Statistical Assigment 2 This statistical assignment gets your hands "dirty" with R. This statistical assignment is due at noon on Monday May 1. You may work in teams of 2 or 3 (or by yourself...) and hand in one assignment for the team. Make sure that all names as they appear on Albert of the team are on the assignment. 20% will be docked for each day late the assignment is handed in. 1 Dataset Details The dataset for this assignment "data_assign2.csv" comes from the US Census. The sample in your dataset covers women with at least 2 children. The dataset consists of 254,645 observations from the 1990 census. There are variables in the dataset are: . thirdkid: indicator equal to one if mother has 3 or more kids (i.e., =1 if kids 3, =0 if kids <3) boy1st: indicator equal to one if first child is a boy (i.e., =1 if First child is boy, =0 if First child is girl) boy2nd: indicator equal to one if second child is a boy (i.e., =1 if Second child is boy, =0 if Second child is girl) ageml: age of the mother in 1990 agefstm: age of the mother at first birth black: indicator equal to one if mother is African American (and = 0 otherwise) hisp: indicator equal to one if mother is Hispanic (and =0 otherwise) othrace: indicator equal to one if mother is other non-white race (and =0 otherwise) (e.g., Filipino, Pacific Islander, Multi-racial) workedm: indicator equal to one if mother is working (=0 if not working) incomem: weekly labour market income of the mother (not used in this assignment, but there if you are interested). General Instructions Please hand in assignment as one document. Please answer the questions succinctly. For this assignment, we are interested in estimating the following relationship: Yi Bo + Bithirdkid; + where: y: Indicator for mother i working (i.e., the 'workedm' variable in your dataset) thirdkid: Indicator for mother i having three children Question 1 What is the probability of having a third child for parents whose first two children are the same gender? What about for parents whose first two children are of different genders? Describe why this provides a 'first-stage' for the instrument. Question 2 Estimate the 'first-stage' and 'second-stage' of the instrumental variable regression using "same gender for first two kids" as the instrument without any additional controls. Interpret the point estimate for both the 'first-stage' and 'second-stage'. Question 3 Run the instrumental variable regression without any controls. Interpret the resulting point estimate and clearly describe which type of individuals is identifying the 'LATE'. Question 4 Discuss the (internal) validity of the instrument. In addition, state who exactly a defier would be in this example and whether the no defier (or monotonicity) assumption is likely to hold. Question 5 Now run the IV regression with the following controls: race, age of the mother, age of the mother squared, age of the mother at first birth, age of the mother at first birth squared. Does the point estimate change relative to question 3? Is this reassuring in terms of (internal) validity? Describe why or why not. Question 6 We could imagine doing a different instrumental variable, but with a similar spirit. Specif- ically, there is a large amount of research that many cultures have a "boy" preference for children (i.e., parents prefer having boys to girls). In that spirit, we could define the in- strumental variable instead as having two girls" relative to "having two boys" (for first two children). Intuitively, if prior research is correct having two girls should induce some individuals to have another child relative to having two boys. Create that instrument and run the IV regression (with controls). Why do you think the estimate differs substantially from the IV estimate in Q5? [hint: think of the LATE!]