Skip to contents

Regression Discontinuity Estimation

rd_est.Rd

rd_est estimates both sharp and fuzzy RDDs using parametric and non-parametric (local linear) models. It is based on the RDestimate function in the "rdd" package. Sharp RDDs (both parametric and non-parametric) are estimated using lm in the stats package. Fuzzy RDDs (both parametric and non-parametric) are estimated using two-stage least-squares ivreg in the AER package. For non-parametric models, Imbens-Kalyanaraman optimal bandwidths can be used,

Usage

rd_est(
  formula,
  data,
  subset = NULL,
  cutpoint = NULL,
  bw = NULL,
  kernel = "triangular",
  se.type = "HC1",
  cluster = NULL,
  verbose = FALSE,
  less = FALSE,
  est.cov = FALSE,
  est.itt = FALSE,
  t.design = NULL
)

Arguments

formula

The formula of the RDD; a symbolic description of the model to be fitted. This is supplied in the format of y ~ x for a simple sharp RDD or y ~ x | c1 + c2 for a sharp RDD with two covariates. A fuzzy RDD may be specified as y ~ x + z where x is the running variable, and z is the endogenous treatment variable. Covariates are included in the same manner as in a sharp RDD.

data

An optional data frame containing the variables in the model. If not found in data, the variables are taken from environment(formula).

subset

An optional vector specifying a subset of observations to be used in the fitting process.

cutpoint

A numeric value containing the cutpoint at which assignment to the treatment is determined. The default is 0.

bw

A vector specifying the bandwidths at which to estimate the RD. Possible values are "IK09", "IK12", and a user-specified non-negative numeric vector specifying the bandwidths at which to estimate the RD. The default is "IK12". If bw is "IK12", the bandwidth is calculated using the Imbens-Kalyanaraman 2012 method. If bw is "IK09", the bandwidth is calculated using the Imbens-Kalyanaraman 2009 method. Then the RD is estimated with that bandwidth, half that bandwidth, and twice that bandwidth. If only a single value is passed into the function, the RD will similarly be estimated at that bandwidth, half that bandwidth, and twice that bandwidth.

kernel

A string indicating which kernel to use. Options are "triangular" (default and recommended), "rectangular", "epanechnikov", "quartic", "triweight", "tricube", and "cosine".

se.type

This specifies the robust standard error calculation method to use, from the "sandwich" package. Options are, as in vcovHC, "HC3", "const", "HC", "HC0", "HC1", "HC2", "HC4", "HC4m", "HC5". The default is "HC1". This option is overridden by cluster.

cluster

An optional vector of length n specifying clusters within which the errors are assumed to be correlated. This will result in reporting cluster robust SEs. This option overrides anything specified in se.type. It is suggested that data with a discrete running variable be clustered by each unique value of the running variable (Lee and Card, 2008).

verbose

A logical value indicating whether to print additional information to the terminal. The default is FALSE.

less

Logical. If TRUE, return the estimates of linear and optimal. If FALSE return the estimates of linear, quadratic, cubic, optimal, half and double. The default is FALSE.

est.cov

Logical. If TRUE, the estimates of covariates will be included. If FALSE, the estimates of covariates will not be included. The default is FALSE. This option is not applicable if method is "front".

est.itt

Logical. If TRUE, the estimates of ITT will be returned. The default is FALSE.

t.design

A string specifying the treatment option according to design. Options are "g" (treatment is assigned if x is greater than its cutoff), "geq" (treatment is assigned if x is greater than or equal to its cutoff), "l" (treatment is assigned if x is less than its cutoff), and "leq" (treatment is assigned if x is less than or equal to its cutoff).

Value

rd_est returns an object of class "rd". The functions summary and plot are used to obtain and print a summary and plot of the estimated regression discontinuity. The object of class rd is a list containing the following components:

type

A string denoting either "sharp" or "fuzzy" RDD.

est

Numeric vector of the estimate of the discontinuity in the outcome under a sharp RDD or the Wald estimator in the fuzzy RDD, for each corresponding bandwidth.

se

Numeric vector of the standard error for each corresponding bandwidth.

z

Numeric vector of the z statistic for each corresponding bandwidth.

p

Numeric vector of the p-value for each corresponding bandwidth.

ci

The matrix of the 95 for each corresponding bandwidth.

d

Numeric vector of the effect size (Cohen's d) for each estimate.

cov

The names of covariates.

bw

Numeric vector of each bandwidth used in estimation.

obs

Vector of the number of observations within the corresponding bandwidth.

call

The matched call.

na.action

The number of observations removed from fitting due to missingness.

impute

A logical value indicating whether multiple imputation is used or not.

model

For a sharp design, a list of the lm objects is returned. For a fuzzy design, a list of lists is returned, each with two elements: firststage, the first stage lm object, and iv, the ivreg object. A model is returned for each corresponding bandwidth.

frame

Returns the dataframe used in fitting the model.

References

Lee, D. S., Lemieux, T. (2010). Regression Discontinuity Designs in Economics. Journal of Economic Literature, 48(2), 281-355. doi:10.1257/jel.48.2.281 .

Imbens, G., Lemieux, T. (2008). Regression discontinuity designs: A guide to practice. Journal of Econometrics, 142(2), 615-635. doi:10.1016/j.jeconom.2007.05.001 .

Lee, D. S., Card, D. (2010). Regression discontinuity inference with specification error. Journal of Econometrics, 142(2), 655-674. doi:10.1016/j.jeconom.2007.05.003 .

Angrist, J. D., Pischke, J.-S. (2009). Mostly harmless econometrics: An empiricist's companion. Princeton, NJ: Princeton University Press.

Drew Dimmery (2016). rdd: Regression Discontinuity Estimation. R package version 0.57. https://CRAN.R-project.org/package=rdd

Imbens, G., Kalyanaraman, K. (2009). Optimal bandwidth choice for the regression discontinuity estimator (Working Paper No. 14726). National Bureau of Economic Research. https://www.nber.org/papers/w14726.

Imbens, G., Kalyanaraman, K. (2012). Optimal bandwidth choice for the regression discontinuity estimator. The Review of Economic Studies, 79(3), 933-959. https://academic.oup.com/restud/article/79/3/933/1533189.

Examples

set.seed(12345)
x <- runif(1000, -1, 1)
cov <- rnorm(1000)
y <- 3 + 2 * x + 3 * cov + 10 * (x >= 0) + rnorm(1000)
rd_est(y ~ x, t.design = "geq")
#> 
#> Call:
#> rd_est(formula = y ~ x, t.design = "geq")
#> 
#> Coefficients:
#>     Linear   Quadratic       Cubic         Opt    Half-Opt  Double-Opt  
#>      10.23       10.67       10.66       10.47       10.57       10.30  
#> 
# Efficiency gains can be made by including covariates (review SEs in "summary" output).
rd_est(y ~ x | cov, t.design = "geq")
#> 
#> Call:
#> rd_est(formula = y ~ x | cov, t.design = "geq")
#> 
#> Coefficients:
#>     Linear   Quadratic       Cubic         Opt    Half-Opt  Double-Opt  
#>     10.049      10.068       9.829      10.047       9.896      10.052  
#>