Labor Field Exam Aug 14

Part II – Oaxaca - Blinder Redux Consider an economy where each individual’s wages are determined by one of two skill pricing regimes: “male” or “female”. These regimes can be represented by the system: Y m i = α m + S i β m + p m ε i Y f i = α f + S i β f + p f ε i where Y m i gives the log wage of individual i under the male pricing regime, Y f i gives i ’s log wage under the female pricing regime, S i denotes i ’s years of schooling, and ε i denotes individual i ’s unobserved skill level. The parameters ( α m , α f ) are scalar intercepts, ( β m , β f ) are scalar “returns” to schooling, and ( p m , p f ) are the scalar “prices” of skill under the gender specific regimes. Suppose additionally that: E [ ε i | S i ] = 0 . Assignment to these regimes involves some randomness. Let the random variable G i evaluate to m in the event that the individual is a man and f in the event that the individual is a woman. We can now define observed wages as: Y i ≡ 1 [ G i = m ] Y m i + 1 [ G i = f ] Y f i . Assume that we have access to a random sample of pairs { Y i , G i } N i =1 . Questions a) Comment on the interpretation of the following conditional independence assumption (CIA): ε i ⊥ G i | S i . What are some reasons why this condition might fail? b) Use the CIA assumption to prove that ( α m , α f , β m , β f ) are identified along with the ratio p m /p f . c) Provide an interpretation of α m and α f . Does the interpretation change if we measure schooling in different units? (e.g. years since 6th grade?) d) Suppose that, for g ∈ { m, f } , the population values of ( α g , β g ) and μ g ≡ E [ S i | G i = g ] are given by: Mean Schooling ( μ g ) Return ( β g ) Intercept ( α g ) Male 10 .12 2 Female 11 .10 1.9 Derive the impact on women’s mean wages of replacing the female distribution of schooling F S | G = f ( . ) with the male distribution F S | G = m ( . ). e) Derive the impact on women’s mean wages of changing the female return to schooling from β f to β m . f) Derive the impact on women’s mean wages of giving them both the male return to schooling and the male schooling distribution F S | G = m ( . ). g) How does this compare to the sum of your answer answers from parts e) and f)? Why? 1