The Econometric SocietyEdited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262
This paper contains supplemental material to Andrews, Moreira, and Stock (2006a), hereafter AMS. Section 2 provides details concerning the sign-invariant power envelope for similar tests introduced in AMS. Section 3 does likewise for the LU power envelope for invariant similar tests. Section 4 reports additional numerical results to those in AMS. Section 5 establishes consistency of the covariance matrix estimator in AMS. Section 6 gives proofs of Lemmas 1 and 2 of AMS. Section 7 proves the claim made in Comment 2 to Corollary 1 of AMS that when k =1 the optimal invariant similar test in terms of two-point weighted average power is the Anderson-Rubin test (which is equivalent in this case to the LM and CLR tests). An Appendix describes numerical methods used in Section 4.
This file contains tables of the conditional critical values of the CLR test presented in Andrews, Moreira, and Stock (2006a).
We extend the model presented in the Note ?Speculation in Standard Auctions with Resale" by the same authors to environments with multiple symmetric-independent-private-value bidders and prove the results stated in Section 5 of the Note.
In this paper we provide additional material on four issues in the main text. The first is an estimator for the covariance matrix Σ in theorem 3.2, precisely defined in (A.15). The second concerns the claim that under our assumptions (3.5) and (3.6) are already implied. The third issue is the calculation of the matrix V in remark 3.3 for general heteroscedasticity. The last issue is the proof of theorem 3.3.
