The Econometric SocietyEdited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262
The Supplementary Appendix contains proofs of some results stated in the paper "Uniform Inference in Autoregressive Models" by Anna Mikusheva. In particular, it provides a proof of a statement about strong approximation, proofs of Lemmas 11 and 12 from the paper about the asymptotic approximations for scheme of series. It also proves results stated in Remarks 2, 3 and 4 for AR(1) processes with a linear time trend. Section 5 proves the validity of parametric and non-parametric grid bootstrap procedures for AR(p) processes with at most one root close to the unit circle. Section 7 contains an extensive Monte-Carlo study of finite sample properties of discussed methods. We keep notations introduced in the paper.
The following supplement was uploaded after the first appearance of the article on December 18, 2007. The following files numerically implement the algorithm of Section 8 to find the set of equilibrium payoffs for the examples of the noisy partnership (scriptpd.m) and duopoly (script_duopoly.m). Differential equations are solved using the 4th-order Runge Kutta method. Figures 11, 12 and 13 in the paper are based on the outputs of these files.
In the main text the true probability measure, P, is the nuisance parameter. In this supplementary material we examine which contiguous perturbations of the original fixed P preserve or do not preserve the estimation and coverage properties of the regions constructed in the main text. A useful feature of the local approach is that the conditions for the robustness of the estimation and coverage properties do not depend on the way the consistent critical values are generated (e.g. bootstrap or other means). The conditions are simple to check and apply to any consistent method of estimating a critical value.
