Ulrich K. Müller

We consider inference about a scalar coefficient in a linear regression model. One previously considered approach to dealing with many controls imposes sparsity, that is it assumed known that nearly all control coefficients are zero. We instead impose a bound on a weighted sum of squared control coefficients, which is interpretable as a bound on the sample variation in the dependent variable induced by the controls. We develop a simple testing procedure that exploits this additional information in general heteroskedastic models. We also show that under asymptotics where the number of controls is a non-negligible fraction of the number of observations, and the bound is not too large, our suggested test comes close to being weighted average power maximizing in the Gaussian homoskedastic model. We compare our procedure to a sparsity-based approach in a Monte Carlo study and by revisiting the empirical relationship between crime and abortion.  

We develop inference methods about the degree of long-run comovement of two time series. The parameters of interest are defined in terms of the population second-moment properties of low-frequency trends computed from the data. These trends are similar to low-pass filtered data and are designed to extract variability that corresponds to periods longer than the span of the sample divided by q/2, where q is a small number, such as 12. We numerically determine confidence sets that control coverage over a wide range of potential bivariate persistence patterns, which include arbitrary linear combinations of I(0), I(1), near unit roots and fractionally integrated models. In an application to U.S. economic data, we quantify the long-run covariability of a variety of series, such as those giving rise to the "great ratios", nominal exchange rates and relative nominal prices, unemployment rate and inflation, earnings and stock prices, etc.  

Many questions in economics involve long-run or "trend" variation and covariation in time series. Yet, time series of typical lengths contain only limited information about this long-run variation. This paper suggests that long-run sample information can be isolated using a small number of low-frequency trigonometric weighted averages, which in turn can be used to conduct inference about long-run variability and covariability. An advantage of this approach is that, because the low-frequency weighted averages have large-sample normal distributions, large sample valid inference can often be conducted using familiar small sample normal inference procedures. Moreover, the general approach is applicable for a wide range of persistent stochastic processes that go beyond the familiar I(0) and I(1) models.  

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.  

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. 

     Credibility of Confidence Sets in Nonstandard Econometric Problems. Accepted for publication at Econometrica. (Joint with ANDRIY NORETS.)

     Measuring Uncertainty about Long-Run Predictions. Accepted for publication at the Review of Economic Studies. (Joint with MARK WATSON.)

     Coverage Inducing Priors in Nonstandard Inference Problems. Accepted for publication at the Journal of the American Statistical Association. (Joint with ANDRIY NORETS.)

     Inference with Few Heterogenous Clusters. Review of Economics and Statistics 98 (2016), 83 – 96. (Joint with RUSTAM IBRAGIMOV.)

     Nearly Optimal Tests when a Nuisance Parameter is Present Under the Null Hypothesis. Econometrica 83 (2015), 771 – 811. (Joint with GRAHAM ELLIOTT and MARK WATSON.)

      HAC Corrections for Strongly Autocorrelated Time Series. Journal of Business & Economic Statistics 32 (2014), 311 – 322. Comments and Rejoinder.

     Pre and Post Break Parameter Inference. Journal of Econometrics 180 (2014), 141 – 157. (Joint with GRAHAM ELLIOTT.) 2012 working paper version.

     Risk of Bayesian Inference in Misspecified Models, and the Sandwich Covariance Matrix, Econometrica 81 (2013), 1805 – 1849.

     Low-Frequency Robust Cointegration Testing, Journal of Econometrics 174 (2013), 66 – 81. (Joint with MARK WATSON.)

      Measuring Prior Sensitivity and Prior Informativeness in Large Bayesian Models, Journal of Monetary Economics 59 (2012), 581 – 597.

     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.)