RECURSIVE VS. NONRECURSIVE SYSTEMS: AN ATTEMPT AT SYNTHESIS (PART I OF A TRIPTYCH ON CAUSAL CHAIN SYSTEMS)

By R. H. Strotz, H. Wold. 1960

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TRYGVE HAAVELMO AND THE EMERGENCE OF CAUSAL CALCULUS (2014, unknown): “Haavelmo’s approach was later transformed by Strotz and Wold (1960) into the operation of “wiping out” the equation altogether and was further translated into graphical models as “wiping out” incoming arrows into the manipulated variable (Pearl, 1993; Spirtes et al., 1993).7 This operation, called…”
Causal Bounds and Observable Constraints for Non-deterministic Models (2012, background): “Such models involve latent deterministic relations, which marginalise to produce observed probabilistic relationships, and are technically equivalent to structural equation models (Strotz and Wold, 1960) and other functional models (Heckerman and Shachter, 1995).”
Granger Causality and Dynamic Structural Systems (2010, methodology): “…(2007c) in using the notation c= to emphasize that the structural equations (3) represent asymmetric causal links (Goldberger, 1972, p.979), in which manipulations of elements of yt; dt; vt; zt result in potentially di¤ering values for yt+1, as in Strotz and Wold (1960) and Fisher (1966, 1970).”
The comparison of estimation methods on the parameter estimates and fit indices in SEM model under 7-point Likert scale (2017, background): “…involves whether a structural theory describes cause-effect sequences that occur over time, although the instantaneous causation (with simultaneous mutual influence of variables on each other) in specific situation also makes sense in a model (Strotz and Wold, 1960; Bentler and Freeman, 1983).”
Axiomatizing Causal Reasoning (1998, background): “The issue of whether nonrecursive system can be given a causal interpretation is discussed at some length by Strotz and Wold (1960).”
Instrumental Variables: An Econometrician's Perspective (2014, background): “Interestingly the pioneers in this literature, Tinbergen (1928) and Haavelmo (1943), did distinguish between these concepts in their notation, but the subsequent literature on simultaneous equations dropped that distinction and adopted a notation that did not distinguish between observed and potenti”
Sequences of Mechanisms for Causal Reasoning in Artificial Intelligence (2013, unknown): “The theoretical development of causality in AI has up to now primarily been based on structural equation models (SEMs) [Strotz and Wold(1960); Simon(1954); Haavelmo(1943)], a formalism which originated in econo-metrics and which is still used commonly in the economic and social sciences.”
Nested Markov Properties for Acyclic Directed Mixed Graphs (2012, methodology): “…a causally interpreted DAG, the consequences of intervention in the system under study can be understood by modifying the graph via removing certain edges, and modifying the corresponding joint probability distribution via re-weighting (Pearl, 2000; Spirtes et al., 1993; Strotz and Wold, 1960).”
A Lewisian Logic of Causal Counterfactuals (2013, unknown): “We can also model the situation where both 6 This approach to modeling interventions originated in econometrics (Strotz and Wold 1960; Fisher 1970), and was masterfully articulated and developed by Pearl (2009). interventions take place by MX=0, Z=1, which has the following structural equations: X…”
Settable Systems: An Extension of Pearl's Causal Model with Optimization, Equilibrium, and Learning (2009, methodology): “of White (2006), White and Chalak (2007), Schennach, White, and Chalak (2007), Chalak and White (2008), and White and Kennedy (2008) provides settable system-based results for identication and estimation of causal e¤ects under varying assumptions.”
3. The Foundations of Causal Inference (2010, methodology): “Such an extension, based on simulating hypothetical interventions in the model, was proposed in Haavelmo (1943), Strotz and Wold (1960), Spirtes et al. (1993), Pearl (1993a, 2000a), and Lindley (2002), and it has led to new ways of defining and estimating causal effects in nonlinear and…”