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# MLE estimation based on Lucchetti, R., Papi, L., and Zazzaro, A.
# (2001) "Banks' Inefficiency and Economic Growth: A Micro Macro
# Approach", Scottish Journal of Political Economy, 48, pp. 400–424.
set echo off
set messages off
open banks91.gdt
# descriptive statistics (Table 1, p. 409)
summary VC Q1 Q2 P1 P2 P3 --simple
# transformations
series cost = ln(VC)
series q1 = ln(Q1)
series q2 = ln(Q2)
series p1 = ln(P1)
series p2 = ln(P2)
series p3 = ln(P3)
# Cobb-Douglas cost function with homogeneity restrictions
# (unreported - used for initialization)
series rcost = cost - p1
series rp2 = p2 - p1
series rp3 = p3 - p1
list X = const q1 q2 rp2 rp3
ols rcost X --quiet
# Cobb-Douglas cost function with homogeneity restrictions
# and inefficiency (Table 2, p. 410)
matrix b = $coeff
scalar su = 0.1
scalar sv = 0.1
series e
mle logl = ln(cnorm(e*lambda)) - (ln(ss) + 0.5*e^2)
scalar ss = sqrt(su^2 + sv^2)
scalar lambda = su/sv
e = (rcost - lincomb(X, b)) / ss
params b su sv
end mle
scalar ss = sqrt(su^2 + sv^2)
scalar lambda = su/sv
series le = lambda * e
series eff = ss*lambda/(1 + lambda^2) * (invmills(-le) + le)
# Table 3, p. 411
summary eff
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