Combining kernel estimators in the uniform deconvolution problem

We construct a density estimator and an estimator of the distribution function in the uniform deconvolution model. The estimators are based on inversion formulas and kernel estimators of the density of the observations and its derivative. Initially the inversions yield two different estimators of the density and two estimators of the distribution function. We construct asymptotically optimal convex combinations of these two estimators. We also derive pointwise asymptotic normality of the resulting estimators, the pointwise asymptotic biases and an expansion of the mean integrated squared error of the density estimator. It turns out that the pointwise limit distribution of the density estimator is the same as the pointwise limit distribution of the density estimator introduced by Groeneboom and Jongbloed (Neerlandica, 57, 2003, 136), a kernel smoothed nonparametric maximum likelihood estimator of the distribution function.     

Divisia price and quantity indices: 80 years after

This paper reviews and extends the theory of price and quantity indices which are defined as line integrals, the two types being those of Divisia and Montgomery. The properties of these indices are systematically explored, whereby in particular attention is paid to the path-(in)dependency issue. Two sections discuss the problem of how to approximate the line integral indices when only data at discrete points of time are available. It appears that every bilateral index can be conceived as the outcome of a line integral index over a particular curve in price–quantity space. The classical position is that chained bilateral indices are rationalized by Divisia indices. This rationalization is only interesting when the Divisia indices themselves possess a proper foundation in economic theory. The final sections are therefore devoted to the role played by the Divisia indices in micro-economic theory.     

Finance as a Driver of Corporate Social Responsibility

Finance is grease to the economy. Therefore, we assume that it may affect corporate social responsibility (CSR) and the sustainability of economic development too. This paper discusses the transmission mechanisms between finance and sustainability. We find that there is no simple one-to-one relationship between financial development and sustainable development but there are various – often indirect – linkages. It appears that most of the literature concentrates on the role of public shareholders when it comes to changing corporate policy and performance in a more sustainable direction. However, this focus neglects the potential impact of the credit channel and private equity on a firm’s non-financial policies and performance. These very powerful mechanisms can govern business policies and practices. Therefore, there appears to be much more scope for finance to promote socially and environmentally desirable activities and to discourage detrimental activities than has been acknowledged in the academic literature so far.Bert Scholtens received his Ph.D. at the University of Amsterdam in 1994. Since 1999 he has been working at the Department of Finance of the University of Groningen, the Netherlands. His research particularly looks into the interactions between financial institutions and sustainable development/corporate social responsibility. He has recently published in, among others, Ecological Economics, Journal of Banking and Finance, Finance letters, Journal of Investing, and Sustainable Development.     

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Efficient Factor Models For Yield Curve Dynamics

Abstract

This paper derives a class of efficient factor models that bridge a gap between factor models and Heath-Jarrow-Morton models. These efficient factor models provide arbitrage-free dynamics for the yield curve, can be readily extended to fit the current yield curve, and have closed-form formulas for pricing default-free zero-coupon bonds. The short rate is a state variable in these efficient factor models. There are no restrictions imposed on the functional form of the volatility of the short rate except for certain technical conditions to ensure the solvability of the associated stochastic differential equations. The stochastic volatility of the short rate can be one of the state variables. The paper also presents a closed-form solution for default-free discount bond prices in the Malkiel model and provides a new method to derive the Ritchken-Sankarasubramanian model.     

An Extreme Value Analysis Of Advanced Age Mortality Data

Abstract

Extreme value theory describes the behavior of random variables at extremely high or low levels. The application of extreme value theory to statistics allows us to fit models to data from the upper tail of a distribution. This paper presents a statistical analysis of advanced age mortality data, using extreme value models to quantify the upper tail of the distribution of human life spans.

Our analysis focuses on mortality data from two sources. Statistics Canada publishes the annual number of deaths in Canada, broken down by angender and age. We use the deaths data from 1949 to 1997 in our analysis. The Japanese Ministry of Health, Labor, and Welfare also publishes detailed annual mortality data, including the 10 oldest reported ages at death in each year. We analyze the Japanese data over the period from 1980 to 2000.

Using the r-largest and peaks-over-threshold approaches to extreme value modeling, we fit generalized extreme value and generalized Pareto distributions to the life span data. Changes in distribution by birth cohort or over time are modeled through the use of covariates. We then evaluate the appropriateness of the fitted models and discuss reasons for their shortcomings. Finally, we use our findings to address the existence of a finite upper bound on the life span distribution and the behavior of the force of mortality at advanced ages.