Contributions to the econometrics of cross-sections

Abstract

This thesis is concerned with problems that arise in the statistical analysis of economic models, when using cross-sectional data. Its contents may be conveniently divided into five parts. V(Wt I comprises Chapter 1, and contains introductory remarks, motivation and overview of the thesis. V(Wt II, formed by Chapters 2 and 3, relates to the data gathering stage of the analysis. Chapter 2 studies the problem of optimal sample design within an econometric (rather than a purely statistical) framework. Chapter 3 is concerned with the problem of efficient aggregation of data that has been gathered through a census or sample survey. In these two Chapters, several design and aggregation criteria are suggested and the use of clustering techniques is indicated. Va/vt III, consisting of Chapters 4, 5, 6, 7 and 8, relates to inferential and estimation aspects of the analysis once the data is available. Regarding inference, a contribution is the suggestion of a procedure for the construction of efficient and computationally simple econometric specification tests. This is based on the application of the Lagrange Multiplier test to the Pearson and other families of disturbance distributions (rather than to families of transformations). Illustrations of the procedure are given in Chapters 4, 5 and 6, where normality and/or homoscedasticity tests for the Multiple Regression Model, the Truncated Model and the Tobit Model are derived. Tests for normality, homoscedasticity and parameter variation in Simultaneous Equations Models are suggested in Chapter 8. Regarding estimation, a two stage procedure is presented in Chapter 7. In the first stage, the observations would be classified into groups of homogeneous parameter values, by the use of a classification criterion suggested. In the second stage, the econometric estimation of the parameters would follow. Vcovt 71/ of the thesis comprises Chapter 9, and contains an empirical illustration of some of the tests and estimation procedures suggested. These are used for the study of Household Consumption and Saving behaviour in Mexico. V(Wt l/, formed by Chapter 10, indicates extensions of some of the results of Vamt III and highlights the fact that many of these results are equally applicable in time-series studies. It also contains some concluding remarks.