UK price levels and inflation targeting

Over the weekend, Andrew Sentance tweeted the graph below in an attempt to show that price levels in the UK are above where they “should” be given the Bank of England’s inflation-targeting regime. In particular, he tried to use this graph as a justification for his continued demands that the Bank of England increase interest rates soon (if not immediately).Sentance inflation

If one were to take Sentance’s graph at face value, then it might seem that he has a point- price levels are above where they would be if the Bank of England had followed its 2% CPI target since 2004.

However, of course one should not take this graph at face value. For a start, it ignores the fact that the Bank of England’s inflation target is not just the central point of 2% per year, but is actually a range around that central point. In fact, the Bank of England’s official inflation target is 2% +/- 1% – in other words, inflation can be as much as 2.9% or as low as 1.1% and the Bank of England would still be within its target. Hence, the graph below also plots these upper and lower bounds of the price level over time (the top dotted line shows the upper bound, while the bottom dotted line shows the lower bound).

Clearly, the path of prices in the UK has always remained within the Bank of England’s target (assuming a start date of January 2004). Moreover, even though the price level came relatively close to breaching the upper bound in 2011/2012, more recently those prices levels are well within the upper bound (albeit above the central target).

CPI Inflation

Of course, the Bank of England did not just start targeting inflation in January 2004 – in actual fact it first started targeting inflation in 1992. However, given that it was only granted independence in May 1997, it is more appropriate to examine the path of prices from that date. This is shown in the graph below, which also takes into account the July 2003 move from targeting RPIX to targeting CPI instead.

Specifically, the red line shows the path of RPIX inflation (re-based to equal 100 in May 1997) until June 2003, from which point it shows the path of CPI. Likewise, the dashed line shows the path of prices under central target of 2.5% from May 1997 until June 2003, and then the path under the central target of 2.0% from July 2003 onwards. The dotted lines show the upper and lower bounds of +/-1% around the central target.

The picture here is even more striking than before. Due to inflation generally being below the centre of the target until about 2007, the price level was below what it would have been if the central target had been achieved (although prices did generally stay within the lower bound). Only more recently (i.e. since about 2007/2008) has inflation been above the central target for a sustained period of time, such that the price level “caught up with” where it would have been if inflation had followed the central target.

RPIX and CPI Inflation

Indeed, the end result is that the prevailing level of prices in the UK of the past 4-5 years have been close to the level that would have been achieved if inflation had stayed at the central target since 1997. In other words, the graph used by Andrew Sentance to try to claim that the level of prices in the UK is higher than it “should” be is mis-leading in the extreme – instead of prices being above the level of the central target, they are actually around the central target level and well within the upper and lower bounds of the inflation target. Hence, trying to claim that interest rates should be raised due to the price level being above “target” is not valid.

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Optimal currency denominations: the case of the penny

A month or so ago, it was announced that Ireland was planning to abolish its 1 and 2 euro cent coins. In this respect, Ireland follows the likes of Belgium, Canada, and the Netherlands abolishing some of their low denomination coins in recent years (see here for more details and examples).

There have been various arguments regarding whether abolishing such low denomination, some in favour and others against doing so. Indeed, such arguments regarding “tradition” and “rounding” have been well covered elsewhere. However, one issue that does not seem to have been mentioned is the optimality (in terms of efficiency) of currency denominations. Although the research regarding this issue is a few years old now (the most recent paper I could find was from about 2001), it is still relevant for this discussion.

The design of a set of optimal currency denominations can be based on two possible approaches. The first follows “the principle of least effort”. This approach is espoused by the likes of van Hove & Heyndels (1996) and states that the number of denominations should be designed so as to allow a cash payment to be made with the fewest number of coins/notes handed over. At the extreme this would imply having one denomination for each possible value of a transaction, but this is impractical.

More practical is a set of denominations that have some “spacing” between them (i.e. the multiple applied to the smallest denomination to get the next largest denomination, and so on), but needing to account for the fact that the number of notes and coins required for a transaction increases with the spacing. (To see this last point, note that if the spacing were 2, such that denominations were 1, 2, 4, 8 etc, in order to pay for an item that cost 18 would require the use of 2 coins – one 16 and one 2. If, on the other hand, a spacing of 10 were used – implying denominations of 1, 10, 100 etc – this would require as many as 9 coins: one 10 and eight 1s.)

Caianello et al (1982) found that a spacing of 2 would be optimal, but due to the need to fit denominations around a decimal system, using a 1-2-5 structure would be best in terms of minimising effort. Indeed, this structure corresponds to the 1p, 2p, 5p, 10p, 20p, 50p set-up present in the UK. Moreover, this set-up is supported by more complicated models that allow for overpayment and change (these were not included in the model used by Caianello et al).

Under this approach it is easy to see why the penny comes in handy – it allows the smallest exchange of coins to occur, while still allowing producers maximum flexibility to set prices at the level of the nearest penny. (Note that if, for example, coins below the 10p denomination were removed, producers would no longer have as much flexibility to set prices – they would need to set prices to the nearest 10p as opposed to the nearest 1p.)

The second, alternative, approach to determining the optimum denominations of a currency is one of minimising the number of denominations. This approach has been suggested by, for example, Wynne (1997) and Tschoegl (1997) and views the problem as one that should be solved by minimising the number of denominations in circulation subject to the constraint that all possible transaction values can still be achieved. In other words, the main aim should be to set the number of denominations at the smallest level that still allows for all transaction values to be paid.

In the “real world” scenario in which overpayments and change occur, it transpires that the optimal system under this approach is one that uses a spacing of 3 – i.e. that denominations should be 1p, 3p, 9p and so on. However, under this approach, (and although the denominations conventionally start at 1p) it is easy to see that getting rid of the 1p could be optimal. Specifically, it reduces the number of denominations. On the other hand, given that the denomination would then start at 2p (or 5p), the optimal form of subsequent denominations would increase by a factor of 3 each time – i.e. 2p, 6p, 18p and so on.

It is unlikely that this change in denomination spacing will actually happen if the penny is abolished, such that even if the minimisation of denominations were used as the justification for getting rid of the penny, the resulting denominations are likely to be sub-optimal. Hence, it seems that getting rid of the penny is unlikely to be optimal from the perspective of designing currency denominations.

The reasons for the prolonged recovery in the UK

In a previous blog post, I demonstrated that the UK’s current recovery from the 2008 crisis has taken longer to reach its pre-recession peak than any other recovery over the past 50-odd years.  Moreover, things look even worse if figures are calculated on a GDP-per-capita basis than they do using simple GDP – GDP-per-capita remains below the pre-crisis peak despite GDP having surpassed it a couple of years ago.

Obviously there is plenty of debate as to why the UK’s recovery has been so protracted. Some, like Simon Wren-Lewis, think that the main (sole?) reason is due to the government’s implementation of fiscal austerity. Others point to the nature of the crisis having been a financial one as the main explanatory factor.

However, one thing that seems to have been neglected in terms of the UK’s recovery is the fact that the crisis was a global one and that the UK is more reliant on exports than some of the other countries that had quicker recoveries. In particular, according to the World Bank the UK’s exports of goods and services amount to about 30% of UK GDP, whereas for the US (commonly held up as the country that has recovered the best post-crisis) this figure is close to 14%. (And although Germany’s exports amount to about 45% of their GDP and Germany has also recovered more quickly than the UK, the fact that the German economy relies much more on manufacturing exports than the UK means that it is not a good comparator for the UK.)

Hence, it seems plausible (at least at first glance) that the global nature of the crisis coupled with the UK’s greater reliance on exports means that the path of exports can explain at least some of the difference between the current UK recovery and previous ones.

The graph below shows the path of the UK’s exports on a quarterly basis since the start of a recession for the past four recessions and recoveries.

ExportsIt is interesting to note that the 1973-1976 recovery was associated with a rapid increase in exports during the recovery period, while exports during the the other three recoveries (1979-1983, 1990-1993, and 2008-2013) followed a more similar path until about three years into the recovery period. At that stage of the recovery, exports during both the 1979-1983 and 1990-1993 recoveries continued to increase at a relatively gradual but noticeable pace. However, exports during the 2008-2013 recovery stagnated and have not increased substantially at all over the past three-to-four years.

In other words, it seems that at least part of the reason the UK’s current recovery has been so slow recently is due to the lack of growth in exports over the past few years. It is important, therefore, that the “blame” for the prolonged nature of the UK’s current recovery is not entirely placed at the foot of fiscal austerity.