*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:

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?

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 aninflation 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.

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.

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.

**Speculation**

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:**

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.

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.

*This research paper was first published at Ajay Shah's Blog under the title - What is the cost of One-Rank-One-Pension? on July 7, 2015 and has been republished under the fair user terms of the source blog.*

**References**

- 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 pensionreform: 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.