Statistical models have a formal definition: they comprise (i) a sample space and (ii) a probability distribution (or set of distributions) over that space.
Economic models, in contrast, do not have a formal definition. The closest I’ve found is by Spiegler (2024, page 152):
“Most economic models have two built-in parts: a description of the model’s primitives and the solution concept that one applies to these primitives.”
Spiegler focuses on game theoretic models. Primitives define the strategic environment: who are the players, what do they know, what can they do? Solution concepts tell us what players actually will do (e.g., whether prisoners will cooperate or defect).
Spielger’s definition also works for non-game theoretic models. Consider the textbook model of supply and demand. Its primitives are the supply and demand schedules. The solution concept is the type of market equilibrium: competitive, monopolistic, or something in-between.
Other authors define economic models informally. Rubinstein (2012, page 16) likens them to “tales:”
“The author of a tale seeks to impart a lesson about life to his readers. He does this by creating a story that hovers between fantasy and reality. … We will take the tale’s message with us when we return from the world of fantasy to the real world, and apply it judiciously when we encounter situations similar to those portrayed in the tale.
… An economic model is also somewhere between fantasy and reality. Models can be denounced for being simplistic and unrealistic, but modeling is essential because it is the only method we have of clarifying concepts, evaluating assumptions, verifying conclusions and acquiring insights that will serve us when we return from the model to real life.”
Rubinstein defines models by analogy. Derman (2011, page 6) says models are analogies; they are “metaphors that compare the object of their attention to something else that it resembles.” He describes an example on EconTalk:
“[S]tock prices or the returns on stock prices behave like smoke diffusing. And there’s something similar about them, but it’s not an accurate description in the way that, say, Newton’s Laws attempt to be an accurate description. It’s really based on an analogy to something you do understand, which is smoke diffusing, and saying maybe stock prices behave a lot like that.”
Statistical models are analogies too. Most real-world data are not normally distributed. We assume they are so that we can describe them in a commonly understood language: we can say things like “Alice’s height is two standard deviations above the mean for her age.”
Statistical models give us parameters to estimate. We can use these estimates to make predictions. Economic models are similar. We build them to describe things we’ve seen before, and can use them to predict things we haven’t seen before. Good models make good predictions.
Good models also give us insights. They focus our attention on some details and abstract away from others. This helps us gain insights without getting confused. As Rubinstein and Derman point out, models may be unrealistic or inaccurate. But the good ones are insightful nonetheless.