Book contents
- Frontmatter
- Contents
- Preface
- List of illustrations
- Notation
- 1 The technology of estimation
- 2 Likelihood
- 3 Tests of simplifying assumptions
- 4 The use of likelihood in econometrics
- 5 Techniques of maximization
- 6 Generalized classical regression
- 7 Systems of linear regression equations
- 8 The transformation of Box and Cox
- 9 Time series data and dynamic models
- 10 Discrete choice models
- 11 Hybrid and mixed dependent variables
- 12 Simple random process models
- References
- Author index
- Subject index
- Frontmatter
- Contents
- Preface
- List of illustrations
- Notation
- 1 The technology of estimation
- 2 Likelihood
- 3 Tests of simplifying assumptions
- 4 The use of likelihood in econometrics
- 5 Techniques of maximization
- 6 Generalized classical regression
- 7 Systems of linear regression equations
- 8 The transformation of Box and Cox
- 9 Time series data and dynamic models
- 10 Discrete choice models
- 11 Hybrid and mixed dependent variables
- 12 Simple random process models
- References
- Author index
- Subject index
Summary
The next four chapters contain a quite general introduction to the statistical theory of Maximum Likelihood estimation and testing, and to the numerical determination of the estimates and of other statistics. We review the main theorems and techniques that are used in current econometric studies, and we sketch the underlying theory, which unifies seemingly unrelated results. Mathematical rigor is beyond our scope; we try to convey the drift of the argument, not to give proofs. A more thorough treatment of the mathematical theory involved can be found in statistical textbooks (Cox and Hinkley 1974; Silvey 1970). But while statistical theory deals with inference about a distribution, econometrics is usually concerned with a relation. We therefore allow from the very start for regressor variables. Apart from this, the discussion is quite general, in the sense that it is not restricted to a particular class of econometric models. Up to Chapter 6 the model formulation is indeed so general that the basic asymptotic properties of Maximum Likelihood estimates, which we quote below and use in Chapter 3, have not in fact been established. These properties have, however, been proved for several variants of the two main classes of econometric models that we shall consider, if only under particular qualifying conditions; moreover, considerable progress has been made in weakening the relevant restrictions. But we shall not take up this matter.
- Type
- Chapter
- Information
- Econometric Applications of Maximum Likelihood Methods , pp. 11 - 29Publisher: Cambridge University PressPrint publication year: 1986