Katrin is investigating whether there is a wage gap between women and men. She has set up the following model: Model 1:

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Katrin is investigating whether there is a wage gap between
women and men. She has set up the following model:
Model 1:
wage = B0 + B1*education + B2*gender + B3*experience +
B4*industry + B5*type_of_employment + error
where
education - is measured in years
gender - is equal to 1 for men and 0 for female (in this dataset
there is information only about 2 genders)
experience - years of experience in the position
industry - set of dummies indicating different
industries
type of employment - set of dummies indicating different
employment types i.e. permanent contract, short-term contract
etc.
She has also estimated a reduced form equation of the following
type:
Model 2:
education = A0 + A2*gender + A3*experience + A4*industry +
A5*type_of_employment + +A6*mother_education + A7*father_education
+ error
Based on the information above, please answer the
following questions. Remember to use your own
words.
1) What type of econometric problem is present in the
Model 1 and is solved in the Model 2? What are the consequences
when that problem is present in a model? (5 points)
2) Under what conditions Model 2 presents a solution to
the problem with Model 1? (10 points)
3) What are the other methods that can be used in order
to solve the econometric problem present in the Model 1? (5
points)
4) Katrin hypothesises that in Model 2
"mother_education" and "father_education" have the same effect on
the "education" (education of their child). How can she test it?
Explain step by step. (10 points)