Bootstrap diagnostic tests

About this event

Violation of the assumptions underlying classical Gaussian limit theory frequently leads to unreliable statistical inference. This paper shows the novel result that the bootstrap can deliver simple and powerful tests of such violations which (a) induce no pre-testing bias under the null, (b) can be performed using the same critical values in a broad range of applications, and (c) consistently detect deviations from asymptotic normality. By focusing on the distance between the conditional distribution of a bootstrap statistic and the (limiting) Gaussian distribution which obtains under valid specification, we show how to assess whether this distance is large enough to indicate specification invalidity. The method, which is computationally straightforward, only require to estimate the distance between the bootstrap distribution and the Gaussian distribution via a sample of i.i.d. draws of the bootstrap statistic. We derive under what conditions the randomness in the data mixes with the randomness in the bootstrap repetitions in a way such that (a), (b) and (c) above hold. To demonstrate the practical relevance and broad applicability of our diagnostic procedure, we discuss five scenarios where the asymptotic Gaussian approximation may fail: (i) detecting infinite variance innovations in a location model for i.i.d. data; (ii) identifying non-stationary behavior in autoregressive time series; (iii) parameters near or at the boundary of the parameter space; (iv) invalidity of the delta method due to (near-)rank deficiency in the implied Jacobian matrix; and (v) weak instruments in instrumental variable regression. An illustration drawn from the empirical macroeconomic literature concludes.