2. A persistent question in labor economics is how having an additional child in
ID: 3358577 • 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 third child and the amount of hours a woman works. 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 (c.g. either both girls or both boys). That is: T-1 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
2. Let us name the variables like:
X: Indicator for having 3rd child
Y: Hours of Labour
2a. Under an OLS setup the basic assumption that X and e (error) are uncorrelated.
However that is not the case here. The indicator for having a 3rd child is influenced by say the educational background of the woman.
In general if the woman is having a high level of education then indicator for 3rd child will mostly be zero but it will also mean that woman will be giving many hours of manual labor. So the effect brought in by the factor - level of education (say '1' if having high school degree or lower and '0' if having graduate degree and above) is confounded in the error term and it is correlated with X. Hence the beta estimate will get distorted since the assumption of no correlation between X and e will be violated.
2b and c. An instrumental variable Z is used to aid X in OLS- Z divides X into 2 parts - Z itself which is correlated with X but not with error and the error of regression of X on Z which is uncorrelated with error e.
Here the instrumental variable is the binary - Gender of first 2 child is same or not.
The instrumental variable is called relevant if Corr(Z,X) not equal to 0. Here probability of having a 3rd child is mostly driven by wheather the first 2 child were of same gender on not and hence the desire for a 3rd child of different gender. Hence X and Z correlated. So the instrumental variable Z is relevant.
2d and e) The instrumental variable is excluded from the main OLS only if Corr(Z,e) is 0, this is the exclusion restriction. Now the indicator of the first 2 child being same gender is a completely random process and not dependant on any other external factor like educational level (mentione in (a) or similar variables.) So Z is uncorrelated with the error term e and hence it satisfies the exclusion criteria.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.