Data sources
The data in this study was taken from several sources deemed to guarantee accuracy and completeness. Table 1 provides a structured summary of the main sources of data used in this study.
Methods used
This study applies robust econometric models to understand the dynamics of bitcoin prices and its interaction with regulatory factors and technological progress. More specifically, Huber’s regression model is used to examine the relationship between the price and the quantity of bitcoin requested. We used a Python program to calculate the PED model from the Sklearn.Linear model. The mathematical expression of the calculation of the PED is as follows.
Huber regression model
Huber’s regression modifies the standard regression of ordinary least squares (OLS) by introducing a robust loss function which limits the impact of aberrant values. This approach is particularly suitable for the analysis of Bitcoin demand, because the markets of cryptocurrencies have high volatility and irregular negotiation models. Unlike OLS, which presupposes normally distributed residues and is very sensitive to extreme values, the regression of Huber minimizes the impact of aberrant values by applying a quadratic loss for small residues and a linear loss for large residues. This guarantees more precise and stable estimates of the elasticity of demand prices (PED) (Feng and WU, 2021).
Robustness is crucial in this context because aberrant values, often caused by sudden market anomalies or economic events, can distort traditional OLS results. By reducing sensitivity to these extreme values, Huber’s regression provides reliable PED estimates that reflect underlying market trends. Huber’s regression minimizes the following objective function:
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Or: β= (β0, β1) are the parameters of the model (interception and slope, respectively). ri= Yi- (β0 + β1XI) is the residue of observationI. Lnge (ri) is the Huber loss function, defined as:
$$ {l} _ {\ delta} \ left ({r} _ {i} \ right) = \ left \ {\ begin} {l} \ frac {1} {2} {r} _ {i} ^ {2} \ qquad \ qquad {\ text {if}} \ left | {r} _ _ {i} \ \ lip \ delta \ cdot \ left | {R} _ {i} \ Right | – \ FRAC {1} {2} {\ delta} ^ {2} \ Quad {\ text {if}} \ left | {R} _ {i} \ Right | \,> \, \ Delta. \ End {Array} \ Right. $$.
For small residues \ ((| {ri} | \ le \ delta |) \)The loss function is quadratic, which makes it behave like OLS. For big residues \ ((| {ri} |> \ delta) \)The loss function becomes linear, reducing the influence of aberrant values.
The parameterΔDetermines the threshold to which the loss function passes from quadratic to linear, balancing sensitivity to inliers and robustness against aberrant values.
Relationship with the elasticity of demand prices (PED)
In the context of the elasticity of demand prices (PED) for Bitcoin trading volumes, the regression model connects the trading volume transformed by log ( Y) at the price transformed into a newspaper ( X):
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Or: \ ({Yi} \): Bitcoin volume exchanged (dependent variable). XI: Bitcoin price (independent variable). \ (\ beta 1 \): The slope coefficient, representing elasticity. \ (\ Epsilon i \): The residual term.
Log-log transformation of logarithm \ (\ beta 1 \) directly interpretable as the demand for demand:
$$ {Ped} = \ Beta 1 = \ Frac {\ Partial \ Log (Y)} {\ Partial \ Log (x)} = \ Frac {\% \ Delta y} {\% \ Delta x} $$
Calculation of the PED using Huber regression
To calculate PED, the following steps are carried out:
$$ {l} _ {\ delta} \ left ({\ beta} _ {0}, {\ beta} _ {1} \ right) = \, {\ rm {arg}}} \, \ mathop {\ min}} _ _ {{\ beta} {\ beta} _ {1}} \ mathop {\ sum} \ limits_ {i = 1} ^ {n} {l} _ {\ delta} \ left (\ log \ left ({y} _ _ {i} \ right) – \ left ({\ beta} beta {{_ \ left ({x} _ {i} \ right) \ right) \ right) $$
This minimizes the robust loss function Lngeensure a reduction in sensitivity to aberrant values \ ({log} ({yi}) \) Or \ ({log} ({XI}). \)
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Estimate the coefficients: The adjusted model provides estimates for β0 (interception) and β1 (slope). Here, β 1 directly represents the pedestal.
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Robustness and interpretation
Robustness to aberrant values: By minimizing Huber’s loss function, the model guarantees that extreme values in the volume or negotiation price do not disproportionately affect the estimate of elasticity.
Ped interpretation: The estimated β 1:
If \ (| \ beta 1 | \, <\, 1 \)The demand is inelastic.
If \ (| \ beta 1 | \, <\, 1, \) The demand is elastic.
If \ (| \ beta 1 | \, <\, 1, \) The demand is unit elastic.
Correlation analysis
Spearman’s correlation of rank is used to explore relations between regulatory executives, adoption rankings, technological progress and PED. Sir Francis Galton developed the concept of correlation at the end of the 19th century. This statistical method highlights the way in which socio-economic and regulatory factors intervene to shape the adoption and demand for Bitcoin, highlighting the broader implications for financial systems and economic policy (Aslanidis et al., 2018). The mathematical expression used for correlation purposes is as follows:
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Or: ρis the Spearman’s row correlation coefficient.dI is the difference between the ranks of each pair of corresponding values.nis the number of observations.
Variables and quantification
The selected variables have been quantified on the basis of standardized criteria to facilitate statistical analysis:
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Regulatory executives::
This variable was noted according to the legality, taxation, anti-money laundering measures (LMA) and consumer protection. Higher scores indicate greater regulatory maturity, the scale ranging from 0 to 5. For example: legality: fully regulated = 5, weakly regulated = 3, no frame = 0. Compliance AML: Strong measurements = 5, minimum conformity = 2, none = 0.
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Technological preparation::
Measured by metrics such as internet penetration, the adoption of fintech and the blockchain infrastructure. These indicators assess the technological capacity of a country to support digital currencies.
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Crypto-money adoption::
Classified by the percentage of the population using or actively holding cryptocurrencies. This variable reflects public and institutional acceptance of digital currencies.
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Consumer protection::
Assesses the safeguarding policies of fraud, theft and cyber attacks. Strong consumer protection policies promote confidence and encourage adoption.
Rating system
The qualitative attributes for each country have been converted into digital scores using a standardized scale (for example, 0–5 for regulatory maturity), guaranteeing consistency and comparability in different regions.
Hypothesis
The existing literature corpus has largely explored the correlation between cryptocurrencies and traditional and conventional assets such as gold, inflation, GDP, crude oil and exchange rates (Bouri et al., 2017; Ghorbel and Jeribi 2021). However, there is a notable gap in research that examines the relationship between cryptocurrencies, regulatory frameworks and technological progress. This study aims to fill this gap by formulating hypotheses that explore these under-determinated areas.
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Regulatory executives
Although direct studies connecting cryptocurrencies and regulatory managers are rare, the broader financial literature provides substantial evidence of the impact of market behavior regulations. (Auer et al., 2022) demonstrate that regulatory environments considerably influence the financial stability and the confidence of investors. By drawing this, it is supposed that:
H1: Regulatory executives considerably influence the rate of adoption of cryptocurrencies.
This hypothesis is based on the expectation that clear and favorable regulatory policies can promote an environment conducive to the adoption of cryptocurrency, while strict or ambiguous regulations can hinder it.
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Technological progress
Likewise, the role of technological infrastructure in the adoption of financial innovations has been highlighted by various studies, but not specifically in the context of cryptocurrencies. The theory of the dissemination of innovation (Bharadwaj and Deka, 2021) suggests that technological preparation is a crucial factor in the adoption of new technologies. Based on this theoretical framework, we hypothesize that:
H1: Technological advancement is correlated with the elasticity of cryptocurrency demand prices.
This hypothesis stems from the understanding that advanced technological infrastructure facilitates the access and use of easier cryptocurrencies, which could influence the reactivity of consumers to price changes.
By integrating information from the general literature of financial and technological adoption, this study seeks to provide empirical evidence on the influence of regulatory and technological factors on the markets of cryptocurrencies, thus filling an important gap in current research.
