by In The World in the Model, Mary Morgan characterizes the modelling tradition of economics as one concerned with “thin men acting in small worlds” and writes: Strangely perhaps, the most obvious element in the inference gap for models … lies in the validity of any inference between two such different media – forward from the real world to the artificial world of the mathematical model and back again from the model experiment to the real material of the economic world. The model is at most a parallel world. The parallel quality does not seem to bother economists. But materials do matter: it matters that economic models are only representations of things in the economy, not the things themselves. Now, a salient feature of modern mainstream economics is the idea of science
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In The World in the Model, Mary Morgan characterizes the modelling tradition of economics as one concerned with “thin men acting in small worlds” and writes:
Strangely perhaps, the most obvious element in the inference gap for models … lies in the validity of any inference between two such different media – forward from the real world to the artificial world of the mathematical model and back again from the model experiment to the real material of the economic world. The model is at most a parallel world. The parallel quality does not seem to bother economists. But materials do matter: it matters that economic models are only representations of things in the economy, not the things themselves.
Now, a salient feature of modern mainstream economics is the idea of science advancing through the use of ‘successive approximations.’ Is this really a feasible methodology?
Allan Gibbard & Hal Varian — as most other mainstream economists — obviously think so, arguing that “in many cases, an economic phenomenon will initially be represented by a caricature, and the representation will then gradually evolve into an econometrically estimable model.”
Yours truly thinks not.
Most models in science are representations of something else. Models ‘stand for’ or ‘depict’ specific parts of a ‘target system’ (usually the real world). 
All theories and models have to use sign vehicles to convey some kind of content that may be used for saying something about the target system. But purpose-built assumptions made solely to secure a way of reaching deductively validated results in mathematical models – like ‘rational expectations’ or ‘representative actors’ — are of little value if they cannot be validated outside of the model.
All empirical sciences use simplifying or unrealistic assumptions in their modelling activities. That is not the issue — as long as the assumptions made are not unrealistic in the wrong way or for the wrong reasons.
The obvious ontological shortcoming of a basically epistemic — rather than ontological — approach such as ‘successive approximations’ is that ‘similarity’ or ‘resemblance’ tout court does not guarantee that the correspondence between model and target is interesting, relevant, revealing or somehow adequate in terms of mechanisms, causal powers, capacities or tendencies. A good model is a model that works and helps us explain and understand the problems we want to research. No matter how many convoluted refinements of concepts made in the model, if the ‘successive approximations’ do not result in models similar to reality in the appropriate respects (such as structure, isomorphism etc), the surrogate system becomes a substitute system that does not bridge to the world but rather misses its target and makes our understanding of why things work the way they do in the real world into an inexplicable mystery. Dramatically simplified and distorted models building on known to be significantly wrong/false assumptions do not deliver much in terms of genuine explanation.
To this may also be added, as noted by Kevin Hoover, that when mainstream economists talk about their models as approximations,
too often the term is used even in cases for which we do not have a clear characterization of the target of approximation. Frequently, it is asserted that a model is a good one if it approximates the ultimate truth about the world. That ultimate truth, however, is not available to us as a standard against which to judge the approximation. The use of the term, then, is not so much wrong as empty and useless.
Yours truly has to conclude that constructing ‘minimal’ economic models — or using microfounded macroeconomic models as ‘stylized facts’ or ‘stylized pictures’ somehow ‘successively approximating’ macroeconomic reality — is a rather unimpressive attempt at legitimizing using fictitious idealizations for reasons more to do with model tractability than with a genuine interest of understanding and explaining features of real economies.
Many of the model assumptions standardly made in mainstream economics are harmfully restrictive and misrepresentative — rather than incomplete and harmless — and can not in any sensible meaning be considered approximations at all. As May Brodbeck has it:
Model ships appear frequently in bottles; model boys in heaven only.