The purpose of this paper is to provide theoretical justification for some existing methods for constructing confidence intervals for the sum of coefficients in autoregressive models. We show that the methods of Stock (1991), Andrews (1993), and Hansen (1999) provide asymptotically valid confidence intervals, whereas the subsampling method of Romano and Wolf (2001) does not. In addition, we generalize the three valid methods to a larger class of statistics. We also clarify the difference between uniform and pointwise asymptotic approximations, and show that a pointwise convergence of coverage probabilities for all values of the parameter does not guarantee the validity of the confidence set. Copyright The Econometric Society 2007.

This Supplementary Appendix contains additional results concerning the interpretation of our conditional critical values, the bounded completeness of our sufficient statistics, the derivation of the conditioning process h T (·) in homoscedastic linear IV, the power of tests in a simple Gaussian model, the power of the conditional QLR tests in linear IV with nonhomoscedastic errors, proofs of asymptotic results stated in the paper, a theoretical analysis and additional simulation results for the quantile IV model, and additional results for Stock and Wright's (2000) setting.

We consider inference in the linear regression model with one endogenous variable and potentially weak instruments. We construct confidence sets for the coefficient on the endogenous variable by inverting the Anderson-Rubin, Lagrange multiplier, and conditional likelihood-ratio tests. Our confidence sets have correct coverage probabilities even when the instruments are weak. We propose a numerically simple algorithm for finding these confidence sets, and we present a Stata command that supersedes the one presented in Moreira and Poi (Stata Journal 3: 57-70).

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This appendix contains supplementary material and proofs for the paper "A Geometric Approach to Nonlinear Econometric Models," by Isaiah Andrews and Anna Mikusheva. Section S1 introduces geometric concepts used in the proofs. Sections S2 and S3 prove Theorems 1 and 2 of the paper, respectively. Section S4 proves Lemma 2 from the paper and gives a related uniform asymptotic result. Section S5 proves Lemma 3 and shows that tests which both minimize critical values over subsets of parameters and restrict attention to curvature on a finite ball continue to control size. Section S6 proves Lemma 1 from the paper. Section S7 shows that models that are weakly identified in the sense of Stock and Wright (2000) imply nonlinear null hypothesis manifolds. Section S8 shows how nonlinearity arises from weak identification in an analytic DSGE example.