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variable = and the cutoff is at 0.5. Because the assignment variable is random, the curves [ (0) ] and [ (1) ]
are known to be flat. The ATE can be computed as the difference in the mean value of Y on either side
of the cutoff. Because the functions are flat everywhere, the “optimal bandwidth” is to use all the
data Thus an important in which an RD differs from a randomized experiment in
actuality The functional form of [ (0) ] and [ (1) ] need not be flat (or linear or
monotonic) and may not even be known. Fortin – Econ 560 Lecture 0 Fortin – Econ 560 Lecture 0 The original RD design (Thistlewaite and Campbell 1960) was implemented by
OLS.
=+
+
+
where τ is the causal effect of interest and is an error term. This regression distinguishes the nonlinear and discontinuous jump from the smooth
linear function. OLS with one linear term in X is seldom used anymore because the functional form
assumptions are very strong. An alternative is to use a flexible function of ( )
= + + ( )+ Perhaps the simplest ( ) is way to approximate via OLS polynomials X
=+
+
+ ⋯+
+
+
+
+⋯+
+ Fortin – Econ 560 Lecture 0 Common practice is to fit different polynomial functions on each side of the cutoff
by including interactions between D and X. Centering X at the cutoff prior to running the regression ensures that the coefficient
on D is the treatment effect. OLS with polynomials is a particularly simple way of allowing a flexible functional
form in X. Fortin – Econ 560 Lecture 0 A drawback is that it provides global estimates of the regression function that use
data far from the cutoff. This leads to the Local Linear Regression approach Instead of locally fitting a constant function (e.g., the mean), we can fit linear
regressions to observations within a distance h on either side of the discontinuity
point:
o A rectangular kernel seems to work best (see Imbens and Lemieux), but
optimal bandwidth selection is an open question
Linear vs. Local Linear Regression VOL. 1 NO. 1 CArpENtEr ANd dOBkiN: EffECt Of ALCOhOL CONsumptiON ON mOrtALity 177 40 35 Death rate per 100,000 30
Alcohol
Homicide
Suicide
MVA
Drugs
External other 25 20 Alcohol fitted
Homicide fitted
Suicide fitted
MVA fitted
Drugs fitted
External o...
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 Fall '13
 NicoleFortin
 Economics

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