Money demand and relative prices during episodes of hyperinflation

Inflation (Finance) ; Money ; Prices

Beyond element-wise interactions: identifying complex interactions in biological processes

Background: Biological processes typically involve the interactions of a number of elements (genes, cells) acting on each others. Such processes are often modelled as networks whose nodes are the elements in question and edges pairwise relations between them (transcription, inhibition). But more often than not, elements actually work cooperatively or competitively to achieve a task. Or an element can act on the interaction between two others, as in the case of an enzyme controlling a reaction rate. We call “complex” these types of interaction and propose ways to identify them from time-series observations. Methodology: We use Granger Causality, a measure of the interaction between two signals, to characterize the influence of an enzyme on a reaction rate. We extend its traditional formulation to the case of multi-dimensional signals in order to capture group interactions, and not only element interactions. Our method is extensively tested on simulated data and applied to three biological datasets: microarray data of the Saccharomyces cerevisiae yeast, local field potential recordings of two brain areas and a metabolic reaction. Conclusions: Our results demonstrate that complex Granger causality can reveal new types of relation between signals and is particularly suited to biological data. Our approach raises some fundamental issues of the systems biology approach since finding all complex causalities (interactions) is an NP hard problem

Measuring the NAIRU – A Structural VAR Approach

We calculate the NAIRU for the U.S. in a framework where inflation and the unemployment rate can respond to each other. The NAIRU is defined as the component of the actual unemployment rate that is uncorrelated with inflation in the long run. Using a structural VAR approach, the NAIRU and core inflation can be estimated simultaneously. Our estimation results show that the NAIRU falls dramatically at the end of 1990s and the long run vertical Phillips Curve shifts back from 6.8 per cent before 1997 to 4 per cent afterwards.