Ulrich K. Müller

It is well known that in misspecified parametric models, the maximum likelihood estimator (MLE) is consistent for the pseudo-true value and has an asymptotically normal sampling distribution with "sandwich" covariance matrix. Also, posteriors are asymptotically centered at the MLE, normal and of asymptotic variance that is in general different than the sandwich matrix. It is shown that due to this discrepancy, Bayesian inference about the pseudo-true parameter value is in general of lower asymptotic risk when the original posterior is substituted by an artificial normal posterior centered at the MLE with sandwich covariance matrix. An algorithm is suggested that allows the implementation of this artificial posterior also in models with high dimensional nuisance parameters which cannot reasonably be estimated by maximizing the likelihood.  

This paper provides a method for conducting inference about the pre and post break value of a scalar parameter in GMM time series models with a single break at an unknown date. 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 a well defined sense. 

Standard inference in cointegrating models is fragile because it relies on an assumption of an I(1) model for the common stochastic trends, which may not accurately describe the data's persistence. This paper discusses efficient low-frequency inference about cointegrating vectors that is robust to this potential 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.

     Efficient Estimation of the Parameter Path in Unstable Time Series Models. Accepted for publication in the Review of Economic Studies. Supplement. (Joint with PHILIPPE-EMMANUEL PETALAS.)

     t-statistic Based Correlation and Heterogeneity Robust Inference. Accepted for publication in the Journal of Business & Economic Statistics. Supplement. 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.) 

     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. 

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

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

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

     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.)

     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.)

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

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

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