The Theil inequality index: a flexible tool for the modern political economist

Contrary to the Gini-index, the Theil inequality index enables us to directly tie estimates of inequality to the class and ownership structure of a society. As such, it’s an indispensable tool for the political economist, requiring a-prori knowledge of political economic theory but also an inductive reading of the sources and the situation. So, why is the Gini and not the Theil index often the economists inequality metric of choice?

The Gini-index is an often used metric to estimate inequality. As such, it is highly useful. But for the political economist it has a fundamental drawback. It does matter if people are rich or poor and it does show the extent of differences in income or wealth. But it doesn’t matter if people are laborers or a capitalists, teachers of ‘precarious workers’, landowners or farmers, men or a women or black or white. The Gini-index can be used to measure but not to analyze inequality in a direct, metric consistent way. The are metrics, like the Theil index, which do enable this. Even then, economists have come to use exactly the Gini index (and not the Theil index) as their favorite tool for the measure inequality. Why? Branco Milanovic has some interesting ideas:

Political economy stopped looking at social inequality through the lens of class, which it did from Quesnay through  Adam Smith and  Ricardo all the way to Marx. It did so precisely around the same time as classical novel disappeared. It was Pareto at the turn of the 20th century who introduced for the first time, studying fiscal data from a number of German and Italian cities and states, interpersonal income inequality. From Pareto onward, we ceased to deal with capitalists, workers, and landlords; we began to deal with individuals, some rich, others poor. The class analysis was definitely pushed out, so much so that in the second half of the 20th century, especially in the United States, even the mention of class in an economic paper would immediately classify you as an unreconstructed Marxist.

It dawned on me that this was not a coincidence: the death of the classical novel, the dissolution of the class structure of the bourgeois society, and the end of a political economy where the subjects were classes in favor of “agents” might have all been related.

But now as the importance of capital incomes increases, and capitalist societies grow increasingly stratified, with the rich attempting to confer and transmit all the advantages to their offspring, may not both the class analysis in economics and the classical novel make a comeback?

This, of course, leads to the question how the Theil index enables us to re-introduce ‘class’ in economic analysis. It’s quite doable – but it requires work and a thorough knowledge of theory as well as an inductive reading of the sources and the situation. It is possible to break down the Theil into constituent parts based on class (or gender, or race of whatever). When one has income and class (or gender, or race) data of a population of for instance 10.000 people one can calculate the Theil index for the entire population as well as ‘baby-Theils’ for specified parts of the population, like sheltered workers and precarious workers or like capitalists and laborers. Adding the Theil inequality within these baby-Theils to inequality between these baby-Theils adds up to the Theil index for the total population. An empirical example: the province of Friesland in the Netherlands, 1749 (sorry, I’m an economic historian, but it fits nicely in the Quesnay (1694 – 1774) framework mentioned by Milanovic).

Table 1. A class based breakdown of the Theil wealth inequality index for Friesland, 1749

  N Share in households Average wealth of subsector as part of average wealth of total population Within subsector contribution Between subsectors contribution Total
Oligarchs 112 0,01 24,5 0,1 0,6 0,7
Pensioned and injured soldiers 159 0,01 0,1 0,0 0,0 0,0
Laborers 2891 0,21 0,1 0,0 -0,1 0,0
Poor 1519 0,11 0,1 0,0 0,0 0,0
Farmers 2369 0,17 1,0 0,1 0,0 0,1
army 331 0,02 0,7 0,0 0,0 0,0
All others 6334 0,46 1,2 0,8 0,1 0,9
   13715      1,0  0,6 1,7 

Source: Van Bavel in Friesland. An inquiry into the relation between economic development, measured wealth inequality and the rise of oligarchy in Friesland in the seventeenth and eighteenth century. In progress.

As can be seen, the 112 ‘oligarchs’ (members of a limited number of families which increasingly monopolized lucrative jobs in the government, including the top of the army) contributed quite a lot to total inequality, partly because of intergroup inequality but to a much larger extent because of the difference between their average wealth and average wealth of the rest of the society. The group ‘all others’ consists of pastors, lots of craftsmen, traders, shell gatherers in coastal cities and the like. Clearly, as the ‘oligarchs’ not only monopolized government jobs but also owned quite some land, this still was a quite Ricardian society, even when the ‘all others’ category might induce one to lable it a Smithian society. Taking the ‘novel’ approach: Friesland resembled the countryside as depicted in Great Expectations from Dickens quite a bit, up to the cows in the mist and the lime kilns but without the explicit, restrictive and detailed contracts of the bound apprenticeships as described in this novel. Miss Havisham was, no doubt, a member of the oligarchy.

The point: based upon the situation the researcher can specify specific groups (classes, gender, race or even a combination of these) to construct ‘baby-Theils’, to re-introduce class and power in economic analysis. As such, the Theil index is a flexible tool which enables us to move away from single agent models. To do this however requires a thorough and broad knowledge of theory as the researcher has to be able to gauge which specification of the groups not only squares with the questions asked but also with the stratification of the society.

About this: the first time I read a Marxist book (‘Kapitalisme en burgerlijke staat’ by Siep Stuurman) I didn’t understand a thing of it. Until, approaching the end, it dawned upon me that ‘class’ as used in the book did not relate to middle class or lower class but in a very strict way to laborers and capital owners. After which I at least understood the logic of the book. It are these economic, historical defined classes to which Milanovic refers. The Theil index enables the researcher to use the ‘lower class-middle class-upper class’ distinction as well as the economic distinction. Remarkably, this economic distinction can also be found in some neoclassical (or should I call these ‘classical’ because they use these definitions) models, more specific some the HANK (Heterogenous Agent Neo Keynesian) models which also use capitalists and laborers as classes: a sign of the times as Milanovic suggests? Anyway – an analysis incorporating ‘power’ as an explanatory variable should, in my opinion, do well to base itself on economic class and the power connected to – and to an extent even defining – the ownership of capital. The Theil index enables measurement of a crucial aspect of the consequences of this power as well as part of the analysis of the situation – as it forces the researcher to be explicit about the class choices made.