Precision performances of terminal conditions for short time horizons forward-looking systems

In this paper, we investigate both theoretically and empirically the numerical bias due to the truncation of structurally infinite time forward-Iooking models, by the means of various terminal conditions. We shed light on the difficulties of numerical control using the latter instrurnents, and recornrnend a prior investigation of the individual dynamics generated by each variable of the models under consideration

The History of Macroeconomics from Keynes’s General Theory to the Present

This paper is a contribution to the forthcoming Edward Elgar Handbook of the History of Economic Analysis volume edited by Gilbert Faccarello and Heinz Kurz. Its aim is to introduce the reader to the main episodes that have marked the course of modern macroeconomics: its emergence after the publication of Keynes’s General Theory, the heydays of Keynesian macroeconomics based on the IS-LM model, disequilibrium and non-Walrasian equilibrium modelling, the invention of the natural rate of unemployment notion, the new classical attack against Keynesian macroeconomics, the first wave of new Keynesian models, real business cycle modelling and, finally, the second wage of new Keynesian models, i.e. DSGE models. A main thrust of the paper is the contrast we draw between Keynesian macroeconomics and stochastic dynamic general equilibrium macroeconomics. We hope that our paper will be useful for teachers of macroeconomics wishing to complement their technical material with a historical addendum.Keynes, Lucas, IS-LM model, DSGE models

From The Keynesian Revolution to the Klein-Goldberger Model: Klein and the Dynamization of Keynesian Theory

According to Klein, Keynes’s General Theory was crying out for empirical application. He set himself the task of implementing this extension. Our paper documents the different stages of his endeavor, focusing on his The Keynesian Revolution book, Journal of Political Economy article on aggregate demand theory, and his essay on the empirical foundations of Keynesian theory published in the Post-Keynesian Economics book edited by Kurihara. Klein’s claim is that his empirical model (the Klein-Goldberger model) vindicates Keynes’s theoretical insights, in particular the existence of involuntary unemployment. While praising Klein for having succeeded in making Keynesian theory empirical and dynamic, we argue that he paid a high price for this achievement. Klein and Goldberger’s model is less Keynesian than they claim. In particular, Klein’s claim that it validates the existence of involuntary unemployment does not stand up to close scrutiny.

Periods for flat algebraic connections

In previous work, we established a duality between the algebraic de Rham cohomology of a flat algebraic connection on a smooth quasi-projective surface over the complex numbers and the rapid decay homology of the dual connection relying on a conjecture by C. Sabbah, which has been proved recently by T. Mochizuki for algebraic connections in any dimension. In the present article, we verify that Mochizuki's results allow to generalize these duality results to arbitrary dimensions also

Precision performances of terminal conditions for short time horizons forward-looking systems.

In this paper, we investigate both theoretically and empirically the numerical bias due to the truncation of structurally infinite time forward-Iooking models, by the means of various terminal conditions. We shed light on the difficulties of numerical control using the latter instrurnents, and recornrnend a prior investigation of the individual dynamics generated by each variable of the models under consideration.Expectations; Large scale models; Solution time horizons; Terminal conditions;

The symplectic and twistor geometry of the general isomonodromic deformation problem

Hitchin's twistor treatment of Schlesinger's equations is extended to the general isomonodromic deformation problem. It is shown that a generic linear system of ordinary differential equations with gauge group SL(n,C) on a Riemann surface X can be obtained by embedding X in a twistor space Z on which sl(n,C) acts. When a certain obstruction vanishes, the isomonodromic deformations are given by deforming X in Z. This is related to a description of the deformations in terms of Hamiltonian flows on a symplectic manifold constructed from affine orbits in the dual Lie algebra of a loop group.Comment: 35 pages, LATE

Involutivity of field equations

We prove involutivity of Einstein, Einstein-Maxwell and other field equations by calculating the Spencer cohomology of these systems. Relation with Cartan method is traced in details. Basic implications through Cartan-Kahler theory are derived.Comment: 13 pages; this version is updated with new field equations (radiation, dust etc) - they are proved involutive, Spencer cohomology calculate

New results on the linearization of Nambu structures

In a paper with Jean-Paul Dufour in 1999 \cite{DufourZung-Nambu1999}, we gave a classification of linear Nambu structures, and obtained linearization results for Nambu structures with a nondegenerate linear part. There was a case left open in \cite{DufourZung-Nambu1999}, namely the case of smooth linearization of Nambu structures with a Type 1 hyperbolic linear part which satisfies a natural signature condition. In this paper, we will show that such hyperbolic Nambu structures are also smoothly linearizable. We will also give a strong version of the analytic linearization theorem in the analytic case, improving a result obtained in \cite{DufourZung-Nambu1999}.Comment: 1st version, 12 page

Every P-convex subset of R2\R^2 is already strongly P-convex

A classical result of Malgrange says that for a polynomial P and an open subset $\Omega$ of $\R^d$ the differential operator $P(D)$ is surjective on $C^\infty(\Omega)$ if and only if $\Omega$ is P-convex. H\"ormander showed that $P(D)$ is surjective as an operator on $\mathscr{D}'(\Omega)$ if and only if $\Omega$ is strongly P-convex. It is well known that the natural question whether these two notions coincide has to be answered in the negative in general. However, Tr\`eves conjectured that in the case of d=2 P-convexity and strong P-convexity are equivalent. A proof of this conjecture is given in this note

Deformation analysis of matrix models

The Tracy-Widom equations associated with level spacing distributions are realized as a special case of monodromy preserving deformations.Comment: 23 page