boundary_var: Variance on the boundary

In xhuang20/rdcqr: Local Composite Quantile Regression Method for Regression Discontinuity

Description

This function computes variance and adjusted variance on the boundary for a sharp RD using the local composite quantile regression method. It also returns several other quantities that will be used in computing the variance in a fuzzy RD.

Usage

boundary_var(dat, kernID = 0, left = TRUE, maxit = 100, tol = 1.0e-4,
 para = 1, grainsize = 1, llr.residuals = TRUE, ls.derivative = TRUE)

Arguments

dat	A list with the following components: y A vector of treatment outcomes, In a fuzzy RD, this variable can also be a vector of treatment assignment variables. x A vector of covariates. q Number of quantiles to be used in estimation. Defaults to 5. It needs to be an odd number. h A scalar bandwidth. tau Quantile positions that correspond to the q quantiles. They are obtained by tau = (1:q)/(q+1). p Degree of polynomial in LCQR estimation. Set it to 1 when estimating the residuals. n_all Total number of observations in the data set. f0_hat Estimated density of the covariate at x = 0. fd1 Estimated first derivative of the density of the covariate at x = 0.
kernID	Kernel id number. Defaults to 0. kernID = 0: triangular kernel. kernID = 1: biweight kernel. kernID = 2: Epanechnikov kernel. kernID = 3: Gaussian kernel. kernID = 4: tricube kernel. kernID = 5: triweight kernel. kernID = 6: uniform kernel.
left	A logical variable that takes the value TRUE for data to the left of (below) the cutoff. Defaults to TRUE.
maxit	Maximum iteration number in the MM algorithm for quantile estimation. Defaults to 100.
tol	Convergence criterion in the MM algorithm. Defaults to 1.0e-4.
para	A 0/1 variable specifying whether to use parallel computing. Defaults to 1.
grainsize	Minimum chunk size for parallelization. Defaults to 1.
llr.residuals	Whether to use residuals from the local linear regression as the input to compute the LCQR standard errors and the corresponding bandwidths. Defaults to TRUE. If this option is set to TRUE, the treatment effect estimate and the bias-correction is still done in LCQR. We use the same kernel function used in LCQR in the local linear regression to obtain the residuals and use them to compute the unadjusted and adjusted asymptotic standard errors and the bandwidths. This option will improve the speed. One can use this opition to get a quick estimate of the standard errors when the sample size is large. To use residuals from the LCQR method, set llr.residuals = FALSE.
ls.derivative	Whether to use a global quartic and quintic polynomial to estimate the second and third derivatives of the conditional mean function. Defaults to TRUE.

Value

boundary_var returns a list with the following components:

var	Estimated variance on the boundary.
var_adj	Adjusted variance estimate on the boundary.
e_hat	Residuals adjusted by the estimated standard deviations.
ss_0	The S matrix in Huang and Zhan (2021) when the degree of the polynomial in estimation is equal to 1.
ss_1	The S matrix in Huang and Zhan (2021) when the degree of the polynomial in estimation is equal to 2.
sig0_hat	Estimated conditional standard deviation at the cutoff 0.
var_bias	Estimated variance of the bias.
var_cov	Estimated covariance between the conditional mean and its bias.
ac	The constant in the bias expression.
bias_fixedn	The bias based on fixed-n approximation.

There are also several returned values with suffix "fixedn", which are the counterparts of the above values based on the fixed-n approximation.

References

Huang and Zhan (2021) "Local Composite Quantile Regression for Regression Discontinuity," working paper.

Examples

## Not run: 
# Use the headstart data.
data(headstart)
data_p = subset(headstart, headstart$poverty > 0)
p = 1
q = 5
tau = (1:q) / (q + 1)
h_d0   = ks::hns(x, deriv.order = 0)
f0_hat = ks::kdde(x, h = h_d0, deriv.order = 0, eval.points = c(0))$estimate
h_d1   = ks::hns(x, deriv.order = 1)
fd1    = ks::kdde(x, h = h_d1, deriv.order = 1, eval.points = c(0))$estimate

# Set up the list to be passed to the boundary_var function.
# Supply a bandwidth equal to 2.0.
dat_p = list("x"      = data_p$poverty,
             "y"      = data_p$mortality,
             "q"      = q,
             "h"      = 2.0,
             "tau"    = tau,
             "p"      = p,
             "n_all"  = n_all,
             "f0_hat" = f0_hat,
             "fd1"    = fd1)

# Use the residuals from local linear regression for a quick try.
boundary_var(dat = dat_p, left = FALSE, llr.residuals = TRUE, ls.derivative = TRUE)

## End(Not run)

xhuang20/rdcqr documentation built on July 1, 2021, 5:22 a.m.