Mankiw is also an exceptional writer and he had two articles in major newspapers over the weekend that are well worth reading. The first, in Sunday's New York Times, is a worthwhile piece on the realities of modern medicine and societies role is its distribution. An excerpt:
An optimist might hope that my doctor, or someone higher up in the health care hierarchy, made a rational cost-benefit calculation on society’s behalf. To figure out whether my treatment makes sense, one would have to weigh the cost of the drug against the benefit of an extended life. And to do that, one would have to put a dollar value on my life — the kind of calculation that makes everyone but economists squirm.
The second is a review of a new book on Keynes by the author of the authoritative three part biography on Keynes, Robert Skidelsky. Skidelsky's new book talks about the sudden and swift revival of Keynes's theories in the recent crisis. Mankiw, writing in the Wall Street Journal, is impressed with Skidelsky as an historian but less so with Skidelsky as an economist. He takes umbrage at Skidelsky's distain for math in economics:
To economists his discussion of macroeconomic theory will seem pedestrian and imprecise. To laymen it will seem abstract and hard to follow.
As an ardent fan, Mr. Skidelsky fails to give Keynes's intellectual opponents their due. In academic circles, the most influential macroeconomist of the last quarter of the 20th century was Robert Lucas, of the University of Chicago, who won the Nobel Prize in 1995. His great contribution to the discipline was to analyze how government policies influence the economy in part through their effect on people's expectations—a lesson that Keynes would likely have appreciated but that early followers of Keynes often ignored.
Yet Mr. Skidelsky chooses to make Mr. Lucas sound like some kind of idiot savant, more interested in playing with mathematical models than in trying to understand how the world actually works. Mr. Lucas, we are told, is following in the tradition of the "French mathematician Leon Walras [who] pictured the economy as a system of simultaneous equations." The very idea is made to sound slightly crazed.
This brings us to the biggest problem with "Keynes." Mr. Skidelsky admits to being poorly trained in the tools that economists use: "I find mathematics and statistics 'challenging,' as they say, and it is too late to improve. This has, I believe, saved me from important errors of thinking."
Has it, really? Mr. Skidelsky would like to think that his math-aversion allows him to focus on the big ideas rather than being distracted by mere analytic details. But mathematics is, fundamentally, the language of logic. Modern research into Keynes's theories—I have conducted such research myself—tries to put his ideas into mathematical form precisely to figure out whether they logically cohere. It turns out that the task is not easy.
Keynesian theory is based in part on the premise that wages and prices do not adjust to levels that ensure full employment. But if recessions and depressions are as costly as they seem to be, why don't firms have sufficient incentive to adjust wages and prices quickly, to restore equilibrium? This is a classic question of macroeconomics that, despite much hard work, is yet to be fully resolved.
Which brings us to a third group of macroeconomists: those who fall into neither the pro- nor the anti-Keynes camp. I count myself among the ambivalent. We credit both sides with making legitimate points, yet we watch with incredulity as the combatants take their enthusiasm or detestation too far. Keynes was a creative thinker and keen observer of economic events, but he left us with more hard questions than compelling answers.
I am like many PhDs of my generation in that I was raised on Keynes as an undergrad (and as a masters policy student) and then disabused of all things Keynes in grad school in economics where the 'real business cycle' school was dominant. To use the vogue term of art, I was taught by a freshwater economist (in this case a Minnesota-trained one). But I also had the very useful experience of having previously taken a graduate level macro class in Keynesian economics which was engaged in just the endeavor to which Mankiw refers: trying to apply modern mathematical logic to Keynes and see if it can survive. [The answer, by the way, was yes, but with some pretty strong assumptions that may or may not be realistic - however the notion is sticky prices and wages is pretty well established now and is perhaps the most important assumption to get Keynes in the modern economic world]
I agree completely with Mankiw in his take on math, it is indeed the language of logic and for that we can all be thankful that it has a prominent place in economics. And just as it can be taken too far, where mathematical elegance is prized above economic insight, dismissing economics too quickly as just mathematical abstraction is equally wrong.