Friday, December 26, 2008

New paper: Calculating Savings Rates in Working Years Needed to Maintain Living Standards in Retirement

Mark Warshawsky and Gaobo Pang of Watson Wyatt are the authors of "Calculating Savings Rates in Working Years Needed to Maintain Living Standards in Retirement." Here's the synopsis:

We establish an empirically based lifecycle model to gauge savings and replacement rates for maintaining a steady living standard over life. We consider a variety of scenarios and demonstrate that savings rates vary substantially with individuals' economic and demographic situations as well as retirement plan provisions. This result highlights that meaningful retirement planning must be specific to individuals or households and be based on a comprehensive knowledge of living means and needs.

This doesn't quite do the paper justice, as it runs through a number of examples of how variations in retirement age, 401(k) matches, investment returns and health care coverage lead to different rates of saving and different target replacement rates at retirement.


Paul Lawin said...

It's certainly true that "meaningful retirement planning must be specific to individuals or households and be based on a comprehensive knowledge of living means and needs."

That has signific public policy implications. Proposals for mandatory savings programs seem to assume that "one size fits all". The typical assumption is that everyone should save the same percent of income, with no variation between workers or over time for any particular worker. This assumption clearly leads to sub-optimal (I'd like to find a stronger word) program design.

This particular piece of software considers a variety of complications, but still overlooks at least one large life-cycle variation. For the married couple with children, the software seems to recommend a level 4.5% savings rate, even though the couple's expenses drop dramatically when the children become self-supporting. I tried a simple, back of the envelope, calculation. Mine showed that the couple would have the same accumulated assets at 65 if they saved nothing while the children were dependent, then saved 18.7% of income after they were gone. This provides a much better fit to the couple's spending pattern.

William said...

Ah, retirement, the dream of being able to stop working, sit back and relax. Is it possible? For decades I have searched for a good method to determine what is needed to retire with a good standard of living. What is a good standard of living is different for each person. A person who has been living on $10 an hour wage has different expectations from say a person making $250 an hour.

The question I had in 1975 was simple. How much do I need to save as a percent of my income so that when I hit a particular age I could withdraw that capital on a yearly basis, adjusted by some replacement rate. What I learned early was this was a gradient where two or more exponential curves influence each other. One might expect a growth in wages of 4%, inflation of 3% and rate of return of 5%. How much would you need to save based on these variables to replace 100% of your income at a particular age.

The mathematical formula is found at

I decided to then convert this to java script and this can be found at
How much do I need to save as a % of income?

How much can I withdrawl yearly based on assets.

Why do these work as well as the complicated life cycle variations? They work because they use the law of averages. Can a person do better, yes? Will all people do better, no? The way the market works is that for every winner there is a loser. Unless you win far more than you lose, you will be an average investor. The same holds for mutual funds. Some funds to better while others do worse. The sum total of the good and the bad average out to exactly the performances of the major indexes.

To go along with these the”>SSA period life tables may be useful in determining the probability of living to a particular age. I like to use age 95.

The basic formula in the first link can be done for different time periods if needed and then grouped together. Different periods of time with different spending time frames might be no kids, buying a home, college and saving years.

However, the best policy and advice I can give is to set it at 12% from day one and learn and adjust to not having that 12%.

Assume a low rate of return and after five years calculate your annual return for the past five years and use the previous five years to calculate your ROR going forward.

Good Luck

Andrew G. Biggs said...


You're right that the assumption of a constant saving rate is generally not a good one. Economic theory says that you should consume roughly the same amount in each period, but that doesn't mean you save the same amount in each period. Things like the birth of a child, paying for their education, paying off your mortgage, etc., alter your cost of living and your saving rate should adjust to these changes.

That said, the paper linked to simplifies to a two-period model (working and retirement) in order to show how different conditions lead to different average saving rates. I'm sure the authors would not argue that, consistent with a given average saving rate, households just further optimize between years. (You may actually alter saving and spending within years as well; farmers, for instance, spend more than they earn during planting time, but repay it when the harvest comes in.)

Paul Lawin said...


I agree with everything you say here. I wanted to take the next step and say that any mandatory savings plan I've seen ignores the fact that it's rational for families to have negative savings rates in some years and positive rates in others.

Andrew G. Biggs said...

Good point. A lot of folks argue that very young people should be saving for retirement as if it's a moral issue, when really it's a practical one. There isn't any point of pushing yourself into poverty at age 20 so you can live at 3x poverty at age 65.

That said, public policy is a blunt instrument: the choice may be between forcing people to save suboptimally from year to year in order to present some of them from under-saving from work through retirement.

In practice, a mandatory 401k plan would probably lead to many younger people dissaving even more through alternate means (less non-401k saving, more debt, etc.). That would un-do much of the macro saving, but would leave in place the dedicated saving part. I.e., we don't care that much whether people are saving for a new car, a home downpayment, etc., but we do care if they're saving for retirement since otherwise they become a public burden.

Short story: there's no perfect solution!

Paul Lawin said...

Right, I especially like your "moral vs. practical" distinction.

I'd differ with your comments in that I'm less optimistic than you are about the additional debt being paid off before retirement.

bug said...

Saving has to go with individual needs and tastes. Many people living in the same demographics or conditions do have different needs at different points of times.