Lecture+5+Regression+with+dummy+variables

Lecture+5+Regression+with+dummy+variables - DummyVariables...

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1 Lecture 5 Regression with dummy variables Dummy Variables A dummy variable is a variable that equals either 1 or 0, representing two groups/categories. Examples : male (= 1 if are male, 0 otherwise), urban (= 1 if in urban area, 0 otherwise), etc. Dummy variables are also called binary variables, for obvious reasons. A Dummy Independent Variable A simple model with one dummy ( d ) independent variable: 0 Yd u α δ =+ + If d = 0, then Y= , and hence ( ) uE Y += , If d = 1, then 00 ( ) , and hence ( ) Yu E Y δα =+ + = + . The case of d = 0 is the base group, and is the intercept for the base group; 0 is the mean difference in the outcome between the represented group ( d =1) and the base group. Testing the significance of 0 tells whether the mean Y’s are significantly different between the two groups. Example : In a study of wage differences between male and female workers of similar age and education, the following equation is estimated using OLS: = + + , WF u β where W is wage in dollars and F is a dummy that equals 1 if a worker is female and 0 if male, and u is an error term. In the data, the average wage for male W f , and for male is W m . (i) How would you interpret the intercept and slope (ii) Based on your interpretation, ˆ ˆ ? and ? αβ = = When there is an intercept in the model, the coefficient of a dummy variable always represents the mean difference between the dummy represented group and the based group.
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2 A model with one dummy and one continuous covariate X : 0 YM X u αδ β =+ + + Example : M =1 if male, and 0 otherwise; X =years of schooling; Y =wage. Note that a dummy for male and a dummy for female provide the same information. In particular, they sum to 1, i.e., they are perfectly collinear, so can’t include both. Similarly, If M = 0, then () . EY X αβ If M = 1, then 0 () ( ) . X αδ β + So 0 δ is the mean wage difference between male and female holding years of schooling constant (given the same education level). The graph for the estimated wage equations consists of two parallel lines , where α is the intercept for the base group ( M =0), i.e., females, and 0 + is the intercept for the group ( M =1), i.e., males. Figure : the estimated wage equation (assuming 0 > 0 ) Program evaluation : Often times, economists are interested in evaluating the impact of some public policy, intervention, or program. Can include a dummy indicating, for example, whether or not an individual participates in a job training program, or receives unemployment insurance; or whether or not a kid enrolls in Head Start. After controlling for all the relevant covariates that determine outcome, the coefficient of the dummy gives the impact of interest, i.e., the impact of the job training program, unemployment insurance, or Head Start.
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3 Dummies for Multiple Categories We can use a set of dummy variables to represent variables with multiple categories.
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Lecture+5+Regression+with+dummy+variables - DummyVariables...

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