Methods in Labor Economics

5 because the assignment variable is random the

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Unformatted text preview: e assignment 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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