{smcl}
{* 7oct2008}{...}
{hline}
help for {hi:rd_obs}
{hline}

{title:Regression discontinuity (RD) estimator: obsolete version provided for backward compatibility}

{title:Syntax}

{p 6 16 2}
{cmd:rd_obs} [{vars}] {ifin} {weight}
[{cmd:,} {it:{help rd_obs##options:options}}]

{p 6 16 2}where
{cmd:varlist} has the form {it:outcomevar} [{it:treatmentvar}]
{it:assignmentvar} 

{marker weights}{dlgtab:Weights}

{pstd}
{cmd:aweight}s, {cmd:fweight}s, and {cmd:pweight}s
are allowed; see help {help weights}.  Under Stata 
versions 9.2 or before (using
{help locpoly} to construct local regression estimates)
{cmd:aweight}s and {cmd:pweight}s will be converted to {cmd:fweight}s
automatically and the data {help expand}ed. If this would
exceed system memory limits, error {search 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 {help expand}ed data correctly representing sampling variability,
which may require rounding or replacing weight variables.
Under Stata 
versions 10 or later (using
{help lpoly} to construct local regression estimates), all weights
will be treated as {cmd:aweight}s.  

{marker note}{dlgtab:Important Note}

{pstd}Standard errors are currently only 
available by {help bootstrap}ping the command like so:

{p 6 16 2}
{cmd: bs} [, {it:{help bootstrap:options}}]: {cmd:rd_obs} {vars} {ifin} {weight}
[{cmd:,} {it:{help rd_obs##options:options}}]

{marker contents}{dlgtab: Table of Further Contents}
{p 6 16 2}

{p 2}{help rd_obs##description:General description of estimator}{p_end}
{p 2}{help rd_obs##examples:Examples}{p_end}
{p 2}{help rd_obs##options:Detailed syntax}{p_end}
{p 2}{help rd_obs##options:Description of options}{p_end}
{p 2}{help rd_obs##macros:Remarks and saved results}{p_end}
{p 2}{help rd_obs##refs:References}{p_end}
{p 2}{help rd_obs##acknow:Acknowledgements}{p_end}
{p 2}{help rd_obs##citation:Citation of {cmd:rd_obs}}{p_end}
{p 2}{help rd_obs##citation:Author information}{p_end}

{marker description}{dlgtab:Description}

{p}{cmd: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 {it:as if} it were randomly assigned in 
the neighborhood of the known cutoff.

{p}{cmd:rd_obs} is an alternative to various regression techniques
that purport to allow causal inference (e.g. panel methods such as {help xtreg}), instrumental
variables (IV) and other IV-type methods
(see the {stata "view http://fmwww.bc.edu/repec/bocode/i/ivreg2.hlp":ivreg2} 
help file and references therein),
and matching estimators (see the {stata "view http://fmwww.bc.edu/repec/bocode/p/psmatch2.hlp":psmatch2} 
and {stata "view http://fmwww.bc.edu/repec/bocode/n/nnmatch.hlp":nnmatch} help files and references therein).
The {cmd:rd_obs} approach is closest in spirit to an IV model with one exogenous variable excluded
from the regression ({it:excluded instrument}),
and one endogenous regressor.

{p}{cmd: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.

{p}Further discussion of {cmd:rd_obs} appears in {help rd_obs##refs:Nichols (2007)}.

{marker examples}{dlgtab:Examples}

{p}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. 

{p}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.
{cmd:rd_obs} estimates local linear regressions on both sides of the cutoff like so:

{col 9}{stata "ssc inst rd, replace" : ssc inst rd, replace}
{col 9}{stata "net get rd" : net get rd}
{col 9}{stata "use votex if i==1" : use votex if i==1}
{col 9}{stata `"rd_obs lne d, gr mbw(100)"' : rd lne d, gr mbw(100)}
{col 9}{stata `"rd_obs lne d, gr mbw(100) line(`"xla(-.2 "Repub" 0 .3 "Democ", noticks)"')"' : rd_obs lne d, gr mbw(100) line(`"xla(-.2 "Repub" 0 .3 "Democ", noticks)"')}
{col 9}{stata "rd_obs lne d, gr ddens" : rd_obs lne d, gr ddens}
{col 9}{stata "bs: rd_obs lne d, x(pop-vet)" : bs: rd_obs lne d, x(pop-vet)}

{p}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:

{col 9}{stata "use votex if i==1" : use votex if i==1}
{col 9}{stata "rd_obs lne win d, gr mbw(100)" : rd_obs lne win d, gr mbw(100)}
{col 9}{stata "bs: rd_obs lne win d, x(pop-vet)" : bs: rd_obs lne win d, x(pop-vet)}
{col 9}{stata "erase votex.dta" : erase votex.dta}

{marker options}{dlgtab:Detailed Syntax and Options}

{p}There should be two or three variables specified after the {cmd: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 {cmd:rd_obs} command, the estimates table is displayed.

{p 6 16 2}
{cmd:rd_obs} {it:outcomevar} [{it:treatmentvar}]
{it:assignmentvar} {ifin} {weight}
[{cmd:,} {it:{help rd_obs##options:options}}]

{pstd}

{dlgtab:Options summary}

{p 0 4}{cmd:mbw({it: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.

{p 0 4}{cmd:z0({it:real})} specifies the cutoff Z0 in {it:assignmentvar}.

{p 0 4}{cmd:x({it:varlist})} requests estimates of jumps in control variables {it:varlist}.

{p 0 4}{cmdab:dd:ens} 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 
{browse "http://www.econ.berkeley.edu/~jmccrary/DCdensity/":http://www.econ.berkeley.edu/~jmccrary/DCdensity/}.{p_end}

{p 0 4}{cmd:s({it:stubname})} requests that estimates be saved as new variables beginning with {it:stubname}.

{p 0 4}{cmdab:gr:aph} requests that graphs for each bandwidth be produced.

{p 0 4}{cmdab:nosc:atter} suppresses the scatterplot on those graphs.

{p 0 4}{cmdab:sco:pt(}{it:string}{cmd:)} supplies an option list to the scatter plot.

{p 0 4}{cmdab:line:opt(}{it:string}{cmd:)} supplies an option list to the overlaid line plots.

{p 0 4}{cmd:n({it: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.

{p 0 4}{cmdab:bw:idth(}{it:real}{cmd:)} 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.

{p 0 4}{cmdab:k:ernel(}{it:kerneltype}{cmd:)} allows specification of a kernel for local linear regressions.

{p 4 6 2}

{synoptset 29}{...}
{marker kernel}{...}
{synopthdr :kerneltype}
{synoptline}
{synopt :{opt epa:nechnikov}}Epanechnikov kernel function{p_end}
{synopt :{opt epan2}}alternative Epanechnikov kernel function{p_end}
{synopt :{opt bi:weight}}biweight kernel function{p_end}
{synopt :{opt cos:ine}}cosine trace kernel function{p_end}
{synopt :{opt gau:ssian}}Gaussian kernel function{p_end}
{synopt :{opt par:zen}}Parzen kernel function{p_end}
{synopt :{opt rec:tangle}}rectangle kernel function{p_end}
{synopt :{opt tri:angle}}triangle kernel function; the default{p_end}
{synoptline}
{p2colreset}{...}
{p 4 6 2}


{marker macros}{dlgtab:Remarks and saved results}

{p}{cmd: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 {cmd:rd_obs} without arguments or type {help ereturn:ereturn list}.

{p}To facilitate {help bootstrap}ping, {cmd:rd_obs} saves the following results in {cmd:e()}:

Scalars
{col 4}{cmd:e(N)}{col 18}Number of observations used in estimation
{p 3 18 2}{cmd:e(w)} {space 8} Bandwidth in base model; other bandwidths are reported in e.g. e(w50) for the 50% multiple.

Macros
{col 4}{cmd:e(cmd)}{col 18}{cmd:rd_obs}
{col 4}{cmd:e(rdversion)}{col 18}Version number of {cmd:rd_obs}
{col 4}{cmd:e(depvar)}{col 18}Name of dependent variable

Matrices
{p 3 18 2}{cmd:e(b)} {space 8} Coefficient vector of estimated jumps in variables at different percentage bandwidth multiples

Functions
{col 4}{cmd:e(sample)}{col 18}Marks estimation sample


{marker refs}{title:References}

{p}Complete references appear in 

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

{p}The interested reader is directed also to

{phang}Imbens, Guido and Thomas Lemieux. 2007. "Regression Discontinuity Designs: A Guide to Practice." 
{browse "http://nber.org/papers/w13039":NBER Working Paper 13039}.

{phang}McCrary, Justin. 2007. "Manipulation of the Running Variable in the Regression Discontinuity Design: 
A Density Test." {browse "http://nber.org/papers/t0334":NBER Technical Working Paper 334}.

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

{marker acknow}{title:Acknowledgements}

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

{marker citation}{title:Citation of {cmd:rd_obs}}

{p}{cmd: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: {p_end}

{phang}Nichols, Austin. 2007.
rd: Stata module for regression discontinuity estimation.
{browse "http://ideas.repec.org/c/boc/bocode/s456888.html":http://ideas.repec.org/c/boc/bocode/s456888.html}{p_end}

{title:Author}

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

{title:Also see}

{p 1 14}Manual:  {hi:[U] 23 {help est: Estimation} and {help postest: post-estimation} commands}{p_end}
{p 10 14}{manhelp bootstrap R}{p_end}
{p 10 14}{manhelp lpoly R} in Stata 10, else {help locpoly} ({stata "findit locpoly":findit locpoly} to install){p_end}
{p 10 14}{manhelp ivregress R} in Stata 10, else {manhelp ivreg R}{p_end}
{p 10 14}{manhelp regress R}{p_end}
{p 10 14}{manhelp xtreg XT}{p_end}

{p 1 10}On-line: help for (if installed)  {help rd} (newer version), {help ivreg2},
{help overid}, {help ivendog}, {help ivhettest}, {help ivreset},
{help xtivreg2}, {help xtoverid}, {help ranktest},
{help condivreg}; {help psmatch2}, {help nnmatch}.
{p_end}