Heteroskedastic Proxy Vector Autoregressions: Testing for Time-Varying Impulse Responses in the Presence of Multiple Proxies

Have the Effects of Shocks to Oil Price Expectations Changed? Evidence from Heteroskedastic Proxy Vector Autoregressions

“…An extension of the test for the case of identifying more than one shock by a set of proxies was proposed by Bruns and Lütkepohl (2022). It does not require identification of the individual shocks identified by the set of proxies and will be used in the empirical analysis when more than one shock is of interest.…”

“…As mentioned earlier, we use tests proposed by Lütkepohl and Schlaak (2022) and Bruns and Lütkepohl (2022) to investigate the timeinvariance of the impact effects of the shocks. These authors show that their tests are robust to misspecifying the volatility change points or the number of volatility regimes.…”

“…We use these shocks, consider a sample period from 1984 to 2019, and assume that the data are generated by a time-invariant VAR process with heteroskedastic residuals. We explore whether the changes in the residual volatility come with a change in the transmission of the structural shocks using statistical tests as proposed by Lütkepohl and Schlaak (2022) and Bruns and Lütkepohl (2022). We find evidence that the impulse responses are different before and after the time of the 1990/91 gulf war.…”

“…Tests for time-varying impact effects(𝑝-values). 𝑝-values based on the identification-robust test ofBruns and Lütkepohl (2022) for time-varying impact effects of both shocks jointly. 𝐵 1∶2 (𝑚) signifies the elements of the impact effects matrix considered in volatility regime 𝑚.…”