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

This paper analyzes estimation and inference in functional linear IV regression over a full range of instrument strengths, from strong to weak and unidentified. Our analysis centers on the Tikhonov regularized IV estimator, an approach to address the ill-posed inverse problem that arises from the inherently infinite-dimensional nature of functional regression. Under strong identification, the Tikhonov regularization bias is well controlled, allowing us to establish the estimator's asymptotic normality and construct a functional t-test for the structural parameter. In contrast, under weak identification, stabilizing the TIV estimator via regularization comes at the cost of a non-negligible bias, which invalidates standard asymptotic theory and makes existing weak-instrument tests inapplicable. Moreover, existing inference procedures robust to weak instruments are inapplicable to functional IV models. To address this, we introduce a Functional Anderson–Rubin test that remains valid under weak instruments in the functional IV setting. Applying our method to Alberta’s electricity market reveals that instrument strength is intermittent across hours, motivating weak-IV-robust inference. The estimates show significant hourly heterogeneity in supply elasticity.

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

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)