Let’s start with a binary mediator, in order to keep things simple: \(M_i\in\left\. Then, I am going to present the fundamental problem of mediation analysis (which turns out to be one version of the confounders problem we know all too well) and the various techniques that have been developed in order to solve for it.ġ5.1.1 Defining mediated and unmediated treatment effects In this chapter, I am going to first delineate the general framework for mediation analysis and the way mediation analysis can be undertaken in the ideal case of a Randomized Controlled Trial. The question of separating between the various channels into which a program impact can be decomposed becomes especially important when a program has several components, and we wish to ascertain which one is the more important.Īnother reason why we might be interested in which channel precisely is responsible for the program impact is because which channel dominates might give us indications about which theoretical mechanism is at play. When we have estimated the treatment effect of a program, we sometimes wonder by which channels the program impact has been obtained.įor example, has a Job Training Program been successful because it has increased the human capital of an agent, or simply by signalling to employers her motivation? A.1 Proofs of results in Chapter A.1.1 Proof of Theorem A.1.2 Proof of Theorem A.2 Proofs of results in Chapter A.2.1 Proof of Theorem A.2.2 Proof of Theorem A.2.3 Proof of Theorem A.3 Proofs of results in Chapter A.3.1 Proof of Theorem A.3.2 Proof of Theorem A.3.3 Proof of Theorem A.3.4 Proof of Theorem A.3.5 Proof of Theorem A.3.6 Proof of Theorem A.3.7 Proof of Theorem A.3.8 Proof of Theorem Published with bookdown.15.6 Mediation analysis with instruments.15.5 Mediation analysis with panel data.15.4.2 Mediation analysis under sequential ignorability in linear models.15.4.1 Non-parametric identification under sequential ignorability.15.4 Mediation analysis under unconfoundedness.15.3.3 Mediation analysis in the Crossover design.15.3.2 Mediation analysis in the Sequential Self-Selection design.15.3.1 Mediation analysis in the Parallel design.15.3 Mediation analysis with experimental data.15.2.1 The Fundamental Problem of Mediation Analysis.15.2 The Fundamental Problem of Mediation Analysis.15.1.2 Decomposing mediated and unmediated effects.15.1.1 Defining mediated and unmediated treatment effects.13.2.6 The value of a statistically significant result.13.2.5 Vote counting and publication bias.13.2.4 Detection of and correction for site selection bias.13.2.3 Getting rid of publication bias: registered reports and pre-analysis plans.13.2.2 Detection of and correction for publication bias.13.2.1 Sources of publication bias and of site selection bias and Questionable Research Practices.13.2 Publication bias and site selection bias.
4.3.3 Difference In Differences with multiple time periods.4.3.2 Reverse Difference In Differences designs with two time periods.4.3.1 Difference In Differences with two time periods.4.1.1 An example where Monotonicity does not hold.3.4.2 Estimating the Local Average Treatment Effect and the Intention to Treat Effect.2.1.6 Using effect sizes to normalize the reporting of treatment effects and their precision.2.1.5 Reporting sampling noise: a proposal.2.1.4 Building confidence intervals from estimates of sampling noise.2.1.3 Sampling noise for the sample treatment effect.2.1.2 Sampling noise for the population treatment effect.2.1 What is sampling noise? Definition and illustration.2 Fundamental Problem of Statistical Inference.1.4.2 The before/after comparison, temporal confounders and time trend bias.1.4.1 With/Without comparison, selection bias and cross-sectional confounders.1.4 Intuitive estimators, confounding factors and selection bias.1.3 Fundamental problem of causal inference.1.2.2 Average treatment effect on the treated.1.2.1 Individual level treatment effects.1 Fundamental Problem of Causal Inference.Introduction: the Two Fundamental Problems of Inference.