This Online Supplementary Appendix contains additional results and proofs to support the main text. Appendix D contains the proof of the limiting experiment results in Appendix A and additional lemmas. Appendix E presents the technical lemmas and their proofs that are used in the proofs of Appendix B and Appendix C. Appendix F contains the proofs of the results in Section 4. Appendix G provides sufficient conditions for verifying Assumption 3.1 in the general nonparametric conditional moment restriction models studied in Section 4. Appendix H provides additional discussion of the Examples in Section 4 as well as a final example.