The issue of One Rank One Pension (OROP) for military personnel has come to the forefront again. OROP implies that a person who retires at the rank of, say, a general in 2015 gets the same pension as a general who retires in 2025. This is akin to wage indexation. As wages increase, so would the pensions.

Before we make up our minds on OROP, it is useful to ask what it would cost. A pension is like an annuity, a stream of payments until the recipient is alive. The price of the annuity is the premium, the cost of providing the stream of payments. What does this premium amount, or cost, depend on? It depends on a) how many people survive and b) the discount rate.

Suppose we promise 100 people (all at age 60) that we will pay them Rs.1 per day for the rest of their lives. Let’s say that the last surviving member lives upto 100 years. This implies a horizon of 40 years of pension payments. So in year 1, Rs.1 per day is paid to 100 people. The total money spent in year 1 is Rs.36,500. In year two, if 2 people die, the pension is paid to 98 people. The total money spent in year 2 is Rs.35,770, and so on. The greater the life expectancy, the more the pension expenditure.

How do we use this to calculate the price of OROP? We obtained the survivor function, the rate at which people die after 60 from UN population tables. We assume a discount rate of 7%. This is because we expect inflation to be 4% in the coming decades, and the real return on government bonds to be 3%. This gives us a price of Rs.3,163 -- put simply, the government would have to spend Rs.3,136 in 2015 if it were paying a nominal annuity of Rs.1 per day (or Rs.30 per month) to someone who retired in 2015. If the pension is actually Rs.10,000 per month, and there are 100,000 such retirees, then the price would increase proportionately.

Suppose the pension were to rise at the rate of inflation , that is if inflation is 4%, the Rs.30 per month becomes Rs.31.20 per month in the next year. The inflation indexed annuity is costlier by a factor of 35% -- the government would have to spend Rs.4,270. Now, suppose we want to also do wage-indexation. The price of this pension works out to be Rs.6,128. This is costlier by a factor of 94%. Thus if the government goes from a nominal annuity to a wage-indexed annuity, pension expenditure may rise by 94%. (The full set of assumptions and code are available here: goo.gl/oEQ04R).

These calculations assume that the person retires at 60. However, 80% of the military retires between the ages of 35 and 40, and 18-19% retires between the ages of 54 and 60. Only about 1% retires at the age of 60. Expenditure on pensions will, therefore, be incurred for a lot longer. We estimate the cost of a pension for a person retiring at age 35.

A nominal pension of Rs.30 per month from the age of 35 will cost Rs.4,520. A wage-indexed pension from age 35 onward would cost Rs.14,998 -- almost 231% more expensive than the nominal pension. Thus if the government goes from a nominal annuity to a wage-indexed annuity for people retiring at age 35, pension expenditures may rise by 231%.

What does this mean for the fiscal deficit? In 2005, when civil servants were moved to the National Pension System, the implicit pension debt on account of civil servants alone was 64.5% of gross domestic product (GDP). With wage indexation of military pensions, this would be even higher. On a horizon of 60 years, we go through four cycles of taking in a person at age 20 who retires at age 35, who will live till 80.

Therefore, for each person who is presently serving there will be four alive who are drawing pensions. We may speculate that the implicit pension debt on account of the armed forces pension may also be in the region of 50% of GDP. If so, policy changes which double or triple the value of the annuity map to 50 or 100% of GDP.

These calculations are approximations. The full information base required to make these calculations correctly can only be accessed through the government. We will require the number of current pensioners, the rank at which each pensioner has retired, current employees, the rank of each employee, and the salary structure.

Using this data, and suitable assumptions on mortality, discount rate and wage growth, we can arrive at actual projections of expenditure on account of the OROP. Only when such calculations are in hand should the political leadership choose between all possible alternative uses of the same money.

Renuka Sane is visiting faculty at the Indian Statistical Institute, New Delhi; Ajay Shah is a professor at National Institute of Public Finance and Policy, New Delhi.