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Über dieses Buch

This book is intended for second year graduate students and professionals who have an interest in linear and nonlinear simultaneous equations mod­ els. It basically traces the evolution of econometrics beyond the general linear model (GLM), beginning with the general linear structural econo­ metric model (GLSEM) and ending with the generalized method of mo­ ments (GMM). Thus, it covers the identification problem (Chapter 3), maximum likelihood (ML) methods (Chapters 3 and 4), two and three stage least squares (2SLS, 3SLS) (Chapters 1 and 2), the general nonlinear model (GNLM) (Chapter 5), the general nonlinear simultaneous equations model (GNLSEM), the special ca'3e of GNLSEM with additive errors, non­ linear two and three stage least squares (NL2SLS, NL3SLS), the GMM for GNLSEIVl, and finally ends with a brief overview of causality and re­ lated issues, (Chapter 6). There is no discussion either of limited dependent variables, or of unit root related topics. It also contains a number of significant innovations. In a departure from the custom of the literature, identification and consistency for nonlinear models is handled through the Kullback information apparatus, as well as the theory of minimum contrast (MC) estimators. In fact, nearly all estimation problems handled in this volume can be approached through the theory of MC estimators. The power of this approach is demonstrated in Chapter 5, where the entire set of identification requirements for the GLSEM, in an ML context, is obtained almost effortlessly, through the apparatus of Kullback information.

Inhaltsverzeichnis

Frontmatter

1. Extension of Classical Methods I

Abstract
Econometrics deals with the problems encountered in measuring or quantifying economic relationships. In contrast to the natural and biological sciences, the data used by economists in studying such relationships are not, typically, experimentally derived. Thus, economists deal primarily with nonexperimental data.
Phoebus J. Dhrymes

2. Extension of Classical Methods II

Abstract
Our purpose in this section is to derive the limiting distribution of the 2SLS and 3SLS estimators obtained in Chapter 1. In that chapter we derived several types of estimators, viz., the standard 2SLS and 3SLS, the restricted 2SLS and 3SLS, unrestricted reduced form (OLS) estimators; we have also presented an alternative derivation of 2SLS and 3SLS, obtained by minimizing the objective function(s) when the prior restrictions are imposed by the device of Lagrange multipliers. This is in contrast to the standard derivation where such, restrictions are imposed directly, by substitution.
Phoebus J. Dhrymes

3. Maximum Likelihood Methods I

Abstract
In dealing with the problem of estimating the parameters of a structural system of equations we had not, in previous chapters, explicitly stated the form of the density of the random terms appearing in the system. Indeed, the estimation aspects of classical least squares techniques and their generalization to systems of equations are distribution free, so that no explicit assumption need be made with respect to the distribution of the error terms beyond the assertion that they have mean zero and finite variance. Furthermore, the identification problem was treated rather indirectly, typically as a condition for the invertibility of certain matrices or for the existence of a solution to a certain set of equations; thus, the deeper significance of the problem may have escaped the reader.
Phoebus J. Dhrymes

4. LIML Estimation Methods

Abstract
As we pointed out in the previous chapter. LIML is an estimation procedure that uses a priori information pertaining only to the equation (or equations) whose parameters we are interested in estimating. A priori restrictions on the parameters of the remaining equations are completely ignored.
Phoebus J. Dhrymes

5. Nonlinear ML Methods

Abstract
In studying the GLSEM we took the structural model as the primitive concept, and dealt with it as such. However, from a formal point of view, we can also look upon it as a particular case of a system of regressions, sometimes termed seemingly unrelated regressions (SUR), which is nonlinear in some basic set of underlying parameters. A little reflection will also convince the reader that (GLSEM) models which are nonlinear in the parameters only are, also, a special case of such systems.
Phoebus J. Dhrymes

6. Topics in NLSE Theory

Abstract
In this chapter we shall examine somewhat briefly topics in the theory of nonlinear simultaneous equations (NLSE), including NLML (nonlinear maximum likelihood), NL2SLS, NL3SLS, the so called generalized method of moments (GMM), as well as issues related to “causality”, and the consequences of misspecification.
Phoebus J. Dhrymes

Backmatter

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