The economics of BitCoin price formation

Figures & data

Figure 1. BitCoin price development, 2009–2015. Source: Blockchain.

Table 1. Augmented Dickey–Fuller test for unit root.

	Whole period			1st period			2nd period
	None	Constant	Constant & trend	None	Constant	Constant & trend	None	Constant	Constant & trend
Levels
BitCoin price	−1.186	−1.635	−2.142	0.865	0.282	−1.061	−0.813	−2.288	−2.857
number of transactions	2.074	0.631	−2.386	0.348	−0.571	−2.420	1.525	−0.431	−2.117
number of BitCoins	0.660	−1.040	−1.300	0.651	−2.550	1.062	2.292	−2.501	−2.292
days destroyed	−4.009***	−6.309***	−7.599***	−4.355***	−6.194***	−7.607***	−5.853***	−8.685***	−9.157***
Dow Jones	1.906	−0.354	−3.673**	1.442	−0.580	−2.932	1.178	−2.065	−4.569***
Views on Wikipedia	−5.995***	−6.997***	−7.768***	−2.797***	−3.326**	−3.874**	−5.484***	−6.653***	−6.861***
number of addresses	2.227	1.025	−1.518	0.981	−0.084	−2.210	1.233	−1.845	−2.334
oil price	−0.579	−1.428	−1.511	0.189	−2.398	−3.081	−1.086	−0.438	−1.137
exchange rate	−1.425	−1.504	−1.847	−0.680	−2.025	−2.680	−1.529	0.267	−1.886
new posts	−0.409	−1.164	−1.237	0.013	−0.826	−2.110	−0.297	−1.469	−3.266*
new members	−3.660***	−4.626***	−5.775***	−1.760*	−2.481	−2.948	−2.222**	−3.892***	−3.986***
1st differences
BitCoin price	−10.933***	−10.935***	−10.933***	−7.827***	−7.920***	−8.050***	−6.014***	−6.009***	−6.149***
number of transactions	−12.903***	−13.074***	−13.038***	−10.363***	−10.444***	−10.459***	−7.102***	−7.249***	−7.260***
number of BitCoins	−2.986**	−6.139***	−6.172***	−3.387***	−4.550***	−5.777***	−2.215**	−3.672***	−6.571***
days destroyed	−15.899***	−15.895***	−15.892***	−14.840***	−14.835***	−14.831***	−10.313***	−10.304***	−10.296***
Dow Jones	−17.235***	−17.364***	−17.366***	−14.448***	−14.535***	−14.539***	−17.640***	−17.696***	−17.696***
views on Wikipedia	−15.284***	−15.280***	−15.277***	−9.786***	−9.783***	−9.780***	−9.101***	−9.093***	−9.087***
number of addresses	−12.554***	−12.817***	−12.991***	−8.919***	−9.028***	−9.072***	−6.950***	−7.239***	−7.243***
oil price	−45.990***	−45.982***	−46.001***	−37.277***	−37.269***	−37.256***	−18.482***	−18.593***	−18.580***
exchange rate	−43.802***	−43.830***	−43.820***	−37.056***	−37.051***	−37.074***	−16.432***	−16.586***	−16.640***
new posts	−10.611***	−10.624***	−10.635***	−7.398***	−7.451***	−7.475***	−7.330***	−7.325***	−7.770***
new members	−14.397***	−14.393***	−14.391***	−9.605***	−9.605***	−9.603***	−12.113***	−12.103***	−12.101***

Notes: *** Significant at 1% level, ** significant at 5% level, * significant at 10% level. The null hypothesis of this test is that the time series has a unit root.

Table 2. DF-GLS unit-root test.

	Whole period		1st period		2nd period
	Constant	Constant & trend	Constant	Constant & trend	Constant	Constant & trend
Levels
BitCoin price	−1.163	−1.976	0.521	−1.165	−1.173	−1.359
number of transactions	1.763	−1.428	0.436	−1.587	0.337	−2.436
number of BitCoins	1.156	0.452	0.335	0.083	0.912	0.092
days destroyed	−3.143***	−6.810***	−2.847***	−6.194***	−8.415***	−8.672***
Dow Jones	1.142	−2.555*	0.778	−2.530	0.331	−2.703*
views on Wikipedia	−5.691***	−7.699***	−3.248***	−4.373***	−6.398***	−6.585***
number of addresses	2.612	−0.551	0.640	−1.817	0.949	−2.350
oil price	−1.423	−1.374	−1.320	−2.142	0.696	−0.937
exchange rate	0.503	−1.586	−0.749	−1.658	0.981	−0.992
new posts	−0.792	−1.740	−0.382	−2.288	−0.757	−0.650
new members	−3.084***	−5.959***	−1.793*	−2.638*	−2.745***	−3.225**
1st differences
BitCoin price	−11.569***	−11.569***	−14.172***	−13.973***	−3.480***	−5.277***
number of transactions	−9.581***	−9.687***	−10.304***	−10.424***	−6.113***	−8.665***
number of BitCoins	−3.064***	−3.225**	−2.572**	−3.195**	−2.953***	−5.116***
days destroyed	−14.730***	−12.252***	−11.864***	−11.813***	−18.413***	−21.435***
Dow Jones	−7.053***	−8.971***	−5.674***	−5.359***	−3.133***	−5.017***
views on Wikipedia	−16.757***	−18.891***	−10.145***	−15.798***	−13.634***	−17.401***
number of addresses	−10.609***	−11.106***	−11.025***	−13.550***	−9.785***	−12.032***
oil price	−8.569***	−7.163***	−4.341***	−7.241***	−5.522***	−10.125***
exchange rate	−7.331***	−13.795***	−6.758***	−12.333***	−2.682***	−5.142***
new posts	−8.922***	−7.915***	−8.724***	−7.764***	−3.075***	−3.615***
new members	−26.932***	−20.317***	−17.075***	−17.149***	−14.450***	−14.340***

Notes: *** Significant at 1% level, ** significant at 5% level, * significant at 10% level. The null hypothesis of this test is that the time series has a unit root.

Table 3. Zivot–Andrews unit-root test.

	Levels			1st differences
	Break in intercept	Break in trend	Break in both intercept & trend	Break in intercept	Break in trend	Break in both intercept & trend
BitCoin price	−4.156 (3.10.2013)	−2.960 (30.6.2014)	−5.466** (4.11.2013)	−14.771*** (1.12.2013)	−14.250*** (6.10.2013)	−14.807*** (1.12.2013)
number of transactions	−4.131 (22.11.2010)	−4.479** (7.10.2011)	−5.095** (3.5.2012)	−25.237*** (11.3.2013)	−25.188*** (1.6.2014)	−25.283*** (4.12.2013)
number of BitCoins	−2.043 (6.10.2010)	−3.941 (15.5.2011)	−3.931 (9.7.2010)	−10.388*** (29.11.2012)	−9.487*** (23.9.2010)	−10.504*** (29.11.2012)
days destroyed	−14.577*** (12.3.2014)	−14.110*** (22.12.2013)	−14.538*** (13.3.2014)	−26.685*** (11.3.2014)	−26.621*** (23.1.2013)	−26.740*** (11.3.2014)
Dow Jones	−6.000*** (25.7.2011)	−4.921** (19.5.2012)	−6.056*** (25.7.2011)	−18.318*** (4.10.2013)	−18.252*** (27.3.2013)	−18.349*** (17.10.2014)
views on Wikipedia	−12.343*** (8.3.2014)	−12.101*** (10.1.2014)	−12.542*** (26.10.2013)	−26.658*** (13.4.2013)	−26.642*** (30.10.2013)	−26.653*** (13.4.2013)
number of addresses	−4.312 (4.11.2013)	−4.816** (28.11.2012)	−5.603*** (4.11.2013)	−27.967*** (7.3.2014)	−27.921*** (11.10.2013)	−28.007*** (7.3.2014)
oil price	−4.065 (29.7.2014)	−3.463 (28.3.2014)	−3.658 (29.9.2014)	−46.063*** (23.6.2014)	−46.007*** (2.10.2010)	−46.250*** (29.9.2014)
exchange rate	−3.097 (29.7.2014)	−3.444 (6.5.2014)	−3.460 (6.9.2013)	−16.959*** (7.5.2014)	−17.027*** (23.9.2010)	−17.179*** (14.6.2010)
new posts	−2.838 (7.10.2013)	−2.353 (27.5.2014)	5.539** (3.11.2013)	−23.904*** (27.1.2014)	−23.718*** (9.12.2013)	−23.928*** (7.10.2013)
new members	−8.530*** (26.10.2013)	−7.964*** (20.5.2012)	−8.947*** (17.11.2013)	−26.904*** (11.3.2014)	−26.557*** (20.11.2013)	−27.139*** (11.3.2014)

Notes: Date of break in parenthesis, *** significant at 1% level, ** significant at 5% level, * significant at 10% level. The null hypothesis of this test is that the time series has a unit root with a structural break in the intercept/trend/both.

Table 4. Clemente–Montańés–Reyes unit-root test.

	Additive Outlier (AO)		Innovational Outlier (IO)
	Min t*	Optimal breakpoint	Min t**	Optimal breakpoint
BitCoin price	−3.022	1.12.2013	−4.426	12.10.2013
number of transactions	−1.671	23.12.2012	−1.648	2.12.2012
number of BitCoins	−2.215	6.9.2012	−6.962	12.7.2010
days destroyed	−9.231	5.3.2014	−10.888	6.3.2014
Dow Jones	−2.865	23.2.2013	−2.587	29.12.2012
views on Wikipedia	−12.268	1.3.2013	−12.124	10.4.2013
number of addresses	−2.314	2.11.2013	−2.486	3.11.2013
oil price	−3.449	29.11.2014	−3.900	27.9.2014
exchange rate	−3.568	9.1.2015	−3.338	16.8.2014
new posts	−1.729	29.3.2013	−2.749	5.10.2013
new members	0.099	8.3.2014	−8.977	9.3.2014

Notes: ‘Min t’ is the minimum t statistics calculated. * 5% crit. value −3.560 ** −4.270 (5% crit. value). The null hypothesis of this test is that the time series has a unit root.

Table 5. Johansen cointegration test.

Period	Model	Maximum rank	Trace statistics	5% critical value	Maximum rank	Max statistics	5% critical value	Lags	Model
1. Period	M 1.1	1	21.033***	24.31	1	13.953***	17.89	9	No constant
	M 1.2	1	31.152***	34.91	1	19.893***	22.00	10	No constant
	M 1.3	1	5.025***	19.96	1	4.752***	15.67	10	Restricted constant
	M 1.4	0	13.721***	24.31	0	10.301***	17.89	10	No constant
	M 1.5	0	14.858***	24.31	0	11.291***	17.89	10	No constant
	M 2.1	1	0.843***	3.84	1	0.843***	3.84	10	No constant
	M 3.1	0	28.204***	39.89	0	13.635***	23.80	6	No constant
	M 4.1	0	29.451***	39.89	0	14.907***	23.80	8	No constant
	M 4.2	3	45.167***	53.12	3	21.171***	28.14	4	Restricted constant
	M 4.3	4	4.326***	9.42	4	4.326***	9.24	5	Restricted constant
	M 4.4	1	12.434***	19.96	1	9.732***	15.67	9	Restricted constant
	M 4.5	2	1.943***	3.76	2	1.943***	3.76	10	Constant
	M 4.6	1	0.600***	3.84	1	0.600***	3.84	9	No constant
	M 4.7	1	8.135***	12.53	1	7.472***	11.44	10	No constant
	M 4.8	1	9.373***	12.53	1	9.229***	11.44	8	No constant
	M 4.9	1	17.099***	24.31	1	13.811***	17.89	7	No constant
2. Period	M 1.1	2	19.898***	19.96	2	14.391***	15.67	4	Restricted constant
	M 1.2	1	7.408***	12.53	1	5.935***	11.44	4	No constant
	M 1.3	2	9.231***	9.42	2	9.231***	9.24	4	Restricted constant
	M 1.4	0	28.582***	29.68	0	18.658***	20.97	8	Constant
	M 1.5	0	22.768***	24.31	0	17.741***	17.89	10	No constant
	M 2.1	1	0.082***	3.84	1	0.082***	3.84	7	No constant
	M 3.1	0	52.280***	53.12	0	28.022***	28.14	2	Restricted constant
	M 4.1	0	50.417***	53.12	0	25.404***	28.14	5	Restricted constant
	M 4.2	4	13.302***	15.41	5	9.203***	14.07	4	Constant
	M 4.3	4	0.208***	3.84	0	0.208***	3.84	6	No constant
	M 4.4	2	2.524***	9.42	2	2.524***	9.24	7	Restricted constant
	M 4.5	3	10.126***	12.53	3	9.410***	11.44	6	No constant
	M 4.6	1	0.082***	3.84	1	0.082***	3.84	7	No constant
	M 4.7	2	2.524***	9.42	2	2.524***	9.24	7	Restricted constant
	M 4.8	2	0.844***	9.42	2	0.844***	9.24	8	Restricted constant
	M 4.9	2	19.357***	19.96	2	15.209***	15.67	10	Restricted constant

Notes: *** Significant at 1% level, ** significant at 5% level, * significant at 10% level. Maximum rank gives the number of cointegration relationships. VAR in first differences was used when 0 cointegration relationship was detected, ARDL was used to estimate 1 cointegration relationship and VEC models were used to model more than 1 cointegration relationships.

Table 6. Specification of the empirically estimated models.

		Models for hypotheses 1, 2 and 3							General models
		M 1.1	M 1.2	M 1.3	M 1.4	M 1.5	M 2.1	M 3.1	M 4.1	M 4.2	M 4.3	M 4.4	M 4.5	M 4.6	M 4.7	M 4.8	M 4.9
Supply–demand Variables	number of BitCoins	x	x	x						x	x		x
	number of transactions	x				x										x	x
	number of addresses		x		x					x	x	x			x
	days destroyed	x	x	x	x	x				x	x	x	x	x	x	x	x
	exchange rate	x	x	x	x	x		x	x	x
BitCoin attractiveness for investors and users	views on Wikipedia						x		x	x	x	x		x		x
	new members						x			x	x		x	x		x	x
	new posts						x			x	x	x	x	x	x	x	x
Macro-financial developments	Dow Jones							x	x	x	x						x
	oil price							x	x	x

Table 7. Short-run effects on BitCoin price for hypotheses 1, 2 and 3.

	M 1.1	M 1.2	M 1.3	M 1.4	M 1.5	M 2.1	M 3.1
1. Period
BitCoin price	8***	9***	8***	8***	8***	8***	6***
number of BitCoins	-	-	-	-	-	-	-
number of transactions	4**	-	-	-	5***	-	-
number of addresses	-	8**	-	4**	-	-	-
days destroyed	5**	4**	4**	5*	5**	-	-
exchange rate	1*	1*	1*	1*	1**	-	1**
views on Wikipedia	-	-	-	-	-	9***	-
new members	-	-	-	-	-	3***	-
new posts	-	-	-	-	-	4***	-
constant	-	-	-	-	-	-	-
2. Period
BitCoin price	3***	2***	3***	5***	6**	3***	2***
number of BitCoins	-	-	-	-	-	-	-
number of transactions	1*	-	-	-	-	-	-
number of addresses	-	1*	-	1*	-	-	-
days destroyed	1*	1**	1*	1*	1*	-	-
exchange rate	-	-	-	-	-	-	-
views on Wikipedia	-	-	-	-	-	-	-
new members	-	-	-	-	-	-	-
new posts	-	-	-	-	-	1*	-
Dow Jones	-	-	-	-	-	-	-
oil price	-	-	-	-	-	-	-
constant	-	-	-	1*	-	-	-

Notes: The table shows the summary results of short-run estimates reported in detail in the Appendix. Each variable has a maximum of 10 lags. The number is the count of statistically significant lags at least at 10% significance level. The reported significance level is that of the majority statistically significant lags where *** significant at 1% level, ** significant at 5% level, and * significant at 10% level. ‘-’ indicates that the coefficient is not significantly different from zero.

Table 8. Short-run effects on BitCoin price for general models.

	M 4.1	M 4.2	M 4.3	M 4.4	M 4.5	M 4.6	M 4.7	M 4.8	M 4.9
1. Period
BitCoin price	7***	3***	4***	7***	9***	8***	9***	7***	6***
number of BitCoins	-	-	-	-	-	-	-	-	-
number of transactions	-	-	-	-	-	-	-	2**	1**
number of addresses	-	2**	2**	6**	-	-	7***	-	-
days destroyed	-	3***	3*	5**	3*	2*	2**	1**	1***
exchange rate	1*	-	-	-	-	-	-	-	-
views on Wikipedia	6***	3*	4***	8***	-	9***	-	6***	-
new members	-	3***	3***	-	5*	4***	-	4***	3**
new posts	-	2**	-	4**	5*	4***	5**	6***	3*
Dow Jones	-	-	-	-	-	-	-	-	2**
oil price	-	-	-	-	-	-	-	-	-
constant	-	-	-	-	-	-	-	-	-
2. Period
BitCoin price	4**	3***	4***	5***	3***	4***	5***	4***	5***
number of BitCoins	-	1*	-	-	-	-	-	-	-
number of transactions	-	-	-	-	-	-	-	2**	2**
number of addresses	-	-	-	-	-	-	-	-	-
days destroyed	-	1**	2**	1*	2*	2**	-	2*	1*
exchange rate	-	-	-	-	-	-	-	-	-
views on Wikipedia	-	-	-	-	-	-	-	-	-
new members	-	1*	-	-	-	-	-	-	-
new posts	-	2**	4***	1***	3***	1**	1**	3***	3***
Dow Jones	1***	-	-	-	-	-	-	-	1*
oil price	2*	2*	-	-	-	-	-	-	-
constant	-	-	-	-	-	-	-	-	-

Notes: The table shows the summary results of short-run estimates reported in detail in the Appendix. Each variable has a maximum of 10 lags. The number is the count of statistically significant lags at least at 10% significance level. The reported significance level is that of the majority statistically significant lags where *** significant at 1% level, ** significant at 5% level, and * significant at 10% level. ‘-’ indicates that the coefficient is not significantly different from zero.

Table 9. Long-run effects on BitCoin price for hypotheses 1, 2 and 3.

	M 1.1	M 1.2	M 1.3	M 1.4	M 1.5	M 2.1	M 3.1
1. Period
number of BitCoins	−2.7E-06	−4.78E-06	−7.74E-05***	-	-	-	-
number of transactions	0.004**	-	-	-	-	-	-
number of addresses	-	0.003***	-	-	-	-	-
days destroyed	−9.3E-06	−4.14E-06	−9.54E-07	-	-	-	-
exchange rate	12.085	14.367	119.595	-	-	-	-
views on Wikipedia	-	-	-	-	-	−0.002	-
new members	-	-	-	-	-	−0.213	-
new posts	-	-	-	-	-	0.023***	-
Dow Jones	-	-	-	-	-	-	-
oil price	-	-	-	-	-	-	-
trend	-	-	0.693***	-	-	-	-
constant	-	-	-	-	-	-	-
2. Period
number of BitCoins	−0.006***	−0.001***	−0.003***	-	-	-	-
number of transactions	0.150***	-	-	-	-	-	-
number of addresses	-	0.043***	-	-	-	-	-
days destroyed	-	-	-	-	-	-	-
exchange rate	1166.965	1808.853	-	-	-	-	-
views on Wikipedia	-	-	-	-	-	0.002	-
new members	-	-	-	-	-	−0.078	-
new posts	-	-	-	-	-	0.035***	-
Dow Jones	-	-	-	-	-	-	-
oil price	-	-	-	-	-	-	-
constant	7.58E+04***	-	7.59E+04***	-		-	-

Notes: Dependent variable: BitCoin price. *** significant at 1% level, ** significant at 5% level, * significant at 10% level. ‘-’ indicates either absence of a variable in the respective model or the coefficient is not significantly different from zero.

Table 10. Long-run effects on BitCoin price for general models.

	M 4.1	M 4.2	M 4.3	M 4.4	M 4.5	M 4.6	M 4.7	M 4.8	M 4.9
1. Period
number of BitCoins	-	−5.69E-06**	−9.46E-06**	-	−4.42E-06***	-	-	-	-
number of transactions	-	-	-	-	-	-	-	0.001*	0.001***
number of addresses	-	0.002***	0.003***	0.001**	-	-	0.001***	-	-
days destroyed	-	-	-	-	-	1.64E-06	-	−3.11E-06	−5.67E-06
exchange rate	-	101.410	-	-	-	-	-	-	-
views on Wikipedia	-	-	-	-	-	−0.002	-	−0.001	-
new members	-	-	-	-	-	−0.325	-	−0.145	0.038
new posts	-	0.028***	0.031***	0.013***	0.025***	0.028**	0.015***	0.015***	0.009**
Dow Jones	-	0.008	−0.008	-	-	-	-	-	−9.97E-05
oil price	-	0.640	-	-	-	-	-	-	-
constant	-	−175.820**	−107.689	6.271**	-	-	-	-	-
2. Period
number of BitCoins	-	−0.001***	−0.001***	-	−6.22E-05***	-	-	-	-
number of transactions	-	-	-	-	-	-	-	0.013***	0.017**
number of addresses	-	0.029***	0.049***	0.004***	-	-	0.003***	-	-
days destroyed	-	-	-	-	-	1.95E-05	-	-	-
exchange rate	-	1585.792	-	-	-	-	-	-	-
views on Wikipedia	-	-	-	-	-	0.001	-	-	-
new members	-	-	-	-	-	−0.181*	-	-	-
new posts	-	0.036**	0.045**	0.066***	0.017**	0.031***	0.056***	0.090***	0.126***
Dow Jones	-	−0.078	−0.052	-	-	-	-	-	0.206**
oil price	-	-	-	-	-	-	-	-	-
constant	-	-	-	-	-	-	933.247***	1865.3***	632.205***

Notes: Dependent variable: BitCoin price. *** significant at 1% level, ** significant at 5% level, * significant at 10% level. ‘-’ indicates either absence of a variable in the respective model or the coefficient is not significantly different from zero.