intro-ects-handout-8

intro-ects-handout-8 - Introductory Econometrics ECON0701...

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Introductory Econometrics ECON0701 (2009) 102 8. Multiple regression analysis with qualitative explanatory variables extends the multiple regression model to situations in which the regression parameters are di f erent for some of the observations in a sample dummy variables are a powerful tool for capturing qualitative characteristics of individuals, such as gender, race, and geo- graph icreg iono fres idence the introduction of dummy variables allows us to construct mod- els in which some or all model parameters change for some of the observations in the sample 8.1. Intercept dummy variables example: a model of car speed to incorporate the hypothesis that the model may di f er with respect to di f erent types of cars, we develop a way to incorporate such non-quantitative, or qualitative, factors into the model one way to capture qualitative characteristics within economic models is to use dummy variables (also called binary or di- chotomous variables): y i = β 0 + β 1 x i + θ D i + ε i (8.1) where y i = speed of car in miles per hour; x i = age of car in years; D i =1 if red car, D i =0 otherwise in the above model, D i
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Introductory Econometrics ECON0701 (2009) 103 for red cars: D i =1 in (8.1) y i =( β 0 + θ )+ β 1 x i + ε i for other cars: D i =0 in (8.1) y i = β 0 + β 1 x i + ε i a hypothesis: red cars travel faster ( H 0 : θ =0 versus H 1 : θ > 0 ) adding the dummy variable D to the regression model in the above way creates a parallel shift (or intercept shift) in the rela- tionship by the amount θ a dummy variable like D that is incorporated into a regression model to capture a shift in the intercept as the result of some qualitative factor is called an intercept dummy variable provided that ε i in (8.1) satis f es the assumptions of the regres- sion model, it is possible to estimate the model parameters via OLS method as usual; the properties of the OLS estimator are not a f ected by the fact that one of the explanatory variables consists of zeros and ones e.g. y =income, x 1 = education level, x 2 = experience, MALE = 0 for female (for the f rst 61 observations), MALE =1 for male (for the last 32 observations)
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intro-ects-handout-8 - Introductory Econometrics ECON0701...

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