Ulrich K. Müller

We propose a framework for making Bayesian parametric models robust to local misspecification. Suppose in a baseline parametric model, a parameter of interest has an interpretation in an encompassing semiparametric model. Bayesian and maximum likelihood estimators are generally biased under local misspecification. We propose to augment the baseline likelihood by a multiplicative factor that involves scores for the baseline model, the efficient scores for the encompassing semiparametric model, and an auxiliary parameter that has the same dimension as the parameter of interest. We show that the marginal posterior for the parameter of interest in the augmented model is asymptotically normal with mean equal to the semiparametrically efficient estimator and variance equal to the semiparametric efficiency bound. The suggested augmentation robustifies the baseline parametric model to local misspecification, while preserving the appeal of Bayesian inference. We develop an MCMC algorithm for the augmented model and illustrate the approach in applications.   

This paper develops a test for coefficient stability in spatial regressions. The test is designed to have good power for a wide range of persistent patterns of coefficient variation, be applicable in a wide range of spatial designs, and to accommodate both spatial correlation and spatial heteroskedasticity in regressors and regression errors. The test approximates the best local invariant test for coefficient stability in a Gaussian regression model with Lévy-Brown motion coefficient variation under the alternative, and is thus a spatial generalization of the Nyblom (1989) test of coefficient stability in time series regressions. An application to 1514 zip-code level bivariate regressions ofU.S. socioeconomic variables reveals widespread coefficient instability.   

We show, using three empirical applications, that linear regression estimates which rely on the assumption of sparsity are fragile in two ways. First, we document that different choices of the regressor matrix that don't impact ordinary least squares (OLS) estimates, such as the choice of baseline category with categorical controls, can move sparsity-based estimates two standard errors or more. Second, we develop two tests of the sparsity assumption based on comparing sparsity-based estimators with OLS. The tests tend to reject the sparsity assumption in all three applications. Unless the number of regressors is comparable to or exceeds the sample size, OLS yields more robust results at little efficiency cost.   

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. Replication files. 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. Supplementary Appendix.

     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.