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Unformatted text preview: Settable Systems: An Extension of Pearl&s Causal Model with Optimization, Equilibium, and Learning Halbert White & Department of Economics University of California, San Diego Karim Chalak Department of Economics Boston College May 5, 2008 Abstract 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 xed-point requirement, and the use of partitioning and partition-specic 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. Keywords: Causal Models, Game Theory, Machine Learning, Recursive Estima- tion, Simultaneous Equations Running Title: SETTABLE SYSTEMS & Halbert White is Chancellor&s Associates Distinguished Professor of Economics, Dept. of Economics 0508, UCSD, La Jolla, CA 92093 (email: firstname.lastname@example.org); and Karim Chalak is Assistant Professor of Economics, Dept. of Economics, Boston College, 140 Commonwealth Ave., Chestnut Hill, MA 02467 (email: email@example.com). The authors are grateful for discussion and comments on previous work by Judea Pearl that stimulated this work, and for the comments and suggestions of James Heckman, Philip Neary, Douglas R. White, Scott White, the editor, and four referees. Any errors are solely the author&s responsibility. The present paper is an expanded version of the foundational and denitional material contained in our earlier unpublished paper "A Unied Framework for Dening and Identifying Causal E/ects." 1 1 Introduction Judea Pearl&s work on causality, especially as embodied in his landmark book Causality (Pearl, 2000), represents a rich framework in which to understand, analyze, and explain causal relations. Although this framework has been adopted and applied in a broad array of disciplines, so far it has not had much impact in economics. This may be due in part to the fact that the Pearl causal model (PCM) is not as well suited to analyzing economic structures as might be desired. Here, we o/er the settable systems framework as an extension...
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.
- Fall '08