How can GDP by state be negative?

GDP by state is estimated as the sum of three income components:

1. Compensation of employees
2. Taxes on production and imports (TOPI) less subsidies
3. Gross operating surplus.

Gross operating surplus includes the losses of corporations and proprietors' losses.  Government subsidies are subtracted from TOPI. Consequently, TOPI less subsidies and/or gross operating surplus for an industry may be negative. When TOPI less subsidies and gross operating surplus are added to the industry's compensation of employees, the sum, GDP by state, may be negative.