Exploring the bidirectional causality between green markets and economic policy: evidence from the time-varying Granger test

Abstract

The vigorous development of green markets and the effective mitigation of economic policy fluctuations are current hotspots that intrigue our interest in exploring the causal relationships between green market returns and economic policy uncertainty (EPU). Green bonds, corporate environmental responsibility, green technology investment, and the carbon trading market are our research objects to comprehensively understand the interaction among them, from both macro and micro perspectives. Considering the importance of temporal heterogeneity and spillover direction in causation, we employ the time-varying Granger causality method to obtain bidirectional real-time identification. We find that green market returns exhibit a time-varying bidirectional causality with EPU over most of the sample period. In contrast, green markets are more a risk spillover than a recipient. Notably, this causality is vulnerable to exogenous financial risks, especially structural changes caused by the COVID-19 pandemic. Overall, this paper provides insights into the deep-seated causes of price fluctuations, volatile market uncertainty, and the interaction mechanism between them, as well as implications for market participants and policymakers.

Appendix

As mentioned earlier, three algorithms are used to generate Wald statistics. With respect to the FE methodology (Thoma, 1994), the Wald test statistic first computes the minimum window size, ${\tau }_{0}={T}_{r0}$, and successively expands the length of the observations until all samples are used (Fig. 1a). The RO procedure (Arora and Shi 2016; Swanson 1998) moves forward by a fixed window length at a time and calculates the Wald statistics for each subsample separately (Fig. 1b). The RE approach (Phillips et al. 2015) provides common endpoints for each subsample given a specific observation interval; then, the algorithm calculates the Wald statistics for each subsample with the window length of ${\tau }_{0}$ or greater when repeating the process (Fig. 1c). Notably, the three algorithms may generate different conclusions in practical causal tests due to their performance differences in limited samples. In a single switch procedure, the dating rule is giving by the crossing times, specifically, for each algorithm we have:

$$\mathrm{FE}: {\widehat{f}}_{e}=\genfrac{}{}{0pt}{}{inf}{f\in [{f}_{0},1]}\left\{f:{W}_{f}(0)>cv\right\} and {\widehat{f}}_{f}=\genfrac{}{}{0pt}{}{inf}{f\in [\widehat{{f}_{e}},1]}\left\{f:{W}_{f}(0)<cv\right\},$$

(1)

$$\mathrm{RO}: {\widehat{f}}_{e}=\genfrac{}{}{0pt}{}{inf}{f\in \left[{f}_{0},1\right]}\left\{f:{W}_{f}(f-{f}_{0})>cv\right\} and {\widehat{f}}_{f}=\genfrac{}{}{0pt}{}{inf}{f\in [\widehat{{f}_{e}},1]}\left\{f:{W}_{f}(f-{f}_{0})<cv\right\},$$

(2)

$$\mathrm{RE}: {\widehat{f}}_{e}=\genfrac{}{}{0pt}{}{inf}{f\in \left[{f}_{0},1\right]}\left\{f:S{W}_{f}({f}_{0})>scv\right\} and {\widehat{f}}_{f}=\genfrac{}{}{0pt}{}{inf}{f\in [\widehat{{f}_{e}},1]}\left\{f:{SW}_{f}(f-{f}_{0})<scv\right\},$$

(3)

where cv denotes the critical value of ${W}_{f}$ and scv denotes the critical value of ${SW}_{f}$.

${\widehat{f}}_{e}$ and ${\widehat{f}}_{f}$ denote the start and end points of the causal relationship, respectively. They are identified as the first observation that exceeds or falls below the causal test threshold. We search the start and end points of episode i in the sample ranges of ${[\widehat{f}}_{i-1f},1]$ and ${[\widehat{f}}_{ie},1]$ respectively.