Generic results for establishing the asymptotic size of confidence sets and tests

Donald W.K. Andrews, Xu Cheng, Patrik Guggenberger

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Abstract

This paper provides a set of results that can be used to establish the asymptotic size and/or similarity in a uniform sense of confidence sets and tests. The results are generic in that they can be applied to a broad range of problems. They are most useful in scenarios where the pointwise asymptotic distribution of a test statistic is a discontinuous function of a parameter. The results are illustrated in several examples. These are: (i) the conditional likelihood ratio test of Moreira (2003) for linear instrumental variables models with instruments that may be weak, extended to the case of heteroskedastic errors; (ii) the grid bootstrap confidence interval of Hansen (1999) for the sum of the AR coefficients in a kth order autoregressive model with unknown innovation distribution, and (iii) the standard quasi-likelihood ratio test in a nonlinear regression model where identification is lost when the coefficient on the nonlinear regressor is zero. In addition, as a simple running example, we consider a two-sided equal-tailed CI for the AR coefficient in an AR(1) model, which is a simplified version of the CI in Andrews and Guggenberger (2014).

Original languageEnglish (US)
Pages (from-to)496-531
Number of pages36
JournalJournal of Econometrics
Volume218
Issue number2
DOIs
StatePublished - Oct 2020

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics

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