"Bias is the expected difference between the population parameter and the value (statistic) used to estimate it. When the value is the parameter itself, that expectation is zero. (In fact, the difference is zero, not just the expectation.) If you do have the whole population, though, testing and other forms of inference do not make sense. The point of inference is to try to guess intelligently about an unknown population."

But to me that seems an incorrect definition of what bias is (or maybe I think about it wrong).

My response (and confusion)

"For instance, if a and b drive the dependent variable, and a and b are related and you leave b out of the model than the relationship between a and the dependent variable would be wrong in your model even with the whole population. To me that is bias, but maybe not. Or if you use a linear relationship for non-linear relationships."