Time-varying relationship between conventional and unconventional monetary policies and risk aversion: international evidence from time- and frequency-domains

See Torrence and Compo (1998) for more details about cross-wavelet spectrum hypothesis and confidence levels.

We refer the reader to Ho et al. (2010) and Tiwari et al. (2020) for definition of these technical issues.

The main principles underlying SSR estimates are: Yield curve data, i.e., market-quoted interest rates of different times to maturity, are influenced by the policy interest rate (PIR) and unconventional monetary policy (UMP) tools (when the latter are in use). The yield curve may be considered as two components: a shadow yield curve without a near-ZLB constraint that can therefore freely take on negative values; and a physical currency option effect that results in a near-ZLB constraint on interest rates. Applying a shadow or lower bound model to yield curve data allows the shadow yield curve and the option effect components to be separately estimated. The SSR is then the shortest-maturity interest rate on the shadow yield curve, just like the PIR is the shortest-maturity interest rate on the actual yield curve. Because the shadow or lower bound model is estimated from yield curve data across UMP and conventional monetary policy (CMP) periods, the resulting SSR series provides a consistent and comparable metric for the stance of monetary policy over both periods.

The data can be downloaded from the following link: https://​www.​rbnz.​govt.​nz/​research-and-publications/​research-programme/​additional-research/​measures-of-the-stance-of-united-states-monetary-policy/​comparison-of-international-monetary-policy-measures.

As a preliminary analysis, we estimate a quantile-on-quantile regression as outlined in Sim and Zhou (2015), to understand the underlying relationship between the time-dependent phases of the two variables, i.e., the risk aversion and the interest rate. The results have been plotted in Figs. A2 and A3 in the online Appendix, and, in general, tend to suggest a theory-consistent negative relationship between the two variables across the various quantiles.

When the phase-difference is converted to an angle in the interval\(\left[ { - \pi ,\pi } \right]\), an absolute value less (larger) than $$\pi /2$$ indicates that the two series move in phase (anti-phase).

Given that the risk aversion data is available monthly as well over the period of 1986:06–2015:02, in Fig. A3 in the online Appendix, we analyzed the impact of an interest rate (i.e., the Shadow Short Rate) shock on risk aversion, and the feedback from risk aversion on to the interest rate in a vector autoregressive (VAR) model, with growth in industrial production and inflation as additional variables. The data on industrial production and consumer price index are derived from the FRED database of the Federal Reserve Bank of St. Louis. The variables in the VAR (12) are ordered as industrial production growth, inflation, interest rate and risk aversion. As can be seen, from the impulse responses, interest rate and risk aversion moves in opposite direction following a positive shock to either of these two variables. When a robustness test is conducted by replacing risk aversion with the variance risk premium (VRP), as developed by Zhou (2018) (with the data downloadable from: https://​sites.​google.​com/​site/​haozhouspersonal​homepage/​?​authuser=​1), in the VAR(12) estimated over 1990:01 to 2018:12, the earlier results continue to hold, as seen from Fig. A5 in the online Appendix.

In fact, preliminary evidence, based on the simultaneous test of causality-in-mean and causality-in-variance using a factor double autoregressive (FDAR) model, as developed by Guo et al. (2014), highlights that the null of simultaneous non-causality is strongly rejected in both directions for the US, Euro Area, Japan and the UK, as reported in Table A1 in the Online Appendix of the paper.