Evaluating the monetary policy stance: back of the envelope calculations

How do we judge whether monetary policy is tight or loose? The central bank has two general ways to impact the supply of money. First is through the price of money i.e. the interest rate. If r is higher than inflation, than the 'real' rate of interest is positive and is the rate at which economic agents base their decisions. The higher the real rate of interest is, the tighter monetary policy could be said to be. When the real price of money is high, the cost of borrowing for investment and consumption is high, and economic activity slows. The converse is true - monetary policy is loose when r is below inflation, and borrowing becomes cheap.

Incidentally, that's why deflation is a dangerous phenomenon - you can get a high real rate of interest even if the nominal r is zero.

The other way to judge the monetary policy stance is to examine the rate of increase in the money supply. Fast money supply growth accommodates faster economic growth but also signals higher future inflation. You can in theory slow down economic growth even with a low real interest rate, by restricting the supply of money. The relationship between money and the economy is described by the Quantity Theory of Money, which takes the form of the following accounting identity:

M x V = P x Y

Which states that money (M) multiplied by velocity (V: the number of times money circulates in the economy), is identical to real output (Y) multiplied by the price level (P). If we transform both sides to natural logs and take first derivatives, and move the price term to the left:

Ln(ΔM) + Ln(ΔV) - Ln(ΔP) = Ln(ΔY)

This states that the rate of increase in (M) less inflation should equal the growth rate of real output if we take velocity as a constant. When this identity doesn’t hold, one of the other variables will need change to bring the identity into balance again. Thus if (ΔM) is greater than (ΔY) + (ΔP), then we would expect inflation to increase if the economy is at full employment, or both output and inflation to rise when the economy has some slack - such as during a recession.

This is the current situation in Malaysia now (log changes in M3 less log changes in CPI, compared to log changes in interpolated, seasonally adjusted monthly rGDP, all relative to the same month in the previous year):



The charts show money supply growth was probably excessive in 2007, but got closer to neutral in 2008. Compare that with this comparison between the overnight interbank rate against CPI inflation:



(Correction:) The policy instruments appear to contradict each other in both 2007 (interest rates indicating tight money, money supply loose) and 2008 (interest rates very far below the rate of inflation, while money supply more neutral). One way to explain the discrepancy in the observable policy stance is if we go back to the original equation just now – what if velocity is NOT a constant? Then:

V = (Y x P)/M

which can be proxied by nominal GDP (real output multiplied by the price level) divided by money. One would expect velocity to (slightly) vary positively with economic activity – higher consumption and investment means money changes hands quicker. Conversely, when economic activity contracts, people and businesses become more cautious and cut spending, which reduces the circulation speed of money. Solving the equation for M3, we get:



We have a better than 10% variation in the velocity of M3 in 2008, although I'd be cautious in taking the level of velocity at face value due to the interpolation I've done on the GDP data. Nevertheless, looking at M3 adjusted for velocity and inflation relative to rGDP is instructive:



The interest rate and money supply variables are better matched in terms of their policy stance, though at this point in time monetary policy is far more expansionary than implied by the real interest rate. At this stage, I'd expect both velocity and inflation to continue dropping, which may cancel each other out as far as impacting output. This further implies that expansion of the monetary base would be more effective in boosting output, and would be non-inflationary given a reduction in velocity. It also implies that should the situation reverse, BNM has to react much more quickly in reining in monetary growth to head off a resumption in inflation.

Update:
Technical notes:

1. Real GDP is arrived at by deflating the value of nominal GDP with the GDP deflator, which is not equivalent to inflation as measured by the CPI. The main difference between the two price series is that the GDP deflator also takes into account export price inflation, which is not relevant in a domestic context except in terms of measuring output - by definition, exports are not consumed in the domestic economy.
2. The interpolation I did on GDP data is very rough and ready, but since I'm using it mainly to contrast the difference between two policy instruments, I hope everybody will give me a pass on that one.