The numbers game
Numbers can cause a lot of problems in economic and financial discussions. Look at the following statements and think about what may be misleading. 1. “Spending on the health service has never been higher; we have never spent more on patients.”
2. “Over the past year, interest rates have increased by two per cent — from one per cent to three per cent.”
3. “The value of the company Pears is now higher than the GDP of 90 of the world’s economies.”
4. “Economic growth is a disaster. The latest figure shows a GDP increase of just 0.8 per cent.”
5. “Investors shouldn’t panic about the recent 20 per cent fall in the value of the stock market. Share prices can easily rise again by 20 per cent over the next year, wiping out the losses.”
6. “The number of students who graduated increased by 2,000 last year — a great success.”
1. Because prices generally rise, it is normal for spending in money/nominal terms always to be at its highest level. More interesting is whether spending is higher in real terms — or, in this case, in real terms per capita. Lesson: Distinguish between nominal increases, real increases and real increases per head.
2. An increase in interest rates from one per cent to three per cent is not a two per cent increase but a 200 per cent increase. More typically, we would speak here of a rise of “two percentage points”.
Lesson: Be clear about the difference between a percentage change and percentage-point change.
3. This is a classic case of comparing apples and oranges. It is like comparing the wealth of one person with the annual income of another. The value of a company should be compared to the net worth of a country, not its GDP, which is its yearly output/income.
Lesson: Make sure you are comparing equivalent concepts.
4. Whether or not 0.8 per cent GDP growth is a disaster depends on the time period. If it is an annual figure, it really isn’t very good. If it is an increase from one quarter to the next, it is very respectable, equivalent to more than three per cent a year.
Lesson: Be clear about the relevant time period.
5. Investors may or may not panic, but the maths don’t add up. Imagine the original level of the stock market was 10,000. A 20 per cent fall would take it down to 8,000. To get back to 10,000 would require a 25 per cent increase — 2,000 is 25 per cent of 8,000 — not a 20 per cent increase.
Lesson: Calculate percentages correctly.
6. An increase of 2,000 in the number of graduates may be good, but we might also want to know about the pass rate — the percentage who passed their exams. We don’t know this here, as we aren’t told how many more (or fewer) students there were in total. The pass rate could, in fact, have fallen.
Lesson: Think about whether absolute or percentage figures are more relevant.