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Settable Systems: An Extension of Pearl’s Causal Model with Optimization, Equilibrium, and Learning
, 2008
"... Judea Pearl’s Causal Model is a rich framework that provides deep insight into the nature of causal relations. As yet, however, the Pearl Causal Model (PCM) has not had much impact on economics or econometrics. This may be due in part to the fact that the PCM is not as well suited to analyzing econo ..."
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Cited by 10 (5 self)
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Judea Pearl’s Causal Model is a rich framework that provides deep insight into the nature of causal relations. As yet, however, the Pearl Causal Model (PCM) has not had much impact on economics or econometrics. This may be due in part to the fact that the PCM is not as well suited to analyzing economic structures as might be desired. We o¤er the settable systems framework as an extension of the PCM that embodies features of central interest to economists and econometricians: optimization, equilibrium, and learning. Because these are common features of physical, natural, or social systems, our framework may prove generally useful. In particular, settable systems o¤er a number of advantages relative to the PCM for machine learning. Important distinguishing features of the settable systems framework are its countable dimensionality, its treatment of attributes, the absence of a …xedpoint requirement, and the use of partitioning and partitionspeci…c response functions to accommodate the behavior of optimizing and interacting agents. A series of closely related machine learning examples and examples from game theory and machine learning with feedback demonstrates limitations of the PCM and motivates the distinguishing features of settable systems.
Granger Causality and Dynamic Structural Systems
, 2008
"... We analyze the relations between Granger (G) noncausality and a notion of structural causality arising naturally from a general nonseparable recursive dynamic structural system. Building on classical notions of G noncausality, we introduce interesting and natural extensions, namely weak G noncaus ..."
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Cited by 6 (2 self)
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We analyze the relations between Granger (G) noncausality and a notion of structural causality arising naturally from a general nonseparable recursive dynamic structural system. Building on classical notions of G noncausality, we introduce interesting and natural extensions, namely weak G noncausality and retrospective weak G noncausality. We show that structural noncausality and certain (retrospective) conditional exogeneity conditions imply (retrospective) (weak) G noncausality. We strengthen structural causality to notions of (retrospective) strong causality and show that (retrospective) strong causality implies (retrospective) weak G causality. We provide practical conditions and straightforward new methods for testing (retrospective) weak G noncausality, (retrospective) conditional exogeneity, and structural noncausality. Finally, we apply our methods to explore structural causality in industrial pricing, macroeconomics, and …nance.
A Nonparametric Copula Based Test for Conditional Independence with Applications to Granger Causality *
, 2009
"... This paper proposes a new nonparametric test for conditional independence, which is based on the comparison of Bernstein copula densities using the Hellinger distance. The test is easy to implement because it does not involve a weighting function in the test statistic, and it can be applied in gener ..."
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Cited by 1 (1 self)
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This paper proposes a new nonparametric test for conditional independence, which is based on the comparison of Bernstein copula densities using the Hellinger distance. The test is easy to implement because it does not involve a weighting function in the test statistic, and it can be applied in general settings since there is no restriction on the dimension of the data. In fact, to apply the test, only a bandwidth is needed for the nonparametric copula. We prove that the test statistic is asymptotically pivotal under the null hypothesis, establish local power properties, and motivate the validity of the bootstrap technique that we use in finite sample settings. A simulation study illustrates the good size and power properties of the test. We illustrate the empirical relevance of our test by focusing on Granger causality using financial time series data to test for nonlinear leverage versus volatility feedback effects and to test for causality between stock returns and trading volume. In a third application, we investigate Granger causality between macroeconomic variables.
_____ Dynamics of Human Behavior *
"... Abstract: I review network aspects of human dynamics that link macrohistorical to microsociological and evolutionary processes. The ability to bond in communities of varying spatial scales is a special property of humans that happens through social networks. These networks have greater cohesion thr ..."
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Abstract: I review network aspects of human dynamics that link macrohistorical to microsociological and evolutionary processes. The ability to bond in communities of varying spatial scales is a special property of humans that happens through social networks. These networks have greater cohesion through invulnerability to disconnection without removal of k nodes. Menger’s (1927) connectivity theorem shows that this property of kcohesion mutually entails k nodeindependent paths between every pair of group members. Because of this property, i.e., by redundancy of communication, humans in such communities can utilize language and longrange communication to compensate for diminishing facetoface interaction as groups grow large. For a given level k of cohesion, the maximally extensive e(k) group size is unbounded and scalable because, for each cohesive intensity level k, the maximal group size e(k) can expand indefinitely without the need to increase the average number of ties per member. Hence, the growth of human community size is scalable at a fixed cost in number of ties per person, unlike those species unable to take advantage of kconnectivity. Strong causal effects, using the k cohesionlevel measure of empirical groups whose boundaries and extent are defined by e(k), have been replicated and validated in various sociological and anthropological network studies. This allows me to examine the micromacro linkages between
2009/69 A Nonparametric Copula Based Test for Conditional Independence with Applications to Granger Causality.
, 2009
"... A nonparametric copula based test for conditional independence with applications to Granger causality ..."
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A nonparametric copula based test for conditional independence with applications to Granger causality