# econometrics.it

Federico Belotti's niche on the web

## Efficiency and Productivity Analysis Summer Programme (EPASP)

CEIS, Centre for Economics and International Studies - Tor Vergata is hosting the 1st ERASMUS Intensive Programme on Efficiency and Productivity Analysis Programme (EPASP) organised with CHE, Centre for Health Economics - University of York and COHERE, Centre for Health Economics Research - University of Southern Denmark.

This course will present the latest contributions and developments in the field of efficiency and productivity growth measurement in manufacturing and services. The objective is to provide a comprehensive and up–to–date survey of the existing models, together with a significant discussion on data and on the core methods of practically measuring efficiency and productivity. First, the students are introduced to the measurement of partial and total factor productivity growth. Different parametric and non–parametric approaches to the productivity measurement in the context of firm–specific modeling are discussed. Second, a detailed survey of the econometric approach to efficiency analysis will be discussed, focusing on modeling, distributional assumptions and estimation methods. The correspondence between a number of hypotheses and empirical findings are examined through a varieties of relevant empirical applications. Third, measurement of inputs and outputs in manufacturing and services are discussed, with a particular emphasis to the analysis of efficiency and productivity growth in the service sector.

Morning classes will cover theoretical topics while computer sessions, in the afternoon, will focus on applied issues that will be analysed, mainly, using the Stata commands sfcross and sfpanel, two new user written packages documented at Stata Journal.

For this reason a good knowledge of STATA (data management, do file programming) is a prerequisite for the admission.

## sfcross and sfpanel: stochastic frontier analysis using Stata

Two new Stata commands for the estimation and post-estimation of cross-sectional and panel data stochastic frontier models. sfcross extends the official 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 inefficiency models compared to the official 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(http://www.econometrics.it/stata)
net install sfpanel, all from(http://www.econometrics.it/stata)