Are Central Banks following a linear or nonlinear (augmented) Taylor rule?

The Taylor rule establishes a simple linear relation between the interest rate, inflation and output gap. However, this relation may not be so simple. To get a deeper understanding of central banks’ behaviour, this paper asks whether central banks are indeed following a linear Taylor rule or, instead, a nonlinear rule. At the same time, it also analyses whether that rule can be augmented with a financial conditions index containing information from some asset prices and financial variables. A forward-looking monetary policy reaction function is employed in the estimation of the linear and nonlinear models. A smooth transition model is used to estimate the nonlinear rule. The results indicate that the European Central Bank and the Bank of England tend to follow a nonlinear Taylor rule, but not the Federal Reserve of the United States. In particular, those two central banks tend to react to inflation only when inflation is above or outside their targets. Moreover, our evidence suggests that the European Central Bank is targeting financial conditions, contrary to the other two central banks. This lack of attention to the financial conditions might have made the United States and the United Kingdom more vulnerable to the recent credit crunch than the Eurozone

The packing number of the double vertex graph of the path graph

Neil Sloane showed that the problem of determine the maximum size of a binary code of constant weight 2 that can correct a single adjacent transposition is equivalent to finding the packing number of a certain graph. In this paper we solve this open problem by finding the packing number of the double vertex graph (2-token graph) of a path graph. This double vertex graph is isomorphic to the Sloane's graph. Our solution implies a conjecture of Rob Pratt about the ordinary generating function of sequence A085680.Comment: 21 pages, 7 figures. V2: 22 pages, more figures added. V3. minor corrections based on referee's comments. One figure corrected. The title "On an error correcting code problem" has been change