and outputs (namely the cost function). Different from stochastic frontier analysis,
econometric production models can only obtain the average production function,
not the production frontier. While the similarity to both methods is that the form of
function should be set before estimation. Some regular forms of function include
linear, Cobb-Douglas, translog, quadratic and so on. The regular parameter esti-
mation techniques in econometric production models include Least Square (LS),
Maximum Likelihood (ML) and Bayesian Estimation, of which LS and ML are
used more widely.
Index measurements are the commonly-used instruments to measure changes in
levels of various economic variables. When measuring productivity, the major role
of index is to measure of changes in TFP, namely the popular TFP index.
Data Envelopment Analysis (DEA) is a non-parametric method. It is based on
Farrrell’s early work of single-input-single-output efficiency, and then developed
into a method to evaluate the relative efficiency of multi-input-multi-output
Decision Making Units (DMUs). This method isfirst proposed by Charnes et al.
( 1978 ), then many researchers made efforts to develop this method, and extend to
Constant Return to Scale (CRS) model, Variable Return to Scale (VRS) model,
Non-Increasing Return to Scale (NIRS) model, and Non-Decreasing Return to
Scale (NDRS) model (Wei 2004 ). DEA has been developed into a relatively mature
method, and widely used in management sciences.
Stochastic Frontier Analysis (SFA) uses econometric model including a special
random error term to estimate production frontier function, and calculate efficiency
and productivity. Aigner et al. ( 1977 ) and Meeusen and Van Den Broeck ( 1977 )
independently proposed similar stochastic frontier production model fit for
cross-sectional data. The model is consisted of a production function and two error
terms: one is a random error term with a mean value of zero, representing statistical
noise; the other is a random error term with a non-negative mean value, repre-
senting technical inefficiency. Afterwards, some researchers applied this model in
empirical studies, and made some modifications to the hypothesized distribution of
inefficient error term, and then put forward truncated normal distribution (Stevenson
1980 ), and gamma distribution (Greene 1990 ). Then Battese and Coelli ( 1992 )
proposed a stochastic frontier modelfit for panel data, which allows for the tech-
nical inefficiency levels to change systematically over time (namely, time-varying
inefficiency model).
The advantage of using SFA to estimate technical efficiency is increasingly
recognized by researchers, but the major barriers hindering its broader application
are the unobservable random error and technical efficiency, as well as the strict
distributional assumptions. Owing to the work of Pitt and Lee ( 1981 ) on extending
ML technique from cross-sectional data to panel data, Battese and Coelli ( 1995 )
used likelihood ratio technique to test the existence of inefficiency effects, the
distributional assumption of stochastic error and technical efficiency. This enables
SFA to have much broader room in application and empirical studies.
Both DEA and SFA belong to frontier estimation methods, and can be used to
obtain estimates of TFP change, and decompose these estimates into components,
such as technical change, scale efficiency change and technical efficiency change.
2.3 Recent Development on Efficiency and Productivity Analysis 17