SMU SOE Seminar Series (April 12, 2024): Optimal Estimation of Heterogeneous Parameters under Unknown Heteroskedasticity

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TOPIC:

OPTIMAL ESTIMATION OF HETEROGENEOUS PARAMETERS UNDER UNKNOWN HETEROSKEDASTICITY

ABSTRACT This paper studies the large-scale estimation of heterogeneous parameters under limited information where the heterogeneity is on a unit-level, e.g., teachers or neighborhoods. We employ a normal sampling model with unknown heteroskedasticity and provide generalized Tweedie’s formula for the posterior means of the heterogeneous parameters. We then use these to characterize the compound optimal estimators (the oracles) of the unit-specific mean and quantile parameters in terms of the density of certain sufficient statistics. Feasible versions are proposed for which we provide asymptotic compound optimal guarantees, where their compound risk is shown to be asymptotically equivalent to that of the infeasible oracles. Numerical experiments show that the proposed estimators are generally within 1–3% of the oracles for an extensive range of data generating processes, including ones calibrated to our empirical application. The estimators are employed in an empirical study of teachers’ effects on students’ test outcomes where we find that the teacher rankings can be highly sensitive to how one defines teacher quality, whether in terms of the mean or lower percentile students. Keywords: Compound Loss, Empirical Bayes Methods, Shrinkage Estimation, Nonparametric Estimation. Click here to view the CV.
		PRESENTER Ho Sheng Chao SMU Overseas Postgraduate Scholar
		RESEARCH FIELDS Econometrics Macro-econometrics Econometric Theory
		DATE: 12 April 2024 (Friday)
		TIME: 10am - 11.30am
		VENUE: Meeting Room 5.1, Level 5 School of Economics Singapore Management University 90 Stamford Road Singapore 178903

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