Three Basic Issues that Arise when Using Informational Restrictions in SVARs*

Abstract

When sign or other informational restrictions are used in SVARs, impulse responses are only set identified. Three issues need to be addressed when finding such sets. One is that the restrictions must be sufficient to separate the shocks. Failure to do so can result in unacceptable structural equations, for example two supply curves in the SVAR. Another is the need to adjust the identified set so that the responses are to the same size shock. Otherwise the range of responses that are being found may simply reflect different shock sizes. The third issue is estimation of the SVAR when all the shocks are not separated. Researchers are often unwilling to set out sign restrictions to separate all shocks and so we describe what can be done to accommodate that attitude by using a triangular SVAR that parallels what is used with exact restrictions.JEL Classification numbers: C01. C18. C32. C52. *We thank three referees for drawing our attention to some recent papers and asking challenging questions.

Assessing the Impact of Policy Changes on a Nowcast

“…It does so without requiring a complete specification of the identifying restrictions. Ouliaris and Pagan (2022) show that once the shock of interest is estimated, the responses of the other variables to the shock can be estimated by regressing these variables on the shock in a single equation from a reduced-form VAR. Based on the sign-restricted approach for estimating structural VARs, this non-parametric method is especially useful in a nowcasting context because (a) the total number of parameters to estimate is low compared to a VAR; (b) by construction, this approach is appropriately agnostic about the identifying restrictions underlying the true impulse response functions in the SVAR.…”

“…As expected, an increase in real oil prices reduces the nowcast of real GDP growth for Dominica, though with a small elasticity, while an increase in US real GDP has a large positive effect on Dominica's real GDP. The second approach applies a non-parametric structural estimator recently introduced in Ouliaris and Pagan (2022) to estimate the responsiveness of a nowcast to a structural shock. This estimator is used to assess the impact on the nowcast for the Kingdom of Tonga's real GDP of a positive unit shock in travel receipts.…”

“…Assume that we are interested in assessing the impact of an increase in tourism on the nowcast for real GDP. The first step in applying the non-parametric approach suggested by Ouliaris and Pagan (2022) is to specify the structural equation that will yield an estimate of the structural error for travel receipts (i.e., 𝜂𝜂 1𝑡𝑡 in equation ( 1)).…”