Zero Marginal Taxes

The graph of marginal tax rates that I posted earlier has some regions of zero marginal rates and a larger version has negative marginal rates at low income.  How is this possible?  It helps to know that the graph is based on a four member family with one young child and one older child attending college.  Assumptions must also be made about 401ks, IRA contributions, education plans etc.  Kevin Hassett, one of the authors, lays out all the assumptions here.  Basic story - the earned income tax credit gets you negative marginal rates; zero rates are possible at higher incomes if you save some money for retirement and take advantage of education tax credits.  Of course, families in different situations would face different graphs but that too demonstrates that the tax system is a hodge-podge.

Thanks to John F. Eckstein for pointing me to the more detailed explanation.