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Projection-based methods of inference on subsets of parameters are useful for obtaining tests that do not over-reject the true parameter values. However, they are also often criticized for being overly conservative. We show that under the standard regularity conditions the usual method of projection can be modified to obtain tests that are as powerful as the conventional plug-in-based tests for subsets of parameters. The new method is described in the context of GMM with possibly weaklydoi:10.2139/ssrn.1395392 fatcat:w2siluo3ijbrvkuspls45l5gr4