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08 February 2015

The stock markets are near all-time highs, unemployment is falling steadily, the GDP is growing at a nice clip. Who would guess amidst such excellent signals that the US is going through a monetary contraction? But that is exactly what the graph below shows.

The YoY growth rate of Corrected Money Supply (CMS) has fallen from 20.2% in February 2014 to 8.4% in December 2014. By the end of 2015 the growth rate will be firmly in negative territory if it continues to fall at the current rate. And that is when nasty things can be expected to happen. The Fed could of course accelerate matters if it decides to raise interest rates.

Overall the economy is following roughly the same trajectory as before the 2008 crash. This time I suspect the end will be much nastier.

Category: **Economics**

15 November 2014

Many commentators have expressed concern that a financial market crash could be coming soon. Others have said the US economy is chugging along nicely and there is nothing that can go wrong in the near future.
The graph below showing Year-on-Year growth of Corrected Money Supply offers insights into what could happen.
It suggests that the danger point for financial markets is when the Y-o-Y growth of CMS approaches the zero mark or falls below it. Right now the Y-o-Y growth is around 14%, so there is still some way to go before a major crash.
It is important to understand what the graph is not saying. It does not say that the instantaneous growth rate of CMS is 14% right now. In fact, as the graph below showing Corrected Money Supply from January 2011 to September 2014 reveals, CMS growth has levelled off. What the first graph suggests is that when CMS remains flat or contracts for a year or more nasty things happen in financial markets.
A natural question springs to mind. If money growth is flat why are the financial markets booming? The explanation is simple. When we say that financial markets are booming we usually mean that stockmarkets are booming as they are now or were from 2006 until the beginning of 2008. But the stockmarket is not the only financial market. We know now with the benefit of hindsight that from 2006 to 2008 the housing market was contracting and that it eventually brought down all other markets.
We can be sure that during the past six months, with money growth flat and the stockmarkets booming, some other financial asset market is contracting. What that market is we can do no more than guess.
For those familiar with the history of the US economy and financial markets the graph below showing Y-o-Y CMS growth from 1961 to 2000 may be interesting.
An especially interesting episode is around 1994 when the sharp monetary contraction resulted in the bond massacre of 1994. If the monetary contraction now under way results in a bond market crash a reasonable guess will be that it will not result in a recession.

Category: **Economics**

14 October 2014

The graph of Corrected Money Supply (M1 non-seasonally adjusted plus Sweeps minus Personal Savings) below shows that monetary growth has levelled off after rising for nearly five straight years. The figures are from January 2001 to August 2014; the lag of two months is because of the lag in savings data.

This graph uses the savings figures revised by the BEA in July 2013. It also assumes that sweeps have remained constant since May 2012 when the Fed discontinued publication of sweeps data.

On October 29 the Fed is expected to announce that it will end its bond-buying programme or QE.

The last monetary contraction which started around January 2006 first had its effect on housing starts, then on housing prices, then on bank fortunes, eventually leading to a crisis in the payments system, and finally decimating all asset markets.

Category: **Economics**

19 August 2014

School children are taught at an early age that 1 apple plus 1 apple equals 2 apples. They go on to learn that 1 orange plus 1 orange equals 2 oranges. Sometimes they painfully discover on their own that 1 caning plus 1 caning equals 2 canings. Eventually they conclude that 1 + 1 = 2, irrespective of what is placed immediately after the 1s and 2 or even if there is nothing after the 1s and 2. The belief that 1 + 1 = 2 is a universal truth is widespread, even among mathematicians. But is it true?

In primary school students are posed with problems of the following kind. If two apples cost Rs 20, how much would four apples cost? And they are taught that it can be solved in this fashion.

First you arrange the data as below:

2 20

4 ?

Then, if you cross multiply you find that ? (or what is in later years called the unknown variable) is equal to 40.

In primary school this seems to be a universal truth. But in secondary school the student comes in for a rude shock. He finds that there are problems that cannot be solved in this manner and in fact yield the wrong answer if he attempts to solve them this way.

Thus, if 2 workers take 20 hours to build a wall, then it is incorrect to conclude that 4 workers will take 40 hours to build the same wall. Before one can solve such a problem, one needs to decide in advance whether it is one of direct or inverse proportion.

A similar argument applies to the equation 1 + 1 = 2. Imagine that I eat one apple between 8 am and 9 am and one apple between 9 am and 10 am. How many apples do I eat between 8 am and 10 am. An operational way of arriving at an answer would be to place 1 on the number line for the first apple and then move 1 unit to the right for the second apple to find that between 8 am and 10 am I have eaten 2 apples.

Imagine, now, that I travel at a speed of 20 km/hr between 8 am and 9 am and at a speed of 40 km/hr between 9 am and 10 am. I cannot use the same operational method to conclude that between 8 am and 10 am I have travelled at a speed of 60 km/hr. Distance objects are amenable to the rule that 1 + 1 = 2 but velocity objects are not. We instinctively apply the 1 + 1 = 2 rule to apples and distances but not to velocities and think no more of it.

At the start of the 20th century A.N. Whitehead and Bertrand Russell set out to prove, among other things, that 1 = 1 = 2, from
even more fundamental notions. The result was *Principia Mathematica* which was published in three volumes in 1910, 1912 and
1913. Ludwig Wittgenstein raised an immediate objection that the book used a circular argument in that by using sets it was using
objects that were known to obey the 1 + 1 = 2 rule. But the prestige of Whitehead and Russell was such that the book was still
acclaimed widely as having achieved a breakthrough.

Some years earlier Gottlob Frege had travelled a similar path. Just when his magnum opus *The Fundamental Laws of Arithmetic*
was dusted and ready for publication he received a letter from Russell asking whether the set of all sets which are not members of
themselves was a member of itself. Frege was gracious enough to conclude his second volume with this acknowledgement: "A scientist
can hardly encounter anything more undesirable than to have the foundation collapse just as the work is finished. I was put in this
position by a letter from Mr Bertrand Russell when the work was almost through the press."

Russell was to suffer a similar fate himself when Kurt Godel in 1931 published a paper titled "*On Formally Undecidable
Propositions in* Principia Mathematica *and Related Systems*". Wikipedia paraphrases the paper thus: "Any effectively
generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any
consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement
that is true, but not provable in the theory." More simply, you cannot prove that 1 + 1 = 2.

But formal proofs apart, there is another reason for doubting the universal truth of 1 + 1 = 2. Primary school mathematics is divided into two compartments: arithmetic and geometry. For centuries it was believed that the only geometry possible was Euclidean geometry in which parallel lines meet at infinity and the sum of the measures of the three angles of a triangle is 180 degrees. At the beginnng of the 19th century Gauss discovered the principles of non-Euclidean geometry but the idea was so outlandish that he did not publish. It was left to the Hungarian mathematician Janos Bolyai and the Russian mathematician Nikolai Ivanovich Lobachevsky to lay out the basic principles around 1830.

Even so it was not thought to be anything more than an academic exercise. Only after Einstein published the General Theory of Relativity in 1916 was it realised that the world was basically non-Euclidean and that space was not flat but curved and that the curvature varied from point to point.

If school geometry was only one of many possibilities then from symmetry considerations one should conclude that the school arithmetic in which 1 + 1 = 2 is also only one of many possible arithmetics. In fairness to Whitehead and Russell it must be pointed out that their work was published before Einstein's General Theory.

Thus one is led to the conclusion that if one cannot prove that 1 + 1 = 2 it is because 1 + 1 is not equal to 2. In deciding to apply the rule to distances but not velocities we demonstrate that we know this. But because so many of the objects of our everyday experience do follow the 1 + 1 = 2 rule we conclude that it is universally true. But this is no more than a reflection of the fact that as human beings we tend to reason inductively, accept those facts which fit our beliefs and thus reinforce them, and reject those facts which do not fit our beliefs.

What we can say at best therefore is that 1 + 1 is sometimes equal to 2 though perhaps we can even go so far as to say that 1 + 1 is often equal to 2.

Category: **Mathematics**

13 May 2014

It has happened often in physics that a single phenomenon is explained, or a single puzzle resolved, by two theories that seem at first sight to be completely divergent but are later shown to be equivalent. Examples that spring to mind are Heisenberg's matrix mechanics and Schrodinger's wave mechanics or the quantum electrodynamic theories of Tomonaga, Schwinger and Feynman. In macroeconomics, the second half of the 20th century was dominated by the dispute between Keynesianism and monetarism, especially their divergent explanations of recessions, a dispute that continues to this day. This paper demonstrates that the conflict hinges on a simple dimensional misinterpretation of one of the variables in the quantity theory of money. At their heart, the two theories are equivalent.

Read the entire paper: The mathematical equivalence of Keynesianism and monetarism

Category: **Economics**

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