In this post, we will perform a simple thought experiment. Imagine:
Disregard whether it is supply or demand side channels through which money may influence GDP and assume that money is a very special cause of production. I consider money as M1 since it is the most available and convertible for both consumers and producers.
I have plotted on X axis M1 and Y axis real GDP for countries that have near zero policy rates (in ascending order):

What we may infer:
1) Almost all countries are demonstrating diminishing returns from money not only during the given ranges but also before the Great Recession. This may mean that as money supply increases, the return from different channels that would increase real GDP is diminishing.
2) Japan has relatively lower statistical significance, we know that the BoJ and the government were the first who piloted unconventional policies.
Implications:
1) Prices were stickier yesterday than today. As technologies are evolving, prices may be more flexible now than half century ago. Special index to track price stickiness should be helpful. Is money losing its real value?
2) If indeed expansionary monetary policies are having diminishing effects, then money will eventually become neutral at least in this experiment.
P.S
1) I have run similar plots for developing countries such as China and India, and the trendlines resembled exponential increasing function. It is possible that money's influence on GDP is S-shaped. (Given the inflation was held under control)
2) Above selected countries have their own merits to be analyzed separately since they share similar traits (Developed, low inflation rate, and other)
3) Notable works that inspired me to write this post were: Calvo's "Price Theory of Money" (2012) where liquidity and money's medium of exchange were emphasized, Brunnermeir and Sannikov proposed comprehensive and continuous "The I Theory of Money" (2016) model where special emphasis was put on money's store of value, and Shin et al. paper on "Breaking free of the triple coincidence of international finance"(2015) where they broadened our perspective on international gross flows of money.
4) All data was taken from https://fred.stlouisfed.org
Addendum (07/14/16) - BIS economists empirically evaluated a link between monetary policy and long-run output trajectories. One of the main conclusions "... monetary policy is indeed not neutral in the long run". The paper is available here.







