Since Bitcoin reached the $100,000 mark, a question has begun to bubble up in the blogosphere and economic discourse: what is the relationship, if any, between the price of gold and Bitcoin?
I wrote code to evaluate the relationship between gold and Bitcoin prices. Using monthly price changes from January 2014 to December 2024, I first ensure the stationary of the date. The data is then split into pre- (2014–2019) and post-pandemic (2020 – present) periods for focused analysis. Granger causality tests are performed to determine whether past values of gold can help predict Bitcoin or vice versa. Correlation coefficients are then calculated to measure the strength and direction of their relationship. A Vector Autoregression (VAR) model to analyze dynamic interactions between the two assets, with Impulse Response Functions (IRFs) applied to illustrate how a shock to one variable (e.g., Bitcoin) affects the other (e.g., gold) over time, providing a detailed view of their economic interplay. The same operations are also performed on the S&P 500 and gold to provide a benchmark for comparison.
Granger Causality Tests:
Gold and Bitcoin (Pre-Pandemic): The Granger causality tests yield high p-values (> 0.05) for all lags, indicating no evidence that gold influences Bitcoin or vice versa in the pre-pandemic period.
Gold and Bitcoin (Post-Pandemic): The p-values drop slightly, particularly at lower lags (0.1492, 0.129, 0.0982), suggesting a weak indication that gold might influence Bitcoin, though still not statistically significant overall.
Gold and S&P 500 (Pre-Pandemic): P-values are lower for certain lags (0.0787, 0.0798, 0.1223), hinting at a modest causal relationship where gold might provide predictive signals for the S&P 500.
Gold and S&P 500 (Post-Pandemic): P-values remain consistently high (> 0.05) across all lags, showing no significant causal relationship between gold and the S&P 500 post-pandemic.
Correlation Analysis:
Pre-Pandemic:
The correlation between gold and Bitcoin is weakly positive at 0.10, reflecting little connection between the two assets.
Gold and the S&P 500 have a slight negative correlation of -0.08, consistent with gold’s historical role as a counterbalance to equities.
Post-Pandemic:
Gold and Bitcoin show a near-zero correlation (-0.01), indicating their relationship has weakened further.
Gold and the S&P 500 exhibit a stronger positive correlation (0.20), suggesting gold moved more in line with equities during this period, potentially due to pandemic-driven monetary policy or broader risk-on sentiment.
Impulse Response Function (IRF) findings:
Gold and Bitcoin:
Pre-Pandemic: A shock to gold has a small and mixed effect on bitcoin over time, with initial responses being slightly negative before stabilizing near zero. Conversely, a bitcoin shock results in noticeable, short-lived fluctuations in gold prices, though the impact diminishes after a few periods.
Post-Pandemic: Bitcoin becomes more responsive to gold shocks, with sharp, significant reactions observed initially, followed by stabilization. Gold, in turn, reacts more prominently to shocks in bitcoin, showing stronger feedback effects compared to the pre-pandemic period.
Gold and S&P 500::
Pre-Pandemic: A shock to gold has a moderate but short-term negative impact on the S&P 500, consistent with gold’s role as a hedge against equity markets. Shocks to the S&P 500 slightly influence gold prices, although the responses are relatively muted.
Post-Pandemic: Both assets exhibit more dynamic interactions. A gold shock now has a more sustained and mixed effect on the S&P 500, including periods of positive and negative responses.Conversely, S&P 500 shocks have a more noticeable influence on gold prices, highlighting an increased link between the two assets in the post-pandemic environment.
Conclusion
With all the caveats that normally attend econometric analysis, the following can be said. In the pre-pandemic period, gold and Bitcoin exhibited little to no relationship in terms of causality or correlation, with Granger causality tests and correlation analyses showing minimal interaction. In that same time period gold maintained a modest counterbalance role against the S&P 500, consistent with its historical function as a safe-haven asset during periods of equity market stress.
The Impulse Response Function (IRF) analysis further supports this: gold shocks had limited and short-lived impacts on Bitcoin, while Bitcoin shocks caused slight, temporary fluctuations in gold. Similarly, gold’s influence on the S&P 500 was modest, with a negative but short-term impact that aligns with its role as a hedge.
Post-pandemic, gold’s relationship with Bitcoin remains weak overall, but the evidence shows hints of evolving dynamics. Correlation remains near zero, but Granger causality and IRFs suggest a slight increase in mutual influence, with Bitcoin exhibiting sharper responses to gold shocks and vice versa. Meanwhile, gold’s correlation with the S&P 500 has turned moderately positive, reflecting a shift in investor behavior where gold may have tracked broader market movements during times of economic uncertainty. The IRF results further highlight this change: post-pandemic, shocks to gold have a more pronounced and sustained impact on the S&P 500, and the S&P 500 in turn influences gold prices more significantly.
Together, the econometric findings suggest a growing interconnectedness across assets in the post-pandemic period, driven by shared macroeconomic forces and evolving investor sentiment.
Peter C. Earle
