Non-linear multivariate adjustment of the UK real exchange rate

Based on a multivariate non-linear model, this paper recognises an important role for the real exchange rate in affecting UK labour market conditions. The short-run real exchange rate adjusts quickly to disequilibrium deviations of the real exchange rate from its long-run level outside a rather wide interval band. When the real exchange rate is undervalued, short-run unemployment falls as firms respond to an improvement in domestic competitiveness by increasing their demand for labour. Further, there is a strong response of short-run unemployment to the disequilibrium error outside a narrow interval band. To the extent that the real exchange rate equation reflects monetary policy considerations, our results imply that unemployment can be targeted by economic policy. Furthermore, if economic authorities want to avoid large swings in unemployment then they should be prepared to intervene in exchange markets with the aim of keeping real exchange rate movements within a narrow interval band

Fusion rings for degenerate minimal models

We study fusion rings for degenerate minimal models ($p=q$ case) for N=0 and N=1 (super)conformal algebras. We consider a distinguished family of modules at the level $c=1$ and $c=3/2$ and show that the corresponding fusion rings are isomorphic to the representation rings for ${\mathfrak sl}(2, {\bf C})$ and ${\mathfrak osp}(1|2)$ respectively.Comment: Revised and enlarged version. It includes all the results from math.QA/0101165 (to appear in Journal of Algebra

A Non-Linear Multivariate Model of the U.K. Real Exchange Rate

This paper discusses linearity testing for the UK real exchange rate within a multivariate framework. First we estimate a long-run real exchange rate relationship within a system involving real wages, the unemployment rate and the real price of oil. Then we adopt a logistic transition function for the estimated relationship and show that non-linearities in the discrepancy between the real exchange rate and its implied long-run level affect the short-run real exchange rate equation. We also find that when the real exchange rate is undervalued, unemployment falls as firms respond to an improvement in domestic competitiveness by increasing their demand for labour. At the same time, workers respond to the improvement in domestic competitiveness by demanding and getting higher wages. Further, the effect on unemployment and wages is nonlinear

Formal differential operators, vertex operator algebras and zeta--values , II

We introduce certain correlation functions (graded $q$--traces) associated to vertex operator algebras and superalgebras which we refer to as $n$--point functions. These naturally arise in the studies of representations of Lie algebras of differential operators on the circle \cite{Le1}--\cite{Le2}, \cite{M}. We investigate their properties and consider the corresponding graded $q$--traces in parallel with the passage from genus 0 to genus 1 conformal field theory. By using the vertex operator algebra theory we analyze in detail correlation functions in some particular cases. We obtain elliptic transformation properties for $q$--traces and the corresponding $q$--difference equations. In particular, our construction leads to correlation functions and $q$--difference equations investigated by S. Bloch and A. Okounkov \cite{BO}.Comment: 46 pages, LaTeX (10pt, small font), 1 figure, BibTe

Ramanujan's "Lost Notebook" and the Virasoro Algebra

By using the theory of vertex operator algebras, we gave a new proof of the famous Ramanujan's modulus 5 modular equation from his "Lost Notebook" (p.139 in \cite{R}). Furthermore, we obtained an infinite list of $q$-identities for all odd moduli; thus, we generalized the result of Ramanujan.Comment: To appear in Comm. Math. Phy