Ethereum Macroeconomics via Dynamics - Daniele Palombi

Transcript

[Music] hello hello everyone um yeah so uh well thanks for being here this late um so today I will report on uh some very interesting research that we've been doing at 20 squares and that was backed by the ethereum foundation on uh ethereum issuance uh so just ah adds up uh this topic is very complex and Technical I'll try to keep it accessible for a general audience so that would be yeah uh so there will be a a pretty

heavy technical part at the start but then I'll tell you what the conclusions are okay uh and it's based on uh my awesome colleagues work um uh Eric uh and and you can go and read the complete blog post or we also have a post on um e research uh about this so if you're interested in getting the full picture um so actually this is part one this blog post of a two-part series um yeah and basically we use a stock and flow model and don't worry if you don't know what a stock and flow

model is I'll give a high level explanation uh of the ethereum staking Dynamics and we look at three possible future issues for ethereum or future concerns for ethereum that are obviously related to ethereum issuance or that we expect ethereum missions to have an effect on uh like changes to to it uh the first one is Runaway staking so the scenario in which uh uh I mean like the tendency towards uh like having near 200% of the eth Stak and this is obviously an undesirable scenario um the second one is excessive inflation which uh has been

kind of the uh the most discussed discussed Point uh around mvi and uh I mean in general ethereum issuance uh a lot of people are concerned for their bags um and the third one is governance Central ation and by that I mean the scenario in which uh basically the ethereum Staker Set uh becomes uh an oligopoly okay highly dominated by uh very restricted amount of uh economic parties so I'm I'm not talking about uh security like in the last talk uh so a

large number of nodes but uh I'm talking about a a small number of economic agents quote unquote uh actually this blog Post and today's talk will only be focused on rway sing but I warmly invite you to go and wait for the second post that's coming uh out somewhere down the line um so uh now what is a stock and flow model and what is the model we're looking at so this picture is not not very clear right now but I'll walk you through it uh this is uh a kind of accurate kind of uh picture of the ethereum staking model so a stock

and flow model is uh so you can imagine it as uh a bunch of uh like bags or tanks containing some liquid and uh um the flows are actually the laws that determine how this liquid flows between the the various stocks or tanks um so in this case the the circles are the the the stocks we're talking about and uh so these are uh basically the uh the the the complete amount of ether that were ever minted okay uh so U here is uh uh The unstaked Ether s is the stake ether and

O is the inaccessible ether so either burned or the key was lost yada yada um so these uh flows are well so first thing as you can see this is not really a closed system because there's this eye that comes out of nothing and this is basically the inflationary part of ethereum so it's it's it's issuance okay uh then this F is um uh is um the um like transaction fees okay plus Meb if you want to take this into account it's it's the same thing if you if you

consider it or not it's it's just a couple of numbers change but it's it's not relevant uh q+ is new stake entering the the validator set Q minus is unstaking and R is reinvestment by um uh by already existing stakers uh right now if you want to reinvest uh you basically spin up a new validator but after Electra uh with increases to the max effective balance you can just increase your your effective balance and uh I mean it's it's it it would be easier to do

reinvestment um reinvestment is particularly important for all these kinds of uh I mean discourse around uh issuance and and runaway taking uh this B Arc or this B flow is uh uh basically The Ether that get get burned um just classic uh EIP 1559 burn and the J is lashing um so actually this is not the complete picture because there should be another uh small tank which is a subset of youu uh which let's call it V it's the uh it's the subset of unstake e

which is a validator rewards and F should should actually go from U to V and R should go from B to S because it's it's validator rewards the the reinvestment uh in this picture it it's it's a bit more accurate this is a table of all the flows uh by the way all these flows are moving average over a like spot values at a given block maybe quarterly I mean pick a uh a time frame that that makes sense we in our research used the quarterly moving average um and these flows are obviously subject to some constraints in order to

make sense this this is not the complete picture because it it it I mean there's no constraints uh just to make a small example a very easy and reasonable one is this the first one on transaction fees it's that like the the base fees that get burned plus the priority fees equal the transaction fees and they have to be the transaction fees have to be less that than all the unstake ether otherwise it doesn't make sense the model it's it's not realistic uh by the way here I have left a footnote so validated rewards is actually this a set v um which is a subset of U um okay so

we're almost done with the technical part uh but this is the model we used uh oh uh there is some things that are not showing up actually uh I don't know why they're not showing up here in these slides uh on my computer they showed up there have to be actually oh dots on top of e a o v u v and S uh which are the time derivatives so this so this is a an Hest to go dynamical system so e in this case sorry if you can see the derivatives uh is the like all ether ever like minted and uh the idea is the

derivative so the the the net change in the amount of ether that gets uh minted is actually the minting the the the inflationary part well uh great you can see the read of this uh by the way another remark is that uh uh we are ignoring willfully um EIP 7514 uh which was added in the neb uh which poses an upper limit so it's it's it's an e about sh rate okay uh an upper limit on like new stake plus reinvestment um we choose to ignore it

and other symmetric limits on like staking and unstaking uh to show what would happen in absence of such limits but will get back to this EIP um so this was actually put in place to uh mitigate the runaway staking scenario okay so the like I percentages of of either that get sted at any given point um so um let's make some more assumptions this is the last technical slide um so well we're making some assumptions on this small Y which is issuance yield the first one is that issuance is

sublinear and this is in order to avoid the what what are called discouragement attacks if you don't know a lot about it I suggest you go and read vitalic paper about the discouragement attacks and this is an important actually an important uh uh portion of U why U matters around issuance and R runaway taking are a bit complicated um and also that uh I mean doing this averaging I was talking about of staking yield over uh like a reasonable period is not uh substantially altered by uh I mean I

mean it doesn't substantially alter the value you would uh See by just looking at spot for for yield okay I mean these are reasonable assumptions but uh uh we we need these to work uh so how did we actually run this model and analyze it well we built a very nice piece of software uh it's a live library in Python it's called EOD uh actually you can go and I mean it's it's open uh and it's basically a an very very light actually wrapper uh that keeps track keeps track of all

units and has some uh nities for modeling uh economic uh like macroeconomics of ethereum uh and it's a wrapper around a like normal different equation solver it's it's nothing very fancy but uh I mean uh we firmly firmly believe that ethereum macroeconomics in general is better studied with this kind of D like looking at at it under the lenses of dynamical systems and so we built some software to go with it uh please go and use it if you're interested in in looking into this stuff um so um now the the non-technical part okay uh

or or I mean the takeaways of of uh um from the model we actually came up with and studied so uh the first one is that uh in order to avoid uh runaway taking we have identified this let's call it a friend a discipline a an a general idea on how to go about this which is uh keep a medium reinvestment rate keep low inflation and keep even lower fees and without this basically convergence to a like a desirable future without long well not non super long-term runaways taking is basically

unlikely uh so yeah um why though okay uh let's let's anal is a couple of scenarios so in case of strong deflation in which like deflation exceeds the reinvestment rate of transaction fees uh this creates like very unstable Dynamics uh and having zero or weak deflation uh the basically the the tendency towards runaway staking can be controlled only by higher high turn rate or slashing which is highly undesirable so we don't want that uh so medium reinvestment rate low inflation even

lower fees remember this um okay so uh but but now for I guess the the interesting question of this talk uh oh well first okay uh one remark uh so runaway taking can be avoided only while inflation is at the same time low enough that uh like concerns over inflation do not dominate reinvestment of profits and but at the same time high enough not to be dominated by the reinvestment of priority fees and M uh so yeah it's this

this low but not too low so the key takeaway of it is should we reduce issurance this has been like a very discussed uh um uh topic for for pectra uh yeah the short answer is no let's not touch it this is very delicate okay uh if if you want a longer answer or if you want to know that well maybe can I I'm really concerned about uh about inflation though maybe in a model in which e P 7514 so the the the the max churn rate is there do we have I mean does

this POS a solution to the problem not really but it doesn't really try to be a solution in the long term just a short-term solution so like over small time Horizons uh but in general reducing reducing isurance doesn't solve it either from from our analysis you can go on the E thought the REO there's a nice tutorial on how to use it and also read the the the blog post and and I mean you can observe and then see for yourself that that this is actually the case um and and basically um this's this uh uh L2 Centric future that's been discussed a lot in which uh near 100% of

uh the stake and it's mostly used for settlement of Al l2s it's kind of baked in uh because uh just to come back to the discouragement attacks thing I mentioned in the start uh like persistent inflation cannot sustain under such an issuance uh curve that that is designed to avoid discouragement so sublinear and stuff like that uh so but but if you're still curious maybe you can uh use EOD or whatever uh um other software or approach you like to

study this kind of microeconomics questions and uh maybe adjust a bit and simulate the constants in EIP 7514 and maybe you will manage to decouple the reinvestment part from the new state part to avoid possible scenarios in which the reinvestment rate is too low because remember medium reinvestment rate uh so I maybe something will come out of it so yeah um thank you for attending this talk and uh yeah [Applause]

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