Comment on "Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains"

Dukelsky, Mart\'in-Delgado, Nishino and Sierra (Europhys. Lett., 43, 457 (1998) - hereafter referred to as DMNS) investigated the matrix product method (MPM), comparing it with the infinite-size density matrix renormalization group (DMRG). For equivalent basis size, the MPM produces an improved variational energy over that produced by DMRG and, unlike DMRG, produces a translationally-invariant wavefunction. The DMRG results presented were significantly worse than the MPM, caused by a shallow bound state appearing at the join of the two DMRG blocks. They also suggested that the DMRG results can be improved by using an alternate superblock construction $[B] \bullet [B]$ for the last few steps of the calculation. In this comment, we show that the DMRG results presented by DMNS are in error and the artificial bound state produced by the standard superblock configuration is very small even for $m=2$ states kept. In addition, we calculate explicitly the energy and wavefunction for the $[B] \bullet [B]$ superblock structure and verify that the energy coincides with that of the MPM, as conjectured by S. Ostlund and S. Rommer (Phys. Rev. Lett., 75, 3537 (1995)).Comment: 2 pages, 1 eps figure included. eps.cls include

The Cumulative Unanticipated Change in Interest Rates: Evidence on the Misintermediation Hypothesis

The term structure of interest rates is carefully analyzed over the period 1947-77 in order to construct a monthly series on cumulative unanticipated changes in long-term interest rates. This series is a sort of synthetic interest rate, changes in which over several months or years represent entirely unanticipated changes in interest rates. The behavior of this series is examined over recognized business fluctuations, and it is found to be actually more reliably pro-cyclic than the raw long-term interest rate, in spite of Kessel's finding that the market tends to correctly predict the direction of change of interest rates over phases. That the series is pro-cyclic supports the hypothesis we have put forward in another paper, that business fluctuations may be caused by "misintermediation", by which we mean the traditional mis-matching of asset and liability maturities on the part of financial intermediaries.

The Kalman Foundations of Adaptive Least Squares: Applications to Unemployment and Inflation

Adaptive Least Squares (ALS), i.e. recursive regression with asymptotically constant gain, as proposed by Ljung (1992), Sargent (1993, 1999), and Evans and Honkapohja (2001), is an increasingly widely-used method of estimating time-varying relationships and of proxying agents’ time-evolving expectations. This paper provides theoretical foundations for ALS as a special case of the generalized Kalman solution of a Time Varying Parameter (TVP) model. This approach is in the spirit of that proposed by Ljung (1992) and Sargent (1999), but unlike theirs, nests the rigorous Kalman solution of the elementary Local Level Model, and employs a very simple, yet rigorous, initialization. Unlike other approaches, the proposed method allows the asymptotic gain to be estimated by maximum likelihood (ML). The ALS algorithm is illustrated with univariate time series models of U.S. unemployment and inflation. Because the null hypothesis that the coefficients are in fact constant lies on the boundary of the permissible parameter space, the usual regularity conditions for the chi-square limiting distribution of likelihood-based test statistics are not met. Consequently, critical values of the Likelihood Ratio test statistics are established by Monte Carlo means and used to test the constancy of the parameters in the estimated models.Kalman Filter, Adaptive Learning, Adaptive Least Squares, Time Varying Parameter Model, Natural Unemployment Rate, Inflation Forecasting

The Pricing of Short-Lived Options When Price Uncertainty Is Log-Symmetric Stable

The well-known option pricing formula of Black and Scholes depends upon the assumption that price fluctuations are log-normal. However, this formula greatly underestimates the value of options with a low probability of being exercised if, as appears to be more nearly the case in most markets, price fluctuations are in fact symmetrics table or log-symmetric stable. This paper derives a general formula for the value of a put or call option in a general equilibrium, expected utility maximization context. This general formula is found to yield the Black-Scholes formula for a wide variety of underlying processes generating log-normal price uncertainty. It is then used to derive the value of a short-lived option for certain processes that generate log-symmetric stable price uncertainty. Our analysis is restricted to short-lived options for reasons of mathematical tractability. Nevertheless, the formula is useful for evaluating many types of risk.

The Effect of Minimum Wage Legislation on Income Equality: A TheoreticalAnalysis

Minimum wage legislation is frequently advocated in the belief that itcreates a more nearly equal distribution of income. A one-sector model of general equilibrium is used to analyze a universally applicable minimum wage, and a two-sector model is used to analyze a minimum wage that is only applied to certain industries. In both cases we find that a minimum wage may well lower equality (as computed by the Gini index) if we consider reasonable values for the parameters of these two models. In the absence of unemployment compensation, equality can increase only if the elasticity of substitution in production is quite low. In the one-sector case, however, equality necessarily rises if unemployment compensation is present and sufficiently generous.

The Term Structure of Interest Rates

This paper consolidates and interprets the literature on the term structure, as it stands today. Definitions of rates of return, forward rates and holding returns for all time intervals are treated here in a uniform manner and their interrelations, exact or approximate, delineated. The concept of duration is used throughout to simplify mathematical expressions. Continuous compounding is used where possible, to avoid arbitrary distinctions based on compounding assumptions. Both the theoretical and the empirical literature are treated. The attached tables by J. Huston McCulloch give term structure data for U. S. government securities 1946-1987. The tables give discount bond yields, forward rates and par bond yields as defined in the paper. The data relate to the concepts in the paper more precisely than does any previously published data series.

An evaluation of a toothbrushing programme in schools

Purpose: This paper assesses the effectiveness of a toothbrushing intervention delivered in primary schools in Yorkshire and the Humber, a Northern district of England. The toothbrushing intervention was designed with the intention of improving the oral health of young children. The paper reports the effectiveness of the intervention and explores process issues related to its co-ordination and delivery. Design/methodology/approach: The evaluation had three data gathering approaches. These were: in-depth case studies of three selected schools participating in the toothbrushing programme; interviews with oral health programme leads; and a small scale questionnaire based survey which was sent to the 18 schools participating in the intervention. Findings: The intervention was accepted by children and they enjoyed participating in the toothbrushing scheme. Moreover, children had often become more knowledgeable about toothbrusing and the consequences of not regularly cleaning their teeth. The scheme was contingent on key staff in the school and the programme was more successful where school’s embraced, rather than rejected the notion of improving children’s health alongside educational attainment. Whether the intervention made differences to brushing in the home requires further investigation, but there is a possibility that children can act as positive ‘change agents’ with siblings and other family members. Practical implications: This paper suggests that schools can be an effective setting for implementing toothbrushing interventions. Originality/value: Toothbrushing in schools programmes are a relatively new initiative that have not been fully explored, especially using qualitative approaches or focussing on the views of children. This paper makes a particular contribution to understanding the process and delivery of toothbrushing interventions delivered in primary schools. The implications for programmes outside of the UK context are discussed