This paper presents and extends the index function model of Karl Pearson (1901) that underlies all recent models in labor econometrics. In this framework, censored, truncated and discrete random variables are interpreted as the manifestation of various sampling schemes for underlying index function models. A unified derivation of the densities and regression representations for index function models is presented. Methods of estimation are discussed with an emphasis on regression and instrumental variable procedures.We demonstrate how a variety of substantive models in labor economics can be given an econometric representation within the index function framework. Models for the analysis of unemployment, labor force participation, job turnover, the impact of interventions on earnings (and other outcomes) and hours of work are formulated as special cases of the general index function model. By casting these diverse models in a common mold we demonstrate the essential commonalities in the econometric approach required for their formulation and estimation.
