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
09 May 2014
Primitive tribes must be the most equal of societies. Few of us, though, aspire to that kind of equality.
The thought occurred on reading about (note, not reading) Thomas Piketty's Capital in the 21st century that seems set to be the best-selling economics text of recent times. Piketty, who has in some quarters been hailed as a latter-day Marx, notes that income inequality in the US remained stable from 1910 to 1920, rose from 1920 to 1929, fell steeply after the Great Crash of October 1929 until the end of the war, remained stable until around 1980, and then rose steadily again, until in 2007 it rose above the level of 1928. A graph can be seen on Piketty's web site. To set right what he sees as a dire situation, possibly to prevent a capture of western governments by its poverty-stricken masses, Piketty suggests a general wealth tax and a top income tax rate of 80%.
Piketty seems to think that greater equality is something much to be desired. To test this I searched on the net for inequality measures for the Soviet Union to compare with the US. And I found some interesting figures in a paper Income Distribution in the USSR in the 1980s by Michael V. Alexeev and Clifford G. Gaddy. For the US some comparable figures can be found on the Federal Reserve Bank of St Louis web site.
The table below compares the two:
Readers may recall that the only revolution that happened was in the USSR, not in the US.
Poring over English factory inspector reports in the sixties and seventies of the 19th century Marx reached the conclusion that the overthrow of capitalism was imminent. If nothing else, Marx's prognostications should serve as a warning that one must not use short-term data to jump to eternal conclusions. In the graph the current trend of rising inequality dates from around 1980. Is there any other variable that could explain this as well as the shifts in inequality mentioned earlier: stable from 1910 to 1920, a rise from 1920 to 1929, a fall thereafter until 1945, stable until 1980, and a rise thereafter?
It is illuminating to look at the following graph of US long term interest rates.
It is taken from The real rate of interest from 1800-1990: A study of the US and UK by Jeremy J. Siegel. The graph of inequality on Piketty's site and the interest rate graph here follow a similar trajectory. The period from 1910 to 1920 is a period of rising rates and stable inequality. Thereafter the interest rate falls and inequality grows. Similarly the period from 1980 is a period of rising inequality, and interest rates begin to fall from around that date. The Depression years were an exception. So were the war years but then that was a period of wage and price controls.
One cannot help but feel that low interest rates help push up asset prices and thus boost those who earn a substantial part of their income from financial assets. Now it so happens that the people who complain about rising inequality, Paul Krugman to take one example, are also the ones clamouring loudest for keeping interest rates low. Talk about the law of unintended consequences.
02 May 2014
A mathematical equation that correctly describes a physical relationship between quantities is dimensionally homogeneous. However, the converse is not true. An equation that is dimensionally homogeneous does not imply the existence of a physical relationship between the quantities in that equation. The dimensions of the velocity of money are generally taken to be t-1. In what follows we examine this assumption and show that it is physically impossible. We then show what the correct dimensions of velocity are and arrive at the surprising inference that at their core Keynesianism and monetarism amount to the same thing.