Bayesian unit-root tests for Stochastic Volatility models

In this article, we consider Bayesian inference procedures to test for a unit root in Stochastic Volatility (SV) models. Unit-root tests for the persistence parameter of the SV models, based on the Bayes Factor (BF), have been recently introduced in the literature. In contrast, we propose a flexible class of priors that is non-informative over the entire support of the persistence parameter (including the non-stationarity region). In addition, we show that our model fitting procedure is computationally efficient (using the software WinBUGS). Finally, we show that our proposed test procedures have good frequentist properties in terms of achieving high statistical power, while maintaining low total error rates. We illustrate the above features of our method by extensive simulation studies, followed by an application to a real data set on exchange rates.     

Diagnostic checks for discrete data regression models using posterior predictive simulations

Model checking with discrete data regressions can be difficult because the usual methods such as residual plots have complicated reference distributions that depend on the parameters in the model. Posterior predictive checks have been proposed as a Bayesian way to average the results of goodness-of-fit tests in the presence of uncertainty in estimation of the parameters. We try this approach using a variety of discrepancy variables for generalized linear models fitted to a historical data set on behavioural learning. We then discuss the general applicability of our findings in the context of a recent applied example on which we have worked. We find that the following discrepancy variables work well, in the sense of being easy to interpret and sensitive to important model failures: structured displays of the entire data set, general discrepancy variables based on plots of binned or smoothed residuals versus predictors and specific discrepancy variables created on the basis of the particular concerns arising in an application. Plots of binned residuals are especially easy to use because their predictive distributions under the model are sufficiently simple that model checks can often be made implicitly. The following discrepancy variables did not work well: scatterplots of latent residuals defined from an underlying continuous model and quantile–quantile plots of these residuals.     

Binary probability maps using a hidden conditional autoregressive Gaussian process with an application to Finnish common toad data

The Finnish common toad data of Heikkinen and Hogmander are reanalysed using an alternative fully Bayesian model that does not require a pseudolikelihood approximation and an alternative prior distribution for the true presence or absence status of toads in each 10 km×10 km square. Markov chain Monte Carlo methods are used to obtain posterior probability estimates of the square-specific presences of the common toad and these are presented as a map. The results are different from those of Heikkinen and Hogmander and we offer an explanation in terms of the prior used for square-specific presence of the toads. We suggest that our approach is more faithful to the data and avoids unnecessary confounding of effects. We demonstrate how to extend our model efficiently with square-specific covariates and illustrate this by introducing deterministic spatial changes.     

Standard errors for EM estimation

The EM algorithm is a popular method for computing maximum likelihood estimates. One of its drawbacks is that it does not produce standard errors as a by-product. We consider obtaining standard errors by numerical differentiation. Two approaches are considered. The first differentiates the Fisher score vector to yield the Hessian of the log-likelihood. The second differentiates the EM operator and uses an identity that relates its derivative to the Hessian of the log-likelihood. The well-known SEM algorithm uses the second approach. We consider three additional algorithms: one that uses the first approach and two that use the second. We evaluate the complexity and precision of these three and the SEM in algorithm seven examples. The first is a single-parameter example used to give insight. The others are three examples in each of two areas of EM application: Poisson mixture models and the estimation of covariance from incomplete data. The examples show that there are algorithms that are much simpler and more accurate than the SEM algorithm. Hopefully their simplicity will increase the availability of standard error estimates in EM applications. It is shown that, as previously conjectured, a symmetry diagnostic can accurately estimate errors arising from numerical differentiation. Some issues related to the speed of the EM algorithm and algorithms that differentiate the EM operator are identified.     

Off‐Time Pubertal Timing Predicts Physiological Reactivity to Postpuberty Interpersonal Stress

We investigated associations between retrospectively assessed timing of pubertal development, interpersonal interactions, and hypothalamic–pituitary–adrenal axis reactivity to an interpersonal stress task in 110 young adult women. Participants provided salivary cortisol samples at points prior and subsequent to a video‐taped conflict discussion with their romantic partner. Participants also provided subjective global ratings of their discussion on dimensions of conflict and support. For earlier developing girls, higher levels of interpersonal conflict were associated with greater physiological stress in anticipation of the discussion task and less physiological recovery following the discussion. In contrast, for later developing girls, low levels of conflict were associated with greater anticipatory stress and less physiological recovery. These findings have implications for understanding the influence of off‐time pubertal development on the lifetime development of young women.     

Die Bedeutung der Zinsschranke

The German Corporate Tax Reform Act of 2008 requires an adjustment of classic valuation concepts because it limits interest deduction from taxable income depending on the operating performance of the company. By using time- and state-contingent discount rates in a risk-neutral valuation with predetermined debt levels, a theoretically sound valuation result is obtained. However, a modified APV-concept which assumes deterministic debt over the planning horizon and constant leverage in the terminal value phase also yields consistent valuation results when two types of tax shields with different levels of risk are distinguished.     

Cultural capital or relative risk aversion? Two mechanisms for educational inequality compared1

In this paper we empirically examined two explanatory mechanisms for educational inequality: cultural reproduction and relative risk aversion, using survey data taken from secondary school pupils in Amsterdam. Cultural reproduction theory seeks to explain class variations in schooling by cultural differences between social classes. Relative risk aversion theory argues that educational inequalities can be understood by between-class variation in the necessity of pursuing education at branching points in order to avoid downward mobility. We showed that class variations in early demonstrated ability are for a substantial part cultural: cultural capital - measured by parental involvement in highbrow culture - affected school performance at the primary and secondary level. However, relative risk aversion - operationalized by being concerned with downward mobility - strongly affects schooling ambitions, whereas cultural capital had no effect. Thus, we conclude that 'primary effects' of social origin on schooling outcomes are manifested through cultural capital and not through relative risk aversion (in addition to other potential sources of class variations such as genetics). Relative risk aversion, and not cultural capital, affects schooling ambitions, which is relevant for our understanding of secondary effects.     

The life-course origins of mastery among older people

In this article, we aim to identify the sources of mastery--the understanding that individuals hold about their ability to control the circumstances of their lives. The sample for our inquiry was drawn from the Medicare beneficiary files of people 65 and older living in Washington, DC, and two adjoining Maryland counties. We find that past circumstances, particularly those reflecting status attainment and early exposure to intractable hardships, converge with stressors experienced in late life to influence elders' level of mastery. The impact of past conditions, however, does not necessarily directly affect the current mastery of older people. Instead, the effect of prior experiences on current mastery is mediated by what we refer to as life-course mastery: one's belief that one has directed and managed the trajectories that connect one's past to the present. Our analyses show that life-course mastery largely serves as the mediating channel through which individuals connect their past to their present.     

Quasi-binomial zero-inflated regression model suitable for variables with bounded support

In recent years, a variety of regression models, including zero-inflated and hurdle versions, have been proposed to explain the case of a dependent variable with respect to exogenous covariates. Apart from the classical Poisson, negative binomial and generalised Poisson distributions, many proposals have appeared in the statistical literature, perhaps in response to the new possibilities offered by advanced software that now enables researchers to implement numerous special functions in a relatively simple way. However, we believe that a significant research gap remains, since very little attention has been paid to the quasi-binomial distribution, which was first proposed over fifty years ago. We believe this distribution might constitute a valid alternative to existing regression models, in situations in which the variable has bounded support. Therefore, in this paper we present a zero-inflated regression model based on the quasi-binomial distribution, taking into account the moments and maximum likelihood estimators, and perform a score test to compare the zero-inflated quasi-binomial distribution with the zero-inflated binomial distribution, and the zero-inflated model with the homogeneous model (the model in which covariates are not considered). This analysis is illustrated with two data sets that are well known in the statistical literature and which contain a large number of zeros.