Estimation using simulation techniques may be very time consuming. Specification tests for structuralstability often require more than one of such computationally demanding estimators. Typically one for thesample, one for the post-sample and one for the combination of sample and post-sample is required. Thispaper describes structural stability tests for use with the Efficient Method of Moments technique.Computationally attractive post-sample estimators and test-statistics for structural stability are proposed.These computationally attractive test-statistics are modifications of the Lagrange Multiplier, LikelihoodRatio and Wald tests for structural stability and of the Hansen-type test statistics for structural stability.The modification ensures the same asymptotic optimality properties against certain local alternatives asthose based on efficient computationally intensive estimators for the post-sample. However no timeconsuming estimators are needed for the post-sample and for the combination of sample and post-sample. Evaluation of these tests has been performed in the context of a stochastic volatility model for theS&P500.