G. Gandolfo – författare

Time elapses continuously not in discrete jumps of, say, a quarter or a month. Hence models specified in continuous time are more realistic than the usual models in which time is taken to elapse in such discrete jumps. However much data available to economists is of the discrete-time kind. This was once thought to render impossible the econometric estimation of continuous time models. Over the past decade a body of theory has been built up to show that such estimation is not only possible but has serious practical applications. This collection of essays aims to provide not only the latest developments in the theory but also with original examples to show how it is possible to implement in real situations. Econometricians may find this book useful reading as may those concerned with macroeconomic issues who wish to keep in touch with the "frontiers" of their subject.

Economic Dynamics: Methods and Models aims to give a simple but comprehensive treatment of mathematical methods used in economic dynamics and show how they are utilized to build and to analyze dynamic models. The text also focuses on methods, and every mathematical technique introduced is followed by its application to selected models. The book is divided into three different parts. Part I: Different Equations discusses general principles; first-order, second-order, higher-order equations; simultaneous systems; and their economic applications. Part II: Differential Equations also discusses the same areas as those in Part I, but instead features differential equations, as what the section name suggests. Part III: More Advanced Material covers comparative statistics and the comparative principle; stability of equilibrium and Liapunov''s second method; and linear mixed differential and difference equations, as well as its other related topics. The text is recommended for mathematicians and economists who have an idea on advanced mathematics and would like to know more about its applications in economics.

There is no lack of good international economics textbooks ranging from the elementary to the advanced, so that an additional drop in this ocean calls for an explanation. In the present writer's opinion, there seems still to be room for a textbook which can be used in both undergraduate and graduate courses, and which contains a wide range of topics, including those usually omitted from other textbooks. These are the intentions behind the present book, which is an outcrop from undergraduate and graduate courses in international economics that the author has been holding at the University of Rome since 1974, and from his on­ going research work in this field. Accordingly the work is organized as two-books­ in-one by distributing the material between text and appendices. The treatment in the body of this book is directed to undergraduate students and is mainly confined to graphic analysis and to some elementary algebra, but it is assumed that the reader will have a good knowledge of basic microeconomics and macroeconomics (so that the usual review material on production functions, indifference curves, standard Keynesian model, etc. , etc. has been omitted) . Each chapter is followed by an appendix in which the treatment is mainly mathematical, and where (i) the topics explained in the text are treated at a level suitable for advanced undergraduate or first-year graduate students and (ii) generalizations and/or topics not treated in the text (including some of those at the frontiers of research) are formally examined.

There is no lack of good international economics textbooks ranging from the elementary to the advanced, so that an additional drop in this ocean calls for an explanation. In the present writer''s opinion, there seems still to be room for a textbook which can be used in both undergraduate and graduate courses, and which contains a wide range of topics, including those usually omitted from other textbooks. These are the intentions behind the present book, which is an outcrop from undergraduate and graduate courses in international economics that the author has been holding at the University of Rome since 1974, and from his on­ going research work in this field. Accordingly the work is organized as two-books­ in-one by distributing the material between text and appendices. The treatment in the body of this book is directed to undergraduate students and is mainly confined to graphic analysis and to some elementary algebra, but it is assumed that the reader will have a good knowledge of basic microeconomics and macroeconomics (so that the usual review material on production functions, indifference curves, standard Keynesian model, etc. , etc. has been omitted) . Each chapter is followed by an appendix in which the treatment is mainly mathematical, and where (i) the topics explained in the text are treated at a level suitable for advanced undergraduate or first-year graduate students and (ii) generalizations and/or topics not treated in the text (including some of those at the frontiers of research) are formally examined.

There is no lack of good international economics textbooks ranging from the elementary to the advanced, so that an additional drop in this ocean calls for an explanation. In the present writer's opinion, there seems still to be room for a textbook which can be used in both undergraduate and graduate courses, and which contains a wide range of topics, including those usually omitted from other textbooks. These are the intentions behind the present book, which is an outcrop from undergraduate and graduate courses in international economics that the author has been holding at the University of Rome since 1974, and from his on­ going research work in this field. Accordingly the work is organized as two-books­ in-one by distributing the material between text and appendices. The treatment in the body of this book is directed to undergraduate students and is mainly confined to graphic analysis and to some elementary algebra, but it is assumed that the reader will have a good knowledge of basic microeconomics and macroeconomics (so that the usual review material on production functions, indifference curves, standard Keynesian model, etc. , etc. has been omitted) . Each chapter is followed by an appendix in which the treatment is mainly mathematical, and where (i) the topics explained in the text are treated at a level suitable for advanced undergraduate or first-year graduate students and (ii) generalizations and/or topics not treated in the text (including some of those at the frontiers of research) are formally examined.

Continuous-time econometrics is no longer an esoteric subject although most still regard it as such, so much so that it is hardly mentioned in standard textbooks on econometrics. Thanks to the work done in the last 20 years, both the theoretical and the applied side are by now well developed. Methods of estimation have been theoretically elaborated and practically implemented through computer programs. Continuous-time macroeconometric models for different countries have been constructed, estimated and used. Being myself involved in these developments, it was with great pleasure that I accepted the invitation to organize a session on continuous-time econometrics in the context of the International Symposium on Economic Modelling (jointly organized by the University of Urbino and the book series International Studies in Economic Modelling, and co-sponsored by the Consiglio Nazionale delle Ricerche). The reaction of 'continuists' from all over the world was so enthusiastic that I was able to arrange two sessions, one on the theory and the other on the applications. The symposium was held in Urbino on 23-25 July 1990. The papers presented in Urbino have been revised in the light of the discussion at the symposium and the referees' comments. Hence, what is published here should become another standard reference in the field of continuous-time econometrics.