Jane Gravelle (Congressional Research Service) & Jennifer Gravelle (Department of Economics, John Hopkins University) have published Horizontal Equity and Family Tax Treatment: The Orphan Child of Tax Policy, 59 Nat’l Tax J. 631 (2006).  Here is the abstract:

Horizontal equity across families has played little role in forming tax policy. Using an index to equate different families, the earned income credit (EIC) is shown to create dramatic effective tax rate differentials at low incomes, favoring families with two children. In the middle, the child credit favors large families. At high incomes, families without children are favored slightly. Tax revisions reducing these inequities include increasing the EIC for singles and childless couples, repealing the alternative minimum tax, eliminating phase outs, and eliminating or reducing the child credit. Making the childcredit fully refundable would magnify inequities.