Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Supplemental Material

Econometrica - Volume 74, Issue 3

Supplement to "Optimal Two-sided Invariant Similar Tests for Instrumental Variables Regression"

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.

Supplement to "Optimal Two-sided Invariant Similar Tests for Instrumental Variables

This file contains tables of the conditional critical values of the CLR test presented in Andrews, Moreira, and Stock (2006a).

Supplement to "Speculation in Standard Auctions with Resale"

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.

Supplementary Material to "Local Partitioned Regression"

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.