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# Calculator Methodology

## Overview of Methodology

This section seeks to explain the core methodology and assumptions used to create the finish line calculator. The main purpose of the calculator is to calculate a monthly spending budget for a person or family living at a particular percentile. For example, selecting the 50% percentile and a household size of 4 would determine the expected budget that a family of 4 should expect when with a standard of living greater than 50% of Americans.

### Process

Step 1: Determine the household income for a selected percentile of the population

Step 2: Scale the median household income by the number of people in the household

Step 3: Subtract estimated federal and state income taxes as well as FICA withholding (social security/medicare)

Step 4: Show the expected annual, monthly, and weekly spending budget

## Household Income Percentile

There are multiple measures of income which are reported by the government to compare different regions and demographics. The two most common of these are individual income and household income.

Individual Income: The sum of all forms of income attributed to a single working citizen

Household Income: The combined incomes of all people sharing a single household, including salaries and wages, retirement income, government support (i.e. food stamps, etc), and investment gains

Considering that the goal of the calculator is to determine a monthly budget for a family unit (whether that is a single person or a family of 4), household income is a more appropriate measure for these purposes.

### Data Source

The US Census Bureau collects a wide range of income data around the country. The Annual ASEC survey is a national survey conducted to produce annual income and migration statistics, including official poverty figures and is typically released in the fall for the previous tax year. The Minnesota Population Center at the University of Minnesota manages the IPUMS CPS project which collects and harmonizes the ASEC data for free and public use.

Using the IPUMS system, microdata for over 68,000 households can be downloaded and imported into a variety of stats software. For this calculator, SPSS was used to breakdown the entire dataset into percentiles.

The full reference for this data is:

Sarah Flood, Miriam King, Renae Rodgers, Steven Ruggles and J. Robert Warren. Integrated Public Use Microdata Series, Current Population Survey: Version 7.0 [dataset]. Minneapolis, MN: IPUMS, 2020. https://doi.org/10.18128/D030.V7.0

### Determining Percentiles

Using the results from SPSS, a simple lookup table was created with the household income for each percentile from 1-99. In the calculator, when a user enters a percentile, the calculator simply looks up the corresponding household income. This method is more accurate than using some form of best fit equation since it is based on real data.

## Scaling by Household Size

The household income determined in Step 1 includes all households, whether the household is a single individual or a family of 6. Therefore, there is a need to scale the income by family size.

One consideration is to simply use real data to calculate income by family size. However, using the census data, it becomes clear that there is a bell shaped income curve as household size increases. The table below shows the median income in 2018 by household size:

 Household Size Income 1 \$31,954 2 \$70,870 3 \$82,139 4 \$97,522 5 \$93,297 6 \$86,820 7 \$84,702

For this reason, a different method was needed to determine scaling by household size.

### Using the Poverty Line

There is actually already a government formula which accounts for family size: the federal poverty line. Take a look at the federal poverty guidelines for 2018:

 Household Size Income 1 \$12,140 2 \$16,460 3 \$20,780 4 \$25,100 5 \$29,420 6 \$33,740 7 \$38,060 8 \$42,380

As you’ll notice, the guidelines can be reduced to a simple formula:

income = \$7820 + (\$4320 x [household size])

The nice thing about this formula is that it has a standardized increase in income per family member. The next step is to apply it to our calculator.

From the previous step, we already have the household income for the percentile we are interested in. In 2018, the average household size was 2.52. Therefore, this income applies to a family of 2.52 people.

In order to scale it to a single person, we can calculate a scaling factor to apply to the poverty line. Let’s say, for example, we’re looking at the 50th percentile income of \$64,021. This is the income for a family of 2.52 people.

In contrast, the poverty line for a family of 2.52 people would be:

poverty line = \$7820 + (\$4320 x 2.52 people) = \$18,706

The scaling factor can be calculated as a simple ratio of the percentile income to the poverty line:

scaling factor = \$64,021 /\$18,706 = 3.42

In English, this means that the 50th percentile household income is 3.42 times the poverty line at the same family size. We can use this scaling factor to calculate a new 50th percentile household income for any family size. Let’s use a family of 4 as an example. First, calculate the poverty line for a family of 4:

poverty line = \$7820 + (\$4320 x 4 people) = \$25,100

And now, applying our scaling factor to calculate the 50th percentile household income for a family of 4:

income = \$25,100 x 3.42 = \$85,842

Therefore, our expected income for a family of 4 at the 50th percentile is \$85,842.

While there aren’t any perfect benchmarks to check these calculations against, one check we can perform is to compare 2018 individual income using another online calculator to our scaled income for one person. Here’s the results for the 25th, 50th, and 75th percentiles:

 Percentile Individual Income(Actual) Scaled Income(Calculated) Difference 25 \$22,000 \$20,759 -5.6% 50 \$40,100 \$41,936 +4.6% 75 \$70,125 \$74,674 +6.5%

Are these results perfect? No, but they are pretty close. Considering that we are trying to calculate something that doesn’t exist (percentile income scaled by household size), the correlation with individual income at least gives us some comfort that the calculated results aren’t totally random.

It’s also important to mention that as soon as we apply our scaling factor, we are no longer comparing our results to actual data. As we already discussed earlier, the actual data shows that larger families have a larger income up to a household of 4. After that, the income starts to decrease again.

Instead, we are trying to calculate the theoretical 50th percentile “lifestyle” rather than the 50th percentile income. The scaling factor only serves to try to determine the income that allows a family of 4 or 5 to life at the same approximate lifestyle of a single person or a married couple without kids.

## Accounting for Taxes

In order to calculate the post-tax, or “take home” pay, the standard taxes and withholding were subtracted from the calculated pretax salary. These include:

Federal Income Tax: Federal tax was calculated using the standard federal income tax brackets for the year that the income data was gathered from.

State and Local Income Tax: There is wide variability in state tax rates. Some states do not collect any income tax at all. Others have a flat rate regardless of income. And the majority have defined tax brackets, similar to the federal tax brackets, but usually with different income cutoffs. The tax rates can vary among states from less than 1% to over 10% for the highest brackets in some states.

Because the income data was standardized across the entire country, we sought to use a blanket state income tax rate for the whole country. Ideally, we would have data for a large volume of households that describes the effective state income taxes paid by each household. In that case, we could simply find the effective tax rate (i.e. the state income taxes paid / total income) for each percentile of Americans based on actual data.

However, this sort of data is not currently publically available (as far as we know). Therefore, we used the income tax calculator at Smart Asset to calculate the effective state and local income tax rate for each state at the median (50th percentile) US household income. Once we had all 51 (including D.C.) state and local income tax rates, we selected the median effective rate of 3.4% for our calculator. For comparison, the upper and lower quartiles were 4.3% and 1.8% respectively, and the mean was 3.0%.

The important things to keep in mind about this value:

• As long as national income data is being used, it does not make sense to use the exact state taxes from the user’s state for the calculator. If state data is being used for taxes, then the income percentile data should be state-specific as well
• For percentiles less than the 50th percentile, state and local taxes will tend to be slightly overestimated, meaning the monthly budget will be slightly low
• For percentiles greater than the 50th percentile, state and local taxes will tend to be slightly overestimated, meaning the monthly budget will be slightly high

FICA Withholding: FICA refers to the Federal Insurance Contributions Act which specifies mandatory contributions for Social Security and Medicare. The FICA withholding rates are pretty standard and easy to calculate.

## Final Output

After taxes and FICA contributions were accounted for, a final “take home pay” could be determined for the chosen percentile. To calculate the monthly budget, this rate was divided by 12. To calculate weekly budget, the rate was divided by 52.

To see the explanations of the charts, see the details on the calculator page.