Demand Elasticity on Arbitrum

Introduction

Crypto is fast-moving and multidisciplinary. In such a context, informative data is essential for good strategic decision making. One of the most important pieces of information is demand elasticity, a measure of how much users change their behavior in response to changes in price.?

• Random changes to supply (or demand) provide valuable opportunities to measure demand elasticity, as they create natural experiments that isolate the effects of price changes on user behavior.?
• The Pantera Research Lab estimated Arbitrum users’ demand elasticity prior to EIP-4844 as near unit elastic.
• This upgrade reduced gas fees for Ethereum’s Layer-2 networks by a factor of 10-100x, likely changing user behavior as a result.?
• Post EIP-4844 analysis suggests that the initial unit elasticity measurement should be considered a lower bound due to structural changes in the data.?

Fee Switches & Demand Elasticity

Consider the question of when/whether to “flip the fee switch” and charge users more for transacting on your app or protocol. The “fee switch” was long a debate in the Uniswap DAO, and is more recently being debated on the Arbitrum governance forums. One important consideration is that if you flip the fee switch and users are extremely elastic, they’ll just leave. But if they’re inelastic, the fee won’t matter to them. So the demand elasticity would be nice to know! Unfortunately demand elasticity is hard to measure. The problem is that prices fluctuate due to demand and supply changes, and it’s hard to tell what is changing what. This is why there’s a saying in economics: “you don’t reason from a price change alone.” Instead, we look for natural experiments where there are changes to price that are sudden and unexpected. If the supply side changed suddenly and the demand side stayed the same, then we can be confident that the result of these changes tells us something about demand.

What natural experiments like this might exist in crypto? Pantera Research Lab and a PhD student in the Pantera Catalyze Fellowship have recently looked into such a design for Arbitrum in order to better inform perspectives in the debate about a potential fee raise.

Estimating Elasticity on Arbitrum:

To estimate demand elasticity on Arbitrum we treated Layer 1 gas fees as external price shocks imposed on the Layer 2 system. Because Arbitrum posts its transactions to Ethereum, users have to pay (some proportion) of this cost. When those costs are high due to activity on the Layer 1 itself, this is like a sudden price increase on Arbitrum users. Using these shocks as natural experiments, we can try to estimate demand Elasticity on Arbitrum.?

Pantera Catalyze Fellow and UCLA PhD Student Dongryeol Lee found that:

• Arbitrum users exhibited a price elasticity of demand of -1.11.
• For every 1 unit increase in gas fees, users' demand decreased by a factor of 1.11.?
• Arbitrum users are roughly “unit elastic.”

But that’s not the end of the story! The implementation of EIP-4844 dramatically reduced gas fees for Layer 2s by a factor of 10-100x. It’s not likely that users have the same elasticity after such an enormous reduction in price, and so we’d like to be cautious in how much to interpret Lee’s results. Pantera Research Lab therefore conducted a test to measure whether demand elasticity after 4844 was fundamentally different. Formally speaking we were testing for a “structural break” in the data following the implementation of 4844.?

We had a pretty good natural experiment for discovering the elasticity of demand pre-4844, but we aren’t sure those results apply post 4844. Our follow-up data work supports the theory that elasticities have changed. As a result, we are probably best off considering Lee’s estimate as more of a lower bound on elasticity, rather than as a precise estimate.

It might seem disappointing to do careful empirical work on elasticities, only to have that work expire and become a “lower bound” for our variable of interest.? But this is what it takes to do good empirical analysis!?

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- Paul Veradittakit