Algorithms of causal inference for the analysis of effective connectivity among brain regions

In recent years, powerful general algorithms of causal inference have been developed. In particular, in the framework of Pearl’s causality, algorithms of inductive causation (IC and IC*) provide a procedure to determine which causal connections among nodes in a network can be inferred from empirical observations even in the presence of latent variables, indicating the limits of what can be learned without active manipulation of the system. These algorithms can in principle become important complements to established techniques such as Granger causality and Dynamic Causal Modeling (DCM) to analyze causal influences (effective connectivity) among brain regions. However, their application to dynamic processes has not been yet examined. Here we study how to apply these algorithms to time-varying signals such as electrophysiological or neuroimaging signals. We propose a new algorithm which combines the basic principles of the previous algorithms with Granger causality to obtain a representation of the causal relations suited to dynamic processes. Furthermore, we use graphical criteria to predict dynamic statistical dependencies between the signals from the causal structure. We show how some problems for causal inference from neural signals (e.g., measurement noise, hemodynamic responses, and time aggregation) can be understood in a general graphical approach. Focusing on the effect of spatial aggregation, we show that when causal inference is performed at a coarser scale than the one at which the neural sources interact, results strongly depend on the degree of integration of the neural sources aggregated in the signals, and thus characterize more the intra-areal properties than the interactions among regions. We finally discuss how the explicit consideration of latent processes contributes to understand Granger causality and DCM as well as to distinguish functional and effective connectivity

Granger Causality and Structural Causality in Cross-Section and Panel Data

Published in Econometric Theory, https://doi.org/10.1017/S0266466616000086</p

Causal discourse in a game of incomplete information

Notions of cause and effect are fundamental to economic explanation. Although concepts such as price effects are intuitive, rigorous foundations justifying causal discourse in the wide range of economic settings remain lacking. We illustrate this deficiency using an N-bidder private-value auction, posing causal questions that cannot be addressed within existing frameworks. We extend the frameworks of Pearl (2000) and White and Chalak (2009) to introduce topological settable systems (TSS), a causal framework capable of delivering the missing answers. Particularly, TSS accommodate choices belonging to general function spaces. Our analysis suggests how TSS enable causal discourse in various areas of economics

Identifiability and transportability in dynamic causal networks

In this paper we propose a causal analog to the purely observational Dynamic Bayesian Networks, which we call Dynamic Causal Networks. We provide a sound and complete algorithm for identification of Dynamic Causal Networks, namely, for computing the effect of an intervention or experiment, based on passive observations only, whenever possible. We note the existence of two types of confounder variables that affect in substantially different ways the identification procedures, a distinction with no analog in either Dynamic Bayesian Networks or standard causal graphs. We further propose a procedure for the transportability of causal effects in Dynamic Causal Network settings, where the result of causal experiments in a source domain may be used for the identification of causal effects in a target domain.Preprin

Geometric and long run aspects of Granger causality

This paper extends multivariate Granger causality to take into account the subspaces along which Granger causality occurs as well as long run Granger causality. The properties of these new notions of Granger causality, along with the requisite restrictions, are derived and extensively studied for a wide variety of time series processes including linear invertible processes and VARMA. Using the proposed extensions, the paper demonstrates that: (i) mean reversion in is an instance of long run Granger non-causality, (ii) cointegration is a special case of long run Granger non-causality along a subspace, (iii) controllability is a special case of Granger causality, and finally (iv) linear rational expectations entail (possibly testable) Granger causality restriction along subspaces

Profitability, investment and capital productivity

Capital accumulation is pivotal to produce goods and services. Common knowledge is that entrepreneurs invest because of potential profit. However, the various theoretical frameworks as well as empirical studies are not providing unequivocal evidence of direct causality between profit and investment decisions. In this document we use Granger symetric causality test as well as asymmetric causality test first proposed by (Hatemi-J, 2012). We examine possible causality between profit and investment, profit and unit labour cost and between investment and productivity