Suppose that you have an iid sample: (Wn, Fn)-1 where Wn is person n's hourly wage...

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Suppose that you have an iid sample: (Wn, Fn)-1 where Wn is person n's hourly wage and F is a binary variable equal to 1 if person n is female and 0 other- wise. Consider the linear model E[log(Wn) |Fn] = Bo + BFn. (a) Consider the null hypothesis that E[log(Wn)|Fn = 1] = E[log(Wn)|Fn = 0]. Show that this is equivalent to 3 = 0. (2 points) (b) Carefully describe how you would estimate the parameters . You can be concise, just describe how you would get from the data in a way that someone else could replicate. Do not just say what command you would use in the R programming language. (2 points) (c) What is the expected value of 3? (1 point) (d) What is the probability limit of as N ? Which theorem guarantees this? (2 points) Suppose that you have an iid sample: (Wn, Fn)-1 where Wn is person n's hourly wage and F is a binary variable equal to 1 if person n is female and 0 other- wise. Consider the linear model E[log(Wn) |Fn] = Bo + BFn. (a) Consider the null hypothesis that E[log(Wn)|Fn = 1] = E[log(Wn)|Fn = 0]. Show that this is equivalent to 3 = 0. (2 points) (b) Carefully describe how you would estimate the parameters . You can be concise, just describe how you would get from the data in a way that someone else could replicate. Do not just say what command you would use in the R programming language. (2 points) (c) What is the expected value of 3? (1 point) (d) What is the probability limit of as N ? Which theorem guarantees this? (2 points)