Answer Happy

Consider the wage equation used given as follows: 𝑙𝑛(𝑊 𝐴𝐺𝐸) = 𝛽1
+ 𝛽2𝐸𝑋𝑃𝐸𝑅 + 𝛽3𝐸𝑋𝑃𝐸𝑅2 + 𝛽4𝐸𝐷𝑈𝐶 + µ (a) Suppose we have a variable
designed to measure ability (AB). This variable is an index created
using 10 different tests of cognitive ability. Using data on 2,178
university graduates in 2004, the ability variable has a sample
mean of 0.04 and a standard deviation of 0.96. (b) The estimated
relationship between years of education and the ability measure is
𝐸𝐷𝑈𝐶 = 12.30 + 0.977𝐴𝐵 with a t−value of 25.81. Is this result
consistent with the usual “omitted variables bias” explanation of
the endogeneity of education? Explain (c) Using these data, a model
for education was the estimated and the results yield the
following: coefficient on EDUC is 0.0609 with standard error 0.005.
Adding AB to the equation reduces the estimated coefficient on EDUC
to 0.054 with standard error 0.006. Is this the effect that you
anticipate? Explain. (d) Assuming that AB and EXPER are exogenous,
along with instrumental variables MOTHEREDUC and FATHEREDUC, what
is the specification of the first-stage equation? That is, what
variables are on the right-hand side?