linear regression with predetermined regressors ... regressions (6. 91) and (6. 92) 6. 21 The original HRGNR proposed by Davidson and MacKinnon (1985a) is ´ ´ ´ ι = UM1X2 b2 + residuals, (6. 96) ´ ´ ´ ´ where U, X1 , and X2 are as defined in Section 6. 8, b2...

Econometric theory and methods, Russell Davidson - Chapter 7 doc

... (see Section 7. 6) When we this, H1 becomes (1 − ρL)yt = (1 − ρL)Xt β + εt , (7. 74) (1 − ρL)yt = Xt β + LXt γ + εt (7. 75) and H2 becomes It is evident that in (7. 74), but not in (7. 75), the common ... of the within-groups, or fixed-effects, estimator (7. 85) and Copyright c 1999, Russell Davidson and James G MacKinnon 7. 10 Models for Panel Data 301 the between-groups estimator (7. 89) For the ... 1999, Russell Davidson and James G MacKinnon 7. 9 Specification Testing and Serial Correlation 295 residuals from (7. 73) are the same as those from its GNR Consequently, we can evaluate (7. 79) with...

Econometric theory and methods, Russell Davidson - Chapter 8 pot

... considered in Section 8. 5, where the null and alternative hypotheses are given by (8. 51) Copyright c 1999, Russell Davidson and James G MacKinnon 8. 8 Bootstrap Tests 341 and (8. 52), respectively ... PW X)−1, ˆ ˆ (8. 88) ˆ ˆ where X ≡ X(β NLIV ), and σ is 1/n times the SSR from IV estimation ˆ of regression (8. 83) Readers may ﬁnd it instructive to compare (8. 88) with expression (8. 34), the covariance ... demand and supply is qt = γd pt + Xtd βd + ud t (8. 06) qt = γs pt + Xts βs + us , t (8. 07) where equation (8. 06) is the demand function and equation (8. 07) is the supply function Here Xtd and...

Econometric theory and methods, Russell Davidson - Chapter 9 potx

... McFadden ( 198 9), who seems to have coined the name, and Pakes and Pollard ( 198 9) Other important early papers include Lee and Ingram ( 199 1), Keane ( 199 4), McFadden and Ruud ( 199 4), and Gallant and Tauchen ... i i=1 and a ˆ Q(θ, y) = l−k yi , i=1 Copyright c 199 9, Russell Davidson and James G MacKinnon (9. 91) 9. 5 GMM Estimators for Nonlinear Models 3 79 where the xi and yi are independent, standard ... treatment of the asymptotic theory of GMM estimation, see Newey and McFadden ( 199 4) Copyright c 199 9, Russell Davidson and James G MacKinnon 9. 6 The Method of Simulated Moments 381 9. 6 The Method of Simulated...

Econometric theory and methods, Russell Davidson - Chapter 10 pps

... c 1999, Russell Davidson and James G MacKinnon 10. 10 Exercises 437 10. 7 Use the result (10. 102) of the preceding exercise to prove the asymptotic information matrix equality (10. 34) 10. 8 Consider ... density (10. 03) with −1 θ = (β20 − 10 ) 10. 3 Generate 10, 000 random samples of sizes 20, 100 , and 500 from the uniform U (0, 1) distribution For each sample, compute γ , the sample mean, and γ ... 1999, Russell Davidson and James G MacKinnon (10. 50) 412 The Method of Maximum Likelihood This is the sum over all t of the product of expressions (10. 46) and (10. 47) We know that E(ut ) = 0, and, ...

Econometric theory and methods, Russell Davidson - Chapter 11 ppt

... 1999, Russell Davidson and James G MacKinnon 11. 5 Models for Count Data 467 (1985, Chapter 9) and McFadden (1984) For a more up-to-date survey, but one that is relatively superﬁcial, see Maddala and ... forms, by Engle (1984) and Davidson and MacKinnon (1984b) Copyright c 1999, Russell Davidson and James G MacKinnon 454 Discrete and Limited Dependent Variables where s is the standard error of the ... Neumann (1999), Gouri´roux and Jasiak (2001), and e van den Berg (2001) Copyright c 1999, Russell Davidson and James G MacKinnon 11. 9 Final Remarks 487 11. 9 Final Remarks This chapter has dealt with...

Econometric theory and methods, Russell Davidson - Chapter 12 pptx

... (12. 97) is a demand function, and equation (12. 98) is a supply function In this system, pt and qt denote the price and Copyright c 1999, Russell Davidson and James G MacKinnon 12. 6 Nonlinear Simultaneous ... β• and Σ by using equations (12. 78) and (12. 17), respectively From the results (12. 62) and (12. 63), it is clear that we can estimate the covariance matrix of the classical 3SLS estimator (12. 78) ... 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 12. 4 Linear Simultaneous...

Econometric theory and methods, Russell Davidson - Chapter 13 potx

... Copyright c 1999, Russell Davidson and James G MacKinnon (13. 17) 13. 2 Autoregressive and Moving Average Processes 553 To see this, note that ρ1 L times the right-hand side of equation (13. 17) is the ... c 1999, Russell Davidson and James G MacKinnon (13. 60) 13. 4 Single-Equation Dynamic Models where λ≡ γ0 + γ1 − β1 569 (13. 61) This is the long-run derivative of y ◦ with respect to x◦, and it ... Copyright c 1999, Russell Davidson and James G MacKinnon (13. 21) 554 Methods for Stationary Time-Series Data and a process with zero mean as − ρ(L) ut = + α(L) εt , (13. 22) where ρ(L) and α(L) are,...

Econometric theory and methods, Russell Davidson - Chapter 14 pot

... hypothesis Dickey-Fuller tests of the null hypothesis that there is a unit root may be based on any of regressions (14. 15), (14. 18), (14. 21), or (14. 22) In practice, regressions (14. 18) and (14. 21) ... c 1999, Russell Davidson and James G MacKinnon (14. 52) 620 Unit Roots and Cointegration where the new parameter α is the short-run multiplier, δ1 = λ2 − 1, and δ2 = (1 − λ2 )η2 Since (14. 52) ... system (14. 36) that, if yt1 and yt2 are cointegrated, then the matrix Φ of (14. 37) has Copyright c 1999, Russell Davidson and James G MacKinnon 14. 5 Cointegration 625 one unit eigenvalue and the...

Econometric theory and methods, Russell Davidson - Chapter 15 docx

... is the number of elements of r, and Zt and rt are, respectively, the t th row and t th element of Z and r Copyright c 1999, Russell Davidson and James G MacKinnon 15. 2 Speciﬁcation Tests Based ... 1999, Russell Davidson and James G MacKinnon 688 Testing the Speciﬁcation of Econometric Models Nadaraya-Watson estimator and the locally linear estimator For the former, use the bandwidth (15. 64) ... H1 from regression (15. 40) related to the F statistic for = in the inclusive regression (15. 39)? Copyright c 1999, Russell Davidson and James G MacKinnon 15. 8 Exercises 685 15. 14 How is the P...

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