kink_estimator {bunchr}

Analyzing Bunching at a Kink

Description

Given a kinked budget set, this function gets a vector of earnings and analyzes bunching. This function could be run independently, but best used through the bunch function.

Usage

kink_estimator(earnings, zstar, t1, t2, cf_start = NA, cf_end = NA,
  exclude_before = 2, exclude_after = 2, binw = 10, poly_size = 7,
  convergence = 0.01, max_iter = 100, correct = TRUE, select = TRUE,
  draw = TRUE, title = "Bunching Visualization", varname = "Earnings")

Arguments

earnings

Vector of earnings, hopefully a very large one.

zstar

Place of kink (critical earning point).

t1

Marginal tax rate before kink.

t2

Marginal tax rate after kink.

cf_start

Number of bins before the kink bin where counter-factual histogram should start.

cf_end

Number of bins after the kink bin where counter-factual histogram should start.

exclude_before

Number of excluded bins before the kink bin.

exclude_after

Number of excluded bins after the kink bin.

binw

Bin width.

poly_size

Order of polynomial used to calculate counter-factual histogram.

convergence

Minimal rate of change of bunching estimate to stop iterations.

max_iter

Maximum number of iterations for bunching estimates.

correct

Should the counter-factual histogram be corrected to compensate for shifting left because of the notch? See details.

select

Should model selection be used to find counter-factual histogram? See details.

draw

Should a graph be drawn?

title

Title for plot output

varname

Name for running variable, to be desplayed in the plot

Details

A histogram is created from the earnings vector, with the kink point zstar as the center of one of the bins.

Correction of the counter-factual is required, as the kink-induced bunching will shift the whole distribution on the right side of the kink to the left. This option follows Chetty et al (2009) in correcting for this.

Model selection works using the step function from the stats package. It runs backwards from the full polynomial model, trying to find the best explanatory model using the Akaike information criterion.

Value

kink_estimator returns a list of the following variables:

e

Estimated elasticity

Bn

The sum of total estimated extra bunching in the excluded bins

b

The rate of extra bunching in the excluded area, divided by the length of area in \$

data

A data frame with bin mids, counts, counter-factual counts, and excluded dummy

References

Chetty, R., Friedman, J., Olsen, T., Pistaferri, L. (2009) Adjustment Costs, Firm Responses, and Micro vs. Macro Labor Supply Elasticities: Evidence from Danish Tax Records, Quarterly Journal of Economics, 126(2).

See Also

bunch, notch_estimator

Examples

ability_vec <- 4000 * rbeta(100000, 2, 5)
earning_vec <- sapply(ability_vec, earning_fun, 0.2, 0, 0.2, 0, 1000)
# bunch_viewer(earning_vec, 1000, 40, 40, 1, 1, binw = 10)
kink_estimator(earning_vec, 1000, 0, 0.2, 40, 40, 1, 1, binw = 10, draw = FALSE)$e