| Having robust methods of inference is important in econometrics to achieve reliable results. This thesis tackles robustness issues in three different contexts: structural change in panel data robust to a short transition period, inference on the mean of a time series robust to the so-called ill-posed problem, inference on the slope of a trend function robust to the stationary or integrated nature of the noise component.;Chapter 1 considers testing for and estimating an unknown structural break date in panel data models in the presence of individual specific effects and serial correlation for both short and long panels. I allow for a time varying effect after a regime change in the form of a short transition period. A statistic that has a pivotal limit distribution under a standard asymptotic framework is proposed. It is shown to be robust to the transition period. The usefulness of the method is illustrated via simulations and empirical applications.;Chapter 2 deals with the relevance of so-called impossibility results in the context of estimating the spectral density function of a stationary process at the zero frequency. As shown previously, any estimate will have an infinite minimax risk. Most often it is a nuisance parameter of which an estimate is needed to obtain test statistics that have a pivotal distribution. In this context, I argue that such an impossibility result is irrelevant. I show that, in the presence of the discontinuities that cause the ill-posedness problem, using the true value leads to tests that have either 0 or 100% size and, hence, lead to confidence intervals that are completely uninformative. On the other hand, tests based on standard estimates will have well defined limit distributions and, accordingly, be more informative and robust.;Chapter 3 is concerned with inference on the slope of the trend function of a time series whose noise component can be stationary or integrated. I focus on a procedure suggested by Perron and Yabu (2009). I prove that it has the correct size uniformly over the specified parameter space but that it is not uniformly asymptotically similar. |
