Imagination Rather Than Observation in Econometrics: Ragnar Frisch’s Hypothetical Experiments as Thought Experiments

In economics, thought experiments are frequently justified by the difficulty of conducting controlled experiments. They serve several functions, such as establishing causal facts, isolating tendencies, and allowing inferences from models to reality. In this paper, I argue that thought experiments served a further function in economics: facilitating the quantitative definition and measurement of the theoretical concept of utility, thereby bridging the gap between theory and statistical data. I support my argument by a case study, the “hypothetical experiments” of the Norwegian economist Ragnar Frisch (1895-1973). Frisch aimed to eliminate introspection and a subjective concept of utility from economic reasoning. At the same time, he sought behavioral foundations for economic theory that enabled quantitative reasoning. By using thought experiments to justify his set of choice axioms and facilitating the operationalization of utility, Frisch circumvented the problem of observing utility via actual experiments without eliminating the concept of utility from economic theory altogether. As such, these experiments helped Frisch to empirically support the theory’s most important results, such as the laws of demand and supply, without the input of new empirical findings. I suggest that Frisch’s experiments fulfill the main characteristics of thought experiments

Reasoning with Models

We develop a model-based approach to reasoning, in which the knowledge base is represented as a set of models (satisfying assignments) rather then a logical formula, and the set of queries is restricted. We show that for every propositional knowledge base (KB) there exists a set of characteristic models with the property that a query is true in KB if and only if it is satisfied by the models in this set. We fully characterize a set of theories for which the model-based representation is compact and provides efficient reasoning. These include cases where the formula-based representation does not support efficient reasoning. In addition, we consider the model-based approach to abductive reasoning and show that for any propositional KB, reasoning with its model-based representation yields an abductive explanation in time that is polynomial in its size. Some of our technical results make use of the Monotone Theory, a new characterization of Boolean functions introduced in [Bsh93]. The notion of restricted queries is inherent to our approach. This is a wide class of queries for which reasoning is very efficient and exact, even when the model-based representation KB provides only an approximate representation of the "world". Moreover, we show that the theory developed here generalizes the model-based approach to reasoning with Horn theories [KKS93], and captures even the notion of reasoning with Horn-approximations [SK91]. Our result characterizes the Horn theories for which the approach suggested in [KKS93] is useful and the phenomena observed there, regarding the relative sizes of the formula-based representation and model-based representation of KB is explained and put in a wider context.Engineering and Applied Science