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st: technical efficiency using -xtrc-

From   Viktor Slavtchev <>
Subject   st: technical efficiency using -xtrc-
Date   Mon, 04 Feb 2008 09:48:38 +0100

Dear all,
I wish to estimate the technical efficiency at firm level in panel data.
The production function (Cobb-Douglas) is considered to have one output and one input, y = a * x^beta
After taking logs of both sides I try to estimate the following equation:
y[i,t]=alpha[i] + beta[i]*x[i,t] + e[i,t].
The technical efficiency can be computed as:
TE[i,t]=exp(y[i,t] - y'[i,t]),
where y[i,t] is the firm's actual output (not the estimated).
y'[i,t] is the technical frontier computed considering the maximum values for alpha and beta: y'[i,t]=max_i(alpha[i]) + max_i(beta[i])*x[i,t] + e[i,t].
That is the firm's observed output is compared to the maximum possible output, i.e. if the firm's production function would have the largest possible intercept and the largest possible slope.
To estimate the alpha and beta I use -xtrc-. However, and that's my problem, the interval for the estimates of both, alpha and beta is huge. Considering the slope (beta), the values become in some cases even negative. Given the huge variation in alpha and beta, the efficiency measure appears in some cases implausible small.
Does anybody has more experience with estimating efficiency? Any help is greatly appreciated.
Best regards,

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