ECON301_Handout_11_1213_02

# ECON301_Handout_11_1213_02 - ECON 301 Introduction to...

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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: Lecture Notes 1 HANDOUT 11 DUMMY VARIABLES I Outline of today’s lecture: I. Introduction ......................................................................................................................................... 1 II. ANOVA and ANCOVA Models ............................................................................................................. 2 II. Dummy Variable Trap ......................................................................................................................... 4 IV. Some Illustrations .............................................................................................................................. 6 V. Model Parametrizations ..................................................................................................................... 7 A. An Example Model .......................................................................................................................... 9 B. Intercept Dummy Example ........................................................................................................... 12 C. More Than Two Dummy Variables ............................................................................................... 13 VI. A Bit Seasonality ................................................................................. Error! Bookmark not defined. I. Introduction In regression analysis the dependent variable is frequently influenced not only by variables that can be readily quantified on some well- defined scale (e.g., income, output, prices, costs, height, and temperature), but also by variables that are essentially qualitative in nature (e.g., sex, race, color, region, nationality, wars, earthquakes, strikes, political upheavals, and changes in government economic policy). For example, holding all factors constant, female college professors are found to earn less than their male counterparts, and nonwhite are found to earn less than whites (USA). This pattern may result from sex or racial discrimination, but whatever the reason, qualitative variables such as sex and race do influence the dependent

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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: Lecture Notes 2 variable and clearly should be included among the explanatory variables. Since such qualitative variables usually indicate the presence or absence of a ‘quality’ or an attribute, such as male or female, or white or non- white, one method of ‘quantifying’ such attributes is by constructing artificial variables that take on values of 1 or 0, 0 indicating the absence of an attribute and 1 indicating the presence of that attribute. For example, 1 may indicate that a person is a male, and 0 may designate a female; or 1 may indicate that a person is a college graduate, and 0 that he is not, and so on. Variables that assume such 0 and 1 values are called dummy variables . II. ANOVA and ANCOVA Models Dummy variables can be used in regression models. As a matter of fact, a regression model may contain explanatory variables that are exclusively dummy, or qualitative, in nature. Such models are called analysis of variance (ANOVA) models. As an example; (1) Y t = + D t + u t where; Y = annual salary of a college professor
ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: Lecture Notes 3 D t = 1 if male college professor 0 otherwise However, in most economic research, a regression model contains some explanatory variables that are quantitative and some that are qualitative. Regression models containing an admixture of quantitative and qualitative variables are called analysis-of- covariance (ANCOVA) models . As an example of the ANCOVA model, let us modify model (1) above as follows; (2) Y t = 1 + 2 D t + X t + u t where Y t = annual salary of a college professor X t = years of teaching experience D t = 1 if male 0

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