## Healthcare Economist

Unbiased Analysis of Today's Healthcare Issues

## Social Security Around the World XI: Measuring Benefits

Written By: Jason Shafrin - Jul• 08•06

Throughout the past week, I have spoke of the work disincentives many social security programs create.  The question is: how do we measure these disincentives.  The economics literature has given three different metrics to measure implicit social security wealth a retiree has and I will discuss each in turn.

Accrual

The accrual method measures how much the value social security benefits would increase (or decrease) if a person decides to postpone retirement by one year at age ‘t‘.

• Accrual=SSW{t+1} – SSW{t}

SSW_{t} is one’s implicit social security wealth if they retire at age ‘t’.  This is calculated by taking the nominal benefits at each future date and multiplying them by the probability of surviving to that date as well as a discount factor.

Take the example below:

 Age Benefit P(Surv) NPV factor Value 64 1000 1 1.00 1000.00 65 1000 0.75 0.94 795.00 66 1000 0.5 0.89 561.80 67 1000 0.25 0.84 297.75 68 1000 0 0.79 0.00 2654.55

Here, a pension for someone who retires at age 64 is \$1000 per year.  I assume that everyone dies at age 68.  The total value of the individuals SSW is \$2654.  What if the person decided to postpone retirement to age 65?

 Age Benefit P(Surv) Discount Value 64 0 1 1.00 0 65 2000 0.75 0.94 1590 66 2000 0.5 0.89 1123.6 67 2000 0.25 0.84 595.51 68 2000 0 0.79 0 3309.11

In my example, the individual receives \$2000 per year if they retire at age 65 (instead of 64).  After taking into account the probability of surviving to each age as well as the discount factor, the person’s new SSW is \$3309.  Thus the accrual amount is \$655.  By postponing retirement, the individual increases their Social Security Wealth.  In many systems, this amount can be a large negative amount which gives individuals an incentive to retire early.

Peak Value

The peak value calculation is similar to the accrual method.

• Peak value=SSW{r*}-SSW{t}

This method takes the SSW at the age of retirement (‘r*‘) where r* is the age of retirement which maximizes the value of social security benefits and subtracts the SSW which would result from retirement this year.  This method may be optimal to capture the fact that many people retire at a target year and don’t calculate their own incentives each year.

Option Value

The option value is the most sophisticated method.  It takes into account utility from not working, but requires the researcher to model a utility function and assume parameter values.  First, let us calculate the value of retirement (V)at date ‘s’.  This is equal to the discounted expected utility of wages earned between the current date t and date ‘s-1’ plus the discounted expected utility of social security benefits earned between date ‘s’ and the end of life.

The option value is equal to: V(r*)-V(t).  This is the difference between the discounted expected utility from retiring at r* (the date that maximizes utility) and the discounted expected utility from retirement today (date ‘t’).  If the option value is positive, the individual will continue to work.  If the option value is negative, the individual will retire.

A more comprehensive treatment is given in Stock and Wise (1990).

Stock and Wise (1990) “Pensions, the Option Value of Work and Retirement”, Econometrica, Vol. 58(5), pp. 1151-1180

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