Estimação em dois estágios de um modelo de fronteira estocástica de produção aplicado a dados do Sistema Nacional de Avaliação da Educação Básica

Abstract

This monograph provides a bibliographical review of the most common stochastic frontier models in the literature (normal-half normal model, normal-truncated normal model and normal-exponential model). We discuss the use of Murphy-Topel s (2002) correction for variance-covariance matrix in two-stage estimation where an estimated probability (first-stage) is used as explanatory variable in the estimation of an SFA model in the second stage. We illustrate the methodology with educational data in the R system. The data consist of schools as observational units and the response variable is the average grade obtained by the school in Prova Brasil for Portuguese and Mathematics. The database was constructed from the Educational Census microdata and from Saeb provided by the Instituto Nacional de Estudos e Pesquisas Educacionais Anísio Teixeira (Inep).