Introduction
This post was prompted by Appendix D of Charles Murray’s In Our Hands: A Plan to Replace the Welfare State. In Our Hands makes a compelling case for replacing all transfer payments with a universal basic income (“UBI”). For a lot of people who are retired or about to be when the UBI regime begins, however, such a replacement would cause a substantial loss of benefits for which they believe they’ve paid. So with a view toward compensating for such losses Appendix D discusses how great the individual losses might be for variously situated older workers.
But it doesn’t present a specific compensation scheme and estimate its total cost, because “a technically defensible estimate” would involve “some extremely complex modeling and the acquisition of detailed economic and demographic data on a wide variety of issues.” So this post will propose a specific scheme.
But our calculations based on the proposed scheme won’t involve complex models or detailed data, so the resultant cost estimates will be be rough. For simplicity, moreover, the scheme will extend only to the losses’ more-predictable components. Specifically, we will ignore Medicare as well as Social Security’s disability and survivor components, focusing only on Social Security’s old-age benefits. But the exercise will still give us a sense of how feasible a compensation scheme might be.
Old-Age-Benefit Calculation
The Social Security Administration bases a worker’s old-age-benefit calculation on the average of his thirty-five highest annual-earnings values. In the case of income earned before the worker turned sixty years old its selection of the years in which his earnings were highest involves first adjusting earnings values in accordance with the national-average wage. Specifically, the ratio that a given year’s adjusted earnings bears to that year’s actual earnings equals the ratio that the national-average wage in the year the worker reached sixty bears to the national-average wage in the given year.
We’ll use 2022 as our benchmark year, and to simplify things we’ll just assume that the national-average wage—as well as the earnings distribution generally—remains constant in 2022 dollars. Although in actuality the national-average wage has increased in real terms, the increase has averaged only about 0.73% per year since 1951, and in making the benefit calculation the Social Security Administration doesn’t adjust earnings after age sixty even for inflation. So the inaccuracy in which this simplification results should be minor.
Fig. 1 depicts the relationship between the thirty-five-year earnings average and the resultant benefits. As that plot shows, there’s a limit beyond which greater average income doesn’t increase benefits. That plot also shows that two bend points divide the range below that limit into three sub-ranges whose respective slopes are 0.90, 0.32, and 0.15.
Income and Age Distributions
Fig. 2’s bars represent the St. Louis Fed’s individual-income-quintiles for Q4 2022, and its dashed lines represent those quintiles’ best gamma-distribution fit. Although in real life the earnings distribution varies somewhat with age we’ll make the simplifying assumption that the Fig. 2 distribution applies equally to every age group in the labor force. This will bias the benefit calculation downward a little, but in the aggregate that bias will be reduced by our ignoring the fact that retirees don’t qualify for benefits if they haven’t worked for some minimum number of years. For the sake of simplicity we’ll also assume that the workforce consists only of workers between the ages of twenty-two and sixty-five and that all retirees are at least sixty-six years old.
Applying the Fig. 1 function to the Fig. 2 earnings distribution produces Fig. 3’s benefit distribution. The distribution that prevails in real life has a wider benefit range, because retirees can increase or decrease their annual benefits by beginning their retirements later or earlier than the normal Social Security retirement age (which is sixty-six for retirees born between 1943 and 1954). But such advances or delays also decrease or increase the number of payments that retirees receive, so using the Fig. 3 values for the sake of simplicity is unlikely to introduce much error into our estimate of total compensation cost.
We’ll also ignore the fact that demographics change. Specifically, we’ll assume a steady state in which the age distribution matches the survival data given by the Social Security Administration and plotted in Fig. 4.
These and other simplifications will obviously make our calculations depart somewhat from reality. Ignoring Social Security’s survivor and the disability components, for instance, makes our number of recipients too low and their average benefit too high. But the resultant approximations should be adequate for our purposes. For example, the ratio of retirement- to working-age people in our assumed age distribution would imply that the number of retirees is 35% as large as the work force’s 164 million. Multiplying the resultant 58 million retirees by Fig. 3’s $22.6K average benefit yields an assumed benefit outlay of $1.3 trillion, which is quite close to the $1.2 trillion reported by the CBO for 2022.
Retiree Compensation
The UBI level we’ll assume is $1,350 per month in 2022 dollars for every citizen who’s at least twenty-one years of age. (Unlike In Our Hands we won’t reduce higher-earnings workers’ UBI payments.) Viewing UBI payments as partially compensating for loss of the $22,600 average annual Social Security benefit would make the net annual loss average only ($22,600 – $1,350/month × 12 months =) $6,400.
But in the case of existing retirees our purpose here is only to estimate how much to compensate those who lose under a UBI scheme, not to claw back others’ gains. This means we can’t offset against the other retirees’ losses the gains of retirees whose Social Security benefits wouldn’t have exceeded the UBI level. So the average retiree loss that remains to be compensated works out to about $9,500 per year instead of $6,400.
Throughout these calculations we’re ignoring any tax effects. For many retirees Social Security benefits are not taxed at all, while for others they’re taxed less than regular income is. Meanwhile, whether UBI receipts are taxed and at what rates would depend on the particular taxation regime. So adjusting for taxation could have made the net loss less than our $9,500 estimate, but it could also have made it greater.
Multiplying that $9500 annual loss by the ratio that Fig. 4’s post-age-65 survival values bear to its age-66 survival value yields Fig. 5’s red curve, which thereby represents a the average newly retired 66-year-old’s expected values of succeeding-year benefits. Here we’re assuming that Social Security’s cost-of-living adjustments will keep benefits constant in 2022 dollars.
According to our assumed compensation scheme workers who retire right at UBI’s inception will be paid the total present value of all those future-payment expectations. For reasons that will be explained later we’ll use a 5% discount rate for this purpose, making the total $109,000. That’s the leftmost point’s y value in the Fig. 6 curve below:
Whereas Fig. 5’s x‑axis values represent successive ages at which a newly retired worker would have received Social Security benefits, Fig. 6’s represent the ages that different retirees have reached when the UBI regime commences. And for the average member of each age group Fig. 6’s corresponding dollar value represents the total present value of all remaining years’ benefit expectations. As we’d expect, Fig. 6 shows that retirees who had retired years before UBI inception lose less than those who’ve just retired; earlier retirees will already have received some benefits, and they will expect fewer years of further benefits.
Worker Compensation
Having thus calculated the compensation for existing retirees’ losses, we turn to workers who haven’t yet retired but have contributed to Social Security for years. Here we’ll make the perhaps-questionable choice not to compensate such workers fully. Our justification is that as a group younger workers have a greater incentive to embrace a UBI regime.
The incentive is that in contrast to the Social Security system a UBI regime provides participants immediate access to their benefits. Social Security taxes are often seen as akin to contributing to an account from which withdrawals can’t be made until retirement. After all, recipients’ monthly benefits are strongly dependent on how much they have paid in Social Security taxes.
In contrast, a worker under the UBI scheme funds his retirement directly rather than through the government, and he can invest some or all of his immediate UBI receipts for that purpose. By doing so he would normally obtain much higher returns than a continuation of Social Security would afford Social Security-tax payments. Since the move to a UBI regime thus benefits current workers to an extent that it doesn’t benefit retirees, our approach is to provide current workers less than full compensation. But we’ll calculate full compensation before we discuss how much less than full compensation younger workers will get.
Again, we’ve made the simplifying assumption that the income distribution is independent of age. For the average older worker this means that the expected yearly losses in retirement benefits would be the same as Fig. 5 illustrated for those who retire just as UBI begins. But for younger workers the calculation of benefits they’ve earned so far is based on averages of thirty-five-year records that result from tacking zeros onto their shorter-than-thirty-five-year actual-earnings records.
As Fig. 7’s black curve indicates, such workers’ average Fig. 1-function inputs are therefore smaller than older workers’. To calculate the black-curve value for each group whose age is less than fifty-six, that is, we not only clip Fig. 2’s earnings distribution at Social Security’s 2022 contribution-base limit ($147,000) but also scale the result by the ratio that the age group’s number of years worked bears to thirty-five. Each black-curve value is the average of the corresponding age group’s clipped and scaled distribution.
The red curve represents the resultant annual lost benefits, and the green curve represents the amounts by which those lost benefits exceed the UBI-payment level. Each of those curves’ values is calculated from the output distribution produced by applying the Fig. 1 function to the respective age group’s clipped and scaled version of the income distribution. Each red-curve point represents the average of the corresponding output distribution’s values, while each green-curve point represents the average only of the amounts by which those values exceed the UBI-payment level. Points on the blue curve represent present values of the green-curve quantities.
Fig. 8’s blue curve is the same as Fig. 7’s except that rather than an average only of single-year retirement benefits each blue-curve value in Fig. 8 has been scaled up to represent the average corresponding-age-group member’s benefit expectations reduced to present values and totaled over his whole retirement. So the blue-curve quantities are the average amounts that respective age groups would receive in compensation if the above-discussed immediate-access advantage were not taken into account.
But we do take it into account and accordingly reduce the compensation to the values that Fig. 8’s black curve depicts. Our approach to making this reduction is based on assuming respective retirement accounts into which workers make annual deposits after UBI inception that are equal to what they (directly and through their employers) had previously been paying into Social Security. Or, rather, the deposits are equal to the portions of those payments that we attribute to old-age as opposed to disability or survivor benefits: 10.6% of each year’s earnings up to the $147,000 contribution-base limit.
We assume that the retirement account’s rate of return is the same as the discount rate we’ve been using: 5%. The red curve represents the present values of the resultant retirement-time nest eggs. Obviously, these nest eggs are greater for younger workers because younger workers have more payments left to make and more time over which those payments will earn returns. (Being further in the future, on the other hand, their nest eggs’ present values are subject to greater discounts.)
Like the red curve, the green and yellow curves represent present values. Each point on the green curve represents the present value of the net benefit afforded by the average associated-age-group member’s avoiding future Social Security taxes and putting the money thus saved into his hypothetical retirement account. That net benefit is the difference between the corresponding red-curve, nest-egg value and the amount by which the Social Security-tax payments avoided by the average member after UBI inception would otherwise have increased his Social Security benefits. Here we again ignore possible tax-treatment differences even though they could affect this calculation particularly.
So we simply subtract from the red curve the vertical distance between the yellow curves. The upper yellow curve represents age-group averages of the retirement benefits that retirees would have received if they’d continued paying into Social Security until retirement, while the lower one represents such averages of the benefits to which previous payments would already have entitled them. That distance is zero for older workers because, having already worked for the thirty-five years on which Social Security benefit calculations are based, they get no benefit on average from further payments, at least under our (admittedly contrary-to-fact) assumption that the earnings distribution is independent of age.
As the black curve shows, we grant compensation only to the extent that the full-compensation values represented by the blue curve exceed the net benefits represented by the green curve.
Aggregate Compensation
We’re now in a position to estimate the proposed compensation’s total cost. Fig. 9’s green curve is a concatenation of the worker- and retiree-compensation values that Figs. 8’s and 6’s black curves represent, while Fig. 9’s red curve is the result of multiplying its green-curve, per-person values by respective age-group populations to obtain the corresponding age groups’ aggregate compensation values. The proposed compensation’s total cost is the sum of all those age-group aggregates: $6.6 trillion.
It wouldn’t be practical to provide so much compensation in full-amount lump-sum payments immediately upon UBI inception. But to assess the compensation’s burden we’ll calculate the debt service on the (implausibly massive) $6.6 trillion bond issue that funding those lump-sum payments would require. If we assume thirty-year treasury bonds paying, say, 4.6% the debt service would come to $407 billion per year, which in 2022 would have equaled 1.8% of the U.S. gross domestic product, 3.4% of all U.S. personal income, and 10% of the total UBI payments we’ve assumed.
Burdensome, to be sure, particularly since the total would have been significantly higher if we’d included Medicare—or assumed bond-interest rates as high as history tells us they can get. But we’ve expressed that debt service in nominal dollars. If UBI payments increase by about 4.6% per annum in nominal terms, as the Social Security Administration’s Average Wage Index did on average between 1951 and 2022, then that 10% of UBI receipts will fall to about 6.4% after ten years, 4.1% after twenty years, and 2.6% by the time the bonds are paid off.
Alternative Parameters
Now, we reached the foregoing results by making not only simplifying assumptions but also some arbitrary design choices. It was an arbitrary choice, for example, to make the monthly payment $1,350 and the age cut-off twenty-one years. So was making the UBI payments completely independent of earnings; In Our Hands proposed making higher-earnings recipients’ payments lower. And in estimating lost benefits we’ve tacitly accepted the questionable proposition that if Social Security isn’t terminated the expected funding shortfalls won’t force its benefits to be reduced. Nothing compels any of those choices.
So we emphasize that our results could have been considerably different if we had considered alternatives. Although we won’t attempt to estimate what the full range of those differences might be, we will consider a few different discount-rate and UBI-level alternatives after explaining the discount rate we employed above.
We based our 5% discount rate on what a retirement account invested in the S&P 500 might earn. If we accept Slickcharts’ values for total return and adjust them for inflation according to the Consumer Price Index we find an average real return of 6.7%. But averages over periods equal to our assumed forty-four-year working-life length ranged between 5.0% and 8.7%, and we chose that range’s lower end as our discount rate.
Even though we chose the range’s lower end, some investors may believe that basing it as we did on a 100% exposure to equities would be sailing too close to the wind. In Our Hands, for example, chose a 4% discount rate. Had we instead employed that rate our compensation-cost estimate would have been $7.3 trillion rather than $6.6 trillion.
Yet at that same, 4% discount rate the compensation-cost estimate falls to $6.4 trillion if we increase the UBI level from $1,350 to $1,500 per month (and thereby increase the income floor for a married couple to $36,000 per year in 2022 dollars). And that higher UBI level would have resulted in a total compensation cost of only $4.9 trillion if we’d based calculations on the S&P 500’s 6.7% average return.
Conclusion
The foregoing analysis could benefit greatly from taking much more demographic and financial information into account. It nonetheless suggests that although such compensation would be expensive it could be feasible and arguably worth it if it resulted in the UBI benefits that In Our Hands describes.