Mathematics forms a justifiably important part of economic analysis. It provides quantitative figures to describe often-qualitative phenomena, and allows us to engage in data comparison, analysis, and prediction. However, it is not the indisputable window into an economy it is often purported to be. The effectiveness of numbers in economics, especially in the field of developmental economics, is debatable.
Note: I have used the phrases “standard of living” and “quality of life” interchangeably in this post.
Real GDP (and the more commonly-used GNI) per capita, adjusted for purchasing power (PPP), are widely understood as the best modern measures for income/economic activity in a country, and are subsequently used near-ubiquitously as measures for standards of living. This is because these figures contain the practical benefits of numeric analysis, like objectivity and comparability, along with the theoretical benefits of economic analysis, i.e. a higher income (GNI/GDP) directly corresponding to a greater purchasing power and therefore, higher quality of life. They allow us to track a country’s progress, analyse the effect of a certain policy, and perform a variety of other analyses on what appears at first sight a quantitative measure of the standard of living of citizens in a country, a qualitative phenomenon.
However, these statistics cannot be taken at face value. Firstly, income is not the sole factor in determining quality of life; indeed, factors like education, health, freedom, and social equality, among others, contribute as well. An increase in a country’s GNI per capita cannot be taken as a surefire indicator of an increase in the standard of living of citizens in that country.
Education and Health
Measuring any of the previous factors like education and health also runs into the above problem of a singular focus on any one factor not presenting a holistic view of the true quality of life of citizens. Singapore, for instance, has one of the lowest expenditures on healthcare (as a % of GDP), close to impoverished countries like Sudan and Eritrea. Nevertheless, the Singaporean healthcare system is one of the best and most efficient in the world, favoured by high society from Europe and Asia equally. There exists a clear gap between the measurement of any single indicator and the effectiveness of its use.
Moreover, the measurement of more holistic factors like education and health is difficult in impoverished or unstable countries due to a lack of data collection infrastructure and poor government support.
Composites and Conformity
By now, the solution to the above problem of singular focus might seem obvious. What about using all these indicators by factoring them into a composite index, which gives a single figure after incorporating the various indicators like income, education, and health? In fact, income, education, and health, respectively, form the three factors of the Human Development Index (HDI) of the United Nations Development Programme (UNDP). There exist other indicators as well, with even broader inputs, like the OECD Better Life Index, and the World Happiness Report. However, these composite indices only add a few additional perspectives to the final number that is supposed to measure the quality of life of citizens. In reality, the hundreds of thousands of variables that truly affect quality of life can never be measured and incorporated into a single index due to their sheer scale.
Nevertheless, let us assume that a quality matrix (similar to Amartya Sen’s proposed capabilities matrix) with all the variables that affect standard of living, correctly measured, exists and is discoverable for any country. The problem of weightages still exists. Even though these myriad variables may be measured, the magnitude of the impact of each variable on quality of life is individually subjective and in constant flux, presenting an even more impossible roadblock to accurately measuring the standard of living in a country.
Back to Numbers
However, in the end, despite all the flaws I have outlined above, mathematical modelling and data analysis seems to be the (relatively) best tool at our disposal to analyse and compare economic phenomena. In the slightly modified words of Alan Turing, any model we make “will be a simplification and an idealization, and consequently a falsification. It is to be hoped that the features retained for discussion are those of greatest importance in the present state of knowledge.”