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

By Donald W. K. Andrews, Xu Cheng, Patrik Guggenberger. Journal of Econometrics, 2020

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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 has a discontinuity in its limit distribution. The results are illustrated in three 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 k-th 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.

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Local Projection Inference Is Simpler and More Robust Than You Think (2020, methodology): “b) To handle both unit roots, stationary processes, and everything in between, we must consider various kinds of sequences of drifting parameters A = AT , following the general logic of Andrews et al. (2019). This is primarily an issue when showing consistency of the standard error ŝ1(h, ν), which r”