Income splitting, specialization, and intra-family distribution

Income splitting for tax purposes results in more specialization of wives, but does this in turn generate more gender inequality? In my dynamic bargaining model with a divorce threatpoint, I find that who controls the couple's labour supply plays a crucial role in establishing this link. If spouses choose their labour supply non-cooperatively, only the husband's increase - but not her own decrease - in labour supply introduces a negative term in the wife's change in welfare. If the wife does not control her own labour supply, a decrease in her own labour supply introduces an additional negative term.