Archive | November 2012

Understanding the UK recovery – The Most Important Chart

So this post is about the Consumer Price Index, and its relevance to monetary policy. First we shall have a little background about what the CPI actually measures, why central banks believe a little inflation is healthy, and the general relevance of inflation to monetary policy.


Inflation, in principle, is the change in prices caused by the changes in the purchasing power of the Medium of Account. Famously, this began when Hume imagined what would happen if the amount of gold in the world suddenly doubled. The answer is that prices and wages would have doubled, but nothing else has changed. (Except gold jewellery would have become cheaper!).

In today’s world UK inflation is controlled by the BoE, since it can print money to increase prices, or destroy it to lower prices. It also affects inflation through changes to the interest rate. This is preferred since it is assumed to be less distortionary. What this means is that if the central bank prints money, it has to buy stuff, and the increased demand for this “stuff” tends to price up the price level asymmetrically  as the prices of the “stuff” increases must faster than the other items the BoE is not buying. In the long run, this leads to an economy that produces more of that “stuff”, since the BoE is making it more profitable to do so. In contrast, changes to the interest rate result in marginally more lending to many different customers, all with different preferences, and so they buy stuff in aggregate in roughly the quantities that you want the economy to produce, so there is no distortion, and prices tend to move roughly together.

The reason why a little inflation is healthy has to do with contracts. In today’s world, for whatever reason, people mostly sign contracts in nominal terms. Very few contracts are inflation linked in any way. In fact, it is usually cheaper and more uncertain to sign a nominal contract and buy interest rate swaps to hedge against inflation, if it is a concern. This is particular true for mortgages. I do not sign a mortgage for a particular sum of consumption, I sign one for a particular number of pounds. This means that if the purchasing power of the pound declines, that is a win for me, as I have, in effect, traded less future consumption for my house than I had planned. However, this has serious knock on effects for the economy. In particular, I have signed a nominal contract based largely on expectations of my nominal income. This means that it is very hard to survive a loss of nominal spending power, it is much easier to survive a loss of actual spending power if my nominal wage is maintained.

This is important, so I will restate it: in theory receiving a ten percent wage cut, and experiencing a wage freeze while there is 10% inflation for one year aught to be the same. In practice, they are not, as the second of these things also decreases the burden of my debts. This plays out into a simple empirical fact: no worker will accept a nominal wage cut. This means that if I am working in an industry with no productivity gains, the fastest I can lower prices is by imposing a wage freeze and waiting for inflation to lower the real cost of labour. In a deflationary period, I cannot lower prices. I end up, effectively, being forced to liquidate my labour force and start again from scratch with new contracts. Not a pretty picture. This is how “zombie companies” are created. They are unable to lower wages in real terms, and so their products remain forever uncompetitive. This is the “Japan Scenario”.

Alternatively, if I have strong productivity growth, I can lower the price of my product without needing to cut wages in real or nominal terms. However, productivity growth in sectors tends to be periodical. There will be a period of strong productivity growth, and then a period of stagnation. You can see the last decades annual productivity growth in the US here. Funeral homes became less productive, in terms of productivity per hour. Software development productivity grew 13% a year. 

This leads us to a nice intuition. We must generate sufficient inflation for most of the sectors of the economy to be able to lower their wage burden when they need do. This tells us, for example, that if there were an oil embargo, which sent the price of oil to infinity (as is happening now in Iran due to trade sanctions), it would be wrong for the central bank to attempt to hit a 2% inflation target by driving every other sector of the economy into deflationary conditions. If that happens, all industries without strong productivity growth would be doomed to becoming uncompetitive “zombie” companies for the foreseeable future.


The consumer price index should be thought of as an average of price increases weighted by the relevance of each sector to the `average’ consumer. This makes some sectors, like Food, energy, and transport, much more important than, say, insurance costs, as UK consumers spend more on the former than the latter. However, the weighting is not too important. Moreover, from the perspective of monetary policy the weighting obscures the truth. Prices change for real reasons, and also because of changes to the value of money, the value of money is clearly a common factor that should affect each price equally, and hence should be susceptible to regression analysis.

The CPI itself is build of out sub indices. Each sub-index takes many prices to cover a small part of the economy, e.g. alcoholic beverages. The CPI is then build out of each of the sub indices weighted by their `sector weights’ which are their relevance to the consumer. The RPI is identical except the sector weights are different, as retailers do not buy quite the same stuff as consumers.

We are going to track the distribution of the sub indices. In particular, if monetary policy is driving the current spike in CPI, we would expect it to be broad based, with many sectors contributing, if it is caused by a few outliers, then it is a `false signal’ about the looseness or tightness of monetary policy, similar to what might happen under an oil embargo.

To do this, we look at the monthly percentage changes, and in each month we will look for a point, \rho which minimises

\sum_{i} (x_{i}-\rho)^{2} \exp\left(\frac{(x_{i}-\rho)^{2}}{L^{2}}\right)

This has several useful features. As L\rightarrow \infty, it produces the sum of least squares, i.e. the usual mean. For smaller values of L it starts to ignore outliers, and will usually give a pretty good approximation of the median. One way of thinking about it intuitively, is to say that it finds the centre of the largest group that is distributed normally with a width (st dev) L. The downside of this is that it is not single valued (\rho \rightarrow \infty also minimises the distribution), and if L is chosen too small it may produce several groups which are each local minima. If we allow L to go to zero this results in it finding a local minima for every individual data point. Nevertheless, for appropriate choices of L it is a powerful way to minimise the distorionary effect of a few outliers on a regression line. To get a feel for what this does, look at this graph of the sum for different values of \rho with a histogram of the frequency of the sub indices in the background.

Figure 1: The effect of the outliers is reduced, and it minimises only with respect to the core grouping. It gives a similar result to choosing the mode or the median.

The value of \rho that is chosen is that which gives the local minima of the red line.

A technical note: the most attractive part of this algorithm is that if the data is normally distributed, it will always yield the same result as the sum of least squares (provided L chosen appropriately), if it differs from the mean it tells you that the data is not normal. The graph below shows the results of this procedure on the CPI sub indices for various values of L. Note that these values mentioned in the legend are for month on month percentage changes, whereas those on the y-axis have been annualised. Figure 1 shows that the vast majority of the data is within \pm 1\% of the median, so even using L = 2 includes more than 90% of the data points. I have also used the twelve month moving average, as that reduces volatility and makes it much easier to read.

Figure 2:Note the huge diversion since the financial crises. This graph represents strong empirical evidence that UK monetary policy is too tight, and is producing close to deflationary conditions for the vast majority of sectors. Prior to the start of this graph the data was given quarterly, rather than monthly, so would not be directly comparable. This graph takes the twelve month moving average, to reduce volatility.

So there is a huge amount of useful information in this graph. In particular, notice the following points:

(1) Much is made of the sector weightings, but the weighted CPI (the black line) tracks the straight mean of the sector averages very closely.

(2) In normal times the different choices of L to not make a huge difference, this indicates that the data is normally distributed.  It suggests that policy was very slightly loose in 1997-2000, and extremely tight right now.

(3) The CPI is clearly dominated by some extreme outliers at the moment, as even a choice of L=10 is moving the average by a full percentage point.

(4) The UK has had some significant changes in VAT, since these are broad based, they probably move the whole graph. It went from 17.5 to 15 in Dec 08, it returned to 17.5 in Jan 2010, and went up to 20% in Jan 2011. Once you account for these changes it seems extremely likely that the median sector of the economy is in outright deflation.


Those who know me know what I think the remedy to this problem is: More NGDP! More Expansionary QE! Unsterilised Purchases!

In all seriousness, the starkness of these results was a surprise to me. As a devotee of Scot Sumner, I believed that the NGDP shock of 2008/9 should have been deflationary, and yet the CPI remained high, so I decided to dig a little deeper into the data. This is the evidence, and it is, as far as the author is concerned, indisputable evidence that the BoE should engage in expansionary monetary policy. Policy is too tight, and the high CPI is an aberration caused by a few sectors. We should be ignoring the CPI at the moment as a measure of the tightness or looseness of monetary policy.