Identifying Shocks via Time-Varying Volatility

45 Pages Posted: 23 Oct 2018 Last revised: 25 May 2019

See all articles by Daniel J. Lewis

Daniel J. Lewis

Federal Reserve Banks - Federal Reserve Bank of New York

Date Written: May 2019


An n-variable structural vector auto-regression (SVAR) can be identified (up to shock order) from the evolution of the residual covariance across time if the structural shocks exhibit heteroskedasticity (Rigobon (2003), Sentana and Fiorentini (2001)). However, the path of residual covariances can only be recovered from the data under specific parametric assumptions on the variance process. I propose a new identification argument that identifies the SVAR up to shock orderings using the autocovariance structure of second moments of the residuals, implied by an arbitrary stochastic process for the shock variances. These higher moments are available without parametric assumptions like those required by existing approaches. The conditions required for identification can be tested using a simple procedure. The identification scheme performs well in simulations. I apply the approach to the debate on fiscal multipliers and obtain estimates lower than those of Blanchard and Perotti (2002) and Mertens and Ravn (2014), but in line with more recent studies.

Keywords: identification, impulse response function, structural shocks, SVAR, fiscal multiplier, time-varying volatility, heteroskedasticity

JEL Classification: C32, C58, E20, E62, H30

Suggested Citation

Lewis, Daniel J., Identifying Shocks via Time-Varying Volatility (May 2019). FRB of New York Staff Report No. 871, Available at SSRN: or

Daniel J. Lewis (Contact Author)

Federal Reserve Banks - Federal Reserve Bank of New York ( email )

33 Liberty Street
New York, NY 10045
United States

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