Northeastern University – ECON 2560

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Applied Econometrics – Fall 2022

Homework #7     Due date:  Thursday Nov 10, by 11:59 pm

  • You may complete this assignment individually or with a group; in either case every student must turn in their own copy.
  • If you miss the due date, you may submit your assignment within the next 24 hours, although there is a penalty for late submission
  • Please upload your assignment answers into Canvas.  Your answers can be in Word, PDF, or Excel.
  • Show work for partial credit.

1.  Consider the system of equations below, where Y variables are endogenous and X variables are exogenous to the system, and a, b, c, etc. are coefficients. Use the order condition to determine whether each equation is underidentified, exactly identified, or overidentified.

                                                       (1)

                                                                    (2)

2.  Using the data in morewages.xlsx,

  1. Estimate an OLS regression of lwage (natural log of wages) against education, experience, experience squared, urban, and married and report the key output.
  2. Concern about endogeneity bias on the educ coefficient, from unmeasured ability, leads you to want to estimate the equation using instrumental variables. It has been proposed that the number of siblings could be a valid instrument for education — since it could be uncorrelated with ability, but being one of more siblings is likely to reduce a child’s education (e.g. affordability of college).  Estimate the equation in a) using 2SLS where the instrument for education is sibs, and report the output for both the first and second stages.

3.  Using the binomial model,

  1. What is the probability of observing a set of independent realizations Y1 = 1, Y2 = 0, Y3 = 1, Y4 = 0 if P1 = .5, P2 = .4, P3 = .6, P4 = .3?
  2. What is the probability of observing the same set of independent realizations Y1 = 1, Y2 = 0, Y3 = 1, Y4 = 0 if P1 = .6, P2 = .4, P3 = .6, P4 = .3?