Federico Belotti's niche on the web

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:

y_{it} = \alpha + X_{it}\beta + v_{it} \pm u

where v_{it} is a normally distributed error term and u is a one-sided strictly non-negative term representing inefficiency. The sign of the u term is positive or negative depending on whether the frontier describes a cost or production function, respectively. Among the time-varying inefficiency models (u=u_{it}), 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 (\alpha=\alpha_i) and time-varying firm inefficiency are considered;

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

iii) the time decay model by Battese and Coelli (1992), in which u_{it}=u_i B(t), and B(t)=\{\exp[-\eta(t-T_i)]\}. u_i is assumed to be truncated-normally distributed with non-zero mean and constant variance, while \eta governs the temporal pattern of inefficiency.

iv) the flexible parametric model by Kumbhakar (1990), in which u_{it}=u_i B(t) , and B(t)=[1+\exp(bt+ct^2)]^{-1}.

Among the time-invariant inefficiency models (u=u_i), sfpanel fits:

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

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

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

y_{it} = \alpha + X_{it}\beta + v_{it}

Among the time-varying inefficiency models (\alpha=\alpha_{it}), sfpanel fits:

vii) the Lee and Schmidt (1993) model, in which \alpha_{it} = \theta_t \delta_i and \theta_t are parameters to be estimated. This model is a special case of Kumbhakar (1990), in which B(t) is represented by a set of dummy variables for time.

viii) the Cornwell et al. (1990) model, in which \alpha_{it} = \delta_{i0} + \delta_{i1} t + \delta_{i2} t^2

Among the time-invariant inefficiency models (\alpha=\alpha_i), sfpanel fits:

ix) the Schmidt and Sickles (1984) model in which \alpha_i 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(
net install sfpanel, all from(

in your Stata command bar.

Click here to access the accompanying paper.


A new Stata command to estimate two-part models for mixed discrete-continuous outcomes is now available at SSC/

In two part models, a binary choice model is estimated for the probability of observing a zero versus positive outcome. Then, conditional on a positive outcome, an appropriate regression model is estimated for the positive outcome.

twopm focuses on continuous outcomes modeled using regress or glm. When the outcome is a count variable, such models are known as hurdle models. Of special note is that twopm allows the user to leverage the capabilities of predict and margins to calculate predictions and marginal effects from the combined first- and second-part models.

It was written together with Partha Deb.
You may install the command by typing

ssc install twopm

in your Stata command bar.


Hi guys! I'm very happy to announce 🙂 that on June 20, 2012 I will receive the "Italian Statistical Society prize 2011" for the best Italian PhD thesis on Applied Statistics and Demography discussed in year 2011. I will present in about 25 minutes some results from my work on panel data stochastic frontier models and robust estimation of finite mixtures of Count regression models. The 46th SIS Scientific Meeting will be held in Sapienza University of Rome -  Faculty of Economics, Via Del Castro Laurenziano, 9. You can find more information on the meeting here.

Follow this link to get a sample research paper for an introductory course in econometrics. I find that it is a good guide on how to write down an empirical paper. The proposed template integrates many writing instructions and rules into a single example and shows how they all fit together. My advice is to pay attention to the structure of the paper and how the descriptive statistics and empirical results are presented.


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