The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference

Background: Wiener-Granger causality (“G-causality”) is a statistical notion of causality applicable to time series data, whereby cause precedes, and helps predict, effect. It is defined in both time and frequency domains, and allows for the conditioning out of common causal influences. Originally developed in the context of econometric theory, it has since achieved broad application in the neurosciences and beyond. Prediction in the G-causality formalism is based on VAR (Vector AutoRegressive) modelling. New Method: The MVGC Matlab c Toolbox approach to G-causal inference is based on multiple equivalent representations of a VAR model by (i) regression parameters, (ii) the autocovariance sequence and (iii) the cross-power spectral density of the underlying process. It features a variety of algorithms for moving between these representations, enabling selection of the most suitable algorithms with regard to computational efficiency and numerical accuracy. Results: In this paper we explain the theoretical basis, computational strategy and application to empirical G-causal inference of the MVGC Toolbox. We also show via numerical simulations the advantages of our Toolbox over previous methods in terms of computational accuracy and statistical inference. Comparison with Existing Method(s): The standard method of computing G-causality involves estimation of parameters for both a full and a nested (reduced) VAR model. The MVGC approach, by contrast, avoids explicit estimation of the reduced model, thus eliminating a source of estimation error and improving statistical power, and in addition facilitates fast and accurate estimation of the computationally awkward case of conditional G-causality in the frequency domain. Conclusions: The MVGC Toolbox implements a flexible, powerful and efficient approach to G-causal inference. Keywords: Granger causality, vector autoregressive modelling, time series analysi

Multivariate Granger Causality and Generalized Variance

Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions between single (univariate) variables within a system, perhaps conditioned on other variables. However, interactions do not necessarily take place between single variables, but may occur among groups, or "ensembles", of variables. In this study we establish a principled framework for Granger causality in the context of causal interactions among two or more multivariate sets of variables. Building on Geweke's seminal 1982 work, we offer new justifications for one particular form of multivariate Granger causality based on the generalized variances of residual errors. Taken together, our results support a comprehensive and theoretically consistent extension of Granger causality to the multivariate case. Treated individually, they highlight several specific advantages of the generalized variance measure, which we illustrate using applications in neuroscience as an example. We further show how the measure can be used to define "partial" Granger causality in the multivariate context and we also motivate reformulations of "causal density" and "Granger autonomy". Our results are directly applicable to experimental data and promise to reveal new types of functional relations in complex systems, neural and otherwise.Comment: added 1 reference, minor change to discussion, typos corrected; 28 pages, 3 figures, 1 table, LaTe

Partisan Conflict and Income Inequality in the United States: A Nonparametric Causality-in-Quantiles Approach

This paper examines the predictive power of a partisan conflict on income inequality. Our study contributes to the existing literature by using the newly introduced nonparametric causality-in-quantile testing approach to examine how political polarization in the United States affects several measures of income inequality and distribution overtime. The study uses annual time-series data between the periods 1917–2013. We find evidence in support of a dynamic causal relationship between partisan conflict and income inequality, except at the upper end of the quantiles. Our empirical findings suggest that a reduction in partisan conflict will lead to a reduction in our measures of income inequality, but this requires that inequality is not exceptionally high

Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches

In the past two decades, functional Magnetic Resonance Imaging has been used to relate neuronal network activity to cognitive processing and behaviour. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this work, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area

Causal Relations via Econometrics

Applied econometric work takes a superficial approach to causality. Understanding economic affairs, making good policy decisions, and progress in the economic discipline depend on our ability to infer causal relations from data. We review the dominant approaches to causality in econometrics, and suggest why they fail to give good results. We feel the problem cannot be solved by traditional tools, and requires some out-of-the-box thinking. Potentially promising approaches to solutions are discussed.causality, regression, Granger Causality, Exogeneity, Cowles Commission, Hendry Methodology, Natural Experiments

Causal Relations via Econometrics

Applied econometric work takes a superficial approach to causality. Understanding economic affairs, making good policy decisions, and progress in the economic discipline depend on our ability to infer causal relations from data. We review the dominant approaches to causality in econometrics, and suggest why they fail to give good results. We feel the problem cannot be solved by traditional tools, and requires some out-of-the-box thinking. Potentially promising approaches to solutions are discussed.Causality, Regression, Exogeneity, Hendry Methodology, Natural Experiments

Granger Causality, Exogeneity, Cointegration, and Economic Policy Analysis

Policy analysis has long been a main interest of Clive Granger's. Here, we present a framework for economic policy analysis that provides a novel integration of several fundamental concepts at the heart of Granger's contributions to time-series analysis. We work with a dynamic structural system analyzed by White and Lu (2010) with well-defined causal meaning; under suitable conditional exogeneity restrictions, Granger causality coincides with this structural notion. The system contains target and control subsystems, with possibly integrated or cointegrated behavior. We ensure the invariance of the target subsystem to policy interventions using an explicitly causal partial equilibrium recursivity condition. Policy effectiveness is ensured by another explicit causality condition. These properties only involve the data generating process; models play a subsidiary role. Our framework thus complements that of Ericsson, Hendry, and Mizon (1998) (EHM) by providing conditions for policy analysis alternative to weak, strong, and super-exogeneity. This makes possible policy analysis for systems that may fail EHM's conditions. It also facilitates analysis of the cointegrating properties of systems subject to policymaker control. We discuss a variety of practical procedures useful for analyzing such systems and illustrate with an application to a simple model of the U.S. macroeconomy.

Comovements and Causality of Sector Price Indices: Evidence from the Egyptian Stock Exchange

Contributing to the meagre published literature on interrelationships amongst stock market sectors of an economy, the present study sets out to examine both the long-run and short-run aspects of the inter-sectoral linkages in the Egyptian stock market. The data correspond to daily closing prices for twelve sectoral indices of the Egyptian stock market, covering the period between January 3, 2007 and January 18, 2010. The multivariate cointegration analysis reports evidence in support of existence of only a single cointegrating vector within the sectoral indices. Moreover, the results of Granger’s causality analysis show that the short-run causal relationships between the sectoral indices are considerably limited and, where they exist, virtually unidirectional. In general, these results lead to the conclusion that there is still room to derive benefits from portfolio diversification in the short run. However, investors with long-term horizon may not benefit from diversifying investments into the different sectors of the Egyptian stock market.Stock Market sectors; Egypt; Domestic portfolio diversification; Johansen’s cointegration analysis; Granger's causality analysis