Ethereum Macroeconomics via Dynamics Daniele Palombi & Eric Downes

Okay, this is a report on uh some really nice piece of research we did under the patronage of the Ethereum Foundation on minimum viable inflation. So this was the talk of the town last year around this time uh due to the proposed inflation schedule changes um that were supposed to happen in the PCRA um update. Then u this was sheld for the moment. Now we're seeing a little bit more buds there talking about re uh like reinstating this this possible changes. And uh this is a short version of a longer blog post.

So that was actually written by my colleague Eric here. Um and uh yeah, if you want to see and read the full picture, uh I highly suggest you go and read about it. Um so what's happening today? We have used a stock and flow model. And if you don't know what a stock and flow model is, don't worry.

I will give you a very short explanation. simp I'll keep it simple um uh to model the Ethereum staking dynamics with reinvestment burn etc and we will look at three possible future scenarios like negative scenarios obviously for Ethereum the first one is runaway staking which is the scenario in which I mean the tendency towards uh uh like over very long time horizons uh to a future in which near 100% of Ether is staked and the chain is very liquid. Obviously, this is a pretty negative scenario for everyone. Uh also runaway inflation, excessive inflation, which is what most of the people who were interested in uh like this kind of changes to Ethereum inflation schedule, right? people want to protect their bags and also governance centralization which is not like physical centralization it it's it's economic centralization right so a very small number of economic parties holding most of the state ETH I mean this is already happening okay so let's focus on runaway staking today though so here is a diagram that represents the Ethereum staking model.

So is it this is part of the stock and flow model we built. So what is a stock and flow model? Imagine these plazas this circles here are uh some kind of tanks holding a liquid. Okay? And uh this liquid is all the ether that were were ever minted.

Okay. All the he either that has ever existed. Uh now these three like tanks. Well, U holds unstake ETH currently unst holds staked ETH and zero O here holds inaccessible ETH. So either burned, sent to the zero address, whatever, lost the key, etc.

Um, so the arrows here are some kind of like if we're we're keeping the fluid analogy going. Imagine this as tubes with one way valves, okay? Uh, which I mean in which the liquid can move only in one direction. Okay? So um here f is fees okay for uh validators and uh I mean it can it can also be uh just me like I mean fees plus me or or just fees.

Um Q+ is uh obviously staking uh like new ETH. uh Q minus is unstaking. Um R is reinvestment. So like the like a more accur accurate picture uh should have a subset of you. Okay, which is validator rewards.

Okay. And then R should go from validator rewards to S and F should go to um from U to validator rewards. Uh then B here is just EIP559 burn. I mean everyone knows about this and J is slashing. Okay.

But we also have this part here that comes from nothing. And this is the inflationary part. Okay. So this is these are the rewards that uh basically get minted out of thin air thin air to just I mean it's the inflationary part of it for uh validator rewards. Okay.

So here's a table. We're not going to go over the whole table. Okay. Here's a table of uh like the flows as I was uh like listing earlier their symbols. Uh here we can see the validator reward subset.

Uh so a bit more precise than the just the picture and some very reasonable constraints we are subjecting these flows uh to uh so for example here let's pick an easy and reasonable one. So like base fees plus priority fees. So in general like transaction fees should be less than all the unstake did. This is reasonable. We're starting from a very reasonable and simple set of assumptions and we're building a complex model.

Okay. So everything you're going to see here it's it's just very simple pieces. Okay, that build up to like something faithful and reasonable. Um oh and all the flows here are listed as averages or spot values. Uh like in our research uh we have picked like quarterly averages but in general whatever uh like time span uh sounds reasonable to you it's fine.

Okay. So here is the actual uh uh like interesting part of this uh uh model which is the dynamical systems part. Okay. So these are the actual laws that govern the movement of the Ethereum like ether fluid through the tanks. uh and it's once again very simple and very reasonable loss.

So for example the net change so this e dot is dot is a derivative like a time derivative okay so the the variation of all the ether that actually exist is given by the inflation reasonable or like the variation of accessible ether. So u stake plus unstake this a is accessible is equal to the inflationary part minus the burn minus the slashing. So like we're stacking up this parts. So here we have chosen not to model EIP7514 which poses some symmetric limits on the churn rate. basically how much can enter or exit the valid uh validator set to and this is to curb um uh like very shortterm uh peaks spikes in uh uh validator centering or exiting.

Okay, so this is some kind of measure to counteract runaway staking but over long uh over short terms. Okay. So I mean we can also add it but the point of this is is also of this research is also to look at uh uh like uh what happens where this is not like in place. Um okay so we also make some more assumptions very reasonable once again. So the first one is that uh is yield is sublinear and this is in order to avoid something called discouragement attacks which are attacks economical attacks on the Ethereum consensus like on the Ethereum validator set and if you want to know more about this this is an very important part of uh like uh looking at uh uh Ethereum like validator uh dynamics and Etheum microeconomics In general, I suggest you go and read by Vitalik's paper about discouragement attacks.

This is important and this is a huge blocker in everything uh Ethereum macroeconomics. Uh and also we assume that uh like the large stake scaling of yield uh is not altered by averaging over a reasonable time horizon rather than picking uh uh spot values. Okay. So how did we do this analysis? And uh I'm sure Eric will show you a bit more later about the nitty-gritty of it.

Uh so Eric built this um uh very nice wrapper around uh like standard differential equation solver uh which is called the uh this has all kinds of nicities to model macroeconomic questions in Ethereum. Uh so I highly suggest that if you're interested in in general studying Ethereum inflation or any other kind of microeconomic topic related to Ethereum, you go and use this or something similar. I mean we are very we at 20 squares are very strong advocates of having a formal approach to studying this kind of economic questions in uh uh I mean in Ethereum and in blockchain in general. Uh we should stop doing vibe based economics. Okay.

No oh deflationary ETH because this protects my bags No quasan inflation. no Twitter storms about uh uh this kind of of stuff. Let's study about it. Okay, let's let's be a like real economists for once. Um so like after our analysis, I'm going to tell you what are the key takeaways of like our research.

So the main takeaway is that we have identified a discipline one would need to follow in order to make runaway st I I mean to push runaway staking as far as possible as a problem which is to keep a medium reinvestment rate low inflation low but positive okay and even lower fees and without at convergence to a decidable future without runaway staking is highly unlikely. Uh so okay why low but positive inflation? uh in case of strong deflation uh in which the magnitude of inflation exceeds the reinvestment rates of transaction fees and and yeah uh like this corresponds to unstable dynamics in in the study uh and uh in case of deflation that's too weak or zero so it's not deflationary sorry I say deflation inflation that's too weak or zero um like the tendency toward uh um runaway staking can be moderated only by some stuff we don't want like I churn rate or slashing I mean we don't want anyone to get slashed and we want to moderate the churn rate okay so in short we can avoid runaway staking or like push it as far as possible only while inflation is held at At the same time, low enough such that concerns over inflation do not dominate their investment rate for validators and uh high enough not to be numerically um like dominated by reinvestment of priority fees. Okay, so it's it's a very delicate equilibrium. Uh but the main question I guess you're all interested in is should we reduce issuance?

Are my bags uh uh going to be uh magically uh improved and and made heavier uh if we reduce issuance? Well, the answer is no. We shouldn't reduce issuance. This is a very delicate subject. The current approach to issuance we have is highly insufficient.

Uh if we want to touch this, we will need a lot more study and it's not because I need to do this uh because it's my job. I mean anyone else can do this. The thing is uh no let's not touch issions for now. Okay. So but Danielle uh EIP7514 you mentioned that this is a measure for limiting runaway staking over short time uh um short time horizons.

Does this also work over long time horizons? No. Okay. It doesn't solve the problem uh like overall it just designed to limit spikes in uh turn rate. Okay.

Uh I mean the problem is that uh like runaway staking is kind of built in and this is a problem that's mostly due to disc attacks. So the the problem is that if we use a static okay uh static I mean just a curve for like um inflation schedule it's very hard to keep inflation sustained high enough but low enough. Okay. Um in such a way that uh uh like taking uh discouragement attacks into account. So we also have to like um work under the assumptions of sublinear yield in in such a way and uh if you're really interested in playing with it maybe you will figure something out that we haven't figured out.

I mean you use you you can go to GitHub use our uh library and maybe try playing with the parameters for EIP7514 and uh maybe try decoupling their investment rate from new stake as much as possible. I mean maybe we'll come out of it but I'm very skeptical about it. Okay. So I mean this is my part. Now on to Eric.

[Applause]

Sit with us a moment. Here it is. You got it. Sorry about that. Okay, I'm going to give I'm going to give a brief uh review of what Daniela said with pictures.

uh in case it was too abstract. Um and uh uh yeah, we'll start with the motivation. So what was going on was people So first of all, what is yield? Yield is the percentage of uh Ethereum that is introduced into uh into the ecosystem every year by validating. Okay.

So this is the yield curve. So you can see that that decreases as the amount that is staked increases. Okay. Uh and then people were noticing that the amount of stake was growing, growing, growing, growing, especially with Lido and other LSTs, which is liquid staking providers. people were very worried that the the sort of uh idea of the yield curve that they had just sort of made up because they had other problems to solve was not going to be sufficient and that the winner take all nature of the uh LSD market would give a positive feedback loop where uh the rate the percentage of ether that is staked increases so that's little s goes to one and then this causes inflation alpha to rise and then this uh because everyone is going, "Oh no, all of my money is being inflated away.

I have to stake just to keep from losing money, just to keep, you know, my bags from withering away, right? Uh and so that then this would cause more stake to go up and so eventually we end up with there is no more raw ether. There's only Lido. Uh and we don't have a decentralized ecosystem. We have Lido which is you know you Lido can be a great protocol but it's it's not the vision of Ethereum right we wanted something a little more uh uh little yeah not not just a smart contract uh that has a you know some DAO or something right okay so uh people were really worried about this and you can hear if you want to listen to what they were worried about and their concerns there's a great uh channel on YouTube and you can find Ethereum staking endgame, that one there in the middle uh wi-i with the the line under it.

Um and you can just hear uh um Kaspar and Ansar talk about um this this concern um and this so this motivated this this research. Okay. So what we did is as Danielle said, I will not spend much time on this, but uh you have a balloon, the balloon inflates itself with the I term and then there are some containers inside the balloon, some some smaller balloons, if you will. Um and so there is the staked, the unstake and the burnt ETH. And then you have some equations that come from that.

Um uh the the so the only the top one is the one we're going to be spending the most time with. They're all sort of important. Um uh let's see. Yeah, I I could explain them. Uh I the one that I didn't mention is V, which is just the this is the amount um that is held by validators that is unstaked.

So because what happens is your you know your your ETH goes into the queue and it it sits there and then you claim it and then it goes into the unstake pool. And the the fear is that well if everyone is just immediately selling all of that then you have this huge sell pressure, right? And that causes this inflation. But what happens is and this is very critical uh what actually ends up happening is that um you have wow I don't know if you can read that uh it's but uh you have something called reinvestment which is for a business to survive you can't just sell all of your uh uh all of your profits right you have to reinvest some of them in the business. So part of that is you have to buy computers, you have to pay all nodes, whatever.

The other part of it is you you have got to increase keep increasing your stake, right? Because that's the thing that makes you money. Every business wants to make more money and they want to make money doing the thing that they are doing. Yes. So if you are serious about staking and not just doing it as a hobby, you will reinvest your profits.

And this is why you don't see this immediate demand uh uh you know this this o this huge supply shock where people are just trying to sell off their ETH. Uh some of it gets reinvested and this reinvestment ratio is absolutely critical if we really want to understand these things. So the re the way that we identified reinvestment as critical is we looked at all of these big you know uh uh the the big capital letters before uh or sort of stocks and then we said there are flows that are that are that can be that can be rat written as ratios of the of the stock because you can't draw draw down more than is there. All right. And the consequence of this is this graph over here which is this is this uh equilibrium staking fraction.

All right. And you will notice that on the the I don't know if you can read this because the it's very dim but on on the on your left basically which is very which is like inflation is too low on your left it is extremely high sticking fraction like 90% and above. So almost all ETH is staked. Maybe there's some that's used for settlement, but but mostly people are not using ETH as a as a as an as a instrument directly. And so whoever has most of the ETH staked has a lot of control in governance.

But if inflation is high enough, this is inflation per fees. If inflation is high enough, you can see intermediate values that are not just 90% and above. Okay. Um, and so the system, we do find the system is drawn toward this stable point. And so you actually see this interesting thing where instead of inflation being this positive feedback loop, it actually has a moderating influence.

Um, uh, let's see. So I now want to talk about so what actually happens with inflation. So Danielle has talked about all of that. I reset it in a different way. Hopefully one of us made sense.

uh the top equation here this is the total amount of accessible ether the change in it over time is issuance minus burn minus slashing okay uh and so we're going to say what what actually happens to this over time and the interesting thing is that there can be strong bond bounds uh you can place on with math and you can say look I can say exactly how big this can be because the thing is that If you as you inflate you're increasing the size of the thing that pushes you further down on the staking uh and you and you will find that e although people think about it as a percentage and that's the easiest that's how I introduced it does not scale this bottom line after you do a bunch of math the bottom line here is that it does not go exponentially so it's not really a percentage rate because it's a constantly decreasing percentage rate it's always smaller than an exponential what does this Mean what this means is that if today so this is a graph of if today staking validating went up to near 100% of ether how high would the inflation rate be if there was negligible burn so we're just ignoring burn on on the left here if you look up on that upper left corner you see it is about 6 and a half%. No, that's not a great uh inflation rate, but this is also this is the kind of inflation rate we have seen before in you know fiat economies and the thing didn't burn down. Uh so with burn that gets reduced but it can't last as long. It doesn't just continue forever because of this subleaning effect this subexonential effect you see about a decade of that and then it's down. It just and it decreas the the higher it is the faster it decreases over time.

Um uh and so uh uh whereas if you if you retain at low levels of staking then uh then you you are looking down at you know a couple percentage of inflation um which once you subtract the burn um right right now it's not even a positive it's like uh it's like 0.5% I think last time I checked um it is uh yeah it's it's it's it's just small enough um and so this gives us the possibility of actually building in inflation hedges. Uh, and there's a lot of really uh, interesting research that could be done here because, you know, mostly we think about Ethereum with the price because it's so volatile. But you might expect that as more institutional players get involved, maybe the volatility goes down and the inflation rate starts to matter. Um and there are a couple you know so classically you would use commodities to hedge inflation because commodities have prices that that there you know if dollars are the thing that's inflating then something that is uh more restricted than dollars and still in demand like oil or uranium or gold right these things go up in price because the thing that they're the the thing that they're they're valued in is is inflating and so there's you know you need more dollars to buy gold.

So, you could do something like that with BTC. Um, but you know, this this gets questionable. Well, if Ethereum is, you know, are we really do we want to depend on another L1? Uh, but you as an investor could do that. You could say, well, I'm going to, you know, use this as a as a hedge against this other thing because it's, you know, it has a different issuance policy.

Um, uh, you could also say, well, I'm going to use stable coins. You know, uh, uh, I think that inflation is going to stay low at 3% like it has usually. That's an opinion you could have and you could say, well, we're going to use USDC or circles eurocoin, you know, whatever you like. Um, but there are other there are other instruments as well. Uh, people might want to look at squeeath.

Uh, the funding rate right now is extremely high. So, it is it is impractical to just buy this thing and leave it. But the mathematics behind it can be used to build something uh that is a little more interesting. The other thing is you have uh oiler finance has uh and many other protocols have done this thing where you split off the inflation uh you split off the the the the issuance or the inflation from the principle um and you can factor them into two different coins. You you people from TRFI love they salivate at stuff like this because they know how to build uh they know how to put these things together to build interesting instruments.

Um and so this is you know this would be a nice uh thing for them. So there there's a lot of work here that being done. I'm happy to talk more about it, but just you know this is this is not just theoretical research. This stuff has real actual practical applications. You could make deep fry D5 protocols based on some of this math.

Um in summary uh as Daniela said uh we don't find a positive feedback loop. In fact we find a negative feedback loop. Inflation has to stay away from zero in order to avoid runaway staking. But eventually, as I said, inflation will glide path to zero. It may take multiple decades.

Okay? Uh uh so this is not an immediate concern, but eventually it does go away. And once it goes away, you're guaranteed to hit 100% inflation if we have not done anything. We have not adopted a dynamic yield curve or something. And yes, as Daniellea said, if you reduce issuance, you are just making this problem worse.

So, you're just speeding up the time until you go to S equals 1, 100% inflation. If you want to read more, uh, if this did not make sense, but you're interested in it, we wrote a whole blog post on this. Um, and you can take one sentence at a time and think about it instead of trying to keep up with us blathering. Um, so yeah, so take a look at it. Uh, the the address is there.

Our blog is easy to find. 20s squares.xyz. Okay. Are there any questions for either of us?

[Applause]