Book Objectives and Problem Format

The objectives of this book are to

1. develop a plausible basis for reasoning in situations involving incomplete-partial econometric model information,

2. develop principles and procedures for learning or recovering information from a sample of indirect noisy data, and

3. provide the reader with a firm conceptual and empirical understanding of basic information theoretic econometrics models and methods.

What makes the econometric information recovery process interesting is that

• economic-behavioral systems, such as physical and biological systems, are statistical in nature;

• the conceptual econometric model contains parameters and noise components that are unknown and unobserved and, indeed, not subject to direct observation or measurement;

• the recovery of information on the unknown parameters or components requires, for analysis purposes, the use of indirect noisy measurements based on observable data and the solution of an inverse problem that maps the indirect noisy observations, into information on the unknown model and its unobservable components;

• the models may be ill-posed or, in the context of traditional procedures, may be undetermined and the solution not amenable to conventional rules of logic or to being written in closed form.

These problems, taken either individually or in some combination, represent the intellectual challenge of modern econometric analysis and research. Building on the productive efforts of our precursors in the areas of theoretical economics and inferential statistics, we hope, in this book, to provide an operational understanding of a rich set of information theoretic methods that may be used in theoretical and applied econometrics.