arXiv subjects

Luther Yap

Publications and source records attributed to Luther Yap.

8 recordsLinked to original sources

arXiv2026

Variance Estimation with Dependence and Heterogeneous Means

This paper develops a framework for variance estimation under dependence and heterogeneous means. This paper shows that consistent estimation of the variance target is impossible in general, and characterizes necessary and sufficient conditions for conservative variance estimation using dual cones. To choose among the valid estimators, this paper formulates three criteria -- minimal correction, pointwise level estimand, and pointwise MSE -- and shows how an eigenvalue truncation solution is optimal under all three criteria. This characterization and solution allow us to assess if existing variance estimators are valid and optimal in their respective settings, and construct the first optimal variance estimator that is simultaneously robust to heterogeneous means and cross-cluster serial correlation.

econ.EM↗

arXiv2024

Clustering with Potential Multidimensionality: Inference and Practice

We show how clustering standard errors in one or more dimensions can be justified in M-estimation when there is sampling or assignment uncertainty. Since existing procedures for variance estimation are either conservative or invalid, we propose a variance estimator that refines a conservative procedure and remains valid. We then interpret environments where clustering is frequently employed in empirical work from our design-based perspective and provide insights on their estimands and inference procedures.

econ.EM↗

arXiv2024

Inference with Many Weak Instruments and Heterogeneity

This paper considers inference in a linear instrumental variable regression model with many potentially weak instruments, in the presence of heterogeneous treatment effects. I first show that existing test procedures, including those that are robust to either weak instruments or heterogeneous treatment effects, can be arbitrarily oversized. I propose a novel and valid test based on a score statistic and a ``leave-three-out" variance estimator. In the presence of heterogeneity and within the class of tests that are functions of the leave-one-out analog of a maximal invariant, this test is asymptotically the uniformly most powerful unbiased test. In two applications to judge and quarter-of-birth instruments, the proposed inference procedure also yields a bounded confidence set while some existing methods yield unbounded or empty confidence sets.

econ.EM↗

arXiv2024

Sensitivity Analysis for Linear Estimators

We propose a novel sensitivity analysis framework for linear estimators with identification failures that can be viewed as seeing the wrong outcome distribution. Our approach measures the degree of identification failure through the change in measure between the observed distribution and a hypothetical target distribution that would identify the causal parameter of interest. The framework yields a sensitivity analysis that generalizes existing bounds for Average Potential Outcome (APO), Regression Discontinuity (RD), and instrumental variables (IV) exclusion failure designs. Our partial identification results extend results from the APO context to allow even unbounded likelihood ratios. Our proposed sensitivity analysis consistently estimates sharp bounds under plausible conditions and estimates valid bounds under mild conditions. We find that our method performs well in simulations even when targeting a discontinuous and nearly infinite bound.

econ.EM↗

arXiv2023

Valid Wald Inference with Many Weak Instruments

This paper proposes three novel test procedures that yield valid inference in an environment with many weak instrumental variables (MWIV). It is observed that the t statistic of the jackknife instrumental variable estimator (JIVE) has an asymptotic distribution that is identical to the two-stage-least squares (TSLS) t statistic in the just-identified environment. Consequently, test procedures that were valid for TSLS t are also valid for the JIVE t. Two such procedures, i.e., VtF and conditional Wald, are adapted directly. By exploiting a feature of MWIV environments, a third, more powerful, one-sided VtF-based test procedure can be obtained.

econ.EM↗

arXiv2023

Robust Conditional Wald Inference for Over-Identified IV

For the over-identified linear instrumental variables model, researchers commonly report the 2SLS estimate along with the robust standard error and seek to conduct inference with these quantities. If errors are homoskedastic, one can control the degree of inferential distortion using the first-stage F critical values from Stock and Yogo (2005), or use the robust-to-weak instruments Conditional Wald critical values of Moreira (2003). If errors are non-homoskedastic, these methods do not apply. We derive the generalization of Conditional Wald critical values that is robust to non-homoskedastic errors (e.g., heteroskedasticity or clustered variance structures), which can also be applied to nonlinear weakly-identified models (e.g. weakly-identified GMM).

econ.EM↗

arXiv2023

Design-Based Multi-Way Clustering

This paper extends the design-based framework to settings with multi-way cluster dependence, and shows how multi-way clustering can be justified when clustered assignment and clustered sampling occurs on different dimensions, or when either sampling or assignment is multi-way clustered. Unlike one-way clustering, the plug-in variance estimator in multi-way clustering is no longer conservative, so valid inference either requires an assumption on the correlation of treatment effects or a more conservative variance estimator. Simulations suggest that the plug-in variance estimator is usually robust, and the conservative variance estimator is often too conservative.

econ.EM↗

arXiv2023

Asymptotic Theory for Two-Way Clustering

This paper proves a new central limit theorem for a sample that exhibits two-way dependence and heterogeneity across clusters. Statistical inference for situations with both two-way dependence and cluster heterogeneity has thus far been an open issue. The existing theory for two-way clustering inference requires identical distributions across clusters (implied by the so-called separate exchangeability assumption). Yet no such homogeneity requirement is needed in the existing theory for one-way clustering. The new result therefore theoretically justifies the view that two-way clustering is a more robust version of one-way clustering, consistent with applied practice. In an application to linear regression, I show that a standard plug-in variance estimator is valid for inference.

econ.EM↗