Ulrich K. Müller

Standard inference about a scalar parameter estimated via GMM amounts to applying a t-test to a particular set of observations. If the number of observations is not very large, then moderately heavy tails can lead to poor behavior of the t-test. This is a particular problem under clustering, since the number of observations then corresponds to the number of clusters, and heterogeneity in cluster sizes induces a form of heavy tails. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the average of the remaining observations to construct a more robust alternative to the t-test. The new test is found to control size much more successfully in small samples compared to existing methods. Analytical results in the canonical inference for the mean problem demonstrate that the new test provides a refinement over the full sample t-test under more than two but less than three moments, while the bootstrapped t-test does not.

We develop a Bayesian latent factor model of the joint long-run evolution of GDP per capita for 113 countries over the 118 years from 1900 to 2017. We find considerable heterogeneity in rates of convergence, including rates for some countries that are so slow that they might not converge (or diverge) in century-long samples, and a sparse correlation pattern (“convergence clubs”) between countries. The joint Bayesian structure allows us to compute a joint predictive distribution for the output paths of these countries over the next 100 years. This predictive distribution can be used for simulations requiring projections into the deep future, such as estimating the costs of climate change. The model’s pooling of information across countries results in tighter prediction intervals than are achieved using univariate information sets. Still, even using more than a century of data on many countries, the 100-year growth paths exhibit very wide uncertainty.

We introduce a generalization of the popular local-to-unity model of time series persistence by allowing for p autoregressive roots and p-1 moving average roots close to unity. This generalized local-to-unity model, GLTU(p), induces convergence of the suitably scaled time series to a continuous time Gaussian ARMA(p,p-1) process on the unit interval. Our main theoretical result establishes the richness of this form of limiting processes, in the sense that they can well approximate a large class of stationary Gaussian processes in the total variation norm. We show that Campbell and Yogo's (2006) popular inference method for predictive regressions fails to control size in the GLTU(2) model with empirically plausible parameter values, and we propose a limited-information Bayesian framework for inference in the GLTU(p) model and apply it to quantify the uncertainty about the half-life of deviations from Purchasing Power Parity.

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 is assumed known that nearly all control coefficients are zero, or at least very nearly so. We instead impose a bound on the quadratic mean of the controls' effect on the dependent variable. We develop a simple inference procedure that exploits this additional information in general heteroskedastic models. We study its asymptotic efficiency properties and compare it to a sparsity-based approach in a Monte Carlo study. The method is illustrated in three empirical applications.  

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. 

     Refining the Central Limit Theorem Approximation via Extreme Value Theory. Statistics & Probability Letters 155 (2019), 1 – 7.

     Nearly Weighted Risk Minimal Unbiased Estimation. Journal of Econometrics, 209 (2019), 18 – 34. (Joint with YULONG WANG.) Replication files. Slides.

     Long-Run Covariability. Econometrica 86 (2018), 775 – 804. Mark Watson’s Fisher-Schultz lecture 2016. (Joint with MARK WATSON.) Appendix and Replication files. Slides.

     Low-Frequency Econometrics. In Advances in Economics and Econometrics: Eleventh World Congress of the Econometric Society, Volume II, ed. by B. Honoré, and L. Samuelson, Cambridge University Press (2017), 53 – 94. (Joint with MARK WATSON.) Replication files. Slides.

     Fixed-k Asymptotic Inference about Tail Properties. Journal of the American Statistical Association, 112 (2017), 1334 – 1343. (Joint with YULONG WANG.) Replication files. Slides.

     Credibility of Confidence Sets in Nonstandard Econometric Problems. Econometrica 84 (2016), 2183 – 2213. (Joint with ANDRIY NORETS.) Supplementary Appendix. Slides.

     Measuring Uncertainty about Long-Run Predictions. Review of Economic Studies 83 (2016), 1711 – 1740. (Joint with MARK WATSON.) Supplementary Appendix. Replication files. Slides.

     Coverage Inducing Priors in Nonstandard Inference Problems. Journal of the American Statistical Association 111 (2016), 1233 – 1241. (Joint with ANDRIY NORETS.) Supplementary Appendix.

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

     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.) Supplementary Appendix. Replication files. Slides.

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

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

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

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

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

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

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

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

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

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

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

     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.)

     Comment on “HAR Inference: Recommendations for Practice” by E. Lazarus, D. J. Lewis and J. H. Stock, Journal of Business & Economic Statistics 36 (2018), 563 – 564.

     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.