I propose a nonparametric iid bootstrap procedure for the empirical likelihood, the exponential tilting, and the exponentially tilted empirical likelihood estimators that achieves asymptotic refinements for t tests and confidence intervals, and Wald tests and confidence regions based on such estimators. Furthermore, the proposed bootstrap is robust to model misspecification, i.e., it achieves asymptotic refinements regardless of whether the assumed moment condition model is correctly specified or not. This result is new, because asymptotic refinements of the bootstrap based on these estimators have not been established in the literature even under correct model specification. Monte Carlo experiments are conducted in dynamic panel data setting to support the theoretical finding. As an application, bootstrap confidence intervals for the returns to schooling of Hellerstein and Imbens (1999) are calculated. The result suggests that the returns to schooling may be higher.