My wife and i are both self employed, filing jointly. My business loss is greater than her profit. Do we need to pay self employment tax?

The owner of the business that made a profit will pay Self-Employment tax on that income. 

Self-Employment tax is the FICA tax that funds the Social Security Account of that Taxpayer. 

Loss on one business does not offset the income on the other as far as "Self-Employment Tax" is concerned. 

The loss will lower your taxable income for "Income Tax" computation. 

Thank you very much for your help!