Economics 4G03/6G03 (Econometrics II) Theory Assignment 3 Fall 2022

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Economics 4G03/6G03 (Econometrics II)

Theory Assignment 3

Fall 2022

Wed. Nov 23, 2022 (in class, on paper)

1) Consider the instrumental variables regression where the equation of interest is: ln(w) = b0 + b1 S + b2Age + b3Age2 + b4F + u

and you want to estimate the causal impact of schooling on ln(w), where w is wages ($/hour), S is years of schooling, age is measured in years and F is an indicator variable for identifying as   female.

You have two instruments: the compulsory schooling age in the location where you lived at age  14 thru 18, and the school start age in the region where you lived at age 4 thru 6. (Ignore issues of people moving in those age ranges.) The idea is that a higher compulsory schooling age, and a younger school start age, cause students to obtain additional years of schooling for “as if” random reasons. You have a single very large cross-section of data from the census with information on individuals as adults.

a.          Is the instrumental variables model under-, over-, or just-identified?

b.         For TSLS, write out the equation for the first and second stages of the estimator and explain their operation.

c.           Do Age and F qualify as control variables? Why or why not?

d.          Briefly outline the two central IV criteria and discuss whether you believe that they are met in this case. How could you test/evaluate whether the IV criteria are met? What happens if either/both of these two criteria are not satisfied?

e.          Will this estimator work in “small” samples?