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Essays on the definition, identification, and estimation of causal effects

  • Author(s): Chalak, Karim Marwan
  • et al.
Abstract

This dissertation studies the definition, identification, and estimation of causal effects within the settable system framework of White and Chalak. Chapter 1 provides definitions of direct and indirect causality, as well as notions of causality via and exclusive of a set of variables, based on functional dependence to study the interrelations between independence or conditional independence and causal relations in recursive settable systems. We provide formal conditions ensuring the validity of Reichenbach's principle of common cause and introduce a new conditional counterpart, the conditional Reichenbach principle of common cause. We then provide necessary and sufficient causal conditions for probabilistic dependence and conditional dependence among certain random vectors in settable systems. We demonstrate how these results relate to and generalize results in the artificial intelligence literature. Chapter 2 studies the structural identification of average effects and average marginal effects with conditioning instruments within the settable system framework. In particular, we build on the results of Chapter 1 to provide causal and predictive conditions sufficient for conditional exogeneity to hold. We provide two procedures based on (Ã)-causality matrices and the direct causality matrix for inferring conditional causal isolation among vectors of settable variables. Similarly, we provide sufficient conditions for conditional stochastic isolation in terms of the sigma algebras generated by the conditioning variables. We distinguish between structural proxies and predictive proxies. Chapter 3 applies the results of chapters 1 and 2 within the structural equations framework to study the identification and estimation of causal effects. We begin by providing a causal interpretation for standard exogenous regressors and standard "valid" and "relevant" instrumental variables. We then build on this interpretation to characterize extended instrumental variables (EIV) methods, that is methods that make use of variables that need not be valid instruments in the standard sense, but that are nevertheless instrumental in the recovery of causal effects of interest. After examining special cases of single and double EIV methods, we provide necessary and sufficient conditions for the identification of causal effects by means of EIV and provide consistent and asymptotically normal estimators for the effects of interest

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