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Inference for High-Dimensional Local Projection

Jiti Gao, Fei Liu, Bin Peng

TL;DR

The study develops a high-dimensional local projection (LP) framework to enable robust $h$-step-ahead impulse-response inference when the cross-sectional dimension $N$ is large. It integrates a HDMA($\infty$) data-generating process with a sparse regression setup, derives concentration bounds, and constructs a debiased, node-wise LASSO-based inference scheme for valid HD inference, including a lag-selection IC$\,$criterion. Theoretical results show convergence and asymptotic normality for the debiased estimator, while simulations validate finite-sample performance under HD settings. The empirical application to business-news attention and industry volatility demonstrates short-run increases in volatility from recession-related news and reveals cross-industry spillovers, illustrating the method’s practical relevance for macro-finance contexts.

Abstract

This paper rigorously analyzes the properties of the local projection (LP) methodology within a high-dimensional (HD) framework, with a central focus on achieving robust long-horizon inference. We integrate a general dependence structure into h-step ahead forecasting models via a flexible specification of the residual terms. Additionally, we study the corresponding HD covariance matrix estimation, explicitly addressing the complexity arising from the long-horizon setting. Extensive Monte Carlo simulations are conducted to substantiate the derived theoretical findings. In the empirical study, we utilize the proposed HD LP framework to study the impact of business news attention on U.S. industry-level stock volatility.

Inference for High-Dimensional Local Projection

TL;DR

The study develops a high-dimensional local projection (LP) framework to enable robust -step-ahead impulse-response inference when the cross-sectional dimension is large. It integrates a HDMA() data-generating process with a sparse regression setup, derives concentration bounds, and constructs a debiased, node-wise LASSO-based inference scheme for valid HD inference, including a lag-selection ICcriterion. Theoretical results show convergence and asymptotic normality for the debiased estimator, while simulations validate finite-sample performance under HD settings. The empirical application to business-news attention and industry volatility demonstrates short-run increases in volatility from recession-related news and reveals cross-industry spillovers, illustrating the method’s practical relevance for macro-finance contexts.

Abstract

This paper rigorously analyzes the properties of the local projection (LP) methodology within a high-dimensional (HD) framework, with a central focus on achieving robust long-horizon inference. We integrate a general dependence structure into h-step ahead forecasting models via a flexible specification of the residual terms. Additionally, we study the corresponding HD covariance matrix estimation, explicitly addressing the complexity arising from the long-horizon setting. Extensive Monte Carlo simulations are conducted to substantiate the derived theoretical findings. In the empirical study, we utilize the proposed HD LP framework to study the impact of business news attention on U.S. industry-level stock volatility.
Paper Structure (22 sections, 16 theorems, 261 equations, 2 figures, 5 tables)

This paper contains 22 sections, 16 theorems, 261 equations, 2 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Setup and Asymptotic Properties
  3. Data Generating Process
  4. The Setup
  5. Estimation
  6. Asymptotic Distribution
  7. Simulation
  8. Empirical Study
  9. Data and Variables
  10. Estimation Results
  11. Conclusion
  12. Additional Results and Information
  13. Finite-Dimensional Setting
  14. Approximation of HDMA
  15. Connection with the Existing Literature
  16. ...and 7 more sections

Key Result

Proposition 1

Suppose that $\mathbf{x}_t$ admits both representations def.IR and def.xth, Assumptions AS1 and AS2.1 hold, and $\mathbf{B}_0 =\mathbf{I}_N$. For $\forall h\ge 1$, we obtain that $\mathbf{A}_{1} = \mathbf{B}_{h} = ({\normalfont \textbf{IR}_{h,1}},\ldots, {\normalfont \textbf{IR}_{h,N}})$.

Figures (2)

  • Figure 1: Sparsity of $\mathbf{B}_h$
  • Figure 2: Estimated Impulse Responses of Industry Volatilities to Recession News Attention.Notes: The solid black line represents the estimated impulse response of volatility to the recession-related news attention index, while the light blue shaded area denotes the associated 90% confidence intervals.

Theorems & Definitions (32)

  • Example 1
  • Example 2
  • Example 3
  • Proposition 1
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Corollary 1
  • ...and 22 more