12 research outputs found
Omitted variable bias of Lasso-based inference methods: A finite sample analysis
We study the finite sample behavior of Lasso-based inference methods such as
post double Lasso and debiased Lasso. We show that these methods can exhibit
substantial omitted variable biases (OVBs) due to Lasso not selecting relevant
controls. This phenomenon can occur even when the coefficients are sparse and
the sample size is large and larger than the number of controls. Therefore,
relying on the existing asymptotic inference theory can be problematic in
empirical applications. We compare the Lasso-based inference methods to modern
high-dimensional OLS-based methods and provide practical guidance
Decentralization Estimators for Instrumental Variable Quantile Regression Models
The instrumental variable quantile regression (IVQR) model (Chernozhukov and
Hansen, 2005) is a popular tool for estimating causal quantile effects with
endogenous covariates. However, estimation is complicated by the non-smoothness
and non-convexity of the IVQR GMM objective function. This paper shows that the
IVQR estimation problem can be decomposed into a set of conventional quantile
regression sub-problems which are convex and can be solved efficiently. This
reformulation leads to new identification results and to fast, easy to
implement, and tuning-free estimators that do not require the availability of
high-level "black box" optimization routines
An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls
We introduce new inference procedures for counterfactual and synthetic
control methods for policy evaluation. We recast the causal inference problem
as a counterfactual prediction and a structural breaks testing problem. This
allows us to exploit insights from conformal prediction and structural breaks
testing to develop permutation inference procedures that accommodate modern
high-dimensional estimators, are valid under weak and easy-to-verify
conditions, and are provably robust against misspecification. Our methods work
in conjunction with many different approaches for predicting counterfactual
mean outcomes in the absence of the policy intervention. Examples include
synthetic controls, difference-in-differences, factor and matrix completion
models, and (fused) time series panel data models. Our approach demonstrates an
excellent small-sample performance in simulations and is taken to a data
application where we re-evaluate the consequences of decriminalizing indoor
prostitution
Detecting p-hacking
We theoretically analyze the problem of testing for -hacking based on
distributions of -values across multiple studies. We provide general results
for when such distributions have testable restrictions (are non-increasing)
under the null of no -hacking. We find novel additional testable
restrictions for -values based on -tests. Specifically, the shape of the
power functions results in both complete monotonicity as well as bounds on the
distribution of -values. These testable restrictions result in more powerful
tests for the null hypothesis of no -hacking. A reanalysis of two prominent
datasets shows the usefulness of our new tests
Practical and robust -test based inference for synthetic control and related methods
This paper proposes a practical and robust method for making inference on
average treatment effects estimated by synthetic control and related methods.
We develop a -fold cross-fitting procedure for bias-correction. To avoid the
difficult estimation of the long-run variance, inference is based on a
self-normalized -statistic, which has an asymptotically pivotal
-distribution. Our procedure only requires consistent (in -norm)
estimation of the parameters, which can be verified for synthetic control and
many other popular estimators. The proposed method is easy to implement,
provably robust against misspecification, more efficient than
difference-in-differences, valid with non-stationary data, and demonstrates an
excellent small sample performance
Conditional quantile estimators: A small sample theory
We study the small sample properties of conditional quantile estimators such
as classical and IV quantile regression.
First, we propose a higher-order analytical framework for comparing competing
estimators in small samples and assessing the accuracy of common inference
procedures. Our framework is based on a novel approximation of the
discontinuous sample moments by a H\"older-continuous process with a negligible
error. For any consistent estimator, this approximation leads to asymptotic
linear expansions with nearly optimal rates.
Second, we study the higher-order bias of exact quantile estimators up to
. Using a novel non-smooth calculus technique, we
uncover previously unknown non-negligible bias components that cannot be
consistently estimated and depend on the employed estimation algorithm. To
circumvent this problem, we propose a "symmetric" bias correction, which admits
a feasible implementation. Our simulations confirm the empirical importance of
bias correction
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A Comparison of Two Quantile Models With Endogeneity
This article studies the relationship between the two most-used quantile models with endogeneity: the instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen 2005) and the local quantile treatment effects (LQTE) model (Abadie, Angrist, and Imbens 2002). The key condition of the IVQR model is the rank similarity assumption, a restriction on the evolution of individual ranks across treatment states, under which population quantile treatment effects (QTE) are identified. By contrast, the LQTE model achieves identification through a monotonicity assumption on the selection equation but only identifies QTE for the subpopulation of compliers. This article shows that, despite these differences, there is a close connection between both models: (i) the IVQR estimands correspond to QTE for the compliers at transformed quantile levels and (ii) the IVQR estimand of the average treatment effect is equal to a convex combination of the local average treatment effect and a weighted average of integrated QTE for the compliers. These results do not rely on the rank similarity assumption and therefore provide a characterization of IVQR in settings where this key condition is violated. Underpinning the analysis are novel closed-form representations of the IVQR estimands. I illustrate the theoretical results with two empirical applications.</p