Ulrich K. Müller

This paper considers nonstandard hypothesis testing problems that involve a nuisance parameter. We establish a bound on the weighted average power of all valid tests, and develop a numerical algorithm that determines a feasible test with power close to the bound. The approach is illustrated in six applications: inference about a linear regression coefficient when the sign of a control coefficient is known; small sample inference about the difference in means from two independent Gaussian samples from populations with potentially different variances; inference about the break date in structural break models with moderate break magnitude; predictability tests when the regressor is highly persistent; inference about an interval identified parameter; and inference about a linear regression coefficient when the necessity of a control is in doubt. 

We propose a Bayesian procedure for exploiting small, possibly long-lag linear predictability in the innovations of a finite order autoregression. We model the innovations as having a log-spectral density that is a continuous mean-zero Gaussian process of order 1/sqrt(T). This local embedding makes the problem asymptotically a normal-normal Bayes problem, resulting in closed-form solutions for the best forecast. When applied to data on 132 U.S. monthly macroeconomic time series, the method is found to improve upon autoregressive forecasts by an amount consistent with the theoretical and Monte Carlo calculations. 

The paper derives measures of prior sensitivity and prior informativeness for posterior results in large Bayesian models that account for the high dimensional interaction between prior and likelihood information. The basis for both measures is the derivative matrix of the posterior mean with respect to the prior mean, which is easily obtained from Markov Chain Monte Carlo output. We illustrate the approach by examining posterior results in the unobserved factor model of Kose, Otrok and Whiteman (2003), the three equation dynamic stochastic general equilibirum model of Lubik and Schorfheide (2004), and Smets and Wouters' (2007) larger scale dynamic stochastic general equilibrium model. 

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.

     Efficient Tests under a Weak Convergence Assumption, Econometrica 79 (2011), 395 – 435. (Formerly circulated under the title "An Alternative Sense of Asymptotic Efficiency".)

     Efficient Estimation of the Parameter Path in Unstable Time Series Models, Review of Economic Studies 77 (2010), 1508 – 1539. Supplement. Correction. (Joint with PHILIPPE-EMMANUEL PETALAS.) 

     t-statistic Based Correlation and Heterogeneity Robust Inference, Journal of Business & Economic Statistics 28 (2010), 453 – 468. Supplement. (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.)