Two new Stata commands for the estimation and post-estimation of cross-sectional and panel data stochastic frontier models. sfcross extends the official frontier capabilities by including additional models (Greene 2003; Wang 2002) and command functionality, such as the possibility to manage complex survey data characteristics. Similarly, sfpanel allows to estimate a much wider range of time-varying inefficiency models compared to the official xtfrontier command. In particular, when estimation is done with likelihood-based methods, the SF model is:

where is a normally distributed error term and is a one-sided strictly non-negative term representing inefficiency. The sign of the term is positive or negative depending on whether the frontier describes a cost or production function, respectively. Among the time-varying inefficiency models , sfpanel fits:

i) the true fixed-effects (TFE) and the true random-effects (TRE) models developed by Greene (2005), in which both time-invariant unmeasured heterogeneity and time-varying firm inefficiency are considered;

ii) the Battese and Coelli (1995) model, in which the is obtained by truncation at zero of the normal distribution with mean , where is a set of covariates explaining the mean of inefficiency;

iii) the time decay model by Battese and Coelli (1992), in which , and . is assumed to be truncated-normally distributed with non-zero mean and constant variance, while governs the temporal pattern of inefficiency.

iv) the flexible parametric model by Kumbhakar (1990), in which , and .

Among the time-invariant inefficiency models , sfpanel fits:

v) the Battese and Coelli (1988) model, in which is truncated-normally distributed with non-zero mean and constant variance;

vi) the Pitt and Lee (1981) model, in which is half-normally distributed with constant variance;

When estimation is done with least squares methods, the SF production model is:

Among the time-varying inefficiency models , sfpanel fits:

vii) the Lee and Schmidt (1993) model, in which and are parameters to be estimated. This model is a special case of Kumbhakar (1990), in which is represented by a set of dummy variables for time.

viii) the Cornwell et al. (1990) model, in which

Among the time-invariant inefficiency models , sfpanel fits:

ix) the Schmidt and Sickles (1984) model in which can be either fixed or random.

The two commands were written together with Silvio Daidone, Giuseppe Ilardi and Vincenzo Atella.

You may install them by typing

net install sfcross, all from(http://www.econometrics.it/stata)
net install sfpanel, all from(http://www.econometrics.it/stata)

in your Stata command bar.

Click here to access the accompanying paper.

HTH,
Federico

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