Ulrich K. Müller

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, and it provides a concrete limit on the scope for more powerful tests in less parametric set-ups.

We develop a general approach to robust inference about a scalar parameter when the data is potentially heterogeneous and correlated in a largely unknown way. The key ingredient is the following result of Bakirov and Székely (2005) concerning the small sample properties of the standard t-test: For a significance level of 5% or lower, the t-test remains conservative for underlying observations that are independent and Gaussian with heterogenous variances. One might thus conduct robust large sample inference as follows: partition the data into q≥2 groups, estimate the model for each group and conduct a standard t-test with the resulting q parameter estimators. This results in valid and in some sense efficient inference when the groups are chosen in a way that ensures the parameter estimators to be asymptotically independent, unbiased and Gaussian of possibly different variances. We provide examples of how to apply this approach to time series, panel, clustered and spatially correlated data.

The paper investigates asymptotically efficient inference in general likelihood models with time varying parameters. Parameter path estimators and tests of parameter constancy are evaluated by their weighted average risk and weighted average power, respectively. The weight function is proportional to the distribution of a Gaussian process, and focusses on local parameter instabilities that cannot be detected with certainty even in the limit. It is shown that asymptotically, the sample information about the parameter path is efficiently summarized by a Gaussian pseudo model. This approximation leads to computationally convenient formulas for efficient path estimators and test statistics, and unifies the theory of stability testing and parameter path estimation.

     Valid Inference in Partially Unstable GMM Models. (Joint with HONG LI.) Accepted for publication in Review of Economic Studies.

      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, forthcoming in Econometric Theory.

     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.)