2. Suppose that the county of Foxfordshire (F) has passed a law requiring employers to provide 6 months of paid maternity leave. You are concerned that women's wages will drop in order to pay for this new benefit. You find a data set that samples men and women in Foxfordshire and in neighboring Wolfordshire (W) and has information on wages. You pool 2 cross-sections, one from the year before the law took effect and one from the year after and find that the mean wage for various groups is as: Wolfordshire Foxfordshire Before Before After After 12 Women 9 7 9 Men 12 14 A. Suppose you estimate the following model using only data from Foxfordshire: wage = b0 + blafter + b2women + b3after*women + u, where after and women are dummy variables for the second period and being a woman respectively. What is your estimate of b3? If this were taken to be the effect of the law, what would your point estimate suggest about the effect that the law had? B. Under what assumption will b3 in part A give us the law's effect? Can you suggest a scenario where this assumption might fail? C. Suppose for the data for Foxfordshire from the above table, we instead ran the regression wage c0 + clafter + c2men + c3after*men + u, i.e., instead of a dummy for women, we used a dummy for men which is 1 for men and zero otherwise. What would be the value of the coefficient c3? D. Suppose instead you estimate the following model on all of the data: wage b0 + blafter + b2women + b3F + b4after*F + b5after*women + b6F*women + b7after*women F + u, where after and women are as before and F is a dummy variable for Fooxfordshire. What is your estimate of b7? E. Under what assumption will b7 give us the effect of the law? Can you describe a scenario that would lead to the violation of this assumption? (Hint: You may find it easier to think about the outcome as the gender gap in wages and then interpret the table as a standard diff-in-diff)