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# Estimate Weibull duration model on Kennan strike data
# Compare W. Greene, "Econometric Analysis", 5e, Chapter 22.
# We first use the mle command, then compare the built-in
# "duration" command.
open kennan
# Initial OLS to get starting values for the coefficients
ols log(Ti) 0 Prod --quiet
scalar b0 = $coeff(0)
scalar b1 = $coeff(Prod)
scalar s = 1
# useful auxiliary variables
series Xb = b0 + b1*Prod
series Z = (l_Ti - Xb) / s
series W = 0
mle loglik = Z - log(s) - exp(Z)
series Xb = b0 + b1*Prod
series Z = (l_Ti - Xb) / s
series W = -(1 - exp(Z)) / s
deriv b0 = W
deriv b1 = Prod * W
deriv s = -Z/s - 1/s + exp(Z) * Z/s
end mle --hessian
printf "p = %g\n", 1/s
# compare the built-in command
duration Ti 0 Prod
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