Tag Archives: econometrics

That South India is more developed than the Hindi-speaking North is a common refrain. Literacy rates and per capita income generally bear this out. Indeed, we worry of the barren villages in Bihar, not fertile landscapes across Tamil Nadu. As per the Human Development Indices across India, the South is just over 25% ahead of the All-India average.

And yet, the story is false. Or so is my conclusion after running into a few “Data Stories” of India (looks like Tyler Cowen is interested, too). While the maps give breathtaking life to the real depth of poverty across India, there are fairly rigorous analytics to vindicate my point. While the commonly-used GINI measure of inequality is very intuitive, it’s handcuffed by its inability to decompose the inequality with certain subgroups. A more appropriate measure is the Theil Index, which I talk about in a recent blog post:

The math behind the measure (between 0 and 1) requires a fair understanding of information theory but the idea is lower index implies a higher economic “entropy”.

Your physics teacher might tell you that this is a bad thing but, economically, it’s a little more complex. As Boltzmann showed, entropy increases as predictability of an event decreases. This means the entropy of a fair coin is higher than a biased one. Similarly, in a very equal economy it is very difficult to distinguish between two earners based only on their income. Indeed in a perfectly equal society this is impossible. However, as society stratifies itself, knowledge of ones income conveys far more information (redundancy), thereby decreasing entropy.

Within a system, Theil makes it easy for econometricians to understand the amount of total inequality due to within-group inequality and across-group inequality. If this is a little hard to grasp, think about it this way. If the total differences in economic output remained constant between countries (that is, India is still poor and Norway rich) but income was equally distributed within each country the residual inequality would be the “across-country” inequality. The residual from the converse, where all countries remain as unequal as they were, but world economic output is distributed equally to countries (not people), represents the “within-country” inequality.

And the same reasoning can be scaled-down to consider inequality within and across Indian states. And this is just what a few researchers from the University of Texas did. Before we discuss this, it’s worth considering what high” decomposed, across-state inequality is. A good benchmark is definitely America. While the Northeast and California are generally considered to be richer than the rest, the real turmoil of inequality – at least the public’s eye – is definitely between individuals and not states. Further, the economic relationship between various American regions has been highly volatile, with some sign that growth is picking up most rapidly (in no small part due to extractive oil and gas industries) across “middle America”. Here is a decomposed map of inequality in the United States:


A few accounting points notes here – while the overall measure can never be negative (greyish or black, in the above figure) individual agents can. A below-zero value here indicates that the given county is actually decreasing overall inequality of the country as a whole. The signal, here, is that American states are, broadly, equal. The real inequality stems from the difference between the rich and poor in Manhattan, not between the New Yorker and Iowan.

So back to Galbraith, Chowdhury, and Shrivastava at Texas, we find that across-State inequality in India is pretty low:


The dynamics of this graph are fascinating. For one, the purple line (within state inequality) is far more cyclical with overall inequality than the green line (between state inequality). While both do a fair job signalling inflections, the former represents approximately 90% of the change. Indeed, the contribution of between state inequality has been in relative decline since the 1980s.

While this chart is too fuzzy to derive any grand conclusions, it’s interesting that the correlation across between state and within state inequalities diminished significantly since the piecemeal reforms of the 1980s. While data isn’t available as far back as the ’50s, I suspect liberalization shifted the onus from the state onto the individual. Further, central bureaucrats weren’t able to throttle State growth in the same uneven manner as the years of Fabian regulation.

Of course, this is just mere conjecture. Here’s a graph from the Data Stories:


It’s surprising how relatively rich Bangalore (the blue oasis straight up from the Southern tip) is. Generally, though, almost all of India is as deprived of all the assets indicated above. Now, some might say this isn’t a good depiction of wealth inequality across India because most of the inequality doesn’t stem from the upper-middle class that owns said assets, but among the poor. However, it’s important noting that in terms of total assets, the 5% that owns these assets controls most of Indian wealth. Division of what’s leftover barely moves overall inequality.

On the other hand, in terms of overall standard of living, the South might actually be significantly better:


The big exception is that a good chunk of the North does as well if not better than the South. The cow-belt of India (it’s heartland) does remarkably badly. While this is commonly parsed as the relative wealth of the South, I think it’s the far more equitable distribution of the little that’s leftover after the 5% have taken their share. The above graph depicts what we may call the “poorest of the poor”. To that end, let’s reference this image against the Theil contributions of various states to overall inequality, again from Galbraith et al.:


It should not be hard to see that there’s a fair overlap between the states listed on here (various incarnations of Maharashtra, West Bengal, Bihar, Madhya Pradesh, and Orissa) are the darkest on the map.

This has some important implications for policy making across India. Indians all over (especially in the anxious time before an election) hear of the Gujarat or Bihar “growth models”. Panagariya and Bhagwati in India’s Tryst with Destiny (which I critically review, here) talk about the importance of pro-growth policies. They fairly argue that redistribution alone cannot better the lives of India’s poor.

And while on a national stage this is definitely true, the data above clearly show that the more habitable states (in the economic sense) are not so because of rapid growth rates, but a more equitable distribution of income between the poor and the not-so-poor-but-not-rich. There are a few future research projects, in America, India, and the world that would be very interesting. The Theil Index is, econometrically, a far more robust measure capable of fantastic insight. It would be fascinating to see a study that decomposes a country not into States, but income percentiles to gauge the extent to which each contributes to overall inequality.

I’m guessing, within the United States, there has been an overwhelming shift in the past thirty years away from general inequality to that between the top 5%. In some sense, policy should be targeted to curing not just inequality, but also inequality of inequality.