Identification and Estimation of Causal Effects of Multiple Treatments Under the Conditional Independence Assumption

By M. Lechner. 1999

The assumption that the assignment to treatments is ignorable conditional on attributes plays an important role in the applied statistic and econometric evaluation literature. Another term for it is conditional independence assumption. This paper discusses identification when there are more than two types of mutually exclusive treatments. It turns out that low dimensional balancing scores, similar to the ones valid in the case of only two treatments, exist and be used for identification of various causal effects. Therefore, a comparable reduction of the dimension of the estimation problem is achieved and the approach retains its basic simplicity. The paper also outlines a matching estimator potentially suitable in that framework.

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Citations in the corpus

Automated versus Do-It-Yourself Methods for Causal Inference: Lessons Learned from a Data Analysis Competition (2017, background): “The most common assumption invoked to identify these effects is the so-called ignorability assumption (Rubin, 1978), which is also known as “selection on observables,” “all confounders measured,” “exchangeability,” the “conditional independence assumption” and “no hidden bias” (see Barnow, Cain and ”
Going green: does it depend on education, gender or income? (2014, unknown): “5 Imbens (2000) and Lechner (2001) extend the method of propensity score matching to multiple mutually exclusive programmes.”
Semiparametric Estimation of Average Treatment Eects under Exogeneity: A Review (2003, methodology): “I will also limit the discussion to binary treatments, excluding models with dynamic treatment regimes as in Ham and Lalonde (1996), and Gill and Robins (2002) and models with static multi-valued treatments as in Imbens (2000) and Lechner (2001) .”
Innovation Subsidies: Does the Funding Source Matter for Innovation Intensity and Performance? Empirical Evidence from Germany (2014, methodology): “We follow Lechner (2001) and calculate his estimator for an asymptotic approximation of the standard errors. organization or external relations (see Eurostat and OECD 2005).”
Evaluation of Swedish Youth Labor Market Programs (2003, methodology): “The following procedure is similar to the random procedure suggested by Lechner (1999).”
Using Innovation Survey Data to Evaluate R&D Policy: The Case of Belgium (2004, background): “This issue linked to the public funding decision had already been described by Lichtenberg (1987) and Klette/Moen (1997).”
Trade, Standards, and Poverty: Evidence from Senegal (2009, background): “the vector of treatments (Lechner, 2000; Wooldridge, 2004) – an issue addressed in the next section.”
Electoral Rules and Corruption (2003, unknown): “Then we can compute (as in Lechner, 2000) the variance of τM as: Var(τM) = ( 1 NT )2[ X i∈T Var(CPITi )+ X i∈C (wi) 2Var(CPICi )] (A2) = 1 NT [Var(CPITi )+ P i∈C(wi)2 NT Var(CPICi )] .”
Evaluating the Differential Effects of Alternative Welfare-to-Work Training Components : A Re-Analysis of the California GAIN Program * by (2005, background): “Imbens (2000) and Lechner (2001) consider alternative definitions of differential treatment effects, including conditioning on those subjects who would otherwise receive either treatment components k or k′.”
The Dangers of Extreme Counterfactuals (2006, background): “Although medical researchers are almost always interested in h, political scientists are also interested in the average causal effect for the entire set of observations, c5EðY1Þ EðY0Þ; ð12Þ 13The analysis of treatments with more than two levels follows analogously (e.g., Imai and Dyk 2004; Lechner 1”
The Curse and Blessing of Training the Unemployed in a Changing Economy: The Case of East Germany After Unification (2007, unknown): “2 Pannenberg (1995), Pannenberg and Helberger (1997), Fitzenberger and Prey (1998, 2000), Hübler (1997, 1998), Staat (1997), Kraus, Puhani and Steiner (1999), Lechner (1999, 2000), Prey (1999), Hujer and Wellner (2000), Bergemann, Fitzenberger and Speckesser (2004).”
Evaluating the impact of education on earnings in the UK: models, methods and results from the NCDS (2003, methodology): “Despite the fact that compared with OLS, matching is implemented in a more flexible way (in particular not imposing linearity or a homogeneous additive treatment effect), both matching and OLS estimates depend on this same crucial assumption of selection on observables, and both are thus as good as…”