This is very useful since we can then use results from the treatment effect

This is very useful since we can then use results

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This is very useful since we can then use results from the treatment effect literature.
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11/5/2013 7 The wage structure effect ( Δ S ) can be interpreted as a treatment effect The conditional independence assumption (E( ε |X)=0) usually invoked in Oaxaca decompositions can be replaced by the weaker ignorability assumption (D g ε |X) to compute the aggregate decomposition For example, ability ( ε ) can be correlated with education (X) as long as the correlation is the same in groups A and B. This is the standard assumption used in “selection on observables” models where matching methods are typically used to estimate the treatment effect. Main result: If we have Y G =m G (X, ε ) and ignorability, then: Δ S solely reflects changes in the m(.) functions (ATET) Δ X solely reflects changes in the distribution of X and ε (ignorability key for this last result). The wage structure effect ( Δ S ) can be interpreted as a treatment effect A number of estimators for ATET= Δ S have been proposed in the treatment effect literature Inverse probability weighting (IPW), matching, etc. Formal results exist, e.g. IPW is efficient for ATET (Hirano, Imbens, and Ridder, 2003) Quantile treatment effects (Firpo, 2007) This has been widely used in the decomposition literature since DiNardo, Fortin, and Lemieux (1996). Formal derivation of the identification result (Handbook chapter) Formal derivation (2)
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11/5/2013 8 Formal derivation (3) Some intuition about Proposition 1 The wage setting model we use, Y g =m g (X, ε ) is very general Includes the linear model y g = x β g + ε as a special case There are three reasons why wages can be different between groups g=A and g=B: Differences in the wage setting equations m a (.) and m b (.) Differences in the distribution of X for the two groups Differences in the distribution of ε for the two groups The ignorability assumption states that the distribution of ε given X is the same for the two groups, though this does not mean that E( ε |X)=0. So once we control for differences between the X’s in the two groups, we also implicitly control for differences in the ε ’s. Only source of difference left is, thus, differences in the wage structures m a (.) and m b (.). A few caveats discussed in the chapter This general result (Proposition 1) only works for the aggregate decomposition. More assumptions have to be imposed to get at the detailed decomposition. We are implicitly ruling out general equilibrium effects under assumption (simple counterfactual treatment). For instance, in the absence of unions, wages in the nonunion sector may change as firms are no longer confronted with the threat of unionization The wage structure observed among nonunion workers, m a (.), is no longer a valid counterfactual for union workers.
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  • Fall '13
  • NicoleFortin
  • Economics, Oaxaca, quantiles, wage structure effect

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