Consider a p-variate $(p geq 4)$ normal distribution with mean ${ heta}$ and identity covariance matrix. For estimating ${ heta}$ under a quadratic loss we investigate the behavior of risks of Stein-type estimators which shrink the usual estimator toward the mean of observations. By using concavity of the function appearing in the shrinkage factor together with new expectation identities for noncentral chi-squared random variables, a characterization of estimators with nondecreasing risk is obtained.