Structural Inference in Sparse High-Dimensional Vector Autoregressions
This work addresses inference challenges in high-dimensional econometric models, providing tools for economists and statisticians, but it is incremental as it builds on existing sparse VAR methods.
The authors tackled statistical inference for impulse responses in sparse, high-dimensional structural vector autoregressive systems by introducing consistent estimators and valid inference procedures, showing that the estimators have a Gaussian limit and presenting a bootstrap method for confidence intervals and tests.
We consider statistical inference for impulse responses in sparse, structural high-dimensional vector autoregressive (SVAR) systems. We introduce consistent estimators of impulse responses in the high-dimensional setting and suggest valid inference procedures for the same parameters. Statistical inference in our setting is much more involved since standard procedures, like the delta-method, do not apply. By using local projection equations, we first construct a de-sparsified version of regularized estimators of the moving average parameters associated with the VAR system. We then obtain estimators of the structural impulse responses by combining the aforementioned de-sparsified estimators with a non-regularized estimator of the contemporaneous impact matrix, also taking into account the high-dimensionality of the system. We show that the distribution of the derived estimators of structural impulse responses has a Gaussian limit. We also present a valid bootstrap procedure to estimate this distribution. Applications of the inference procedure in the construction of confidence intervals for impulse responses as well as in tests for forecast error variance decomposition are presented. Our procedure is illustrated by means of simulations.