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11 Understanding in Economics Gray-Box Models m a R C e L b o u m a n S Economists use models to understand the economy. Models are theories that summarize, often in mathematical terms, the relationships among economic variables. Models are useful because they help us to dispense with irrelevant details and to focus on important economic connections more clearly. N. G. Mankiw, Macroeconomics L In economics, models are built to answer specific questions. Each type of question requires its own type of model; it defines the empirical criteria that a model should meet and thereby instructs how the model should be constructed. This chapter will investigate a particular kind of question: namely, questions that ask for understanding, and which will be labeled as how’s thatquestions . To do so, these questions will be compared with other types of scientific questions, labeled as why-questions and how much-questions. The answer to a why-question is an explanation (see Nagel 1961, 15; van Fraassen 1988, 138). The answer to a how much-question is a measurement. This investigation will be done by clarifying the differences between three types of models: (1) models that provide an explanation (answering a why-question ); (2) models that provide understanding (answering a how’s that-question); and (3) models that provide a measurement (answering a how much-question). I will show that in economics a white-box model provides an answer to a whyquestion . To answer how much-questions, economists can make use of black210 marcel boumans de Regt Txt•.indd 210 9/8/09 11:27:13 AM 211 box models. Many, if not most, economic phenomena cannot be investigated in a laboratory, so any explanation of them will also have to include an account of the environment in which the phenomena manifest themselves. As a result, white-box models that function as explanations of economic phenomena outside the laboratory are generally so comprehensive and complex that they are not intelligible. Their comprehensiveness and complexity prevent these models from providing understanding of the phenomena under investigation.1 It will be shown that for how’s that-questions, gray-box models are more adequate. In other words, with respect to phenomena outside the laboratory, there is a crucial distinction between providing understanding of these phenomena and explaining them. For these phenomena, due to their complexity and comprehensiveness , white-box models do not provide understanding; therefore, economists have developed another type of model, the gray-box model. Gray-box models are modular designed models; or to put it differently, gray-box models are assemblies of modules; these latter items are black boxes with standard interface. Because models are built with the purpose of answering questions, their assessment is closely connected to the type of question for which they are designed. An important way to assess models is to evaluate their validity. In Barlas’s essay on model validation in system dynamics, validity of a model is defined as “usefulness with respect to some purpose” (Barlas 1996, 184). I will show that, although Barlas’s account aims to discuss model validity in system engineering, it also helps us to understand the assessment of models in economics . Barlas notes that for an exploration of the notion of validation, it is crucial to make a distinction between white-box models and black-box models (in his account, gray-box models do not appear). In black-box models, what matters is the output behavior of the model: “the model is assessed to be valid if its output matches the ‘real’ output within some specified range of accuracy, without any questioning of the validity of the individual relationships that exists in the model” (185). White-box models, in contrast, are causal-descriptive statements on how real systems actually operate in some aspects. Generating accurate output behavior is not sufficient for model validity; the validity of the internal structure of the model is crucial too. A white-box model must not only reproduce or predict the behavior of a real system, “but also explain how the behavior is generated” (185–86). Barlas discusses three stages of model validation: direct structure tests, structure-oriented behavior tests, and behavior pattern tests. Direct structure tests assess the validity of the model structure by direct comparison with knowledge about real system structure. This involves taking each relationship individually and comparing it with available knowledge about the real system. The list of direct structure tests includes tests such as structure-confirmaunderstanding in economics de Regt...

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