help for rd_obs

Regression discontinuity (RD) estimator: obsolete version provided for backward > compatibility


rd_obs [varlist] [if] [in] [weight] [, options]

where varlist has the form outcomevar [treatmentvar] assignmentvar

+---------+ ----+ Weights +----------------------------------------------------------

aweights, fweights, and pweights are allowed; see help weights. Under Stata versions 9.2 or before (using locpoly to construct local regression estimates) aweights and pweights will be converted to fweights automatically and the data expanded. If this would exceed system memory limits, error r(901) will be issued; in this case, the user is advised to round weights. In any case, the validity of bootstrapped standard errors will depend on the expanded data correctly representing sampling variability, which may require rounding or replacing weight variables. Under Stata versions 10 or later (using lpoly to construct local regression estimates), all weights will be treated as aweights.

+----------------+ ----+ Important Note +---------------------------------------------------

Standard errors are currently only available by bootstrapping the command like so:

bs [, options]: rd_obs varlist [if] [in] [weight] [, options]

+----------------------------+ ----+ Table of Further Contents +---------------------------------------

General description of estimator Examples Detailed syntax Description of options Remarks and saved results References Acknowledgements Citation of rd_obs Author information

+-------------+ ----+ Description +------------------------------------------------------

rd_obs implements a set of regression-discontinuity estimation methods that are thought to have very good internal validity, for estimating the causal effect of some explanatory variable (called the treatment variable) for a particular subpopulation, under some often plausible assumptions. In this sense, it is much like an experimental design, except that levels of the treatment variable are not assigned randomly by the researcher. Instead, there is a jump in the conditional mean of the treatment variable at a known cutoff in another variable, called the assignment variable, which is perfectly observed, and this allows us to estimate the effect of treatment as if it were randomly assigned in the neighborhood of the known cutoff.

rd_obs is an alternative to various regression techniques that purport to allow causal inference (e.g. panel methods such as xtreg), instrumental variables (IV) and other IV-type methods (see the ivreg2 help file and references therein), and matching estimators (see the psmatch2 and nnmatch help files and references therein). The rd_obs approach is closest in spirit to an IV model with one exogenous variable excluded from the regression (excluded instrument), and one endogenous regressor.

rd_obs estimates local linear or "kernel" regression models on both sides of the cutoff. Estimates are sensitive to the choice of bandwidth, so by default several estimates are constructed using different bandwidths.

Further discussion of rd_obs appears in Nichols (2007).

+----------+ ----+ Examples +---------------------------------------------------------

In the simplest case, assignment to treatment depends on a variable Z being above a cutoff Z0. Frequently, Z is defined so that Z0=0. In this case, treatment is 1 for Z>=0 and 0 for Z<0, and we estimate local linear regressions on both sides of the cutoff to obtain estimates of the outcome at Z=0. The difference between the two estimates (for the samples where Z>=0 and where Z<0) is the estimated effect of treatment.

For example, having a Democratic representative in the US Congress may be considered a treatment applied to a Congressional district, and the assignment variable Z is the vote share garnered by the Democratic candidate. At Z=50%, the probability of treatment=1 jumps from zero to one. Suppose we are interested in the effect a Democratic representative has on the federal spending within a Congressional district. rd_obs estimates local linear regressions on both sides of the cutoff like so:

ssc inst rd, replace net get rd use votex if i==1 rd lne d, gr mbw(100) rd_obs lne d, gr mbw(100) line(`"xla(-.2 "Repub" 0 .3 "Democ", noticks > )"') rd_obs lne d, gr ddens bs: rd_obs lne d, x(pop-vet)

In a fuzzy RD design, the conditional mean of treatment jumps at the cutoff, and that jump forms the denominator of a Local Wald Estimator. The numerator is the jump in the outcome, and both are reported along with their ratio. Note that any sharp RD design may be estimated using the fuzzy RD syntax, since the denominator in that case is just one:

use votex if i==1 rd_obs lne win d, gr mbw(100) bs: rd_obs lne win d, x(pop-vet) erase votex.dta

+-----------------------------+ ----+ Detailed Syntax and Options +--------------------------------------

There should be two or three variables specified after the rd_obs command; if two are specified, a sharp RD design is assumed, where the treatment variable jumps from zero to one at the cutoff. If no variables are specified after the rd_obs command, the estimates table is displayed.

rd_obs outcomevar [treatmentvar] assignmentvar [if] [in] [weight] [, options]

+-----------------+ ----+ Options summary +--------------------------------------------------

mbw(numlist) specifies a list of multiples for bandwidths, in percentage terms. The default is "100 50 200" (i.e. half and twice the requested bandwidth) and 100 is always included in the list, regardless of whether it is specified.

z0(real) specifies the cutoff Z0 in assignmentvar.

x(varlist) requests estimates of jumps in control variables varlist.

ddens requests a computation of a discontinuity in the density of Z. This is computed in a relatively ad hoc way, and should be redone using McCrary's test described at http://www.econ.berkeley.edu/~jmccrary/DCdensity/.

s(stubname) requests that estimates be saved as new variables beginning with stubname.

graph requests that graphs for each bandwidth be produced.

noscatter suppresses the scatterplot on those graphs.

scopt(string) supplies an option list to the scatter plot.

lineopt(string) supplies an option list to the overlaid line plots.

n(real) specifies the number of points at which to calculate local linear regressions. The default is to calculate the regressions at 50 points above the cutoff, with equal steps in the grid, and to use equal steps below the cutoff, with the number of points determined by the step size.

bwidth(real) allows specification of a bandwidth for local linear regressions. The default is to choose a bandwidth that gives positive weight to at least 30 observations on each side of the discontinuity when estimating the conditional mean at the cutoff.

kernel(kerneltype) allows specification of a kernel for local linear regressions.

kerneltype Description ------------------------------------------------------------------------- epanechnikov Epanechnikov kernel function epan2 alternative Epanechnikov kernel function biweight biweight kernel function cosine cosine trace kernel function gaussian Gaussian kernel function parzen Parzen kernel function rectangle rectangle kernel function triangle triangle kernel function; the default -------------------------------------------------------------------------

+---------------------------+ ----+ Remarks and saved results +----------------------------------------

rd_obs does not report standard errors by default, nor does it report all saved estimates. Instead, it reports the Local Wald Estimate for each bandwidth used, and its components where applicable. To get all saved estimates, type rd_obs without arguments or type ereturn list.

To facilitate bootstrapping, rd_obs saves the following results in e():

Scalars e(N) Number of observations used in estimation e(w) Bandwidth in base model; other bandwidths are reported in e.g. e(w50) for the 50% multiple.

Macros e(cmd) rd_obs e(rdversion) Version number of rd_obs e(depvar) Name of dependent variable

Matrices e(b) Coefficient vector of estimated jumps in variables at different percentage bandwidth multiples

Functions e(sample) Marks estimation sample


Complete references appear in

Nichols, Austin. 2007. "Causal Inference with Observational Data." Prepublication draft available as http://pped.org/stata/ciwod.pdf

The interested reader is directed also to

Imbens, Guido and Thomas Lemieux. 2007. "Regression Discontinuity Designs: A Guide to Practice." NBER Working Paper 13039.

McCrary, Justin. 2007. "Manipulation of the Running Variable in the Regression Discontinuity Design: A Density Test." NBER Technical Working Paper 334.

Shadish, William R., Thomas D. Cook, and Donald T. Campbell. 2002. Experimental and Quasi-Experimental Designs for Generalized Causal Inference. Boston: Houghton Mifflin.


I would like to thank Justin McCrary for helpful discussions. Any errors are my own.

Citation of rd_obs

rd_obs is not an official Stata command. It is a free contribution to the research community, like a paper. Please cite it as such:

Nichols, Austin. 2007. rd: Stata module for regression discontinuity estimation. http://ideas.repec.org/c/boc/bocode/s456888.html


Austin Nichols Urban Institute Washington, DC, USA austinnichols@gmail.com

Also see

Manual: [U] 23 Estimation and post-estimation commands [R] bootstrap [R] lpoly in Stata 10, else locpoly (findit locpoly to install) [R] ivregress in Stata 10, else [R] ivreg [R] regress [XT] xtreg

On-line: help for (if installed) rd (newer version), ivreg2, overid, ivendog, ivhettest, ivreset, xtivreg2, xtoverid, ranktest, condivreg; psmatch2, nnmatch.