Who follows whom? : A Causality analysis between price and hashrate of Bitcoin and Ethereum
1. ABSTRACT
Cryptocurrency has emerged from the market as a fascinating matter. Bitcoin(BTC) and Ethereum(ETH) occupy the top two positions, counting 60% of the total market value. The percentage is decreasing as more cryptocurrencies are added to the market.
With the growing investment in the crypto market, the statistical analysis of the crypto market has drawn great interest, not only for academic research but also for the general public. The prices of cryptos are mainly influenced by several factors, for example, the supply and demand of the market, the cost of producing this crypto through the mining process, competing cryptocurrencies, and government regulations. The intrinsic value of one crypto should be estimated by the cost for its production, which depends on blockchain reward, the price of electricity, energy efficiency of mining hardware, and mining difficulty. So it may seem reasonable that the price of cryptos depends strongly on the network hash rates that decide the mining difficulty. On the other hand, higher prices will attract more miners into mining competition, which will eventually increase the total network hash rates, in this sense, maybe the hash rates should depend on the crypto prices. So who comes first？ The objective of this article is to find which is the cause of the other, we focus this article on the top two cryptos and try to dive more information into the Granger causality test between their prices and hashrates.
2. Hash Rates and crypto prices
Network hash rates are the total amount of mining computational power connected to the network. For Bitcoin, mining involves the use of computational power to run hashing algorithms to process the most recent block; the information that a user needs to mine is found in the block’s header. The cryptocurrency network sets a target value for this hash — called the target hash — and miners try to determine what this value is by testing out all possible values. The process of cycling through solutions is referred to as proof of work (PoW). Ethereum is mined similarly to Bitcoin, but unlike Bitcoin, Ethereum miners can charge a fee for confirming a transaction.
The difficulty of mining new blocks can either increase or decrease over time, and this is highly dependent on the combined hash rates of computational power connected to the network. The more miners there are, the more hash rates there will be and the more difficult will be the cryptocurrency mining. As Bitcoin and Ethereum prices took off during the past decades, more and more computational power is connected to the network. The hash rates and price histories(lag=1Day) of Bitcoin and Ethereum are shown in Figure.1, and Figure.2:
From these two figures, we can clearly see some relationship patterns between the hash rates and their corresponding prices: both have a clear increasing trend, and in June 2021 the hash rates and prices both tumbled due to China’s crypto-crackdown. The objective of this article is to find out which one is the driving force between the two, and see what information may imply from this relationship.
3. Granger causality test
3.1 Introduction of Granger causality test
To analyze the causality between the hash rates and their corresponding prices, we try to use the Granger causality[Granger, C. W. J. (1969)] test to test our hypothesis. Prof. Clive W.J. Granger, recipient of the 2003 Nobel Prize in economics developed the concept of causality to improve the performance of forecasting. The Granger causality test is a statistical hypothesis test for determining whether one-time series is useful in forecasting another. The mathematical foundation of the test can be summarized as follows:
Consider two variables Xₜ and Yₜ, if the forecast Xₜ is based on the past value of Xₜ and Yₜ:
The formula is very straightforward, the current value of Xₜ is a combination of past Xₜ values and Yₜ values (𝑝 is the number of lags), plus a constant value α.
Then the Granger causality test is given as: Null hypothesis (H₀):Yₜ does not “Granger cause” Xₜ₊₁, i,e α₁+α₂+αₚ=0.
Alternate Hypothesis (Hₐ): Yₜ does “Granger cause” Xₜ₊₁, i.e at least one α₁ is significant.
The p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct. The p-value serves as an alternative to rejection points to provide the smallest level of significance (0.05, for example) at which the null hypothesis would be rejected. A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.
3.2 Granger causality test between prices and hash rates
Because the Granger test is only valid for stationary time series, we need firstly convert both hash rates and price series of BTC and ETH into stationary series(no trend and seasonal effects). This can be done by simply differentiating the original time series. In Figure.3.1 and Figure.3.2, after 1 order differentiating, the original time series and differentiated series of BTC and ETC prices and corresponding hash rates are shown.
Next, we use the Granger causality hypothesis test to test their dependency. First, we test whether the price Granger causes the hash rates: Null hypothesis(H₀):price does not Granger cause hashrate
Alternate Hypothesis(Hₐ): price does Granger cause hashrate
We use the symbol “>>” to denote “Granger cause”,
The test results at maximum 7 lags (1 week) is shown in Table.3.1 and Table.3.2.
We can see the BTC results from Table.3.1, after 5 lags, the p-value is smaller than the significance value 0.05, we can then reject the null hypothesis and accept the alternate hypothesis that the price DOES granger cause hash rate after 5 days. For ETH results from Table.3.2, we can see similar results, but the lag is shorter, which is about 3 days. The reason for this lag may be explained by the fact that the miners are reacting slower than price change, around 3 days for ETH and 5 days for BTC to adjust their mining strategies. Next, we try to test the inverse relationship, and see whether the hash rates influence the prices. And accordingly, the Granger causality test then becomes:
Null hypothesis(H₀):hashrate does not Granger cause price.
Alternate Hypothesis(Hₐ): hashrate does Granger cause price.
The BTC and ETH results are shown in Table.3.3 and Tabe.3.4 respectively:
We can see from Table.3.3, for BTC, the p-value is always bigger than the significance value 0.05, we have no reason to reject the null hypothesis. So we can not say that the hashrate Granger causes the price. For ETH, it’s more complex, after 6 days, the p-value is also smaller than 0.05, meaning that we can reject the null hoposis, and suggest that the hash rates Granger cause price. But still, from Table.3.2, the p-value is much smaller than the corresponding p-value of Table.3.4, and the lag is shorter(3 days compared to 6 days), we conclude that the price change happens earlier than the hash rates change.
3.4 Discussion of Granger causality test
From the definition of Granger causality from formula(1), we can clearly see the limitations of the Granger causality test, which may give erroneous results and misleading conclusions. First, the Granger causality test only counts for linear relationships. For our case, we are not certain whether the hashrate influences the price in a non-linear way.
Second, the Granger causality test only tests the relationship between two variables. For our problem, there obviously exist multiple sources that can have an influence on crypto prices, or total connected hash rates.
Regardless of the limitations, our test still finds interesting results. The cost of production of bitcoin does not truly reflect the prices of BTC or ETH, or at least not linearly. The Granger causality test results suggest that the miners often adjust their mining strategy according to the crypto prices, with a delay of 4–6 days.
4.Conclusion.
In this article, we discussed the connection between hash rates and prices of Bitcoin and Ethereum, from our analysis, we see the prices can Granger cause the hash rates but not vice versa. The prices of these two cryptos are not decided by the mining cost but by other factors. From the analysis, miners should also pay close attention to the price changes of crypto markets and adjust their mining strategy accordingly.
Hileman, G., Rauchs, M., 2017. Global cryptocurrency benchmarking study (April 6, 2017). Available at SSRN: https://ssrn.com/abstract=2965436.
Granger, C. W. J. (1969). “Investigating Causal Relations by Econometric Models and Cross-spectral Methods”. Econometrica. 37 (3): 424–438. doi:10.2307/1
