Question

1. In the following model, “white” is a dummy indicating a person is a white:

wage=β0+β1edu+β2white+u

If you run this model, the regression will produce two regression lines, one for white and the other for non-white.

If you run the regression without the dummy wage=β0+β1edu+u separately for white and for non-white (for example, if there are 1000 people; 500 of them are white and 500 are non-white; run the regression of wage on edu for the 500 white and then run it for the 500 non-white), you will also get two regression lines, one for white and the other for non-white. Are the two ways of getting wage differential essentially the same? Say “yes” or ‘no”, then explain. (10pts)

Answer 1

1. In the following model, “white” is a dummy indicating a person is a white:

wage=β0+β1edu+β2white+u

If you run this model, the regression will produce two regression lines, one for white and the other for non-white.If you run the regression without the dummy wage=β0+β1edu+u separately for white and for non-white (for example, if there are 1000 people; 500 of them are white and 500 are non-white; run the regression of wage on edu for the 500 white and then run it for the 500 non-white), you will also get two regression lines, one for white and the other for non-white. Are the two ways of getting wage differential essentially the same? Say “yes” or ‘no”, then explain.

The given regression equation of wage

​​​​​​​wage=β0+β1edu+β2white+u

According to the question YES , the two ways here of getting the differential wage is actually same.where the dummy variable is white , here it only takes the value of either 0 or 1 or we can say that it only show the absence or presence of the white person. If we are getting the two regression fitted plot lines with the dummy variable , its value dont change , it will plot the same way and if we dont include this dummy variable thgen again it will have the same fitted line plot which means that both are the same output of the equation of wage differential for whites and non whites. Also , here the white variable is only significant for showing the absence or presence , that is it .

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