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Chapter 9, Exercise Solutions, Principles of Econometrics, 3e 203 EXERCISE 9.3 (a) Equation (9.49) can be used to conduct two Lagrange multiplier tests for AR(1) errors. The first test is to test whether the coefficient for ˆ 1 et− is significantly different from zero. The null hypothesis is H0:0.ρ= The value of the test statistic is 0.428

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Chapter 3, Exercise Solutions, Principles of Econometrics, 3e 33 Exercise 3.1 (continued) (d) Testing H 0 : β1 = 0 against H1 : β1 > 0, uses the same t-value as in part (b), t = 1.92. Because it is a one-tailed test, the critical value is chosen such that there is a probability of 0.05 in the right tail. That is, tc = t(0.95,38) = 1.686 .

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Chapter 2, Exercise Solutions, Principles of Econometrics, 3e 7 EXERCISE 2.4 (a) If β=1 0, the simple linear regression model becomes yiii=β +2xe (b) Graphically, setting β=1 0 implies the mean of the simple linear regression model E()yxii=β2 passes through the origin (0, 0). (c) To save on subscript notation we set β2 =β. The sum of squares function becomes

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Chapter 10, Exercise Solutions, Principles of Econometrics, 4e 366 Exercise 10.3 (continued) (c) The robust standard errors are compared to the least squares standard errors in the following table Coefficient Estimate Least Squares Standard Errors Robust Standard Errors (White’s) b 1 = í 0.2342 0.979925 0.619615 b 2 = 1.0331 0.009042 0 ...

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Chapter 8, Exercise Solutions, Principles of Econometrics, 3e 191 EXERCISE 8.10 (a) The transformed model corresponding to the variance assumption σi2 = σ 2 xi is ⎛ 1 ⎞ = β1 ⎜ ⎟ + β x + ei∗ ⎜ x ⎟ 2 i xi ⎝ i⎠ ⎛ e ⎞ where ei∗ = ⎜ i ⎟ ⎜ x ⎟ ⎝ i ⎠ yi

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Chapter 2, Exercise Solutions, Principles of Econometrics, 3e 6 Exercise 2.3 (continued) (d) The values of the least squares residuals, computed from 1 2 ˆ i i i e y b b x = − −, are: 1 ˆ 0.19048 e = − 2 ˆ 0.55238 e = 3 ˆ 0.29524 e = 4 ˆ 0.96190 e = − 5 ˆ 0.21905 e = − 6 ˆ 0.52381 e = Their sum is ˆ 0.

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Exercise Solutions. Chapter 9, Exercise Solutions, Principles of Econometrics, 3e 203. EXERCISE 9.3. (a) Equation (9.49) can be used to conduct two Lagrange multiplier tests for AR(1) errors. The first test is to test whether the coefficient for 1. ˆt e − is significantly different from zero. The null hypothesis is 0 : 0.

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