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Topics in Microeconometrics Professor William Greene Stern School of Business, New York University at Curtin Business School Curtin University Perth July 22-24, 2013. 2. Stochastic Frontier Model. Stochastic Frontier Models. Motivation: Factors not under control of the firm
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Professor William Greene
Stern School of Business, New York University
Curtin Business School
July 22-24, 2013
Meeusen, van den Broeck (1977),
Battese, Corra (1977)
ui > 0, but vi may take any value. A symmetric distribution, such as the normal distribution, is usually assumed for vi. Thus, the stochastic frontier is
and, as before,ui represents the inefficiency.
Average inefficiency is embodied in the third moment of the disturbance εi= vi - ui.
So long as E[vi - ui] is constant, the OLS estimates of the slope parameters of the frontier function are unbiased and consistent. (The constant term estimates α-E[ui]. The average inefficiency present in the distribution is reflected in the asymmetry of the distribution, which can be estimated using the OLS residuals:
N = 247 farms, T = 6 years (1993-1998)
Waldman (1982) result on skewness of OLS residuals: If the OLS residuals are positively skewed, rather than negative, then OLS maximizes the log likelihood, and there is no evidence of inefficiency in the data.
From Coelli, Frontier4.1 (page 16)
We can insert our maximum likelihood estimates of all parameters.
Note: This estimates E[u|vi – ui], not ui.
Horrace, W. and Schmidt, P., Confidence Intervals for Efficiency Estimates, JPA, 1996.
y*|technology = bt’x + v –u
Firm chooses technology = 0 or 1
based on c’z+e
e is correlated with v
Sample Selection Model:
Choice of organic or inorganic
Adoption of some technological innovation
di = 1[′zi + wi > 0], wi ~ N[0,12]
yi = ′xi + i, i ~ N[0,2]
(yi,xi) observed only when di = 1.
i = vi- ui
ui = |uUi| = u |Ui| where Ui ~ N[0,12]
vi = vVi where Vi ~ N[0,12].
(wi,vi) ~ N2[(0,1), (1, v, v2)]
Kumbhakar, Sipilainen, Tsionas (JPA, 2008)
The simulation is over the inefficiency term.