For example, if we want to study the impact of gender on wage. What is the difference if I collect a sample I run a regression and let gender as a dummy variable to compare the impact of gender on wage or I further divided the sample into 2 subgroups which contain female and male separated. Then I separately run the regression model twice.
In other word,
General model:
Wage=b1*gender+b2*educ+error (gender is dummy variable)
Separate model:
Wage=b1*educ+error
Why separate model is not good compared to general model
It looks very weird to me if you put "gender" in a regression. Regression is designed for continuous variables.
According to my theoretical framework, the salary is a form of class structure, between those who work with and without income. It's not a money question
The answer is depend on your task: if you want to research influence of the education level separatly from gender or somthing else, your should use one-parametric model. If your task is reseching a combination of factors your model will be multiparametric.
But the main question is how measure discrets parameters of model? Education: 1, 2, 3, 4, 5... What does it mean? For the gender is the same situation. Is one more important than the other? The result of regression will be absolutly depends on values of these parameters.
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