Functional Linear Projection and Impulse Response Analysis

Won-Ki Seo; Dakyung Seong

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arXiv · 2503.08364

Functional Linear Projection and Impulse Response Analysis

Won-Ki Seo·Dakyung Seong

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Abstract

This paper proposes econometric methods for studying how economic variables respond to function-valued shocks. Our methods are developed based on linear projection estimation of predictive regression models with a function-valued predictor and other control variables. We show that the linear projection coefficient associated with the functional variable allows for the impulse response interpretation in a functional structural vector autoregressive model under a certain identification scheme, similar to well-known Sims' (1972) causal chain, but with nontrivial complications in our functional setup. A novel estimator based on an operator Schur complement is proposed and its asymptotic properties are studied. We illustrate its empirical applicability with two examples involving functional variables: economy sentiment distributions and functional monetary policy shocks.

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BibTeX RIS

Won-Ki Seo, Dakyung Seong. 2025-03-11. Functional Linear Projection and Impulse Response Analysis. https://arxiv.org/abs/2503.08364

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