Use the data in LABSUP to answer the following questions. These are data on almost 32,000 black or Hispanic women. Every woman in the sample is married. It is a subset of the data used in Angrist and Evans (1998). Our interest here is in determining how weekly hours worked, hours, changes with number of children (kids). All women in the sample have at least two children. The two potential instrumental variables for kids, which is suspected as being endogenous, work to generate exogenous variation starting with two children. See the original article for further discussion.

(i) Estimate the equation

by OLS and obtain the heteroskedasticity-robust standard errors. Interpret the coefficient on kids. Discuss its statistical significance.

(ii) A variable that Angrist and Evans propose as an instrument is samesex, a binary variable equal to one if the first two children are the same biological sex. What do you think is the argument for why it is a relevant instrument for kids?

(iii) Run the regression

and see if the story from part (ii) holds up. In particular, interepret the coefficient on samesex. How statistically significant is samesex?

(iv) Can you think of mechanisms by which samesex is correlated with u in the equation in part (i)? (It is fine to assume that biological sex is randomly determined.) [Hint: How might a family’s finances be affected based on whether they have two children of the same sex or two children of opposite sex?]

(v) Is it legitimate to check for exogeneity of samesex by adding it to the regression in part (i) and testing its significance? Explain.

(vi) Using samesex as an IV for kids, obtain the IV estimates of the equation in part (i). How does the kids coefficient compare with the OLS estimate? Is the IV estimate precise?

(vii) Now add multi2nd as an instrument. Obtain the F statistic from the first stage regression and determining whether samesex and multi2nd are sufficiently strong.

(viii) Using samesex and multi2nd both as instruments for kids, how does the 2SLS estimate compare with the OLS and IV estimates from the previous parts?

(ix) Using the estimation from part (viii), is there strong evidence that kids is endogenous in the hours equation?

(x) In part (viii), how many overidentification restrictions are there? Does the overidentification test pass?

Transcribed Image Text:

hours Bo + Bikids + B,nonmomi + Bzeduc + Bage + Bsage + Boblack + Bzhispan + u