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Econometrics, Volume 6, Issue 4 (December 2018)

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Open AccessArticle State-Space Models on the Stiefel Manifold with a New Approach to Nonlinear Filtering
Econometrics 2018, 6(4), 48; https://doi.org/10.3390/econometrics6040048
Received: 30 July 2018 / Revised: 25 November 2018 / Accepted: 10 December 2018 / Published: 12 December 2018
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Abstract
We develop novel multivariate state-space models wherein the latent states evolve on the Stiefel manifold and follow a conditional matrix Langevin distribution. The latent states correspond to time-varying reduced rank parameter matrices, like the loadings in dynamic factor models and the parameters of
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We develop novel multivariate state-space models wherein the latent states evolve on the Stiefel manifold and follow a conditional matrix Langevin distribution. The latent states correspond to time-varying reduced rank parameter matrices, like the loadings in dynamic factor models and the parameters of cointegrating relations in vector error-correction models. The corresponding nonlinear filtering algorithms are developed and evaluated by means of simulation experiments. Full article
(This article belongs to the Special Issue Filtering)
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Open AccessArticle Interval Estimation of Value-at-Risk Based on Nonparametric Models
Econometrics 2018, 6(4), 47; https://doi.org/10.3390/econometrics6040047
Received: 13 August 2018 / Revised: 25 November 2018 / Accepted: 6 December 2018 / Published: 10 December 2018
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Abstract
Value-at-Risk (VaR) has become the most important benchmark for measuring risk in portfolios of different types of financial instruments. However, as reported by many authors, estimating VaR is subject to a high level of uncertainty. One of the sources of uncertainty stems from
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Value-at-Risk (VaR) has become the most important benchmark for measuring risk in portfolios of different types of financial instruments. However, as reported by many authors, estimating VaR is subject to a high level of uncertainty. One of the sources of uncertainty stems from the dependence of the VaR estimation on the choice of the computation method. As we show in our experiment, the lower the number of samples, the higher this dependence. In this paper, we propose a new nonparametric approach called maxitive kernel estimation of the VaR. This estimation is based on a coherent extension of the kernel-based estimation of the cumulative distribution function to convex sets of kernel. We thus obtain a convex set of VaR estimates gathering all the conventional estimates based on a kernel belonging to the above considered convex set. We illustrate this method in an empirical application to daily stock returns. We compare the approach we propose to other parametric and nonparametric approaches. In our experiment, we show that the interval-valued estimate of the VaR we obtain is likely to lead to more careful decision, i.e., decisions that cannot be biased by an arbitrary choice of the computation method. In fact, the imprecision of the obtained interval-valued estimate is likely to be representative of the uncertainty in VaR estimate. Full article
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Open AccessConcept Paper Micro-Macro Connected Stochastic Dynamic Economic Behavior Systems
Econometrics 2018, 6(4), 46; https://doi.org/10.3390/econometrics6040046
Received: 8 November 2018 / Revised: 30 November 2018 / Accepted: 30 November 2018 / Published: 4 December 2018
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Abstract
In this paper, we borrow some of the key concepts of nonequilibrium statistical systems, to develop a framework for analyzing a self-organizing-optimizing system of independent interacting agents, with nonlinear dynamics at the macro level that is based on stochastic individual behavior at the
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In this paper, we borrow some of the key concepts of nonequilibrium statistical systems, to develop a framework for analyzing a self-organizing-optimizing system of independent interacting agents, with nonlinear dynamics at the macro level that is based on stochastic individual behavior at the micro level. We demonstrate the use of entropy-divergence methods and micro income data to evaluate and understand the hidden aspects of stochastic dynamics that drives macroeconomic behavior systems and discuss how to empirically represent and evaluate their nonequilibrium nature. Empirical applications of the information theoretic family of power divergence measures-entropic functions, interpreted in a probability context with Markov dynamics, are presented. Full article
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Open AccessReview A Review on Variable Selection in Regression Analysis
Econometrics 2018, 6(4), 45; https://doi.org/10.3390/econometrics6040045
Received: 31 May 2018 / Revised: 16 November 2018 / Accepted: 20 November 2018 / Published: 23 November 2018
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Abstract
In this paper, we investigate several variable selection procedures to give an overview of the existing literature for practitioners. “Let the data speak for themselves” has become the motto of many applied researchers since the number of data has significantly grown. Automatic model
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In this paper, we investigate several variable selection procedures to give an overview of the existing literature for practitioners. “Let the data speak for themselves” has become the motto of many applied researchers since the number of data has significantly grown. Automatic model selection has been promoted to search for data-driven theories for quite a long time now. However, while great extensions have been made on the theoretical side, basic procedures are still used in most empirical work, e.g., stepwise regression. Here, we provide a review of main methods and state-of-the art extensions as well as a topology of them over a wide range of model structures (linear, grouped, additive, partially linear and non-parametric) and available software resources for implemented methods so that practitioners can easily access them. We provide explanations for which methods to use for different model purposes and their key differences. We also review two methods for improving variable selection in the general sense. Full article
Open AccessArticle On the Stock–Yogo Tables
Econometrics 2018, 6(4), 44; https://doi.org/10.3390/econometrics6040044
Received: 31 March 2018 / Revised: 17 October 2018 / Accepted: 8 November 2018 / Published: 13 November 2018
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Abstract
A standard test for weak instruments compares the first-stage F-statistic to a table of critical values obtained by Stock and Yogo (2005) using simulations. We derive a closed-form solution for the expectation from which these critical values are derived, as well as
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A standard test for weak instruments compares the first-stage F-statistic to a table of critical values obtained by Stock and Yogo (2005) using simulations. We derive a closed-form solution for the expectation from which these critical values are derived, as well as present some second-order asymptotic approximations that may be of value in the presence of multiple endogenous regressors. Inspection of this new result provides insights not available from simulation, and will allow software implementations to be generalised and improved. Finally, we explore the calculation of p-values for the first-stage F-statistic weak instruments test. Full article
(This article belongs to the Special Issue Celebrated Econometricians: Peter Phillips)
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Open AccessArticle Estimation of Treatment Effects in Repeated Public Goods Experiments
Econometrics 2018, 6(4), 43; https://doi.org/10.3390/econometrics6040043
Received: 16 February 2018 / Revised: 9 October 2018 / Accepted: 26 October 2018 / Published: 29 October 2018
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Abstract
This paper provides a new statistical model for repeated voluntary contribution mechanism games. In a repeated public goods experiment, contributions in the first round are cross-sectionally independent simply because subjects are randomly selected. Meanwhile, contributions to a public account over rounds are serially
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This paper provides a new statistical model for repeated voluntary contribution mechanism games. In a repeated public goods experiment, contributions in the first round are cross-sectionally independent simply because subjects are randomly selected. Meanwhile, contributions to a public account over rounds are serially and cross-sectionally correlated. Furthermore, the cross-sectional average of the contributions across subjects usually decreases over rounds. By considering this non-stationary initial condition—the initial contribution has a different distribution from the rest of the contributions—we model statistically the time varying patterns of the average contribution in repeated public goods experiments and then propose a simple but efficient method to test for treatment effects. The suggested method has good finite sample performance and works well in practice. Full article
(This article belongs to the Special Issue Celebrated Econometricians: Peter Phillips)
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Open AccessEditorial Econometrics and Income Inequality
Econometrics 2018, 6(4), 42; https://doi.org/10.3390/econometrics6040042
Received: 11 October 2018 / Accepted: 11 October 2018 / Published: 15 October 2018
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Abstract
It is well-known that, after decades of non-interest in the theme, economics has experienced a proper surge in inequality research in recent years. [...] Full article
(This article belongs to the Special Issue Econometrics and Income Inequality) Printed Edition available
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