Proof of Stake: an economic analysis

Some people have voiced concern that proof of stake (PoS) as it will be implemented on the Ethereum blockchain is a consensus algorithm that will benefit the rich and lock in capital where it already exists today. Another concern commonly raised is that PoS may lead to hoarding, undermining the use of ether as a currency.

I do not believe these concerns are valid and will address them in this article.

I will add here a disclaimer that I am an economist, not a programmer. For a more technical understanding of how PoS works, please refer to the official Github page.

Proof of Stake: making the rich richer?

The PoS algorithm allows validators to participate in generating blocks by having them lock up their ether into a deposit. Ether are locked up in this way to incentivise prudence and honesty: inadvertent mistakes or wilful dishonesty will be punished by losing your ether deposit. To incentivise participants to validate at all, honest and correctly functioning nodes will be rewarded with an ether pay-out in proportion to their deposited stake. This means that a validator with a large ether stake will receive a greater reward, in absolute numbers, than a validator with a small ether stake.

Why must this be the case? Why can’t we introduce a regressive system whereby the relative ether pay-out decreases as your ether deposit grows, in the same way that people with higher incomes enter a higher income tax bracket? Why can’t we simply pay out a fixed amount of ether considered to provide a sufficient incentive to any participating node, regardless of the stake deposited?

There is first of all the practical consideration that any such measures would inevitably affect staking pools as well, which will presumably be made up mostly of users who cannot stake themselves and are therefore as a group, if anything, poorer than average. More importantly, any differentiation does not make sense economically and jeopardises the security of the consensus algorithm. A decreasing relative reward or fixed ether pay-out as described above would be broken to the very core: risk (the loss of your ether deposit) would scale in direct proportion to your ether holdings while rewards (the ether pay-out) would not. Such a system would lower the propensity to validate in direct proportion to wealth.

In the short term, the biggest holders of ethers would be less likely to participate in validating, drastically reducing the safety of the Ethereum blockchain, as a 51% attack would require significantly fewer holdings. In the long term, seeing the dilution of their wealth in favour of other holders, big holders would be more likely simply to sell their ether in favour of another cryptocurrency or other asset.

We should also be aware of the fact that if everyone stakes and receives a certain return in proportion to their stake, the rich don’t actually get richer. In fact, in that scenario no one gets any richer at all. That is how any currency works. If we were to suddenly double every ether address’s holdings, then not a single holder of ether would be any better off in dollar terms (or bitcoin terms, or any other terms). The demand for ether hasn’t changed, the supply has doubled, therefore the value per ether will have halved.

By the same token (no pun intended), if staking were automatic and every ether address would join, it wouldn’t matter whether the annual return (in the form of newly created ether) on staking was 5%, 10% or any other rate. Whatever the nominal rate of return was, it would be consumed entirely by the equivalent inflation of the currency, and the real return would always be 0%. The scenario many imagine whereby if annual staking returns are, say, 5%, they now have an asset that pays a 5% annual net yield, is largely imaginary: the yield on ether staking is directly related to the dilution of the value of the existing ether deposit in the form of inflation. The higher the nominal staking return, the higher currency inflation will be.

Let’s compare ether staking to renting out a house. Rental payments have no impact on the property value of your house: it’s not like doubling your rent would halve the property value of your house. In ether staking, the rate of return paid for staking (the rental payments) directly impacts the value of your ether holdings (your house): it’s as if the higher your rental payments go, the more the value of your house is reduced. Even if you are the only person staking, the real return of staking would still not quite exactly be equal to the nominal return. The greater the proportion of ether tied to staking nodes, the more your real staking returns tend to 0%.¹

You can compare the return on staking more to a dividend paid out by stocks. When stocks pay a dividend, shareholders get a real monetary pay-out. But you’re not actually any better off than if the company had not paid out a dividend; in principle and ignoring other factors (including, in particular, taxation systems), the value of the company will have gone down by the amount paid out in dividends. You’d have the same total value in assets if the company had not paid out a dividend, because your shares would be worth more by the amount of the dividend not paid out.

To the extent that a majority of ether holdings will be tied to staking nodes, you would have more to lose by not staking than you have to gain by staking. In that situation, participation in staking should be seen more as a way to avoid the dilution of your holdings than as a way to generate a real return on them (incidentally, that should provide an even stronger incentive for staking to current holders). If anything, in nominal amounts, wealthy ether holders would actually have comparatively more to lose than to gain.

Not all, and maybe not even most, ether holders will stake. Some people will be wary of participating in validating for example because they do not trust their technological prowess or simply because they do not want to risk losing their deposit. In general, PoS would make the tech-savvy richer at the expense of the technophobes (though not nearly in the same way that PoW does), and the risk-loving or risk-neutral at the expense of the risk-averse.

Proof of Stake versus Proof of Work

As we’ve seen above, PoS is about as wealth-neutral as any inflation-generating system could possibly be. How does PoW compare? Anyone who can afford a mining rig is free to mine, creating a barrier to entry as PoS also does in the form of its required minimum stake. At the time of writing, the mining capacity of the smallest miner that has actually mined a block is 17.2 GH/s. Such a set-up will set you back several million dollars. In PoS, by contrast, you may be eligible for staking by yourself with 32 ether or more, which comes out to a little under $10 000 at the time of writing. More recently, Vitalik Buterin himself has reported that staking may be possible with as little as 10 ether.

If you ever want to receive rewards from validating, you are therefore much more likely to have to join a pool in PoW than you are in PoS. Setting up a profitable mining rig so as to be able to join a mining pool at all will cost you about $2000 or so, whereas joining a PoS pool, while not knowable at the time of writing, may be possible with as little as a single ether. In addition, setting up a PoW mining rig requires an amount of technical savvy far beyond that expected of PoS.

Barriers to entry for participating in validation are therefore significantly higher in the current Ethereum PoW consensus algorithm than they would be under PoS. But barriers to entry do not tell us the whole story. While PoW locks out many more participants at the bottom of the wealth scale than PoS does, in both systems a majority of participants would probably be able to validate profitably if they so pleased.

In PoS, every validator gets the same return on investment. There are no economies of scale. While the Ethereum PoW consensus algorithm certainly doesn’t favour scale in the same way that the Bitcoin PoW consensus algorithm does, some economies of scale can be assumed since they arise in almost any economic activity. In the case of Ethereum PoW mining, miners may for example be able to receive discounts on their electricity bills or hardware purchases or be able to hook up more graphical cards per rig and more rigs per available surface area.

In conclusion we can say that the Ethereum PoW consensus algorithm therefore makes the rich and the technologically savvy richer at the expense of the poor and the technophobic.

The disincentive to “spend” money under Proof of Stake

When it comes to hoarding behaviour, a first question may be to wonder if there would be any problem if ether were affected by it. Gold has a market capitalisation of about $7 trillion and is generally considered to be “hoarded”. Fiat money on checking accounts can be considered to be held for spending while money on savings accounts can be considered to be held for hoarding. In the US, demand for the latter is vastly greater, at $8.7 trillion held compared to around $2 trillion for checking accounts.

A second question may be to wonder whether hoarding behaviour would really discourage actual use. The use of both checking and savings accounts shows pretty well that a currency can perfectly be held both for spending and for hoarding. That only makes sense: mandatory expenses such as rent or groceries should be paid with whichever method is most accepted or most convenient, or has whatever other characteristics desired by the user, such as privacy. Expectations of future financial returns is not a relevant characteristic. If I have to pay $500 in rent and 1 ether is $250, from a financial perspective it doesn’t matter if I pay in dollars or in ether; if I pay in ether I can simply subsequently purchase 2 ether with the $500 I didn’t use and come out the same. My landlord can similarly exchange the currency he receives for whichever currency (or other asset) he prefers. Therefore the extent to which ether is expected to appreciate or depreciate should not be a meaningful factor in determining the extent to which it is used for payment.

The above is true in the abstraction of transaction costs. Currently, transaction costs (waiting time for your deposit to an exchange to be cleared, the fee charged by the exchange when buying your cryptocurrency, gas paid when transferring deposits to your address, etc.) are quite significant. Due to the nascent stage of the technology we are in, we can expect these transactions costs to go down considerably with time and technological progress. What will be key for PoS is that a staking node can close down and set up shop again quickly, in the same way that you can transfer money from your savings account to your checking account and back instantly.

As a technological neophyte (which may, unfortunately, be obvious from the preceding text) holding ether, I am actually hoping that the nominal returns on staking will be low. If the return on staking was, say, 1% per year, I’d be happy to go about my business and ignore the possibility of staking, knowing that I won’t lose my ether due to some unintentional screw-up and that my holdings will inflate by max. 1% per year.

Imagine that I believe I have a 5% annual probability of messing up my validation somehow and losing my ether deposit. If annual returns on staking were 1% and holding demand for ether constant, I’d lose at least 4% of my ether holdings annually if I staked: 5% expected loss of deposit - 1% * (1-proportion of ether holdings in staking deposits), and at most 1% in value per year if I didn’t: 1% * proportion of ether holdings in staking deposits. So I would decide not to stake.

Now imagine annual returns on staking are 4%. Under the same conditions described above, I will now lose at most 4% annually if I don’t stake, and at least 1% if I do. I will decide to stake. But even though staking returns are nominally 4 times higher, I’m actually worse off than I was in the previous situation.

Let’s take this scenario to an extreme, and imagine that annual staking returns would be 5000%. The dilution of your ether holdings resulting from not staking would be so enormous that we can assume that pretty much everyone would stake. Since everyone is staking under this scenario, the real returns on staking (net of inflation) are 0%. I am the worst off in this situation, as I am now losing an expected value of 5% each year (the probability of me losing my ether deposit).

In general, we can expect the quality of the average validating node to increase inversely to the rate of return offered on staking. An ether holder who understands the process of validation keenly and knows how to secure his computer from hackers will estimate his chances of losing his ether deposit to be comparatively low. He will be enticed to start staking at comparatively low rates of return. The higher the rates of return on offer, the lower-skilled any newly-enticed validators will be. Working against this is the need to secure the system from wilful cheating. Strong defences will require many validators in total.

Between these two competing forces, an equilibrium should be found. I do not have the answer for where, in terms of the rate of return offered, this equilibrium lies. But the rate of return could, for example, be adjusted in order to target a certain proportion of total ether holdings to be held in staking deposits. Alternatively, it could target a certain monetary amount of ether to be held in staking deposits considered sufficient to secure the system from attack. It could also simply target a certain level of inflation (the rate of return on offer will have to be higher than the inflation target, as not everyone will stake).

As Ethereum grows, stronger security will be possible with relatively fewer staking nodes and, therefore, lower rates of return offered. That would lower the incentives for hoarding and generate a reinforcing cycle of ether either being used or being hoarded out of a belief that it is an attractive asset with increasing demand, as opposed to out of the desire to capture annual nominal returns. If ether was hoarded in this scenario, it would be in the way that stocks or bonds are (or dollars, on saving accounts). That hoarding behaviour should not affect ether’s use as a method of payment in any way, and is in fact likely to happen on a large scale only if its use, including as a method of payment, has been proven.

¹ Let’s say you hold 10 out of a total of 100 ether, and nominal annual returns to staking are 10%. If you are the only person staking, after a year you will have 11 ether out of a total of 101. The proportion of total ether you hold has increased from 10% to 10.89%, or by 8.9%. If everyone stakes, you will own 11 ether out of a total of 110, or still 10%. In general, after a year of staking the porportion of total ether in circulation you hold will have increased from H/E in year T to H * (1+r) / (E * (1+ r * p)) in year T+1 with H your ether holdings, r the nominal annual return on staking, E the total amount of ether in circulation and p the proportion of ether holdings tied up in staking nodes. The total real annual return on staking can then be depicted as ((H * (1+r) / (E * (1+ r * p))) - (H/E)) / (H/E).