I am an incoming Senior Lecturer (Assistant Professor) of the Department of Economics at the University of Melbourne, and a PhD candidate in Economics at University College London.

Email: tian.xie.20@ucl.ac.uk

My research focuses on econometrics, particularly empirical Bayes, statistical decision theory, and mixture models, with applications in labor economics.

Working Papers

• Automatic Inference for Value-Added Regressions (JMP)
  [abstract] [arXiv]
  A large empirical literature regresses outcomes on empirical Bayes shrinkage estimates of value-added, yet little is known about whether this approach leads to unbiased estimates and valid inference for the downstream regression coefficients. We study a general class of empirical Bayes estimators and the properties of the resulting regression coefficients. We show that estimators can be asymptotically biased and inference can be invalid if the shrinkage estimator does not account for heteroskedasticity in the noise when estimating value added. By contrast, shrinkage estimators properly constructed to model this heteroskedasticity perform an automatic bias correction: the associated regression estimator is asymptotically unbiased, asymptotically normal, and efficient in the sense that it is asymptotically equivalent to regressing on the true (latent) value-added. Further, OLS standard errors from regressing on shrinkage estimates are consistent in this case. As such, efficient inference is easy for practitioners to implement: simply regress outcomes on shrinkage estimates of value-added that account for noise heteroskedasticity.
• Compound Selection Decisions: An Almost SURE Approach
  with Jiafeng (Kevin) Chen, Lihua Lei, Timothy Sudijono, and Liyang Sun.
  [abstract] [arXiv]
  This paper proposes methods for compound selection decision problems in a Gaussian sequence model. Inspired by Stein's unbiased risk estimate (SURE), we introduce ASSURE, a family of estimators for welfare, defined as the expected utility of a selection decision rule. ASSURE enables robust evaluation of selection decisions. For empirical Bayes decisions derived from random-effects models of unknown parameters, ASSURE estimates their welfare even when the models are misspecified. Optimizing ASSURE-estimated welfare over a pre-specified class of decision rules further borrows strength across noisy estimates and yields decision rules with favorable regret properties. These regret properties are again robust to potential misspecification of random effects models, thereby robustifying empirical Bayes methods. We apply ASSURE to selecting Census tracts for economic mobility, identifying discriminating firms, and evaluating p-value decision rules in A/B testing.

Work in Progress

• Robust Empirical Bayes Under Misspecification