A short proof of Kneser's addition theorem for abelian groups

Martin Kneser proved the following addition theorem for every abelian group $G$. If $A,B \subseteq G$ are finite and nonempty, then $|A+B| \ge |A+K| + |B+K| - |K|$ where $K = \{g \in G \mid g+A+B = A+B \}$. Here we give a short proof of this based on a simple intersection union argument.Comment: 3 page

Dark Light Higgs

We study a limit of the nearly-Peccei-Quinn-symmetric Next-to-Minimal Supersymmetric Standard Model possessing novel Higgs and dark matter (DM) properties. In this scenario, there naturally co-exist three light singlet-like particles: a scalar, a pseudoscalar, and a singlino-like DM candidate, all with masses of order 0.1-10 GeV. The decay of a Standard Model-like Higgs boson to pairs of the light scalars or pseudoscalars is generically suppressed, avoiding constraints from collider searches for these channels. For a certain parameter window annihilation into the light pseudoscalar and exchange of the light scalar with nucleons allow the singlino to achieve the correct relic density and a large direct detection cross section consistent with the CoGeNT and DAMA/LIBRA preferred region simultaneously. This parameter space is consistent with experimental constraints from LEP, the Tevatron, and Upsilon- and flavor physics.Comment: 4 pages, 4 figures, final version for Phys. Rev. Let

Assessing simple policy rules: a view from a complete macro model

We explore two popular approaches to empirical analysis of monetary policy: the New Keynesian and the identified vector autoregression approaches. Stylized models of private behavior coupled with simple rules describing policy behavior characterize New Keynesian work. Vector autoregressions consist of minimally identified dynamic descriptions of private behavior coupled with a detailed rule for policy behavior. The simplicity of New Keynesian models aids in communication but leaves the models’ implications vulnerable. By relating the New Keynesian models to identified vector autoregressions, we explore the differences and similarities in the two approaches and assess some of the key conclusions to emerge from New Keynesian research.Vector autoregression ; Monetary policy ; Forecasting

Modest policy interventions

The authors present a framework for computing and evaluating linear projections of macro variables conditional on hypothetical paths of monetary policy. A modest policy intervention is a change in policy that does not significantly shift agents' beliefs about policy regime and does not generate quantitatively important expectations-formation effects of the kind Lucas (1976) emphasizes. The framework is applied to an econometric model of U.S. postwar monetary policy behavior. It finds that a rich class of interventions routinely considered by the Federal Reserve are modest and their impacts can be reliably forecast by an accurately identified linear model. Moreover, modest interventions can matter: They may shift the projected paths and probability distributions of macro variables in economically meaningful ways.Monetary policy ; Forecasting ; Vector autoregression

Modest policy interventions

The authors present a theoretical and empirical framework for computing and evaluating linear projections conditional on hypothetical paths of monetary policy. A modest policy intervention does not significantly shift agents' beliefs about policy regime and does not induce the changes in behavior that Lucas (1976) emphasizes. Applied to an econometric model of U.S. monetary policy, the authors find that a rich class of interventions routinely considered by the Federal Reserve is modest and their impacts can be reliably forecast by an identified linear model. Modest interventions can shift projected paths and probability distributions of macro variables in economically meaningful ways.Equilibrium (Economics) ; Monetary policy ; Macroeconomics ; Inflation (Finance) ; Econometric models