An unequal attention: the questionable continued use of averages

Debates, quite often, may miss key points, especially if they kept following one path, as it has in the debates over inequality, especially of incomes. On the one hand, we debate the extent of inequalities of income and assets in any economy, with the consensus that there are extreme inequalities in most countries. On the other hand, we keep using averages such as PCI (per capital income), GDP per capita and such like metrics. In what follows, I am going to focus on the argument and not get into data. There are any number of sources of data and you can pick your choice based on your preferences. The World Inequality Lab at the Paris School of Economics (https://www.parisschoolofeconomics.eu/en/research/pse-research-centers/the-world-inequality-lab-wil/) or The World Equality Institute (https://www.equalityinstitute.org/) if you are interested in feminist themes or The European Institute for Gneder Equality ( https://eige.europa.eu/) or the World Resources Institute (https://www.wri.org/) or the World Parity Institute (http://theworldparityinstitute.org/) and many more. I have no preferences and am merely putting together a short list to provide an idea of how important the problem of inequality is. Let me add that there are serious methodological issues affecting the measurement of inequality, which I hope to address later.

Let me start with a simple numerical example. Let us say there are ten people with incomes from Rs 1 to Rs 10. This totals 55 and gives an average income of Rs 5.5 (55/10). Now when you compare each income with this average, you can see significant differences positive and negative – some incomes are greater than and some lower than the average. Now let us assume that the total income has risen by 6, all accruing to the last, (the tenth). The total income now is 61 and the average 6.1. Anyone who looks at the average without examining the actual distribution of income will conclude that per capita income has risen and draw inappropriate conclusions. Or consider a new addition 11, which raises the total to 66 and the average to 6.6, with the rest remaining unchanged.

This has been my favourite example to explain the shortcomings of using averages to students of statistics at FY B Com level. It is obvious that when individual incomes (incomes actually received by people) are significantly different, the average does not represent what is really happening to the distribution of incomes. I am sure there are objections here pointing out that we can calculate the dispersion (how spread out) from the average. Of course, it can be and will only prove what I am describing – the dispersion will be huge (called standard deviation – the average deviation, again an average!). By the way, you can calculate an average and therefore deviation too for anything but do remember a basic point – if individual values are far apart from one another, the average is rendered devoid of any meaning. What is important is how we analyse.

Average, but which one?

Let us take an area of interest to a lot of people – investment. Say there is a portfolio of stocks (equity) each producing a different rate of return. You can calculate the average rate of return and of course the dispersion. Now, what you do further is really a matter of imagination. You may consider the average return of all the stocks whose returns are below the average and of course those above. This will give you a clear idea of which stock has helped positively and which has had a negative influence pulling down the average. Rather than looking at the average dispersion (standard deviation) you may examine individual dispersions to decide if you wish to continue to hold that stock in your portfolio. You can start evaluating the data in many ways depending on what you wish to do and what is your time horizon. The size of the portfolio is a factor but given a skilled use of software, this should not be an obstacle.

Much the same thing can be done in the case of incomes too. Even if we have to calculate (and use) an average or averages, we must be cautious in what we extract from them. At the risk of sounding monotonous let me repeat that drawing inferences from an average or a set of averages (without any qualifications whatsoever) is simply wrong. Period. At a time when we keep reading how 1% of a population enjoy more than 50% of incomes and wealth, what is the relevance of an average? While the degree of inequality varies across countries, including and especially the advanced economies, the sustained presence of inequality is now a widely accepted fact. And thanks to Thomas Piketty’s book ‘Capital in the 20^th century’ and the (surprising) success it has enjoyed, there has been an extensive discussion on the subject. However, as often happens, the ‘public’ discussion has disappeared behind the walls of professional economists. At some infrequent intervals, the media does cover issues relating to and arising out of inequality but the business media has had an abiding fascination with wealth and valuation, going into raptures over Unicorns (valuations of at least $ one billion). I cannot help feel that the media is completely taken in by valuations and how some rich people’s wealth became larger because of valuations. It takes all sorts to make a world!

Inequalities, not just inequality

There are different kinds of inequalities and you may pick and choose what you wish. To a student of economics, the most basic variable is inequality of incomes since people must first have incomes to do anything at all. You can trace all the inequality that this can give birth to such as inequality of access to education (based on the cost of education, government assistance or the lack of it, cost of educational loans), healthcare and housing, to mention the most basic requirements of any civilized living. What is important to note here is that as people start experiencing some increase in incomes, their expectations for themselves and or their children also start rising – they want more. Growth and development are all about movement – of people from lower to higher levels. The subject of development should focus on capturing this movement.

Typically, mainstream economics uses the Gini coefficient, which compares the incomes of the top and bottom 20% of a population, under the assumption that the middle 60% (split into three groups of 20%) are fairly equally distributed.  Obviously, a high Gini coefficient signifies higher degree of inequality than a smaller number. But when you read what the share is of the top 1% of the population, of income and assets, it does raise questions about the continued relevance of the Gini coefficient. And yet, this is what is routinely referred to, although many studies will deal with the distribution of income across the five quintiles but that is not part of popular consumption. Which raises questions about educating people about the finer points of what happens in an economy. Governments talk of improving financial literacy. I would like to make a case for initiating a genuine economic literacy. I will keep visiting the question of inequality and also simultaneously explore how to explain the critical aspects in an engaging manner.

Income elasticity of demand for comforts & luxuries

To put it in the language of economics, the income elasticity of demand for comforts and luxuries is greater than one, which simply means that people want more than is indicated by the change in their incomes. In most middle class families, this usually leads to a bet on (expensive) higher education, invariably funding it through savings and educational loans. However, things can go wrong if the future did not work out as planned, plunging families into worse positions, especially if they have more than one loan to service. EMIs become a burden causing an unacceptable decline or shift in certain consumption. Access to education may have been at the cost of providing for better healthcare (through appropriate insurance), leading to decline in health or increase in fatalities because of limited or no access, at least to private healthcare.

This is an important point in understanding the link between inequality and access. The cost of higher education, domestic and overseas, has increased far more than any increase in incomes of people opting for such education. Clearly, it is a long way off before the family enjoys any benefit of such education, during which interval the same family may not have had funds for say medical treatment. The trade-off operates at all levels. It is a matter of utmost importance to know how many families sacrificed either healthcare or housing for education. Hence, for one aspect of development at a family level, there is the sacrifice of another aspect. Capturing such data is vital as they will reveal the hard truths of (lack of) development or at least drive home the fact that development is uneven.

If you preferred a more ‘technical economic’ language, observe the disaggregated data and see what it ‘says’. All that you need is a facility and skill to work with data sets to unearth meaningful observations. If development is a predominantly economic phenomenon, these studies of disaggregated data are what will tell us who have developed and who have not and, hopefully, why. These are likely to inform us whether development has taken place and for whom. The simplicity of calculation should not blind us to an average. Its pitfalls should open our eyes and bring attention to the reality unearthed by disaggregated data and studies. Just change your pair of spectacles.

Takeaways

The use of averages is questionable in the presence of inequalities

Addressing one inequality may plunge families more into another

Inequalities of income may be camouflaged by facilities such as EMI but only to become real later when circumstances change

Studies of development should focus on movements not on averages

Families address one inequality at the cost of another

Traditional measures must give way to newer ways of approaching inequality