The following are the formal statements of the

The identification of the explained component and the unexplained component of the Oaxaca-Blinder decomposition or its generalized counterpart, the FFL method, respectively dubbed “composition effects” and “wage structure effects” in the labour economics literature, hinges upon two assumptions, namely: the conditional independence/ignorability (or unconfoundedness or “selection on observables” assumption) and the overlapping or common support assumption. The following are the formal statements of the assumptions as contextualized for this study: Assumption 1: Conditional Independence/Ignorability (or “Unconfoundedness” or “Selection on Observables” in the treatment effects literature) Suppose  are jointly distributed, where  when a woman was interviewed in 2015 and   when the woman was interviewed in 2004 (in the treatment effects literature, T would be a “treatment assignment”);  is a real valued vector of explanatory variables and  is a vector of unobservable characteristics. For all   :  is independently distributed of  given  .  The ignorability assumption is weaker than the conditional mean assumption. Unlike the conditional mean assumption in linear regression, this assumption does not require that unobservables, , be independent of the vector of observables, . Under the weaker ignorability assumption, what is required is that the dependence structure between the unobservable and observable explanatory factors be the same across the two periods i.e. the conditional distribution of  given  is the same across the two periods. This is also known as the “unconfoundedness” or “selection based on observables” assumption in the treatment effects literature. The ignorability assumption is one of only two assumptions required to identify the “unexplained” component in the aggregate decomposition. Assumption 2: Overlapping or common support Let   be the conditional probability that a woman was interviewed in 2015 given X=x (this is also called the

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