Analyzes the major economic issues confronting less-developed countries.

The articles collected in this volume have two features in common: they wantto integrate economics, demography and geography, and they want to overcome the stationary approach in modelling in favour of a dynamic one. The book is subdivided into three parts, where Part I is focussing on economic evolution, Part II on geographical development and Part III is related to demographic change. The present volume aims at providing a new look at this triangle in view of the classical background of discussions by introducing new research ideas focussing in nonlinear dynamics and stochastic modelling. Thus the main purpose of this book is to make a contribution to the interdisciplinary work needed to integrate the effortsbetween these three research fields and to serve as a research source in demonstrating the current state of art in dynamic modelling. The book isaddressed to social scientists in general, and those in particular with a background in economics, geographics and demographics. It should also be of interest to mathematicians, physicists, and systems analysts interested in model building and applications of nonlinear dynamics.

A collection of papers prepared for the European Forum on Integrated Environmental Assessment's (EFIEA) Policy Workshop on Scaling Issues in Integrated Assessment, held from 12-19 July 2000.

Our interest in problems of aggregation originates from about seven years ago when we became involved in research in the field of applied microeconomics. To our astonishment a vast majority of researchers in this area took it for granted that their, mostly thoroughly derived, micro models could meaningfully be confronted with per capita data. Nany of them did not even realize - at least they gave no utterance to it - that applying macro data in micro models raises considerable problems. Those who did mention the difficulty, almost always belittled its importance. Fortunately, there are noteworthy exceptions. Thinking about aggregation raises at least two questions: "Why or why not aggregate?" and "How to aggregate and, in particular, to what degree?" General answers to these questions can only be given in uninformative wording (as many assertions in economics): one aggregates for the sake of tractability, because of the lack of (individual) data, to avoid or to reduce multicollineartiy, to save degrees of freedom; one abstains from aggregation to avoid loss of information, to avoid aggregation biases and one aggregates such and to such degree as to bypass or reduce the drawbacks mentioned above.

This study is concerned with forecasting time series variables and the impact of the level of aggregation on the efficiency of the forecasts. Since temporally and contemporaneously disaggregated data at various levels have become available for many countries, regions, and variables during the last decades the question which data and procedures to use for prediction has become increasingly important in recent years. This study aims at pointing out some of the problems involved and at pro viding some suggestions how to proceed in particular situations. Many of the results have been circulated as working papers, some have been published as journal articles, and some have been presented at conferences and in seminars. I express my gratitude to all those who have commented on parts of this study. They are too numerous to be listed here and many of them are anonymous referees and are therefore unknown to me. Some early results related to the present study are contained in my monograph "Prognose aggregierter Zeitreihen" (Lutkepohl (1986a)) which was essentially completed in 1983. The present study contains major extensions of that research and also summarizes the earlier results to the extent they are of interest in the context of this study.