2. A persistent question in labor economics is how having an additional child in
ID: 3359308 • Letter: 2
Question
2. A persistent question in labor economics is how having an additional child influences a woman's labor supply (i.e. the decision whether or not to work, how many hours to work). To make things as simple as possible, suppose we are interested in the causal effect of having a third child on labor supply. Using OLS to estimate an equation such as: Hours of work = + Had Third Child + e is problematic because having a third child is not randomly assigned. 2a. Describe a factor that would lead to bias in the estimate of in the above equation. You should explain how this factor affects both the probability of a woman having a th the amount of hours a woman works. ird child and To get around the problem you described above, consider using an instrument for having a third child. Proposed Instrumental Variable -A woman's first two children are the same gender (e.g. either both girls or both boys). That is: T-l if first 2 children are same gender T-0 if first 2 children are boy and girl 2b. State the relevance condition in this context 2c. Do you think the relevance condition is satisfied in this case? Explain. 2d. State the exclusion restriction in this context 2e. Do you think the exclusion restriction is satisfied in this case? Explain.Explanation / Answer
Answer to the question)
Part 2a)
The fact that not many people go for a third child , will automatically influence the value of beta if we assign the samples randomly.
Firstly , the probability of woman to have a third child would be really low
Secondly, if a woman goes for a third child , it would be difficult for her to give more hours to work. This implies it would cause reduction in working hours
since we consider the factor "not many women go for third child " this means beta would be biased towards no third child , and probability of having a third child would be greatly reduced, plus women will have more time to work.
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Answer to part 2 b)
The relevance condtion is that the fact that there are two children of same gender , and the fact that the women goes for third chidl must be correlated
If they are correlated only then the instrument variable is relevant
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Answer to part 2c)
Since we know that is a woman has one boy and one girl child , she will mostly not go for third child. But if a child has both girls or both boys, then there are more chances for the woman to go for a third child with th expectation fo being blessed with a boy or girl repectively. Hence we consider the instrument variable and chances of third child to be related to each other
thus the relevance condition thus satisfy in this case
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Answer to part 2d)
The exclusion restirction in this case means that the instrument variable , that women having kids of same gender , must not suffer from the same problem as the original variable.
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Answer to part 2e)
Yes in this case including the insturment variable , helps us find the nedd for the third child , and thus provides us the women who are more likely to go for the third child , thus eliminating the problem of random assigment for third child
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