A researcher would like to estimate the causal effect of education on fertility (the number of children) in the following model: children; = B1 + B2educ; + B3age; + Uj for a sample of 18-40 year old women in Botswana, where children; : the number of children woman i has, educ; : the woman's education level, in years age; : the woman's age, in years. Explain why educ; is likely to be endogenous: O a. Because educ; may be directly affected by the number of children a woman has. O b. Because age impacts both education and the number of children. O c. Both a) and b) are true. To address the endogeneity problem, the researcher wants to use the variable firsthalf;, which is a dummy variable equal to 1 if the woman was born during the first six months of the year and 0 otherwise, as an instrument for educ;. May firsthalf; be a good instrument? O a. It is a good instrument if being born in the first or the second half of the year impacts the minimal years of education required, but is not directly correlated with variables that can impact the number of children (other than through education per se). O b. It is not a good instrument if there is evidence that families with working mothers (generally of higher socioeconomic status) have children more often in the first half of the year. O c. Both a) and b) are true