This paper studies inference about the values of the parameters in the threshold model in a generalized method of moments (GMM) framework. First, we establish that the extensively studied least squares method leads to substantially oversized tests and confidence intervals when the coefficient change is not large. Second, by re-ordering the data to recast the threshold model as a structural break problem, we construct tests that control size under a large range of empirically relevant moderate coefficient changes and are approximately efficient in a well-defined sense. Finally, we modify our approach to encompass inference problems in a variety of additional widely studied models. The accuracy of the asymptotic approximations is evaluated by Monte Carlo simulations. The empirical applicability is illustrated through the tipping point problem studied by Card, Mas, and Rothstein (2008). We find a substantially different confidence interval of the tipping point from the one obtained by the least squares method, which might deliver a coverage that is much lower than the nominal level.Nearly Weighted Risk Minimal Unbiased Estimation. (Joint with Ulrich K. Müller.) Supplementary Matlab code.
We study non-standard parametric estimation problems, such as the estimation of the AR(1) coefficient close to the unit root. We develop a numerical algorithm that determines an estimator that is nearly (mean or median) unbiased, and among all such estimators, comes close to minimizing a weighted average risk criterion. We demonstrate the usefulness of our generic approach by also applying it to estimation in a predictive regression, estimation of the degree of time variation, and long-range quantile point forecasts for an AR(1) process with coefficient close to unity.