Numbers are everywhere,especially about the economy.
Inflation,unemployment,migration,pay,debt,poverty,taxes….the list goes on. We see the numbers all the time,we digest them,we use them,we quote them. They help us make sense of the world around us. They can surprise us,shock us,divide us,bore us. They are extraordinarily important. They influence decisions,policies,practices,public attitudes and beliefs. They appear daily in the media,often as headlines in newspapers. Politicians quote numbers all the time,on almost any issue.
Most of the time we accept them at face value,as facts,even as truths. This is especially true of non specialists,of ‘ordinary’ citizens. But numbers are more complicated than often realised and we need to be careful in generating them and, in particular, in using them. To do so we need to understand them better. The UK has a numeracy problem by international standards and ,more intuitively, you might feel, as I do, that many people are uncomfortable around data,figures and statistics. And,frankly, too many people ‘get it wrong’ when they play the numbers game!
Michael Blastland and Andrew Dilnot provided a great service to the nation by creating and presenting the wonderful ‘More or Less’ series of programmes on Radio 4,a show now hosted by Tim Harford. This short article cannot hope to cover all that ground. Instead it takes a different approach, one that has something in common with that of Lynne Truss, focusing on just 3 often used very simple (?!) terms,illustrating them using economic data and drawing attention to the care that needs to be taken when using them. They are: Percentages(%) ; Stocks and Flows; and Averages. Of course,what I say here is well known to statisticians,economists and many others, but not to a surprisingly large number of ‘numbers’ producers and users! Stick with me,this is more interesting and important than it may first seem. And reading this might just help you or some of those around you ,to avoid some all too common,simple,errors in understanding vital economic numbers. So let’s deal with each of these 3 in turn:
‘Interest rates set to rise by 0.5%’
‘Unemployment falls by 1% to a new low of 7%’
‘Inflation down by 1% from a 3% high’
Really? None of these statements are actually correct, irrespective of the accuracy of the underlying data. In all 3 cases there is confusion between a ‘percentage change’ and a’ percentage point’ change. The first of these,the percentage change, compares the old/previous data with the new/current data and expresses the latter as a percentage of the former. The second of these,the percentage point change,is the actual change and is NOT expressed in terms of the old/previous data.
So, in the interest rate example, the 0.5 is the actual percentage point rise in the interest rate,say from 2.0 to 2.5. The percentage increase is actually 25% i.e.(.5/2.0 x100)! The statement therefore should say: interest rates set to rise by 0.5% point or,legitimately,interest rates set to rise by 25%. Honestly.
In the unemployment example,the 1% fall is actually the percentage point fall(and that’s what it should have said) in the rate (itself a %) of unemployment. The percentage fall is actually 12.5% (1/8 x100). The statement should therefore say:unemployment falls by 1% point or,legitimately, by 12.5%.
On inflation,the fall of 1% is a percentage point fall in the inflation rate/rate of increase in prices. The percentage fall is actually 33% (1/3 x100). The statement should thus say: inflation falls by 1% point,or legitimately,by 33%.
Similar examples could be taken from other important domains eg Growth data. The point is,to be careful when expressing oneself and interpreting what others are writing or saying,especially when expressing a change based on an existing percentage figure.Much economic reportage is about trends and comparing this year with last year or this Government’s record with the previous one,and so on. Such comparisons and assessment of trends in data over time always involve stating the ‘change’ that has taken place (negative or positive).
Stocks and Flows
It is important to distinguish clearly between stocks and flows. They are often confused ,conflated or fail to be distinguished. The latter is measured over a given period of time, for example a month or a year, and is indicative of the rate,speed or pace of change. Such flows may be of two kinds,inflow and outflow,with the balance between the two referred to as the ‘net’ flow and the sum of the two being often referred to as the ‘gross’ flow . The net flow will add too or take away from the existing stock,the accumulation of the net flows over time. It is measured at a specific point in time. The analogy of a bath is a good one. Water ‘flows’ ‘in’ through the taps and ‘out’ through the drain,with the level (‘stock’),and changes in the level/stock, being determined by the relative scale of both the flows in and out.
Such distinctions are crucial. For example between the debt (stock) and the deficit (flow) ;between wealth (stock) and income (flow). We take 2 important examples: migration and unemployment.
The net flow of migrants into the UK over recent years amounts to around 190,000 per annum,being the balance between an inflow of around 590,000 and an outflow of 400,000. Net migration is thus around 190,000 and gross in migration 590,000. It is essential to distinguish between the two. The outcome of these flows is to augment the existing stock of migrants (defining these as foreign born) of some 7.7 million,or 11.4% of the UK population,which itself arises from the accumulation of net migration flows over previous time. The Government’s migration target is to reduce ‘net migration’ to the tens of thousands. This will of course not reduce the stock. And could in any case be achieved as much through increasing the outflow (emigration) as reducing the inflow (immigration).
Unemployment in 2012 stood at around 2.6 million. This was the ‘stock’ of unemployed people. When it falls,or increases, it is often referred to as ‘unemployment fell by 70,000’ or,less accurately, as ‘70,000 left the dole queues’. Conversely if unemployment increased by 70,000, the impression is often given, or taken, that 70,000 more people have become unemployed. This is highly misleading. Indeed,it is not true.. In the first quarter of 2012,for example,unemployment actually did fall by around 70,000- but this does not mean that 70,000 people moved from unemployment into employment and that the remaining 2.53 million still remained unemployed.In fact, 530,000 i.e. more than 7 times this figure, moved from unemployment into employment! And a further 460,000 moved from employment into unemployment. It was the ‘net change’ of 70,000 that led to a reduction in unemployment by this number. The gross flows in this quarter,( both in/out of unemployment) amounted to just about 1,000,000 i.e. about 40% of the total unemployment stock! The composition of the 2.6/2.53 million has changed markedly,these are a very different group of people from the previous quarter. The stock was changed by the enormous gross flows that are ‘hidden’ beneath the net change.
Everyone knows what an average is,right? What could possibly be a problem here? We know that the expected temperatures,sunshine and rain in holiday locations are averages from the past and we know what cricketers’ batting and bowling averages are. We might refer to our school , university or football team as ‘average’. In short,an average is seen as a generalisation about a ‘population’ in general:their height,weight,qualifications,health,car ownership,food consumption or whatever. ‘We’ (as a country,a group of people,a city,an ethnic group,a sector of the economy) are better off (or poorer),better fed,more at risk,travel more or whatever. We,as a whole,overall,in general, on the ‘average’.
Actually there are 2 big potential problems here.
The first problem is that there are different measures of what constitutes the ‘average’. The (arithmetic) ‘mean’ is calculated by dividing the total/sum of the variable by the number of relevant observations of it eg the sum of the heights of everyone in a class divided by the number of people in it provides their ‘mean’ height. This is what colloquially is most often used as the average
It is however not the only,or always the ‘best’ means of so doing. The ‘mode’ is the most frequently occurring number in a set of observations eg the most common height,the most frequently occurring observation. This can of course be quite different from the mean,which may not occur frequently or even,with small numbers,at all.And the ‘median’ is a further possible measure of the average. This refers to the middle observation when they are all ranked in order eg in order of height. Here,half of all observations are below and half above,the median.
The second issue is linked to the first. If the population we are dealing with is,let’s say it is the people of the UK, heterogeneous in respect of the variable we are measuring,then the average,however measured,will not capture the characteristics of the whole very well.If there is considerable variety,difference,variation then what is the average saying? It is a bit like adding together all the colours of the rainbow and getting….white (or black: this is controversial!). This is especially important in socio-economic matters.
For example,what do average earnings (for the UK workforce) really mean,given the extraordinarily wide variations in earnings between people? For example,the top 10% of male full time earners earn ‘3.8 times that of the bottom such 10%.What does the average unemployment rate mean,when it varies so much between social groups and geographical areas? For example, ‘JSA’ unemployment in England varies between 1.3% in Wokingham to 8.4% in Hull.What does economic growth of 2% mean,if that is an average which reflects rapid growth in London and actual decline in Yorkshire? For example, through the recession from 2007-12, Inner London grew (in terms of nominal GVA) by 4% a year compared to an actual decline in South Yorkshire.
In consequence,we really need to capture,alongside the average,a measure of the variation,the distribution,the polarisation,the degree of inequality if you will,across the population. The mode and median at better at capturing some of this in unequal distributions (eg the mode is below the mean when the majority earn less than the mean and the high earnings at the very top skew the distribution) but the best way is to focus,in parallel to the pursuit of what is happening to the average,on the overall distribution of observations-this means looking at the percentile distribution ie each tenth of the population under observation,grouped if required in order to simplify,into say,quartiles, so that ‘difference’ can be observed and articulated.
There are many more related issues that are worth reviewing in the Numbers Game. And the issues at stake are very important. I may return to them in due course. Do you think I should?