arXiv subjects

Deborah Kim

Publications and source records attributed to Deborah Kim.

5 recordsLinked to original sources

arXiv2026

Testing Sign Agreement

This article considers the problem of testing sign agreement among a finite number of parameters. This problem arises in empirical settings such as detecting treatment effects with opposite signs across subgroups, outcomes, or time periods, and testing instrument validity for local average treatment effects. For the null hypothesis that the parameters are either all non-negative or all non-positive, I propose two novel tests: a least favorable test and a conditional test. The least favorable test uses a worst-case null critical value, while the conditional test first screens components with large positive or negative estimates and then tests the remaining sign-unresolved components conditional on the screening event. Unlike existing sign agreement tests, both procedures accommodate arbitrary dependence among estimators; in the special case of independent estimators, the critical values depend only on the dimension and testing levels. We show that both tests control asymptotic size uniformly over a large class of nonparametric distributions. Local asymptotic power analysis reveals a tradeoff: the least favorable test is more powerful near boundary configurations where sign restrictions bind, whereas the conditional test is more powerful when some components are well separated from zero. Simulation evidence supports these theoretical predictions in finite samples.

econ.EM↗

arXiv2026

On the Rates of Convergence of Induced Ordered Statistics and their Applications

Induced order statistics (IOS) arise when sample units are reordered according to the value of an auxiliary variable, and the associated responses are analyzed in that induced order. IOS play a central role in applications where the goal is to approximate the conditional distribution of an outcome at a fixed covariate value using observations whose covariates lie closest to that point, including regression discontinuity designs, k-nearest-neighbor methods, and distributionally robust optimization. Existing asymptotic results allow the dimension of the IOS vector to grow with the sample size only under smoothness conditions that are often too restrictive for practical data-generating processes. In particular, these conditions rule out boundary points, which are central to regression discontinuity designs. This paper develops general convergence rates for IOS under primitive and comparatively weak assumptions. We derive sharp marginal rates for the approximation of the target conditional distribution in Hellinger and total variation distances under quadratic mean differentiability and show how these marginal rates translate into joint convergence rates for the IOS vector. Our results are widely applicable: they rely on a standard smoothness condition and accommodate both interior and boundary conditioning points, as required in regression discontinuity and related settings. In the supplementary appendix, we provide complementary results under a Taylor/Holder remainder condition. Our results reveal a clear trade-off between smoothness and speed of convergence, identify regimes in which Hellinger and total variation distances behave differently, and provide explicit growth conditions on the number of nearest neighbors.

econ.EM↗

arXiv2025

Testing Conditional Stochastic Dominance at Target Points

This paper introduces a test for conditional stochastic dominance between two distributions at prespecified values of a conditioning covariate, referred to as target points. The test uses a one-sided Kolmogorov--Smirnov statistic computed from induced order statistics, the outcomes attached to the conditioning observations closest to the target point, and compares it to a critical value that, given the number of neighbors, requires no resampling, kernel smoothing, or parametric assumptions. The same procedure applies whether the outcomes are continuous, discrete, or mixed, and requires only continuity of the conditional distributions in the conditioning variable. We establish asymptotic validity under two frameworks: one in which the number of neighbors is held fixed, where the induced order statistics converge to independent draws from the conditional distributions at the target point; and one in which it grows with the sample size, where we obtain an explicit rate that accommodates both an estimated target point and a data-dependent choice of the number of neighbors. We connect the test to permutation-based inference, provide a refined critical value for discrete outcomes, propose a rule for selecting the tuning parameters, and illustrate the procedure in two empirical applications whose recorded outcomes exhibit mass points. Monte Carlo simulations confirm its strong finite-sample performance.

econ.EM↗

arXiv2021

On the implementation of Approximate Randomization Tests in Linear Models with a Small Number of Clusters

This paper provides a user's guide to the general theory of approximate randomization tests developed in Canay, Romano, and Shaikh (2017) when specialized to linear regressions with clustered data. An important feature of the methodology is that it applies to settings in which the number of clusters is small -- even as small as five. We provide a step-by-step algorithmic description of how to implement the test and construct confidence intervals for the parameter of interest. In doing so, we additionally present three novel results concerning the methodology: we show that the method admits an equivalent implementation based on weighted scores; we show the test and confidence intervals are invariant to whether the test statistic is studentized or not; and we prove convexity of the confidence intervals for scalar parameters. We also articulate the main requirements underlying the test, emphasizing in particular common pitfalls that researchers may encounter. Finally, we illustrate the use of the methodology with two applications that further illuminate these points. The companion {\tt R} and {\tt Stata} packages facilitate the implementation of the methodology and the replication of the empirical exercises.

econ.EM↗

arXiv2020

On the Size Control of the Hybrid Test for Predictive Ability

We analyze theoretical properties of the hybrid test for superior predictability. We demonstrate with a simple example that the test may not be pointwise asymptotically of level $\alpha$ at commonly used significance levels and may lead to rejection rates over $11\%$ when the significance level $\alpha$ is $5\%$. Generalizing this observation, we provide a formal result that pointwise asymptotic invalidity of the hybrid test persists in a setting under reasonable conditions. As an easy alternative, we propose a modified hybrid test based on the generalized moment selection method and show that the modified test enjoys pointwise asymptotic validity. Monte Carlo simulations support the theoretical findings.

econ.EM↗