A Lucas Critique to the Difficulty Adjustment Algorithm of the Bitcoin System

50 Pages Posted: 4 Jul 2019 Last revised: 14 Sep 2019

See all articles by Shunya Noda

Shunya Noda

Vancouver School of Economics, University of British Columbia

Kyohei Okumura

University of Tokyo, Graduate School of Economics, Students

Yoshinori Hashimoto

BUIDL, Ltd.

Date Written: June 26, 2019

Abstract

The design of the difficulty adjustment algorithm (DAA) of the Bitcoin system is vulnerable as it dismisses miners' response to the difficulty adjustment. We develop an economic model of the Proof-of-Work based blockchain system. Our model allows miners to pause operation when the expected reward is below the shutdown point. Hence, the supply of aggregate hash power can be elastic in the cryptocurrency price and the difficulty target of the mining puzzle. We prove that, when the hash supply is elastic, the Bitcoin DAA fails to adjust the block arrival rate to the targeted level. In contrast, the DAA of another blockchain system, Bitcoin Cash, is shown to be stable even when the cryptocurrency price is volatile and the supply of hash power is highly elastic. We also provide empirical evidence and simulation results supporting the model's prediction. Our results indicate that the current Bitcoin system might collapse if a sharp price reduction lowers the reward for mining denominated in fiat money. However, this crisis can be prevented through the upgrading of DAA.

Keywords: Blockchain, Proof-of-Work, Difficulty Adjustment, Mining, Market Design

JEL Classification: C61, D47, G20, L86

Suggested Citation

Noda, Shunya and Okumura, Kyohei and Hashimoto, Yoshinori, A Lucas Critique to the Difficulty Adjustment Algorithm of the Bitcoin System (June 26, 2019). Available at SSRN: https://ssrn.com/abstract=3410460 or http://dx.doi.org/10.2139/ssrn.3410460

Shunya Noda (Contact Author)

Vancouver School of Economics, University of British Columbia ( email )

6000 Iona Dr
Vancouver, British Columbia V6T 1L4
Canada

Kyohei Okumura

University of Tokyo, Graduate School of Economics, Students ( email )

Tokyo
Japan

Yoshinori Hashimoto

BUIDL, Ltd. ( email )

12-10, Sakuragaoka, Shibuya-ku
Neutrino
Tokyo, 150-0031
Japan

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