intro-ects-handout-7

# intro-ects-handout-7 - Introductory Econometrics ECON0701...

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Introductory Econometrics ECON0701 (2009) 91 7. Further topics of the multiple regression model testing the equivalence of two regressions: Chow test prediction polynomial and interaction variables 7.1. Testing the equivalence of two regressions: The Chow test consider the classic example: GE versus Westinghouse the multiple regression model for gross investment in plant and equipment ( INV ) for a particular f rm: INV = β 0 + β 1 V + β 2 K + ε where V stands for share value of the f rm and K stands for stock of capital f rst n 1 observations (=20, for this example): GE; last n 2 obser- vations (=20, for this example): Westinghouse unrestricted model: 2 di f erent regressions INV i = β GE 0 + β GE 1 V i + β GE 2 K i + ε i ; i =1 ,..., 20 INV i = β W 0 + β W 1 V i + β W 2 K i + ε i ; i =21 ,..., 40 restricted model: equivalence of 2 regressions β GE j = β W j = β j ; j =0 , 1 , 2 procedure:

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Introductory Econometrics ECON0701 (2009) 92 (a) obtain SSR R by regressing y on a constant and the explana- tory variables for the whole sample ( n = n 1 + n 2 ; n =40 for this example) SSR R = 40 X i =1 ³ INV i b β 0 b β 1 V i b β 2 K i ´ 2 (7.1) (b) obtain SSR 1 by regressing y on a constant and the explana- tory variables for the f rst n 1 observations; obtain SSR 2 by re- gressing y on a constant and the explanatory variables for the last n 2 observations; then obtain SSR U = SSR 1 + SSR 2 i.e., SSR U = 20 X i =1 μ INV i b β GE 0 b β GE 1 V i b β GE 2 K i 2 + 40 X i =21 μ INV i b β W 0 b β W 1 V i b β W 2 K i 2 = SSR 1 + SSR 2 (7.2) SSR 1 SSR 2 : Table 7.1 (c) form the F -test statistic for the equivalence of the two re- gressions as: F = [ SSR R ( SSR 1 + SSR 2 )] / ( k +1) ( SSR 1 + SSR 2 ) / ( n 1 + n 2 2 k 2) F ( k +1 ,n 1 + n 2 2 k 2) (7.3) where k =2 in the above example example: tutorial (obtain SSR R , and calculate F test statistic)
Introductory Econometrics ECON0701 (2009) 93 7.2. The least-squares predictor f rst, consider the simple regression model given the simple regression model and its assumptions, we want to predict for a given value of the explanatory variable x 0 the value of the dependent variable y 0 ,wh ichisg ivenby y 0 = β 0 + β 1 x 0 + ε 0 (7.4) according to the population regression model replacing the unknown parameters by their estimators and the random error ε 0 by its expectation, the least-squares predic- tor of y 0 is b y 0 = b β 0 + b β 1 x 0 (7.5) which is given by the point on the OLS f tted line when x = x 0 (Figure 7.1) example (earlier): a household with a weekly income of \$12000 is predicted to spend 738 . 32 + 0

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## This note was uploaded on 09/06/2010 for the course FBE ECON0701 taught by Professor Paul during the Spring '09 term at HKU.

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intro-ects-handout-7 - Introductory Econometrics ECON0701...

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