Calculating Federal and State Income Taxes

Shane Orr

This article presents two use cases for usincometaxes. The first shows users how to estimate income taxes from a data frame containing financial information and other characteristics of tax payer units. This income could come from surveys such as the Consumer Expenditure survey or the Panel Study of Income Dynamics survey. The second use case focuses on running simulations.

Calculating income taxes from survey data

For the first example we will use an internal data set called taxpayer_finances. The data is randomly generated and formatted for use with usincometaxes. Guidance on formatting data can be found in the Description of Input Columns article.

The data set contains financial and other household characteristics that help estimate income taxes.

data(taxpayer_finances)

taxpayer_finances %>%
  head() %>%
  kable()
taxsimid year mstat state page sage depx age1 age2 age3 pwages swages dividends intrec stcg ltcg
1 2000 single NC 37 0 4 6 7 8 26361.75 0.00 2260.86 4340.19 2280.16 2060.29
2 2000 single NC 29 0 1 7 0 0 33966.34 0.00 1969.54 868.10 1064.50 2234.61
3 2000 married, jointly NC 36 30 1 13 0 0 174191.53 102286.98 1972.47 2048.31 1009.11 1226.34
4 2000 married, jointly NC 37 34 3 5 6 7 67604.57 53205.76 1173.95 881.67 3582.74 1405.74
5 2000 married, jointly NC 38 39 0 0 0 0 21176.78 21687.72 4614.91 1588.52 560.93 825.04
6 2000 single NC 36 0 1 2 0 0 53397.72 0.00 2067.41 1320.01 687.23 3548.07

Each row in the data set is a tax paying unit. Thus, each row files one tax return. Columns represent items reported on tax returns that impact taxes. Of course, the information in the data set does not represent everything people report on tax returns. For this reason, the income tax calculations are simply estimates.

We call taxsim_calculate_taxes() to estimate federal and state income taxes for each tax paying unit. taxsim_calculate_taxes() sends the data to the NBER’s TAXSIM 35 program for calculation and returns the results as a data frame.

We are only interested in federal and state tax liabilities, not line item credits and deduction, so we are using return_all_information = FALSE.

family_taxes <- taxsim_calculate_taxes(
  .data = taxpayer_finances,
  return_all_information = FALSE
)

family_taxes %>%
  head() %>%
  kable()
taxsimid fiitax siitax fica frate srate ficar tfica
1 924.97 1046.23 4033.35 15.00 7.00 15.3 2016.67
2 3596.23 1947.22 5196.85 15.00 7.00 15.3 2598.42
3 78080.32 20429.27 26915.48 36.58 8.12 2.9 13457.74
4 23279.56 7783.72 18483.98 30.83 7.75 15.3 9241.99
5 5584.33 2619.27 6558.27 15.00 7.00 15.3 3279.13
6 8358.38 3411.43 8169.85 28.00 7.00 15.3 4084.93

The taxsimid column is required for any input data frame used in taxsim_calculate_taxes. This column is also returned in the output data frame containing tax calculations, allowing us to link the input and output data frames.

income_and_taxes <- taxpayer_finances %>%
  left_join(family_taxes, by = 'taxsimid')

income_and_taxes %>%
  head() %>%
  kable()
taxsimid year mstat state page sage depx age1 age2 age3 pwages swages dividends intrec stcg ltcg fiitax siitax fica frate srate ficar tfica
1 2000 single NC 37 0 4 6 7 8 26361.75 0.00 2260.86 4340.19 2280.16 2060.29 924.97 1046.23 4033.35 15.00 7.00 15.3 2016.67
2 2000 single NC 29 0 1 7 0 0 33966.34 0.00 1969.54 868.10 1064.50 2234.61 3596.23 1947.22 5196.85 15.00 7.00 15.3 2598.42
3 2000 married, jointly NC 36 30 1 13 0 0 174191.53 102286.98 1972.47 2048.31 1009.11 1226.34 78080.32 20429.27 26915.48 36.58 8.12 2.9 13457.74
4 2000 married, jointly NC 37 34 3 5 6 7 67604.57 53205.76 1173.95 881.67 3582.74 1405.74 23279.56 7783.72 18483.98 30.83 7.75 15.3 9241.99
5 2000 married, jointly NC 38 39 0 0 0 0 21176.78 21687.72 4614.91 1588.52 560.93 825.04 5584.33 2619.27 6558.27 15.00 7.00 15.3 3279.13
6 2000 single NC 36 0 1 2 0 0 53397.72 0.00 2067.41 1320.01 687.23 3548.07 8358.38 3411.43 8169.85 28.00 7.00 15.3 4084.93

Now we have a single data frame containing both wages and income tax liabilities. Let’s take a look at the relationship between wages and estimated federal income taxes. The colors represent the number of children 18 or younger.

# custom theme for all plots in the vignette
plt_theme <- function() {
  
    theme_minimal() +
    theme(
      legend.text = element_text(size = 11),
      axis.text = element_text(size = 10),
      axis.title=element_text(size=11,face="bold"),
      strip.text = element_text(size = 11),
      panel.grid.minor = element_blank(),
      plot.title = element_text(face = "bold"),
      plot.subtitle = element_text(size = 12),
      legend.position = 'bottom'
    )
}
# color palettes for number of children
dep_color_palette <- rev(c('#4B0055','#353E7C','#007094','#009B95','#00BE7D','#96D84B'))

income_and_taxes %>%
  mutate(
    tax_unit_income = pwages + swages,
    num_dependents_eitc = factor(depx, levels = as.character(0:5)),
    filing_status = tools::toTitleCase(mstat)
  ) %>%
  ggplot(aes(tax_unit_income, fiitax, color = num_dependents_eitc)) +
    geom_point(alpha = .5) +
    scale_x_continuous(labels = scales::label_dollar(scale = .001, suffix = "K"), limits = c(0, 200000)) +
    scale_y_continuous(labels = scales::label_dollar(scale = .001, suffix = "K"), limits = c(-10000, 50000)) +
    scale_color_discrete(type = dep_color_palette) +
    facet_grid(rows = vars(mstat), cols = vars(year)) +
    labs(
      title = "Federal Income Taxes by Filing Status, Year, and Number of Children",
      x = "\nHousehold Wages",
      y = "Federal Income Taxes"
    ) +
    plt_theme() +
    guides(color = guide_legend(title = "Number of Childern 18 or Younger", title.position = "top", byrow = TRUE))
#> Warning: Removed 134 rows containing missing values (geom_point).

The plots shows what we would expect: higher income families pay more in taxes and households pay less the more children they have. We also see the reduction in federal marginal tax rates from 2000 to 2020, as shown by the decrease in income tax liabilities when comparing the two years.

Income tax simulations

Association between income taxes paid and household wages

An additional use of usincometaxes is to run simulations. This could be as simple as plotting the relationship between wages and income taxes paid. To do this, we first need to create a data set that holds everything constant except for wages. The code block below does this, except it also creates different data sets for households with zero and four children 18 or younger, so we can compare differences on this characteristic as well.

# calculate taxes from 0 to 200,000 in wages
wage_linespace <- seq(0, 200000, 100)

n_kids <- 4

base_family_income <- data.frame(
  year = 2020,
  mstat = 'married, jointly',
  state = 'NC',
  page = 40,
  sage = 40,
  depx = n_kids,
  age1 = n_kids,
  age2 = n_kids,
  age3 = n_kids,
  pwages = wage_linespace,
  swages = 0
)

# create an additional data set with no dependents and add it to the original
family_income <- base_family_income %>%
  bind_rows(
    # make all numeber of dependent columns 0
    base_family_income %>%
      mutate(across(c(depx, age1, age2, age3), ~0))
  ) %>%
  # add unique ID to each row
  mutate(taxsimid = row_number()) %>%
  select(taxsimid, everything())

family_income %>%
  head() %>%
  kable()
taxsimid year mstat state page sage depx age1 age2 age3 pwages swages
1 2020 married, jointly NC 40 40 4 4 4 4 0 0
2 2020 married, jointly NC 40 40 4 4 4 4 100 0
3 2020 married, jointly NC 40 40 4 4 4 4 200 0
4 2020 married, jointly NC 40 40 4 4 4 4 300 0
5 2020 married, jointly NC 40 40 4 4 4 4 400 0
6 2020 married, jointly NC 40 40 4 4 4 4 500 0

Now, we will calculate federal and state income taxes for our simulated data set. Note that return_all_information = TRUE. This allows us to examine credit amounts like the Child Tax Credit and Earned Income Tax Credit (EITC).

family_income_taxes <- taxsim_calculate_taxes(
  .data = family_income,
  return_all_information = TRUE
)

family_income_taxes %>%
  head() %>%
  kable()
taxsimid fiitax siitax fica frate srate ficar tfica v10_federal_agi v11_ui_agi v12_soc_sec_agi v13_zero_bracket_amount v14_personal_exemptions v15_exemption_phaseout v16_deduction_phaseout v17_itemized_deductions v18_federal_taxable_income v19_tax_on_taxable_income v20_exemption_surtax v21_general_tax_credit v22_child_tax_credit_adjusted v23_child_tax_credit_refundable v24_child_care_credit v25_eitc v26_amt_income v27_amt_liability v28_fed_income_tax_before_credit v29_fica v30_state_household_income v31_state_rent_expense v32_state_agi v33_state_exemption_amount v34_state_std_deduction_amount v35_state_itemized_deduction v36_state_taxable_income v37_state_property_tax_credit v38_state_child_care_credit v39_state_eitc v40_state_total_credits v41_state_bracket_rate v42_self_emp_income v43_medicare_tax_unearned_income v44_medicare_tax_earned_income v45_cares_recovery_rebate
1 -6900 0 0.0 -45 0 0.0 0.00 0 0 0 24800 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0 0.01 0 0.01 0 21500 0 0 0 0 0 0 0 0 0 0 6900
2 -6945 0 15.3 -45 0 15.3 7.65 100 0 0 24800 0 0 0 0 0 0 0 0 0 0 0 45 100 0 0 15.3 101.01 0 100.01 0 21500 0 0 0 0 0 0 0 100 0 0 6900
3 -6990 0 30.6 -45 0 15.3 15.30 200 0 0 24800 0 0 0 0 0 0 0 0 0 0 0 90 200 0 0 30.6 201.01 0 200.01 0 21500 0 0 0 0 0 0 0 200 0 0 6900
4 -7035 0 45.9 -45 0 15.3 22.95 300 0 0 24800 0 0 0 0 0 0 0 0 0 0 0 135 300 0 0 45.9 301.01 0 300.01 0 21500 0 0 0 0 0 0 0 300 0 0 6900
5 -7080 0 61.2 -45 0 15.3 30.60 400 0 0 24800 0 0 0 0 0 0 0 0 0 0 0 180 400 0 0 61.2 401.01 0 400.01 0 21500 0 0 0 0 0 0 0 400 0 0 6900
6 -7125 0 76.5 -45 0 15.3 38.25 500 0 0 24800 0 0 0 0 0 0 0 0 0 0 0 225 500 0 0 76.5 501.01 0 500.01 0 21500 0 0 0 0 0 0 0 500 0 0 6900

As before, let’s merge our tax data with the original input data set.

family_income <- family_income %>%
  left_join(family_income_taxes, by = 'taxsimid')

Now, let’s look at the relationship between household wages and estimated income tax liabilities.

family_income_long <- family_income %>%
  select(pwages, depx, fiitax, siitax) %>%
  pivot_longer(cols = c('fiitax', 'siitax'), 
               names_to = 'jurisdiction', values_to = 'taxes_paid') %>%
  mutate(
    jurisdiction = recode(jurisdiction, 'fiitax' = 'Federal Income Taxes', 'siitax' = 'NC State Income Taxes'),
    num_dependents_eitc = factor(depx, levels = as.character(0:5)),
    post_tax_wages = pwages - taxes_paid
  )
# primary_wages, taxes_paid, color = as.character(num_dependents_eitc)
taxes_line_plot <- function(.data, x_var, y_var, color_var) {
  ggplot(.data, aes({{x_var}}, {{y_var}}, color = {{color_var}})) +
    geom_line(size = 1, alpha = .8) +
    geom_hline(yintercept = 0) +
    scale_x_continuous(labels = scales::label_dollar(scale = .001, suffix = "K")) +
    scale_y_continuous(labels = scales::label_dollar(scale = .001, suffix = "K")) +
    scale_color_brewer(type = 'seq', palette = 'Set2')  +
    plt_theme()
  
}
taxes_line_plot(family_income_long, pwages, taxes_paid, num_dependents_eitc) +
  facet_wrap(vars(jurisdiction)) +
  labs(
    title = "Relationship Between Wages and Income Taxes Paid",
    subtitle = "Taxpayer is married, filing jointly, in 2020",
    x = "\nPre-Tax Household Wages",
    y = "Federal Income Taxes",
    color = 'Number of Children 18 or Younger:'
  )

Note that North Carolina had a flat tax of 5.25% in 2020. That’s why their taxes increase linearly.

Relationship Between Pre and Post-Tax Wages

We’ll create a additional plot comparing pre-tax and post-tax household wages.

taxes_line_plot(family_income_long, pwages, post_tax_wages, num_dependents_eitc) +
  facet_wrap(vars(jurisdiction)) +
  labs(
    title = "Relationship Between Pre and Post-Tax Wages",
    subtitle = "Taxpayer is married, filing jointly, in 2020",
    x = "\nPre-Tax Household Wages",
    y = "Post-Tax Hosuehold Wages",
    color = 'Number of Children 18 or Younger:'
  )

Child Tax Credit and Earned Income Tax Credit (EITC)

As noted previously, setting return_all_information = TRUE lets us retrieve additional output. Included in this additional output are amounts for the Child Tax Credit and EITC. Let’s look at the amounts for both credits, while varying household wages. The values reflect a household with four children 18 or younger.

tax_items_mapping <- c(
  v25_eitc = 'Earned Income Tax Credit',
  child_tax_credit = 'Child Tax Credit'
)

family_income %>%
  filter(depx == 4) %>%
  mutate(child_tax_credit = v22_child_tax_credit_adjusted + v23_child_tax_credit_refundable) %>%
  select(pwages, fiitax, v25_eitc, child_tax_credit) %>%
  pivot_longer(cols = names(tax_items_mapping), names_to = 'tax_item', values_to = 'amount') %>%
  mutate(tax_item = recode(tax_item, !!!tax_items_mapping)) %>%
  taxes_line_plot(pwages, amount, tax_item) +
  labs(
    title = "Relationship Between Wages and Credits",
    subtitle = "Taxpayer is married, filing jointly, in 2020 and has four children under 19",
    x = "\nPre-Tax Wages",
    y = "Credit Amount",
    color = NULL
  )