You often hear defenders of the DSGE modeling framework say something like this: "You can't attack DSGE. Its just a framework. You can use it to model anything." But this isn't true. If it were true, we wouldn't have the label "DSGE", we'd just call it "modeling".
The "E" in DSGE stands for "Equilibrium." DSGE models define an equilibrium in which markets clear. The economy is then assumed to move toward that equilibrium; the motion is called "transition dynamics", and is usually left unspecified.
Some economists have argued that transition dynamics are not that important. For example, in "Econometric Policy Evaluation: A Critique" (1976), Robert Lucas writes:
[O]ne hears talk of a "disequilibrium dynamics" which will somehow...[go] beyond the sterility of dp/dt = k(p - p_e)...[but this] will fail...
In other words, prices will move smoothly and steadily toward the equilibrium, so we should just focus on finding the equilibrium.
But this is not necessarily true. Why would "disequilibrium dynamics" be important? I can think of several reasons.
Reason 1: The equilibrium may shift at about the same speed that convergence happens. If the economy is trying to hit a moving target, chaos will result. See this paper by Andrew Lo for a semi-technical explanation of why this true. (In math-speak, this happens when the rate of convergence, k, may be of the same order as the parameters governing the time-scale of the shock process.)
Reason 2: The equilibrium may not be stable. See this blog post by Jonathan Schlefer (whose book I just ordered off of Amazon):
In 1960 Herbert Scarf of Yale showed that [even the most ideal kind of] economy can cycle unstably. The picture steadily darkened. Seminal papers in the 1970s, one authored by [General Equilibrium inventor] Debreu, eliminated "any last forlorn hope," as the MIT theorist Franklin Fisher says, of proving that markets would move an economy toward equilibrium. Frank Hahn, a prominent Cambridge University theorist, sums up the matter: "We have no good reason to suppose that there are forces which lead the economy to equilibrium."
In other words, the smooth convergence equation that Lucas wrote down may simply not be true.
Reason 3 (the biggie): There may be multiple equilibria. You rarely see famous and influential DSGE papers with multiple equilibria, and when you do see them, there are usually only two equilibria. But I know of absolutely no reason why the real economy should have a unique equilibrium. And I know of absolutely no reason why the number of equilibrium in the economy should be small! But there seems to be a huge publication bias in favor of smaller number of equilibria (Roger Farmer's efforts notwithstanding). This annoys me.
So in a Robert Lucas DSGE world, we have one slow-changing equilibrium toward which the economy smoothly and rapidly converges. But the real world may be one of multiple, rapidly-shiftng equilibria toward which the economy does not move smoothly.
Now, you could still formally model that sort of world with a DSGE model, but your results would be useless gibberish. You'd have classical chaos.
What do you do when you have classical chaos? One thing you can do is to use a weather-forecasting approach. Basically, you identify the economy's microfoundations, and then you use big powerful computers to make very short-term predictions using those microfoundations. Here's a Bloomberg article in which theoretical physicist Mark Buchanan suggests exactly this kind of approach:
No mathematician can “solve” the complex equations for air in the atmosphere...It’s natural to wonder if a similar mechanism might be driving the financial crises and business cycles that typify the economic “weather” we’ve experienced over the centuries. Unfortunately, today’s equilibrium theories refuse to entertain the possibility...
While an appreciation of instability propelled atmospheric science forward, economics was binding itself into a rigid framework...when studies in the 1970s found that [economic] equilibrium is generally unstable - and so should tend to fall apart...[economic] theorists for the most part simply ignored this inconvenient fact and went on as before. Most still do.
American economist Milton Friedman set the tone. “The study of the stability of general equilibrium is unimportant” because “it is obvious that the economy is stable,” he was quoted as saying. Friedman was notoriously mischievous and slippery in his argument, so I’m not sure he really believed what he said. But most economists today act as if they do.
This is too bad, because a focus on the origins of instability just might help financial economics achieve a conceptual liberation akin to that which atmospheric scientists achieved in the 1950s. Economists might come to accept that equilibrium doesn’t describe everything, or even very much, and that natural elements of instability and turbulence drive the outcomes that matter most.
This is an alternative to DSGE. Go directly from microfoundations to some variety of agent-based modeling. Ignore the equilibrium and focus entirely on the micro-level "transition" dynamics. Incidentally, I think this kind of approach could have other advantages - for example, because you wouldn't have to solve for a simple equilibrium, it might be easier to add large numbers of frictions to the model.
But the main reason to contemplate using a weather-forecasting approach is that the real economy may just be too chaotic for DSGE to be very useful in modeling it.