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Partial Identification of Heteroskedastic Structural VARs: Theory and Bayesian Inference

Discussion Papers 2081, 57 S.

Helmut Lütkepohl, Fei Shang, Luis Uzeda, Tomasz Woźniak


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We consider structural vector autoregressions identified through stochastic volatility. Our focus is on whether a particular structural shock is identified by heteroskedasticity without the need to impose any sign or exclusion restrictions. Three contributions emerge from our exercise: (i) a set of conditions under which the matrix containing structural parameters is partially or globally unique; (ii) a statistical procedure to assess the validity of the conditions mentioned above; and (iii) a shrinkage prior distribution for conditional variances centred on a hypothesis of homoskedasticity. Such a prior ensures that the evidence for identifying a structural shock comes only from the data and is not favoured by the prior. We illustrate our new methods using a U.S. fiscal structural model.

Topics: Monetary policy

JEL-Classification: C11;C12;C32;E62
Keywords: Identification through heteroskedasticity, stochastic volatility, non-centred parameterisation, shrinkage prior, normal product distribution, tax shocks