A desk should hesitate before trading on Bitcoin's 15,139.8 ESG coefficient. Across six years, the score moves only from 98.01 to 99.48.

The trade the paper imagines

In "Cryptocurrencies in a Sustainable Era", Mhamid and Hajji ask whether environmental innovation and US stock indices move Bitcoin and Ethereum returns. They use 74 months of data. Their flow story is plausible: Bitcoin's proof of work carries a carbon footprint that could deter climate-conscious capital, while greener mining and a better ESG climate could draw it in. Ethereum supplies the contrast. Its 2022 move to proof of stake, which the paper cites as cutting energy use by 99.98%, should matter to that story. Institutional ownership supplies another channel. If funds hold both crypto and US equities, moves in the S&P 500, the Dow and the Nasdaq could reach crypto too.

The authors estimate two static OLS regressions, one per coin, using 74 monthly observations from January 2019 to February 2025. Each has eight regressors dated t and no lags: mining CO2 emissions; an "environmental innovation" series defined as the networks' green energy consumption; an ESG score; the three US indices; gold; and Brent.

CO2 is insignificant for both coins, including Bitcoin at −8.979 (p=0.298). Green energy enters positively for Bitcoin at 64.478 (p=0.069) and is insignificant for Ethereum (p=0.167). Bitcoin's ESG coefficient is +15,139.8 (p=0.000). Gold and oil are positive and significant for both. A Johansen test is reported as confirming cointegration, with χ² of 47.70 for Bitcoin and 26.08 for Ethereum. The paper describes Bitcoin as exhibiting "a strong positive correlation with environmental innovations and ESG scores."

What is the Bitcoin regression measuring?

Start with the units. The paper measures each coin by its monthly closing price in USD, yet Table 1 gives the Bitcoin "return" a mean of 1327.25, a standard deviation of 6947.33 and a range from −20,116.96 to 26,900. These are dollar price changes. Their size rises with the price level, giving high-price months the largest swings and more pull on the fit. Ethereum has the same problem: its series has a mean of 43.27 and runs from −1008.32 to 1269.99.

The regressors raise a further question. The paper says first differencing made every series stationary, while Table 1 gives the S&P 500 a mean of 4101.70, a level. Bitcoin's constant is −1,517,758. Multiply the ESG coefficient by the ESG mean, 15,139.8 × 98.75, and the result is roughly 1,495,000. Such a near-offset is what one would expect if ESG entered in levels and the constant absorbed it. If so, the regression puts price changes against trending levels, a textbook route to a spurious fit. The unit-root table adds a slip: the Dow's no-constant augmented Dickey-Fuller statistic is 1.297 and its Phillips-Perron statistic is 1.773. Both are positive against a −1.950 critical value; both are marked stationary.

Green energy, at the 10% bar

Even taken as estimated, the sustainability result is narrow. Green energy clears only the 10% bar for Bitcoin and fails for Ethereum, whose energy transition supplies the paper's contrast. The ESG score has a standard deviation of 0.26. A one-standard-deviation move therefore maps to about $3,900 of monthly Bitcoin change. The paper names no provider for the score, and its hypotheses describe it both as a U.S. ESG score and as a global one.

The bivariate numbers face the other way. ESG's correlation with Bitcoin is −0.1030; green energy's is −0.0505. The authors say the first contradicts H3 and the second is insufficient to confirm H2. Neither supports the phrase "strong positive correlation".

Ethereum's ESG coefficient is −319.493 at p=0.070, flagged in the results table as a slightly negative effect. The discussion says Ethereum "shows no significant relationship" with these factors, despite the paper's own 10% threshold. And without a dummy for the September 2022 Merge in either regression equation, the proof-of-stake contrast goes untested directly.

An association at p=0.069 across 74 months deserves one more sample. No more than that.

Three indices, nearly one series

The equity coefficients are especially hard to read. The S&P 500 correlates with the Dow at 0.9889 and with the Nasdaq at 0.9764; the Dow and Nasdaq correlate at 0.9500. Even the S&P and gold reach 0.9022. OLS can trade one input against another when they move together this closely. Bitcoin's estimates have the expected instability: S&P −5.778 (p=0.030), Dow +0.583 (p=0.084), Nasdaq −1.075 (p=0.031).

All three signs oppose the paper's hypotheses, which predict positive coefficients for the S&P (H4) and Nasdaq (H6) and a negative one for the Dow (H5). The S&P and Nasdaq also reverse their positive bivariate correlations with Bitcoin, 0.1870 and 0.2174. Oil reverses too, from −0.1184 in the correlation matrix to +179.145 in the Bitcoin OLS regression. The paper offers safe-haven behaviour as a possible explanation for the negative index signs. We did not find a variance-inflation check or a specification using one index rather than three. Without either, the safe-haven reading is the paper's least reliable inference.

The authors say the Ethereum model's high adjusted R² "highlights the relevance of the selected variables". They also say it "should be interpreted with caution, particularly given the risk of overfitting associated with highly volatile financial time series". Volatility is the risk they identify; they do not address the collinearity or levels question raised here. We did not find an R² for either model in the regression table, leaving readers unable to weigh that claim against its caveat. We also did not find an error-correction model to support the abstract's long-run versus short-term framing. The Johansen output gives one χ² per equation, without rank or lag order.

Why we could not rebuild the environmental series

A faithful test requires the paper's three environmental series. Mining CO2 is attributed both to Bloomberg and to estimates in published studies. Green energy is reported "in millions of cubic metres"; the ESG score has no named provider. None of the three is in our data. Substituting a public emissions or ESG proxy would test a different claim from Mhamid and Hajji's.

One result would change our view: rerun the Bitcoin regression on log returns against differenced regressors with a single equity index, then see whether the green-energy coefficient holds at 5%. For now, gold and oil alone are significant at the 0.1% level in both equations (gold p=0.000 in both; oil p=0.001 for Bitcoin, p=0.000 for Ethereum). Those estimates inherit the same levels question. They also have the least to do with the paper's title.