The table below provides results on regressions in a two-stage least squares analysis of the effect of education on earnings. The data are for 428 employed individuals. The variable lwage is the log of wages for received by each individual, exper is the years of experience for each individual, experSq is experience squared, educ is the years of education each individual has obtained prior to working, and fatheduc and motheduc are the years of education obtained by each individual's father and mother.

a. Briefly explain why instrumental variables might be needed for the variable educ in the final model.

b. Are the instruments fatheduc and motheduc useful instruments in the first stage regression? Briefly explain why or why not and write down any specific hypothesis tests you would rely on in answering this question.

c. Do the results presented below present sufficient evidence to argue that education has no effect on wage? Explain why or why not.

d. Predict the expected effect of a one-year increase in educ on expected wage. Show your work.

ivreg lwage (educ = fatheduc motheduc) exper experSq, first

First-stage regressions

Number of obs =428

R-squared=0.2115

educ |Coef.Std. Err.TP>|t|[95% Conf. Interval]

-------------+----------------------------------------------------------------

exper |.0452254.04025071.120.262-.0338909.1243417

experSq |-.0010091.0012033-0.840.402-.0033744.0013562

fatheduc |.1895484.03375655.620.000.1231971.2558997

motheduc |.157597.03589414.390.000.087044.2281501

_cons |9.10264.426561421.340.0008.2641969.941084

Instrumental variables (2SLS) regression

Source |SSdfMSNumber of obs =428

-------------+------------------------------F(3,424) =8.14

Model |30.3074256310.1024752Prob > F=0.0000

Residual |193.020015424.455235885R-squared=0.1357

-------------+------------------------------Adj R-squared =0.1296

Total |223.327441427.523015084Root MSE=.67471

lwage |Coef.Std. Err.TP>|t|[95% Conf. Interval]

-------------+----------------------------------------------------------------

educ |.0613966.03143671.950.051-.0003945.1231878

exper |.0441704.01343253.290.001.0177679.0705729

experSq |-.000899.0004017-2.240.026-.0016885-.0001094

_cons |.0481003.40032810.120.904-.7387744.834975

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Instrumented:educ

Instruments:exper experSq fatheduc motheduc