By Giovanni Cerulli

This booklet offers complex theoretical and utilized instruments for the implementation of recent micro-econometric strategies in evidence-based software review for the social sciences. the writer offers a entire toolbox for designing rigorous and potent ex-post software review utilizing the statistical software program package deal Stata. for every procedure, a statistical presentation is constructed, by means of a pragmatic estimation of the therapy results. through the use of either genuine and simulated info, readers turns into accustomed to review strategies, reminiscent of regression-adjustment, matching, difference-in-differences, instrumental-variables and regression-discontinuity-design and are given functional instructions for choosing and making use of appropriate equipment for particular coverage contexts.

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In this case we have that: αa ¼ fEðY j D ¼ 1Þ À EðYjD ¼ 0Þ g À β ÁfEðx j D ¼ 1Þ |{z} |ﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄ} |ﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄ} |ﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄ} 70 20 À2 À EðxjD ¼ 0Þ g ¼ 50 À ðÀ2Þ Á 40 ¼ À30 |ﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄ} 60 ð1:59Þ 20 showing that the “actual” effect of the policy—once groups are balanced over age—was even negative. In this case, in fact, the BIAS (À80) outweighs the value of DIM (50), thus leading to a final negative value of αa (À30). It is now quite clear that randomness is the way in which nature balances samples.

24) restricts the independence only over the mean. The CMI is the basis for (consistent) estimation of ATE, ATET, and ATENT by both parametric and nonparametric methods. Showing how these parameters are identified under CMI is straightforward. 27) we obtain: EðYjx, D ¼ 1Þ À EðYjx, D ¼ 0Þ ¼ EðY 1 jxÞ À EðY 0 jxÞ ¼ ATEðxÞ ð1:28Þ that, once rewritten, shows that: ATEðxÞ ¼ EðYjx, D ¼ 1Þ À EðYjx, D ¼ 0Þ ð1:29Þ where the RHS consists of all “observable quantities,” meaning that ATE(x) is correctly identified and no bias emerges.

23–24). Some tests for assessing the degree of overlap have been proposed in the literature and will be discussed in Chap. 2 along with sensitivity tests for assessing the reliability of conditional (mean) independence. 4 Characterizing Selection Bias 25 so that: α ¼ EðYjD ¼ 1Þ À EðYjD ¼ 0Þ ¼ DIM ð1:51Þ Assume now that the selection-into-treatment was driven by a factor x. It entails that the outcome is also a function of x: Y ¼ μa þ αa D þ βa x þ ua ð1:52Þ Y * ¼ μa þ αa D þ ua ð1:53Þ or equivalently: with Y* ¼ Y À βax.