, Figure 3.5: Voter Turnout in the US and EDR Laws, by Wave of Adoption Turnout %, 1920.

, Wave 1 (ME, MN, WI) Pen. Synthetic Control .95 Confidence Interval Turnout %, 1920.

I. A. Ct and . Mt)-pen, Synthetic Control .95 Confidence Interval Note: The top left panel is the first wave of adoption, vol.3

, Note: This table reports point estimates, .95 confidence interval and p-value for the test of nullity of each coefficient from the weighted linear regression (BLP) for the private program

, Dimension of Heterogeneity (CLAN)

E. |x and Z. , Since we detected some heterogeneity in both the take-up and the intent-to-treat, we perform the CLAN. If the dimensions of heterogeneity differs between ?(X)

?. |x and Z. , then we can conclude that there is some heterogeneity in the condiof characteristics, suggesting heterogeneity in the conditional LATE. In particular, for the public program, there are more individuals targeting managerlevel positions amongst the least likely to enter, although they are not particularly overrepresented amongst the "low-responders" in terms of ITT. The unskilled and high-school dropouts are over-represented among the least likely to enter

, Note: This table reports results from the regression of an unbiased signal of entry intro the program,D = D(Z ? p(X))/(p(X)(1 ? p(X))), on the ML proxies for the individual baseline outcome and the individual treatment effect

, Note: This table reports results from the regression of an unbiased signal of entry intro the program,D = D(Z ? p(X))/(p(X)(1 ? p(X))), on the ML proxies for the individual baseline outcome and the individual treatment effect

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;. .. Lemma, Model Selection Consistency)

. Lemma, Density of the Post-Selection estimator, 2006.

. Lemma, Balancing Weights)

). .. Robustness,

;. .. Theorem, Asymptotic Normality of the Immunized Estimator), p.31

;. .. Theorem, Nuisance Parameter Estimation), p.49

(. Lemma and ;. .. Taylor, Expansion Lemma), p.61

. Lemma,

). .. Sparsity, , p.70

. Theorem, Delaunay Property I)

. Theorem,

. Lemma,

). .. Theorem-(consistency,

. Theorem,

. Lemma, Control of S(?))

. Lemma, Optimality of Delaunay for the Compound Discrepancy, Rajan, 1994)

. Lemma, Sum of Weights)

;. .. Theorem, Martingale Central Limit Theorem), p.100

;. .. Lemma, Conditional Probability of a Link), p.103

, Theorem (Adaptation of Th. 2.1 in, 2018.

, Finite-sample density of ? n(? ? ? 0 )

, Finite-sample density of ? n(? ? ? 0 )

. .. , Sparsity patterns of ? (crosses) and µ (circles), p.32

, The effect of Proposition 99 on per capita tobacco consumption, p.40

. .. , Cigarette consumption in California, actual and counterfactual, p.41

. .. A-simple-example,

, Geometric properties of penalized synthetic control estimator, p.73

, Abnormal Returns after Geithner Announcement

. Us and . .. Laws, , p.92

, Voter Turnout in the US and EDR Laws, by Wave of Adoption, p.93

, List of Tables

M. , Simulations (DGP1)

M. , Simulations (DGP2: Outcome Independent from X), p.35

M. , Simulations (DGP3: Heterogeneous Treatment Effect), p.36

M. Simulations, Non-Linear Outcome Equation), vol.4, p.37

. .. , Average Treatment Effect on the Treated for NSW, p.39

M. Simulations,

M. Simulations,

M. Simulations,

M. Simulations, , vol.100

, Connections to Geithner and Reactions to Treasury Secretary Announcement, Synthetic Control Inference

. .. Program--blp,

. .. Program--blp,

, Dimensions of Heterogeneity (CLAN) in Take-Up and ITT, p.119

, Dimensions of Heterogeneity (CLAN) in Take-Up and ITT, Private Program120

, Selection into the Public Program -Group Comparison, p.122

, Selection into the Public Program -Regression

, Selection into the Private Program -Group Comparison, p.124

, Selection into the Private Program -Regression

. .. , Descriptive characteristics among experimental groups, p.127