The mean, the median and the GDP – part I

A version of this post was originally published in Portuguese as a guest post at Walter Hupsel’s blog On The Rocks @ Yahoo! Brasil.

For over 50 years we have had Huff’s “How to Lie with Statistics” telling us that we should know better. And yet, we still rely on the wrong average in one of our most important tools for evaluating the world and countries’ economies: the GDP per capita. We are still using a mean in places where a median would be the better choice.

Gross Domestic Product (GDP) per capita1 is a simple and effective indicator, coming from a straightforward division of GDP by the population, being used appropriately and elegantly in many instances. Nonetheless, the GDP per capita cannot escape the hard reality that it is a mean average. Thus, as Huff warns us, it has shortcomings and flaws: it fails to capture the effects of inequality in a given reality. From this, one could say that this “mean” average is mean in the sense that it’s cruel and unkind.

But… Can we do better now?

The GINI index has reached mainstream status and is now the de facto standard for measuring income inequality. It measures how much the distribution of income deviates from an even division. A value of 0 in GINI would then be found only in an absolutely egalitarian society where everyone earns exactly the same. In contrast, a value of 100 would imply the entire income earned by a single individual or household. In the real world, it ranges from the low 20s (better distribution) for countries like Denmark and Belarus, to over 60, in the case of such unequal societies as Namibia or Botswana. Brazil’s GINI is 552.

It is time to move on to the median GDP, derived from GDP and GINI. It is a fresh metric that may better reflect both the changes in the economy’s output and trends in income distribution, while accounting for population sizes. It is to the GDP per capita what the median is to the mean.

While the mean is the average of all values in a given set of values (the sum of all values divided by the set size), the median represents the value found in the middle of the set, dividing it in two equally sized halves. Means are affected by extreme values, whereas medians are not. As we can see in the classical “How to lie…” example, an increase in earning of the best paid employee would change mean pay, whereas the median would not move. To move the median requires a change of pay for those in the middle section of the population, those that are neither the wealthiest nor the poorest. This is to say that this median GDP would better reflect the reality of our imaginary average Sally or Joe.

Policies that target economic growth regardless of its [human] costs have support in GDP per capita, which rises even if only a few benefit from these policies. Median GDP would not be fooled or let us be fooled by that.

 to be followed with more detail and examples. I kindly thank  comments and suggestions received from Andre Luchine, Beto Boullosa, Camilo Telles, Eduardo Viotti, Emilia Spitz, Joniel da Silva, Leonardo Fialho, René Dvorak, Vini Pitta and Walter Hupsel.

1. The article could similarly discuss GNI per capita. GDP per capita is chosen due to its wider use;
2. Unless otherwise noted, all figures from World Development Indicators, access on December, 31st , 2013. Indicators: GDP per capita, PPP (constant 2005 international $): NY.GDP.PCAP.PP.KD; GINI:SI.POV.GINI, latest available year.

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