Suppose I have an estimate (say an OLS coefficient), I can obtain its standard error using the standard OLS formula. I can also use nonparametric bootstrap and compute the standard error. My question is: should these two ways always give (almost) the same answer? If not, what are possible reasons for the difference?
(Note that there could be heteroscedasticity or autocorrelation in the regression error term but I am ignoring them both in the OLS estimation or in performing bootstrap).