How Much Income Does Social Security Replace

Introduction

There are numerous articles pointing out that Social Security Retirement Benefit (SSRB) is designed to replace 40% of income – at most. See https://www.fool.com/retirement/2017/04/24/social-security-is-designed-to-replace-this-much-o.aspx, or https://humbledollar.com/2018/08/ten-commandments-2/). Even the Social Security Administration (SSA) estimates an average income replacement rate (RR) of 40% (https://www.ssa.gov/planners/retire/r&m6.html).

Interestingly the calculation of RRs is not without controversy. Generally speaking, the RR is some measure of the yearly retirement benefits divided by some measure of the yearly income prior to retirement. While this sounds straightforward, there are several possible values for each that can be used.

Most (but not all) of the argument centers on calculating income prior to retirement. There are several ways to measure the income: Final year, average of final 5 years, average indexed earnings, earnings indexed by CPI etc. (see https://www.ssa.gov/policy/docs/ssb/v68n2/v68n2p1.html). For this analysis I shall start using average indexed earnings (AIE). This, generally speaking is the number that SS believes represents the income associated with the individual’s lifestyle. It is the income that SS purports to replace.

What I intend to do here is show what is meant by this 40% replacement figure and show just how wrong it really is. Once we see the real RRs, we may begin to understand how 10,000 people a day somehow mange to retire – despite all of the “expert” opinion that they are unprepared and unable to retire comfortably. However, that (understanding how they manage) is beyond the purpose of this article, which is merely meant to show that the 40% RR figure significantly understates the experience of the majority of retirees.

How SSA might calculate the average RR

The current average SSRB is $1422. The National Average Wage Index (NAWI) is $50,322. The simple calculation is 12*1422/50321 = 34%. That is not even 40%. Further, it uses the 2019 SSRB and the 2019 NAWI – which is based on average salaries in 2017.

Using the NAWI, one can calculate a PIA equal to 1879 using the 2019 bend points. That RR is 12*1879/50322 = 45%. If we use the NAWI (which is based on 2017 salaries) and the 2017 bend points (885 and 5336), we find a PIA equal to 1855 or a 44% RR.

I suspect the difference between SSRB and PIA comes from benefits that tend to be claimed earlier rather than later than at Full Retirement Age (FRA). For analysis purposes here we will assume PIA as the SSRB for comparison purposes. Public policy addressing RRs should not be made based on the propensity of people to retire early.

Calculating Income and SSRB

All calculations of income shall start with an assumed final year salary that has kept pace with the NAWI throughout the workers lifetime (or at least for 35 years). Then the AIE will look pretty much identical to the last year’s salary. While this may overestimate his true AIE (due to significant salary increase late in his career) it also over estimates his SSRB.

I believe in order to fairly calculate an income RR requires that we look at income – not gross salary, but at a minimum, income after FICA withholding. A $100,000 salary cannot result in a paycheck greater than $92,350. RRs should be concerned with the latter figure, not the gross figure. If I received $92,350 with no withholding (there is no FICA withholding of SSRB) I would think that 100% of my income was replaced.

Subtracting FICA withholding from gross income is the minimum correction necessary. Federal income taxes are also withheld (and or paid at the end of the year). These taxes too are unavailable to spend. Of course there are taxes in retirement, and SSRB are often subject to tax.

According to the SSA trustee report https://www.ssa.gov/oact/TRSUM/ , total taxes collected on OASI payments were 36 Billion on benefit payments of 799 Billion. That is Overall SSRB were taxed at just under 5%. That would be essentially slightly less than half of the benefits being taxed at the lowest marginal rate – 10%.

Whether income taxes should be considered is debatable. Again, the availability and quality of public pensions is a separate issue from tax policy. However, I will use PIA, not accounting for possible taxation, because SSRB alone have no tax consequences. The maximum SSRB (at FRA) in 2019 ($2861/mo) would have no tax liability for a single individual. The same is true for a married couple filing jointly even if each had the maximum SSRB.

Calculating RR

SSRB is calculated using the 2019 bend points and assumes that claimant is FRA using Salary as indicative of the AIE for the individual.

RR is calculated using three variations of income:

1. Salary – the gross salary before any deductions
2. Salary less FICA
3. Salary less FICA and federal taxes – referred to as After Tax Income (ATI)

Given that the goal of SS is to help people maintain their lifestyle in retirement, the important feature is how much of an individual’s ATI is replaced – it is ATI that people spend (or save) and it is spending that maintains the lifestyle. The difficulty lies in determining ATI as federal taxes differ from one person to another.For comparison purposes here I shall use singly or Married filing jointly tax rates assuming that the standard deduction is used.

The RR is then simply SSRB/income.  (as calculated three separate ways)

I shall calculate RR for single and for married couples with one person working. I will also discuss RRs for married couples with two incomes. Given the disparity of incomes and benefits I shall show the results for a variety of salaries.

Results: RR for various incomes and marital status.

The RR for single individuals is shown in Table 1 for various salaries. Listed are the salaries, salary less FICA withholding, salary less FICA and federal income tax, SSRB, and RR using the three income variations.

Table 1. RR for various incomes for a single individual

Salary	10,000	20,000	40000	50,000	70,000	100,000
Salary less FICA	9235	18470	36940	46175	64655	92350
ATI	9635	17690	33798	41833	56071	77176
SSRB	9000	12845	19245	22445	28334	32834
RR vs ATI	93%	73%	57%	54%	51%	43%
RR vs Salary less FICA	98%	69%	52%	49%	44%	36%
RR vs Salary	90%	64%	48%	45%	40%	33%

It is readily apparent that RRs are significantly higher than 40% for a vast majority of the single population – regardless of the comparison income chosen. In fact when compared to replacing ATI – the comparison that I think is appropriate – it exceeds 40% for essentially all of the population.

SSRB replaces more than half of ATI for 85% of the working population (those with salaries under $70,0000/yr.).

For married couples that have had only one income there is a significant spousal benefit. The spouse (at FRA) can claim a spousal benefit equal to one half the PIA of the qualified worker. This comes at no increase in FICA withholding but generally a decrease in federal taxes. Table 2. shows the results for one income couples at the same salary levels. It is assumed that each of the couple has reached FRA.

Table 2. RR for One Income Married Couples

Salary	10,000	20,000	40000	50,000	70,000	100,000
Salary less FICA	9235	18470	36940	46175	64655	92350
ATI	9754	18541	35380	43491	59561	83866
SSRB	13500	19267	28867	33667	42451	65668
RR vs ATI	138%	104%	82%	77%	71%	59%
RR vs Salary less FICA	146%	104%	78%	73%	66%	53%
RR vs Salary	135%	96%	72%	67%	61%	49%

For married couples that have lived on one income, the RR is significantly higher than 40%, without exception. For those at the low end of income, RR near or greater than 100% is achievable.

For two income married couples, differing claiming strategies and the soon to be discontinued restricted application may affect the RR. Also, age differences may cause differing claiming ages. We will not consider these strategies.

For a working couple that has essentially the same incomes and claims at FRA – the RR is essentially the same as shown in Table 1 for a single individual. There are some small differences at the very low-income end due to the phase out of earned income credits. The results are shown again in Table 3.

Table3. RR for two equal income Married Couples.

Salary Each	10,000	20,000	40,000	50,000	70,000	100,000
Total Salary	20000	40000	80000	100000	140000	200000
Salary less FICA	18470	36940	73880	92350	129290	184700
ATI	18541	35380	67596	83666	112141	154207
SSRB	18000	25690	38490	44890	56669	98502
RR vs ATI	97%	73%	57%	54%	51%	43%
RR vs Salary less FICA	97%	70%	52%	49%	44%	36%
RR vs Salary	90%	64%	48%	45%	40%	33%

Basically, each individual claims a single benefit and thus the RR is unaffected by the presence of a second income in the marriage.

Finally, what happens when there are significant salary differences? The first thing to note is that half a salary generates an SSRB of more than half of the SSRB for the full salary. E.G. a $40,000 salary has an SSRB of $19,245. A non-working spouse is eligible for half of that benefit at FRA. However, if he worked and earned half of that salary, $20,000, his benefit would be $12,845 – significantly more than half of the higher benefit. However, because of the increased income, the RR may be less than that for Married couples with one income. Some results are shown Table 4.

Table 4. RR for Married Couple with Unequal Income

High Salary	30000	40000	40,000	60,000	60000	100,000
Low Salary	10000	10000	20000	20000	40000	40000
Salary	30000	50000	60000	80000	100000	140000
Salary less FICA	36940	46175	55410	73880	92350	129290
ATI	35380	43491	51526	67596	83666	112141
SSRB	25045	28867	32090	38490	44890	52079
RR vs ATI	71%	66%	62%	57%	54%	46%
RR vs Salary less FICA	68%	63%	58%	52%	49%	40%
RR vs Salary	63%	58%	53%	48%	45%	37%

Mostly the result of two different salaries is only slightly lower than two identical salaries with the same total value. Note that a 100,000 salary split 60/40 (Table 4.) is identical to the split 50/50 (Table 3.). The same is true for 80,000 split 60/20 versus 40/40. But 40,000 split 30/10 is slightly lower than if the salaries were evenly split (20/20). The same is true for 140,000.

Still there is but one comparison where the actual RR is less than 40%.

Discussion

The major item of note in all of the RR listed data is that SSRB replaces about 60% of ATI for all salary levels up to 40,000/yr. This is true for single individual and married couples with 80,000 dollars of income – regardless of how that income is split. The idea that social security replaces but 40% of your income is totally inaccurate.

Until recently, many “experts” suggested that people needed 70% of their gross income in retirement. This figure was meant to estimate the idea that ATI was about 70% of your gross salary. I believe a more reasonable goal is that you will need 100% of ATI.

Clearly, SS replaces nowhere near 100% of ATI for the vast majority of people. The very poor have RR near or higher than 100%. As much as these people are poor while working, they will continue to be poor in retirement. They will likely need assistance with housing and health costs that will continue to rise.

Single income married couples will receive the best benefits. Even those with total salaries up to 100K will have RR greater than 60%.

Those with individual salaries in the 30,000 – 40,000 (60K-80K total married) range can expect SSRB to replace about 60% of their ATI.

 

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Comments On the [mis]Use of Gaussian (Normal) Distribution Functions

Introduction

Most everyone, especially scientists and engineers, are familiar with what is commonly called the Bell Curve. This is of course the famous Gaussian distribution function (GDF) that is often normalized so that it has a mean of zero and a standard deviation of one.

It is commonly used to represent the distribution of many experimental results. Often it is known that the distribution of the data are other than Gaussian and that the use of this distribution is an approximation of the actual distribution – one that is often not known.

Widespread use of the GDF is based on the Central Limit Theorem (CLT). The CLT shows that the distribution of the mean of a set of collected data will tend toward a GDF as the number of collected data increases – irrespective of the underlying distribution of the collected data.

It is important to note that this is different from implying that large sets of data will have a Gaussian distribution. Taking a large sampling of a binary distribution (Say the toss of a coin) will always have a binary distribution regardless of how many times we sample. The coin will always be either heads (assigned a value one) or tails (assigned a value zero). It will never be some combination that might have a value 0.67’ although the mean of the sample could easily have a value of 0.67. Further, the distribution of the mean of that sample (0.67) depends upon the size of the sample taken and it will approach a GDF about the actual mean as the sample size tends to infinity.

To my knowledge there are no natural occurrences of normal distributions of data in nature. Even the classic “Bell” curve of student IQs cannot be a GDF. IQs cannot be negative – therefore they cannot follow a GDF – which has tails towards both positive and negative infinity.

GDFs exhibit significant complexity. First, there is no closed form solution for the integral – to determine probabilities. Second, it requires two distinct variables to describe the function – neither of which is known.

Regardless of its complexity many researchers assume a GDF for data that are clearly not Gaussian in nature. Defense analysts assume targeting errors are Gaussian, engineers often apply Gaussian analysis to failure studies – totally inappropriately as there cannot be a negative number of failures.

The question that comes to mind (at least it comes to my mind) is why assume a GDF for the collected data that we know to be incorrect? Assuming a GDF does not simplify the problem and is not necessarily a good approximation to reality.

Alternative to GDF assumption.

A Poisson curve would probably be a much better approximation to real world data in most cases. Arrival statistics (failure analysis) are almost certainly Poisson rather than Gaussian distributed. A Poisson distribution may be just as complicated to analyze as the GDF, but it requires only one variable to describe it.

Clearly data that has a binomial (polynomial) distribution should be analyzed using the appropriate distribution function. Modern computers make counting easy – at least as easy as integrating the GDF.

A Uniform Distribution Function (UDF) is a two parameter function that can be used to approximate any distribution that a GDF can approximate. The appropriate UDF is never different from the GDF by more than 13%. It is easier to visualize, easily and intuitively integrated to calculate probabilities, and since it is an approximation to reality (just as the GDF is) it is possible that it is no less accurate.

The remainder of this article centers on how the UDF can be used in place of the GDF.

Comparing UDF to GDF

For comparison between the Gaussian and uniform distribution functions I shall focus on a normal distribution function (that is a GDF with mean 0 and standard deviation 1) and compare it to a UDF with mean zero and width three (a constant height of 1/3 to guarantee the integral of the entire distribution is 1) This function will be referred to as U(0,3).

Calculating the Probability confidence intervals about the mean for both functions is shown in Table 1.

Table 1. Comparison of Normal and U(0,3)

x lower	x upper	Confidence Limit of Normal Distribution	Confidence Limit of U(0,3)	difference
-2	2	0.95	1.00	-0.05
-1.9	1.9	0.94	1.00	-0.06
-1.8	1.8	0.93	1.00	-0.07
-1.7	1.7	0.91	1.00	-0.09
-1.6	1.6	0.89	1.00	-0.11
-1.5	1.5	0.87	1.00	-0.13
-1.4	1.4	0.84	0.93	-0.09
-1.3	1.3	0.81	0.87	-0.06
-1.2	1.2	0.77	0.80	-0.03
-1.1	1.1	0.73	0.73	0.00
-1	1	0.68	0.67	0.02
-0.9	0.9	0.63	0.60	0.03
-0.8	0.8	0.58	0.53	0.04
-0.7	0.7	0.52	0.47	0.05
-0.6	0.6	0.45	0.40	0.05
-0.5	0.5	0.38	0.33	0.05
-0.4	0.4	0.31	0.27	0.04
-0.3	0.3	0.24	0.20	0.04
-0.2	0.2	0.16	0.13	0.03
-0.1	0.1	0.08	0.07	0.01
0	0	0	0.00	0.00

The maximum difference between the two distribution functions when used to calculate confidence limits is never more than 13% and the average (RMS) difference is about 6%. These results can be improved slightly by using U(0,3.12).

Conclusions

A gaussian distribution function is just an approximation to reality, it is difficult to integrate (to determine probabilities) and has no closed form solution for the cumulative distribution function. A uniform distribution function is also an approximation to reality but it is easy to visualize, easy to integrate and has a simple closed form solution for the cumulative distribution function. And, finally, the UDF is not significantly different from the GDF for the purposes of estimations and approximations.

So to answer the question posed earlier “why assume a GDF for the collected data that we know to be incorrect?” I think the answer is that it is complicated enough to justify the need for the analyst, and simple enough that the analyst knows how to handle it.

Why not a UDF (or a triangular or even a Poisson) distribution function? Well the first two are too simple – they don’t justify the analysts job. A Poisson, while needing only one variable to describe it and probably being more reflective of reality is just not understood by most engineers/analysts.

 

 

 

 

On the Dangers of “The Other Guy”

When considering driving during a winter storm, most people (at least it seems to me) are very confident in their own abilities to navigate the treacherous conditions that wintertime driving presents. They do however recognize one condition for which they cannot control and for which they have a healthy fear: “The other guy”.

I have discussed this with an unscientific but large set of people and they essentially wholeheartedly and universally agree that the biggest problem with winter driving is “the other guy”.

I find it interesting that I have never met anyone that is “the other guy”.

Just in case you are interested – I am not the other guy – I don’t drive in winter driving conditions – but somebody must be. Hmmm?

 

In Memory of Bernie

Over the years – I spent 20 summers in Swains Creek – I experienced many things, learned a lot about nature, met quite a few good folks and made a lot of friends and memories. At the top of the list are the Osterhouts and their pets – Blacquer and Bernie.

We (Kathy and I) were surrogate parents for both of those animals: Blacquer on a permanent basis and Bernie on an ephemeral and temporary basis. If anyone has a claim to part “ownership” of Bernie, Kathy and I have that right.

We took care of Bernie one whole summer in California while the Osterhouts traveled east; for a week one year in Hawthorne, NV when he was evacuated from the fire; and for one week in Swains while house sitting for the Osterhouts. We also looked after him for innumerable days at the Ranch when he just felt like spending time with one of his favorite buds. He had many a sleepover with us.

I don’t remember Bernie as a puppy – he was always the Big Dog – but he was always the puppy to me.

Blacquer passed away – he died in my lap – a couple years ago. I knew at the time that Bernie’s days were numbered. It doesn’t make his passing any easier to take. I will miss that dog – he made my life better.

Below are some of my favorite memories collected in no specific organization.

Bernie and the Truck

We regularly used Becca’s kitchen to make pizzas (my Hacienda did not have a working oven) on Friday or Saturday evenings. One night after enjoying an evening at the Osterhouts we were packing up to drive home and discovered that Bernie was sitting in the front seat of my truck.

Now I only have a small Tacoma, so when Bernie was in the front seat there was no room for anyone else – including Kathy. I asked Bernie to get out – he said no. I even attempted to force him out. Believe it or not, he growled at me. No, I’m not moving. So, Kathy got to ride in the back of the truck – just so we could get home.

As soon as we arrived at “the Ranch” Bernie hopped right out. All he wanted was a free ride to my place. Go Figger.

Bernie and the Turkey, the Porcupine and the Bear.

The final score was 2-2. The interesting part is Bernie’s two victories came at the expense of the bear.

While walking on one of the myriad of closed roads in the Swain’s creek area with Bernie we came across a nice Turkey. Bernie as was his wont was running ahead and so naturally discovered the bird first. Sure enough, in an act of bravery he literally ran behind me and cowered. Turkey 1 Bernie 0

On one walk, he got into a fight with a porcupine. I’m sure the porcupine lived to tell the tale as did Bernie, but Bernie had so many quills in his face he looked like a pincushion. Some were so close to his eyes and in his gums that he would not let me, or even Andy, remove them. A couple of hundred bucks and a trip to the vet (anathesia for a 165 pounds of dog ain’t cheap) and Bernie was fit to fight again.

During the summer that Bernie visited me in California he encountered (to my knowledge) two bears. Both times his size and incessant barking convinced the bear that discretion was the better part of valor and the bear went another way. It was probably a good thing that Bernie was “on the hook”.

Bernie and the Bar.

In 2012 there was a major fire (the Shingle Fire) threatening Swains Creek and a mandatory evacuation. As I was leaving I thought I should drive by Andy’s and see if there was anything I could do to help. Andy, for the only time I knew him looked to be at a bit of a loss as he tried to pack up the family, the pets, the appropriate mementos, clothing, and lord knows what else. It was possible that this would be his last chance to get anything from his home.

Well, he looked at me and said, “Can you take the Dog?” Can I take the Dog!!? Of course I can take the Dog. Hey, if Swains were to burn to the ground at least I’d have Bernie. We took Bernie home with us for a week while the fire burned.

We took Bernie to the local bar every day. He was a big hit around town. I loved going for walks with Bernie whether here in Hawthorne, NV; at the Woods in Markleeville, CA; or around Swains Creek.

Bernie and Breakfast Dishes

It was quite common for us to wake up in the morning at the Ranch and find Bernie on our deck.

We would usually let him lick the remains off of our breakfast dishes. Kathy would put the dishes down on the deck and Bernie would chase them around the deck for a while as he scraped the paltry remains from the plate.

He would finish by placing a paw onto the plate to hold it in place as he finished the cleaning job. Then … he would pick the plate up with his mouth and return it to the hacienda.

We always assume that if he could talk he would be saying “More please”.

Bernie and Lightning

Bernie was deathly afraid of lightning. He might hate being indoors – until the thunder rolled. You sure didn’t want to be in his way when he tried to hide from the thunder. He shivered and cowered and even lost bladder control with regularity when the thunder struck.

Poor dog –it thunders a lot on cedar Mountain.

The National Average Wage Index and Social Security Retirement Benefits

Introduction

Every year the Social Security (SS) Administration (SSA) calculates the National Average Wage Index (NAWI). This index is used to adjust the Salary Index Series (SIS) used to adjust past wages in the calculation of Average Indexed Monthly Earnings (AIME). It is also used to adjust the Salary Cap (wages subject to with SS withholding) and the Bend Points (BP) used to calculate Primary Insurance Amount (PIA) from the AIME and ultimately your Social Security Retirement Benefit (SSRB).

That’s a lot of gobbledygook to say the SSA raises your expected SSRB each year based on an increase in average wages. Those that have attained age 62 no longer experience expected (or realized) benefit increases based on the NAWI, but rather on increases in the Consumer price index – but that is a different matter and not the subject of this article. The intent of using increases in the NAWI (rather than the increase in consumer prices) is that the NAWI is more reflective of increases in the overall standard of living. Increases in consumer prices do not reflect increases in living standards – but rather the cost to maintain the same standard.

How raising both the BP and the SIS act to increase your PIA (and ultimately your SSRB),  is not totally clear.  What I intend to do here is show the mechanics of each of the detailed steps. How each of the steps effects your benefit, and how combined the result will increase your expected benefit by an amount equal to the increase in average wages across the nation.

The National Average Wage Index

The SSA calculates the NAWI – two years in arrears – as the average wages of all persons, nationwide, in jobs subject to SS withholding. How this number is calculated is, I’m sure, a most interesting subject in its own right. For now, we will just take it as a given. The NAWI for 2017 is 50,321.89. The NAWI for 2016 was 48,642.15. The 2017 index is 3.45 percent higher than the index for 2016.

The NAWI series for 1951 thru 2017 can be found at https://www.ssa.gov/oact/cola/AWI.html .

The Salary Index Series

The SIS is the set of numbers (the SSA refers to these as indexing factors) reflecting the cumulative effect of changes in the NAWI. Wages are indexed to the NAWI to ensure that a worker’s future benefits reflect the general rise in the standard of living that occurred during his or her working lifetime.

Your SIS – used to calculate your AIME and ultimately PIA – is updated each year until you reach age 62. Table 1 shows part of the actual SIS for persons reaching age 62 in 2019 and 2018

Table 1. Salary Index Series for Persons attaining age 62 in 2018 and 2019.

2018 SIS			2019 SIS
Year	Salary Index		Year	Salary Index
2012	1.09748		2012	1.135379
2013	1.08363		2013	1.12105
2014	1.046484		2014	1.082621
2015	1.0113		2015	1.046223
2016	1		2016	1.034533
2017	1		2017	1
			2018	1

I will show how this is used in the update the salary cap and BP next, but first note that as a result of the NAWI increasing by 3.45% (it technically increased by 3.4533%) the Salary Index for any given year has increased by 3.45%.

For example, the salary index for the year 2015 has increase for the 2019 SIS vs. the 2018 SIS from 1.0113to 1.046223: an increase of 3.45%. Each of the Salary indices has increased by precisely the amount of the NAWI increase – 3.45%.

Your specific SIS can be found at https://www.ssa.gov/oact/cola/awifactors.html .

The Salary cap and Bend Points

The salary cap (the cap on wages subject to SS withholding) and the BP (used in determining you AIME) each increase by the percentage increase in the NAWI subject to the SSA’s round up or truncate rules which will not be discussed.

In 2018 the salary cap was $128,400. In 2019 it increased to$132,900 – An increase just over 3.45% (just over as a result of the aforementioned rounding rules).

The BP move similarly. Each changing precisely by the increase in NAWI – again subject to rounding rules.

Table 2 summarizes NAWI, Salary cap, and BP for 2018 and 2019. These data will be used in upcoming calculations to show how they work to increase benefits. A complete series of BP is available at https://www.ssa.gov/oact/cola/bendpoints.html .

Year	NAWI	Salary Cap	First BP	Second BP
2018	48,642.15	128,400	895	5397
2019	50,321.89	132,900	926	5583

Calculating Average Indexed Monthly Earnings

To calculate AIME, you must:

1. assemble all of your yearly wages (only those wages subject to SS withholding).
2. multiply the raw wages by the appropriate SIS for that year to determine the yearly indexed incomes.
3. sum the highest 35 years of yearly indexed incomes.
4. divide the sum by 420 (the number of months in 35 years).

One can easily recognize that if the SIS for every year has increased by the NAWI increase, then each yearly indexed income will increase, the sum will increase, and the AIME will increase by the identical amount.

Finally Determining Your Primary Insurance Amount

Now your primary insurance amount is calculated using the BP. Your actual PIA is only calculated once the BP are determined in the year you turn 62. From that point on your BP are fixed. But, to see how this works to increase you SSRB, we will consider someone under age 62 – one shoes BP are still in flux.

The formula is simple. Your PIA is the sum of:

1. 90% of AIME up to the first BP
2. 32% of your AIME above the first BP but below the second BP, and
3. 15% of your AIME above the second BP.

Your PIA is used to determine your SSRB; more if claiming after Full Retirement Age (FRA), less if claiming before FRA. It is also the number used to calculate a spousal benefits.

How All the Numbers Work Together

Now that we have all of the numbers and formulae, let’s take a look in detail how they work together to give an individual a benefit increase equal to the increase in NAWI.

First case: AIME in 2018 less than first BP

Assuming only an average change in salary (3.45%) from 2018 to 2019 then as pointed out above each yearly indexed salary will increase by the same 3.45%. The new AIME will increase by 3.45% but, per force, will remain below the 2019 first BP as it too increases by 3.45%.

Therefore the PIA, which remains 90% of AIME, will increase by the increase in AIME or 3.45%

Second Case: Income above first BP

While it is not as clear as the first case, the result will be the same. An example is probably best to show the arithmetic details.

Suppose the AIME in 2018 were $2500. The 2018 PIA is calculated as the sum of

1. 0.9 * 895 = 805.5
2. 0.32 * (2500-895) = 0.32 * 1605 = 513.6

A total of 1319.1

In 2019 his AIME increase to 2587 (a 3.5% increase). His PIA calculation changes as follows (using the new income and the new BP):

1. 0.9 * 926 = 833.4
2. 0.32 * (2587 – 926) = 0.32 * 1661 = 531.52

a total of 1364.92

We note that the contribution to PIA up to the first BP has increased (from 805.5 to 833.4) by 3.45% due to the increase in the BP. The contribution above the first BP has also increased because the AIME in excess of the first BP has increased. It is easily seen using the distributive law that (2587 – 926) is 1.0345 * (2500-895) so that the excess income above the new first bend point has also increased by 3.45%.

The end result is that raising the SIS, the salary cap, and the BPs will give a PIA calculation that keeps pace with salary inflation. A similar example could be given for AIMEs greater than the second bend point.

Conclusion

The NAWI impacts the salary cap, the BP, and the SIS – all similarly. The net result is that an individual that has yet to reach initial retirement age can expect that his AIME will also increase as the NAWI does.

Increases in AIME and the BP tend to increase the PIA by an amount just equal to the NAWI increase. This article has shown that “Such indexation ensures that a worker’s future benefits reflect the general rise in the standard of living that occurred during his or her working lifetime” – the stated goal of the SSA.

The SSA has an excellent pair of examples showing AIME calculations and PIA calculations (plus how COLA effects PIA calculations after age 62). It can be found at https://www.ssa.gov/OACT/ProgData/retirebenefit1.html .

 

 

Thoughts On the Social Security Actuarial Imbalance

Wage inequality effects

There have been several articles discussing how the growth in wage inequality has been a major (if not the sole) cause of the Social Security (SS) trust fund’s current actuarial under funding. (Google “wage inequality effect of SS” for a series of articles.) Essentially everyone agrees that the growth of wage inequality has hurt the actuarial balance of the SS trust fund (and some suggest that it is entirely at fault).

In 1983 about 90% of wages were subject to SS withholding and it was expected that that percentage would remain basically constant. However due to growing wage inequality, only 83% of the current wage base is subject to SS withholding – that is, it is below the salary cap.

Further, everyone seems to come to the conclusion that the shortfall in the trust fund’s long term viability is caused by the diminished tax collection due to the increase of incomes above the salary cap – that is, due to increasing wage inequality.

This is disingenuous at best.

While increases in wages earned above the salary cap are not fully taxed, they also garner minimal increases in benefits. They do, however, have the effect of raising the National Average Wage Index (NAWI) – and that index is used to increase benefits for everyone – including those below the salary cap that may not have experienced any wage increase. It is the imbalance of the benefits increase vs. the new tax revenue that is the problem.

To put it simply, SS benefits rise with NAWI, but tax revenue only rises with wages below the salary cap. The solution could be raising the salary cap. The solution could also be correcting the unintended rise in benefits conferred on lower incomes by upper incomes effects on NAWI.

For a full description of the problem see https://shawnpheneghan.wordpress.com/2019/02/28/wage-inequality-and-social-security/

I fully support raising, or even eliminating, the salary cap. However, my support for its increase does not stem from the current under funding situation caused by increasing wage inequality, but rather from the still unfunded legacy costs – see https://shawnpheneghan.wordpress.com/2018/04/06/social-security-problems-and-solutions-perceptions-and-realities/ .

In addition to increasing/eliminating the salary cap the formulas benefit increases should be changed to adjust the benefit bend points and salary indices used to calculate the Primary Insurance Amount. The original salary cap and its definition could be maintained and used to cap benefit calculations. The bend point and salary index calculations should use the average wage of all those that earn less than the Salary Cap. Bend points and salary index calculations could also depend on median incomes. These would be more in keeping with the original intent to set retirement benefits based on your lifetime income – and yet intended to reflect the general increase in lifestyle of generally rising incomes.

The original idea behind using NAWI to determine the salary cap and bend points was that benefits would grow to match the indexed salaries of the beneficiaries. The growing wage inequality has put that correlation out of whack – benefits are growing based on the NAWI that no longer reflects (and has not reflected for nearly 40 years) the salary of the beneficiaries.

How big is this problem

In 1990 The median and average wages for workers in SS covered jobs were $14,500 and $20,200 respectively. The Salary cap in 1990 was $51,300, and the average wage for the 120 million workers earning 50K/yr or less was $15,800.

By 2017 the median and average wages were $31,600 and $48,300 respectively. The salary cap had risen to $127,200 and the average wage for the 155 million workers earning 125,000/yr or less had risen to $35,400.

Between 1990 and 2017:

1. The median worker saw a salary increase of 117%
2. Workers below the SS salary cap saw a salary increase of 124%
3. The average worker saw a benefit increase of 139% (https://www.ssa.gov/oact/cola/central.html)
4. The NAWI has increased 147%.

Remember that benefits rise with average wage increases. The average worker with salary  below the SS salary cap experienced a 124% salary increase and a benefit increase of 139% or a 15% unexpected, unintended, and essentially unfunded increase.

To put that into dollar terms, a 1990 beneficiary receiving $585/month would receive about $1400/month in 2017 – those are just about the average benefit amounts and represent the 139% increase in NAWI. Had the benefits been tied more closely to the actual average wage increase of the actual beneficiary (those with salaries below the salary cap) the 2017 benefit would be $1312. The average worker is today receiving 7% more than was expected when the SS rules for determining benefits was established.

The under collection of taxes (83% vs 90%) of the wage base is essentially the same problem as the benefit increase (7%). It is likely that changing either of these will make a significant (if not total) correction to the actuarial imbalance of the SS trust funds. Doing both would certainly fix the problem. Raising the cap beyond 90% would help address the legacy cost issues and over fund the trust fund – allowing a decrease in the tax rates of those currently paying SS withholding.

Conclusion

The Greenspan Commission recognized several issues facing both the short and long-term health of the SS trust fund including increasing life expectancy and a diminishing ratio of workers to retirees. It attempted to address these issues – even if it may have done so inadequately. However, in its attempt to ensure a 75-year actuarial lifetime for the trust fund it failed to foresee significant changes in wage distribution that would negatively impact the trust fund balance.

The growth of wage inequality has resulted in a significant fraction of the national wage base occurring above the salary cap– and therefore not subject to the SS withholding, but also caused benefits to rise faster than anticipated (or originally planned). The combination is a major cause of the current actuarial imbalance in the SS trust fund.

Fixing the imbalance by both raising the cap and adjusting how benefits are calculated – possibly even rolling back some of the unintended increases – can re-secure the trust fund, correct at least some of the legacy cost issues and possibly even allow for a small rollback in SS withholding taxes.

 

Wage inequality and Social Security

Introduction

SS taxes are collected on income up to the salary cap. The salary cap as of 2018 is $128,400. It has been (and continues to be) adjusted each year to reflect gains in the National Average Wage Index (NAWI). The NAWI is also used to adjust the “bend points” in Social Security’s formula for calculating your benefit amount.

What we will do here is set up a simple system and show how SS benefits are calculated. Then we will use that system to show how the SS system works to adjust benefits to match NAWI gains; first by using across the board salary gains and then making changes that increase salary inequality.

This simple analysis shows that increasing wage inequality enhances average benefits while reducing tax collections relative to the benefit growth.

The Experimental system

To show how the system works and how things change with increasing salaries and increasing inequalities we shall use a very simplistic model. It does however capture the essence the effects of salary changes on the salary cap, the bend points and the Primary Insurance Amount (PIA) calculation.

Start with a population of four people (or groups); one each earning yearly salaries of 10,000; 20,000; 30,000 and 40,000 dollars. These people pay 10% tax on earnings up to the salary cap; which for this example is 30,000 dollars. We will further assume that these are representative of the average indexed yearly incomes (AIYI) and thus can be used to calculate expected benefits

Table 1. Wages, Taxes, Benefits of the baseline population

	wages	tax rate	taxes		benefit
	10000	10%	1000		9000
	20000	10%	2000		12200
	30000	10%	3000		13700
	40000	10%	3000		13700

Table 2. Bend Points and Salary cap for the initial calculations

Salary Cap	30000
First bend point	10000
Second Bend Point	20000

Annual benefits are calculated using the standard SS formula to calculate the PIA. Specifically 90% of income up to the first bend point (10K) 32% of the income above the first bend point and below the second bend point (20K) and 15% of income above the second bend point up to the salary cap (30K).

From Table 1 we can see the following:

• Total income: 100,000
• Average income 25,000
• Total taxes: 9,000 – 9% of total income
• Total benefits: 48,600

Obviously these incomes, the distribution of these incomes, the salary cap, the bend points, and the tax rates are all set specifically to show a result – not to reflect reality. They do however show how things actually work. Specifically, they show how the bend points work to calculate PIA and they show how the salary cap limits taxes, and benefits, at higher incomes.

Benefits and taxes for equitable pay increases

Now let’s consider what happens to each of the details if salaries increase by 10% across the board (an equitable salary increase). If all salaries increase by 10% the NAWI increases by 10%. The salary cap and bend points also each increase by 10%. Table 3 shows the results of the wages, taxes and benefits while Table 4 shows the new bend points and salary cap

Table 3. Wages, Taxes, Benefits after 10% across the board increase in salary

wage growth	wages	tax rate	taxes total		benefits
10%	11000	10%	1100		9900
10%	22000	10%	2200		13420
10%	33000	10%	3300		15070
10%	44000	10%	3300		15070

Table 4. Bend Points and Salary cap after 10% across the board increase in salary

Salary Cap	33000
First bend point	11000
Second Bend Point	22000

From Table 3 we can see the following:

• Total income: 110,000 – a 10% increase
• Average income 27,500 – a 10% increase
• Total taxes: 9,900 – 9% of total income and a 10% increase in total dollars
• Total benefits: 53460 – a 10% increase

The bottom line on a 10% across the board salary increase is that SS retirement benefits increase by 10%. This increase is matched by the tax increase – also 10% increase. Further, comparing Tables 1 and 3 one can see that each individual has experienced a 10% gain in benefits. So, not only has the benefit gain been matched by a revenue gain (each increasing by 10%) but the benefit gain is enjoyed equally by all beneficiaries.

But, what happens if the increase in salary is inequitable.

Benefits and taxes for inequitable pay increases

Let’s consider what happens if the salary increase is concentrated on the highest income levels. To see what happens we examine this in the extreme – all of the 10% salary gain goes to the person earning 40K. In this case the result is shown in Tables 5 and 6.

Table 5. Wages, Taxes and Benefits after an inequitable 10% salary increase.

wage growth	wages	tax rate	taxes total	indexed wages	benefits		benefit increase
0%	10000	10%	1000	11000	9900		10.0%
0%	20000	10%	2000	22000	13420		10.0%
0%	30000	10%	3000	33000	15070		10.0%
25%	50000	10%	3300	44500*	15070		10.0%

* This number is estimated – but as it is well above the salary cap, its true value is unimportant.

Table 6. Bend Points and Salary cap after an inequitable 10% salary increase.

Salary Cap	33000
First bend point	13000
Second Bend Point	22000

It is most important to note that while wages for the lowest three individuals did not increase – their indexed salary does increase. Assuming (as I did at the start) that the baseline number was the AIYI, then a 10% increase in the NAWI will result in an increase to the AIYI of all individuals. N.B. Taxes are collected on income; benefits are paid on AIYI.

From Table 5 we can see/calculate the following (vs. the baseline case):

• Total income: 110,000 – a 10% increase
• Average income 27,500 – a 10% increase
• Total taxes: 9,300 – 8.5% of total income and a 3.3% increase
• Total benefits: 53460 – a 10% increase

The important things to note in the case of an inequitable average salary increase:

1. Average salary increase – 10%
2. Salary cap and Bend Points each increase by 10%
3. Average Benefit increase – 10%
4. Average tax increase – 3.3%
5. The increased benefit has been enjoyed by all people (that is, at all incomes) .

Looking at Notes 3 and 4 we can see that average benefits increase faster than tax revenue. This is not seen with an across the board salary increase. The difference is that the 10K of income gain was not fully subject to the 10% tax rate. As the salary cap increased by 10% (from 30K to 33K) only an additional 3K of this individual’s income was subject to the tax. At a 10% rate that equals an additional $300 – which is 3.3% of the baseline 9000. No one else’s wages or taxes paid increased.

Comparing tables 4 and 6 show that the bend points and salary caps care not which cohort enjoys the salary increase – they vary only with the NAWI.

The total tax rate on total income has fallen to 8.5% from a baseline rate of 9%.

And most interestingly, benefits have increased for all people even while income remained the same for most of the population.

This leads us to the final question – what would have happened had the benefits stayed the same for those individual whose salary remained the same?

Inequitable pay increases but equitable benefit increases.

Let’s take a look at how things change if we allow the salary cap to increase, but index benefits to the actual gains experienced by the individuals. That is, we don’t allow the gains above and beyond the salary cap to influence the benefit calculation for those that did not see a salary increase.

Again we will examine the extreme case where all NAWI gains are due to the highest income individual. However, benefits for those that experienced no income gain also experience no benefit gain. The results are shown in Table 7.

Table 7. Inequitable wage increases but equitable benefit increases

wage growth	wages	tax rate	taxes total		benefits		benefit increase
0%	10000	10%	1000		9000		0.0%
0%	20000	10%	2000		12200		0.0%
0%	30000	10%	3000		13700		0.0%
25%	50000	10%	3300		15070		10.0%

From Table 5 we can see/calculate the following (vs. the baseline case):

• Total income: 110,000 – a 10% increase
• Average income 27,500 – a 10% increase
• Total taxes: 9,300 – 8.5% of total income and a 3.3% increase
• Total benefits: 49970 – a 2.8% increase
• Only the individual at the highest level contributed to the NAWI, and only this individual experiences any gain in benefit.

The important thing to note here is that tax revenue has grown faster than benefits (3.3% vs. 2.8%).

Discussion

There have been several articles discussing how the growth in wage inequality has been a major (if not the sole) cause of the SS trust funds current actuarial under funding. (Google “wage inequality effect of ss” for a series of articles.) Most of these articles are either not detailed or are so convoluted as to be totally opaque.

Still, most articles confirm that wage inequality is hurting the actuarial balance (and some suggest that it is entirely at fault) of the SS trust fund. I have no intention of delving into the details of all of these analyses.

Most (all?) people that study this problem (growing wage inequality) come to the conclusion that the shortfall is caused by the diminished tax collection (8.5% vs. 9% of total income). But I think this analysis shows that the problem can be equally attributed to increased (and unearned) benefits.

As shown in Table 5, 75% of the population was rewarded with a benefit increase due to the increased indexing – that was entirely attributable to only 25% of the population. Table 7 shows how removing that “unearned” benefit gain actually enhances the actuarial balance of the SS trust fund as revenue growth exceeds benefit growth.

I undertook this simple analysis to see how rising inequality really does under fund the SS trust funds because it was not clear to me how this worked – short of the obvious more income is not taxed. However, while the income is not taxed – there was apparently no benefit gain either and so it should not have affected the system balance.

After reviewing this simple system it is obvious how wage disparity has put the system out of whack. Higher incomes even while not taxed (or at least not fully taxed) do result in higher benefits (benefits grow in excess of revenue growth) for everyone.

This analysis makes no claim as to the size of the impact of growing wage inequality on the SS trust funds longevity. I only intended to show that it is real and try to understand some of the mechanics of how it works.

Conclusions

Growing wage inequality causes benefits to rise disproportionately to the taxes collected. This impacts the long-term viability of the SS trust funds.

The cause of the imbalance can be traced to

1. inadequate tax collection – due to the salary cap, or
2. unearned (and unfunded and probably unintentional ) benefit increases due to salary indexing.

It would take a lot more effort, modeling, data, etc. than I have the time or resources to devote to fully analyze the situation and assess the total impact. But make no mistake – the effect is real. It is disingenuous to attribute the entire imbalance to a failure to collect taxes on income above the salary cap as it can equally well be attributed to the benefit formula that rewards lower incomes with increased (and unearned) benefits based on the NAWI increase.