intro-ects-handout-7

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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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:
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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)
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

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

Page1 / 11

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online