TY - JOUR
T1 - Generic results for establishing the asymptotic size of confidence sets and tests
AU - Andrews, Donald W.K.
AU - Cheng, Xu
AU - Guggenberger, Patrik
N1 - Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/10
Y1 - 2020/10
N2 - 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).
AB - 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).
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U2 - 10.1016/j.jeconom.2020.04.027
DO - 10.1016/j.jeconom.2020.04.027
M3 - Article
AN - SCOPUS:85084728750
SN - 0304-4076
VL - 218
SP - 496
EP - 531
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 2
ER -