# Does the Hashrate Affect the Bitcoin Price?

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Materials and Methods

- We test each variable for unit roots allowing for a structural break.
- If the null of a unit root is rejected and a significant break is found, the sample is divided into two subperiods, and we test for cointegration between the market price and the cost-of-production price, or between the market price and the hashrate, in all sub-samples. Depending on the test result, either a bivariate cointegrated model or a bivariate vector-autoregression (VAR) model with variables in the first differences is estimated.
- We test for Granger causality using the approach by Toda and Yamamoto (1995), which is consistent even if the processes may be integrated or cointegrated of arbitrary order. More specifically, this approach requires the determination of the optimal VAR lag length k for the variables in levels using information criteria, and then to estimate a ($k+{d}_{max}$)th-order VAR where ${d}_{max}$ is the maximum order of integration for our group of time-series. Toda and Yamamoto (1995) show that we can test linear or nonlinear restrictions on the first k coefficient matrices using standard asymptotic theory, while the coefficient matrices of the last $k+{d}_{max}$ lagged vectors must be ignored. This Granger-causality test is performed in all subsamples.

#### 3.1. An Exponential Smoothing Approach to Model the Dynamics of the Bitcoin Network Energy Efficiency

- This type of smoothing naturally trails the data and it can model the gradual replacement of old equipment with the new one. Changing the coefficients of the smoothing function impacts the length of such lag.
- It accounts for a trend that is present in the data.
- The energy efficiency of future ASICs cannot be used to infer today’s performance, so any smoothing function referring to future values cannot be used.

#### 3.2. The Cost-of-Production Model and Electricity Prices

#### 3.3. The Cost-of-Production Model and the Bitcoin Reward Halving

## 4. Results

#### 4.1. Data

#### 4.2. Bivariate Analysis

#### 4.3. Multivariate Analysis

## 5. Robustness Checks

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. A Brief Overview of Bitcoin’s Operation

## Appendix B. Model Estimates

#### Appendix B.1. Bivariate Analysis

**Table A1.**VAR(0) for the Log-returns of the pair: Log(Bitcoin price), Log(CPM model 1). First sample: 01/08/2016–04/12/2017.

Variables | DLog(Bitcoin Price) | DLog(CPM_model_1) |
---|---|---|

Constant | 0.046586 | 0.019783 |

−0.01353 | −0.0046 | |

[3.44263] | [4.30423] |

**Table A2.**VAR(0) for the Log-returns of the pair: Log(Bitcoin price), Log(CPM model 2). First sample: 01/08/2016–04/12/2017.

Variables | DLog(Bitcoin Price) | DLog(CPM_model_2) |
---|---|---|

Constant | 0.046586 | 0.021165 |

−0.01353 | −0.00536 | |

[3.44263] | [3.94997] |

**Table A3.**VAR(1) for the Log-returns of the pair: Log(Bitcoin price), Log(Hashrate). First sample: 01/08/2016–04/12/2017.

Variables | DLog(Bitcoin Price) | DLog(Hashrate) |
---|---|---|

DLog(Bitcoin price(−1)) | 0.011607 | −0.02143 |

−0.13052 | −0.16834 | |

[0.08893] | [−0.12730] | |

DLog(Hashrate(−1)) | −0.08538 | −0.596435 |

−0.07991 | -0.10306 | |

[−1.06849] | [−5.78708] | |

Constant | 0.049622 | 0.047781 |

−0.01481 | −0.0191 | |

[3.35113] | [2.50179] |

**Table A4.**VECM(0) for the variables Log(Bitcoin price) and Log(CPM model 1). Second sample: 11/12/2017–24/02/2020.

Error Correction (EC) Term | ||
---|---|---|

Log(Bitcoin price(−1)) | 1 | |

Log(CPM_model_1(−1)) | −0.663981 | |

−0.21282 | ||

[−3.11985] | ||

Constant | −2.97009 | |

−1.81363 | ||

[−1.63765] | ||

Variables | DLog(Bitcoin price) | DLog(CPM_model_1) |

EC | −0.03118 | 0.044423 |

−0.01726 | −0.00559 | |

[−1.80600] | [7.95227] |

**Table A5.**VECM(2) for the variables Log(Bitcoin price) and Log(CPM model 2). Second sample: 11/12/2017–24/02/2020.

Error Correction (EC) Term | ||
---|---|---|

Log(Bitcoin price(−1)) | 1 | |

Log(CPM_model_2(−1)) | −0.692219 | |

−0.21357 | ||

[−3.24116] | ||

Constant | −2.806945 | |

−1.84646 | ||

[−1.52017] | ||

Variables | D(Log(Bitcoin price)) | D(Log(CPM_model_2)) |

EC | −0.029855 | 0.042844 |

−0.03116 | −0.01095 | |

[−0.95809] | [3.91310] | |

0.098178 | 0.02819 | |

D(Log(Bitcoin price(−1))) | −0.09641 | −0.03388 |

[1.01832] | [0.83217] | |

−0.039484 | 0.045213 | |

D(Log(Bitcoin price(−2))) | −0.09497 | −0.03337 |

[−0.41575] | [1.35492] | |

−0.004661 | 0.171544 | |

D(Log(CPM_model_2(−1))) | −0.24632 | −0.08655 |

[−0.01892] | [1.98206] | |

−0.05507 | 0.274415 | |

D(Log(CPM_model_2(−2))) | −0.23794 | −0.0836 |

[−0.23145] | [3.28235] |

Error Correction (EC) Term | ||
---|---|---|

Log(Bitcoin price(−1)) | 1 | |

Log(Hashrate(−1)) | −0.409183 | |

−0.1125 | ||

[−3.63727] | ||

Constant | −1.256762 | |

−2.00595 | ||

[−0.62652] | ||

Variables | D(Log(Bitcoin price)) | D(Log(Hashrate)) |

EC | −0.049126 | 0.147903 |

−0.02597 | −0.02708 | |

[−1.89180] | [ 5.46226] | |

D(Log(Bitcoin price(−1))) | 0.183584 | −0.050318 |

−0.09211 | −0.09605 | |

[1.99306] | [−0.52390] | |

D(Log(Bitcoin price(−2))) | −0.032037 | 0.157578 |

−0.08781 | −0.09156 | |

[−0.36485] | [1.72106] | |

D(Log(Bitcoin price(−3))) | 0.108266 | 0.04156 |

−0.08754 | −0.09127 | |

[1.23682] | [0.45532] | |

D(Log(Bitcoin price(−4))) | −0.14961 | −0.149548 |

−0.08646 | −0.09016 | |

[−1.73033] | [−1.65877] | |

D(Log(Bitcoin price(−5))) | −0.034145 | 0.077298 |

−0.08735 | −0.09108 | |

[−0.39092] | [0.84871] | |

D(Log(Bitcoin price(−6))) | 0.170596 | 0.072128 |

−0.08667 | −0.09038 | |

[1.96824] | [0.79808] | |

D(Log(Hashrate(−1))) | −0.076181 | −0.736701 |

−0.08894 | −0.09273 | |

[−0.85659] | [−7.94419] | |

D(Log(Hashrate(−2))) | 0.009311 | −0.438379 |

−0.10961 | −0.11429 | |

[0.08495] | [−3.83559] | |

D(Log(Hashrate(−3))) | 0.099676 | −0.273345 |

−0.11133 | −0.11608 | |

[0.89533] | [−2.35471] | |

D(Log(Hashrate(−4))) | 0.105471 | −0.275003 |

−0.11083 | −0.11556 | |

[0.95169] | [−2.37976] | |

D(Log(Hashrate(−5))) | −0.005624 | −0.29404 |

−0.1056 | −0.11011 | |

[−0.05326] | [−2.67035] | |

D(Log(Hashrate(−6))) | 0.171554 | −0.154059 |

−0.08442 | −0.08803 | |

[2.03213] | [−1.75014] |

#### Appendix B.2. Multivariate Analysis

**Table A7.**VECMX(1) for Log(Bitcoin price) and Log(Google), with Log(transaction volume) and Log(Transaction fees) as exogenous variables. First sample: 01/08/2016–04/12/2017. This model turned out to be the same, independently of whether we used the hashrate, or the CPM1, or the CPM2.

Error Correction (EC) Term | ||
---|---|---|

Log(Bitcoin price(−1)) | 1 | |

Log(Google(−1)) | −1.000538 | |

−0.04603 | ||

[−21.7368] | ||

Constant | −5.4321 | |

Variables | D(Log(Bitcoin price)) | D(Log(Google)) |

EC | −0.020082 | 0.604649 |

−0.05422 | −0.12658 | |

[−0.37039] | [4.77691] | |

D(Log(Bitcoin price(−1))) | −0.071363 | 0.143743 |

−0.09649 | −0.22527 | |

[−0.73957] | [0.63810] | |

D(Log(Google(−1))) | −0.012273 | 0.134782 |

−0.04903 | −0.11446 | |

[−0.25031] | [1.17753] | |

Constant | 0.02109 | 0.010608 |

−0.01033 | −0.02413 | |

[2.04073] | [0.43967] | |

D(Log(Transaction fees)) | 0.172323 | 0.040111 |

−0.04195 | −0.09793 | |

[4.10790] | [0.40958] | |

D(Log(Transaction Volume)) | 0.335968 | 0.443305 |

−0.06704 | −0.15652 | |

[5.01110] | [2.83227] |

**Table A8.**VECMX(6) for Log(Bitcoin price), Log(Hashrate) and Log(Transaction fees), with Log(transaction volume), Log(Google), and Log(Transaction fees) as exogenous variables. Second sample: 11/12/2017-24/02/2020.

Error Correction (EC) Term | ||
---|---|---|

Log(Bitcoin price(−1)) | 1 | |

Log(Hashrate(−1)) | −0.442911 | |

−0.12766 | ||

[−3.46936] | ||

Constant | −0.620773 | |

−2.27623 | ||

[−0.27272] | ||

Variables | D(Log(Bitcoin price)) | D(Log(Hashrate)) |

EC | −0.009204 | 0.143938 |

−0.01909 | −0.02662 | |

[−0.48217] | [ 5.40721] | |

D(Log(Bitcoin price(−1))) | 0.105778 | −0.053536 |

−0.07226 | −0.10077 | |

[1.46388] | [−0.53126] | |

Variables | D(Log(Bitcoin price)) | D(Log(Hashrate)) |

D(Log(Bitcoin price(−2))) | 0.032122 | 0.159914 |

−0.06866 | −0.09575 | |

[0.46786] | [ 1.67010] | |

D(Log(Bitcoin price(−3))) | −0.026725 | 0.040566 |

−0.06826 | −0.0952 | |

[−0.39151] | [ 0.42612] | |

D(Log(Bitcoin price(−4))) | −0.04931 | −0.138195 |

−0.06636 | −0.09255 | |

[−0.74303] | [−1.49317] | |

D(Log(Bitcoin price(−5))) | −0.064049 | 0.073961 |

−0.06817 | −0.09507 | |

[−0.93961] | [0.77800] | |

D(Log(Bitcoin price(−6))) | 0.132207 | 0.070274 |

−0.06677 | −0.09312 | |

[ 1.97995] | [0.75465] | |

D(Log(Hashrate(−1))) | −0.119478 | −0.741459 |

−0.06751 | −0.09415 | |

[−1.76969] | [−7.87490] | |

D(Log(Hashrate(−2))) | −0.016763 | −0.442022 |

−0.08292 | −0.11564 | |

[−0.20217] | [−3.82241] | |

D(Log(Hashrate(−3))) | 0.077149 | −0.277793 |

−0.08467 | −0.11808 | |

[0.91118] | [−2.35258] | |

D(Log(Hashrate(−4))) | −0.033626 | −0.285352 |

−0.08528 | −0.11893 | |

[−0.39432] | [−2.39936] | |

D(Log(Hashrate(−5))) | −0.035212 | −0.297643 |

−0.08005 | −0.11164 | |

[−0.43989] | [−2.66622] | |

D(Log(Hashrate(−6))) | 0.075737 | −0.157866 |

−0.06518 | −0.09091 | |

[1.16190] | [−1.73659] | |

DLog(Google) | −0.164882 | 0.015363 |

−0.04637 | −0.06467 | |

[−3.55586] | [0.23757] | |

DLog(Transaction fees) | 0.074418 | 0.004869 |

−0.02798 | −0.03902 | |

[2.65972] | [0.12477] | |

DLog(Transaction Volume) | 0.326196 | 0.020172 |

−0.04868 | −0.06789 | |

[6.70053] | [0.29711] |

**Table A9.**VECMX(2) for Log(Bitcoin price), Log(CPM model 1), and Log(Transaction volume), with Log(transaction fees), Log(Google), and Log(SP500) as exogenous variables. Second sample: 11/12/2017–24/02/2020.

Error Correction (EC) Term | |||
---|---|---|---|

Log(Bitcoin price(−1)) | 1 | ||

Log(CPM_model_1(−1)) | −0.631559 | ||

−0.07653 | |||

[−8.25280] | |||

Log(Transaction Volume(−1)) | −0.767616 | ||

−0.06355 | |||

[−12.0782] | |||

Constant | 12.95172 | ||

−1.78079 | |||

[7.27301] | |||

Variables | D(Log(Bitcoin price)) | D(Log(CPM_model_1)) | D(Log(Transaction Volume)) |

EC | 0.012154 | 0.144569 | 0.024845 |

−0.07358 | −0.02403 | −0.11201 | |

[0.16519] | [6.01564] | [0.22181] | |

D(Log(Bitcoin price(−1))) | −0.033971 | −0.051945 | 0.214159 |

−0.13416 | −0.04382 | −0.20424 | |

[−0.25321] | [−1.18544] | [1.04859] | |

D(Log(Bitcoin price(−2))) | −0.080567 | 0.02964 | −0.16257 |

−0.11971 | −0.0391 | −0.18223 | |

[−0.67304] | [0.75810] | [−0.89212] | |

D(Log(CPM_model_1(−1))) | −0.222182 | −0.052122 | 0.520264 |

−0.25878 | −0.08452 | −0.39394 | |

[−0.85858] | [−0.61668] | [1.32066] | |

D(Log(CPM_model_1(−2))) | −0.175314 | 0.122105 | −0.855809 |

−0.25048 | −0.08181 | −0.38131 | |

[−0.69991] | [1.49252] | [−2.24437] | |

D(Log(Transaction Volume(−1))) | −0.000195 | 0.05502 | −0.342822 |

−0.08185 | −0.02673 | −0.1246 | |

[−0.00238] | [2.05804] | [−2.75130] | |

D(Log(Transaction Volume(−2))) | −0.011235 | 0.028662 | −0.220672 |

−0.07227 | −0.0236 | −0.11002 | |

[−0.15546] | [1.21424] | [−2.00577] | |

DLog(Transaction fees) | 0.170783 | −0.007478 | 0.27153 |

−0.03007 | −0.00982 | −0.04578 | |

[5.67931] | [−0.76138] | [5.93147] | |

DLog(Google) | −0.139925 | 0.013245 | 0.106468 |

−0.05695 | −0.0186 | −0.0867 | |

[−2.45686] | [0.71203] | [1.22800] | |

DLog(SP500) | 0.323125 | 0.287191 | 0.429537 |

−0.38611 | −0.12611 | −0.58779 | |

[0.83686] | [2.27729] | [0.73077] |

**Table A10.**VECMX(2) for Log(Bitcoin price) and Log(CPM model 2), with Log(transaction fees), Log(Google), and Log(Transaction volume) as exogenous variables. Second sample: 11/12/2017–24/02/2020.

Error Correction (EC) Term | ||
---|---|---|

Log(Bitcoin price(−1)) | 1 | |

Log(CPM_model_2(−1)) | −0.788774 | |

−0.22735 | ||

[−3.46937] | ||

Constant | −1.965044 | |

−1.96566 | ||

[−0.99969] | ||

Variables | D(Log(Bitcoin price)) | D(Log(CPM model 2)) |

EC | −0.003327 | 0.04146 |

−0.02119 | −0.01049 | |

[−0.15697] | [3.95174] | |

D(Log(Bitcoin price(−1))) | 0.054894 | 0.029597 |

−0.07037 | −0.03484 | |

[0.78005] | [0.84959] | |

D(Log(Bitcoin price(−2))) | 0.054567 | 0.041797 |

−0.0712 | −0.03525 | |

[0.76640] | [1.18588] | |

D(Log(CPM model 2(−1))) | −0.367229 | 0.173548 |

−0.17893 | −0.08858 | |

[−2.05231] | [1.95926] | |

D(Log(CPM model 2(−2))) | 0.2832 | 0.287279 |

−0.17388 | −0.08608 | |

[1.62872] | [3.33752] | |

D(Log(Google)) | −0.181629 | 0.030859 |

−0.04477 | −0.02216 | |

[−4.05680] | [1.39236] | |

DLog(Transaction fees) | 0.072612 | −0.00575 |

−0.02712 | −0.01342 | |

[2.67784] | [−0.42836] | |

DLog(Transaction Volume) | 0.372787 | 0.000915 |

−0.04758 | −0.02355 | |

[7.83514] | [0.03883] |

#### Appendix B.3. Robustness Checks

**Table A11.**Weak exogeneity tests: variables for which the null hypothesis of weak exogeneity can be rejected after re-testing at the 5% probability level.

First sample: 01/08/2016–04/12/2017 | |||||
---|---|---|---|---|---|

Log(Transaction Fees) | Log(Transaction Volume) | Log(CPM_model_1) | Log(SP500) | Log(GOLD) | Log(Google) |

V | |||||

Log(Transaction Fees) | Log(Transaction Volume) | Log(CPM_model_2) | Log(SP500) | Log(GOLD) | Log(Google) |

V | |||||

Second sample: 11/12/2017–24/02/2020 | |||||

Log(Transaction Fees) | Log(Transaction Volume) | Log(CPM_model_1) | Log(SP500) | Log(GOLD) | Log(Google) |

Log(Transaction Fees) | Log(Transaction Volume) | Log(CPM_model_2) | Log(SP500) | Log(GOLD) | Log(Google) |

**Table A12.**Multivariate Johansen cointegration tests. The null hypothesis is the absence of cointegration. The tests considered either the case of an intercept in the cointegration equa- tion (CE) and a trend in the variables (first sample) or the case of an intercept in the CE only (second sample). (*) The final model turned out to be the same, independently of whether we used the CPM1 or the CPM2.

First Sample: | 01/08/2016–04/12/2017 |
---|---|

Variables | N. of CEs at 5% level |

Log(Bitcoin_price), Log(Google) (*) | 1 |

Second sample: | 11/12/2017–24/02/2020 |

Variables | N. of CEs at 5% level |

Log(Bitcoin_price), Log(CPM_model_1) | 0 |

Log(Bitcoin_price), Log(CPM_model_2) | 0 |

**Table A13.**Misspecification tests on the residuals from the multivariate models. p-values smaller than 5% are reported in bold font. (*) The final model turned out to be the same, independently of whether we used the CPM1 or the CPM2.

First Sample: 01/08/2016–04/12/2017 | ||
---|---|---|

Variables: | Variables: | |

Log(Bitcoin_price), | Log(Bitcoin_price), | |

Log(Google) (*) | Log(Google) (*) | |

Model selected | VECMX(1) | VECMX(1) |

Multivariate LM test (lag 4) | 0.99 | 0.99 |

Multivariate LM test (lag 8) | 0.88 | 0.88 |

Multivariate LM test (lag 12) | 0.45 | 0.45 |

Multivariate White test | 0.10 | 0.10 |

Multivariate Normality test | 0.00 | 0.00 |

BDS (dim = 6) residuals 1st eq. | 0.53 | 0.53 |

BDS (dim = 6) residuals 2nd eq. | 0.37 | 0.37 |

Is bitcoin price weakly exogenous? | Yes (long-run: p value = 0.72) | Yes (long-run: p value = 0.72) |

(short-run: p value = 0.83) | (short-run: p value = 0.83) | |

Second sample: 11/12/2017–24/02/2020 | ||

Variables: | Variables: | |

Log(Bitcoin_price), | Log(Bitcoin_price), | |

Log(CPM_model_1) | Log(CPM_model_2) | |

Model selected | VAR(0) for log-returns | VAR(4) for log-returns |

Multivariate LM test (lag 4) | 0.05 | 0.18 |

Multivariate LM test (lag 8) | 0.29 | 0.17 |

Multivariate LM test (lag 12) | 0.95 | 0.87 |

Multivariate White test | 0.00 | 0.02 |

Multivariate Normality test | 0.01 | 0.09 |

BDS (dim = 6) residuals 1st eq. | 0.00 | 0.00 |

BDS (dim = 6) residuals 2nd eq. | 0.00 | 0.00 |

Is bitcoin price weakly exogenous? | Yes | Yes (short-run: p value = 0.16) |

**Table A14.**Correlation matrices of the log-returns for the bitcoin price, the baseline CPMs with constant electricity, and the CPMs computed with the Nord pool prices.

First Sample: 01/08/2016–04/12/2017 | |||||
---|---|---|---|---|---|

Bitcoin Market | CPM1 (constant | CPM2 (constant | CPM1 (Nord | CPM1 (Nord | |

price | electricity price) | electricity price) | Pool price) | Pool price) | |

Bitcoin Market p. | 1 | ||||

CPM1 (constant e. p.) | 0.09 | 1 | |||

CPM2 (constant e.p.) | 0.16 | 0.89 | 1 | ||

CPM1 (Nord P. p.) | −0.08 | 0.12 | 0.12 | 1 | |

CPM2 (Nord P. p.) | −0.04 | 0.13 | 0.22 | 0.98 | 1 |

Second sample: 11/12/2017–24/02/2020 | |||||

Bitcoin Market | CPM1 (constant | CPM2 (constant | CPM1 (Nord | CPM2 (Nord | |

price | electricity price) | electricity price) | Pool price) | Pool price) | |

Bitcoin Market p. | 1 | ||||

CPM1 (constant e. p.) | −0.13 | 1 | |||

CPM2 (constant e.p.) | −0.12 | 0.89 | 1 | ||

CPM1 (Nord P. p.) | −0.07 | 0.40 | 0.42 | 1 | |

CPM2 (Nord P. p.) | −0.07 | 0.42 | 0.51 | 0.98 | 1 |

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1. | However, we want to remark that in the period examined in this paper, the daily transaction volume was approximately 1–2 million BTCs, while the daily trading volume on the exchanges was up to 5–7 million BTCs. Instead, the total daily supply of new bitcoins was equal to 1800 BTCs, which indicates that the miners’ influence on the bitcoin price may be actually very small. The authors want to thank the anonymous CIO of one of the world’s leading full-service blockchain technology companies for highlighting this issue. |

2. | The VIX Index is an estimate of the 30-day expected volatility of the U.S. stock market, based on real-time, mid-quote prices of SP500 Index call and put option, see http://www.cboe.com/vix for more details. |

3. | The authors want to thank Adam Hayes for providing this information through private communications. |

4. | When buying new ASICs in the market, it usually takes 6-8 months from the release date to the widespread implementation. Instead, if the company employs its miners, then the implementation time is down to 1 month from the release. The authors want to thank again the anonymous CIO of one of the world’s leading full-service blockchain technology companies for providing this information. |

5. | Pagnotta and Buraschi (2018) and Pagnotta (2020) developed two theoretical models to address the determination of bitcoin prices, which involve the bitcoin hashrate, the reward halving, and several other variables. They showed that the effect of the reward halving on the bitcoin price is rather complex, and may be positive or negative, depending on the other market factors. |

6. | All the cryptocurrencies professionals that we contacted for this research work informed us that the effect of the reward halving on the bitcoin price may take up to 9–12 months, from the official moment when the bitcoin reward is halved, up to the moment it is reflected in the market prices. |

7. | The numbers of lags in the final VAR/VEC models were selected using the Akaike information criteria and to make the residuals no more auto-correlated. |

8. | These results are not reported for the sake of space and interest and are available from the authors upon request. |

9. | The Nord Pool is a European power exchange owned by Euronext and the continental Nordic and Baltic countries’ Transmission system operators (TSOs). At the time writing this paper, the Nord Pool operates power trading markets in Norway, Denmark, Sweden, Finland, Estonia, Latvia, Lithuania, Germany, the Netherlands, Belgium, Austria, Luxembourg, France, and the United Kingdom. See www.nordpoolgroup.com and references therein for more details. |

10. | See www.nordpoolgroup.com/trading/Day-ahead-trading/Price-calculation for more details about its calculation. |

11. | The estimated parameters of the final models for both subsamples are not reported here for the sake of interest and space and are available from the authors upon request. |

12. | A one hundred millionth of a bitcoin is the smallest unit of the bitcoin currency and it is called a Satoshi. |

**Figure 1.**Modeling strategy to investigate the nature of the relationship between the bitcoin market price and the hashrate (either directly or through the proxy of production costs).

**Figure 3.**Energy efficiency curves estimated with models 1 and 2 in (4) for the whole Bitcoin network, and the respective ASIC releases. The reported data are measured in Joule/Giga-Hash.

**Figure 4.**A sudden jump can be seen just before August 2016, highlighting the drawback of cost of production model. Logarithmic scale.

**Figure 6.**Cost-of-production model prices: Model 1 and Model 2 from Equation (4).

**Figure 8.**Bitcoin cost-of-production prices computed using both constant electricity prices and Nord Pool prices, together with the bitcoin market price.

Variable | Description | Source |
---|---|---|

Bitcoin price (USD) | Coinmarketcap computes an average price weighted by the trade volume of the exchanges that offer bitcoin trading pairs. | Coinmarketcap.com |

Hashrate | It is measured in tera-hashes per second (one hash is equal to a double SHA-256 computation) | Coinmetrics.io |

Transaction fees (USD) | This is the total amount of money paid by the users for the service of moving their funds. It is computed as the weekly average of the total daily transaction fees in bitcoin multiplied with the weekly average of the bitcoin price. | Coinmetrics.io |

Transaction volume (USD) | This is the total value transacted on the Bitcoin network multiplied with the weekly average of the bitcoin price. | Coinmetrics.io |

Google Trends | Weekly search data for the word “bitcoin” worldwide | trends.google.com |

Gold Price ($/Ounce) | Price in USD per troy ounce as reported by the London Bullion Market Association. Gold is often compared with bitcoin, and the reported similarities include: limited supply, low correlation with stock markets, and its main use as store of value rather than unit of account. | Quandl.com |

SP500 | This index is taken as an indicator of the general public perception of the global markets. We assume public optimism towards investment to play a certain role in the demand for bitcoin. | Yahoo Finance |

**Table 2.**Unit root tests. Null hypothesis: the time series has a unit root. * Significant at the 5% level.

Vogelsang and Perron (1998) | Lee and Strazicich (2003) | |||
---|---|---|---|---|

Variable | t-Statistic | Break Date | t-Statistic | Break Date |

Log(Bitcoin price) | −3.43 | 20/03/2017 | −1.72 | 10/07/2017 |

Log(Hashrate) | −3.46 | 06/11/2017 | −2.05 | 06/11/2017 |

Log(Transaction_fees) | −2.69 | 04/12/2017 | −2.56 | 18/06/2018 |

Log(Transaction_volume) | −3.55 | 17/04/2017 | −2.07 | 24/07/2017 |

Log(Google) | −3.01 | 24/04/2017 | −2.11 | 15/05/2017 |

Log(Gold) | −3.14 | 03/06/2019 | −2.59 | 05/08/2019 |

Log(SP500) | −2.84 | 17/12/2018 | −3.36 | 15/10/2018 |

DLog(Bitcoin price) | −13.45 * | 04/12/2017 | −7.89 * | 27/11/2017 |

DLog(Hashrate) | −25.75 * | 30/07/2018 | −4.32 * | 19/11/2018 |

DLog(Transaction_fees) | −11.68 * | 01/04/2019 | −5.73 * | 27/11/2017 |

DLog(Transaction_volume) | −15.66 * | 04/12/2017 | −7.71 * | 15/01/2018 |

DLog(Google) | −15.18 * | 27/11/2017 | −8.45 * | 06/11/2017 |

DLog(Gold) | −12.61 * | 19/12/2016 | −5.22 * | 16/04/2018 |

DLog(SP500) | −15.20 * | 17/02/2020 | −8.54 * | 03/12/2018 |

**Table 3.**p-values for the Granger causality tests using the Toda and Yamamoto (1995) approach. The tests for the CPM(model 1)-CPM(model 2), CPM(model 1)-Hashrate, and CPM(model 2)-Hashrate pairs were not computed for obvious reasons, given how the CPMs are constructed. p-values smaller than 0.05 are in bold font.

First Sample: 01/08/2016–04/12/2017 | |||||
---|---|---|---|---|---|

Dependent variable (Y) | |||||

Log(Bitcoin Price) | Log(CPM_model_1) | Log(CPM_model_2) | Log(Hashrate) | ||

Log(Bitcoin price) | / | 0.92 | 0.66 | 0.82 | |

Regressor | Log(CPM_model_1) | 0.92 | / | / | / |

(X) | Log(CPM_model_2) | 0.95 | / | / | / |

Log(Hashrate) | 0.52 | / | / | / | |

Second sample: 11/12/2017–24/02/2020 | |||||

Dependent variable (Y) | |||||

Log(Bitcoin Price) | Log(CPM_model_1) | Log(CPM_model_2) | Log(Hashrate) | ||

Log(Bitcoin price) | / | 0.06 | 0.01 | 0.00 | |

Regressor | Log(CPM_model_1) | 0.90 | / | / | / |

(X) | Log(CPM_model_2) | 0.33 | / | / | / |

Log(Hashrate) | 0.10 | / | / | / |

**Table 4.**Bivariate Johansen cointegration tests. The null hypothesis is the absence of cointegration. All the tests considered the case of an intercept in the cointegration equation (CE) only.

Bivariate Variable Pair | 01/08/2016–04/12/2017 | 11/12/2017–24/02/2020 |
---|---|---|

N. of CEs at 5% Level | N. of CEs at 5% Level | |

Log(Bitcoin price), Log(CPM_model_1) | 0 | 1 |

Log(Bitcoin price), Log(CPM_model_2) | 0 | 1 |

Log(Bitcoin price), Log(Hashrate) | 0 | 1 |

**Table 5.**Misspecification tests on the residuals from the bivariate models. p-values smaller than 5% are reported in bold font.

First Sample: 01/08/2016–04/12/2017 | |||
---|---|---|---|

Bivariate variable pair: | Bivariate variable pair: | Bivariate variable pair: | |

Log(Bitcoin price), | Log(Bitcoin price), | Log(Bitcoin price), | |

Log(CPM_model_1) | Log(CPM_model_2) | Log(Hashrate) | |

Model selected | VAR(0) for Log-returns | VAR(0) for Log-returns | VAR(1) for Log-returns |

Multivariate LM test (lag 4) | 0.33 | 0.59 | 0.45 |

Multivariate LM test (lag 8) | 0.87 | 0.85 | 0.26 |

Multivariate LM test (lag 12) | 0.45 | 0.64 | 0.60 |

Multivariate White test | 0.00 | 0.08 | 0.00 |

Multivariate Normality test | 0.00 | 0.00 | 0.58 |

BDS (dim = 6) residuals 1st eq. | 0.16 | 0.16 | 0.47 |

BDS (dim = 6) residuals 2nd eq. | 0.48 | 0.31 | 0.50 |

Is bitcoin price weakly exogenous? | Yes | Yes | Yes (short-run: p value = 0.29) |

Second sample: 11/12/2017–24/02/2020 | |||

Bivariate variable pair: | Bivariate variable pair: | Bivariate variable pair: | |

Log(Bitcoin price), | Log(Bitcoin price), | Log(Bitcoin price), | |

Log(CPM_model_1) | Log(CPM_model_2) | Log(Hashrate) | |

Model selected | VECM(0) | VECM(2) | VECM(6) |

Multivariate LM test (lag 4) | 0.08 | 0.15 | 0.20 |

Multivariate LM test (lag 8) | 0.44 | 0.21 | 0.36 |

Multivariate LM test (lag 12) | 0.64 | 0.54 | 0.91 |

Multivariate White test | 0.00 | 0.00 | 0.07 |

Multivariate Normality test | 0.00 | 0.00 | 0.58 |

BDS (dim = 6) residuals 1st eq. | 0.00 | 0.00 | 0.02 |

BDS (dim = 6) residuals 2nd eq. | 0.02 | 0.85 | 0.88 |

Is bitcoin price weakly exogenous? | Yes (long-run: p value = 0.08) | Yes (long-run: pvalue = 0.37) | Yes (long-run: p value = 0.06) |

(short-run: p value = 0.97) | (short-run: p value = 0.07) |

**Table 6.**Weak exogeneity tests: variables for which the null hypothesis of weak exogeneity can be rejected after re-testing at the 5% probability level.

First Sample: 01/08/2016–04/12/2017 | |||||
---|---|---|---|---|---|

Log(Transaction Fees) | Log(Transaction Volume) | Log(Hashrate) | Log(SP500) | Log(GOLD) | Log(Google) |

V | |||||

Log(Transaction Fees) | Log(Transaction Volume) | Log(CPM_model_1) | Log(SP500) | Log(GOLD) | Log(Google) |

V | |||||

Log(Transaction Fees) | Log(Transaction Volume) | Log(CPM_model_2) | Log(SP500) | Log(GOLD) | Log(Google) |

V | |||||

Second Sample: 11/12/2017–24/02/2020 | |||||

Log(Transaction Fees) | Log(Transaction Volume) | Log(Hashrate) | Log(SP500) | Log(GOLD) | Log(Google) |

V | |||||

Log(Transaction Fees) | Log(Transaction Volume) | Log(CPM_model_1) | Log(SP500) | Log(GOLD) | Log(Google) |

V | V | ||||

Log(Transaction Fees) | Log(Transaction Volume) | Log(CPM_model_2) | Log(SP500) | Log(GOLD) | Log(Google) |

V |

**Table 7.**Multivariate Johansen cointegration tests. The null hypothesis is the absence of cointegration. The tests considered either the case of an intercept in the cointegration equation (CE) and a trend in the variables (first sample) or the case of an intercept in the CE only (second sample). (*) The final model turned out to be the same, independently of whether we used the hashrate, or the CPM1, or the CPM2.

First Sample: | 01/08/2016-04/12/2017 |
---|---|

Variables | N. of CEs at 5% level |

Log(Bitcoin_price), Log(Google) (*) | 1 |

Log(Bitcoin_price), Log(Google) (*) | 1 |

Log(Bitcoin_price), Log(Google) (*) | 1 |

Second sample: | 11/12/2017-24/02/2020 |

Variables | N. of CEs at 5% level |

Log(Bitcoin_price), Log(Hashrate) | 1 |

Log(Bitcoin_price), Log(CPM_model_1), Log(Transaction volume) | 1 |

Log(Bitcoin_price), Log(CPM_model_2) | 1 |

**Table 8.**Misspecification tests on the residuals from the multivariate models. p-values smaller than 5% are reported in bold font. (*) The final model turned out to be the same, independently of whether we used the hashrate, or the CPM1, or the CPM2.

First Sample: 01/08/2016–04/12/2017 | |||
---|---|---|---|

Variables: | Variables: | Variables: | |

Log(Bitcoin_price), | Log(Bitcoin_price), | Log(Bitcoin_price), | |

Log(Google) | Log(Google) | Log(Google) | |

(*) | (*) | (*) | |

Model selected | VECMX(1) | VECMX(1) | VECMX(1) |

Multivariate LM test (lag 4) | 0.99 | 0.99 | 0.99 |

Multivariate LM test (lag 8) | 0.88 | 0.88 | 0.88 |

Multivariate LM test (lag 12) | 0.45 | 0.45 | 0.45 |

Multivariate White test | 0.10 | 0.10 | 0.10 |

Multivariate Normality test | 0.00 | 0.00 | 0.00 |

BDS (dim = 6) residuals 1st eq. | 0.73 | 0.73 | 0.73 |

BDS (dim = 6) residuals 2nd eq. | 0.28 | 0.28 | 0.28 |

Is bitcoin price weakly exogenous? | Yes (long-run: p value = 0.72) | Yes (long-run: p value = 0.72) | Yes (long-run: p value = 0.72) |

(short-run: p value = 0.83) | (short-run: p value = 0.83) | (short-run: p value = 0.83) | |

Second sample: 11/12/2017–24/02/2020 | |||

Variables: | Variables: | Variables: | |

Log(Bitcoin_price), | Log(Bitcoin_price), | Log(Bitcoin_price), | |

Log(Hashrate) | Log(CPM_model_1) | Log(CPM_model_2) | |

Log(Transaction volume) | |||

Model selected | VECMX(6) | VECMX(2) | VECMX(2) |

Multivariate LM test (lag 4) | 0.58 | 0.34 | 0.68 |

Multivariate LM test (lag 8) | 0.21 | 0.59 | 0.18 |

Multivariate LM test (lag 12) | 0.99 | 0.73 | 0.28 |

Multivariate White test | 0.40 | 0.00 | 0.04 |

Multivariate Normality test | 0.93 | 0.03 | 0.00 |

BDS (dim = 6) residuals 1st eq. | 0.01 | 0.05 | 0.03 |

BDS (dim = 6) residuals 2nd eq. | 0.70 | 0.01 | 0.66 |

BDS (dim = 6) residuals 3rd eq. | / | 0.01 | / |

Is bitcoin price weakly exogenous? | Yes (long-run: p value = 0.60) | Yes (long-run: p value = 0.86) | Yes (long-run: p value = 0.88) |

(short-run: p value = 0.09) | (short-run: p value = 0.81) | (short-run: p value = 0.07) |

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Fantazzini, D.; Kolodin, N.
Does the Hashrate Affect the Bitcoin Price? *J. Risk Financial Manag.* **2020**, *13*, 263.
https://doi.org/10.3390/jrfm13110263

**AMA Style**

Fantazzini D, Kolodin N.
Does the Hashrate Affect the Bitcoin Price? *Journal of Risk and Financial Management*. 2020; 13(11):263.
https://doi.org/10.3390/jrfm13110263

**Chicago/Turabian Style**

Fantazzini, Dean, and Nikita Kolodin.
2020. "Does the Hashrate Affect the Bitcoin Price?" *Journal of Risk and Financial Management* 13, no. 11: 263.
https://doi.org/10.3390/jrfm13110263