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# Variables that assume such 0 and 1 values are called

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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

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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 otherwise Model (2) contains one quantitative variable (years of teaching experience) and one qualitative variable (sex) that has two classes, namely, male and female. Assuming, as usual, that E( u t ) = 0, we see that Mean salary of a female college professor: E (Y t \ X t , D t = 0 ) = 1 + X t Mean salary of a male college professor: E(Y t \X t , D t =1) = ( 1 + 2 )+ X t
ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: Lecture Notes 4 So, model (2) postulates that the male and female college professors’ salary functions in relation to the years of teaching experience have the same slope ( ) but different intercepts. In other words, it is assumed that the level of the male professor’s mean salary is different from that of the female professors’ mean salary (by 2 ) but the rate of change in the mean annual salary by years of experience is the same for both sexes. II. Dummy Variable Trap To distinguish the two categories, male and female, we have introduced only one dummy variable D t . For if D t = 1 always denotes a male, when D t =0 we know that it is a female since there are only two possible outcomes. Hence, one dummy variable suffices to distinguish two categories (this is the second parameterization). Let us assume that the regression model contains an intercept term; if we were to write model (2) as: Y t = 1 + 2 D t1 + 3 D t2 + X t + u t (3) where Y and X are as defined before D t1 = 1 if male professor 0 otherwise

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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: H. Ozan ERUYGUR e-mail: Lecture Notes 5 D t2 = 1 if female professor 0 otherwise then model (3), as it stands, can not be estimated because of perfect collinearity between D t1 and D t2 . To see this, suppose we have a
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Variables that assume such 0 and 1 values are called dummy...

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