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]
  We propose methods to construct compound selection decisions in a Gaussian sequence model. Given unknown, fixed parameters \( \mu_{1:n} \), known \( \sigma_{1:n} \), and observations \( Y_i \sim \mathcal{N}(\mu_i, \sigma_i^2) \), the decision maker chooses a subset \( S \subseteq [n] \) to maximize utility \( \frac{1}{n}\sum_{i \in S} (\mu_i - K_i) \) for known costs \( K_i \). Inspired by Stein’s unbiased risk estimate (SURE), we introduce an almost unbiased estimator, ASSURE, for the expected utility of a proposed decision rule. ASSURE selects a welfare-maximizing rule within a pre-specified class by optimizing the estimated welfare, thereby borrowing strength across noisy estimates. We show that, within the pre-specified class, ASSURE’s decisions are asymptotically no worse than the optimal (infeasible) rule. We apply ASSURE to the selection of Census tracts for economic opportunity, the identification of discriminating firms, and the analysis of \( p \)-value decision procedures in A/B testing.

Work in Progress

• Robust Empirical Bayes Under Misspecification