VOW to Hire Heroes Extension Act of 2013 - Amends the Internal Revenue Code to: (1) extend through 2017 the work opportunity tax credit for hiring a qualified veteran (defined as an unemployed veteran who is certified as being a member of a family receiving food stamp assistance and who is entitled to compensation for a service-connected disability), (2) revise tax credit eligibility requirements for documenting the status of veterans and their receipt of unemployment compensation, and (3) extend the payroll tax offset for such credit to certain for-profit employers.

Directs the Commissioner of the Internal Revenue Service, in consultation with the Secretary of Labor, to make annual reports on the effectiveness and cost-effectiveness of this Act in increasing the employment of veterans.

Requires the Secretary of the Treasury to pay: (1) each U.S. possession (i.e., American Samoa, Guam, the Commonwealth of the Northern Mariana Islands, the Commonwealth of Puerto Rico, and the U.S. Virgin Islands) with a mirror code tax system amounts equal to the loss to such possession due to this Act; and (2) each U.S. possession without such a tax system an amount estimated to equal the loss to such possession that would have occurred due to this Act if such a tax system had been in effect in such possession.