Causality, structural modelling and exogeneity

Lecture Notes in Computer Science, 2001

The term "changes in structure," originating from work in econometrics, refers to structural modifications invoked by actions on a causal model. In this paper we formalize the representation of reversibility of a mechanism in order to support modeling of changes in structure in systems that contain reversible mechanisms. Causal models built on our formalization can answer two new types of queries: (1) When manipulating a causal model (i.e., making an endogenous variable exogenous), which mechanisms are possibly invalidated and can be removed from the model?

2011

This paper provides an overview of structural modelling in its close relation to explanation and causation. It stems from previous works by the authors and stresses the role and importance of the notions of invariance, recursive decomposition, exogeneity and background knowledge. It closes with some considerations about the importance of the structural approach for practicing scientists. Keywords: Background knowledge, Causality, Exogeneity, Invariance, Latent Variables, Structural Modelling.

arXiv (Cornell University), 2022

Structural causal models (SCMs) are a widespread formalism to deal with causal systems. A recent direction of research has considered the problem of relating formally SCMs at different levels of abstraction, by defining maps between SCMs and imposing a requirement of interventional consistency. This paper offers a review of the solutions proposed so far, focusing on the formal properties of a map between SCMs, and highlighting the different layers (structural, distributional) at which these properties may be enforced. This allows us to distinguish families of abstractions that may or may not be permitted by choosing to guarantee certain properties instead of others. Such an understanding not only allows to distinguish among proposal for causal abstraction with more awareness, but it also allows to tailor the definition of abstraction with respect to the forms of abstraction relevant to specific applications.

2011

This paper provides an overview of structural modelling in its close relation to explanation and causation. It stems from previous works by the authors and stresses the role and importance of the notions of invariance, recursive decomposition, exogeneity and background knowledge. It closes with some considerations about the importance of the structural approach for practicing scientists.

Decision Support Systems, 1995

Propagation of change based on causal ordering is a central element of causal reasoning in economic models. While causal reasoning has most often been applied in qualitative models, we demonstrate a technique for causal reasoning that offers explanations of ...

International Journal of Epidemiology, 2002

Following a long history of informal use in path analysis, causal diagrams (graphical causal models) saw an explosion of theoretical development during the 1990s, 1-3 including elaboration of connections to other methods for causal modelling. The latter connections are especially valuable for those familiar with some but not all methods, as certain background assumptions and sources of bias are more easily seen with certain models, whereas practical statistical procedures may be more easily derived under other models. We provide here a brief overview of graphical causal models, 1-6 the sufficient-component cause (SCC) models of Rothman, 7,8 Ch. 2 the potential-outcome (counterfactual) models now popular in statistics, health, and social sciences, 9-15 and the structural-equations models long established in social sciences. 11-14 We focus on special insights facilitated by each approach, translations among the approaches, and the level of detail specified by each approach. Graphical models The following is a brief summary of terms and concepts of causal graph theory; see Greenland et al. 4 and Robins 5 for more detailed explanations. Figure 1 provides the graphs used for illustration below. An arc or edge is any line segment (with or without arrowheads) connecting two variables. If there is an arrow from a variable X to another variable Y in a graph, X is called a parent of Y and Y is called a child of X. If a variable has an arrow into it (i.e. it has a parent in the graph) it is called endogenous; otherwise it is exogenous. A path between two variables X and Y is a sequence of arcs connecting X and Y. A back-door path from X to Y is a path whose

This paper provides an overview of structural modeling in its close relation to explanation and causation. It stems from previous works by the authors and stresses the role and importance of the notions of invariance, recursive decomposition, exogeneity and background knowledge. It closes with some considerations about the importance of the structural approach for practicing scientists.

Institute de Statistique Discussion Paper, 2006

Philosophers and statisticians have been debating on causality for a long time. However, these discussions have been led quite independently from each other. An objective of this paper is to restore a fruitful dialogue between philosophy and statistics. As is well known, at the beginning of the 20th century, some philosophers and statisticians dismissed the concept of causality altogether. It will suffice to mention Bertrand Russell (1913) and Karl Pearson (1911). Almost a hundred years later, causality still represents a central topic ...

Journal of Reviews on Global Economics, 2013

Causality is a notion that occurs often in economics. In using the words 'cause' and 'effect,' economists seek to distinguish causation from association, recognizing that causes are responsible for producing effects, whereas noncausal associations are not. The identification of causes is accorded a high priority because it is viewed as the basis for understanding economic phenomena and developing policy implications. In this survey we look at different approaches to causality in economics and set out the general principles of each approach, so as to assist in the communication and teaching role. Specifically, we confine attention to five approaches to causality in economics (narrative, comparative statics, theoretical, structural, and experimentalist) and elucidate their distinctive characteristics without entering into philosophical discussions. In particular, we pay close attention to the debate between the structuralist and experimentalist schools because this controversy has been extremely useful to clarify a number of fundamental points concerning causality in economics.

2009

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.

Journal of the American Statistical Association, 2005

Judea Pearl has been at the forefront of research in the burgeoning field of causal modeling, and Causality is the culmination of his work over the last dozen or so years. For philosophers of science with a serious interest in causal modeling, Causality is simply mandatory reading. Chapter 2, in particular, addresses many of the issues familiar from works such as Causation, Prediction and Search by Peter Spirtes, Clark Glymour, and Richard Scheines (New York: Springer-Verlag, 1993). But philosophers with a more general interest in causation will also profit from reading Pearl's book, especially the material in chapters 7, 9, and 10 (not to mention the delightful epilogue), which is selfcontained and less technical than other parts of the book. The present review is aimed primarily at readers of the second type. Pearl represents a system of causal relationships by a causal model. A causal model consists of a set of variables, a set of functions, and a probability measure representing our ignorance of the actual values of the variables. Each function generates an equation of the form V i = f i (V i1 ,…,V im), where V i is distinct from each V ij. These equations represent "mechanisms" whereby the value of one variable is causally determined by the values of others. Mechanisms differ from what philosophers call "laws" in that the former are asymmetric. If it is a law that Y = f(X) (and f is an invertible function), then it is also a law that X = f-1 (Y). By contrast, if a causal model contains the mechanism Y = f(X), then it will not also contain the mechanism X = f-1 (Y) (except in very special cases). The system of equations may be represented qualitatively in a directed graph, with an "arrow" drawn from V i to V j just in case V i figures in the function for V j. The directed graph representation greatly facilitates inferences about the model. A causal model may be used to evaluate counterfactuals of the following form: if the value of V i were v i , then the value of V j would be …. The resultant value of V j is determined by replacing the equation V i = f i (V i1 ,…,V im) with V i = v i , and then solving the resulting system of equations. This replacement indicates that V i is set directly to v i by an intervention from outside the system, rather than having its value causally determined by the values of the variables within the system. The intervention need not be miraculous: mechanisms are not inviolable laws, but rather ceteris paribus laws that can be disrupted by external interventions. Such an intervention will not affect the functional forms of the other mechanisms in the causal system: the mechanisms are autonomous. The bulk of Pearl's book deals with inference problems where we have only partial information about the causal system being modeled. Our partial information may be of various kinds. Observational evidence may give us information about probabilistic correlations between variables; background assumptions may give us information about the graphical structure; and con

2006

In a previous paper, Russo et al.(2006), causality is considered in the framework of structural models, ie statistical models characterized by parameters that are stable over a large class of interventions or of environmental changes and that take into account background and contextual knowledge. From this statistical viewpoint, causality is defined in terms of exogeneity in a structural model. This approach allows us to attain a concept of causality that is internal or relative to the structural model itself. Thus our knowledge of causal relations ...