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What are typical examples in literature of large scale simulations of macro-economies of our time as of 2019 and what will change with the introduction of exascale computing? In terms, are there problems which might become feasible to assess then?

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Some example of large macro models would be the the World Banks macro-fiscal model or Smets-Wouters DSGE model.

How will having access to high computing power change the models is very opinion based question I don’t think anyone can predict that but I will indulge you. With increasing computer power it will be definitely possible to make these models more detailed, perhaps even to the point where you don’t just model demand and supply in a given market based on just representative agents but also explicitly modeling interactions of heterogenous individuals and firms and deriving demand and supply from that. Also this is my two cents on the issue but I don’t think that in current macroeconomic modeling lack of computer power would be a main hurdle, I would say lack of available data is far more bigger problem but getting better. In the end no amount of computer power will help if you don’t have enough data to properly parametrize the model.

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Just to add to @1muflon1's point: availability and standardization of data aside, the mere ability to run more detailed models can potentially have drastic effects on output. In complex systems, activity at small scales can impact phenomena at larger scales through mechanisms that are not always completely understood in the literature. This is a potentially large source of error when you have to use the literature to parameterize small-scale behavior due to a tradeoff of detail for scope. As a non-econ example, I once worked on a global climate model that failed to reproduce certain continent-scale observations because it was unable to explicitly model kilometer-scale processes.

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