Magnetic fields in the overshoot zone: The great escape

In order that magnetic flux be confined within the solar interior for times comparable to the solar cycle period it has been suggested that the bulk of the solar toroidal field is stored in the convectively stable overshoot region situated beneath the convection zone proper. Such a magnetic field, though, is still buoyant and is therefore subject to Rayleigh-Taylor type instabilities. The model problem of an isolated region of magnetic field embedded in a convectively stable atmosphere is considered. The fully nonlinear evolution of the two dimensional interchange of modes is studied, thereby shedding some light on one of the processes responsible for the escape of flux from the solar interior

The alpha-effect in rotating convection: a comparison of numerical simulations

Numerical simulations are an important tool in furthering our understanding of turbulent dynamo action, a process that occurs in a vast range of astrophysical bodies. It is important in all computational work that comparisons are made between different codes and, if non-trivial differences arise, that these are explained. Kapyla et al (2010: MNRAS 402, 1458) describe an attempt to reproduce the results of Hughes & Proctor (2009: PRL 102, 044501) and, by employing a different methodology, they arrive at very different conclusions concerning the mean electromotive force and the generation of large-scale fields. Here we describe why the simulations of Kapyla et al (2010) are simply not suitable for a meaningful comparison, since they solve different equations, at different parameter values and with different boundary conditions. Furthermore we describe why the interpretation of Kapyla et al (2010) of the calculation of the alpha-effect is inappropriate and argue that the generation of large-scale magnetic fields by turbulent convection remains a problematic issue.Comment: Submitted to MNRAS. 5 pages, 3 figure

On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference

Nonparametric methods play a central role in modern empirical work. While they provide inference procedures that are more robust to parametric misspecification bias, they may be quite sensitive to tuning parameter choices. We study the effects of bias correction on confidence interval coverage in the context of kernel density and local polynomial regression estimation, and prove that bias correction can be preferred to undersmoothing for minimizing coverage error and increasing robustness to tuning parameter choice. This is achieved using a novel, yet simple, Studentization, which leads to a new way of constructing kernel-based bias-corrected confidence intervals. In addition, for practical cases, we derive coverage error optimal bandwidths and discuss easy-to-implement bandwidth selectors. For interior points, we show that the MSE-optimal bandwidth for the original point estimator (before bias correction) delivers the fastest coverage error decay rate after bias correction when second-order (equivalent) kernels are employed, but is otherwise suboptimal because it is too "large". Finally, for odd-degree local polynomial regression, we show that, as with point estimation, coverage error adapts to boundary points automatically when appropriate Studentization is used; however, the MSE-optimal bandwidth for the original point estimator is suboptimal. All the results are established using valid Edgeworth expansions and illustrated with simulated data. Our findings have important consequences for empirical work as they indicate that bias-corrected confidence intervals, coupled with appropriate standard errors, have smaller coverage error and are less sensitive to tuning parameter choices in practically relevant cases where additional smoothness is available

The Relative Space: Space Measurements on a Rotating Platform

We introduce here the concept of relative space, an extended 3-space which is recognized as the only space having an operational meaning in the study of the space geometry of a rotating disk. Accordingly, we illustrate how space measurements are performed in the relative space, and we show that an old-aged puzzling problem, that is the Ehrenfest's paradox, is explained in this purely relativistic context. Furthermore, we illustrate the kinematical origin of the tangential dilation which is responsible for the solution of the Ehrenfest's paradox.Comment: 14 pages, 2 EPS figures, LaTeX, to appear in the European Journal of Physic

Exchange rate pass-through to import prices in South Africa: Is there asymmetry?

There is growing emphasis on the role played by the private sector in alleviating poverty in Africa. At the same time, greater focus is being placed on cash transfers as a poverty alleviation tool. This paper provides an economic rationale for private sector involvement in the provision of cash transfers. Previous research has focused on how the financial sector can provide payment solutions. In addition to payment mechanisms, the paper examines other avenues through which the private sector can contribute to cash transfer programmes .business taxes and Corporate Social Responsibility (CSR). Reducing corruption in tax administration and an enabling investment climate are essential if business taxes are to be a sustainable financing source for cash transfers. Governments can incorporate CSR into national policies and strategies which identify cash transfers as a poverty alleviation instrument. Cell phone banking, mobile branches, Point of sale (POS) technology and low cost banking are increasing access to financial services by the poor. These financial innovations can be used to make cash transfer payments.Exchange rate pass-through, Asymmetric pass-through, VECM, South Africa

On Binscatter

Binscatter is very popular in applied microeconomics. It provides a flexible, yet parsimonious way of visualizing and summarizing large data sets in regression settings, and it is often used for informal evaluation of substantive hypotheses such as linearity or monotonicity of the regression function. This paper presents a foundational, thorough analysis of binscatter: we give an array of theoretical and practical results that aid both in understanding current practices (i.e., their validity or lack thereof) and in offering theory-based guidance for future applications. Our main results include principled number of bins selection, confidence intervals and bands, hypothesis tests for parametric and shape restrictions of the regression function, and several other new methods, applicable to canonical binscatter as well as higher-order polynomial, covariate-adjusted and smoothness-restricted extensions thereof. In particular, we highlight important methodological problems related to covariate adjustment methods used in current practice. We also discuss extensions to clustered data. Our results are illustrated with simulated and real data throughout. Companion general-purpose software packages for \texttt{Stata} and \texttt{R} are provided. Finally, from a technical perspective, new theoretical results for partitioning-based series estimation are obtained that may be of independent interest

Bootstrap-Based Inference for Cube Root Asymptotics

This paper proposes a valid bootstrap-based distributional approximation for M-estimators exhibiting a Chernoff (1964)-type limiting distribution. For estimators of this kind, the standard nonparametric bootstrap is inconsistent. The method proposed herein is based on the nonparametric bootstrap, but restores consistency by altering the shape of the criterion function defining the estimator whose distribution we seek to approximate. This modification leads to a generic and easy-to-implement resampling method for inference that is conceptually distinct from other available distributional approximations. We illustrate the applicability of our results with four examples in econometrics and machine learning