I've got into a couple of discussions recently about the relevance of accounting to economics, so I'd thought I'd put my views down here.
The first point is that any model or other analysis in economics should be accounting consistent. By this I simply mean that things should add up without any black holes or inconsistencies. Each item of expenditure should be someone else's income; changes in stocks should relate to flows within the appropriate timeframe.
This is a pretty important point - if a model doesn't pass on this, it's just wrong. However, I don't actually think this is a particularly big problem. I see models from time to time that definitely fail this test, but most don't, or at least they don't appear to have anything that is necessarily inconsistent.
Models should be about providing insight. To be able to do so, they need to have ways to illustrate the connection between all the various quantities. Even in very simple models, the full consequences of the interaction between variables can be quite obscure. For me, models that do not pay much attention to the accounting, even if they are actually fully consistent, often miss important insights.
I would say that there are very few models of monetary economics that would not benefit from having their implicit accounting structure explicitly set out. The ideal tool for this is the social accounting matrix: at the very least a balance sheet and possibly a flow of funds. These show at a glance the form of the simplified economy within which the model is constructed and how the various quantities relate to each other. They are not sufficient on their own, of course, but they can provide a great deal of insight before one even starts to look at agent choices and behaviour and they help us see the results in a more comprehensive context.
Setting out the model this way also helps us relate it to the real world. However conceptual a model, at some point we want to be able to relate it to actual economies and hard data. Setting out the model variables in a form that corresponds to national accounts gives us an immediate head start in doing so.
And really that's it. Accounting can help us understand the economics better, but it doesn't tell us everything. It still leaves most of the questions to be answered, but hopefully it allows us answer them with the benefit of a greater insight into the way everything hangs together.