arXiv subjects

Zhiheng You

Publications and source records attributed to Zhiheng You.

4 recordsLinked to original sources

arXiv2026

Variance or Standard Deviation? Shell Geometry and Global-Scale Priors in High-Dimensional Shrinkage

We study how the choice of default prior for a common Gaussian scale affects high-dimensional shrinkage risk, highlighting the role played by high-dimensional geometry. Formally, we consider a high-dimensional setting in which the near-zero behavior of the common scale prior has first-order consequences for shrinkage risk, and show that priors that are flat on the variance and those flat on the standard deviation allocate markedly different mass near the zero-scale boundary, leading to distinct shrinkage behavior and informing principled default prior selection. Specifically, under a radial-power benchmark, we establish that the SD-flat benchmark has a one-unit asymptotic risk advantage near the origin, crosses over in the critical regime, and is second-order equivalent to the variance-flat benchmark for strong signals. Proper single global-scale hyperpriors and bounded coordinate-multiplier mixtures inherit these limits through the near-zero exponent of their SD-scale density. For heavier-tailed or sparse priors, that exponent still classifies the common global-scale component, while local-scale tails, model-size priors, or allocation priors can also affect risk.

stat.ME↗

arXiv2026

How Well Are State-Dependent Local Projections Capturing Nonlinearities?

We use quadratic vector autoregressions, motivated by pruned second-order perturbation solutions to DSGE models, as a laboratory to evaluate how well popular local projection (LP) specifications recover true impulse responses in nonlinear environments. We derive closed-form population impulse responses under each specification and compare them to truth. Linear LP fails to capture nonlinearities when the shock is symmetrically distributed. State-dependent LP specifications capture distinct aspects of nonlinearity: interacting the shock with its sign captures asymmetric effects, while interacting the shock with observable state proxies captures state dependence. However, their gains over linear LP are concentrated in tail shocks or states, and for the latter depend on proxy quality. Our proposed specification -- augmenting linear LP with a squared shock term and shock-state proxy interactions -- best approximates true responses. We also establish valid estimation and inference procedures for this specification. In a monetary policy application, we find state dependence, while higher-order effects differ across outcomes.

econ.GN↗

arXiv2026

Model Restrictiveness in Functional and Structural Settings

We extend the restrictiveness measure of Fudenberg, Gao & Liang (2026) to functional and structural econometric settings using Gaussian process priors. We find that models evaluated over continuum domains appear more restrictive than when evaluated over finite sets of observations. We also extend the restrictiveness framework to structural models with endogeneity, instrumental variables, multiple equilibria, and nonparametric nuisance components. We explain why the choice of discrepancy function is a substantive modeling decision, and why the Rademacher complexity and GMM criterion functions are unsuitable as discrepancies. We further show that restrictiveness equals the normalized limit of the noise-free average-case learning curve. In applications to preferences under risk, and multinomial choice under exogenous and endogenous settings, we find that the same models exhibit uniformly higher restrictiveness when evaluated over continuum domains than based on their predictions on finite sets, and that moment restrictions from endogeneity substantially increase restrictiveness and alter model rankings.

econ.GN↗

arXiv2026

Using Prior Studies to Design Experiments: An Empirical Bayes Approach

We develop an empirical Bayes framework for experimental design that leverages information from prior related studies. When a researcher has access to estimates from previous studies on similar parameters, they can use empirical Bayes to estimate an informative prior over the parameter of interest in the new study. We show how this prior can be incorporated into a decision-theoretic experimental design framework to choose optimal design. The approach is illustrated via propensity score designs in stratified randomized experiments. Our theoretical results show that the empirical Bayes design achieves oracle-optimal performance as the number of prior studies grows, and characterize the rate at which regret vanishes. To illustrate the approach, we present two empirical applications--oncology drug trials and the Tennessee Project STAR experiment. Our framework connects the Bayesian meta-analysis literature to experimental design and provides practical guidance for researchers seeking to design more efficient experiments.

econ.EM↗