Marginal Tax Rates

Appendix

Considerations

Not included are the child support deduction, excess shelter deduction, the dependent care deduction (which includes only expenses related to work or training) and deduction alterations for households with an elderly or disabled member. Additionally, some people are eligible for SNAP through categorical eligibility (e.g. people who receive cash benefits through TANF are automatically eligible for SNAP), which does not include a gross income limit. This chart does not show marginal tax rates for the small proportion of SNAP recipients who are categorically eligible for SNAP and have gross incomes above 130% of the poverty line.

Calculating SNAP Effective Marginal Tax Rates

SNAP is based around the idea that recipients should dedicate 30% of their income towards food purchases, with SNAP making up any shortfall between the 30% contribution and the amount of money needed to purchase a "nutritionally adequate low-cost diet".^[1]Aussenberg, Randy Allison (October 4, 2022). "Supplemental Nutrition Assistance Program (SNAP): A Primer on Eligibility and Benefits" . Congressional Research Service. Archived from the original on June 4, 2022. Consequently, the SNAP benefit formula takes a maximum benefit, defined as the amount of money needed to purchase such a diet (which varies by household size), and then subtracts from that 30% of net income: $$\text{Benefit} = \text{Maximum Benefit} - \text{30% of Net Income} $$

In 2023, maximum benefits were:^[2]"SNAP – Fiscal Year 2023 Cost-of-Living Adjustments" (August 2022). United States Department of Agriculture (USDA). Archived from the original on October 6, 2022.

Family Size	Maximum Benefit	Maximum Possible Annual Benefit
One	$281/month	$3,372
Two	$516/month	$6,192
Three	$740/month	$8,880
Four	$939/month	$11,268
Five	$1,116/month	$13,392

Note that these are the values for the 48 contiguous states and Washington D.C. They differ for Alaska, Hawaii, Guam, and the US Virgin Islands. SNAP is not available in Puerto Rico, American Samoa, or the Northern Mariana Islands.

Net income is calculated by subtracting from gross income a number of deductions. I include the two universally-available deductions: the SNAP standard deduction (this is separate from the standard deduction used for personal income tax) and the earned income deduction, which allows recipients to deduct 20% of their gross income. Some recipients can use additional deductions, like the deduction for court-order child support, but we will not consider them here. This results in the following formula for net income: $$ \text{Net Income} = \text{Gross Income} - .2 (\text{Gross Income}) - \text{Standard Deduction}$$ $$= .8 (\text{Gross Income}) - \text{Standard Deduction}$$

In 2023, SNAP standard deductions were:^[3]"SNAP – Fiscal Year 2023 Cost-of-Living Adjustments" (August 2022). United States Department of Agriculture (USDA). Archived from the original on October 6, 2022.

Family Size	Monthly Standard Deduction	Annualized Standard Deduction
Four or less	$193/month	$2,316
Five	$225/month	$2,700
Six or More	$258/month	$3,096

We can now establish a formula for SNAP benefit values. With $ B_{max} $ the maximum benefit and $SD$ the standard deduction, a person's SNAP benefit $B$ at gross income $I$ equals $$ B(I) = B_{max} - .3 (.8I - SD) $$

The effective marginal tax rate is calculated by considering the reduction in benefits as a result of an additional dollar of gross income, $ \Delta B = B(I+1) - B(I) $. This works out to: $$ \Delta B = B_{max} - .3 (.8(I+1) - SD) - (B_{max} - .3 (.8I - SD)) = -$0.24 $$

A $1 increase in income thus results in a $0.24 loss in benefits, which means the effective marginal tax rate is 24%. Intuitively, you can think of it this way: when gross labor income increases by $1, the 20% earnings deduction rises by $0.20, resulting in additional net income of only $0.80. Since recipients are required to dedicate 30% of their net income to food purchases, the overall result of a $1 increase in gross income is a .3($0.80)=$0.24 decrease in benefits.

This, however, only holds when net income is greater than 0. When net income is less than zero, the SNAP benefit is simply the benefit max. There is thus a 0% marginal tax rate until gross income reaches the level at which net income is greater than zero. We determine this by solving $.8I - SD = 0 $ for $I$, which results in $I = 1.25 SD$. These values for different family sizes are listed in the table below:

Family Size	Annualized Gross Income at Which Annualized Net Income Exceeds $0
Four or less	$2,895
Five	$3,375
Six or More	$3,870

There is one additional consideration we must take into account. While SNAP's benefit formula naturally phases down to $0, SNAP also includes a net income limit of 100% of the federal poverty line and a gross income limit of 130% of the poverty line. In other words, SNAP eligibility will abruptly cut off if either gross income exceeds 130% percent of the poverty line or net income exceeds 100% of the poverty line. These limits are listed by family size in the table below.^[4]"Texas Works Handbook: C-120, Supplemental Nutrition Assistance" (October 2022). Texas Health and Human Services Commission. Archived from the original on February 1, 2023.

Family Size	Gross Income Limit	Annualized Gross Income Limit	Net Income Limit	Annualized Net Income Limit
One	$1,473/month	$17,676	$1,133/month	$13,596
Two	$1,984/month	$23,808	$1,525/month	$18,312
Three	$2,495/month	$29,940	$1,920/month	$23,040
Four	$3,007/month	$36,084	$2,313/month	$27,756
Five	$3,518/month	$42,216	$2,706/month	$32,472

We need to determine which max, if either, beneficiaries will hit. The maximum eligible gross income $I_{max} $ can be determined by finding the minimum of the gross income limit and net income limit. From the gross income limit, $ I_{max} = 1.3 PL $. From the net income limit, $ \text{Net Income Limit} = PL = .8I_{max} - SD $, so $I_{max} = 1.25 (PL + SD) $. The condition is then $I_{max} = \text{min} \{1.3 PL, 1.25 (PL + SD)\} $.

We can plug in the values for each family size to determine which is the min. For households with one person, for instance, the standard deduction equals about $.17PL$, so $1.25 (PL + SD) = 1.25(PL + .17PL) \approx 1.46 PL$. Therefore, $I_{max} = 1.3PL $. Indeed, the gross income limit is the limiting factor for all family sizes considered, so $I_{max} = 1.3PL $ in all cases.

We might pause for a minute to wonder why the net income limit even exists, as the net income limit will always exceed the gross income limit simply as a result of the standard deduction. That is because in states with broad-based eligibility, people who are eligible for TANF or SSI are categorically eligible for SNAP, meaning they are not subject to the gross income limit. In this case, it is the net income limit that caps the gross income at which people are eligible for SNAP benefits. (You might notice that it is still somewhat nonsensical—the benefit formula is already based off of net income, so why not just let it phase down to $0?)

Next, we need to determine whether $I_{max} $ is less than the income $I_{zero}$ at which the benefit $B$ reaches zero. We solve $B(I) = 0 = B_{max} -.3(.8I_{zero} - SD ) $. This results in $ I_{zero} = 1.25( \frac{10}{3} B_{max} + SD ) $. We compare this with $I_{max}$ by plugging in the relevant values. The results of these calculations are listed in the table below.

Family Size	Gross Income at Which Gross Income Limit is Hit	Gross Income at Which Calculated Benefit Reaches Zero
One	$17,676	$16,945
Two	$23,808	$28,695
Three	$29,940	$39,895
Four	$36,084	$49,848
Five	$42,216	$59,175

Unsurprisingly, the gross income limit does indeed tend to work as a limit: for all household sizes except single-person households, benefits cut off before the calculated benefit reaches $0. This means that households with more than one person face a benefit cliff at the gross income limit. On the marginal tax chart, this manifests as a vertical line: an additional dollar of income over the gross income limits results in much more than a dollar reduction in SNAP benefits (to keep the axes reasonable, the actual EMTR of the benefit cliff—which is over 100,000%, is not depicted in its entirety). We can calculate the size of the benefit cliff by plugging $ I_{max} $ into the benefit formula, i.e. $ B(I_{max}) = B_{max} - .3 (.8 I_{max} - SD ) $, for households with more than one person. These values are shown in the table below:

Family Size	Eligibility Cutoff Income	Size of Benefit Cliff
One	$16,945	$0
Two	$23,808	$1,173
Three	$29,940	$2,389
Four	$36,084	$3,303
Five	$42,216	$4,070

As you can see, the gross income limit results in sizeable benefit cliffs.

Now we have all that we need to fully describe the marginal tax rates of the SNAP program under our assumptions. From $0 to $1 below $1.25SD$, the marginal tax rate is 0%, since net income is less than $0 and hence the benefit remains $B_{max}$. For households with more than one person, from $1.25SD$ to $1 below the gross income limit ($1.3PL $), the marginal tax rate is 24%, since a dollar of additional income results in a 24 cent reduction in benefits. For single-person households, from $1.25SD$ to $16,945 (the income at which the calculated benefit reaches $0), the marginal tax rate is 24%. For households with more than one person, at the gross income limit the marginal tax rate is some very large number, since a dollar of additional income results in thousands of dollars of lost benefits. Above the gross income limit/$16,945, the marginal tax rate is 0%, since there are no benefits to lose. The precise values are listed in the tables below:

**Family Size: One**
Gross Income	Benefit	EMTR
Less than $2,895	$3,372	0%
$2,895–$16,944	$3,372$–$.3($.8I-$$2,316)	24%
Above $16,944	$0	0%

**Family Size: Two**
Gross Income	Benefit	EMTR
Less than $2,895	$6,192	0%
$2,895–$23,807	$6,192$–$.3(.8$I-$$2,316)	24%
$23,808	$1,173	117,300%
Above $23,808	$0	0%

**Family Size: Three**
Gross Income	Benefit	EMTR
Less than $2,895	$8,880	0%
$2,895–$29,939	$8,880$–$.3($.8I-$$2,316)	24%
$29,940	$2,389	238,900%
Above $29,940	$0	0%

**Family Size: Four**
Gross Income	Benefit	EMTR
Less than $2,895	$11,268	0%
$2,895–$36,083	$11,268$–$.3(.8$I-$$2,316)	24%
$36,084	$3,303	330,300%
Above $36,084	$0	0%

**Family Size: Five**
Gross Income	Benefit	EMTR
Less than $2,895	$13,392	0%
$2,895–$42,215	$13,392$–$.3($.8I-$$2,316)	24%
$42,216	$4,070	407,000%
Above $42,216	$0	0%

Calculating SSI Effective Marginal Tax Rates

SSI imposes very high marginal tax rates. Nominally, it is 100%: every dollar of earned or unearned income (unearned includes in-kind benefits like food and shelter provided by other people) results in a $1 reduction in SSI benefits. However, SSI excludes the first $20 of any income (earned or unearned) made in a month, the first $65 of earned income made in a month, one-half of earned income above the first $65 (and any remainder from the $20 exclusion), and several quarterly exclusions for infrequent or irregular unearned income.(supCRS SSI Long: 17) Note that these figures are not adjusted for inflation each year—they have been the same since 1972.(supCRS SSI Long: 18)

Income after these exclusions is referred to as countable income, and SSI imposes a 100% effective marginal tax rate on countable income. EMTR's on gross income, however, are less than 100%, because some of gross income is exempted when computing countable income.

Several assumptions I've made will affect the marginal tax rates we calculate. First, this chart deals specifically with labor income, which means that it is assumed that the income the user inputs is entirely earned income. To keep things entirely within the realm of labor income, I will not include the $20 exclusion, which can be applied to non-labor income. So, for our calculations, the first $65 of monthly income plus one-half of additional monthly income is exempted.

Second, the chart looks at income on an annual basis, while SSI benefit amounts are based on monthly income. This requires some simplifications to make the monthly benefit appear as a single, annual curve. I assume that income is uniform over the year, i.e. if someone has an income of $12,000 then it is assumed that they made $1,000 each month. This allows us to take the monthly benefit and monthly exemptions and multiply them by 12 to get annual figures. Note that this means our calculations can deviate from people's actual benefits. A person who makes all of their annual income in one month and none in the remaining 11, for instance, would only get to exclude $65 and one-half of the remaining, while under our assumptions we would calculate that they were able to exclude $780 and one-half of the remaining. The consequence of this is two-fold: (1) the amount of income subject to a 0% marginal tax rate from the $65/month exclusion is slightly extended, and more importantly (2) benefit values will differ substantially if income is not uniform over the year.

Finally, I do not take into consideration asset tests. SSI has a $2,000 asset limit for individuals and a $3,000 asset limit for married couples in which both spouses are SSI-eligible. Assets include "cash or other liquid assets or any real or personal property that an individual (or spouse, if any) owns and could convert to cash to be used for his or her support and maintenance".(sup: CRS SSI Long) SSI excludes one car and a house from the asset test (how, you might ask, is someone supposed to buy a car or a house when they can never save more than $2,000?). Because I do not take into consideration these asset limits, our calculations may indicate that somebody would receive an SSI benefit even though they would be disqualified by the asset test. For more information on asset tests, see the page Asinine Asset Tests.

With these considerations in mind, we can now go about determining the benefit values and effective marginal tax rates of SSI on labor income. SSI benefits are calculated by subtracting from a maximum benefit, adjusted for inflation each year. In 2023, these figures were:^[SSA]"Fact Sheet: 2023 Social Security Changes" (2022). Social Security Administration. Archived from the original on January 23, 2023.

Household Type	Maximum Benefit	Annualized Maximum Benefit
Individual	$914/month	$10,968
Married Couple	$1,371/month	$16,452

Note that the married couple maximimum only applies if both spouses are eligible for SSI. A person who is married to someone who is non-SSI-eligible receives the individual benefit. You may notice that this results in sizeable marriage penalties for disabled people. You can read more about these at the page Marriage Penalties.

The SSI benefit is calculated by subtracting countable income from the maximum benefit. Since it is assumed that annual income is uniform over the year, the annual exclusion on earned income is $$65 \times 12 = $780 $. And since 50% of earned income after $780 is exempted, i.e. countable income rises by only $0.50 for every dollar of labor income, the benefit $B$ at gross income $I$, with $B_{max}$ denoting the max benefit, is: $$B(I) = B_{max} \text{ if } I \leq \$780 $$ $$B(I) = B_{max} - .5 (I - 780) \text{ if } I> \$780$$

Since the first $780 of income is excluded, there is no decrease in SSI benefits for the first $780 in income. This means there is a 0% effective marginal tax rate on the first $779 (at $780, an additional dollar of income results in $781 of income, so there is a non-zero EMTR): $$EMTR_{I < \text{\$780} } = 0\% $$

Half of labor income above the first $780 is exempted, and a 100% marginal tax is imposed on the remaining 50%. Clearly, this results in a 50% effective marginal tax rate: $$EMTR_{I \geq \text{\$780}}(I) = B_{max} - .5((I+1) - 780) - (B_{max} - .5(I-780)) = 50\% $$

Finally, we have to take into consideration when the benefit equals $0. Once the benefit hits $0, the EMTR drops to 0%, since there is no more benefit to lose as a result of additional income. The calculation is straightforward, we just set $B(I)$ for income greater than $780 equal to zero and solve: $I= 2(B_{max} + 390) $. The benefits thus reaches zero at the following values:

Household Type	Zero Benefit Income
Individual	$22,716
Married Couple	$33,684

Now we have a full accounting of benefits and effective marginal tax rates. These are shown in the tables below:

**Individual**
Income	Benefit	EMTR
Less than $780	$10,968	0%
$780–$22,715	$10,968$–$.5($I-$$780)	50%
Above $22,715	$0	0%

**Married Couple**
Income	Benefit	EMTR
Less than $780	$16,452	0%
$780–$33,683	$16,452$–$.5($I-$$780)	50%
Above $33,683	$0	0%

Calculating Premium Tax Credit Effective Marginal Tax Rates

Under the Inflation Reduction Act, the required contribution percentages instituted by the American Rescue Plan Act were extended through 2025. These are shown in the below left table, obtained from the text of the American Rescue Plan Act.^[5]Text of the American Rescue Plan Act of 2021 . Congress.gov. The table is on page 181 of the document (page included in hyperlink). Archived from the original on January 6, 2023. They are based on the federal poverty line, shown in the below right table.^[6]"HHS Poverty Guidelines for 2023". Office of the Assistant Secretary for Planning and Evaluation. Archived from the original on January 27, 2023.

Family Size	2023 Poverty Level
One	$14,850
Two	$19,720
Three	$24,860
Four	$30,000
Five	$35,140

Note that household incomes refers to modified adjusted gross income (MAGI), so the income used to determine the required contribution does not include the standard deduction/itemized deductions. Note also that for the purposes of this chart, we assume that users have no untaxed foreign income and no tax-exempt interest, so MAGI equals AGI. We also assume that user's gross income equals their AGI, so the income users input into the chart is assumed to be exactly the income used to calculate the the required contribution.

Within each group, the premium percentages scale linearly (e.g. at 175% of the poverty line, the required contribution percentage is 1%). So with $h_1$ denoting the initial household income in dollars of a particular income tier, $h_2$ the final income in dollars, $p_1$ the initial premium percentage, and $p_2$ the final premium percentage, the required contribution as a percent of income at income $I$ is: $$ C_{\text{%}}(I) = \frac{p_2 - p_1}{h_2 - h_1} (I - h_1) + p_1$$

The required contribution in dollars is thus: $$ C(I) = C_{\%}(I) \times I = \frac{p_2 - p_1}{h_2 - h_1} I^2 + I \left(p_1 - \frac{h_1 (p_2 - p_1)}{h_2 - h_1} \right)$$

The primary consequence of this equation is that it was very tedious for me to type it into Javascript, wasting 15 minutes that could have been spent on more productive activities like wage labor or rewatching Dune. Additionally, there are two important secondary consequences. First, this equation is quadratic. Intuitively, this occurs simply because the premium grows by a constant percentage of income for every dollar of additional income; so as income grows, the dollar value of this percentage grows. Second, the equation demonstrates that it is actually quite complicated for people to determine the value of their premium tax credit. This is made more complicated still by the fact that the advance premium tax credits paid out in a given year to insurers on behalf of a recipient is based upon the recipient's expected income in that year. So anyone attempting to plan around the premium tax credit has to compare the benefit they are currently receiving, which the IRS determines by guessing what their income will be that year, with the true value that will be determined at the end of the year when they file their taxes and their precise annual income is known.

The effective marginal tax rate is the loss in benefits as a result of a $1 increase in income, so the effective marginal tax rate at income $I$ equals $ C(I+1) - C(I) $ (divided by $1). This works out to: $$EMTR(I) = \frac{p_2 - p_1}{h_2 - h_1} (I+1)^2 + (I+1) \left(p_1 - \frac{h_1 (p_2 - p_1)}{h_2 - h_1} \right) - \left( \frac{p_2 - p_1}{h_2 - h_1} I^2 + I \left(p_1 - \frac{h_1 (p_2 - p_1)}{h_2 - h_1} \right) \right)$$ $$= \frac{p_2 - p_1}{h_2 - h_1} (2I - h_1 +1) + p_1 $$

You can confirm that the only difference between this and the derivative of $C(I)$ is the addition of the constant $\frac{p_2 - p_1}{h_2 - h_1}$.

So, for instance, a person in a two-member household with an income of $35,000 (between 150% and 200% of the poverty line) faces an EMTR of $ \frac{.02}{39,440 - 29,580} (2(35,000) - 29,580 + 1 ) = 8.2 \% $. In other words, if person in a two-member household who has made $35,000 so far this year were to increases their income by $1, the amount of their health insurance premium that the government would cover decreases by 8.2 cents (when actually filing taxes, the final calculation is rounded to the nearest dollar).

We can check the correctness of our equation. Since the EMTR tells us by how much the required contribution grows (in dollars) for an additional dollar of income, it stands that we can calculate the required contribution at a particular income by summing the EMTRs up to $1 below that income. If we want to know the required contribution at 225% of the poverty line for a person in a two-person household ($44,370), for instance, we get: $$ \sum_{i=29,580}^{39,439} \left( \frac{.02 - 0}{39,440 - 29,580}(2i - 29,580 + 1) \right) + \sum_{i=39,440}^{44,369} \left( \frac{.04-.02}{49,300 - 39,400}(2i - 39,400 + 1) + .02 \right) $$ $$ = \$1,331.10 $$ The statutorily defined required contribution at $44,370 is 3% of income, or $1,331.10, exactly as our equation said it would be.

We can simply things for the income tier above 400% of the poverty line. If you plug into the above equation (with $p_1 = p_2 = .085$), you can see that the EMTR above 400% is a constant 8.5%. It is straightforward to see why: an additional dollar of income results in the premium contribution growing by: $$EMTR_{\geq \text{400%}}(I) = \Delta \text{premium contribution} = .085(I + 1) - .085I = 8.5 \% $$

In other words, above the 8.5% of income cap, the required contribution grows by 8.5 cents for every additional dollar of income.

We can also simplify things for the three income tiers from 150% to 300% of the poverty line. If you run the numbers you'll notice that the required contribution percentage for each of these three tiers scale at the same rate. This means we can consider them as one income group, and calculate any premium contribution within them using $ p_2 = .06 $ and $p_1 = 0 $, as well as the corresponding income tier values for 300% and 150% of the poverty line. That makes our equation for this combined income tier a little simpler: $$EMTR_{ \text{150%–300%} }(I) = \frac{.06}{h_{\text{300%}} - h_{\text{150%}}} (2I - h_{\text{150%}} + 1)$$

It also means that we only have one other equation, for the 300–400% of the poverty line tier. Here, $p_2 = .085 $ and $p_1 = .06 $, so our equation is: $$ EMTR_{ \text{300%–400%} }(I) = \frac{.025}{h_{\text{400%}} - h_{\text{300%}}} (2I - h_{\text{300%}} + 1) + .06$$

Now we have just have to take into account the cost of the premium. While the required contribition technically grows indefinitely, the actual amount someone has to pay for their premium does not. Once someone's required contribution equals their premium, they are paying the full cost of the premium, so additional income doesn't impose any additional costs.

Premium tax credits are based on the cost of a silver plan on the ACA exchanges. Costs vary by state and age, so to keep things simple we'll use the 2023 national average silver plan premiums for 40 year olds (the median age in the United States is 39^[ref]Duffin, Erin (December 12, 2022). "Median age of the resident population of the United States from 1960 to 2021". Statista. Archived from the original on December 12, 2022.). These are shown in the tables below.^[7]Masterson, Les; Megna, Michelle (January 2, 2023) "How Much Does Health Insurance Cost?". Forbes. Archived from the original on February 2, 2023.

Household Type	Average Silver Plan Premium
Individual, no children	$6,312
Individual + 1 Child	$10,032
Individual + 2 Children	$13,764
Individual + 3 Children	$17,484

Household Type	Average Silver Plan Premium
Couple, no children	$12,626
Couple + 1 Child	$16,344
Couple + 2 Children	$20,076
Couple + 3 Children	$23,796

Once a person's required contribution equals the cost of the premium their effective marginal tax rate drops to 0%, since they face no additional costs for income made after this point. For every household type, this occurs above 400% of the poverty line, so we can calculate each by determining when 8.5% of income equals the cost of the premium. These values are shown in the table below, rounded to the nearest dollar.

Household Type	Full Premium Income
Individual, no children	$74,259
Individual + 1 Child	$118,024
Individual + 2 Children	$161,929
Individual + 3 Children	$205,694

Household Type	Full Premium Income
Couple, no children	$148,541
Couple + 1 Child	$192,282
Couple + 2 Children	$236,188
Couple + 3 Children	$279,953

We now have a full description of the effective marginal tax rates of the premium tax credits, shown in the table below. The income tier values (the $h$'s) come from the poverty level table, and the required contribution=premium values come from the table above.

Income Tier	Effective Marginal Tax Rate
0–150% of Poverty Line	$$ 0\% $$
150–300% of Poverty Line	$$ \frac{.06}{h_{\text{300%}} - h_{\text{150%}}} (2I - h_{\text{150%}} + 1) $$
300–400% of Poverty Line	$$ \frac{.025}{h_{\text{400%}} - h_{\text{300%}}} (2I - h_{\text{300%}} + 1) + .06 $$
400% of Poverty Line up to Required Contribution=Premium	$$ 8.5\% $$
Required Contribution=Premium and above	$$ 0\% $$

Appendix: Cost Sharing Reductions

The Affordable Care Act includes not only tax credits to help pay the cost of premiums, but also reductions in cost sharing to help cover deductibles and copayments. These, too, phase out with income.

There are two ways in which cost sharing reductions reduce out-of-pocket costs to those eligible.¹¹ The first caps total out-of-pocket costs, while the second increases the actuarial value of exchange plans. The second is too complicated to try to incorporate into our marginal tax rate chart, so we will only consider the first.

The basic way that the cap on out-of-pocket expenses work is as follows. When a person signs up for a silver plan, the insurer has in mind some deductible $D$. However, if the person has an income below 250% of the poverty line, the government ensures that they will never pay out-of-pocket costs greater than $C_{max}$. If their income is low enough, then their max out-of-pocket expenses will be less than their deductible, and they will have to pay for medical expenses only up to the cap. If the person's income is somewhat higher, then their max out-of-pocket costs will be greater than their deductible. In this situation, they will have to cover the full cost of medical payments up to the deductible. Above the deductible, they will have to pay some co-payment and co-insurance determined by the required actuarial value of the plan, up to the out-of-pocket max. After the out-of-pocket max, they do not pay anything.

It is also important to note that the cost sharing reductions are not provided as a tax credit. When a person eligible for cost sharing reductions signs up for a plan, they are not advertised the deductible $D$, with the government reimbursing them for any difference between $C_{max}$ and the higher amount that they paid. Instead, the government reimburses the insurer directly for the costs. Or rather, that is how it basically appears to insurees and how the ACA intended it to work. However, the actual financing mechanism differs from described as a result of congressional inaction and a 2014 court case by House Republicans. In short, the government doesn't actually pay for the cost sharing reductions, even though insurers are still required to provide them. This has resulted in "silver loading"—the practice of insurers raising silver plan premiums to cover the cost of lower deductibles and copays for those who receive cost sharing reductions—and in turn has produced larger premium tax credits. For now, though, we can dispense with this complication because it doesn't affect the marginal tax rates of cost sharing reductions. See the section below ("Considerations with Cost Sharing Reductions") for a fuller discussion.

The capped out-of-pocket expenses are a blunt instrument. They do not scale up continuously, but rather increase abruptly at defined income levels. These are defined in the table below.

Income Tier	Individual Coverage	Family Coverage
100–200% of Poverty Line	$2,900	$5,800
200–250% of Poverty Line	$6,950	$13,900
Above 250% of Poverty Line	No Cap	No Cap

There are two basic ways we could go about considering the marginal tax rates of capped out-of-pocket expenses. The first is to directly consider the costs of medical expenses in a year. This works well for people who have fairly steady medical expenses, like those with chronic diseases requiring medication or persistent hospitalization. In this case, an increase in income that pushes a person over an out-of-pocket max income tier could directly increase their out-of-pocket medical expenses.

This method, however, does not do near as well a job of incorporating people who do not have consistent medical expenses. For these people, there is no clearly applicable monetary cost to increased max out-of-pocket costs, since in any given year they are unlikely to have sudden medical expenses that are larger than the out-of-pocket max of the previous income tier. The best we could do in this case would be to assign a monetary value to the utility of having in place a cap on potential future expenses. This would not be a particularly strange thing to incorporate, since this is precisely what a premium is—a monetary value placed on the assurance that potential future medical costs will not have to be paid entirely out-of-pocket.

However, I think incorporating a monetary value for cost-sharing reductions into the post-tax-and-transfer income chart in this way could be confusing to users. So I have instead simply shown a benefit cliff in the effective marginal tax rate chart when income jumps from one income tier to the next, while leaving cost sharing reductions out of the post-tax-and-transfer chart. This compromise highlights the sudden increase in max out-of-pocket costs (and is fairly safe to include in the EMTR chart as a large vertical line, since any value placed on the out-of-pocket max greater than $1 results in a vertical spike exceeding 100%) while not confusing the post-tax-and-transfer chart with assumptions about the monetary value placed on the utility of cost sharing reductions.

Considerations with Cost Sharing Reductions

There is one peculiar complication with cost sharing reductions.⁹ They are intended to seamlessly incorporate into the silver plans of eligible people by directly advertising silver plans with lower deductibles and copays than plans for non-eligible people. Consequently, insurers are required by law to provide lower deductibles and copays to those eligible, with the government reimbursing the insurers directly. However, following a series of court cases, the government has not reimbursed insurers since the Obama Administration.

In short, Congress has never explicitly appropriated funds for cost sharing reductions. As a result, the Obama Administration reimbursed insurers using money appropriated for several tax credits, the premium tax credit among them. The Republican-controlled House of Representatives in 2014 sued the Obama Administration, alleging that this was unconstitutional. The case worked its way through the courts until Trump was elected, at which point Congress had still not allocated funds and the Trump administration announced that it would terminate cost sharing payments.

Insurers are still required by law, however, to offer lower deductibles and copays to those eligbile for cost sharing reductions. This has resulted in insurers "silver loading"–raising premiums on silver plans to cover the costs of unreimbursed cost sharing reductions. This has certainly been an unwelcome development for anyone who pays for an unsubsidized silver plan (there are likely not very many such people), but mainly this has simply resulted in people receiving larger premium tax credits (recall that for people with moderate incomes, the amount they pay towards their premium is principally determined by their income, not by the size of the premium). As a result, most people on silver plans are not the ones who have paid for the price increases attributable to silver loading—it's the government who has worked itself back into paying the cost of cost sharing reductions. This had some rather unintended consequences for the notoriously ACA-unfriendly Trump Administration: as Aviva Aron-Dine has pointed out, silver loading accompanied with premium tax credits has likely increased enrollment in the exchanges.¹⁰

This has a very direct effect on our post-tax-and-transfer income chart. Since the monetary value we assigned to Medicaid and premium tax credits were based on the premium of a silver plan, silver-loading has the effect of increasing the value we assign to Medicaid and premium tax credits relative to what they would be without it.

At the margins, there are also some consequences for our calculations of effective marginal tax rates. While it doesn't change anything when we are thinking about the marginal tax rates people face under current policy—and current policy includes not reimbursing insurers for cost sharing reductions—it means that the income levels at which people continue to receive premium subsidies are higher than they would be if cost sharing reductions were actually reimbursed. Recall that people stop receiving subsidies for their premiums when their premium equals 8.5% of income. This means that the higher the premium is, the higher the income it takes to stop receiving subsides. For our purposes, that means the income ranges at which people continue to face effective marginal tax rates for premium tax credits is extended. And, importantly, silver loading does not affect marginal tax rates for cost reductions. Out-of-pocket maxes under cost sharing reductions are established by law to the dollar value, and eligibility is set at 250% of the poverty line. This means that silver loading has the effect of extending marginal tax rates for premium tax credits while leaving those for cost sharing reductions unchanged.

Child Tax Credit	Earned Income Tax Credit
Head of Household	CDCC
SNAP (Food Stamps)	TANF
WIC	Medicaid & CHIP

Family Security Act	Build Back Better
Working Families Tax Relief Act	End Child Poverty Act
SSI Restoration Act

Effective Marginal Tax Rates (2023)

General

Personal Income Tax

FICA

SNAP

SSI

Premium Tax Credits

What are Effective Marginal Tax Rates?

High Effective Marginal Tax Rates Discourage Work

How to Reduce Marginal Tax Rates