Noah Smith provides a convenient summary of a blogospheric conversation on "microfoundations." This illustrates a key principle, which I think we should all take to heart. If one's goal is to learn macroeconomics, one's time would be much better-spent, say, by spending a year participating in Tom Sargent's NYU macro reading group than by spending a year reading the macro blogospherians.
Some of the ideas in this post can also be found in this extended piece, if you want more detail. The term "microfoundations" comes from the Phelps volume, Microeconomic foundations of employment and inflation theory (1970), which, along with Lucas's 1972 JET paper, represents the watershed in modern macroeconomics. I have never been too fond of the term "microfoundations," as this gives you the impression that the theory is somehow hidden from view - its in the foundation, and the working parts you are seeing are some kind of reduced form. For me, the theory is not just the foundation, but the walls, the roof, the plumbing, the electrical work, etc. A macroeconomic model is a coherent whole built up from all the useful economic theory we have available. The bits and pieces are the preferences, endowments, technology, and information structure, and we tie those bits and pieces together with optimizing behavior and an equilibrium concept.
Optimization is pretty weak. It's just some notion that the people living in the fictional world we have constructed are doing the best they can under the circumstances. The circumstances could be pretty bad, in that these people may not know a lot about what is going on. They may not know things about the people they are supposed to be trading with, and/or they may not be able to observe some aggregate variables, for example. There are many equilibrium concepts - standard competitive equilibrium, Nash equilibrium, pricing using bargaining solutions, competitive search, etc. All that we require from the equilibrium concept is that it coherently yields consistency among the decisions made by individuals.
Why do we do it this way? There are two reasons. First, from the point of view of doing pencil-and-paper economics, we are going to learn a lot more. Given the structure of the model, we can evaluate how changes in the technology affect the trading arrangements among economic agents, and we can evaluate how these changes affect economic welfare in a well-defined way. We can also evaluate the effects of government policies sensibly. We have been explicit about preferences in the model, so we can theoretically determine what optimal policies look like.
Second, from the point of view of practical policy evaluation - what working economists are doing - or should be doing - in the Federal Reserve System and at the U.S. Treasury, we want models that are structurally invariant to the policies that we have constructed the model to evaluate. That's what the Lucas critique is all about, though earlier writers understood what "structure" meant. That's part of what the early work (and later work too) of the Cowles Foundation was about. See in particular the 1947 quote from Koopmans here.
Structural models are useful in other fields of economics as well - not just in macro problems. A lazy econometrician would like the data to do the work for him/her, or to design the perfect experiment that he/she can run to test a particular theory, or to evaluate a particular government policy. But the value of experimental work is debatable, and much experimental work would benefit if more weight were put on the theoretical input. Oftentimes, in any field, and particularly in macroeconomics (where experiments are typically impractical and natural experiments hard to find), researchers and policy evaluators have to invest in serious theoretical and empirical tools in order to make any progress.
But how do we differentiate between what is structural and what is not? That's very subtle. We know that any model is an abstraction, and will therefore be wrong - literally. But the art of building a good model is to make it less wrong on the dimensions we are going to use it for than on the dimensions we will not use it for. Here, we need examples to show how, if we use the structural model, we are going to do "pretty well" in terms of policy evaluation, but taking the astructural approach will give us really stupid policy. The standard example, which Lucas used in his critique paper, is the Phillips curve. Following the astructural approach, I stare at the data, and observe that the unemployment rate and the inflation rate are negatively correlated. I infer that there is a tradeoff between inflation and unemployment - I can get less unemployment if the central bank acts in a way that increases the inflation rate. Central banks in the 1970s actually acted on that advice, in spite of what Milton Friedman had said in 1968, and Lucas had written down in his 1972 structural model. Friedman and Lucas advised that no long-run Phillips curve tradeoff existed, and that exploiting any short-run Phillips curve tradeoff would be the wrong thing to do. Policymakers did not listen, and then had to spend the early 1980s correcting the inflation problem they created in the 1970s.
The Phillips curve example makes Friedman and Lucas look good, but another example makes that pair look bad. Central to Old Monetarism - the Quantity Theory of Money - is the idea that we can define some subset of assets to be "money". Money, according to an Old Monetarist, is the stuff that is used as a medium of exchange, and could include public liabilities (currency and bank reserves) as well as private ones (transactions deposits at financial institutions). Further, Friedman in particular argued that one could find a stable, and simple, demand function for this "money," and estimate its parameters. Lucas does that exercise here, and then uses the estimated money demand function parameters to measure the costs of inflation.
What's wrong with that? The key problem, of course, is that the money demand function is not a structural object. Some central bankers, including Charles Goodhart, figured that out. Goodhart's idea is a bit subtle, but there are more straighforward reasons to think that the parameters we estimate as "money demand" parameters are not structural. First, all assets are to some extent useful in exchange, or as collateral. "Moneyness" is a matter of degree, and it is silly to draw a line between some assets that we call money and others which are not-money. Second, the technology determines how different assets are used in exchange. Financial innovations made asset backed securities very useful as collateral, and in financial market exchange. Those innovations changed the relationships among what we measure as monetary aggregates, inflation, asset prices, and aggregate activity. Third, regulations matter for how assets are used in exchange. Paying interest on reserves matters; paying interest on transactions deposits at banks matters; reserve requirements matter; deposit insurance matters; moral hazard problems and how they are regulated matter.
But how structural do we want to get? More structure in our models means more detail, but more detail increases technical complexity, and we want our models to be simple. The model can't be a literal description of the world, as then it would fail to be a model, which simplifies the world so we can understand it. Nevertheless, economists sometimes pay lip service to structure while writing down models that have astructural features. If you have read Woodford's Interest and Prices, you know that he cares about structure. There are plenty of references in Woodford's book to Lucas's critique paper. But some of Woodford's work looks very astructural. Some New Keynesian analysis is done in linearized models with quadratic loss functions that capture the "preferences" of policymakers. That all looks very astructural 1975, in spite of the excuses that are typically given for taking that type of approach.
Astructural stuff is all around us - habit persistence, adjustment costs, cash-in-advance constraints, money-in-the-utility-function. Sometimes those things can be convenient short-cuts, but they have to make you suspicious. In some cases, they help you fit the data - as Larry Christiano well knows - but are not well-rooted in structure.
One thing we know from long ago is that the structural approach is completely unneceessary if all we want to do is forecast the future paths of macroeconomic variables. At the Minneapolis Fed in the late 1970s and early 1980s, Neil Wallace and Tom Sargent understood the Lucas critique and why structure was important for evaluating alternative economic policies. But no one objected to what Robert Litterman was doing, which was conducting forecasts using an astructural Bayesian Vector Autoregression. Indeed, one could argue that the behemoth Keynesian macroeconometric models developed at the Fed, MIT, and Penn in the 1960s and 1970s, and their modern counterparts are perfectly acceptable forecasting tools, though no one in their right mind would use those models to evaluate policy.