Question

Question 1 from chapter 10: "Explain how economists use regression analysis to measure discrimination. Is a significant coefficient on the attribute (e.g. race/gender/ethnicity/sexual orientation/beauty/weight/color/religion/etc. variable proof of the existence of discrimination? Explain."

Answer 1

In regression analysis we try to predict our dependent variable on the basis of some independent variables by using a mathematical equation. Now, some “qualitative variable” also have power to influence our dependent variable such as “gender”, “race”, “region” etc. So, we should also include “qualitative” variables to our model, usually we use dummy variables to include these quantitative variables takes “1” in the presence of the event and “0” in the absence of the events. Let’s assume an example “Consumption” model.

=> C = b0 + b1*Y, where “C=consumption”, “Y=disposable income”, “b1=MPC”. Now, the value of “MPC=marginal propensity to consume” must be more than equal to “0” and less than equal to “1”. Now, as we know that “Consumption spending” are differ across region even if family income are same. So, here we should include the “region” into the model. So, the new model is given by.

=> C = b0 + b1*Y + c*R, “R=1 for “north region” and “0 for south”. So, here we have two different regression model these are as follows.

=> C = (b0+c) + b1*Y, for “north”.

=> C = b0 + b1*Y, for “south”. So, there is a fixed difference in the intercept term between these two region, => for same family income the “consumption expenditure” are different by “c” between these two region, => the slope of the dummy variable measure the discrimination.

So, these how we use regression to measure the discrimination across qualities. Now, if the coefficient of the dummy variable is significant, => the difference across quality is significant, => discrimination exists.