Source-linked AI summary
The digital traces of bubbles: feedback cycles between socio-economic signals in the Bitcoin economy
David Garcia, Claudio Juan Tessone, Pavlin Mavrodiev, Nicolas Perony
TL;DR
The paper examines how social interactions contribute to Bitcoin price bubbles, using digital traces to quantify price, online word of mouth, information search, and user adoption. A vector autoregression identifies two positive feedback loops involving word of mouth and new adopters, while search spikes precede sharp price declines.
Problem
The paper asks how social interactions contribute to Bitcoin price bubbles and how collective behavioural traces can capture links between social signals and price.
Method
The study quantifies Bitcoin price, online word of mouth, information search, and user adoption, then analyzes their temporal relations with vector autoregression.
Results
The analysis identifies two positive feedback loops—one involving search volume, word of mouth, and price, and another involving search volume, new users, and price—and finds that search spikes precede sharp price declines.
Takeaways & Limitations
The combined digital traces provide an analytical picture of interdependence among Bitcoin’s user base, information search, information sharing, and price.
Takeaways & Limitations
The two feedback cycles are rooted in the final study period, so their appearance may be recent or may reflect the larger quantity of data and higher signal-to-noise ratio there.
Abstract
from arXiv · showhide
What is the role of social interactions in the creation of price bubbles? Answering this question requires obtaining collective behavioural traces generated by the activity of a large number of actors. Digital currencies offer a unique possibility to measure socio-economic signals from such digital traces. Here, we focus on Bitcoin, the most popular cryptocurrency. Bitcoin has experienced periods of rapid increase in exchange rates (price) followed by sharp decline; we hypothesise that these fluctuations are largely driven by the interplay between different social phenomena. We thus quantify four socio-economic signals about Bitcoin from large data sets: price on on-line exchanges, volume of word-of-mouth communication in on-line social media, volume of information search, and user base growth. By using vector autoregression, we identify two positive feedback loops that lead to price bubbles in the absence of exogenous stimuli: one driven by word of mouth, and the other by new Bitcoin adopters. We also observe that spikes in information search, presumably linked to external events, precede drastic price declines. Understanding the interplay between the socio-economic signals we measured can lead to applications beyond cryptocurrencies to other phenomena which leave digital footprints, such as on-line social network usage.
1 Introduction
The paper asks how social interactions shape Bitcoin’s volatile price dynamics and uses digital traces to examine links among price, attention, communication, and user adoption. It frames Bitcoin growth as an interdependent socio-economic process involving social feedback and user-driven adoption.
- Motivation: Bitcoin’s market value rose from about USD $277K in July 2010 to over USD $14B in December 2013, a fifty-thousand-fold increase.Over the same period, Bitcoin-related Google searches grew by over 10’000%.
- Research question: The paper investigates whether online actions and interactions leave digital traces that capture links between market dynamics and public interest.It focuses on the relationship between Bitcoin exchange rates and social aspects of the economy.
- Signals: The analysis combines four socio-economic signals: exchange prices, social-media word of mouth, information search, and Bitcoin user adoption.The data set includes exchange records, social-media activity, search trends, and user-adoption records.
- Signals: User adoption is approximated using new users inferred from the Bitcoin block chain and downloads of the Bitcoin software client.The block chain provides a public transaction record, while SourceForge downloads provide a second proxy.
- Conceptual framework: The framework links rising prices to collective attention and then to word of mouth or user growth, while high search volumes precede selling and lower prices.Figure 1 presents these relationships as feedback loops among the measured variables.
- Signals: Bitcoin-related communication is measured using daily Bitcoin tweets per million messages in the Twitter feed.The measure captures online word-of-mouth communication rather than private information search.
2 Materials and Methods
The study constructs daily Bitcoin indicators from blockchain, software-download, exchange, search, and online communication data. It estimates temporal relationships among the signals with a stationary first-difference vector autoregression and an energy-based lower-bound estimate of fundamental value.
- Data sources: The study combines blockchain, SourceForge, Google Trends, Wikipedia, Twitter, Facebook, and exchange-market data to construct its empirical signals.The sources cover user adoption, information search, word of mouth, and trading prices.
- Information search: Search interest is measured from normalized daily Google Trends volumes for “bitcoin” and cross-validated with daily English Wikipedia page views.Google queries combine whole-period weekly data with rolling two-month daily data.
- Information sharing: Word-of-mouth activity is measured as the daily number of Bitcoin-related tweets divided by the total number of tweets, with additional Facebook reshare data collected.Bitcoin-related tweets contain terms such as “BTC”, “#BTC”, “bitcoin”, or “#bitcoin”.
- User reconstruction: Bitcoin user numbers are approximated from daily software-client downloads and blockchain transaction analysis using key aggregation and change-identification heuristics.The blockchain procedure maps sets of public keys approximately to unique users.
- Time-series preparation: Stationarity tests show that Ut, Pt, St, and Wt are integrated of order 1, so the analysis uses differentiated time series ∆x(t) = x(t) − x(t −1).The differences are stationary while the level series cannot be assumed stationary.
- Statistical analysis: A lag-1 vector autoregression with linear and seasonal trends estimates time-dependent relations among daily changes and supports impulse-response analysis.Low p-values test whether one variable’s changes have a linear relation to another variable’s changes on the previous day.
- Fundamental value: The fundamental-value lower bound is estimated from mining energy costs using hashes per bitcoin, an efficiency of 0.5W per MHash/s, and electricity costs of $0.15/KWh.The estimate is expressed in $/BTC and is intended as a production-cost lower bound.
3 Results
A one-day-lag vector autoregression identifies two positive feedback cycles involving price, social communication, search, and user adoption, alongside a negative search-to-price relation. Impulse-response analysis supports these relationships, robustness checks reproduce them across alternative signals and markets, and the model is used to examine Bitcoin bubbles and price dynamics.
- Feedback loops: The one-day-lag VAR models daily changes in price, search, user adoption, and word of mouth as linear combinations of the preceding day’s changes.The model also includes deterministic, periodic, and error terms.
- Feedback loops: The social cycle runs from price to search (φP,S = 0.386), search to word of mouth (φS,W = 0.243), and word of mouth to price (φW,P = 0.1).These positive links form a reinforcing cycle among price, information search, and communication.
- Feedback loops: Search has a negative relation with price (φS,P = −0.233); 3 of the 4 largest daily price drops followed one of the 1st, 4th, or 8th largest search increases.The cited extremes refer to Google search volume increases on the preceding day.
- Robustness: The feedback cycles and negative search effect persist when replacing client downloads, Google searches, and tweets with network users, Wikipedia views, and Facebook reshares, and when using other currency pairs and exchanges.These alternatives provide robustness checks for the reported relationships.
- Impulse-response analysis: Impulse responses show significant propagation across the feedback cycles: search rises two to four days after price shocks, while word of mouth and users rise one to two days after search shocks.Price also increases after user-adoption and word-of-mouth shocks, while search negatively influences price.
- Reproducing price and social dynamics: The study identifies two price–fundamental-value crossing events, around October 18th, 2011 and November 28th, 2012, that delimit characteristic analysis periods.The price remained almost always above the estimated energy-cost-based fundamental value during the study period.
- Model assessment: A four-day VAR lag has the optimal explanatory power under the Schwarz criterion, although it is less straightforward to interpret than the one-day-lag model.The extended model combines changes in all variables from up to four days earlier.
4 Discussion
The discussion interprets Bitcoin’s growth and price dynamics through interactions among users, social activity, information search, and price. It identifies feedback cycles as explanations for sustained increases while treating crashes as involving external stimuli and noting limits to the cycles’ temporal scope.
- The study combines user base, information search, information sharing, and price to analyse Bitcoin’s coupled socio-economic dynamics.The approach integrates social, economic, and technological signals from digital traces over the period from mid-2010 through 2013.
- Two positive feedback loops link search volume, word of mouth, new users, and price, with the cycles rooted in the final study period.Their late emergence may reflect a recent phenomenon or the greater signal-to-noise ratio provided by more data in that period.
- The analysis was reproduced across USD, EUR, and CNY markets and remained robust across alternative sources for search, word of mouth, and user adoption.Processed blockchain-based user identification contained price-change information that raw Bitcoin addresses did not.
- The validated VAR fit significantly matched empirical levels, normally distributed residuals, qualitative dynamics, and the signs of the largest price variations.The model also produced estimates of future variable levels from the system’s past history.
- The feedback loops imply sustained price increases and help explain successive growth periods, but they do not explain sudden crashes.The discussion attributes crashes to external stimuli such as the June 2011 attack on Mt. Gox.
- Bitcoin’s growing technological, social, and economic importance motivates consideration of policies regulating its usage and exchange.By December 2013, the mining network’s computational power was reported as roughly 300 times that of the top 500 supercomputers combined.
S1 Electronic Supplementary Material
The supplementary material documents procedures for reconstructing daily search data and identifying users from the Bitcoin blockchain. It also reports simulation-based validation of the search reconstruction method and details the relevant data sources and assumptions.
- Reconstructing Google search time series: Google Trends supplies weekly normalized search volumes for the full period but daily volumes only for intervals up to three months.The reconstruction therefore combines whole-period weekly data with rolling two-month daily queries.
- Reconstructing Google search time series: The reconstruction rescales intra-week daily volumes and adds them to weekly volumes to approximate a complete daily search series.The procedure uses one whole-period weekly query followed by rolling-window daily queries.
- Validating the reconstruction: The method was tested on simulated Brownian-motion, white-noise, and pink-noise series by comparing original and reconstructed time series.The Brownian-motion example is shown as black simulated points and red reconstructed lines, with a scatter plot of daily values.
- Validating the reconstruction: The reconstruction loses less than 0.2% of variance for Brownian motion and less than 0.05% for additional white- and pink-noise tests.
- Reconstructing Bitcoin users: Blockchain-based user identification uses transaction inputs and change-address patterns, while assuming that multiple input addresses generally belong to one user.The supplementary method treats input addresses as controlled by the same private-key holder and identifies likely change addresses from output reuse patterns.
S2 Time series stationarity
Table S1 reports stationarity tests for each study variable and for its first difference. It is intended to document whether differencing changes the time-series properties used in the analysis.
- Table S1 reports stationarity-test results for each variable X.
- The table also reports stationarity-test results for each variable’s first difference, ∆X.
- The table compares the original series with their first-differenced forms for time-series analysis.
S3 Lagged correlation analysis
Lagged correlations reveal temporal ordering among price, searches, downloads, and word of mouth, while motivating vector autoregression for dependency analysis.
- Lagged relationships: Price changes lead search-volume changes, peaking at a one-day lag, while increased searches precede subsequent price decreases.The search-to-price decline occurs after a few days.
- Lagged relationships: Price increases precede increases in client downloads by 1–2 days.
- Lagged relationships: Search volume precedes tweet-ratio changes by one day, indicating that information search comes before information sharing.
- Method: The analysis uses lagged Pearson cross-correlations across all pairs of the four variables, with 95% confidence intervals and permutation-based reference intervals.
- Analytical limitation: Faint correlations between downloads and word of mouth, and between word of mouth and price, do not establish dependencies.These results motivate the vector autoregression analysis.
S4 VAR Results without normalisation
The supplementary material reports vector autoregression results for price on Mt. Gox, tweet ratio, Google search volume, and client downloads without renormalisation.
- VAR specification: Table S2 reports vector autoregression results without renormalisation.
- Variables: The VAR uses Mt. Gox price as P_t, tweet ratio as W_t, Google search volume as S_t, and client downloads as U_t.
- Supplementary analysis: The material presents these results as supplementary analysis of the Bitcoin bubble study.
S5 VAR results with variable replacements
The supplementary analysis examines VAR results using alternative metrics for the socio-economic variables while retaining the study’s core signal framework.
- Variable definitions: The VAR specification represents price as P_t, tweet ratio as W_t, Google search volume as S_t, and a user measure as U_t.
- Analytical scope: The supplementary material uses the VAR framework to examine the relationship among price, word-of-mouth activity, search volume, and user activity.
- Alternative metrics: Table S3 reports vector autoregression results with alternative metrics for U, W, and S.
S6 VAR results for other markets and currencies
Supplementary VAR analyses extend the model across user measures, exchange markets, currencies, time periods, lag selection, prediction, and residual diagnostics.
- Variable replacements: The supplementary material reports VAR specifications using client downloads as the user measure alongside BTC-de price, tweet ratio, and Google search volume.
- Markets and currencies: Table S4 reports VAR results using alternative exchange markets and currencies to measure price.
- Time periods: Table S5 compares VAR results for identified blockchain users across the periods covering the second and third bubbles.
- Lag selection: The Schwarz Bayesian information criterion selects a four-day VAR lag as its minimum among lags from 1 to 30 days.
- Prediction: The VAR correctly estimates the sign of all top 10 price increases and 9 of the top 10 price decreases.
- Diagnostics: Studentised residuals resemble normal distributions, but Shapiro–Wilk tests reject normality and indicate possible improvement for outliers.
S7 Detailed results of impulse response functions
Table S7 reports response function estimates for lags 1 and 2, evaluated at specified confidence levels.
- Response function estimates are reported for lag 1.
- Response function estimates are also reported for lag 2.
- The table uses a 97.5% confidence level, with 95% after Bonferroni correction.