I would like to know whether I should/shouldn't split a categorical variable into separate dummy variables for an OLS regression.
For example, I am regressing income on education using data from the Basic Feb 2016 data set from the U.S. Census Current Population Survey.
The dataset has a variable for highest level of education coded as follows:
-1 - not in universe 31 - Less than 1st grade 32 - 2nd, 3rd, or 4th grade ... 38 - 12th Grade No Diploma 39 - High School Grad-Diploma Or Equiv (GED) 40 - Some College But No Degree 41 - Associate Degree-Occupational/Vocational 42 - Associate Deg.-Academic Program 43 - Bachelor''s Degree(ex: BA, AB, BS) 44 - MASTER''S DEGREE(ex: MA, MS, MEng, MEd, MSW) 45 - Professional School Deg(ex: MD, DDS, DVM) 46 - DOCTORATE DEGREE(ex: PhD,EdD)
In my regression I would use an indicator variable to represent each group, and I would drop one group.
But, I could also make a dichotomous variable for each group and include each one in the regression. This sort of makes sense because a person can have a PhD and not a Masters.
Which should I do and why? Are there other variables where it should be different?