Tag: compensation

Means, medians and power laws

Following the disbursement of Rs. 10 lakh by the Andhra Pradesh government for the family of each victim killed in the stampede on the Godavari last week, we did a small exercise to put a value on the life of an average Indian.

The exercise itself is rather simple – you divide India’s GDP by its population to get the average productivity (this comes out to Rs. 1 lakh). The average Indian is now 29 and expected to live to 66 (another 37 years). Assume a nominal GDP growth rate of 12%, annual population increase of 2%  and a cost of capital of 8% (long term bond yield) and you value the average Indian life at 52 lakhs.

People thought that the amount the AP government disbursed itself was on the higher side, yet we have come up with a higher number. The question is if our calculation is accurate.

We came up with the Rs. 1 lakh per head figure by taking the arithmetic mean of the productivity of all Indians. The question is if that is the right estimate.

Now, it is a well established fact that income and wealth follow a power law distribution. In fact, Vilfredo Pareto came up with his “Pareto distribution” (the “80-20 rule” as some people term it) precisely to describe the distribution of wealth. In other words, some people earn (let’s stick to income here) amounts that are several orders of magnitude higher than what the average earns.

A couple of years someone did an analysis (I don’t know where they got the data) and concluded that a household earning Rs. 12 lakh a year is in the “top 1%” of the Indian population by income. Yet, if you talk to a family earning Rs. 12 lakh per year, they will most definitely describe themselves as “middle class”.

The reason for this description is that though these people earn a fair amount, among people who earn more than them there are people who earn a lot more.

Coming back, if income follows a power law distribution, are we still correct in using the mean income to calculate the value of a life? It depends on how we frame the question. If we ask “what is the average value of an Indian life” we need to use mean. If we ask “what is the value of an average Indian life” we use median.

And for the purpose of awarding compensation after a tragedy, the compensation amount should be based on the value of the average Indian life. Since incomes follow a Power Law distribution, so does the value of lives, and it is not hard to see that average of a power law can be skewed by numbers in one extreme.

For that reason, a more “true” average is one that is more representative of the population, and there is no better metric for this than the median (other alternatives are “mean after knocking off top X%” types, and they are arbitrary). In other words, compensation needs to be paid based on the “value of the average life”.

The problem with median income is that it is tricky to calculate, unlike the mean which is straightforward. No good estimates of the median exist, for we need to rely on surveys for this. Yet, if we look around with a cursory google search, the numbers that are thrown up are in the Rs. 30000 to Rs. 50000 range (and these are numbers from different time periods in the past). Bringing forward older numbers, we can assume that the median per capita income is about Rs. 50000, or half the mean per capita income.

Considering that the average Indian earns Rs. 50000 per year, how do we value his life? There are various ways to do this. The first is to do a discounted cash flow of all future earnings. Assuming nominal GDP growth of about 12% per year, population growth 2% per year and long-term bond yield of 8%, and that the average Indian has another 37 years to live (66 – 29), we value the life at Rs. 26 lakh.

The other way to value the life is based on “comparables”. The Nifty (India’s premier stock index) has a Price to Earnings ratio of about 24. We could apply that on the Indian life, and that values the average life at Rs. 12 lakh.

Then, there are insurance guidelines. It is normally assumed that one should insure oneself up to about 7 times one’s annual income. And that means we should insure the average Indian at Rs. 3.5 lakh (the Pradhan Mantri Suraksha Bima Yojana provides insurance of Rs. 2 lakhs).

When I did a course on valuations a decade ago, the first thing the professor taught us was that “valuation is always wrong”. Based on the numbers above, you can decide for yourself if the Rs. 10 lakh amount offered by the AP government is appropriate.

 

The Question About Adarsh No One Is Asking

Nikhil Service Station is one of the more popular petrol bunks in South Bangalore. If you wonder why you have never heard of it, however, it is because nobody refers to the petrol bunk by its real name. The bunk is owned by Anitha Kumaraswamy, wife of former Karnataka Chief Minister HD Kumaraswamy and daughter-in-law of former Prime Minister HD Deve Gowda. The service station came into service in the early 2000s. It had been allotted by Indian Oil in the “Kargil martyrs” quota. It is now a landmark in South Bangalore, and popularly known as “Deve Gowda Petrol Bunk”.

The reason I’m bringing up the issue of the petrol bunk is to draw a parallel with the scam-ridden Adarsh Cooperative Housing Society in Mumbai, which was again ostensibly built for “serving and retired army personnel”. The Adarsh scam is in the news once again due to the rejection of the report by the Maharashtra cabinet and the connection with arrested diplomat Devyani Khobragade.

The question about Adarsh that nobody is asking is this – why is it the government’s business to construct housing for “serving and retired army personnel”? Why is it that the government should compensate families of martyrs with petrol bunks and LPG dealerships and not cash? Aren’t these structures designed to be scammed?

Nobody argues that the army must be paid well. Nobody argues, either, that army personnel should be generously insured and compensated, given the hazardous nature of their jobs. My argument, however, is that this insurance and compensation should be universal and standardized. Allotments such as housing and LPG dealerships are discretionary by nature, and that makes them prone to abuse.

Consider for example, a housing society the government constructs for “serving and retired army personnel”. Let us say that the society has 500 apartments. How does the government choose who gets these apartments? And in what way are the 500 such chosen personnel different from those that did not get the allotment? Does this discretionary allotment not leave the system to abuse? Does this not lead to unhealthy competition among the “serving and retired army personnel”? Do we want that in our armed forces?

On a similar note, after each railway accident, we have the railway minister announcing a discretionary compensation for the dead and injured. The question is why this should be discretionary. Cannot the railways simply buy group insurance for all its passengers, which is automatically paid out upon an accident?

The argument I’m making is that some of  the processes we follow are designed to be scammed. In the time of tragedy, either in an accident or in battle, what we need is a standardized and predictable response on behalf of the government agencies. By not putting that in place, the system is prone to abuse.