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Tuesday, July 07, 2015

What is the cost of one-rank-one-pension?

by Renuka Sane and Ajay Shah.

The question

If we switch one person from a simple nominal annuity to `one rank one pension', how much more expensive does the pension become?

Backdrop of India's pension reform

The traditional civil servants pension in India has proved to be very expensive. Bhardwaj and Dave (2006) estimated that the implicit pension debt on account of current civil servants alone, was already 64.5% of GDP. If one were to add new recruits to civil services, and military personnel, this would be even higher. Pension payments were growing sharply. In December 2002, the NDA government made a decision to move new recruits into an individual account defined contribution program, the National Pension System (NPS) [link, link].

The reform was never carried over into defence even though that was long expected to be done the moment NPS had stabilised. As a consequence, we now run two parallel worlds: uniformed defence personnel are on the traditional civil servants pension while others have shifted out to the NPS if they were recruited after 1/1/2004.

The present debate concerns one-rank-one-pension (OROP). In order to understand the fiscal implications of OROP, we must calculate what it costs to produce such a pension.

Calculations about one rank one pension

A pension, which is a stream of payments while the recipient is alive, is an "annuity". There are three kinds of annuities: nominal annuity, inflation indexed annuity i.e. where the annuity value is linked to inflation, and wage indexed annuity, where the annuity value is linked to wage growth. The third is the costliest and is also generally not produced by private insurance companies worldwide. In the extreme, OROP is tantamount to wage indexation i.e. the value of the pension is linked to the wage growth. Hence, in order to price a pension, we have to price the annuity embedded in it.

The full information base required to make these calculations correctly can only be accessed through the government. In the calculations shown here, we make suitable assumptions and proceed. At every step, we have complete transparency about assumptions and computer programs. The gentle reader is requested to actually run the code, and experiment with modified assumptions. The program is written in the free statistics software system, R.

How to price a pension?

Suppose we promise 100 people (all at age 60) that we will pay them Rs.1 per day for the rest of their lives. What is the cost of such a promise today? This depends on two things: the discount rate, and the number of people of this cohort who survive every year. Lets say that the last surviving member lives upto 100 years. This implies a horizon of calculation of 40 years. So in year 1, Rs.1 per day is paid to 100 people. In year two, if 2 people die, this is paid to 98 people and so on.

An approximate survivor function

The rate at which people die away is called the `survivor function'. Our first job is to obtain a survivor function for India and to look at its graph. We use the male mortality rate (as of 2015) from the 2010 the UN Population Projections for India and convert this into the survivor function:

# Convert conditional death probabilities into the survivor function.
calculate.survivorfn <- function(age){
    cooked <- rep(NA, 101)
    cooked[age+1] <- 100
    for(i in (age+2):100) {
        cooked[i] <- cooked[i-1] - a$qxm[i]*cooked[i-1]

# Work out two survivor functions, starting at age 60 and starting at age 35 --
a <- read.csv("", sep=",")
a$cooked.60 <- calculate.survivorfn(60)
a$cooked.35 <- calculate.survivorfn(35)

# Draw a graph with the two survivor functions --
plot(35:100,a$cooked.35[36:101], type="l", lwd=2,col="blue", xlab="Age",ylab="Survivors")
lines(60:100,a$cooked.60[61:101], type="l", lwd=2,col="red", xlab="Age", ylab="Survivors")
legend(x="bottomleft",lwd=2,col=c("blue","red"), bty="n",
       cex=.75, legend=c("Starting at age 35","Starting at age 60"))

This shows that as the age of the cohort increases, the number of people surviving decreases. Of the 100 people who start out at age 60, by age 75, roughly half are still alive.

The data used here to calculate the survival function is the mortality rate of the general population. Survival is likely to be better for those with higher income and better access to health care, as is the case with employees of the government. Hence, our use of this survivor function makes annuities appear cheaper than they are in the context of government pensions.

Pricing the annuity using this survivor function

Once we have the survivor function, we work out the NPV of the annuity. Lets say we are paying Rs.1 per day or Rs.365 per year to this cohort, and that the discount rate is 7%. What is the cost of this promise?

# Make the NPV of an annuity p, where people die off based on the
# survivor function S, when the interest rate is r, l is the number of
# years the pension has to be paid.
value.of.pension <- function(p, S, r, l=0) {
  (1/r)^(1:l) %*% (p * S)

# As an example: Price an annuity of Rs.1 per day at age 60:
value.of.pension(rep(365,40), a$cooked.60[61:100]/100, 1.07,l=40)

Why has the interest rate of 7% been chosen, for the next 40 years? Here is a long answer. The short answer: Because India now has an inflation target of 4%, and assuming this works, the real return on government bonds may work out to roughly 3 per cent.

The code above yields an answer of Rs.3,163.22. This is a little lower than the price charged by LIC for this annuity, of Rs.3,800. That is to be expected, as our survivor function is of the general population, and not of the annuitant population. Also, our calculations do not take into account the administrative costs of providing the annuity.

This gives us the price of a nominal annuity. Now let's make things more difficult, by introducing inflation indexation and wage indexation.

Pricing inflation indexed and wage indexed annuities

In order to do this, we have to make assumptions about inflation and wage growth.

India now has an inflation target of 4%. This suggests three scenarios for inflation: 3%, 4% and 5%.

We also need to make a range of assumptions for wage growth. We propose three scenarios at 7%, 8% and 9% wage growth. At the baseline scenario of 4% inflation, these correspond to 3%, 4% and 5% real wage growth.

# Do scenarios based on inflation and wage growth --
inflation <- c(0.03, 0.04, 0.05)
wagegrowth <- c(0.07, 0.08,0.09)

# A function to make the stream of pension payments. l is the number
# of years these have to be paid, and index is either the inflation or
# wage index.
make.pension.mat <- function(l, index){
    p1 <- matrix(NA, l, 3)
    p1[1,] <- 365
    for(i in 2:l){
        p1[i,1] <- p1[i-1,1] + index[1]*p1[i-1,1]
        p1[i,2] <- p1[i-1,2] + index[2]*p1[i-1,2]
        p1[i,3] <- p1[i-1,3] + index[3]*p1[i-1,3]

# Now do lots of cases.
                                       # Price indexation
p1 <- make.pension.mat(40, inflation)
value.of.pension(p1, a$cooked.60[61:100]/100, 1.07,l=40)
                                       # Wage indexation
p1 <- make.pension.mat(40, wagegrowth)
value.of.pension(p1, a$cooked.60[61:100]/100, 1.07,l=40)

This gives us the following annuity prices (in Rs.):

  • Inflation at 3% - 3940.37
  • Inflation at 4% - 4269.79
  • Inflation at 5% - 4644.56
  • Wage growth at 7% - 5563.41
  • Wage growth at 8% - 6128.46
  • Wage growth at 9% - 6781.57

How does all this change when retirement is at 35?

The retirement age of the military is different from that of civil services. Approximately 80% of the military retires between the age of 35-40, 18-19% retires between the ages of 54 and 60. Only about 1% retire at the age of 60. This implies that expenditure on pensions will be incurred for a lot longer than if the workforce retired at 60. We estimate the cost of a pension for a person retiring at age 35. As before, we first estimate the survival function, and then the cost of the pension under a price and wage indexed annuity.

# Retirement at 35
value.of.pension(rep(365,65), a$cooked.35[36:100]/100, 1.07,l=65)

                                       # Price indexation
p1 <- make.pension.mat(65, inflation)
value.of.pension(p1, a$cooked.35[36:100]/100, 1.07,l=65)
                                       # Wage indexation
p1 <- make.pension.mat(65, wagegrowth)
value.of.pension(p1, a$cooked.35[36:100]/100, 1.07,l=65)

The code above yields an answer of Rs.4,518.73 for the simple nominal annuity at age 35. This rises to Rs.7,488.54 for an inflation indexed annuity (assuming 4% inflation), and Rs.14,998.25 for the wage indexed annuity (assuming wage growth at 8%.).

These calculations are conservative

All the steps of this calculation have made conservative assumptions:

  • The survivor function is for the general population. Civil servants are likely to be healthier than the general population, and uniformed armed forces are likely to healthier than civil servants. When correct survivor functions are plugged into this calculation, annuity prices will go up.
  • We have used the survivor function for males. Females live longer. Some employees are women. When this is taken into account, annuity prices will go up.
  • We have used the mortality rate as of 2015. As life expectancy in India improves, this will go down, implying that more people will live till older ages. Annuity prices will go up.
  • We have assumed that RBI will deliver on its inflation target of 4%.

While our assumptions are conservative, we have assumed an extreme form of wage indexation. It is possible that some variant of OROP is constructed without full wage indexation. The estimates of the implicit pension debt would be lower in that case. We have also assumed a constant discount rate of 7%. If the discount rate is higher, the expenditures will be lower than those described here.

Summary of calculations

We treat our computation for the nominal annuity for a 60 year old as the base line. For all other cases, the extent to which it is higher, in per cent, is also shown.
At age 60:
  LIC nominal annuity 3800+20%
  Our computation for nominal annuity 3163+0%
  Inflation indexed at 4% inflation 4270+35%
  Wage indexed at 8% wage growth 6128+94%
At age 35:
  Our computation for nominal annuity 4519+42%
  Inflation indexed at 4% inflation 7489+136%
  Wage indexed at 8% wage growth 14998+374%

We start at the old system: a nominal annuity at age 60. If we change this to an inflation indexed annuity, the implicit pension debt goes up by 35%. If we change this to one-rank-one-pension, the implicit pension debt goes up by 94%. If we do one-rank-one-pension at age 35, the implicit pension debt goes up by 374%.

Please experiment with alternative assumptions

Here's the R program.


Civil servants are a tiny slice of the Indian economy. It was a real surprise when Bhardwaj and Dave, 2006, found that the implicit pension debt on account of the civil servants pension came up to 64% of GDP. This was an important impetus for the NPS reform.

Uniformed armed force personnel are also a tiny slice of the economy. Even if all they had was a nominal annuity, this could prove to be quite expensive, as the pension starts at a young age, and the health of this group is very good. On top of this, there is the problem of rapid turnaround. 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 percent of GDP.

Policy process

When such questions are being analysed, policy makers should arm themselves with the full calculations, before making decisions.

The calculations that are needed are:

  1. Replace the general population survivor function, which we have used, with the actual survivor function for armed folk. We suspect they are much healthier than the general population.
  2. Use data for the stock of employees and pensioners, and rules about retirement, to work out the implicit pension debt associated with present or potentially modified pension arrangements.

Once such calculations are in hand, the political leadership can choose between alternative uses of the same money. E.g. 50% of GDP could pay for complete suburban metro systems for 50 cities, or for 50 aircraft carriers.


Towards Estimating India's Implicit Pension Debt by Gautam Bhardwaj and Surendra A. Dave, 2006. The Second International Workshop on The Balance Sheet of Social Security Pensions, Organised by PIE and COE/RES, Hitotsubashi University.

India's pension reforms: A case study in complex institutional change by Surendra Dave, page 149--170 in `Documenting reforms: Case studies from India', edited by S. Narayan, Macmillan India, 2006.

Indian pension reform: A sustainable and scalable approach by Ajay Shah, Chapter 7 in `Managing globalisation: Lessons from China and India', edited by David A. Kelly, Ramkishen S. Rajan and Gillian H. L. Goh, World Scientific, 2006.


We thank Ashish Aggarwal, Josh Felman, Shekhar Hari Kumar and Robert Palacios for valuable comments.


  1. Wow!! That is some calculation. Perhaps this is why the Govt. is stuck between the rock * hard place. However all said and done the arrow has already left the bow & it would be stupid and politically most unwise to not implement this. What is required is an out of box solution as to where the money is to come from. Perhaps, I could be very wrong, the Govt could consider absorbing more former armed forces into other disciplines. Or the Govt. could start downsizing aggressively civilian employees. Whether this will help or not I can not say. However issue has to be closed out urgently as it is emotionally charged.

  2. That cleared my mathematical cobwebs for sure. And the numbers are indeed scary.

    Having read your earlier article and the highly emotional and vitriolic comments I would keep away from those complex emotional retorts - but what needs to be acknowledged is that a significant of ex servicemen who retire early do get alternative employment in addition to the pension and benefits they get and this approach must be pursued aggressively to maximize their gainful employment post exit from the armed forces.

    To me, the most relevant point of the above article, vis a vis the future was this:
    "Once such calculations are in hand, the political leadership can choose between alternative uses of the same money. E.g. 50% of GDP could pay for complete suburban metro systems for 50 cities, or for 50 aircraft carriers."

    I am not sure how the Government will be able to handle the legacy of OROP but it is critical that the future spends be more focused on building the technological strength of the armed forces instead of only relying on the ability to throw more people into the ring. Make in India, to borrow a political statement, is more critical in our defense and space industries than probably anywhere else and it must get all the financial support it can.

    Tarun Hukku

  3. One Rank , One Pension ( OROP )

    As against 14 lakh serving military personnel , there are some 25 lakh retired military persons , in India , today

    They are demanding , " One Rank , One Pension "

    In simple terms :

    > Col Mhatre retired in 1985 , with last drawn salary of Rs 10,000 pm

    > Col Chari retired in 2000 , with last drawn salary of Rs 50,000 pm , and

    > Col Patel retired in 2015 , with last drawn salary of Rs 100,000 pm

    They all served for 30 years at the time of retirement

    As per present Pension Rules, by way of pension :

    > Col Mhatre may be getting Rs 2000 pm

    > Col Chari may be getting Rs 10,000 pm

    > Col Patel may be getting Rs 20,000 pm

    Under OROP , all of them would today , get Rs 20,000 pm !

    And as salaries keep climbing , with each passing year , they will all keep getting the same amount as pension, as the latest retiree in the same rank , who has put in same length of service , at the time of retirement

    A kind of " Indexation " , aimed at neutralizing the ever-rising " cost of living " which is same for all three retirees !

    And , the argument goes :

    " Why not ?

    Those who are serving , get their " cost of living " neutralized thru DA ( Dearness Allowance ) which automatically keeps rising every month , as CPI / WPI etc rise !

    Why should early-retirees be made to suffer , for having been born earlier / served earlier ? "

    One cannot find fault with such an argument !

    But if OROP is implemented , the Governments ( Central + States ) must get ready with answers to the following :

    > Will this lead to similar demands from millions of retired para-military forces and Police personnel , in all the States ?

    > Could this lead to similar demands from all retired Civil Servants , at the Centre as well as , in the States ?

    > Can this demand find an " Echo " in all retired Municipal / Panchayat employees , all over India ?

    > Will private sector retired employees make similar demands on Corporate Employers ?

    After all , no retiree ( of any kind ) , can escape the ravaging effects of ever - rising inflation ( cost of living ) ! Be rest assured , they will all be justified in making similar demands !

    This raises following further questions :

    > Will this set in motion , a Vicious Circle ?

    > Will this make India , a " High Cost Economy " ?

    Only time will tell

    But one thing is crystal clear

    Each succeeding generation will be required to bear the burden of ensuring that its preceding generation manages to live a life of dignity , which could well run into Rs lakhs of Crores !

    I cannot escape comparing this potential scenario with the present Greek Tragedy , where almost all citizens ( whether serving in Government or in private companies ) ,

    > Retire at the age of 50

    > For the rest of their lives , draw a pension equal to 90 % of their last drawn salary !

    I am not against OROP

    I am for creating awareness of the issues and for starting a National Debate


    hemen parekh
    09 July, 2015

    1. My salutations to you. The Military Pensions (70% of last pay drawn) were given to Veterans upto 31.12.1972.(The last pay used to be less because of less number of years of service). The then Govt (especially babus)led by Smt Indira Gandhi, envious of Field Marshal SHFJ Manekshaw's huge success of 1971 Bangladesh Liberation, reduced it to 50% and at the same time increased Civilian pensions to 50% for all (33%- since they were getting more pay due to maximum number of years of service). (33 years service stipulation for earning full (was applicable to Civ employees, then applied to AF Veterans). Thus, the veterans pensions were reduced to half of approved 50%(25% in realily) pensions wef 1.1.1973. The veterans resented and represented to various authorities. A plethora of Committees were appointed to look into the problem. All the same, the Govt and the babus justied denial of OROP mainly on admin, legal and financial grounds.DEFENCE VETERANS specially JCOs and OTHERS RANKS retirers at the age of 36 to 37 years of his main life,whereas civilians counterpart of any department from bank,state govt,central govts,local panchayat retiers at 60 years of age. YOU CAN NOT COMPARE THEIR LIFE TO SAFE GUARD THE FRONTIERS TO CIVILIANS LIFE IN PEACE.. Finally the Koshiari Committee rejected the illogical reasoning of babus and the report was okayed by the august house. The previous regime, Half heartedly, allotted a 500 cr budget for OROP and your Govt gave 1000 CR.Although the DGL was prepared by Services HQ in Apr 2014, the CGDA never really tried to sort out the impasse. True, the MOD should have framed this policy (as per business rules) but deliberately asked CGDA (an unwilling horse) to chair and decide. The net result is nil as of date.

      And the same person (CGDA earlier) is now in MoF (Secy Finance). So, the relentless obstacles, appear, one at a time, all the time. And the OROP could not be announced by the PM at Mathura Meeting in May 15. Sir, the Raksha Mantri has already done the homework, and the exact finances figure of 8298 crores was also given. The FM stated that everytime provision in budget is not necessary. The PM's statement that OROP definition is 'PECHIDA" had hit the Veterans very hard, for they were hopeful that this Govt will come to their rescue.
      So, therefore, the babus succeeded and the jawans failed.

  4. That was an answer that I am sure many of us were looking for. Thanks for that first principles approach. But what about the large subsidies that a retired defence pensioner recieves through subsidised purchases at the 'canteen'. Will that not count towards cost of pension? In all cases the cost to company approach must be brought in be it for civilian and defence saleries while in service or as pensioners. Finally, it is the efficient use of scarce resources and a full costing of them alone will allow for better economic choice by Govt. In fact the entire govt and defence medical cost could be replaced at a much lower cost to govt. by replacing the existing medical services by an insurance scheme. The pilferage and administrative costs would also come down sharply.
    Also as a possible solution emanating from your analysis, Govt could permit pension inlcusive of wage inflation only form the age of 60 as is the case for civilian pension thereby reducing the pension burden to the same as that of the civilian pensioner. If the defence pensioner anyway is working till the age of 60, as most of them do, then the allegations of inequity that may arise in such a proposal may not hold good.

  5. Hello genius
    ALL your calculations are wrong. You made ALL the pensions start at Rs1.00 in your example
    You are comparing civil pensions where the employee gets pension on his LAST drawn salary at the age of 60 with the military where 90% of the soldiers retire at 35 with MUCH MUCH lower salary. The military is NOT like the civil forces, where people at kept employed even if disabled till they reach 60. In the military, the disabled are discharged or if they don't get promoted in time. Civil employees go through 3 or 4 more pay hikes than military soldiers. Civilians also have the assurance of time bound increases in rank and position, whether they are fit for the post or not, where as the military hierarchy is a very steep triangle, with only very very few reaching the higher ranks. ONLY the highest generals are able to retire at 60+, most of the remaining officers are eliminated by the age of 50-54. 85% of the men retire between 34-37. The officer to men ratio in the military is around 25:1. As regarding the canteen subsidies, they are ONLY on the excise and other duties. Please people, understand, if you were to be given a job where you could be called at anytime (24/7) for 15 years, get killed at any time by any terrorist or enemy, as well be called to attend/support/relieve any calamity or disaster that strikes the nation, be prepared to stand with 20+ pounds of guns and ammo at 5000 meters in -50C temperature, and have doubts about whether the job and the people that you are sacrificing so much (keep in mind that these people have virtually no family life in forward areas) to look after will look after you and your family when you are in your sunset years, is expecting too much from those brave souls who truly commit themselves to their country, which is unlike ANY other profession in terms of commitment. It is time we stopped thinking with our pockets, at least for these brave and selfless brothers and sisters. Do all these calculations on the so called "netas" who are bigger parasites and utter non performers than any other form of society, and the civil NFFU beneficiaries, the govt servants who don't pay anything for their usage of all govt utilities, etc. Calculate the money being drained there, as well as the enormous white elephant public sector companies and organizations that not only do not produce anything noteworthy, but annually waste and lose humongous quantities of material and money. Do not equate a soldier with any other form of society, because they are the only people who are ready to give up their lives for the protection of the nation, truly.

  6. continuing from my last post
    Hello again Genius, you need to read up on so many more things before you take out your calculator.

    1. compare Indian military spending with the GDP. For 2015 we are at 1.5% of GDP with 247KCrore, without including expenditure on pensions at 55Kcrore, which is at about 20% of the defence spending amount today. You have posted that the "implicit pension debt on account of current CIVIL servants alone, was already 64.5% of GDP" compare that with 20% of 1.5% of GDP.

    2. Further, read this post to understand the drain that today's MP and MLA are on the exchequer:

    3. Calculate the effect the proposed 100% gain will have on the economy. Also keep in mind that in their case they also get lifetime pensions if they attend parliament for one day, that is increased for every term in parliament.

    4. Also see how the other nations pay and take care of their protectors, including our financially insecure neighbors. Compare the percentages they pay for retiring personnel with our percentages.

    5. Check the way the civil services in the third pay commission literally stole 25% of the pensions of the soldiers and gave it to themselves.

    6. Also, if we assume that a fund is set up to cater to a soldiers' pay and pension, what happens to the fund after the soldier retires and dies. Where does that fund go? Who does it benefit? Keep in mind that the dead always outnumber the living.

    I hope you will at least now, try and "get" what the military ethos and mindset is about, then do your calculations on those brave souls who form our nations sole non communal, merit based, non caste/language/creed based organization that performs at 100% every time.

  7. Thanks for this blog I have given my comments. As these exceed given character limits I am posted it as blog link is

    Cost of 231% as worked out will be far lesser if correct figures of life expectancy of soldiers and inflation are taken. It shall then not be more than 150%. Even with figures of 231% extra cost it is pea nuts for the quality of defense which nation is getting.

    Please read the blog as per link as given above.

  8. What is the need to pay lifelong pensions to the 80 percent who retire before the age of 40 and are healthy ? They should be absorbed into other government services (if possible) or they should look for jobs in the private sector. Yes, life long pensions should be paid to the injured soldiers and the families of soldiers who sacrified their lives in the service of the nation !

  9. 64 % of gdp?? Indias gdp was 2067 billion usd in 2014!!! Are you trying to say that it could cost around a trillion usd to implement orop? I have my doubts....I agree it will almost double the existing pay and pension bill....ball park calculation....25 lakh veterans drawing 50% of pay as pension......13 lakh serving drawing 100% pay.....almost twice the expenditure if 25 lakh have to be given 100% pay... (50% increase).....please educate me if my assumptions are wrong.....

  10. The govt. Should start up its own public security co. With branches all over the nation. Employ these 85% 35+ aged retired military personnel & give them jobs. Ranging from manual secirity to administration to management. The burden of such pensions can be reduced by upto 70%. Retired military personnel can earn more, pressure on the economy can be lowered & all institutions requiring quality security can be satisfied. Its a win win situation for all. Its all a matter of demand meet supply - simple economics.

    1. This is the same logic by which government started making HMT watches .... we can do a better job. I agree government should try to absorb them or help them get placed but starting a security company would be bad idea. Also which soldier would want to be a guard at a mall....not the good ones I am sure.


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