Stochastic kriging has been studied as an effective metamodeling technique for approximating response surfaces in the context of stochastic simulation. In a simulation experiment, an analyst typically needs to estimate relevant metamodel parameters and further do prediction; therefore, the impact of parameter estimation on the performance of the metamodel-based predictor has drawn some attention in the literature. However, how the standard stochastic kriging predictor is affected by the presence of bias in finite-sample estimates has not yet been fully investigated. In this article, we study the predictive performance and investigate optimal budget allocation rules subject to a fixed computational budget constraint. Furthermore, we extend the analysis to two-level or nested simulation, which has been recently documented in the risk management literature, with biased estimators.