Contents
1. Introduction 2
2. Identication: What Can We Estimate Using Decomposition Methods? 13
2.1. Case 1: The aggregate decomposition 14
2.1.1. The overall wage gap and the structural form 14
2.1.2. Four decomposition terms 17
2.1.3. Imposing identication restrictions: overlapping support 17
2.1.4. Imposing identication restrictions: ignorability 18
2.1.5. Identication of the aggregate decomposition 21
2.1.6. Why ignorability may not hold, and what to do about it 24
2.2. Case 2: The detailed decomposition 25
2.2.1. Nonparametric identication of structural functions 27
2.2.2. Functional form restrictions: decomposition of the mean 29
2.2.3. Functional form restrictions: more general decompositions 29
2.3. Decomposition terms and their relation to causality and the treatment eects literature 33

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