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17
Causal Inference from Graphical Models
, 2001
"... Introduction The introduction of Bayesian networks (Pearl 1986b) and associated local computation algorithms (Lauritzen and Spiegelhalter 1988, Shenoy and Shafer 1990, Jensen, Lauritzen and Olesen 1990) has initiated a renewed interest for understanding causal concepts in connection with modelling ..."
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Cited by 80 (6 self)
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Introduction The introduction of Bayesian networks (Pearl 1986b) and associated local computation algorithms (Lauritzen and Spiegelhalter 1988, Shenoy and Shafer 1990, Jensen, Lauritzen and Olesen 1990) has initiated a renewed interest for understanding causal concepts in connection with modelling complex stochastic systems. It has become clear that graphical models, in particular those based upon directed acyclic graphs, have natural causal interpretations and thus form a base for a language in which causal concepts can be discussed and analysed in precise terms. As a consequence there has been an explosion of writings, not primarily within mainstream statistical literature, concerned with the exploitation of this language to clarify and extend causal concepts. Among these we mention in particular books by Spirtes, Glymour and Scheines (1993), Shafer (1996), and Pearl (2000) as well as the collection of papers in Glymour and Cooper (1999). Very briefly, but fundamentally,
Nonlinear causal discovery with additive noise models
"... The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuousvalued data linear acyclic causal models with additive noise are often used because these models are well understood and there are wellknown methods to fit them to data. In ..."
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Cited by 78 (30 self)
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The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuousvalued data linear acyclic causal models with additive noise are often used because these models are well understood and there are wellknown methods to fit them to data. In reality, of course, many causal relationships are more or less nonlinear, raising some doubts as to the applicability and usefulness of purely linear methods. In this contribution we show that in fact the basic linear framework can be generalized to nonlinear models. In this extended framework, nonlinearities in the datagenerating process are in fact a blessing rather than a curse, as they typically provide information on the underlying causal system and allow more aspects of the true datagenerating mechanisms to be identified. In addition to theoretical results we show simulations and some simple real data experiments illustrating the identification power provided by nonlinearities. 1
Causal Modelling Combining Instantaneous and Lagged Effects: an Identifiable Model Based on NonGaussianity
"... Causal analysis of continuousvalued variables typically uses either autoregressive models or linear Gaussian Bayesian networks with instantaneous effects. Estimation of Gaussian Bayesian networks poses serious identifiability problems, which is why it was recently proposed to use nonGaussian model ..."
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Cited by 12 (6 self)
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Causal analysis of continuousvalued variables typically uses either autoregressive models or linear Gaussian Bayesian networks with instantaneous effects. Estimation of Gaussian Bayesian networks poses serious identifiability problems, which is why it was recently proposed to use nonGaussian models. Here, we show how to combine the nonGaussian instantaneous model with autoregressive models. We show that such a nonGaussian model is identifiable without prior knowledge of network structure, and we propose an estimation method shown to be consistent. This approach also points out how neglecting instantaneous effects can lead to completely wrong estimates of the autoregressive coefficients. 1.
Vector autoregressions, policy analysis, and directed acyclic graphs: an application to the US
 Economy, Journal of Applied Economics
, 2003
"... The paper considers the use of directed acyclic graphs (DAGs), and their construction from observational data with PCalgorithm TETRAD II, in providing overidentifying restrictions on the innovations from a vector autoregression. Results from Sims ’ 1986 model of the US economy are replicated and c ..."
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Cited by 10 (4 self)
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The paper considers the use of directed acyclic graphs (DAGs), and their construction from observational data with PCalgorithm TETRAD II, in providing overidentifying restrictions on the innovations from a vector autoregression. Results from Sims ’ 1986 model of the US economy are replicated and compared using these datadriven techniques. The directed graph results show Sims ’ sixvariable VAR is not rich enough to provide an unambiguous ordering at usual levels of statistical significance. A significance level in the neighborhood of 30 % is required to find a clear structural ordering. Although the DAG results are in agreement with Sims ’ theorybased model for unemployment, differences are noted for the other five variables: income, money supply, price level, interest rates, and investment. Overall the DAG results are broadly consistent with a monetarist view with adaptive expectations and no hyperinflation.
Search for additive nonlinear time series causal models
 JMLR
, 2008
"... Pointwise consistent, feasible procedures for estimating contemporaneous linear causal structure from time series data have been developed using multiple conditional independence tests, but no such procedures are available for nonlinear systems. We describe a feasible procedure for learning a class ..."
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Cited by 8 (3 self)
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Pointwise consistent, feasible procedures for estimating contemporaneous linear causal structure from time series data have been developed using multiple conditional independence tests, but no such procedures are available for nonlinear systems. We describe a feasible procedure for learning a class of nonlinear time series structures, which we call additive nonlinear time series. We show that for data generated from stationary models of this type, two classes of conditional independence relations among time series variables and their lags can be tested efficiently and consistently using tests based on additive model regression. Combining results of statistical tests for these two classes of conditional independence relations and the temporal structure of time series data, a new consistent model specification procedure is able to extract relatively detailed causal information. We investigate the finite sample behavior of the procedure through simulation, and illustrate the application of this method through analysis of the possible causal connections among four ocean indices. Several variants of the procedure are also discussed.
Discovering Cyclic Causal Models with Latent Variables: A General SATBased Procedure
"... We present a very general approach to learning the structure of causal models based on dseparation constraints, obtained from any given set of overlapping passive observational or experimental data sets. The procedure allows for both directed cycles (feedback loops) and the presence of latent varia ..."
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Cited by 6 (3 self)
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We present a very general approach to learning the structure of causal models based on dseparation constraints, obtained from any given set of overlapping passive observational or experimental data sets. The procedure allows for both directed cycles (feedback loops) and the presence of latent variables. Our approach is based on a logical representation of causal pathways, which permits the integration of quite general background knowledge, and inference is performed using a Boolean satisfiability (SAT) solver. The procedure is complete in that it exhausts the available information on whether any given edge can be determined to be present or absent, and returns “unknown ” otherwise. Many existing constraintbased causal discovery algorithms can be seen as special cases, tailored to circumstances in which one or more restricting assumptions apply. Simulations illustrate the effect of these assumptions on discovery and how the present algorithm scales. 1
Graphical Models for Structural Vector Autoregressions
, 2004
"... The identification of a VAR requires differentiating between correlation and causation. This paper presents a method to deal with this problem. Graphical models, which provide a rigorous language to analyze the statistical and logical properties of causal relations, associate a particular set of va ..."
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Cited by 5 (2 self)
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The identification of a VAR requires differentiating between correlation and causation. This paper presents a method to deal with this problem. Graphical models, which provide a rigorous language to analyze the statistical and logical properties of causal relations, associate a particular set of vanishing partial correlations to every possible causal structure. The structural form is described by a directed graph and from the analysis of the partial correlations of the residuals the set of acceptable causal structures is derived. This procedure is applied to an updated version of the King et al. (American Economic Review, 81, (1991), 819) data set and it yields an orthogonalization of the residuals consistent with the causal structure among contemporaneous variables and alternative to the standard one, based on a Choleski factorization of the covariance matrix of the residuals.
Comment On Hausman & Woodward On The Causal Markov Condition
"... Hausman & Woodward present an argument for the Causal Markov Condition (CMC) on the basis of a principle they dub ‘modularity ’ ([1999, 2004]). I show that the conclusion of their argument is not in fact the CMC but a substantially weaker proposition. In addition, I show that their argument is i ..."
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Cited by 3 (0 self)
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Hausman & Woodward present an argument for the Causal Markov Condition (CMC) on the basis of a principle they dub ‘modularity ’ ([1999, 2004]). I show that the conclusion of their argument is not in fact the CMC but a substantially weaker proposition. In addition, I show that their argument is invalid and trace this invalidity to two features of modularity, namely, that it is stated in terms of pairwise independence and ‘arrowbreaking ’ interventions. Hausman & Woodward’s argument can be rendered valid through a reformulation of modularity, but it is doubtful that the argument so revised provides any substantially new insight regarding the basis of the CMC.
Identi cation of Monetary Policy Shocks: a Graphical Causal Approach
, 2005
"... This paper develops a structural VAR methodology based on graphical models to identify the monetary policy shocks and to measure their macroeconomic eects. The advantage of this procedure is to work with testable overidentifying models, whose restrictions are derived by the partial correlations am ..."
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This paper develops a structural VAR methodology based on graphical models to identify the monetary policy shocks and to measure their macroeconomic eects. The advantage of this procedure is to work with testable overidentifying models, whose restrictions are derived by the partial correlations among residuals plus some institutional knowledge. This permits to test some restrictions on the reserve market used in several approaches existing in the literature. The main ndings are that neither VAR innovations to federal funds rate nor innovations to nonborrowed reserves are good indicators of monetary policy shocks. JEL classication: C32, C49, E52.