Ulrich K. Müller

Stanley G. Ivins ’34 and Henrietta Bauer Ivins Professor in Economics
Princeton University

Contact Information
Department of Economics
204 Julis Romo Rabinowitz
Princeton University
08544-1021 Princeton, NJ
Phone: (609) 258 4520
Fax: (609) 258 6419
Email: umueller@princeton.edu

Personal Information
CV (pdf)

Research Interests

Working Papers
     Testing Coefficient Variability in Spatial Regression. (Joint with  MARK WATSON.) Appendix. Replication Files.

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.   

     Time Varying Extremes. (Joint with  MARK WATSON.) Replication Files.

Standard extreme value theory implies that the distribution of the largest observations of a large cross section is well approximated by a parametric model, governed by a location, scale and shape parameter. The extremes of a panel of independent cross sections are all governed by the same parameters as long as the underlying distribution as well as the size of the cross sections are time invariant. We derive inference about these parameters, and tests of the null hypothesis of time invariance, under asymptotics that do not require the number of extremes or the number of time periods to increase. We further apply Hamiltonian Monte Carlo techniques to estimate the path of time-varying parameters. We illustrate the approach in four examples of U.S. data: damages from weather-related disasters, financial returns, city sizes andfirm sizes.   

     The Fragility of Sparsity. (Joint with MICHAL KOLESÁR and SEBASTIAN ROELSGAARD.)

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.   

     Spatial Unit Roots. (Joint with MARK WATSON.) Slides. Replication Files.

This paper proposes a model for, and investigates the consequences of, strong spatial dependence in economic variables. Our approach and findings echo those of the corresponding "unit root" time series literature: We suggest a model for spatial I(1) processes, and establish a functional central limit theorem that justifies a large sample Gaussian process approximation for such processes. We further generalize the I(1) model to a spatial "local-to-unity" model that exhibits weak mean reversion. We characterize the large sample behavior of regression inference with spatial I(1) variables, and establish that spurious regression is as much a problem with spatial I(1) data as it is with time series I(1) data. We develop asymptotically valid spatial unit root tests, stationarity tests, and inference methods for the local-to-unity parameter. Finally, we consider strategies for valid inference in regressions with persistent (I(1) or local-to-unity) spatial data, such as spatial analogues of first-differencing transformations.

     Low-Frequency Analysis of Economic Time Series. (Joint with MARK WATSON.) Draft chapter for Handbook of Econometrics, Volume 7, edited by S. Durlauf, L.P. Hansen, J.J. Heckman, and R. Matzkin.

     Forecasts in a Slightly Misspecified Finite Order VAR. (Joint with JAMES STOCK.) Slides.

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. 

Forthcoming and Published Papers
     A More Robust t-Test. Accepted for publication in the Review of Economis and Statistics. (Previously presented under the title "Inference for the Mean".) Replication files. Link to Stata implementation. Slides.

     Comprehensive Evidence Implies a Higher Social Cost of CO2Nature 610 (2022), 687 – 692. (Joint with K. RENNERT, F. ERRICKSON, B. C. PREST, L. RENNELS, R. G. NEWELL, W. PIZER, C. KINGDON, J. WINGENROTH, R. COOKE, B. PARTHUM, D. SMITH, K. CROMAR, D. DIAZ, F. C. MOORE, R. J. PLEVIN, A. E. RAFTERY, H. ŠEVČÍKOVÁ, H. SHEETS, J. H. STOCK, T. TAN, M. WATSON, T. E. WONG and D. ANTHOFF.)

     Spatial Correlation Robust Inference in Linear Regression and Panel ModelsJournal of Business and Economic Statistics 41 (2023), 1050  1064. (Joint with MARK WATSON.) Appendix and replication files. Link to Stata implementation.

     Spatial Correlation Robust InferenceEconometrica 90 (2022), 2901 –  2935. Link to Stata implementation. Link to Matlab implementation. Slides. (Joint with MARK WATSON.) 

     An Econometric Model of International Growth Dynamics for Long-horizon ForecastingReview of Economics and Statistics 104 (2022), 857 876. (Joint with JAMES STOCK and MARK WATSON.) Appendix and Replication files. Slides.

     Generalized Local-To-Unity Models, Econometrica 89 (2021), 1825 1854. (Joint with LIYU DOU.) Replication files. Slides.

     Linear Regression with Many Controls of Limited Explanatory Power, Quantitative Economics 12 (2021), 405 442. (Joint with CHENCHUAN LI.) 

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

     , 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.

     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), 8396. (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 SeriesJournal of Business & Economic Statistics 32 (2014), 311322. Comments and Rejoinder. Slides.

     Pre and Post Break Parameter Inference, Journal of Econometrics 180 (2014), 141157. (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 TestingJournal 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 ModelsReview of Economic Studies 77 (2010), 1508 – 1539. (Joint with PHILIPPE-EMMANUEL PETALAS.)  SupplementCorrection. Slides.

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

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

     Testing Models of Low-Frequency VariabilityEconometrica 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.)

     Minimizing the Impact of the Initial Condition on Testing for Unit Roots, Journal of Econometrics 135 (2006), 285 – 310. (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.)

     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.)


      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.