bunchit {bunching}

Bunching Estimator

Description

Implement the bunching estimator in a kink or notch setting.

Usage

bunchit(
  z_vector,
  binv = "median",
  zstar,
  binwidth,
  bins_l,
  bins_r,
  poly = 9,
  bins_excl_l = 0,
  bins_excl_r = 0,
  extra_fe = NA,
  rn = NA,
  n_boot = 100,
  correct = TRUE,
  correct_above_zu = FALSE,
  correct_iter_max = 200,
  t0,
  t1,
  notch = FALSE,
  force_notch = FALSE,
  e_parametric = FALSE,
  e_parametric_lb = 1e-04,
  e_parametric_ub = 3,
  seed = NA,
  p_title = "",
  p_xtitle = deparse(substitute(z_vector)),
  p_ytitle = "Count",
  p_title_size = 11,
  p_axis_title_size = 10,
  p_axis_val_size = 8.5,
  p_miny = 0,
  p_maxy = NA,
  p_ybreaks = NA,
  p_freq_color = "black",
  p_cf_color = "maroon",
  p_zstar_color = "red",
  p_grid_major_y_color = "lightgrey",
  p_freq_size = 0.5,
  p_freq_msize = 1,
  p_cf_size = 0.5,
  p_zstar_size = 0.5,
  p_b = FALSE,
  p_e = FALSE,
  p_b_e_xpos = NA,
  p_b_e_ypos = NA,
  p_b_e_size = 3,
  p_domregion_color = "blue",
  p_domregion_ltype = "longdash"
)

Arguments

z_vector

a numeric vector of (unbinned) data.

binv

a string setting location of zstar within its bin ("min", "max" or "median" value). Default is median.

zstar

a numeric value for the the bunching point.

binwidth

a numeric value for the width of each bin.

bins_l

number of bins to left of zstar to use in analysis.

bins_r

number of bins to right of zstar to use in analysis.

poly

a numeric value for the order of polynomial for counterfactual fit. Default is 9.

bins_excl_l

number of bins to left of zstar to include in bunching region. Default is 0.

bins_excl_r

number of bins to right of zstar to include in bunching region. Default is 0.

extra_fe

a numeric vector of bin values to control for using fixed effects. Default includes no controls.

rn

a numeric vector of (up to 2) round numbers to control for. Default includes no controls.

n_boot

number of bootstrapped iterations. Default is 100.

correct

implements correction for integration constraint. Default is TRUE.

correct_above_zu

if integration constraint correction is implemented, should counterfactual be shifted only above zu (upper bound of exclusion region)? Default is FALSE (i.e. shift from above zstar).

correct_iter_max

maximum iterations for integration constraint correction. Default is 200.

t0

numeric value setting the marginal (average) tax rate below zstar in a kink (notch) setting.

t1

numeric value setting the marginal (average) tax rate above zstar in a kink (notch) setting.

notch

whether analysis is for a kink or notch. Default is FALSE (kink).

force_notch

whether to enforce user's choice of zu (upper limit of bunching region) in a notch setting. Default is FALSE (zu set by setting bunching equal to missing mass).

e_parametric

whether to estimate elasticity using parametric specification (quasi-linear and iso-elastic utility function). Default is FALSE (which estimates reduced-form approximation).

e_parametric_lb

lower bound for elasticity estimate's solution using parametric specification in notch setting. Default is 1e-04.

e_parametric_ub

upper bound for elasticity estimate's solution using parametric specification in notch setting. Default is 3.

seed

a numeric value for bootstrap seed (random re-sampling of residuals). Default is NA.

p_title

plot's title. Default is empty.

p_xtitle

plot's x_axis label. Default is the name of z_vector.

p_ytitle

plot's y_axis label. Default is "Count".

p_title_size

size of plot's title. Default is 11.

p_axis_title_size

size of plot's axes' title labels. Default is 10.

p_axis_val_size

size of plot's axes' numeric labels. Default is 8.5.

p_miny

plot's minimum y_axis value. Default is 0.

p_maxy

plot's maximum y_axis value. Default is optimized internally.

p_ybreaks

a numeric vector of y-axis values at which to add horizontal line markers in plot. Default is optimized internally.

p_freq_color

plot's frequency line color. Default is "black".

p_cf_color

plot's counterfactual line color. Default is "maroon".

p_zstar_color

plot's bunching region marker lines color. Default is "red".

p_grid_major_y_color

plot's y-axis major grid line color. Default is "lightgrey".

p_freq_size

plot's frequency line thickness. Default is 0.5.

p_freq_msize

plot's frequency line marker size. Default is 1.

p_cf_size

plot's counterfactual line thickness. Default is 0.5.

p_zstar_size

plot's bunching region marker line thickness. Default is 0.5.

p_b

whether plot should also include the bunching estimate. Default is FALSE.

p_e

whether plot should also include the elasticity estimate. Only shown if p_b is TRUE. Default is FALSE.

p_b_e_xpos

plot's x-axis coordinate of bunching/elasticity estimate. Default is set internally.

p_b_e_ypos

plot's y-axis coordinate of bunching/elasticity estimate. Default is set internally.

p_b_e_size

size of plot's printed bunching/elasticity estimate. Default is 3.

p_domregion_color

plot's dominated region marker line color in notch setting. Default is "blue".

p_domregion_ltype

line type for the vertical line type marking the dominated region (zD) in the plot for notch settings. Default is "longdash".

Details

bunchit implements the bunching estimator in both kink and notch settings. It bins a given numeric vector, fits a counterfactual density, and estimates the bunching mass (normalized and not), the elasticity and the location of the marginal buncher. In the case of notches, it also finds the dominated region and estimates the fraction of observations located in it.

Value

bunchit returns a list of results, both for visualizing and for further analysis of the data underlying the estimates. These include:

plot

The bunching plot.

data

The binned data used for estimation.

cf

The estimated counterfactuals.

B

The estimated excess mass (not normalized).

B_vector

The vector of bootstrapped B's.

B_sd

The standard deviation of B_vector.

b

The estimated excess mass (normalized).

b_vector

The vector of bootstrapped b's.

b_sd

The standard deviation of b_vector.

e

The estimated elasticity.

e_vector

The vector of bootstrapped elasticities (e).

e_sd

The standard deviation of e_vector.

alpha

The estimated fraction of bunchers in dominated region (notch case).

alpha_vector

The vector of bootstrapped alphas.

alpha_sd

The standard deviation of alpha_vector.

model_fit

The model fit on the actual (i.e. not bootstrapped) data.

zD

The value demarcating the dominated region (notch case).

zD_bin

The bin above zstar demarcating the dominated region (notch case).

zU_bin

The location of zU (upper range of excluded region) as estimated from notch setting by setting force_notch = FALSE.

marginal_buncher

The location (z value) of the marginal buncher.

marginal_buncher_vector

The vector of bootstrapped marginal_buncher values.

marginal_buncher_sd

The standard deviation of marginal_buncher_vector.

See Also

plot_hist

Examples

## Not run: 
# First, load the example data
data(bunching_data)

# Example 1: Kink with integration constraint correction
kink1 <- bunchit(z_vector = bunching_data$kink, zstar = 10000, binwidth = 50,
                 bins_l = 20, bins_r = 20, poly = 4, t0 = 0, t1 = .2,
                 p_b = TRUE, seed = 1)
kink1$plot
kink1$b
kink1$b_sd

# Example 2: Kink with diffuse bunching
bpoint <- 10000; binwidth <- 50
kink2_vector <- c(bunching_data$kink_vector,
                 rep(bpoint - binwidth,80), rep(bpoint - 2*binwidth,190),
                 rep(bpoint + binwidth,80), rep(bpoint + 2*binwidth,80))
kink2 <- bunchit(z_vector = kink2_vector, zstar = 10000, binwidth = 50,
                 bins_l = 20, bins_r = 20, poly = 4,  t0 = 0, t1 = .2,
                 bins_excl_l = 2, bins_excl_r = 2, correct = FALSE,
                 p_b = TRUE, seed = 1)
kink2$plot

# Example 3: Kink with further bunching at other level in bandwidth
kink3_vector <- c(bunching_data$kink_vector, rep(10200,540))
kink3 <- bunchit(kink3_vector, zstar = 10000, binwidth = 50,
                 bins_l = 40, bins_r = 40, poly = 6, t0 = 0, t1 = .2,
                 correct = FALSE, p_b = TRUE, extra_fe = 10200, seed = 1)
kink3$plot

# Example 4: Kink with round number bunching
rn1 <- 500;  rn2 <- 250
bpoint <- 10000
kink4_vector <- c(bunching_data$kink_vector,
                  rep(bpoint + rn1, 270),
                  rep(bpoint + 2*rn1,230),
                  rep(bpoint - rn1,260),
                  rep(bpoint - 2*rn1,275),
                  rep(bpoint + rn2, 130),
                  rep(bpoint + 3*rn2,140),
                  rep(bpoint - rn2,120),
                  rep(bpoint - 3*rn2,135))
kink4 <- bunchit(z_vector = kink4_vector, zstar = bpoint, binwidth = 50,
                 bins_l = 20, bins_r = 20, poly = 6, t0 = 0, t1 = .2,
                 correct = FALSE, p_b = TRUE, p_e = TRUE, p_freq_msize = 1.5,
                 p_b_e_ypos = 880, rn = c(250,500), seed = 1)
kink4$plot

# Example 5: Notch
notch <- bunchit(z_vector = bunching_data$notch_vector, zstar = 10000, binwidth = 50,
                 bins_l = 40, bins_r = 40, poly = 5, t0 = 0.18, t1 = .25,
                 correct = FALSE, notch = TRUE,p_b = TRUE, p_b_e_xpos = 8900,
                 n_boot = 0)
notch$plot

## End(Not run)