PDF Introduction Frequentist Estimation STATA commands

Introduction Frequentist Estimation

Bayesian inference STATA commands Empirical application

Frequentist and Bayesian stochastic frontier models in Stata

Federico Belotti Silvio Daidone Giuseppe Ilardi

Universit? di Roma Tor Vergata, Bank of Italy

Florence, November 19th, 2009

Federico Belotti , Silvio Daidone , Giuseppe Ilardi

Frequentist and Bayesian stochastic frontier models in Stata

Summary

Introduction Frequentist Estimation

Bayesian inference STATA commands Empirical application

1 Introduction 2 Frequentist Estimation 3 Bayesian inference 4 STATA commands 5 Empirical application

Federico Belotti , Silvio Daidone , Giuseppe Ilardi

Frequentist and Bayesian stochastic frontier models in Stata

Introduction Frequentist Estimation

Bayesian inference STATA commands Empirical application

Objectives of the paper

This paper focuses on stochastic frontier models for both cross-section and longitudinal data with a parametric approach to estimation

Novel features: the newly available STATA command will

be the first bayesian estimator of frontier parameters be comprehensive of most used and state-of-art frequentist estimators make extensive use of MATA functions

Federico Belotti , Silvio Daidone , Giuseppe Ilardi

Frequentist and Bayesian stochastic frontier models in Stata

Introduction Frequentist Estimation

Bayesian inference STATA commands Empirical application

General framework -1-

- Starting from seminal study by Aigner, Lovell and Schmidt (1977), theoretical literature on stochastic frontier has grown vastly.

- The range of applications of the techniques described is huge. - The economic meaning of a frontier is to represent the best-practice

technology in a production process or in a particular economic sector. - Cost frontiers describe the minimum level of cost given a certain output

level and certain input prices. - Production frontiers represent the maximum amount of output that can

be obtained from a given level of inputs. - The gap between the actual and the maximum output is a measure of

inefficiency and an important issue in many application fields, such as production studies.

Federico Belotti , Silvio Daidone , Giuseppe Ilardi

Frequentist and Bayesian stochastic frontier models in Stata

Introduction Frequentist Estimation

Bayesian inference STATA commands Empirical application

General framework -2-

- A general stochastic frontier model may be written as

yi = xi + ui + vi

(1)

where yi is the performance of firm i (output, profits, costs), is the vector of technology parameters, vi is the classical symmetric disturb, while ui is the inefficiency.

- As well as the functional assumption on the form of the frontier, we must make some assumptions on the distribution and on the relations between the two errors in order to complete the statistical model.

- The typical assumptions in this model are

1 The independence between v e u. 2 vi N(0, 2). 3 ui F , where F (x) is a generic family of distributions with x R+

- Objectives: in the first step we estimate the vector of technology parameters and in the second the efficiency of each producer.

Federico Belotti , Silvio Daidone , Giuseppe Ilardi

Frequentist and Bayesian stochastic frontier models in Stata

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