Inference for Functional Instrumental Variables Regression with Possibly Weak Identification (Job Market Paper) [Paper] [Slide]

This paper analyzes estimation and inference in linear instrumental variables regression where random variables can be function-valued, such as curves or trajectories. While functional data offer a richer, more flexible framework for understanding economic relationships, we show that weak identification poses a more complex challenge than in the conventional IV setting. We propose a framework to classify instrument strength in this functional setting, ranging from strong to weak. Considering a regularized IV estimator, we establish a baseline under strong identification, demonstrating that the estimator is consistent and asymptotically normal, which enables us to develop a novel functional t-test for the structural parameter. When identification is weak, however, these baseline asymptotics fail to hold. The regularization introduces a non-vanishing bias that invalidates standard inference and makes conventional weak-instrument tests ineffective. Furthermore, existing inference procedures robust to weak instruments are not directly applicable to the functional IV setting. To address this gap, we develop an identification-robust inference procedure, the Functional Anderson-Rubin test. An application of our methodology to Alberta's real-time electricity market shows that instrument strength is intermittent across hours, highlighting the need for weak-IV-robust inference. Our estimates demonstrate significant hourly heterogeneity in supply elasticity.

Instrumental Factor Model for High Dimensional Functional Data (with Jihyun Kim) [Paper]

This paper introduces an instrumental factor model that extends conventional factor models in two directions. First, we allow data observations to be function-valued rather than scalar, accommodating modern big data structures. Second, we achieve consistent estimation with short time series by using observed characteristics as instruments for the factor model. Unlike standard principal-components methods, which require both a large cross-section (N) and a long time dimension (T), our proposed estimator is consistent for large N even when T is fixed and small. We develop eigenvalue-ratio estimators for the number of factors suitable for short-T panels and establish their consistency on large N. Monte Carlo experiments show substantial efficiency gains relative to standard principal-components estimation, particularly when the time dimension is small. We conclude by conducting an empirical study to examine the long-term relationship between climate change and the European cereal market.

Identification and Estimation of Functional Simultaneous Equations Model (with Jean-Pierre Florens and Nour Meddahi)