# Wooldridge 4e, Problem C7.8

open loanapp -q
# simple regression on "white"
ols approve 0 white 
list X = hrat obrat loanprc unem male married dep sch cosign \
 chist pubrec mortlat1 mortlat2 vr
ols approve 0 white X
# generate and add interaction effect
genr inter = white * obrat
add inter

# investigate "white" derivative at obrat = 32
scalar obval = 32
# magnitude of effect (derivative)
scalar wderiv = $coeff(white) + obval*$coeff(inter)
# get std error using the covariance matrix
matrix V = $vcv
scalar irow = rows(V)
scalar v_wderiv = V[2,2] + (obval^2)*V[irow,irow] + 2*obval*V[2,irow]
scalar se_wderiv = sqrt(v_wderiv)
scalar maxerr = 1.96 * se_wderiv
printf "95%% CI: %.3f to %.3f\n", wderiv - maxerr, wderiv + maxerr