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# Replicate illustrative NLS model from Russell Davidson
# This example is associated with his econometrics program
# ECTS; see http://russell.vcharite.univ-mrs.fr/ects4/
open ects_nls.gdt
ols y 0 x1 x2 --vcv
scalar alpha = $coeff[1]
scalar beta = $coeff[2]
scalar a0 = alpha
scalar b0 = beta
# with analytical derivatives
nls y = alpha + beta*x1 + (1/beta)*x2
deriv alpha = 1
deriv beta = x1 - x2/(beta*beta)
end nls --vcv
# with numerical derivatives
alpha = a0
beta = b0
nls y = alpha + beta*x1 + (1/beta)*x2
params alpha beta
end nls --vcv
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