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What is meant by the abbreviation MSV solution, used in the context of adaptive learning in DSGE modeling? E.g. see Bullard and Mitra (2002)

minimum state variable (MSV) solutions it is in full, but what does that mean?

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Minimum state variable (MSV) solution is a special technique used to find an unique equilibrium with desirable properties in DSGE models. Often DSGE models can have multiple paths that will satisfy the conditions given by the system you are modelling.

Hence to provide some meaningful results you have to somehow choose between the all possible paths/solutions possible. There are multiple ways how to do that. MSV solution is a solution that helps to avoid sunspot equilibria and bubbles (see McCallum (1999)). In addition huge advantage of this approach as pointed out by McCallum is that "the MSV criterion is designed to yield a single bubble-free solution by construction." It can be also shown that this kind of method is quite efficient and guaranteed to yield unique solution for wide ranges of models (albeit not all).

As you can see in Bullard and Mitra (2002), they talk about MSV solution when they want to show that there is unique solution that can determine their model coefficients $a,b,c$, so when they talk about MVS solution they are just saying that they applied this approach to select an unique solution this way as opposed to some other one.

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  • $\begingroup$ Ok, thanks a lot for your answer. If I understood it correctly, it is a selection method and a computation method at the same time? As such, you are actively ignoring other solutions (is each solution a different path to an (or the same) equilibrium (steady state), or is a solution a different equilibrium (steady state)? So saying you have a unique MSV solution, is saying as much as I arbitrarily selected this steady state amongs all others? $\endgroup$ – Beck Batucada Jun 17 '20 at 13:03
  • $\begingroup$ @BeckBatucada well it’s a method to find a special kind of equilibria that are neither sun-spot, neither bubble ones. In principle it’s just a criterion so I would say it’s more of the former but since it can be incorporated into the algorithm you are making it can also be considered both. Also it’s not arbitrary that’s the whole point of MSV is to avoid just arbitrary cherry-picking some equilibria $\endgroup$ – 1muflon1 Jun 17 '20 at 13:15
  • $\begingroup$ Och ok. And is there a certain intuition as to how it selects? I mean, is it a more likely equilibrium, or just one that fits all these properties like unique, non bubble, non sunspot, etc. ? Just possessing these properties does not make it the most likely equilibrium I guess? It has nothing to do with adaptive learning/learnability I guess? $\endgroup$ – Beck Batucada Jun 17 '20 at 13:32
  • $\begingroup$ @BeckBatucada there is some intuition behind it a MSVS is also solution which is parsimonious as if a set of state variables is minimal you should not be able to remove any variable while still getting a valid solution given the constraints on variables. It could also be argued that you want to avoid for example bubble solutions because they are uninformative they are not useful in forecasting bubbles and we know that some would occur but eventually they burst and things go back to normal however it’s not easy to explicitly model that so just ignoring bubble paths is a way how to do that $\endgroup$ – 1muflon1 Jun 17 '20 at 13:40
  • $\begingroup$ Ok, ........... thanks! $\endgroup$ – Beck Batucada Jun 17 '20 at 13:43

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