# William Greene, Econometric Analysis, 5e, Chapter 9
open greene5_1.gdt

# Use OLS to initialize the parameters
ols realcons 0 realdpi
scalar a = $coeff[1]
scalar b = $coeff[2]
scalar g = 1.0

# Run NLS with analytical derivatives
nls realcons = a + b * (realdpi^g)
 deriv a = 1
 deriv b = realdpi^g
 deriv g = b * realdpi^g * log(realdpi)
end nls

# Compare result using numerical derivatives
nls realcons = a + b * (realdpi^g)
 params a, b, g
end nls