What does it mean if a economic model is internally consistent? What happens if it is not? Is it not closed anymore? Can it still be solved? Does it still have an equilibrium?
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$\begingroup$ I would liken an inconsistent economic model to a movie with plot holes. While possibly entertaining and able to reach a conclusion, it does not actually make sense and hence cannot be the basis for scientific discovery. $\endgroup$– BB KingCommented May 22, 2020 at 18:13
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In theoretical modeling the consistency is applied in the same way as in philosophy/logic. Internal consistency simply means that the argument is consistent with itself and has no contradiction within itself (as opposed to external consistency where its not enough for argument to be valid on its own but it should also not contradict other facts).
A simple verbal example of internal inconsistency would be statement: "I always lie". The statement is internally inconsistent because if I always lie then the statement above must be also lie. But if the statement is lie that implies I do not always lie so it is not correct and it contradicts itself.
Math can reveal if a model is internally inconsistent. If you have model relaying on following system: $$a+b =1$$ $$5a+5b=15$$
You would get that $5 = 0$ which means that the model is clearly inconsistent with itself. However, sometimes the model might be internally inconsistent because the assumptions made in the model are not consistent with each other but the model might still solve and even have equilibrium (if the logical fallacy is made in a step where you build equations based on the assumptions - or make assumptions that are not consistent with each other but the consistency of assumptions is not checked) and finding the inconsistency is harder.
Moreover, note that internal consistency of model has also some special meaning in statistics, but from your question I assume that was not the meaning you were looking for.
answered May 22, 2020 at 17:01
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$\begingroup$ Thanks. I was looking for what it means in e.g. a DSGE model (Dynamic stochastic general equilibrium modeling Dynamic stochastic general equilibrium modeling (abbreviated as DSGE, or DGE, or sometimes SDGE) is a method in macroeconomics that attempts to explain economic phenomena, such as economic growth and business cycles, and the effects of economic policy, through econometric models based on applied general equilibrium) $\endgroup$ Commented May 22, 2020 at 17:06
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$\begingroup$ but I guess your answer also applies for DSGE $\endgroup$ Commented May 22, 2020 at 17:06
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1$\begingroup$ @BeckBatucada for DSGE models the above would apply. You can say the model is for sure inconsistent if there is some mathematical contradiction in it. However, I seen people criticizing models where math checked out on the grounds that the assumptions that model makes is inconsistent with each other. I can’t think of concrete example right now but if some equations in the model would imply that people must be only rational and then other set of equations would imply the same people can’t be rational - equations could solve but model would still be inconsistent. $\endgroup$– 1muflon1 ♦Commented May 22, 2020 at 17:09
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1$\begingroup$ @BeckBatucada also note in the example in the comment above I did not have in mind some models that allow for people’s behavior to switch but rather some hypothetical example which clearly contains a mistake as it would at the same time say people must be rational as well as saying the same people can’t be rational. $\endgroup$– 1muflon1 ♦Commented May 22, 2020 at 17:10