*
* Griliches exercise from page 236
*
open data grilic.xls
data(org=columns,format=xls) 1 758 $
    rns rns80 mrt mrt80 smsa smsa80 $
    med  iq   kww  year $
    age age80 s s80 expr expr80 tenure tenure80 lw lw80
*
* Generate year dummies
*
set y66 = year(t).eq.66
set y67 = year(t).eq.67
set y68 = year(t).eq.68
set y69 = year(t).eq.69
set y70 = year(t).eq.70
set y71 = year(t).eq.71
set y73 = year(t).eq.73

*
* (a) Table I
*
table
cmom(print,corr)
# s iq

*
* (b1) wage equation by OLS, ability ignored
*
linreg(title="OLS, Ability ignored") lw
# s expr tenure rns smsa y66 y67 y68 y69 y70 y71 y73
*
* (b2) wage equation by OLS, IQ included
*
linreg(title="OLS, IQ included") lw
# s iq expr tenure rns smsa y66 y67 y68 y69 y70 y71 y73
*
* (b3) 2SLS on wage equation: schooling predetermined
*
instruments s expr tenure rns smsa y66 y67 y68 y69 y70 y71 y73 med kww mrt age
linreg(inst,title="IV with Schooling Predetermined") lw / res0
# s iq expr tenure rns smsa y66 y67 y68 y69 y70 y71 y73
*
* (c) Sargan statistic. This differs from the "J" statistic in the regression output
*     only by a degrees of freedom correction in the variance estimator
*
compute sargan=%uzwzu/(%rss/%nobs)
cdf(title="Sargan Specification Test") chisquare sargan 3
*
* (d) 2SLS as two OLS's
*
linreg iq
# s expr tenure rns smsa y66 y67 y68 y69 y70 y71 y73 med kww mrt age
prj iqhat
linreg lw
# s iqhat expr tenure rns smsa y66 y67 y68 y69 y70 y71 y73
*
* (e) 2SLS on wage equation: schooling endogenous
*
instruments expr tenure rns smsa y66 y67 y68 y69 y70 y71 y73 med kww mrt age
linreg(inst,title="IV with Schooling Endogenous") lw
# s iq expr tenure rns smsa y66 y67 y68 y69 y70 y71 y73
compute sargan=%uzwzu/(%rss/%nobs)
cdf(title="Sargan Specification Test") chisquare sargan 2
*
* (f) GMM estimation of wage equation
*
* 1st GMM: schooling predetermined
*
* Method 1 - using the OPTIMALWEIGHTS option. This will pick the "optimal"
* weights for this regression. You don't have to use ROBUSTERRORS with this.
*
instruments s expr tenure rns smsa y66 y67 y68 y69  y70 y71 y73 med kww mrt age
linreg(inst,optimalweights) lw
# s iq expr tenure rns smsa y66 y67 y68 y69 y70 y71 y73
*
* Method 2 - computing the weight matrix directly. We need to do this in this
* application, because we want to make sure that the same set of residuals go
* into each weight matrix or we might end up with a poorly behaved test statistic
*
instruments s expr tenure rns smsa y66 y67 y68 y69  y70 y71 y73 med kww mrt age
mcov(instruments) / res0
linreg(inst,wmatrix=inv(%cmom),robusterrors) lw
# s iq expr tenure rns smsa y66 y67 y68 y69 y70 y71 y73
compute j0=%uzwzu
*
* 2nd GMM: schooling endogenous
*
instruments expr tenure rns smsa y66 y67 y68 y69 y70 y71 y73 med kww mrt age
mcov(instruments) / res0
linreg(inst,wmatrix=inv(%cmom),robusterrors) lw
# s iq expr tenure rns smsa y66 y67 y68 y69 y70 y71 y73
compute j1=%uzwzu
compute cstat=j0-j1
cdf(title="Test for Exogeneity of Schooling") chisquare cstat 1
*
* (g) 2SLS on wage equation: don't use MED and KWW
*
instruments expr tenure rns smsa y66 y67 y68 y69 y70 y71 y73 mrt age
linreg(inst) lw
# s iq expr tenure rns smsa y66 y67 y68 y69 y70 y71 y73
*
* What's going on?
*
linreg s
# expr tenure rns smsa y66 y67 y68 y69 y70 y71 y73 mrt age
linreg iq
# expr tenure rns smsa y66 y67 y68 y69 y70 y71 y73 mrt age