Kareken-Wallace and Cryptoassets: because Bitcoin and Beam are not perfect substitutes

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Some eminent economists have begun to formally analyze the market for privately issued private money that they associate with Bitcoin. Rodney Garratt and Neil Wallace (2018) (undefined version here) model the relative values ​​of (exchange rates between) "Bitcoin 1" and other hypothetical cryptoassets ("Bitcoin 2", etc.). Linda Schilling and Harald Uhlig (2018) adopt a correlated approach to the exchange rate between "Bitcoin" and "US Dollar". I use quotation marks here to indicate that the authors' subjects are modeling entities, which take the name but not the real things. Their correspondence with real things should not be taken for granted.

Both pairs of authors are based on a well-known theoretical result of Kareken and Wallace (1981): when two fiat currencies are perfect substitutes, the equilibrium rate between them is indeterminate. To get insight, imagine that any payment made in US dollars can still be made in Canadian dollars valued at the current exchange rate. Therefore, no one has a reason to exchange a currency with an equivalent amount of the other. Regardless of the exchange rate level, there is no pressure to change. Only the combined offer of real money and demand is important, and any exchange rate is consistent with the real combined real offering that equates to the combined demand for real money. The combined real money stock could be 99% of US dollars (at an exchange rate that makes one USD of many CAD) or 99% of Canadian dollars. Or the rate is compatible with the monetary equilibrium.

It is easy to see, of course, that in the real world the fiat currencies are not perfect substitutes in all uses. Obviously, the laws on the legal offer and the tax payment restrictions imposed by the nation states make any two non-interchangeable legal currencies. Canadians can not pay their debts or their taxes in Canadian dollars with equivalent amounts of US dollars; they need Canadian dollars. Garratt and Wallace (p1887) are aware of this objection to the relevance of the result of Kareken-Wallace (d & # 39; now onwards KW). But, they assert, no such objection can be made in the case of Bitcoin and coins identical to Bitcoin in all respects, but the brand name:

Bitcoin and its current and potential competitors – in the title intentionally labeled bitcoin 1, bitcoin 2, … to indicate that there could be many – seem to satisfy all the assumptions made by Kareken and Wallace to get the exchange rate indeterminateness .

As a result, they write (page 1896):

Much of the uncertainty in bitcoin's value comes from the ease of creating perfect replacements. It is easy to clone bitcoins and the creation of very close substitutes makes the value of bitcoins based on beliefs that can be difficult to define.

Without questioning the Garratt-Wallace analysis of their hypotheses, I want to emphasize that a key hypothesis – that perfect substitutes are easy to create – is actually false compared to the cryptoassets of the real world. Bitcoin and its current and potential rivals are not actually perfect substitutes and therefore do not meet the KW hypotheses. The reason does not derive from legal law or tax laws, but mainly from network economies in monetary systems that apply to cryptocurrency systems. The size of the Bitcoin network is important and is not easy or cheap to replicate.

The concern that the new cryptoassets will come close to perfect Bitcoin substitutes, and that, since they are very cheap to produce, will bring the value of Bitcoin to zero, was expressed in a less formal way in the blog posts by John Cochrane and much earlier from Brad DeLong. DeLong wisely included the warning that Bitcoin could retain its value if it could remain differentiated from its rivals, but doubted that it could do so, erroneously suggesting that its differentiation is tenuous because it is based on nothing other than the older cryptoasset.

To understand the relevance of network effects, it is important to note the fundamental fact that each currency has its own blockchain. The new cryptocurrencies do not provide access to the established Bitcoin system, but only to their much smaller systems. The thousands of Bitcoin validation nodes are not the validation nodes, which count many less. The most recent coins are not widely accepted in payments. They do not offer an equivalent ecosystem of portfolios, retail payment processors like Bitpay and other ancillary service providers. They are not traded on as many stock exchanges, or in similar volumes, and as a result have higher bid-ask spreads. Given the network benefits of a larger system with greater acceptance and consolidated robustness, the new coins that simply clone the Bitcoin code are not in fact Bitcoin's close substitutes.

Economic theory predicts that marginal currency, with an almost zero production cost, will have a market capitalization close to zero. Such coins will not bring down the market capitalization of Bitcoin (or other consolidated cryptoassets) when potential investors and users have no reason to prefer them. In general, to attract users and thus achieve a positive market capitalization, a new currency needs to offer improvements above the Bitcoin system. The cost of making significant technical improvements is obviously not negligible, so the new cryptoassets that provide them will never be easy to create or overflowing.

The cryptoassets that to have it has gained a positive value in competition with Bitcoin, it did not do it by cloning it but offering new and better features. The most important improvements were in four areas: greater speed in payment validation (eg Ripple, Stellar, Bitcoin Cash, Litecoin), more privacy (Monero, Dash, Zcash), greater security against attacks of 51% (NEO, Peercoin, Decred) and a better infrastructure for contracts and smart applications (Ethereum, EOS). The stability of the value can be considered a fifth area, or the so-called stablecoin projects can be considered alternatively a completely different proposition.

New and improved coin projects continue to be launched. The advertising of new coin projects typically underlines how their technology differs and improves the Bitcoin protocol. He never says: we're just a Bitcoin clone. For a recent example, on January 3, 2019, the same day of the tenth anniversary of the launch of Bitcoin, a new currency called Beam was launched.[1] Beam implements a next generation blockchain technology ("Mimblewimble") that allows more privacy (less transaction information is publicly disclosed on its blockchain) and faster validation.

To say that a particular cryptoasset is distinct, and not a perfect substitute for Bitcoin, does not mean that its market value in Bitcoins or dollars is stable or readily predictable. Nor can it be denied that its value can go to zero, if the market abandons it completely as no longer a plausible competitor. But it is to say that news that increases or reduces the chances of a future wider adoption of the currency will drive changes in its relative value. Therefore, the correlations of the prices measured between other cryptoassets and Bitcoin are significantly lower than one and equal to 0.2 in the case of Ripple.[2] If two coins with predetermined quantity paths were perfect substitutes, on the contrary, it would be difficult to explain why any news should influence their relative values. These news affect the relative values ​​of the cryptoassets of the real world is proof that they do not fit the assumptions of the result of uncertainty KW.

The philosophers distinguish a purely valid argument – the conclusion follows from the premises – from a valid argument, which is valid and has the true premises. Arguments that presuppose perfect substitutability among the cryptoassets may be valid, but they are not valid.


[1] I'm a Beam consultant.

[2] Charles Bovaird writes about Bitcoin and Ripple (XRP) in an article for Coindesk: "The two currencies are quite distinct, a situation detected by the fund manager of cryptocurrency Jacob Eliosoff, and this situation could help explain their weak price relationship Bitcoin and litecoin have different value propositions and target audiences separated by XRP. "

[Cross-posted from Alt-M.org]

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