Hypothesis tests when decomposing differences in the first moment

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Poverty In Rural India: Caste And Tribe (2008, methodology): “The covariance of b/s is, in turn, used for hypothesis testing (Yun, 2005a).”
Identification problem and detailed Oaxaca decomposition: A general solution and inference (2008, unknown): “where G∆X and G∆β are 1× T and 1× 2T vectors of gradients [10].”
A Stata implementation of the Blinder-Oaxaca decomposition (2008, methodology): “Furthermore, the results are equal to the simple averages of the results one would get from a series of decompositions in which the categories are used one after another as the base category (Yun 2005b).”
7. Multivariate Decomposition for Hazard Rate Models (2009, methodology): “Regression decomposition has been extended to nonlinear models including probit (Gomulka and Stern 1990), logit (Even and Macpherson 1993; Fairlie 2005; Nielsen 1998; Yun 2005a), and count models (e.g., see Bauer et al. 2007; Heitmueller 2004; Park and Lohr 2008).”