SS (Social Security) EMTR (Effective Marginal Tax Rate)

By Alan Silverstein, Fort Collins, Colorado. Email me at ajs@frii.com.
Last update: April 5, 2016
Much appreciation to Cloud Swift and Tom von Alten for reviewing this webpage.

Here are some thoughts about the EMTR (effective marginal tax rate for federal income taxes) experienced by people receiving SS (Social Security) payments (and in fact railroad benefits too) in the USA, when they have other non-SS income that pushes some or all of their SS receipts into the taxable range. (So far so good?)

Note:

The SS taxation details are in the IRS Social Security Benefits Worksheet. This worksheet pulls information from various Form 1040 lines, especially 20a "Social security benefits" (as of 2015), to calculate your number for line 20b "Taxable amount". And while like many tax forms the instructions are straightforward, the math behind them is hidden by "elbonian logic."

Whenever you have a progressive tax system like this, there are unexpectedly high marginal effects in the middle somewhere as you transition from zero to max phase-in of taxability. -- Or in other cases for the phase-out of deductions or credits, such as the 9.5-18% marginal loss of ACA PTC (premium tax credits) below 400% of FPL (federal poverty line).

(Uh oh, readers' eyes glazing over now? If you just want to see the bottom line, drop to the example table below.)

I got curious, "how does this really work?" In particular, what's the effect (EMTR) of earning one more non-SS dollar? Note that additional non-SS income is somewhat optional for retired people doing tax-efficient financial planning to support their spending needs.

In several IRS or SS webpages (such as this one), it says:

  If you:
  - file a federal tax return as an "individual" and your combined
    income is
    + between $25,000 and $34,000, you may have to pay income tax on
      up to 50 percent of your benefits.
    + more than $34,000, up to 85 percent of your benefits may be
      taxable.
    ...(and similar text for joint returns)

Where "combined income" = CI = AGI (adjusted gross income) + SS/2 + non-taxable interest; minus a few items not mentioned in the IRS or SS webpages but built into the worksheet on line 6, to whit: Above-the-line deductions on lines 33-35 (student loan interest, tuition and fees, and domestic production activities) apparently don't reduce your SS taxability. The reason SS is divided by 2 is to account for the fact that it's only 50% taxable above the first breakpoint (X1 below).


I reversed engineered the math from the worksheet for just the most two common filing statuses as shown in the table below. Looks complicated, right? Yeah that might be your main take-away here. It's very hard to model and predict this effect without using software! Barreling ahead anyway --

To figure the EMTR, first you must consider the taxability of SS income, then relate that to tax brackets as applied to TI = taxable income. TI (Form 1040 line 43 in 2015) is AGI (Form 1040 line 37) less exemptions and standard or itemized deductions. More explanation and some examples follow the table.

(as of TY2015) Single Married filing jointly
SS taxability thresholds:
50% = X1 $25,000 $32,000
85% = X2 $34,000 $44,000
X2 - X1 (for use below) $9,000 $12,000
Combined income CI = (AGI + SS/2 + tax-exempt - a few items)
  0% taxable, CI ≤ X1 $0 $0
50% taxable, X1 < CI ≤ X2 0.50 * min(SS, (CI - 25K)) 0.50 * min(SS, (CI - 32K))
85% taxable, X2 < CI (*) 0.85 * min(SS, (CI - 34K) + 5294.11) 0.85 * min(SS, (CI - 44K) + 7058.83)
(single overall form) min(0.85 * SS, max(0, 0.50 * min(SS, CI - X1, X2 - X1)) + max(0, 0.85 * (CI - X2)))
TI = taxable income = AGI - minimums below if no special cases (blind, 65+, dependents, etc):
standard deduction $6,300 $12,600
exemptions $4,000 $8,000
minimum total $10,300 $20,600
Tops of federal tax brackets applied to TI (per Form 1040-ES):
10% = B10 $9,225 $18,450
15% = B15 $37,450 $74,900
25% = B25 $90,750 $151,200
And so on for higher tax brackets...
SS EMTR:
0% = 0.50 * 0% MTR CI < X2, TI ≤ B10 (see below)
5% = 0.50 * 10% MTR CI < X2, B10 < TI ≤ B15
7.5% = 0.50 * 15% MTR CI < X2, B15 < TI ≤ B25 (unlikely in reality)
8.5% = 0.85 * 10% MTR CI ≥ X2, B10 < TI ≤ B15
12.75% = 0.85 * 15% MTR CI ≥ X2, B15 < TI ≤ B25
21.25% = 0.85 * 25% MTR CI ≥ X2, B25 < TI
And so on for higher tax brackets...

* On the "85% taxable" row, the odd constants (5294.11 and 7058.83) are just the X2-X1 differences times 50% then pre-divided by 0.85, that is, ($4500 / 0.85) or ($6000 / 0.85), to make the two SS taxability equations easier to compare. In other words, any taxable SS falling in the X1-X2 range is 50% taxable before the rest is 85% taxable.

The "single overall form" row shows the combined math (no need to identify the proper range) by adding some "max" functions to clip low ends at zero. See later in this webpage for its derivation.

The table above illustrates how your SS income can be:

The table rows below "SS EMTR" are based on combining SS taxability due to CI thresholds (X1, X2) with TI tax brackets (B10, B15, B25, etc). As mentioned above, this is really the AMTR for SS income only.


For example, a single filer with CI in at least the lower part of the 50% taxable range (CI > $25K), a standard deduction, and one exemption, likely falls in the 10% federal marginal tax bracket/rate (MTR) because their AGI is at least X1 = $25K after adding taxable SS income (50% of total SS), so their TI is at least $14,700 after minimal deductions and exemptions, which exceeds B10 = $9,225. Each extra non-SS dollar of income costs them at least 50% of 10% = 5% as their (unchanged in this example) SS income rises in taxability.

Remember that EMTR (really AMTR for SS income only here) is the marginal rate for the next dollar of income. It is the marginal level of SS taxability (0%, 50%, or 85%) multiplied by the overall marginal tax bracket (10%, 15%, etc) applied to taxable income (including 50% or 85% of SS income). And it applies in addition to the ordinary federal MTR. Say you're in the 10% MTR and your non-SS income goes up $20, then you might owe $2 more of income tax on that plus $1 more income tax on a previously untaxed portion of your SS income that got "pushed above X1."

So this SS EMTR is kind of a double whammy on your discretionary non-SS income. In fact if the combined increased taxable income pushes you into a higher tax bracket, it's a triple whammy!

More examples: This math can be hard to follow partly because non-SS and SS income are independent variables, and the SS EMTR really depends on both, along with many other factors mentioned earlier. Here are some actual dollars, assuming nearly all income is non-SS, the SS portion is unrealistically trivial (rounded down to zero here), and no other complications, meaning just a standard deduction, minimal exemptions, and MAGI = AGI. Here "na" means "not applicable". Amounts in bold font are the SS income or TI (tax bracket) breakpoints that matter.

SS EMTR (really AMTR) (with trivial SS) for non-SS income exceeding (resulting in TI = taxable income at most):
(as of TY2015) Single Married filing jointly Comments
0% $19,525 (TI = $9,225) na SS still 0% taxable, TI now in 10% bracket
0% na $32,000 (TI = $11,400) SS becomes 50% taxable, but TI in 0% bracket
5% $25,000 (TI = $14,700) $39,050 (TI = $18,450) SS becomes/still 50% taxable, TI still/now in 10% bracket
7.5% na na SS still 50% taxable, TI now in 15% bracket (unlikely)
8.5% $34,000 (TI = $23,700) $44,000 (TI = $23,400) SS becomes 85% taxable, TI still in 10% bracket
12.75% $47,750 (TI = $37,450) $95,500 (TI = $74,900) SS still 85% taxable, TI now in 15% bracket
21.25% $101,050 (TI = $90,750) $171,800 (TI = $151,200) SS still 85% taxable, TI now in 25% bracket

You can see that the SS EMTR question is non-trivial. Even with many simplifying assumptions, the EMTR increases in odd steps as non-SS income and/or TI (taxable income) ratchets up through either SS taxability breakpoints or tax bracket boundaries.

Also, reducing non-SS income and increasing SS income equivalently is not a direct substitution since the SS portion is only 50% or 85% taxed. Furthermore itemizing deductions and/or adding special deductions, or adding more exemptions (for dependents), changes the relationship between AGI (including the taxable portion of SS income) and taxable income (bracket boundaries). This math is "left as an exercise for the reader" (grin).


Reverse engineering the math from the Social Security Benefits Worksheet, by L = line number:

 L1 = SS + RRB         # just call this SS here though it might include RRB.
 L2 = L1/2 = SS/2
 ...
 L5 = L2 + MAGI        # see worksheet for specific lines in this modified AGI.
 L6 = various (but not all) deductions
 L7 = L5 - L6 = CI     # combined income; STOP if not positive.
 L8 = X1               # first threshold depending on filing status.
 L9 = L7 - L8 = max(0, CI - X1)   # excess over X1; note that CI includes SS/2.
L10 = X2 - X1 = X      # size of the 50%-taxable range.
L11 = L9 - L10 = max(0, CI - X2)  # excess over X2; note that CI includes SS/2.
L12 = min(L9, L10)     # excess over X1, capped at X.
L13 = L12 / 2          # capped excess at 50%-taxable rate.
L14 = min(L2, L13)     # further capped at SS/2.
L15 = 0.85 * L11       # excess over X2 at 85%-taxable rate.
L16 = L14 + L15        # sum of 50% and 85% taxable portions.
L17 = 0.85 * SS        # overall cap for high incomes.
L18 = min(L16, L17)    # whichever is less.

Top-down expansion of L18:

min(L17, L16)          # swap terms, start expanding:
min(0.85 * SS, L14 + L15)
min(0.85 * SS, min(L2, L13) + (0.85 * L11))
min(0.85 * SS, min(SS/2, L12 / 2) + (0.85 * max(0, CI - X2)))
min(0.85 * SS, (min(SS, L12) / 2) + (0.85 * max(0, CI - X2)))
min(0.85 * SS, (0.50 * min(SS, min(L9, L10))) + (0.85 * max(0, CI - X2)))
min(0.85 * SS, (0.50 * min(SS, min(max(0, CI - X1), X))) + (0.85 * max(0, CI - X2)))

And finally with some judicious simplification:

min(0.85 * SS,                                  # (a)
    max(0, 0.50 * min(SS, (min(CI, X2) - X1)))  # (b)
  + max(0, 0.85 * (CI - X2)))                   # (c)

(a) Overall limited to 85% of SS in the case where non-SS ≥ X2 + SS/2, pushing all of SS into the 85% range.
(b) In other words, 50% of min(SS, CI-X1, X2-X1), clipped at 0.
(c) In other words, 85% of CI - X2, clipped at 0.