The paper deals with the asymmetric effects on output of tight and easy monetary policy: the output reduction following a negative monetary policy shock appears bigger than the expansion induced by similar sized positive shock. The paper first reviews historical evidence of asymmetry, focusing on the United States, Japan and Italy. This is followed by a review of the econometric literature on monetary policy asymmetry and consideration of the theoretical reasons that can explain this asymmetry.

In various speeches, former Fed Chairman Ben Bernanke contrasted the proposal of setting a higher inflation target by claiming that it could unanchor inflation expectations. A standard New Keynesian framework with learning supports this claim both asymptotically, because a higher inflation target shrinks the E-stability region when a central bank follows a Taylor rule, and in the transition phase, because a higher inflation target slows down the speed of convergence of expectations. Transparency helps anchoring expectations. However, the importance of being transparent diminishes with the level of the inflation target. Finally, the higher the inflation target, the more policy should respond to inflation and the less to output to guarantee E-stability. Hence, a policy that increases both the inflation target and the monetary policy response to output would be "reckless".

For a C 1 diffeomorphism f : R 2 → R 2 isotopic to the identity, we prove that for any value l ∈ R of the linking number at finite time of the orbits of two points there exists at least a point whose torsion at the same finite time equals l ∈ R. As an outcome, we give a much simplier proof of a theorem by Matsumoto and Nakayama concerning torsion of measures on T 2 . In addition, in the framework of twist maps, we generalize a known result concerning the linking number of periodic points: indeed, we estimate such value for any couple of points for which the limit of the linking number exists.

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The aim of this paper is to study in detail the relations between strong chain recurrence for flows and Lyapunov functions. For a continuous flow on a compact metric space, uniformly Lipschitz continuous on the compact subsets of the time, we first make explicit a Lipschitz continuous Lyapunov function strict -that is strictly decreasing-outside the strong chain recurrent set of the flow. This construction extends to flows some recent advances of Fathi and Pageault in the case of homeomorphisms; moreover, it improves Conley's result about the existence of a continuous Lyapunov function strictly decreasing outside the chain recurrent set of a continuous flow. We then present two consequences of this theorem. From one hand, we characterize the strong chain recurrent set in terms of Lipschitz continuous Lyapunov functions. From the other hand, in the case of a flow induced by a vector field, we establish a sufficient condition for the existence of a C 1,1 strict Lyapunov function and we also discuss various examples. Moreover, for general continuos flows, we show that the strong chain recurrent set has only one strong chain transitive component if and only if the only Lipschitz continuous Lyapunov functions are the constants. Finally, we provide a necessary and sufficient condition to guarantee that the strong chain recurrent set and the chain recurrent one coincide.