The problem with graphs of data based on indices..

Fig 1 - from Daily Telegraph

Fig 1 – from Daily Telegraph

This blog is based on my comments on Tim Wigmore’s blog in the Daily Telegraph  where I attempted to show an error in his interpretation of the above graph (figure 1). I’m not knocking Tim, but there is a problem with many graphs that compare two variables both based on an index that starts both variables at 1 or 100 rather than on absolute numbers.

The graph does appear to suggest that there was some kind of a connection between change in per capita GDP and change in average real incomes from 1997 to about 2002, where the two lines run almost on top of each other.

However, it seems that through the “boom” years from 2002 to 2008 while GDP per head was rising, average real pay per worker was falling slightly rather than rising. What the graph suggests happened was that the average workers’ slice of the cake didn’t grow as fast as the economy as a whole, but the size of the workers’ slice did not get too much smaller over the period either.

After a blip in 2009 when 2002 real wage levels were reached again, real wages fell away more rapidly than GDP per capita, following the credit crunch. It is this fall during the period of the coalition government that Ed Milliband has taken to calling the “cost of living crisis”.

Tim Wigmore was making the point that during the majority of the last Labour Government, while the economy, as measured by GDP per capita, was growing, median real wages were stagnant or falling. Looking solely at the median wages line, I think that the downward slope is pretty shallow, and by 2009 real wages had largely recovered anyway.

However, there is an element of hypocrisy on the part of Labour in complaining about living standards, which is the point that Tim was trying to make, and I can agree with. It is, however, no surprise that Labour are making a point of issues of the cost of living now, when real wages are falling so much faster 2010-2013 than over the period 1997-2009. It would be very strange if they didn’t.

Tim asked “why did the link between GDP and real wages break in 2002, and persist for another 8 years of Labour governments? What went wrong here?” and this got me thinking about the graph, and the comparison between GDP per head and median real wages. This blog is my answer.

The link between GDP per and wages may be more apparent from the graph than real. As both are based equal to 100 as at 1997 they are bound to start together. The divergence is likely to become bigger over time unless there is a genuine correlation between the two. You would need to look at un-indexed data and perform some econometrics to establish even a statistical correlation – and that is beyond me!

But we can look at other graphs created on the same basis – comparing two indexed amounts both starting with the same index value at a given date. Here is a very similar one to the previous one, this from the Daily Mail from 2011.

Figure 2 from Daily Mail

Figure 2 from Daily Mail

The Mail was reporting on a paper by the Resolution-Foundation, and said “It found that, between 2003 and 2008, average wages ‘flatlined’ and disposable income per head actually fell in every region of England apart from London.” This is apparently supported by the line in the graph for men’s earnings, but not for women’s earnings. The conclusion is consistent with Tim Wigmore’s analysis of the first graph. However, here the graph provided splits out men’s and women’s earnings so it is hard to compare the two graphs.

The Resolution Foundation’s graph is such that the figures for GDP, men’s and women’s earnings, are all indexed, but in this case based on 1971 as equal to 100. Note how the women’s’ earnings line roughly rises with the GDP per capita line throughout but men’s’ earnings don’t! The “de-couple” (for men) here is at 1981, not 2002. It is possible, but by no means certain, that the women’s pay line rises more strongly than men’s as in 1970 wages for jobs done by women were much lower than wages for work done by men. The gap between the two gender’s earnings is generally narrowing over time due to a relative rise in women’s earnings.

Another graph, this time from the USA, shows a similar pattern. This one is a graph of GDP per worker and real earnings, indexed at 1948 as equal to 1.000.

Figure 3 from realitybase.org

Figure 3 from realitybase.org

As in previous graphs, the two lines start rising together, but begin to diverge (or de-couple if you prefer) from the early 1960s. Perhaps there was a genuine economic reason for this divergence, but I begin to doubt it. Each line tells a fair story (assuming the underlying data is reasonably accurate) but I think that putting the two sets of data together can be misleading.

Here is a made up example. I have fiddled the numbers to prove the point! The data is the GDP per head and average earnings for the fictional state of Atlantis over a 19 year period. Tables showing the data are provided at the end of this blog.

The first figure (figure 4 below) shows the yearly in the form of an index where year 1 is 100 for both GDP per head and average earnings. The graph shows lines representing the index figures.

Figure 4 - Atlantis indexed on year 1

Figure 4 – Atlantis indexed on year 1

Using the same data for GDP per head and average earnings, but basing the index on year 7 and starting the graph from period 7, we get a different emphasis, as shown in figure 5:

Figure 5 - Atlantis indexed on year 7

Figure 5 – Atlantis indexed on year 7

While the data in both graphs is fundamentally the same, by choosing a specific start point and a specific index year, a quite different first impression is given.

Firstly, the average wages in figure 4 appear to be doing reasonably well as compared to GDP per head. This is partly due to the simple fact that the data is presented in such a way that the average earnings line is on or above the GDP line for most of the data points. While the average earnings line does fall below the GDP line in some of the final years, by year 19 it is back on the GDP line, so that’s alright then! Secondly, the fact that average earnings and GDP per head rise at about the same rate for years 7 through 10 does not look particularly significant – it could easily be coincidental.

However, looking at figure 5, it would be easy to come to quite different conclusions. Here the average earnings line is on or below the GDP line for nearly all the data points – even for years when it is clearly above in figure 4. It is apparent that there is some correlation between GDP per head and average earnings for years 7 to 10, which appears to breakdown thereafter, which might make one ask “why has the link between the two been broken?”

It seems that creating a graph by indexing each line on the graph so they both start at a single point (suggesting no divergence at the initial point) will by necessity (unless there really is perfect correlation) create a divergence at some point later.  Secondly, it is possible to emphasise or de-emphasise something in the data by carefully selecting the point at which to start the index. In my made-up data, year 7 is a year when average earnings is quite high relative to GDP, so selecting  it as the base year for the index and start of the graph (as in figure 5) makes what happens later seem worse – in the sense that average wages fall relative to GDP per head. If I had based the index at year 2, which is the lowest point for average earnings as compared to GDP per head, then everything that follows would seem much better.

This is making what is an “artefact” of the nature of the graph into a rhetorical point largely unsupported by any real data. Each data set does, of course mean something, and is no word of a lie, but comparing two things on the same graph by means of an arbitrary index doesn’t necessarily mean much and can be used deceptively.

——————————————————————————————————————

Table 1 Data for figure 4

Year GDP/capita Average earnings GDP/capita (Index) Average earnings (index)
Atlanta $ Atlanta $ Index Index

1

550

438

100

100

Indexed at year 1

2

575

385

105

88

3

600

403

109

92

4

625

541

114

124

5

650

500

118

114

6

675

520

123

119

7

700

610

127

139

8

725

630

132

144

9

750

650

136

148

10

775

670

141

153

11

800

736

145

168

12

825

690

150

158

13

850

663

155

151

14

875

652

159

149

15

900

749

164

171

16

925

656

168

150

17

950

830

173

189

18

975

689

177

157

19

1000

789

182

180

Table 2 Data for figure 5

Year GDP/capita Average earnings GDP/capita (Index) Average earnings (index)
Atlanta $ Atlanta $ Index Index

1

550

438

79

72

2

575

385

82

63

3

600

403

86

66

4

625

541

89

89

5

650

500

93

82

6

675

520

96

85

7

700

610

100

100

Indexed at year 7

8

725

630

104

103

9

750

650

107

107

10

775

670

111

110

11

800

736

114

121

12

825

690

118

113

13

850

663

121

109

14

875

652

125

107

15

900

749

129

123

16

925

656

132

108

17

950

830

136

136

18

975

689

139

113

19

1000

789

143

129

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