# Understanding importance of regression coefficient standard errors in prediction

When being used for prediction on new individuals, I'm having some difficulty in understanding whether the standard error of coefficients in logistic or Cox proportional hazards regression models are important. When evaluating in-sample performance, regression scores are only determined by the $\hat{\beta}_i$'s. Performance, with or without optimism correction, are again determined using $Y$ and $\hat{Y}_i$, which are functions of model coefficients. Do the standard errors have any impact then on prediction performance? If so, can you help me understand why?