In my study of econometrics, I have encountered an assumption called the "Zero Conditional Mean" for time series regression models. The assumption states that the expected value of the error term, $E[u_t|X]=0$, $t=1,2,\cdots,n$. My professor said that this means that "the mean value of the unobserved factors is uncorrelated to the values of the explanatory variables in all periods." He defined this as strict exogeneity. He said that this (strict exogeneity), was a stronger assumption than "contemporaneous exogeneity," which said that $E[u_t | x_t]=0$. Contemporaneous exogeneity, he said, means that "the mean of the error term is uncorrelated to the explanatory variables of the same period. So what determines the strength of an assumption? And how can we compare the strengths of different assumptions?
As a sidenote, I was wondering if the phrase "the mean value of the unobserved factors is uncorrelated to the values of the explanatory variables in all periods" means all periods lumped together or for each and every individual period.