IV and Panel Methods
Paper Session
Sunday, Jan. 3, 2027 8:00 AM - 10:00 AM (EST)
- Chair: Mahrad Sharifvaghefi, University of Pittsburgh
IV Regression with Distribution-Valued Outcomes
Abstract
We develop IV Fréchet regression (IVFR), an instrumental-variable (IV) method for settings where the outcome is an entire distribution. Framing the problem as an IV regression in 2-Wasserstein space, IVFR extends global Fréchet regression to the endogenous case. IVFR projects IV-weighted quantile curves onto the space of valid distributions and recovers coefficient functions by OLS. The projection provably reduces the estimation error in finite samples and guarantees valid fitted distributions. We show that the IVFR estimator converges weakly to a mean-zero Gaussian process and establish the validity of a multiplier bootstrap procedure for uniform inference. In simulations, the projection reduces the integrated mean squared (IMSE) error by up to 82% relative to existing methods. Revisiting the effects of Chinese import competition on the wage distribution within commuting zones, the proposed method produces 9--10% narrower confidence bands than existing methods. Using our novel uniform confidence bands, we find no evidence that import competition reduced wages at the very bottom of the distribution, but only between the 10th and 40th quantile. We also revisit the effect of county food stamp programs on the county’s birth weight distribution and find no significant effects.Panel Quantile Regression with Common Shocks
Abstract
This paper develops an asymptotic and inferential theory for fixed-effects panel quantile regression (FEQR) that delivers inference robust to pervasive common shocks. Such shocks induce cross-sectional dependence that is central in many economic and financial panels but largely ignored in existing FEQR theory, which typically assumes cross-sectional independence and requires $T gg N$. We show that the standard FEQR estimator remains asymptotically normal under the mild condition $(log N)^2/T o 0$, thereby accommodating empirically relevant regimes, including those with $T ll N$. We further show that common shocks fundamentally alter the asymptotic covariance structure, rendering conventional covariance estimators inconsistent, and we propose a simple covariance estimator that remains consistent both in the presence and absence of common shocks. The proposed procedure therefore provides valid robust inference without requiring prior knowledge of the dependence structure, substantially expanding the applicability of FEQR methods in realistic panel data settings.Power Bounds and Efficiency Loss for Asymptotically Optimal Tests in IV Regression
Abstract
We characterize the maximal attainable power-size gap in overidentified instrumental variables models with heteroskedastic or autocorrelated (HAC) errors. Using total variation distance and Kraft's theorem, we define the decision theoretic frontier of the testing problem. We show that Lagrange multiplier and conditional quasi likelihood ratio tests can have power arbitrarily close to size even when the null and alternative are well separated, because they do not fully exploit the reduced-form likelihood. In contrast, the conditional likelihood ratio (CLR) test uses the full reduced-form likelihood. We prove that the power-size gap of CLR converges to one if and only if the testing problem becomes trivial in total variation distance, so that CLR attains the decision theoretic frontier whenever any test can. An empirical illustration based on Yogo (2004) shows that these failures arise in empirically relevant configurations.JEL Classifications
- C2 - Single Equation Models; Single Variables