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Smoothing Consumption vs. Online Calculators

The financial press likes to review online planning calculators and compare results. USA TODAY recently ran this review comparing free calculators at Choose to Save, T. Rowe Price, AARP, and Principal Financial Group.

The context is the 2008 stock market. The question they ask in this case is, "Can you still afford to retire?"

In this article we learn the answer is "No but . . ." Each company presents its findings a bit differently: one says $3000 per month short; another says 60% shy, another says $280,000 shortfall.

Yet not one of these free financial calculators uses "consumption smoothing" and thus they each beg the question: short or shy of what? And how meaningful is this imagined goal to begin with? As the USA TODAY graphic indicates, the couple's goal is to replace 70% of their pre-retirement income. Is this a sensible goal? Does it make sense to measure retirement needs by pre-retirement income in the first place? With less income, taxes will change in retirement leaving more money to spend. The mortgage may be paid off. Is this why only 70% is needed instead of 100%? But wait, why all this guesswork? Isn't there a more sensible way to do this calculation?

Ask a Different Question
There certainly is, and it's called "consumption smoothing," an approach to life-cycle planning adapted from economics by the economists that developed ESPlanner.

Rather than ask, how much should I save in order to have a 70% income replacement? we should ask, how much should I save so that my living standard (regardless of my income) now and in retirement is the same?

So let's take a little closer look at this USA TODAY case and see if we can see why the methodology used by these online calculators (as well as their downloadable counterparts) and many others is so misleading.

First of all, this couple should not be setting arbitrary retirement goals ("rules of thumb" suggested by the financial fund industry). This couple has an annual income of 140K in today's dollars through age 62. They are saving 10% annually of their gross income in qualified saving plans. So, they are told, they need to replace 70% of this income--i.e., $98,000--for each year in retirement? Is this really necessary? Perhaps the 70% is way too much (starve now/splurge later?). Perhaps it's not enough (splurge now/starve later?). How would we know one way or another? (Given this methodology, there is no way of knowing--one must just trust the rule of thumb--and we're about to see how far off it is in this case.)

Instead, let's ask a different question. How much should they save so that they have the same living standard now and in retirement? In other words, how can we smooth our consumption so that our living standard doesn't change when income, taxes, and expenses change?

Let's assume this fictional couple has the $255,500 in retirement saving that they had on Jan. 1, 2009 (see graphic). What is the prognosis for their future economic lives? Well, if they don't save more (it's being assumed that they spend all they earn after they make their 10% retirement account contribution), the prognosis is not good--and this has little to do with the 2008 market as is suggested in this article. The prognosis wasn't good before the year began either--a point that the article ignores.

ESPlanner knows how to calculate future Social Security benefit as well as the lifetime payout on their retirement funds given their assumed nominal interest rate of 6% and their 10% annual contribution.

If this couple continues down this spending path, come retirement at age 63, their living standard will drop 49%. That is, their living standard would drop from $79,587 to $40,670. This drop is not unaware that their federal and state taxes will also drop from $36,048 to $2,649. This accounting also does not ignore the fact that they will no longer be contributing 10% to retirement and that in their last year of work they will make their last mortgage payment.

So before we make any recommendations, we should first describe the present economic situation for this family. The fact is that this family currently lives on about 79K through age 62 and will live on about 49K after retirement at age 63. And when I say "lives on" I refer to discretionary spending after they pay housing, taxes, insurance and Medicare Part B premiums through age 100. This "living standard" is, after all, how we should measure the success of our planning, not by "income." Income is not a "bottom line" number. For example, some families have a lot of income but spend it all on taxes and housing. They are, we might say, "tax poor" or "house poor." Living standard (discretionary spending after taxes, housing, and a few other off the top expenditures) not "income" should be our bottom line measure.

So how much more must this couple save for later in life if they wish to keep the same living standard pre- and post-retirement? In order to determine this saving amount, we'll first do some quick optimization on their personal economy. We are not going to "cheat" here and have them inherit money or move to a state with lower taxes. Instead, we'll simply postpone their Social Security benefit to age 70 so as to make the most of their available resources. In the base case we just looked at, they really had no alternative but to take their Social Security at age 63 since they were not saving any extra money. In this "consumption smoothing" case, we'll do some saving and use just this one basic optimization strategy—postponing Social Security to age 70—because consumption smoothing makes it both possible and prudent.

How much do they need to save in order to have a smooth living standard? On average, they should save $1,729 per month until they retire and thus they will create for themselves a smooth living standard.

If they do this, ESPlanner calculates a smooth living standard of $58,482 for each year of their life from age 50-100. That's about $21K lower per year than what they were living on prior to retirement but about 18K higher from age 63 through 100 than what they would have had without saving. Using consumption smoothing also allows us to take the premium on Social Security by postponing it to age 70 with no material lowering of living standard prior to age 70. The living standard has now been smoothed. If they can average a nominal return of 6% on their retirement accounts, this living standard amount is realistic and sustainable through age 100.

This is a very different plan from what they are given by the standard "replacement rate" advice (which dominates the planning industry). Because we are using consumption smoothing, we don't have to guess or use a rule of thumb to determine how much is needed in retirement. In other words, if we don't approach the problem by telling the calculator what we want the answer to be (e.g., replace 70% of pre-retirement income) we can instead let the calculator tell us how much to save so that living standard never changes from age 50-100 in spite of the radical changes in labor income, taxes, mortgage, Medicare premiums, Social Security benefits, and retirement contributions.

If they use a qualified plan like a 401(k) instead of regular savings as I've done for this illustration, they can actually save more than this and increase their smooth, annual living standard even more because of the tax advantages. But let's save "raising your living standard" for another study.


According to the USA TODAY article:

Specifically, the [AARP] calculator said the couple would have a shortfall of about $280,000 unless they upped their savings to $2,935 a month, or 25% of their income. (This was based on a life expectancy of 90 for each spouse; a longer expectancy would widen the gap.)"

With the consumption smoothing option, we left the life expectancy at age 100. What about the T. Rowe Price calculator?

[The T. Rowe Price calculator] was the most sophisticated of the calculators tested. As befitting a mutual fund company, it takes into account portfolio mix, then projects your investment returns, instead of asking you to come up with your own estimate. This calculator allows you to include information for both spouses but generates results on an individual basis. Once again, though, our couple face a severe shortfall: nearly $3,000 a month.

Not $2,935, not $3000: ESPlanner's analysis shows that setting aside $1,729 more each month until they retire will get them through age 100 assuming a 6% average nominal return and 3% inflation.

The difference in these two approaches is not merely about a different (and quite significant) saving recommendation. The most interesting difference is in the approach used, the methodology for tackling this problem or question. These calculators (except ESPlanner) are making a critical guess about how much the family needs in retirement--they all assume the need to replace 70% of pre-retirement income. If the guess is wrong, the calculation is wrong since the guess is the main variable that determines the results of the calculation.

In fact--and this is not a guess--the family only needs to replace 22% of their pre-retirement income in the first year. So the estimate at 70% is way off and thus the saving recommendation is too high.

Where does the money come from in the year 2021 at age 63? If you look at the tables below, you’ll see that they have $3,210 from retirement accounts and regular interest income; they pay $3,719 in Federal and Mass state taxes, and they dissave $32,992 from their accumulated pool of regular asset saving; they pay 3000 on home taxes and insurance, and this provides a remaining discretionary spending of $58,482 (which, you recall, is their smooth lifetime living standard). It's much easier to see these numbers in the tables below. The point is, forecasting one's retirement needs on rule of thumb like income replacement percentage is a big mistake. In this case you can even see that income is changing--sometimes drastically--in each year of retirement. Nevertheless, living standard (seen in the "consumption" column) remains smooth.


If ESPlanner doesn't guess at the percent of pre-retirement income that needs replacing, how does it make its recommendation? How does it know that this couple can have discretionary income in today's dollars in the amount of $58,482 from age 50 through 100? Anyone can examine these balance sheets and the income and spending reports and see how it works. Its assumptions about state and federal taxes and Social Security are all calculated based on current tax tables.

ESPlanner uses dynamic programming, a mathematical technique that economists and others (but until ESPlanner, not financial planners) have been using for 40 years. ESPlanner knows or can assume the variables in this finite personal economy--it knows inflation, it knows future Social Security benefits, current income, future income, the federal and state taxes, the tax consequences of the 401(k) and, most importantly, it knows the mutual and changing influence of all of these variables on each other over time. Finally, it knows precisely how much to set aside now so that the future will provide the exact same living standard as the present. If a financial calculator doesn't know all of these things, it must begin with a guess about how much is needed in the future, stick with it whether that's too much or too little, and then do some relatively simple math. If we don't want to guess but instead calculate exactly how much saving is needed to smooth consumption over time (from age 50-100) given these known and assumed variables, well, then, we must do some very complicated math. The result is a living standard that emerges out of the numbers as a "solution" not as an initial guess.

As surprising as it may sound, every planning calculator except ESPlanner asks you to tell it how much you need in retirement. They are simply not set up to do the complicated math required to provide your highest smooth living standard over time. This is why they all request this exogenous input--the 70% figure. If they could do the math like ESPlanner, they would do so and point out that $1,729 more each month is all that is needed to provide the same living standard before and after retirement (given these other known variables). This is not an "opinion" or an industry rule of thumb, but rather the answer to a complex math problem.

The amount of income in the first and subsequent years of retirement happens, in this case, to be 22% of the income in the last year of work. This 22% number should never be used as a rule of thumb--indeed, the percentage of replacement income is really irrelevant. This percentage is going to be different in every family's case--the fact that the planning industry has resorted to a rule of thumb and chosen 70% or 80% or 100% simply reveals a shortcoming in their calculators, nothing more. These calculators ask for a percentage number simply because they need a number to set up their equation in order to begin the calculation. Any economist using Matlab or some other sophisticated software that is capable of dynamic programming would get the same results as ESPlanner--although ESPlanner's internal logic is unique and patented, there's nothing secret about dynamic programming. It's been used for nearly half a century and it solves all kinds of problems where one must begin at the end and iterate backward to the present.

So consumption smoothing is not so "new" really. We do it all the time when we look at our paycheck at the beginning of the month and figure how much we can spend each week so that we have the same amount in the last week as we had in the first week. It can get complicated when we figure that the car payment is due on the 20th and we have an unexpected repair bill due on the 10th. We set aside these "off the top" expenses and we smooth our month's discretionary spending.

ESPlanner takes a similar approach to lifetime spending. Of course it's far more complex--there's inflation, housing that "deflates" because of our fixed mortgage, Medicare Part B premiums that outpace inflation, college costs, children that are born then leave the home, college costs, and more. We can't predict everything, but we know a lot and we can make reasonable, safe assumptions. Given all of that, we also need a planning calculator like ESPlanner that asks the right questions.