Polygons in billiard orbits

We study the geometry of billiard orbits on rectangular billiards. A truncated billiard orbit induces a partition of the rectangle into polygons. We prove that thirteen is a sharp upper bound for the number of different areas of these polygons.Comment: 14 page

How econometric models help policy makers; theory and practice

Frisch and Tinbergen founded the standard framework for finding the optimal economic policy by maximizing the welfare function under constraints supplied by the econometric model. Frisch worried about the reliability of the model and Tinbergen thought that it would be too difficult to specify the welfare function. Looking at current practice in Dutch policy making, both worries are relevant but the solutions proposed by the founders are not very helpful. Rather, the solution is found in applying an iterative trial-and-error procedure interfacing between the policy maker and the model-cum-expert system. The main contributions of the standard framework are its useful set of concepts, the famous order condition for a feasible solution, and the clear definition of role models for the two parties in the interaction.

Synchronizing non-deterministic finite automata

In this paper, we show that every D3-directing CNFA can be mapped uniquely to a DFA with the same synchronizing word length. This implies that \v{C}ern\'y's conjecture generalizes to CNFAs and that the general upper bound for the length of a shortest D3-directing word is equal to the Pin-Frankl bound for DFAs. As a second consequence, for several classes of CNFAs sharper bounds are established. Finally, our results allow us to detect all critical CNFAs on at most 6 states. It turns out that only very few critical CNFAs exist.Comment: 21 page

Models and methods for economic policy; 60 years of evolution at CPB

The Netherlands Bureau for Economic Policy Analysis (CPB) has been involved in econometric model building since its foundation in 1945. During the 60 years of model building and use reviewed in this Discussion Paper, CPB's models have evolved significantly. Over this period, a shift of emphasis can be observed from econometrics and empiricism to economic theory. New questions from policymakers and new features in the national economy have guided research, while new developments in econometrics and economic theory were taken on board wherever they helped to improve the quality and scope of the analysis. Although considerable progress has been achieved in several spheres, the models continue to be riddled with some long-standing limitations and weaknesses which the model users should take into account.

Ambitie en voorzichtigheid in het economisch beleid

De ambitie van het begrotingsbeleid van het nieuwe kabinet valt tegen. Dit stelt prof. dr. Henk Don in zijn inaugurele rede 'Ambitie en voorzichtigheid in het economisch beleid'De nieuwe hoogleraar concludeert dat de coalitiepartners het laten vervallen van de voorzichtigheids­marge in het begrotingsbeleid niet hebben gecompenseerd met een hogere ambitie voor het wegwerken van het houdbaarheids­tekort in de overheidsfinanciën. Ook de hogere levensverwachting heeft nog geen beleidsmatig antwoord gekregen.Rede, in verkorte vorm uitgesproken bij de aanvaarding van het ambt van bijzonder hoogleraar aan de Faculteit der Economische Wetenschappen van de Erasmus Universiteit Rotterdam vanwege de Vereniging Trustfonds EUR met de leeropdracht Econometrie en economisch beleid, op 5 april 200

Agenda for the Housing Market

The housing market is the theme of the Reports to the 2008 Annual Meeting of the Royal Netherlands Economic Association. Current housing market policies in the Netherlands generate substantial welfare losses. The direct and indirect subsidies on housing distort the housing market, house moving behaviour, the labour market and the asset portfolio of households. The welfare loss is estimated at more than 6 billion euro per year. In addition, physical planning restrictions cost at least 3 billion euro per year, a price which is paid for the conservation of open space and nature, especially in the Green Heart of the Randstad. Developments on the housing market over the last fifteen years and the sizeable welfare losses from current policies are sufficient reason to develop an agenda for reform. The Reports suggest several elements for such an agenda, including a gradual reduction of housing subsidies in the owner-occupier sector as well as in the rental sector, an easier land policy to better meet the qualitative housing needs of the population, and an extension of the social tasks for the housing societies

SAFE: a quarterly model of the Dutch economy for short-term analyses

SAFE is the name of th large-scale macro econometric quarterly model that is currently in use at CPB Netherlands Bureau for Economic Policy Analysis in preparing short-term forecasts and analyses of the Dutch economy. Read also the accompanying press release .This document gives a comprehensive description of the SAFE model. The description of the model's equations and results concerns the model version used since the preparation of the Macroeconomic Outlook 2003. In order to explain the working of the model, the results of�a number of standard shocks and scenarios are presented.