Ulrich K. Müller

This paper discusses inference about the pre and post break value of a scalar parameter in GMM time series models with a single break at an unknown point in time. We show that treating the break date estimated by least squares as the true break date leads to substantially oversized tests and confidence intervals unless the break is large. We develop an alternative test that controls size uniformly and that is approximately efficient in some well defined sense. 

Standard inference in cointegrating models is fragile for two distinct reasons. First, inference assumes an I(1) model for the common stochastic trends, which may not accurately describe the data's persistence; second, while cointegration concerns low-frequency variability, inference relies on higher frequency variability in the data. This paper discusses efficient inference about cointegrating vectors that is robust to both sources of misspecification. A simple test motivated by the analysis in Wright (2000) is developed and shown to be approximately optimal in the case of a single cointegrating vector.

The paper studies the asymptotic efficiency and robustness of hypothesis tests when models of interest are defined in terms of a weak convergence property. The null and local alternatives induce different limiting distributions for a random element, and a test is considered robust if it controls asymptotic size for all data generating processes for which the random element has the null limiting distribution. Under weak regularity conditions, asymptotically robust and efficient tests are then simply given by efficient tests of the limiting problem--that is, with the limiting random element assumed observed--evaluated at sample analogues. These tests typically coincide with suitably robustified versions of optimal tests in canonical parametric versions of the model. This paper thus establishes an alternative and broader sense of asymptotic efficiency for many previously derived tests in econometrics, such as tests for unit roots, parameter stability tests and tests about regression coefficients under weak instruments.

The paper investigates inference in nonlinear and non-Gaussian models with moderately time varying parameters. We show that for many decision problems, the sample information about the parameter path can be summarized by an artificial linear and Gaussian model, at least asymptotically. The approximation allows for computationally convenient path estimators and parameter stability tests. Also, in contrast to standard Bayesian techniques, the artificial model can be robustified so that in misspecified models, decisions about the path of the (pseudo-true) parameter remain as good as in a corresponding correctly specified model.

      t-statistic Based Correlation and Heterogeneity Robust Inference, forthcoming in the Journal of Business & Economic Statistics. Alternative proof of small sample conservativeness. (Joint with RUSTAM IBRAGIMOV.)

     Valid Inference in Partially Unstable GMM Models, Review of Economic Studies 76 (2009), 343 – 365. (Joint with HONG LI.) 

     Testing Models of Low-Frequency Variability, Econometrica 76 (2008), 979 – 1016. (Joint with MARK WATSON.) 

     Comment on "Unit Root Testing in Practice: Dealing with Uncertainty over the Trend and Initial Condition" by D. I. Harvey, S. J. Leybourne and A. M. R. Taylor, Econometric Theory 25 (2009), 643 – 648.

     The Impossibility of Consistent Discrimination between I(0) and I(1) Processes, Econometric Theory 24 (2008), 616 – 630.

      Minimizing the Impact of the Initial Condition on Testing for Unit Roots, Journal of Econometrics 135 (2006), 285 – 310. (Joint with GRAHAM ELLIOTT.)

      Confidence Sets for the Date of a Single Break in Linear Time Series Regressions, Journal of Econometrics 141 (2007), 1196 – 1218 . (Joint with GRAHAM ELLIOTT.)

      A Theory of Robust Long-Run Variance Estimation, Journal of Econometrics 141 (2007), 1331 – 1352. (Substantially different 2004 working paper).

      Efficient Tests for General Persistent Time Variation in Regression Coefficients, Review of Economic Studies 73 (2006), 907 – 940. Formerly circulated under the title “Optimally Testing General Breaking Processes in Linear Time Series Models”. (Joint with GRAHAM ELLIOTT.)

      Tests for Unit Roots and the Initial Condition, Econometrica 71 (2003), 1269 – 1286. (Joint with GRAHAM ELLIOTT.)

      Size and Power of Tests for Stationarity in Highly Autocorrelated Time Series, Journal of Econometrics 128 (2005), 195 – 213.

     Are Forecasters Reluctant to Revise their Predictions? Some German Evidence, Journal of Forecasting 25 (2006), 401 – 413. (Joint with GEBHARD KIRCHGÄSSNER.)

     Ecological Tax Reform and Involuntary Unemployment: Simulation Results for Switzerland, Schweizerische Zeitschrift für Volkswirtschaft und Statistik 134 (1998), 329 – 359. (Joint with GEBHARD KIRCHGÄSSNER and MARCEL SAVIOZ.)