Are NFTs and Emissions Correlated?

By May 29, 2021Polygon
Click here to view original web page at medium.com
Autoglyph NFT, generative on-chain art.

tl;dr: A by-day analysis yields a small if any association between NFTs and variation in Ethereum’s energy usage. Further analysis would be needed to be certain. This may be moot with forthcoming PoS-based solutions. Nevertheless, preliminary results here suggest the special ire directed at NFTs on Ethereum was inconsistent with a weak association with energy consumption.

There has been much heat generated about the carbon footprint of NFTs. This discussion unfolded without a clear idea of how much NFTs actually contribute to the energy expenditure of Ethereum. Thanks to an amazing data dashboard produced by artist and coder Kyle McDonald (inspired by a Nic Carter challenge), we now have a solid estimate of the percentage of network activity associated with NFT transactions. The wonderful dashboard shows the overall percentage of network gas, fees, and transactions across 75 major NFT projects. It’s great:

Screenshot of Kyle’s dashboard.

From Kyle’s plot, we already see that the network impact of NFTs is generally low — below 10%. An obvious major exception is the CryptoKitties congestion in late 2017. Despite this blip, the median percentage of NFT gas usage across this time period is 3%. 95% of these dates have NFT gas usage at less than 7%. Compare this to Uniswap. In early May 2021, Uniswap (v2 + v3) by itself could account for 20% or more of gas usage.

Etherscan’s gas guzzler list on 5/11/21.

This reveals a small network footprint for NFTs, so how do we assign emissions responsibility to them? The typical approach would be to take estimated energy expenditure (or emissions) and simply divide it by number of transactions, or over a transaction’s gas usage. This per-transaction model of energy responsibility and its variants assume that all uses of the Ethereum network are equal. It implies that the ebb and flow of energy expenditure can be equally attributed to all kinds of transactions, across distinct segments of the Ethereum ecosystem.

This brief post summarizes another approach to this issue, motivated by a Nic Carter statistical proposal here. His proposal is meant to go beyond per-transaction estimates of energy responsibility. Nic’s idea is that we should measure how NFT transactions alter energy-related metrics of the Ethereum network as a whole. This suggests an analysis by segment — to reason about energy responsibility by measuring how segments of the market are associated with increased energy consumption.

Consider the cryptoart community, perhaps the primary target of the NFT energy debate. Shortly after ERC-721 was codified in 2017/2018, a collection of artists and other creatives were building a foundation for a new conception of digital art ownership, curation and community. When their works were minted and first sold, the hash rate was far below what it is at the time of this writing — much less than half. But the rapid appreciation of ether, the growing number of exchange platforms and then the onslaught of DeFi (like Uniswap) likely brought the vast majority of rising hash rate. Now the artists who were once operating on a network of more modest expenditure are being assigned responsibility in proportion to every single DeFi transaction. This seems odd, an instance of the classic tragedy of the commons.

Josie’s “Tune In.” See here.

Nic’s idea is that it would be useful to look at correlational (and even better, causal) relationships between NFTs and the main proxy for energy expenditure: hash rate. Responsibility should be assigned in accordance with the underlying relationships between energy expenditure and segments of the Ethereum ecosystem. Artists are minting as usual, and their gas-heavy transactions are being assigned emissions responsibility in precise proportion to other market segments that may actually be doing most of the moving and shaking of hash rate.

This post describes the simplest initial approach to Nic’s proposal. Let’s assess the strength of association between NFT gas usage and hash rate. The results below are, indeed, correlational in nature, but there are proposals for how to conduct a causal analysis on hash rate and other variables. I revisit these subtle statistical issues below. To start, let’s conduct the simplest analysis.

Preliminary findings

Let’s combine Kyle’s great data with measures from the amazing community API at Coin Metrics. Variables that may impact hash rate include overall fees, price appreciation of the mining rewards (USD price of ETH), and percentages associated with NFTs (Kyle’s data: gas, fees, transactions).

We can first calculate the simple correlation between the 7-day moving average of these variables with hash rate. The percentage of activity associated with NFTs bears the weakest relationships with hash rate. The strongest is simply price: about 0.80 correlation between price of ETH and hash rate.

Pearson correlation from late 2017 — early 2021 (7d moving average)

These correlations are not based on log transformed data. This transformation does not alter the general observation that NFT correlations are the lowest, though the raw bivariate correlations do rise to 0.50 or so. But again, these results are trivial: many of these variables are generally rising from 2017 to 2021. We want to correlate change in these variables — when hash rate goes up from one day to the next, which of these metrics is most associated with that rise in energy expenditure? If gas-heavy NFT transactions have the impact (via miner fees) that recent rhetoric implies, we’d expect hash rate to go up when NFT transactions go up (and vice versa). Running these correlations on daily change we obtain the following:

Correlation from late 2017 — early 2021 (7d moving average of daily changes)

Again, price is the highest correlation at over 0.20. This correlation is small, but statistically significant (p < .00001; note: daily change in logged scores yields similar results). You may notice that the NFT correlations are negative. We can see why this might be by visualizing some of the raw data, comparing overall fees to NFT percentages. At various points in time, NFT share of fees drops while all fees rise (and vice versa). Similar subtle patterns seem to be frequent in the dataset:

Daily fees all (ETH) by share of fees (NFT). Dots illustrate where NFT activity seems to rise relative to cost in fees. This tendency is statistical, imperfect. To confirm a trend, a follow-up 14-day window analysis is shown in the next figure.

If the NFT market segment is responsive to when fees are high or low, this responsiveness would probably be relative to some recent period of time: NFT users may wait for gas prices to drop from some recent high. Let’s take a timespan of 2 weeks (it does not depend on this exact time window). When fees are high in a two-week timespan, NFT share of gas tends to be low; when fees are low in a two-week time period, NFT gas usage tends to be high:

Relative gas usage by NFTs and fees in 14-day window (z-score). Correlation = –0.35.

This is a modest correlation, but it suggests that the NFT market is measurably responsive to recent fees. Individuals minting and transacting on ERC-721 contracts might make economic decisions on the basis of gas prices. This is, of course, an intuitive result, but these data reveal this trend quantitatively. An artist, for example, may monitor the network’s cost in fees over days or weeks, determining when it is more cost effective to mint an NFT. A stark instance of this occurred just recently. With the recent crypto correction (May 18th, 2021), Ethereum-based NFT sales on OpenSea almost ground to a halt for a few hours while gas prices went beyond 1,000 gwei.

All of this paired correlation is still insufficient. To assign emissions responsibility to a market segment we need to enter these variables in a larger model. We can run a multiple regression model in which price, all fees, and NFT fees compete to predict energy expenditure in hash rate. When doing this, we can assign a responsibility to the NFT market segment. Only one NFT variable, fees, is included here because the three NFT variables already correlate with each other at almost 0.90, suggesting they all point to the same underlying thing: NFT concentration on the network. Entering the daily-change values into a regression model, we obtain the following result. The higher along the y-axis, the greater the relationship with hash rate in competition with the other variables:

R² = .07 (7d moving average of daily changes).

Price is the most dominant relationship, and the only one that appears to relate positively to daily change in hash rate (p < .000001). And again we find the association with NFT gas usage to be negligible and perhaps even negative. So in an important sense, NFTs are not strongly associated with a rise in energy expenditure. If anything, the frantic increase in hash rate is associated with other segments of the Ethereum ecosystem, and especially the price appreciation of mining rewards (USD/ETH). Those transacting with ERC-721 contracts may lie in wait for more auspicious network conditions. One may argue that without NFTs in those moments of quieter fees we’d have even lower hash rate and energy expenditure. This seems likely. Still, there has been a recent recommendation that cryptoartists should try to minimize cost in fees to avoid emissions. The preliminary results above suggest cryptoartists and NFT users in general have been doing this (at least a bit) all along.

These analyses are the simplest first steps. They are correlational, not causal. They are based on minimal transformations of the data. They do not develop more sophisticated autoregressive controls, or even tests for multicollinearity. A more detailed analysis would import complex time series modeling and other tricks. Still, as a first pass, the simplest search for the impact of NFTs on energy consumption (as hash rate) yields a fairly weak and sometimes inverse relationship. This is inconsistent with the rhetoric surrounding NFTs.

Conclusion

These results do not imply that NFTs do not contribute to emissions at all. They do not mean that cryptoartists should ignore environmental issues. Anyone using a blockchain is participating in this overall collective energy consumption. Nevertheless, the results do suggest that NFTs as a segment were unlikely to have contributed substantially to the rapid rise in hash rate over the past few years. They suggest that if NFT transactions had never occurred on chain, the hash rate would have likely progressed in similar ways, driven by the more dominant forces of native asset appreciation and other segments like DeFi.

Proof-of-work (PoW) chains require a lot of energy. This was observed well before NFTs on Ethereum even existed. We can debate about the benefits of PoW, and the value it offers such as in security and in discouraging data bloat. For some, the benefit may outweigh the cost. This is a calculation we make in all our energy usage. For others, the energy expended by Ethereum (Eth1) may not be worth it; but such a consideration holds for the whole network, not for NFT transactions in particular. There are other NFT platforms using more energy efficient consensus mechanisms. The #HEN community is growing rapidly on Tezos. OpenSea’s Matic (Polygon-based) integration is now complete, and Gods Unchained is aflutter on Immutable X. And we wait for a fully deployed Eth2.

Curiously, the major concern with NFT energy expenditure occurred as gas prices (and fees) were reaching record highs in 2020. Considering the long history of energy discussion and PoW chains that preceded it, one can wonder why, and too easily come to a more cynical take about the sudden concern with cryptoart. (Importantly though, cost in fees to an artist posting their work is not a trifling matter.)

In any case, the foregoing analysis suggests it is not obvious how segments of market activity relate to energy expenditure. This is because transactions are not directly related to hash rate. Despite the rhetoric surrounding per-transaction models, this is not how hash rate works. Hash rises when miners are competing for fees and mining rewards, and even there it may primarily be a function of the value of ether itself. NFT transactions individually are certainly gas heavy, but their overall distribution on the network may not have been strongly associated with a rise in emissions. There is even evidence in the above preliminary analyses that the reverse is true — relative to local conditions, NFTs might be associated with lower fees and energy precisely because of their gas-heavy nature.

Takens Theorem is on Twitter.

Thanks to Nic Carter for feedback.

Notes

Corrections, etc. Feedback welcomed. I will update with any corrections or concerns and note them here.

Disclosures. I have minted and exchanged NFTs. Most of this activity was involved in a charitable project on visualizing Ethereum history, and the proceeds from all minting and sales were given to charity (minus… fees). See here for charities and other detail. I also have some smaller development projects with PoS chains, including a new project on Polygon/Matic. I have participated in the NFT landscape since 2018, including conducting ENS market analysis in 2019 and creating an NFT recommender system in early 2020. I hold a few dozen NFTs on Eth1.

Statistical notes. I am exploring Granger-based causal analysis on these data and will eventually share a repository of full code and data snapshots. For those who wish to repeat these preliminary analyses, here are some notes. This link to Kyle’s data above includes a raw data download. This Coin Metrics link points to their community API. Begin by pulling down both sources and aligning by date. After obtaining transformed variables, primarily with rollmean(x, k = window size), I use the cor() function in R, which by default obtains Pearson correlation coefficient:

Pearson between x and y of length k + 1.

For multiple regression use lm() under transformation of the data columns with diff() to obtain daily-change time series. The code in R specifies a simple linear formula of this sort:

Predicted hash rate (h-hat) estimated by price ($), fees (all) and NFT fee density (in percentage) estimates three beta coefficients (plus an intercept). ε represents error in estimation (residual).

The daily change models (including correlations) were calculated with first-order differencing by date across the whole time series for all variables.

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