Real value of money

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.

Cyclical preferences and the exchange economy

Some experimentation on assumptions of competitive equilibrium yields very interesting results. Suppose in an exchange economy, the first individual has a year long utility function:

(1) U = X1*Y1

And the second individual:

(2) Z1= X2*Y2 during summertime

(3)  Z2=X2*(Y2)^2 during wintertime

Suppose the first individual was endowed with the basket w1(90,80), and the second individual  w2(10,20).

Solving for X1,Y1,X2,Y2 where individuals maximize their utility given their constraints each season gives the following table:

Years	Season	X1	Y1	X2	Y2	Py/Px	Px/Py
Endowement		90	80	10	20
1	Summer	85.00	85.00	15.00	15.00	1.0000	1.0000
	Winter	80.95	89.47	19.05	10.53	0.9048	1.1053
2	Summer	85.21	85.21	14.79	14.79	1.0000	1.0000
	Winter	81.21	89.63	18.79	10.37	0.9061	1.1037
3	Summer	85.42	85.42	14.58	14.58	1.0000	1.0000
	Winter	81.46	89.78	18.54	10.22	0.9073	1.1022
4	Summer	85.62	85.62	14.38	14.38	1.0000	1.0000
	Winter	78.82	93.71	21.18	6.29	0.8412	1.1888
5	Summer	86.26	86.26	13.74	13.74	1.0000	1.0000
	Winter	79.70	94.01	20.30	5.99	0.8477	1.1796
6	Summer	86.85	86.85	13.15	13.15	1.0000	1.0000
	Winter	80.50	94.29	19.50	5.71	0.8538	1.1713

(Py/Px is a price ratio)

While it is not possible to compare allocations during Summer and Winter seasons, we can compare Summers of the each year. The second individual who has cyclical preferences is worse off, not only he was unlucky to be poor at  the beginning, but also he is getting poorer in consequent years. Inequality between them gradually expanding. Nevertheless, all points are Pareto efficient.

Is it realistic to assume that the second individual has different preferences during different seasons? One explanation could be that people's needs during summer are different than in winter, and they frequently trade their goods to match their urgent needs in both periods. Especially if they are poor.

It is also curious that once preference of the individual has shifted, it is impossible to get to the original basket anymore. Given that utility function is Cobb-Douglas type and that other individual's preference does not change.

        (each dot represents X1, Y1 allocation in particular season,  they are approaching to 100 ).