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.

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.

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.

Lower-bound collapse load Of square footing

Based on a radial moment field and the square yield criterion, a lower-bound collapse load is developed for a square footing subjected to a generalized contact pressure distribution. The current lower-bound collapse load compares well with the available upper-bound solutions.

Lower Bound Limit Analysis of Rectangular Slabs

A general method for the development of valid lower bound solutions to uniformly distributed and orthotropically reinforced rectangular concrete slabs obeying normal moment criterion is described. General expressions for moment field have been obtained for nine cases of slabs having all combinations of simply supported and clamped-edge conditions. The lower bound collapse loads have been compared with the upper bound values obtained by the yield line theory. The paper also focuses attention to the need for the development of valid upper bound solutions with the satisfaction of kinematical admissibility and the flow rules associated with the normal moment criterion.

A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space

We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.

Bearing capacity of interfering multiple strip footings by using lower bound finite elements limit analysis

The ultimate bearing capacity of a number of multiple strip footings, identically spaced and equally loaded to failure at the same time,is computed by using the lower bound limit analysis in combination with finite elements. The efficiency factor due to the component of soil unit weight, is computed with respect to changes in the clear spacing (xi(gamma)) between the footings. It is noted that the failure load for a footing in the group becomes always greater than that of a single isolated footing. The values of xi(gamma) for the smooth footings are found to be always lower than the rough footings. The values ofxi(gamma) are found to increase continuously with a decrease in the spacing between footings. As compared to the available theoretical and experimental results reported in literature, the present analysis provides generally a little lower values of xi(gamma). (C) 2010 Elsevier Ltd. All rights reserved.

Bearing capacity factors of circular foundations for a general c-phi soil using lower bound finite elements limit analysis

By using the lower bound limit analysis in conjunction with finite elements and linear programming, the bearing capacity factors due to cohesion, surcharge and unit weight, respectively, have been computed for a circular footing with different values of phi. The recent axisymmetric formulation proposed by the authors under phi = 0 condition, which is based on the concept that the magnitude of the hoop stress (sigma(theta)) remains closer to the least compressive normal stress (sigma(3)), is extended for a general c-phi soil. The computational results are found to compare quite well with the available numerical results from literature. It is expected that the study will be useful for solving various axisymmetric geotechnical stability problems. Copyright (C) 2010 John Wiley & Sons, Ltd.

Layered Tabu Search Algorithm for Large-MIMO Detection and a Lower Bound on ML Performance

In this paper, we are concerned with low-complexity detection in large multiple-input multiple-output (MIMO) systems with tens of transmit/receive antennas. Our new contributions in this paper are two-fold. First, we propose a low-complexity algorithm for large-MIMO detection based on a layered low-complexity local neighborhood search. Second, we obtain a lower bound on the maximum-likelihood (ML) bit error performance using the local neighborhood search. The advantages of the proposed ML lower bound are i) it is easily obtained for MIMO systems with large number of antennas because of the inherent low complexity of the search algorithm, ii) it is tight at moderate-to-high SNRs, and iii) it can be tightened at low SNRs by increasing the number of symbols in the neighborhood definition. Interestingly, the proposed detection algorithm based on the layered local search achieves bit error performances which are quite close to this lower bound for large number of antennas and higher-order QAM. For e. g., in a 32 x 32 V-BLAST MIMO system, the proposed detection algorithm performs close to within 1.7 dB of the proposed ML lower bound at 10(-3) BER for 16-QAM (128 bps/Hz), and close to within 4.5 dB of the bound for 64-QAM (192 bps/Hz).

A lower bound for the hitting set size for combinatorial rectangles and an application

We prove a lower bound of Omega(1/epsilon (m + log(d - a)) where a = [log(m) (1/4epsilon)] for the hitting set size for combinatorial rectangles of volume at least epsilon in [m](d) space, for epsilon is an element of [m(-(d-2)), 2/9] and d > 2. (C) 2002 Elsevier Science B.V. All rights reserved.

Bearing capacity of two interfering strip footings from lower bound finite elements limit analysis

A rigorous lower bound solution, with the usage of the finite elements limit analysis, has been obtained for finding the ultimate bearing capacity of two interfering strip footings placed on a sandy medium. Smooth as well as rough footingsoil interfaces are considered in the analysis. The failure load for an interfering footing becomes always greater than that for a single isolated footing. The effect of the interference on the failure load (i) for rough footings becomes greater than that for smooth footings, (ii) increases with an increase in phi, and (iii) becomes almost negligible beyond S/B>3. Compared with various theoretical and experimental results reported in literature, the present analysis generally provides the lowest magnitude of the collapse load. Copyright (c) 2011 John Wiley & Sons, Ltd.

Linearization of Drucker-Prager yield criterion for axisymmetric problems: implementation in lower-bound limit analysis

The linearization of the Drucker-Prager yield criterion associated with an axisymmetric problem has been achieved by simulating a sphere with the truncated icosahedron with 32 faces and 60 vertices. On this basis, a numerical formulation has been proposed for solving an axisymmetric stability problem with the usage of the lower-bound limit analysis, finite elements, and linear optimization. To compare the results, the linearization of the Mohr-Coulomb yield criterion, by replacing the three cones with interior polyhedron, as proposed earlier by Pastor and Turgeman for an axisymmetric problem, has also been implemented. The two formulations have been applied for determining the collapse loads for a circular footing resting on a cohesive-friction material with nonzero unit weight. The computational results are found to be quite convincing. (C) 2013 American Society of Civil Engineers.

Lower-Bound Axisymmetric Formulation for Geomechanics Problems Using Nonlinear Optimization

A lower-bound limit analysis formulation, by using two-dimensional finite elements, the three-dimensional Mohr-Coulomb yield criterion, and nonlinear optimization, has been given to deal with an axisymmetric geomechanics stability problem. The optimization was performed using an interior point method based on the logarithmic barrier function. The yield surface was smoothened (1) by removing the tip singularity at the apex of the pyramid in the meridian plane and (2) by eliminating the stress discontinuities at the corners of the yield hexagon in the pi-plane. The circumferential stress (sigma(theta)) need not be assumed. With the proposed methodology, for a circular footing, the bearing-capacity factors N-c, N-q, and N-gamma for different values of phi have been computed. For phi = 0, the variation of N-c with changes in the factor m, which accounts for a linear increase of cohesion with depth, has been evaluated. Failure patterns for a few cases have also been drawn. The results from the formulation provide a good match with the solutions available from the literature. (C) 2014 American Society of Civil Engineers.