Media and statistics, beware of the tricks of the numbers

We live in an age that worships numbers. An era in which many believe that numbers always speak for themselves. But it's not like that: it's a myth. Numbers are important, but precisely for this reason they must be used with care, knowing that we will see different phenomena – or at least different aspects of the same phenomenon – depending on which numbers we use and how we use them. Levels, ratios, differences, odds, rates of change tell us very different things. Not to mention the statistics (which will be said another time). Those who use numbers do not always declare (or know) what they are doing and why. The result is a deficient, often misleading message. Sometimes deceptive. 

Let's take healthcare spending as an example, the importance of which we have all finally understood and which we have learned is not just a waste (even if there can always be waste). And we make comparisons between countries, as commentators often do, to say that we spend more here than elsewhere or vice versa, that cuts have been made or that it is not true.

Typically, these comparisons are made by looking at the ratio of spending to GDP, either at a given point in time or at its growth over time. But none of these numbers really tell us what the level of health protection is available to citizens of different countries or how it has varied over time.

Suppose that, in year zero, health expenditure in country A was 5% of GDP and in country B 4% of GDP. This does not mean that health expenditure in B is lower than in A. If in country A the GDP per capita was 20 and in country B 50, the health expenditure per capita was 1 in country A and equal to 2 in country B. That is, in B exactly double that in A, while representing a smaller share of per capita GDP. Thanks to a per capita GDP in B more than double that in A. It is clear that, with the same health prices, the citizen of country B has potentially much greater/better health care than the citizen of country A. If they actually are , then, will depend on the quality of the expenditure, therefore on the extent of the waste, on the qualification of the healthcare personnel, on the endowment of structures and machinery, etc. All things that aggregate numbers cannot tell us, no matter how much we torture them.

And now the fallacy of growth rates. Suppose that after twenty years the real per capita GDP of country A has grown overall by 10% (slightly), reaching 22 and the real per capita health expenditure has become 1,5, a growth of 50%. That is, it has increased as a share of GDP up to 6,8%. Not bad some would say. Even in country B, the GDP grew by 10% (that is, still little, in twenty years), reaching 55. The per capita health expenditure also increased, as in A, by 50%, reaching 3, i.e. the 5,45% of country B's GDP. The ratio between the two levels of per capita health expenditure has obviously not changed (the one in B is still double that in A). But, assuming price parity for services, the absolute gap in per capita expenditure on health care between the two countries increased by 50%, from 1 to 1,5, still in favor of citizens of B, while the gap in terms of shares of GDP increased in favor of A (6,8%-5,45%=1,35%>1%=5%-4%).

If then the average cost of healthcare services is growing faster than inflation (with a consequent increase in the price of health services relative to the "basket" of GDP), we would be faced with another interesting case. Suppose that, after the usual 60s, the cost of health services has risen, in both countries, by 1,5% above the general price level. Then, in country A the per capita health expenditure in real terms would have decreased (1,6/0,9375 =1, i.e. less than 3), while in country B it would still have increased (1,6/1,875 =XNUMX).

In country A, real healthcare services would have undergone a "cut", despite the increase in spending in absolute terms, in per capita terms and as a share of GDP. The health protection of citizens of A would have been reduced in absolute terms. And this is not because of higher inflation (general or health care) or lower economic growth in A than in B, because we have assumed that all changes are identical in the two countries.

What makes the difference is only what we could call it an “endowment effect” or “stock effect”: in year zero country B had a much higher per capita GDP than country A and doubled per capita health expenditure. The starting points matter and have a lot of influence on the finishing points. If you don't emphasize these aspects, you end up misusing numbers and sending distorted messages. They seem elementary things, even obvious. But, reading the media and sometimes even "reports" claiming to be scientific, one would not think so.