"Wu, Xun" <WuX@wharton.upenn.edu> wrote on July 10th:
"My question is about frontier's conditional mean model. I appreciate the
advice from Weihua. I also notice from the manual (pp423 of Frontier) that
"You can, in fact, apply frontier's conditional mean model to panel data".
My question is that whether I can obtain the "within" effects with this
method with my panel data. It is like using Xtreg, where it fits
fixed-effects (within) with panel data. We might just add firm dummies
besides the exogenous variables or demean the exogenous variables. However,
I have almost 10,000 firms, which I am afraid won't work with my intercooled
Yes, you can include time and firm fixed effects, however demeaning would
not be advised. In the recent Journal of Business and Economic Statistics
Vol 21, Num 3 July 2003 "A Stochastic Frontier Analysis of Financing
Constraints on Investment: The Case of Financial Liberalization of Taiwan"
by Hung-Jen Wang, does just that.
He writes (page 408 - 409) "Without firm-specific effects, the model
effectively treats multiple observations of the same firm as being obtained
form independent samples, leaving the data's panel nature unexploited. As
emphasized in studies by Kumbhakar (1991) and Kumbhakar and Hjalmarsson
(1995), failure to include firm specific effects in a panel stochastic
frontier model is also likely to bias the estimates of the one-sided error,
uit......because of the truncated error distribution, one cannot take first
differences or subtract means from the data to eliminate the effects;
differenced truncated normal distributions do not result in a known
distribution. Instead, the dummy variable approach is used as suggested in
the formulation of Kumbhakar (1991)."
In your case, is there a logical criteria to sort the 10,000 firms into
smaller subsamples (number of employees, type of firm, total assets,
debt-to-asset ratio,....)? Or you take multiple samples of 2000 firms for
The next question is: do you include these fixed effects (and/or other
factors) in production function or in the inefficiency equation
(using -uhet- you can possibly solves two problems at once - correcting for
heteroskedasticity and incorporating environmental factors on efficiency,
see Kumbhakar and Lovell, 2000).
One approach, following Good et al. (1993), embeds environmental factors
directly into the production function assuming that the environment alters
the shape of the production function. The second approach, following Battese
and Coelli (1995), assumes that environmental factors affect the degree of
technical inefficiency but not the shape of the production technology. The
first approach (the environment in the production function) produced
technical efficiency scores that are net of environmental factors. The
second approach (environment in the inefficiency equation) produces
technical efficiency scores that incorporate environmental factors. Coelli,
Perelman, and Romano (1999) has termed these gross technical efficiency
Hope this helps,
Battese, G. and T. J. Coelli (1995), "A Model for Technical Inefficiency
Effects in a Stochastic Frontier Production for Panel Data." Empirical
Coelli, T.; Perelman, Sergio; and Elliot Romano (1999), "Accounting for
Environmental Influences in Stochastic Frontier Models: With Applications
to International Airlines." Journal of Productivity Analysis 11.
Good, D., Nadiri, M., Roller, L., Sickles R. (1993), "Efficiency and
Productivity Growth Comparisons of European and U.S. Air Carriers: A First
Look at the Data." The Journal of Productivity Analysis 4.
Kumbhakar, S. (1991), "Estimation of Technical Inefficiency in Panel Data
Models with Firm and Time Specific Effects" Economic Letters, 36, 43-48.
Kumbhakar and Hjalmarsson (1995), "Labour-Use Efficiency in Swedish Social
Insurance Offices," Journal of Applied Econometrics, 10, 33 - 47.
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