In FanWangEcon/PrjOptiAlloc: The Optimal Allocation of Resources Among Heterogeneous Individuals

In 2008, the Bush administration sent out stimulus checks as tax rebates (Economic Stimulus Act of 2008). The checks are a function of income, marital status, and the number of children. We have functions that computable taxable income given income, tax liability given income, and also stimulus amount given income.

Taxable Income and Tax Liability in 2008

First, we test the taxable income function.

ar_income <- c(1e4, 2e4, 4e4, 8e4, 1.6e5)
ls_taxable <- ffp_snw_tax_liability(ar_income)
mn_taxable_income <- ls_taxable$mn_taxable_income
mn_tax_liability <- ls_taxable$mn_tax_liability

Second, show the taxable income schedule.

print('mn_taxable_income')
print(mn_taxable_income)

Third, show the tax liability schedule.

print('mn_tax_liability')
print(mn_tax_liability)

Stimulus Checks (Tax Rebate) Under Bush Economic Stimulus Act of 2008

Find taxable income, tax liability, and then finally stimulus checks (tax-rebates) amounts for households with 10k, 20k, 30k, 40k, 50k, 60k, 70k, 80k, 90k, 100k, and 160k income, and all kids and marital status combinations.

# Income array
ar_income <- c(1e4, 2e4, 3e4, 4e4, 5e4, 6e4, 7e4, 8e4, 9e4, 1.6e5)

# Store stimulus checks amounts
mn_stimulus_check <- array(NA, dim=c(length(ar_income), 2, 5))

# Solve and Store stimulus by kids count and marital status
for (it_kids in 0:4){
  for (bl_marital in c(0,1)){
    # Solve and Store
    ar_stimulus_check <- ffp_snw_stimulus_checks_bush(ar_income, it_kids, bl_marital)
    mn_stimulus_check[, bl_marital+1, it_kids+1] <- ar_stimulus_check
  }
}

# Labeling
dimnames(mn_stimulus_check)[[1]] = paste0('income=', round(ar_income, 0))
dimnames(mn_stimulus_check)[[2]] = paste0('married=', 0:1)
dimnames(mn_stimulus_check)[[3]] = paste0('kids=', 0:4)

# Print
print('mn_stimulus_check')
print(mn_stimulus_check)

Compute Average Stimulus by Income Bin for Multiple Households in Dataframe

We have a dataframe of households, where each household is defined by the number of kids in the household, marital status, and also income bin. Note that this is an income bin, not a specific income level. We computes an approximate income-bin (and marital status and kids count) specific stimulus amount by evaluating the stimulus checks function along a fine grid of income levels from the min to the max point of the income-bin, and simply take the average.

We do this first for the actual stimulus that households should receive under the Economic Stimulus Act of 2008. We then adjust parameters for the stimulus function and compute alternative max-stimulus bounds for each income bin.

Test the Stimulus Determiniation Function Line by ine

We develop the function by testing out the code line by line first.

First, load in the testing dataframe df_nsw_tiny_chk168_df_id.

# Load file
data(df_nsw_tiny_chk168_df_id)
df_id <- df_nsw_tiny_chk168_df_id
# Print results
print(df_id)

Second, parse the ymin_group group.

# what 1 in model equals to
fl_multiple <- 58056

# Define input variables
svr_ymin_group <- 'ymin_group'

# Parse the ymin group
df_id <- df_id %>%
    rowwise() %>%
    mutate(!!sym(svr_ymin_group) := as.character(!!sym(svr_ymin_group))) %>%
    mutate(y_group_min = substring(strsplit(!!sym(svr_ymin_group), ",")[[1]][1], 2),
           y_group_max = gsub(strsplit(!!sym(svr_ymin_group), ",")[[1]][2],  pattern = "]", replacement = "")) %>%
    mutate(y_group_min = fl_multiple*as.numeric(y_group_min), 
           y_group_max = fl_multiple*as.numeric(y_group_max)) %>%
    ungroup()
# Print results
print(df_id[1:10,])

Third, generate an income array with y_group_min and y_group_max, and call the stimulus function to solve for stimulus along the income array, and then take average. Set various parameters

# Dollar per Check
fl_percheck_dollar <- 100

# Define input variables
svr_id <- 'id_i'
svr_marital <- 'marital'
svr_kids <- 'kids'

# Define other parameters
fl_stimulus_child <- 300
fl_stimulus_adult_min <- 300
fl_stimulus_adult_max <- 600
fl_per_adult_phase_out <- 75000
fl_phase_out_per_dollar_income <- 0.05

# fl_stimulus_child <- ls_stimulus_specs$fl_stimulus_child
# fl_stimulus_adult_min <- ls_stimulus_specs$fl_stimulus_adult_min
# fl_stimulus_adult_max <- ls_stimulus_specs$fl_stimulus_adult_max
# fl_per_adult_phase_out <- ls_stimulus_specs$fl_per_adult_phase_out
# fl_phase_out_per_dollar_income <- ls_stimulus_specs$fl_phase_out_per_dollar_income

# Compute stimulus, averaging over array of income-specific stimulus
df_id <- df_id %>% 
  group_by(!!sym(svr_id)) %>%
  do(bush_rebate = 
       mean(ffp_snw_stimulus_checks_bush(
         ar_income = seq(.[['y_group_min']],
                         .[['y_group_max']], 
                         length.out=100),
         it_kids = .[[svr_kids]], 
         bl_marital = .[[svr_marital]],
         fl_stimulus_child=fl_stimulus_child,
         fl_stimulus_adult_min=fl_stimulus_adult_min,
         fl_stimulus_adult_max=fl_stimulus_adult_max,
         fl_per_adult_phase_out=fl_per_adult_phase_out,
         fl_phase_out_per_dollar_income=fl_phase_out_per_dollar_income
       ))) %>%
  unnest(c(bush_rebate)) %>%
  mutate(bush_rebate_n_checks = round(bush_rebate/fl_percheck_dollar)) %>% 
  left_join(df_id, by=svr_id)

# Display results
print(df_id)

Test the Function

Now we test the function ffp_snw_stimulus_checks_bush_add2dfid().

Test Actual Stimulus Allocation

First, we add in the actual policy bounds:

# Call and solve
df_id <- df_nsw_tiny_chk168_df_id
df_id_checkadded_actual <- ffp_snw_stimulus_checks_bush_add2dfid(
  df_id,
  it_income_n_in_seg = 100,
  fl_multiple = 58056,
  fl_percheck_dollar = 100,
  fl_stimulus_child=300,
  fl_stimulus_adult_min=300, fl_stimulus_adult_max=600,
  fl_per_adult_phase_out=75000,
  fl_phase_out_per_dollar_income=0.05)
# Display
print(df_id_checkadded_actual[1:10,])
# Summarize
vars.group <- c('kids', 'marital')
var.numeric <- 'bush_rebate'
str.stats.group <- 'allperc'
ar.perc <- c(0.01, 0.05, 0.10, 0.20, 0.30, 0.40, 0.50, 0.70, 0.90)
ls_summ_by_group <- ff_summ_bygroup(df_id_checkadded_actual, 
                                    vars.group, var.numeric, str.stats.group, ar.perc)
df_table_grp_stats <- ls_summ_by_group$df_table_grp_stats
print(round(df_table_grp_stats,0) %>% 
        select(vars.group, one_of(
          'mean', '1%', '5%', '10%', '20%', '30%', '50%', '90%')))

Test Tripling Tax Rebate Bound for Higher Income Households

Second, we will triple the amount of stimulus received for adult and for kids, but keep the base amount the same, and set phase-out per_dollar income to 0. By doing this, we are no longer finding the stimulus under the actual policy, but generating upper allocation bounds based on tax-liability.

# Child stimulus triple
fl_stimulus_child=300*3
fl_stimulus_adult_max=600*3
fl_phase_out_per_dollar_income=0
# Call and solve
df_id <- df_nsw_tiny_chk168_df_id
df_id_checkadded_x3chd_x3adthgbd <- ffp_snw_stimulus_checks_bush_add2dfid(
  df_id,
  fl_multiple = 58056,
  fl_percheck_dollar = 100,
  fl_stimulus_child=fl_stimulus_child,
  fl_stimulus_adult_min=300, fl_stimulus_adult_max=fl_stimulus_adult_max,
  fl_phase_out_per_dollar_income=fl_phase_out_per_dollar_income)
# Display
print(df_id_checkadded_x3chd_x3adthgbd[1:10,])
# Summarize
ls_summ_by_group <- ff_summ_bygroup(df_id_checkadded_x3chd_x3adthgbd, 
                                    vars.group, var.numeric, str.stats.group, ar.perc)
df_table_grp_stats <- ls_summ_by_group$df_table_grp_stats
print(round(df_table_grp_stats,0) %>% 
        select(vars.group, one_of(
          'mean', '1%', '5%', '10%', '20%', '30%', '50%', '90%')))

Test Tripling Tax Rebate Bound for Higher Income Households and Tripling Upper Bound for Lower Income Households As Well

Third, we will triple the amount of stimulus received for adult and for kids, and also triple the base amount (upper-bound) for lowest income group, and set phase-out per_dollar income to 0.

# Child stimulus triple
fl_stimulus_child=300*3
fl_stimulus_adult_max=600*3
fl_stimulus_adult_min=300*3
fl_phase_out_per_dollar_income=0
# Call and solve
df_id <- df_nsw_tiny_chk168_df_id
df_id_checkadded_x3chd_x3adthgbdlwbd <- ffp_snw_stimulus_checks_bush_add2dfid(
  df_id,
  fl_multiple = 58056,
  fl_percheck_dollar = 100,
  fl_stimulus_child=fl_stimulus_child,
  fl_stimulus_adult_min=fl_stimulus_adult_min, fl_stimulus_adult_max=fl_stimulus_adult_max,
  fl_phase_out_per_dollar_income=fl_phase_out_per_dollar_income)
# Display
print(df_id_checkadded_x3chd_x3adthgbdlwbd[1:10,])
# Summarize
ls_summ_by_group <- ff_summ_bygroup(df_id_checkadded_x3chd_x3adthgbdlwbd, 
                                    vars.group, var.numeric, str.stats.group, ar.perc)
df_table_grp_stats <- ls_summ_by_group$df_table_grp_stats
print(round(df_table_grp_stats,0) %>% 
        select(vars.group, one_of(
          'mean', '1%', '5%', '10%', '20%', '30%', '50%', '90%')))

FanWangEcon/PrjOptiAlloc documentation built on Jan. 25, 2022, 6:55 a.m.