Some Implications of the Zero Lower Bound on Interest Rates for the Term Structure and Monetary Policy

In an economy where cash can be stored costlessly (in nominal terms), the nominal interest rate is bounded below by zero. This paper derives the implications of this nonnegativity constraint for the term structure and shows that it induces a nonlinear and convex relation between short- and long-term interest rates. As a result, the long-term rate responds asymmetrically to changes in the short-term rate, and by less than predicted by a benchmark linear model. In particular, a decrease in the short-term rate leads to a decrease in the long-term rate that is smaller in magnitude than the increase in the long-term rate associated with an increase in the short-term rate of the same size. Up to the extent that monetary policy acts by affecting long-term rates through the term structure, its power is considerably reduced at low interest rates. The empirical predictions of the model are examined using data from Japan.

A lower bound on the size of k-neighborhood in generalized cubes

The determination of the minimum size of a k-neighborhood (i.e., a neighborhood of a set of k nodes) in a given graph is essential in the analysis of diagnosability and fault tolerance of multicomputer systems. The generalized cubes include the hypercube and most hypercube variants as special cases. In this paper, we present a lower bound on the size of a k-neighborhood in n-dimensional generalized cubes, where 2n + 1 <= k <= 3n - 2. This lower bound is tight in that it is met by the n-dimensional hypercube. Our result is an extension of two previously known results. (c) 2005 Elsevier Inc. All rights reserved.

Determination of a lower bound on Earth’s climate sensitivity

Transient and equilibrium sensitivity of Earth's climate has been calculated using global temperature, forcing and heating rate data for the period 1970–2010. We have assumed increased long-wave radiative forcing in the period due to the increase of the long-lived greenhouse gases. By assuming the change in aerosol forcing in the period to be zero, we calculate what we consider to be lower bounds to these sensitivities, as the magnitude of the negative aerosol forcing is unlikely to have diminished in this period. The radiation imbalance necessary to calculate equilibrium sensitivity is estimated from the rate of ocean heat accumulation as 0.37±0.03W m^−2 (all uncertainty estimates are 1−σ). With these data, we obtain best estimates for transient climate sensitivity 0.39±0.07K (W m^−2)^−1 and equilibrium climate sensitivity 0.54±0.14K (W m^−2)^−1, equivalent to 1.5±0.3 and 2.0±0.5K (3.7W m^−2)^−1, respectively. The latter quantity is equal to the lower bound of the ‘likely’ range for this quantity given by the 2007 IPCC Assessment Report. The uncertainty attached to the lower-bound equilibrium sensitivity permits us to state, within the assumptions of this analysis, that the equilibrium sensitivity is greater than 0.31K (W m^−2)^−1, equivalent to 1.16K(3.7W m^−2)^−1, at the 95% confidence level.

On the lower bound on the exchange-correlation energy in two dimensions

We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit determination of the prefactor of the bound and testing its tightness. Next we focus on finite two-dimensional systems and examine how their distance from the bound depends on the system geometry. The results for the high-density limit suggest that a finite system that comes as close as possible to the ultimate bound on the exchange-correlation energy has circular geometry and a weak confining potential with a negative curvature. (c) 2009 Elsevier B.V. All rights reserved.

Determination of lower-bound ductility for AZ31 magnesium alloy by use of the bulge specimens

Despite the high demand for industrial applications of magnesium, the forming technology for wrought magnesium alloys is not fully developed due to the limited ductility and high sensitivity to the processing parameters. The processing window for magnesium alloys could be significantly widened if the lower-bound ductility (LBD) for a range of stresses, temperature, and strain rates was known. LBD is the critical strain at the moment of fracture as a function of stress state and temperature. Measurements of LBD are normally performed by testing in a hyperbaric chamber, which is highly specialized, complex, and rare equipment. In this paper an alternative approach to determine LBD is demonstrated using wrought magnesium alloy AZ31 as an example. A series of compression tests of bulge specimens combined with finite element simulation of the tests were performed. The LBD diagram was then deduced by backward calculation.

A lower bound on effective performance testing for digital forensic tools

The increasing complexity and number of digital forensic tasks required in criminal investigations demand the development of an effective and efficient testing methodology, enabling tools of similar functionalities to be compared based on their performance. Assuming that the tool tester is familiar with the underlying testing platform and has the ability to use the tools correctly, we provide a numerical solution for the lower bound on the number of testing cases needed to determine comparative capabilities of any set of digital forensic tools. We also present a case study on the performance testing of password cracking tools, which allows us to confirm that the lower bound on the number of testing runs needed is closely related to the row size of certain orthogonal arrays. We show how to reduce the number of test runs by using knowledge of the underlying system

Lower bound to the mass of a relativistic three-boson system in the lightcone

The lower bound masses of the ground-state relativistic three-boson system in 1 + 1, 2 + 1 and 3 + 1 spacetime dimensions are obtained. We have considered a reduction of the ladder Bethe-Salpeter equation to the lightfront in a model with renormalized two-body contact interaction. The lower bounds are deduced with the constraint of reality of the two-boson subsystem mass. It is verified that, in some cases, the lower bound approaches the ground-state binding energy. The corresponding non-relativistic limits are also verified.

The Fundamental Gap For Hyperbolic Triangles

In 1983, M. van den Berg made his Fundamental Gap Conjecture about the difference between the first two Dirichlet eigenvalues (the fundamental gap) of any convex domain in the Euclidean plane. Recently, progress has been made in the case where the domains are polygons and, in particular, triangles. We examine the conjecture for triangles in hyperbolic geometry, though we seek an for an upper bound for the fundamental gap rather than a lower bound.

Unconventional Monetary Policy and the Great Recession: Estimating the Macroeconomic Effects of a Spread Compression at the Zero Lower Bound

We explore the macroeconomic effects of a compression in the long-term bond yield spread within the context of the Great Recession of 2007–09 via a time-varying parameter structural VAR model. We identify a “pure” spread shock defined as a shock that leaves the policy rate unchanged, which allows us to characterize the macroeconomic consequences of a decline in the yield spread induced by central banks’ asset purchases within an environment in which the policy rate is constrained by the effective zero lower bound. Two key findings stand out. First, compressions in the long-term yield spread exert a powerful effect on both output growth and inflation. Second, conditional on available estimates of the impact of the Federal Reserve’s and the Bank of England’s asset purchase programs on long-term yield spreads, our counterfactual simulations suggest that U.S. and U.K. unconventional monetary policy actions have averted significant risks both of deflation and of output collapses comparable to those that took place during the Great Depression.

A new model construction by making a detour via intuitionistic theories II: Interpretability lower bound of Feferman's explicit mathematics T0

We partially solve a long-standing problem in the proof theory of explicit mathematics or the proof theory in general. Namely, we give a lower bound of Feferman’s system T0 of explicit mathematics (but only when formulated on classical logic) with a concrete interpretat ion of the subsystem Σ12-AC+ (BI) of second order arithmetic inside T0. Whereas a lower bound proof in the sense of proof-theoretic reducibility or of ordinalanalysis was already given in 80s, the lower bound in the sense of interpretability we give here is new. We apply the new interpretation method developed by the author and Zumbrunnen (2015), which can be seen as the third kind of model construction method for classical theories, after Cohen’s forcing and Krivine’s classical realizability. It gives us an interpretation between classical theories, by composing interpretations between intuitionistic theories.

Lower bound cost estimation for logic programs

It is generally recognized that information about the runtime cost of computations can be useful for a variety of applications, including program transformation, granularity control during parallel execution, and query optimization in deductive databases. Most of the work to date on compile-time cost estimation of logic programs has focused on the estimation of upper bounds on costs. However, in many applications, such as parallel implementations on distributed-memory machines, one would prefer to work with lower bounds instead. The problem with estimating lower bounds is that in general, it is necessary to account for the possibility of failure of head unification, leading to a trivial lower bound of 0. In this paper, we show how, given type and mode information about procedures in a logic program, it is possible to (semi-automatically) derive nontrivial lower bounds on their computational costs. We also discuss the cost analysis for the special and frequent case of divide-and-conquer programs and show how —as a pragmatic short-term solution —it may be possible to obtain useful results simply by identifying and treating divide-and-conquer programs specially.