Stephen Williamson has written an impassioned defense of the "neoclassical" (or "Minnesota" or "RBC") approach to macroeconomics. This provides me with an opportunity to have hours of fun
The first point I want to address is Williamson's defense of the way math is used in macroeconomics:
There seems to be a view among some people that interest in Minnesota macro is all about the aesthetics of mathematics. I certainly think that a functional equation is an object of beauty. I also think that the average North American has a bad attitude toward mathematics. Indeed, some people seem quite proud, rather than ashamed, of the fact that they don't know it. Mathematics is a language that, in some circumstances, is simply an efficient tool for getting the job done. I could be like Adam Smith, and write it in words, or I could be like Bob Lucas and write down an economic model and analyze it using some mathematics. I can walk 8 miles from the University to the Fed (and maybe get lost on the way), or I can get there on the train.\I agree that Americans tend to be math-phobic (though this seems to be common to all rich countries; I've encountered a lot of it in Japan, which once was known for its math prowess). Math is a useful thing to be able to do.
This does not mean that we should always do it. Some things are easy to understand with scientific thinking, but hard to model with math. As an example, take Louis Pasteur's discovery that germs cause disease. Explaining infection in the language of math would have been an impossible task in 1862 (even now, with supercomputers solving partial differential equations using algorithms written by hordes of biophysics PhDs, we've barely begun to get results with this approach), but understanding the basic principle of infection was easily possible given the science of Pasteur's day.
Neoclassical/Minnesota macro people would have us believe that formal mathematical models are the best language to describe the economy, because math is the most precise descriptor of the natural world. But precision and accuracy are two very different things; the amount of math needed to accurately describe a system as huge and complex as an economy is far beyond what Minnesota macroeconomists can do, and the data they have to work with is far patchier than what Pasteur knew about the human body in 1862.
And so the neoclassical people resort to making the models that their math permits them to make - simplistic silly models with easy math that describe little and predict absolutely nothing. Yet this approach survives and dominates, because A) the sneering of the Minnesota people lowers the reputation of any macroeconomist who refuses to speak in pure math, and B) Republican types are willing to shell out big bucks to economists who produce simplistic silly models (i.e. models too simple for government to have a useful role).
I am not suggesting that economists give up math as an analytical tool. Indeed, economists should get a lot better at math, and diversify their mathematical toolkits. But we should recognize that an economy is a very complex system - possibly as complex as a human body - and that we should therefore rely on naturalistic observation first and foremost. Only once we understand a few things about how the economy works, from watching how it works and from poking around in it, should we whip out the math and start making formal predictive models. And to be honest, I don't think macro is there yet. Williamson is putting the cart before the horse.