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A Structural Analysis of Bitcoin Cash’s Emergency
Difficulty Adjustment Algorithm
Vipul Aggarwal
Michael G. Foster School of Business, University of Washington
Seattle, Washington 98195
aggarv@uw.edu
Yong Tan
Michael G. Foster School of Business, University of Washington
Seattle, Washington 98195
ytan@uw.edu
Abstract
In this paper, we analyze the equilibrium behavior of cryptocurrency miners in the wake of
a major cryptocurrency fork. Miners are responsible for validating transactions and ensuring
smooth functioning of the cryptocurrency platform. Specifically, we are interested in their
strategic interactions with the incentives provided by the developers of the newly born minority
chain to prioritize its transactions over that of the dominant parent currency. We focus our
attention on the Bitcoin (BTC) fork of August 2017 that resulted in the birth of Bitcoin Cash
(BCH). BCH’s developers introduced emergency difficulty adjustment (EDA) algorithm to
incentivize miners to process BCH’s transactions over that of BTC’s. Based on the strategic
actions of the miners, EDA dynamically altered the difficulty adjusted profitability of BCH,
which resulted in miners exhibiting waiting (waiting for the EDA to trigger) and switching
(switching to mining BCH after EDA activation) intents on the BCH chain despite BTC’s much
1
higher market price. We use a two-step structural approach to estimate the dynamic mining
competition among miners for BTC and BCH blocks to uncover their profit motivations. Policy
and transition functions governing equilibrium behavior are estimated in the first stage. Using
a forward simulation procedure, we estimate the payoff parameters in the second stage. With
the help of publicly available chain data, we find competition among miners for BCH blocks
was a major contributor to profits during EDA-active periods. We also find that waiting was
beneficial. Contrary to available online evidence, switching had a negative effect on miners’
profits. Through our counterfactual simulations, we demonstrate BTC’s robust stability and
find that the implemented design of EDA resulted in maximal miners’ profits when compared
with other plausible designs. We also provide a comparative analysis of different EDA designs
with respect to developers’ tolerance for changes in the rewards schedule.
Keywords— cryptocurrencies, bitcoin fork, bitcoin cash, emergency difficulty adjustment, structural
modeling
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1 Introduction
Cryptocurrencies rely on computer code, secured through cryptography, to regulate money-creation, trans-
action, and spending mechanisms and as such, are developed in a fashion similar to software projects.
Bitcoin (BTC) is the most dominant and the oldest cryptocurrency and commands a 51% market share. It is
followed by other cryptocurrencies such as Ethereum, Ripple, Bitcoin Cash, Litecoin, etc. Many such pro-
jects are a result of collaboration efforts under the principles of Open Source Software (OSS) development.
As a consequence, cryptocurrency development witnesses forking activities, i.e. splitting of one software
project into two separate projects that share common codebase but differ in their future development and
economic aims, at regular intervals (Forkdrop 2018). Similarity with OSS ends at the development stage
and cryptocurrencies start resembling fiat currencies or tradeable tokens in the ensuing economic activities.
Their economic ecosystem comprises of currency users, traders, and miners. Miners are the back-end work-
ers who are responsible for validating the transactions occurring on the platform and thus, ensure smooth
functioning of the ecosystem. In August 2017, following years-long contentious debates among BTC stake-
holders, BTC fork was initiated that led to the creation of Bitcoin Cash (BCH). In this paper, we analyze the
strategic behavior of BTC and BCH miners in the aftermath of this very popular fork.
Miners are responsible for collecting all transactions originating on the cryptocurrency platform and
verifying whether their originators own the funds being transferred. The mining process is quite compet-
itive where miners compete to be the first in producing a valid block of verified transactions by solving a
cryptographic puzzle (proving whether validation services have been rendered correctly) using specialized
equipment and large amounts of electricity. Generally, miner with more powerful equipment has a higher
likelihood of winning but is not guaranteed to win. The winner is rewarded with the associated transaction
fees and a very substantial reward (also known as coinbase) for generating a block of validated transac-
tions. Efforts required to solve the cryptographic puzzle are correlated with the difficulty levels which are
dynamically decided by the rate of block generation in the recent past.
When BCH was created through the fork, it inherited, not only the transaction history of BTC chain, but
also its defining characteristics, such as its cryptographic puzzle and difficulty adjustment algorithm (DAA).
DAA is responsible for regulating the dynamic difficulty level of the puzzle and creates economically-
sensible incentives for miners. The difficulty is adjusted every 2016 blocks with the aim of maintaining
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a block generation rate of a block every 10 minutes. Since BTC and BCH shared the same cryptographic
puzzle and DAA, miners could effortlessly switch between the two depending on their expectations of prof-
itability. Being the dominant parent currency, BTC’s market price (price at which BTC is traded) was much
higher than BCH’s. However, BCH started its journey with the same difficulty level as BTC’s and hence,
was less profitable. To incentivize the generation of BCH blocks, its developers instituted the emergency
difficulty adjustment (EDA) algorithm. It was active from the day of fork, 1st August 2017, until 13th
November 2017. It reduced BCH difficulty for block number tby 20% if the time difference between the
(t−6)th block and the (t−12)th block was more than 12 hours.
Miners base their mining decisions on difficulty adjusted profitability index or DARI to decide which
coin’s chain is more profitable to focus on. Immediately after the fork, some miners could strategically mine
BCH so that the overall rate of BCH block generation would hit the EDA thresholds and reduce its difficulty.
Ideally, it was possible to reduce BCH’s difficult by 75%. Such difficulty changes would make BCH’s DARI
greater than BTC’s. As such, miners switched from mining BTC to BCH regularly based on profitability
calculations. These drops in difficulty, using EDA, were timed through an ostensible understanding among
major mining groups. Their goal was to cooperatively mine BCH in order to consecutively trigger EDA
a few times and then, engage competitively in mining BCH when it was relatively easy. This cooperation
worked as a signal for every other miner to wait until the difficulty dropped to the maximum possible level.
That is, some miners were willing to pay a waiting cost (e.g., idle mining equipment) by not mining BCH
to ensure EDA activation.
After EDA had reduced the difficulty to an acceptable level, miner were faced with a choice: to allocate
more mining power to higher-priced but more difficult BTC or to lower-priced but relatively easy BCH. A
miner could only generate a very few BTC blocks given its high difficulty. However, some rival miners
would switch to mining BCH resulting in less competition for these higher-priced BTC blocks. Conversely,
a miner could prefer BCH over BTC, albeit with high competition on BCH, to generate many lower-priced
but relatively easier BCH blocks. High competition on BCH was a resultant of influx of miners due to its low
difficulty. Consequently, EDA ensured BCH’s survival by incentivizing profit-seeking miners to contribute
their precious computational power to mining BCH. Figure 1a illustrates the effect of EDA through the
massive spikes in BCH mining during the periods EDA was active. Online observers and experts were
unclear whether switching to BCH after triggering EDA was beneficial or not for the miners because they
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were observed to switch even when BTC was more profitable and much more in demand (Song 2017c). This
has been attributed to the alleged presence of backroom subsidies for BCH.
Cryptocurrency mining is just a decade-old nascent industry where long-term implications of such phe-
nomenon are not very clear. We did not find any empirical academic literature examining such policy’s
impact (EDA). Thus, our goal is to investigate these mining dynamics and recover the profit parameters mo-
tivating the observed behavior. Our specific interests lie in ascertaining the switching incentive and waiting
cost that were observed during the EDA-active periods and seeking a deeper understanding of EDA-like
policy. Our empirical strategy involves setting up a theoretical model governing mining on the BTC and
BCH chains during the periods when EDA was active (1st August 2017 - 13th November 2017) and when it
was not (13th November 2017 - 16th February 2018). Thereafter, we recover the structural parameters of the
posited model using publicly available chain data. Since EDA was essential to keep the BCH chain oper-
ational, we run counterfactual policy simulations, using the recovered parameters, to estimate the expected
revenue gains/losses for different EDA designs that satisfy critical concerns of the developers.
Our dynamic model of mining assumes that miners’ strategic behavior is in line with Markov perfect
equilibrium (MPE) ,i.e., miners’ actions are only dependent on the values of their current states and their
private shocks (Maskin and Tirole 2001). These actions impact the commonly observed state variables such
as, difficulty levels, which affect future strategic interactions. Using models based on MPE is fraught with
computational difficulties owing to the load of computing the allowed equilibria in the theoretical model and
then, matching those equilibria to the ones in the data. This difficulty prohibits using Nested Fixed-Point
types of estimators (Rust 1987). We follow the economics literature in estimating dynamic games using
two-step estimators, based on Hotz et al. (1994), that make it possible to recover the model parameters
without solving for equilibria even once (e.g. Bajari et al. 2007, Aguirregabiria and Mira 2007, Pesendorfer
and Schmidt-Dengler 2008). These two-step estimators are built on the assumption that in equilibrium,
agents exhibit rational behavior conditional on their beliefs about competitors and environment. Therefore,
recovering the probability distributions governing what agents do during equilibrium is akin to recovering
their equilibrium beliefs. Imposition of the theoretical model’s restrictions on these beliefs allows us to
recover the structural parameters.
We follow the two-step estimator proposed by Bajari et al. (2007) to recover the model primitives for
mining during and after EDA. Using the computationally-lite counterfactual procedure of Benkard et al.
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(2010), we run policy simulations to estimate miners’ profits associated with other plausible EDA designs.
Our results indicate that competition among miners for BCH blocks was a big driver of profits during EDA-
active periods. As expected, waiting for the EDA to trigger is found to benefit miners overall. Contrary to
expectations, switching incentives enter negatively ,i.e. miners’ revenues were adversely affected because
of switching tendencies indicating inadequateness of the alleged subsidies. Our counterfactual exercises
illustrate the dominance of BTC via its stability for every plausible EDA design scheme. We also find that
the selected EDA configuration was optimal for the miners given the concerns of BCH’s developers about
its future. Our research sheds light on the impact of such interventions (EDA) after a fork and provides a
comparative analysis to understand their optimal designs.
In next section, we discuss BTC/BCH mining and the BTC-BCH fork in detail. We elaborate on our
theoretical model in the third section. Our empirical strategy is presented in the fourth section. In the fifth
section, we present our results and conclude in the sixth section.
2 Cryptocurrencies
In their seminal paper, Haber and Stornetta (1990) outlined the principles of blockchain technology, which
is a chronologically-chained collection of data blocks. Their distributed (multiple copies reside on different
nodes), decentralized (participating agents have equal voting rights), and append-only property (data can be
added but not removed) made them the preferred underlying technology for BTC (Conley 2017, Nakamoto
2008). BTC’s consensus mechanism, Proof-of-Work, enabled agents to agree on the state of the underlying
blockchain without requiring trust in any central authority.
For every initiated transaction, BTC/BCH client or wallet (software used to initiate transactions and
store BTC/BCH) will create a new set of private-public key pair. Public key is shared with the network and
private key is kept a secret. Using public key cryptography, BTC miners can verify whether the initiator
of the transaction is the actual owner of the coins being transacted as these coins are associated with the
hashed public key of the sender. After verifying whether the coins being sent are owned by the sender and
whether those coins have been spent already or not, information regarding amount to transfer and recipient’s
hashed public key is processed and the transacted amount is associated with the hashed public key of the
recipient. Effectively, transacting amount is referenced to the recipient’s hashed public key from that of the
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sender’s. Miners detect these initiated transaction requests from users, verify their information contents, and
add a block of validated transactions to the blockchain (Peck 2017a). Usually, every transaction includes
transaction fees which incentivizes the miner to include it into the block being processed. This entire process
of verification and block generation is referred to as mining.
The process of block generation results in creation of new coins (known as coinbase) which act as a
major incentive for participation in mining. During the period of our study, 12.5 coins of their respective
currencies were created for every valid block of BTC and BCH. After all the verified transaction are bundled
into a block, the current block’s header (which includes information about the transactions in the block)
and hash of the most recently generated block are hashed using the hashcash proof of work algorithm. A
cryptographic hash function, like hashcash-SHA2562, is a complex mathematical function which generates
a fixed length output for any data of arbitrary size and is designed to be a one-way function (very hard to
invert). The goal of this mining exercise is to find a hash value that is less than the publicly-known difficulty
target that all the BTC/BCH clients share. The winner (first miner to find the valid hash value) transmits
its proof or proof-of-work on the network for every other miner to verify and update their copies of the
underlying blockchains.
The difficulty target is a 256-bit number which is a measure of how difficult it is to find a hash value
below a given target. It is revised after every 2016 blocks in BTC to keep the rate of coin generation at
roughly a block every 10 minutes. If 2016 blocks are mined in less than two weeks, target is lowered to
increase the rate of difficulty for the next set of 2016 blocks (Figure 1c). The difficulty never changes by
more than a factor of 4. Since it is a append-only ledger, transactions once buried under enough number
of blocks (6 in BTC case) are considered confirmed and cannot be reversed. This irreversibility is also a
result of immense difficulty in computing valid proof-of-works (hash value below the target) which deters
malicious actors from attempting to modify the existing records (theoretically, a group of malicious actors
can capture 51% of the total network mining power and reverse the recorded transactions. This is referred
to as 51% attack and almost impossible to carry out.).
In the early days of Bitcoin mining, individual enthusiasts would use their personal computing resources
such as central processing units or graphics processing units to mine. However, with growing demand and
popularity, the level of difficulty has also risen by many orders of magnitude. It has led to establishment of
mining pools and usage of Application-Specific Integrated Circuits (ASIC) mining equipment (Pilkington
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2016). A mining pool is a collection of individual miners who pool in their computing resources to reduce
the volatility of their returns. Antpool, ViaBTC, BTC.TOP, BTC.COM, etc. are some of the prominent
mining pools. This mining equipment can be quite expensive and is a voracious consumer of electricity.
Energy-intensive nature of BTC mining adds significant costs to its production. Almost 80% of the mining
pools are located in China due to availability of cheap electricity. BTC.com, Antpool, BTC.TOP, and Vi-
aBTC possess more than the half of the global Bitcoin mining power (Wanlin 2018). Therefore, we focus
our analysis on their actions only. Mining pool with more powerful ASIC mining equipment can compute
trials of the proof-of-work faster than its rivals and thus, has a better chance of winning. However, such a
powerful mining pool is not guaranteed success in block generation due to inherent randomness owing to
brute-force calculations in proof creation.
The mining process for BCH is very similar to BTC’s as BCH inherited BTC’s characteristics such
as the SHA-2562based hashcash proof-of-work mechanism. BCH’s developers did modify the difficulty
adjustment algorithm for BCH. We elaborate on the new algorithm and its properties in the next subsection.
2.1 Bitcoin Fork
Nakamoto (2008) conceived BTC as a distributed, temper-proof, and decentralized peer-to-peer cryptocur-
rency. It did not require trust in third-party to perform verification. However, BTC was limited to processing
7 transactions per second. This was a resultant of BTC’s technical architecture that restricted the sizes of its
blocks to 1 MB and effectively, limited the number of transactions that could be accommodated in a single
block to roughly 1500-2200. In comparison, Visa could handle up to 25K transactions per second (Raul
2018). During higher network activity periods, block size limitation lead to slower confirmation times and
higher transaction fees.
BTC stakeholders could not agree on the means and methods to scale BTC’s throughput. Some of them
felt the need for larger block sizes (8 MB) to process greater number of transactions. Though it partially
solved the scaling issue, it created another problem with respect to centralization. Large blocks require
mining nodes to possess expensive storage and bandwidth facilities that was expected to disproportionately
affect the smaller miners and result in consolidation of mining power in the hands of big players. The core
developers were strictly opposed to such centralization of mining power in lieu of higher throughput. They
proposed their own scaling solution, however, the two groups could not reconcile. With the proposition of
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faster transaction processing times and lower fees, Bitcoin Cash was forked from the Bitcoin chain on 1st
August 2017.
Since BTC and BCH share the same codebase, BCH also inherited BTC’s hashing algorithm (hashcash
SHA-2562), its difficulty adjustment algorithm (DAA), and its transaction history. Initially, they shared the
same difficulty levels but BTC was priced much higher in comparison to BCH (Figure 1d,1c). To incentivize
mining on BCH chain, its developers proposed Emergency Difficulty Adjustment (EDA) algorithm, which
would lower the difficulty of BCH chain by 20% if the time difference between the 12th and the 6th blocks
leading up to the current block was greater than 12 hours (Song 2017a). This ensured that profit-maximizing
miners would allocate a majority chunk of their mining power to BCH when difficulty adjusted profitability
was in its favor (Song 2017b). EDA helped the newly born minority chain, BCH, to survive by garnering the
support of mining pools (Menegerian 2017). The inherited BTC difficulty adjustment algorithm (adjustment
after every 2016 blocks) was responsible for any upward revisions in BCH difficulty. BCH deprecated EDA
on November 13th 2017 and switched to a rolling DAA (BitcoinABC 2017). This algorithm was based on a
144-period simple moving average. The difficulty was adjusted every block, based on the amount of work
done for and the elapsed time of the previous 144 blocks.
Wild fluctuations in computation or mining hash power were observed between BTC and BCH during
the EDA-active periods (Figure 1b). Miners measure profitability in terms of difficulty adjusted rewards
index or DARI (Equation 1). Triggering of EDA would result in reduction of BCH difficulty. This would
increase BCH’s DARI and incentivize miners to allocate more hash power to BCH at the cost of BTC (Figure
1e). Influx of mining power resulted in higher competition among miners for the limited low-difficulty BCH
blocks. Such shifts, inadvertently, led to higher confirmation times on BTC network and also pushed up
BTC’s transaction fees as BTC users competed for the attention of reduced number of miners (Figure 1f).
Therefore, miners were faced with a choice: to switch chains by allocating more power to BCH (i.e., prefer
highly-competitive low-priced low-difficulty BCH blocks) or to keep their hash power focused on BTC (i.e.,
prefer high-priced high-difficulty BTC blocks with lower competition and higher transaction fees).
DARI =block reward in USD + transaction fees in USD
block difficulty (1)
Prior to actively mining on low-difficulty BCH blocks, miners need to trigger thresholding conditions
9
Figure 1: The plots for different states during the period of our study, August 2017 - February
2018 are presented here. Vertical line marks the deactivation of Emergency Difficulty Adjustment
algorithm.
(a) (b)
(c) (d)
(e) (f)
(a) Daily count of mined Bitcoin and Bitcoin Cash blocks. Before EDA was deprecated in mid-November,
BCH chain witnessed extreme mining where 2016 blocks would be mined within 2-3 days. (b) Hash-power
allocations for Bitcoin and Bitcoin Cash. (c) Difficulty Levels. (d) Price in USD. (e) Difficulty Adjusted
Reward Index for Bitcoin and Bitcoin Cash. (f) Average fees per transaction for Bitcoin and Bitcoin Cash.
10
for EDA. As such, their rate of BCH mining has to be sufficiently low irrespective of BCH profitability.
Some miners would mine BCH even during low DARI periods and trigger conditions for EDA activation
(Haywood 2017, Song 2017b) that would result in lowering of BCH difficulty. They would incur a waiting
cost by either not mining at all or mining lower than usual. This cost represents equipment idling due to
suboptimal usage of mining equipment. After suitable drops in BCH difficulty due to EDA, miners were
faced with the option to mine more of BCH and less of BTC. Many sections of miners chose to increase
their BCH mining at the cost of BTC’s even when BTC was more profitable (Song 2017c). Though, we
do not know of their exact motivations for switching, it has been attributed to possibility of unobservable
subsidies (Song 2017c). Thus, there seems to be a switching incentive to keep BCH operational for others
regardless of profitability.
These waiting and switching intents, though empirically observed, do not seem to be the result of
straightforward motivations. Prima facie, there appears to be value in waiting for the BCH chain to drop
in difficulty but value of directing more power to mine BCH at the cost of BTC is not clear. Mining pools
are comprised of individual miners who have different preferences over BTC and BCH. We abstract away
from their individualness and treat the outcomes of their collective preferences as the overall decision of the
mining pool. Our goal is to estimate the parameters associated with waiting cost and switching incentive
while accounting for miners’ strategic behavior and the dynamic changes in the BCH and BTC difficulty.
2.2 Data Sources
The data for our study has been generously provided by Blockchair (2018). The data consists of the entire
BTC and BCH blockchains right from their genesis blocks (the very first block in the blockchain). This
includes information such as timestamp of each block, name of the successful miner, number of transactions
in the block, total transaction fees, miner reward, and level of difficulty. We collected price-level and trading
data from CoinAPI (2018). Using their services, we aggregated price data from multiple exchanges such
as Bitfinex, CoinBase, OKCoin, Cexio, and Kraken. We aggregated data at 30 minute intervals ,i.e., the
number of coins mined by our selected mining pools in every 30 minute interval along with information
about market prices, difficulty levels, and transaction fees.
Electricity consumption is a significant cost factor, however, we do not have any reliable data on miners’
consumption levels. It is possible to approximate these costs using the level of difficulty and the number of
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coins mined. Majority of miners have set up operations in China where electricity is quite cheap. The rate
is estimated to be $0.04 per kilowatt-hour (Peck 2017b). Bitmain’s Antminer S9 is one of the most widely
used ASIC mining equipment consuming 1.5 kilowatt-hour and has a computation power of 14 terahashes
or 14 trillion hashes every second (Peck 2017b). The level of difficulty allows us to ascertain the required
hash rate to have a competitive shot at successful mining. For a Ddifficulty coin, D×232 expected hashes
are required. This can be used to approximate the number of mining equipment in service in a particular
period with difficulty D. Given the number of equipment in service, along with the electricity cost and time
to mine each block, we arrive at an approximate cost figure for mining BTC and BCH blocks.
Electricity Cost per time period (USD) =cost of running one machine per time period×
# of machines running
= 0.04 ×1800
3600 ×1.5×#blocks ×difficulty ×232
1800 ×14 ×1012 (2)
There are other expenses, such as coolant services, maintenance services, etc., which we assume scale
linearly with the number of mined blocks #blocks and are implicitly included in our formulation.
3 Model
We consider a theoretical model of i= 1,2,3,4,5,6forward-looking mining pools, namely, Antpool,
BTC.TOP, BTC.com, ViaBTC, Unknown, and Other. Unknown refers to mining pools or miners who chose
to hide their identities. Other constitutes all the remaining miners and mining pools. Time is discrete
and a single time period is an interval of 30 minutes. At the beginning of every time period t, miners
make a decision regarding their willingness to participate in mining BTC or BCH or neither or both. As
such, every miner draws private shocks, at the beginning of the time period, regarding mining feasibility
of BTC and BCH. We model their choices as a partial equilibrium, dynamic decision problem. In our
setup, miners decide on the number of blocks of each chain to mine; that is ni,t,btc ∈ {0,1, ..., Kbtc }and
ni,t,bch ∈ {0,1, ..., Kbch}. We use the terms miner and mining pool interchangeably.
Each forward-looking miner makes two decisions ni,t,btc and ni,t,bch to maximize its expected discoun-
ted profits in every time period t. Miner incurs computational costs while mining the said blocks. Inclusion
12
of coinbase reward and transaction fees brings revenue to the miner conditional on the market prices. Let χit
be the set of payoff-relevant state variables for miner iat time t, i.e., χit =sR
it , sC
it .sR
it is the set of state
variables which affect the revenue accrual to the miner such as market prices of mined coins and transaction
fees associated with mined blocks. sC
it is the set of variables affecting the cost such as difficult levels. The
reduced-form one-shot payoff function is defined as
Π(ni,t,btc, ni,t,bch , n−i,t,btc, n−i,t,bch , χit, it )=Πbtc + Πbch
=R(ni,t,btc, n−i,t,btc , sR
it )−C(ni,t,btc, n−i,t,btc , sC
it )
+i,t,btc +R(ni,t,bch, n−i,t,bch , sR
it )
−C(ni,t,bch, n−i,t,bch , sC
it ) + i,t,bch (3)
Miners’ per-period profit (3) comprises of revenues and costs associated with mining BTC and BCH.
R(·)is the revenue function and C(·)is the cost function. it = (i,t,btc , i,t,bch)∈R2is a private bivariate
profit shock that miners receive every period. These shocks or structural errors are independent and identic-
ally distributed, and drawn from a known bivariate distribution, F(i|χit )with support i⊂R2. These
shocks can represent miners’ private information about hash power contribution of different pool members
or information regarding profit distribution among pool members or the inherent randomness in mining. The
per-period payoff is parametrically defined as follows:
Πi(ni,t,btc, ni,t,bch , n−i,t,btc, n−i,t,bch , χit, i,t,btc , i,t,bch;θ) = eπbtc
i(ni,t,btc, n−i,t,btc , χit;θ)
+i,t,btc.1{ni,t,btc >0}+eπbch
i(ni,t,bch, n−i,t,bch , χit;θ) + i,t,bch .1{ni,t,bch >0}
−ψ1.1{Waitingt= 1}+ψ2.1{Switchingt= 1}(4)
waiting =
1,if edat= 1, ni,t,bch +n−i,t,bch ≤1
0,otherwise
(5)
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switching =
1,if edat= 1, ni,t,btc ≤ni,t−1,btc, ni,t,bch >0, ni,t,bch ≥ni,t−1,bch
0,otherwise
(6)
eπbtc
i(ni,t,btc, n−i,t,btc , χit;θ) = 12.5×ni,t,btc ×pricet,btc ·θ1−12.5×n−i,t,btc ×pricet,btc ·θ2+
feest,btc ×ni,t,btc ×pricet,btc ·θ3−feest,btc ×n−i,t,btc ×pricet,btc ·θ4−miningCostt,btc ·θ5(7)
eπbch
i(ni,t,bch, n−i,t,bch , χit;θ) = 12.5×ni,t,bch ×pricet,bch ·θ6−12.5×n−i,t,bch ×pricet,bch ·θ7+
feest,bch ×ni,t,bch ×pricet,bch ·θ8−feest,bch ×n−i,t,bch ×pricet,bch ·θ9−miningCostt,bch ·θ10 (8)
The per-period payoff function (4) represents the net revenue that accrues to the miner ifrom sim-
ultaneously mining on BTC and BCH chains. BTC’s (7) and BCH’s (8) profit functions have similar
specifications. The profit from mining on each chain increases linearly in the number of mined blocks.
Every block carries a reward of 12.5 coins of the underlying chain. 12.5×ni,t,btc ×pricet,btc ·θ1and
12.5×ni,t,bch ×pricet,bch ·θ6is the revenue earned by miners through coinbase rewards for BTC and BCH
respectively. They face competition from each other. The erosion of profits due to competition is quantified
by 12.5×n−i,t,btc ×pricet,btc ·θ2and 12.5×n−i,t,bch ×pricet,bch ·θ7. Transaction fees incentivize miners
further, in addition to coinbase rewards, to allocate precious mining power and enter additively into the profit
function as feest,btc ×ni,t,btc ×pricet,btc ·θ3and feest,bch ×ni,t,bch ×pricet,bch ·θ8. The fees are given per
block in every time period. Miners compete on the basis of fees as well and this part of competition reduces
profits by feest,btc ×n−i,t,btc ×pricet,btc ·θ4and feest,bch ×n−i,t,bch ×pricet,bch ·θ9. We show how to
calculate mining costs in Equation (2). It is the cost of operating specialized equipment for mining ni,t,btc
(or ni,t,bch) blocks at the given difficulty levels.
Cost associated with waiting on the BCH chain during the EDA period is represented by ψ1. Our
formulation (5) of waiting is inspired from the observations in data during periods preceding EDA activation.
We assume that the miner is waiting for the BCH difficulty to drop if the collective number of BCH blocks
mined during the EDA periods is less than or equal to 1. This cost denotes expenses related to idle equipment
due to lower than usual mining rate. Lastly, ψ2is the value derived from incentives for switching from BTC
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chain to BCH chain during the EDA period. We assume that miner has switched if its number of mined
BTC blocks are less than or equal to previous time period’s and the number of BCH’s blocks are positive
and more than or equal to previous time period’s. This captures the presence of backroom subsidies, if any,
to justify the rational behind switching.
Ideally, miners are required to wait until 100 new blocks have been added to the chain after their
block before they can monetize their coinbase rewards and transaction fees by selling them on the sec-
ondary market (coin exchanges). Since, we do not know the actual time of their sale (it cannot be traced
on the blockchain either), we assume that they are able to sell in the same time period. Thus, the struc-
tural parameters defined in our model for mining during EDA can be succinctly represented by the vector,
θ=θ1, θ2, θ3, θ4, θ5, θ6, θ7, θ8, θ9, θ10, ψ1, ψ2.
In the BTC and BCH mining process, difficulty changes are a function of the collective mining rate in
the recent time periods. Higher rate of mining leads to upward adjustment in the difficulty levels and vice
versa to maintain a constant rate of mining in the long run. Introduction of EDA led to one-way downward
difficulty adjustments on the BCH chain during the time EDA mechanism was active. These difficulty levels
are the dynamic variables that are affected by miners’ actions and eventually, affect their future profits.
Given an initial state χit at time t, the firm’s expected discounted profits, before the realization of private
shocks, i,t,btc and i,t,bch, are given by
E∞
X
τ=t
βτ−t·Πi(ni,τ,btc , ni,τ,bch , n−i,τ,btc, n−i,τ,bch, χiτ , i,τ,btc, i,τ,bch)χit,(9)
where β∈[0,1) is the discount factor. The goal of miner iis to maximize its expected discounted profits,
taking the actions of rival miners as given. The expectation in (9) is taken over i’s private shocks and other
firms’ actions in time period tas well as over the future values of state variables, private shocks, and miners’
actions.
We focus on pure strategy Markov Perfect Equilibria (MPE) in specifying the equilibrium behavior.
Miners follow anonymous, symmetric, and Markovian strategies ,i.e., miners’ actions depend only on the
current state vector and their individual private shocks. Let Sibe the state space of all possible values of
χit for miner iand Sbe the collection of Si. Let Ni⊂N0×N0denote the choice set for miner i,i.e.,
(ni,t,btc, ni,t,bch )∈Ni. Also, t⊂R×Ris the collection of i.i.d. bivariate private shocks (i,t,btc, i,t,bch)
15
for all miners at time t. The markov strategy profile for miner ican be characterized as a function σi:
S×R×R→Nithat maps the payoff-relevant state variables and private information to the set of possible
choices. The profile of Markov strategies is denoted by σ= (σ1, ..., σ6).
Given the Markov profiles σ, expected profit of miner iin state χ(dropping the time subscripts) is
defined recursively as
Vi(χ;σ) = EΠi(σ(χ, ), χi, i) + βEVi(χ0;σ)|χ, σ(χ, )|χ(10)
Viis the miner i’s ex-ante value function. It reflects expected profits before the private shocks are drawn.
σ(χ, )is the action profile (σ1(χ, 1), ..., σ6(χ, 6)). The inner expectation is with respect to future value
of state variable, χ0, conditional on the current state χand the action of all the firms in current time period.
The outer expectation is over the current values of the private shocks.
An action profile σis a MPE if miner ihas no incentive to unilaterally deviate from its strategy σiwhile
the opponent miners are playing by σ−i. This implies that there is no alternative Markov strategy eσithat
will yield a higher ex-ante value function than σi. Therefore, σis a MPE if for all miners i, states χ, and
alternative Markovian strategies eσi,
Vi(χ;σi, σ−i)≥Vi(χ;eσi, σ−i)(11)
≥EΠi(eσi(χ, i), σ−i(χ, −i), χi, i) +
βEVi(χ0;eσi, σ−i)|χ, eσi(χ, i), σ−i(χ, −i)|χ(12)
After EDA was deprecated, BCH switched to a new difficulty adjustment algorithm. The new algorithm
smoothed the future estimates of difficulty levels by using a simple moving average of the hash power
contributed to the BCH blockchain for the previous 144 blocks. The purpose of this new algorithm was
to avoid wild fluctuations in difficulties (due to EDA) that led to erratic block generation. Also, post-EDA
period coincided with the infamous cryptocurrency boom. This implies that during-EDA and post-EDA
equilibria will be different. The post-EDA period did not see any wild fluctuation in the rate of mining and
hash power contributions. As such, we estimate the structural parameters for the two equilibria separately.
The post-EDA equilibrium’s structural parameters, θ0, do not include the waiting, ψ1, and the switching, ψ2
16
parameters. Equation (13) represents the payoff function for the post-EDA periods.
Πini,t,btc, ni,t,bch , n−i,t,btc, n−i,t,bch , χit, i,t,btc , i,t,bch;θ0=eπbtc
ini,t,btc, n−i,t,btc , χit;θ0
+i,t,btc.1{ni,t,btc >0}+eπbch
ini,t,bch, n−i,t,bch , χit;θ0+i,t,bch .1{ni,t,bch >0}
(13)
Though studies have proven the existence of MPE in general Markovian games (Dutta and Sundaram
1998), however, little is known about equilibrium existence in a dynamic game with continuous states as
ours. As such, we assume that an MPE exists and the same MPE is expected to be played in all time periods.
4 Empirical Strategy
Searching for an equilibrium in dynamic games is computationally prohibitive and mathematically intract-
able. Maximum likelihood approaches to estimate dynamic game parameters are computationally very
demanding as the estimation procedure needs to solve for an equilibrium at every guess of parameters when
even solving for an equilibrium for a single set of candidate values is computationally prohibitive. Moreover,
existence of multiple equilibria complicates the procedure further as the econometrician is required to com-
pute the set of all equilibria and then, match these equilibria to the data (Ryan 2012).
We follow the two-step estimation approach to alleviate these computational issues. These methods do
not require one to solve the theoretical equilibrium model explicitly even once (Hotz et al. 1994). The two-
step empirical strategy posited in Bajari et al. (2007), henceforth referred to as BBL, is our preferred method
to solve the miners’ dynamic decision-making problem. In the first step, we compute the reduced-form es-
timates of the miners’ policy functions. We do not impose any structure here and compute the estimates
with a flexible specification. We also recover the probability distribution governing the evolution of relevant
state variables using standard time series methods. This avoids computing the equilibrium of the game be-
cause the policy functions are estimated from the actual equilibrium that is played in the data. Therefore, by
estimating the probability distributions for actions and states, we ultimately recover the miners’ equilibrium
beliefs because they are expected to have correct opinions about their environment and competitors in an
equilibrium model. In the second step, we impose optimality conditions (11) to recover the structural para-
meters through a minimum distance estimation routine. We simulate the ex-ante value functions using the
parameters recovered in first stage of BBL. We assume that the data follows a first-order Markov process,
17
are generated through a single MPE, and all the miners expect the same equilibrium to be played in all time
periods.
4.1 First-Stage Estimation
Let φbe the vector of all first stage parameters. φincludes the reduced-from policy function coefficients
and the coefficients of the transition functions for the exogenous state variables. The estimated coefficients
in φare tabulated in the appendix.
4.1.1 Policy Functions
We estimate the policy functions dictating the decision to simultaneously mine on the BTC and BCH block-
chains. We model the BTC and BCH decision-making process as a bivariate ordered probit model. The
choice set for BTC is ni,t,btc ∈ {0,1,2,3,4,5,6,7}. Though, the range for mined BCH blocks goes from 0
to 17, however, values above 10 have little empirical support. Therefore, we assume 11 ordered categories,
ni,t,bch ∈ {0,1,2,3,4,5,6,7,8,9,10}, by censoring ni,t,bch >10 observations to 10.
Let Wi,t,btc and Wi,t,bch be the vectors of BTC’s and BCH’s policy-relevant state variables. These
vectors consists of their respective prices, difficulty levels, transaction fees, lagged decisions for both chains,
EDA-active period, price ratio, and difficulty ratio. We also include miner fixed effects. A miner’s decision
depends on the values of the latent variables, y∗
i,t,btc and y∗
i,t,bch, which are determined by the vectors Wi,t,btc
and Wi,t,bch respectively.
y∗
i,t,btc =φbtcWi,t,btc +ηi,t,btc
y∗
i,t,bch =φbchWi,t,bch +γy∗
i,t,btc +ηi,t,bch (14)
We follow the maximum likelihood procedure outlined in Sajaia (2009) to estimate the index coefficients
and the cutoff points (BTC has 7 and BCH has 10). γallows for the potential endogeneity of the two
outcomes through the exclusion restriction on the instrument variable, lagged BTC count, which does not
appear in Wi,t,bch. Since regularity conditions in BBL require consistent estimates in the first stage, inclusion
of γserves to improve the model fit without violating consistency. The error terms, ηi,t,btc and ηi,t,bch are
distributed as bivariate standard normal with correlation ρ. The estimated cutoffs, c1,1, c1,2, ..., c1,7for BTC
18
and c2,1, c2,2, ..., c2,10 for BCH, determine the mining decisions where every cutoff value corresponds to the
mining outcomes (Equations 15,16). We try different specifications of the vectors Wi,t,btc and Wi,t,bch and
select the best fit based on AIC values.
ni,t,btc =
0,if y∗
i,t,btc ≤c1,1
1,if c1,1< y∗
i,t,btc ≤c1,2
...
7,if c1,7< y∗
i,t,btc
(15)
ni,t,bch =
0,if y∗
i,t,bch ≤c2,1
1,if c2,1< y∗
i,t,bch ≤c2,2
...
10,if c2,10 < y∗
i,t,bch
(16)
4.1.2 Transition Equations
The set of exogenous state variables in χtconsists of pricebtc,pricebch,transaction feesbtc ,transaction feesbch,
and an indicator variable denoting whether EDA was active in that time period or not. The prices for BTC
are modeled using a GARCH(1,1) process and ARMA(1,1) process for others. We use the logarithm of the
ratio of current time’s value to last time’s value as the dependent variables in ARMA and GARCH models.
Evolution of EDA is deterministic. EDA was activated with the BTC fork and deactivated on November
13th 2017.
pricebtc,t ∼(i.i.d.)N0, ν2
1,t
ν2
1,t =ζ1,1+ζ1,2price2
btc,t−1+ζ1,3ν2
1,t−1(17)
ν2,t ∼(i.i.d.)N0, κ2
1
pricebch,t =ν2,t +ζ2,1pricebch,t−1+ζ2,2ν2,t−1(18)
ν3,t ∼(i.i.d.)N0, κ2
2
transaction feesbtc,t =ν3,t +ζ3,1transaction feesbtc,t−1+ζ3,2ν3,t−1(19)
19
ν4,t ∼(i.i.d.)N0, κ2
3
transaction feesbch,t =ν4,t +ζ4,1transaction feesbch,t−1+ζ4,2ν4,t−1(20)
4.2 Second-Stage Estimation
In the first stage, we recover the parameters ˆ
φof the reduced-form policy functions governing miners’
mining decisions and transition equations for the evolution of exogenous state variables assuming first-order
Markov processes. The estimated policy functions inform us about the beliefs of miners in equilibrium and
how they will respond in a given market condition. In an equilibrium model, we assume miners have rational
beliefs about state transitions and the actions of their rivals. We can use estimated ˆ
φto simulate many paths
of plays starting from different market conditions. Therefore, we can effectively simulate miners’ reactions
under different policy regimes for the same market conditions.
We use these simulations to construct empirical estimates of the ex-ante value function. Then, we use
the equilibrium condition (11) to form the minimum distance criterion function to recover the underlying
structural parameters. θ(or θ0) denotes the set of structural parameters that needs to be estimated. We will
use the subset of the estimates ˆ
φfrom first-stage to approximate the MPE profile σ.ˆσis the actual policy
employed by miners to make mining decisions and is an approximation for σ.eσis the behavior under
alternative policy (generated via perturbation of ˆσ). Using θ(or θ0) and ˆσ, we can simulate ex-ante values
for any miner istarting with initial conditions χt1.
V(χi,t1; ˆσ, θ) = E"T
X
τ=t1
βτ−1Πi(ˆσ(χτ, τ), χτ, τ;θ)χt1,ˆσ#
=1
S
S
X
s=1
T
X
τ=t1
βτ−1Πi(ˆσ(χs
τ, s
τ), χs
τ, s
iτ ;θ)(21)
where we simulate Spaths of play until T time periods. Superscript sdenotes different paths generated
starting from χt1. We repeat this procedure Btimes with different χ. To compute ex-ante value functions
for the alternative policies eσ, we repeat the above procedure using eσin place of ˆσ. We generate 300 alternate
polices with additive (15) and multiplicative (285) perturbations following the recommendations in Srisuma
(2013). Our linear-in-parameters specification of the one-shot profit function results in massive computa-
20
tional saving as we only need to forward simulate once. The simulated V(·; ˆσ, θ)and V(·;eσ, θ)can then be
evaluated for different candidate values of θ.
BBL posits that in equilibrium, actual policy is always weakly preferred to other feasible alternatives at
every other state. Therefore, the policy ˆσifor miner iwill yield a weakly higher value of expected present
discounted profits than any other policy eσiwhen the rival miners are playing by ˆσ−i. The differences in
value functions generated by these two class of policies, actual and alternative, are used to estimate the
structural parameters. Given Binequalities with different initial conditions (χb
t1), we minimize the sum of
squared negative deviations from the equilibrium play. In effect, our simulated minimum distance estimator
minimizes the violations of the optimality condition through the objective function, Q(θ), defined as
Q(θ) = 1
B
B
X
b=1 min nViχb
t1; ˆσ, θ−Viχb
t1;eσi,ˆσ−i, θ,0o2
(22)
A positive value of the minimum distance, Q(θ), at ˆ
θsignifies that at least one miner has a profitable
deviation. We include all but 151 observed states in our simulation procedure. We use them as the starting
values for the ex-ante value function simulations. We simulate each inequality 300 times for 100 time
periods.
In the context of multi-player games, identification of structural parameters requires some strong re-
strictions. We make a zero-profit assumption for the cases with zero BTC and zero BCH (Pesendorfer and
Schmidt-Dengler 2003, 2008).
eπbtc
i(ni,t,btc, n−i,t,btc , χit) + i,t,btc = 0 if ni,t,btc = 0 ∀i, t
eπbch
i(ni,t,bch, n−i,t,bch , χit) + i,t,bch = 0 if ni,t,bch = 0 ∀i, t (23)
Our identification scheme relies on exploiting the temporal variations in miners’ decisions throughout the
observation period. In the period of our study, spanning 56,196 miner-time period observations, the observed
price volatility created conditions where one coin was more profitable than the other. Exogenous variation
in the transactions fees, which is reflective of varying investor/speculator appetites, varied the profitability
further and helps to identify the utility parameters.
21
5 Results
The goal of this study is to investigate the driving forces behind the observed mining decisions made by
BTC and BCH miners immediately after the contentious fork of August 2017. Introduction of EDA to BCH
blockchain, immediately after the fork, created incentives for miners to prefer BCH over BTC. During the
EDA period, miners’ responses were characterized by waiting and switching behavior whose net impact is
of main academic interest (Equation 4). We also estimate the profit parameters for the post-EDA period
(Equation 13) separately.
First-stage results are presented in the Appendix in Table 6 and Table 7. In the second stage, we sampled
9366 inequalities (out of a total sample of 9517). Each inequality comprises of a randomly sampled miner,
starting time period, tuple of state variables (prices, fees, difficulty levels) for that time period, and the
set of alternative policies. We simulated 300 paths of play for every inequality for 100 time periods each
for actual and all the alternative policies. The discount factor βwas set to 0.9. The standard errors for
second stage were calculated by bootstrapping using 125 replications with replacement. Table 1 presents
our estimates of structural parameters for during EDA and post-EDA periods. The parameter vectors, θ(and
θ0) are normalized by setting ||θ|| = 1 (and ||θ0|| = 1) where || · || is the standard L2norm (Ellickson et al.
2013).
During the periods when EDA was active, we find BTC’s coinbase rewards (θ1)contributed substantially
to miners’ profits. High transaction fees incentivize miners to contribute their hash power to BTC mining
during high demand periods. However, miners find it to affect their overall profits negatively (θ3). Miners
are quite sensitive to competition for BTC blocks with positive and statistically significant (θ2, θ4). Cost of
mining BTC (θ5)is statistically insignificant.
Like for BTC, we find mining rewards (θ6)contribute to miners’ profits and transaction fees (θ8)has a
negative effect. However, competition is found to be of immense help to the miners. Coefficients on rivals’
transaction fees (θ9)and cost of competition (θ7)are strongly negative. This implies that miners benefited
from each others’ participation in mining BCH blocks. As miners’ actions allowed them to reduce BCH
difficulty at will (using EDA) and upward adjustments in difficulty were only allowed after 2016 blocks,
miners’ engaged in intense BCH mining during EDA-triggered low-difficulty periods. This allowed them to
repetitively hit EDA threshold leading to many cycles of mining frenzy where 2016 blocks were mined in a
22
Table 1: Estimates for the structural parameters during EDA and post-EDA.
Parameters During EDA (θ)Post-EDA(θ0)
Coinbase Rewardbtc (θ1;θ0
1) 0.1307 0.0819
(0.0015) (0.0037)
Competition Cost Rewardbtc (θ2;θ0
2) 0.2424 0.0256
(0.0059) (0.0041)
Transaction Feesbtc (θ3;θ0
3)−0.2127 −0.0277
(0.0082) (0.0129)
Competition Cost Feesbtc (θ4;θ0
4) 0.3466 0.1469
(0.0125) (0.0145)
Mining Costbtc (θ5;θ0
5) 0.0014 0.9753
(0.0035) (0.0041)
Coinbase Rewardbch (θ6;θ0
6) 0.2366 0.1252
(0.0134) (0.0235)
Competition Cost Rewardbch (θ7;θ0
7)−0.5152 0.0267
(0.0097) (0.0189)
Transaction Feesbch (θ8;θ0
8)−0.197 −0.0127
(0.0211) (0.0074)
Competition Cost Feesbch (θ9;θ0
9)−0.1539 0.0282
(0.0168) (0.0062)
Mining Costbch (θ10;θ0
10)−0.0275 0.0145
(0.0344) (0.0069)
Waiting Cost (ψ1)−0.605 n.a.
(0.0108) n.a.
Switching Incentive (ψ2)−0.0733 n.a.
(0.0132) n.a.
Note. Standard Errors in paranthesis.
matter of days as opposed to 2 weeks (Figure 1a).
Not only did the miners benefit from competition, but they also benefited by waiting (ψ1)for the BCH
difficulty to drop. Negative waiting cost (ψ1)implies that deliberate reduction in the rate of BCH mining to
enable difficulty reductions was helpful to the miners. This is akin to lowering the entry barrier to participate
in BCH mining. However, contrary to miners’ expectation about switching, we find that their profits were
impacted negatively as ψ2is negative and statistically significant. Miners demonstrated switching to BTC,
irrespective of profitability, during EDA periods for the alleged BCH subsidies. As such, they forwent the
lucrative BTC blocks leading to an overall dent in the profits. Cost of mining BCH (θ10 )is insignificant.
After EDA was deactivated, we find BTC’s coinbase rewards (θ0
1)become more economically-significant
23
contributor to profits in relation to the cost of competition (θ0
2)which is still positive. One’s own transaction
fees (θ0
3)has a negative effect whereas the coefficient for competition in fees (θ0
4)is still positive. Cost of
mining BTC (θ0
5)is extremely high during the post-EDA period. This is corroborated with observational
evidence owing to high demand during that time (Nov 2017 - Feb 2018) which pushed up the BTC block
generation rates. This led to many upward revisions in difficulty (Figure 1c).
We find quite a contrast in the BCH parameters after EDA was deactivated. Competition for coinbase,
which was very useful during EDA, is statistically insignificant now (θ0
7). We find coefficient for transaction
fees is insignificant (θ0
8)as well. Rivals’ transaction fees (θ0
9)decrease profits now as opposed to being
helpful during EDA. Cost of mining BCH (θ0
10)becomes positive and statistically significant. Coefficient
for coinbase rewards (θ0
6)is still positive.
5.1 Model Fit
We find our estimated model performs well during simulation runs. We contrast the actual rate of block
generation with the outcomes using our model. Figure 2 presents a succinct overview of its effectiveness in
predicting the mining decisions. Model simulations are implemented via the forward simulation approach
of Benkard et al. (2010).
5.2 Counterfactual Policy Simulations
BCH developers introduced EDA with the intent to motivate miners to contribute their hash power to the
newly born minority BCH chain over BTC. However, their reasons to prefer the implemented design for
EDA, 20% difficulty reduction after a 12 hours gap, is not very clear. Coinbase rewards are halved after
every 210,000 blocks to keep the underlying currency’s inflation in check by lowering the supply of new
coins (Nakamoto 2008). Halved rewards would adversely affect individuals’ incentives to participate in
mining. As such, there is a tension between miners’ goals (maximize revenues) and BCH developers’
(survival of BCH). We run this set of counterfactual simulations to ascertain the comparative effectiveness
of the chosen EDA design with respect to other possible schemes from the perspectives of miners and
developers. We also compare the net revenue accrual to miners over different EDA designs. We look to the
forward simulation procedure elaborated in Benkard et al. (2010) and applied by Blevins (2016) to estimate
24
Figure 2: Actual vs Simulated number of mined blocks for BTC and BCH during and after EDA.
Vertical line marks the deactivation of Emergency Difficulty Adjustment algorithm.
(a) BTC blocks.
(b) BCH blocks.
these counterfactuals. This approach does not require one to solve the computationally intractable dynamic
model.
Simulated counts of mined BTC blocks, BCH blocks, advancement in halving of rewards, and the
accrued net revenue to miners are presented in Tables 2, 3, 4 and 5 respectively. Our simulations indicate
BTC’s unwavering dominance even after the BTC-BCH split. BTC block generation remains robust to
almost all the configurations of EDA except for the most extreme ones (e.g., difficulty reductions after every
3 hours). Overall level of dispersion (standard deviation) in the block counts is 242 which drops to 132 after
removal of the extreme 3 hours regime. BCH’s standard deviation, on the other hand, is 12,911 and 5,460
blocks respectively. This simulation result highlights BTC’s overall stability, irrespective of BCH’s choice
of incentives to miners.
Simulations for BCH mining under different EDA designs display very dispersed counts. Extreme
design configurations, such as, 20-50% difficulty adjustment after every 3 hours or 40-50% after 6 hours,
25
Table 2: Simulated counts of mined BTC blocks during the EDA-active periods for different EDA
designs.
Reduction Factor
50% 40% 30% 20% 10%
Time Difference (in hours)
3 14718 14862 14992 15086 15172
6 15262 15309 15349 15366 15430
9 15405 15430 15440 15467 15554
12 15467 15489 15530 15562 15601
15 15524 15555 15585 15637 15643
18 15606 15607 15645 15678 15684
21 15639 15652 15663 15723 15706
24 15690 15712 15720 15748 15736
Note. Highlighted cell represents the count of BCH blocks for the actual EDA design.
Table 3: Simulated counts of mined BCH blocks during the EDA-active periods for different EDA
designs.
Reduction Factor
50% 40% 30% 20% 10%
Time Difference (in hours)
3 78359 64932 53176 41088 31453
6 41538 36315 30549 25930 21257
9 31442 28508 24862 21741 19848
12 28524 25600 22378 20417 19255
15 26475 24055 21217 19423 18370
18 24582 22638 20485 19208 17784
21 23274 22054 20032 18696 16985
24 23082 21638 19313 17945 16371
Note. Highlighted cell represents the count of BCH blocks for the actual EDA design.
26
will hasten the arrival of the day when mining rewards would be halved. Ideally, a block should be generated
every 600 seconds. For extreme designs, we find that almost 2x-4x BCH blocks would have been mined in
comparison to the actual design’s simulated rate, which would advance halving of rewards by another 4-12
months (Table 4). However, it would have resulted in a net revenue increment of up to 34% (Table 5) for the
miners.
Table 4: Halving of BCH rewards would be advanced by the above number of months for different
EDA designs.
Reduction Factor
50% 40% 30% 20% 10%
Time Difference (in hours)
314.19 11.19 8.55 5.84 3.69
65.95 4.78 3.48 2.45 1.40
93.68 3.03 2.21 1.51 1.09
12 3.03 2.38 1.65 1.21 0.95
15 2.57 2.03 1.39 0.99 0.76
18 2.15 1.71 1.23 0.94 0.62
21 1.85 1.58 1.13 0.83 0.45
24 1.81 1.49 0.97 0.66 0.31
Note. Highlighted cell represents the count of BCH blocks for the actual EDA design.
Given the tussle between developers and miners’ goals, we are also interested in EDA regimes which
would have resulted in higher or equivalent profits for the miners while satisfying the developers tolerance
for over-mining. Ideally, BTC and BCH should be mined at an equal rate of a block every 10 minutes. 10%
difficulty reduction after 24 hours would have resulted in an almost similar rate of BCH block generation as
BTC but 2.5% ($26.7 M) lesser net revenue for the miners. We can also estimate net revenues for equivalent
EDA designs that would result in a similar advancement in halving of block rewards. Implemented EDA
design advanced the halving date by 1.21 months. 30% difficulty reductions after 18 hours would have
resulted in advancement by 1.23 months but miners’ revenues would have reduced by 0.8% ($8.43 M).
The simulated BCH count for the actual EDA design can also be viewed as its developers’ threshold for
the level of over-mining. Therefore, if they were to reduce their tolerance for halving by one week, miners
profits would have reduced by 1.18% ($12.55M). On the other hand, if they were willing to advance the
halving by another week, we find miners’ profits would have increased by 0.6% ($7.29M). Similar exercise
at a month level indicates a 2.51% ($26.7 M) drop in profits for lower tolerance and a 1.81% ($19.33
27
Table 5: Simulated total revenue, in millions of USD, for mining BTC and BCH blocks during the
EDA-active periods for different EDA designs.
Reduction Factor
50% 40% 30% 20% 10%
Time Difference (in hours)
31427.60 1350.69 1277.43 1198.51 1135.85
61203.12 1173.17 1134.14 1103.99 1076.03
91121.31 1105.20 1084.31 1072.27 1061.72
12 1096.17 1081.52 1066.24 1064.98 1051.18
15 1084.11 1071.89 1059.91 1059.83 1044.49
18 1074.43 1063.44 1056.55 1058.94 1044.02
21 1065.80 1061.10 1054.74 1058.34 1040.57
24 1068.65 1064.27 1052.43 1055.43 1038.28
Note. Highlighted cell represents the count of BCH blocks for the actual EDA design.
M) increment in profits for higher tolerance. In summary, we find that perturbations of BCH developers’
tolerance for over-mining and advancement of halving of rewards does not lead to wild fluctuations in
miners’ profits. The actual EDA design was found to result in maximal miners’ profits when compared with
other equivalent designs (resulting in similar halving dates).
6 Conclusions
Over the last couple of years, cryptocurrency valuations have wildly fluctuated between $100 B and $
800 B. Their volatility and sky-high valuations have piqued the interest of everyone in industry, academia,
and government. Many new currencies have been proposed which aim to provide lightning-fast payments
facilities, smart contracts, utilization of idle computing resources, data storage, etc. Quite a few of the
proposed currencies are derivatives of older currencies and have been created via code forks. The dynamic
ecosystem developing around cryptocurrencies will lead to more code forks and increase the limelight on
role played by incentives like EDA.
In this paper, we investigate a very popular cryptocurrency fork that resulted in the creation of Bitcoin
Cash from Bitcoin. We are specifically interested in the introduction of Emergency Difficulty Adjustment
(EDA) algorithm to the forked BCH chain. Since BTC and BCH shared the same difficulty algorithms,
EDA was introduced to incentivize miners to process BCH’s transactions over those of the more popular
28
and dominant BTC’s. We aim to estimate the structural parameters that motivate the observed strategic
behavior of the forward-looking miners during and after EDA using the two-step estimator of Bajari et al.
(2007). We use the publicly-available chain data to find that competition between miners for BCH during
EDA periods was immensely useful. We also find that reducing BCH mining output while waiting for
EDA to reduce BCH’s difficulty lead to higher miner profits. However, miners’ tendency to switch chains
(from BTC to BCH) had a overall negative impact indicating the unsatisfactoriness of subsidies. Through
our counterfactual policy simulations, we demonstrate the robust stability of BTC in the face of a very
contentious fork. We also find implemented EDA design was optimal with respect to miners’ profits given
BCH developers’ halving concerns.
Our work, to the best of our knowledge, is the first to investigate the dynamic changes in the eco-
nomic ecosystem surrounding a cryptocurrency fork. Our structural analysis uncovers the decision-making
mechanism during the introduction of emergency difficulty adjustment algorithm as well as afterwards. We
believe cryptocurrency developers would find our research helpful in understanding economic implications
of incentives like EDA and their overall impact on participating miners’ profits in comparison to their cur-
rency’s rewards schedule. Using our analysis, individuals and groups involved in mining can benefit by
making better-informed decisions when faced with competing cryptocurrencies.
We make some simplifying assumptions in our modeling which also provide avenues for future research.
In our formulation, we assume all profits are realized in the same time period. However, many miners hold
on their earned coins and sell them at a later stage. This limitation can be relaxed in future works through
investigation of exchange-level trading data of miners. We also assume that miners apply computational
power commensurate with the observed mined coins but the relationship is not exactly linear. In future,
scholars can analyze the dynamic relationship between hash power contributions and realized mining out-
comes using data from mining pools. Scholars will also find evidence of recent regulatory interventions
in the cryptocurrency industry whose long-term impacts aren’t fully understood and are topics for future
research.
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7 Appendix
7.1 First Stage Results
We estimate a flexibly specified form for the latent variables, y∗
i,t,btc and y∗
i,t,bch in first stage using a bivariate
ordered probit model. Results for different specifications are presented in Table 6.
Table 6: First-Stage Reduced-Form Bivariate Ordered Probit Policy Results for different specific-
ations of the policy function are presented. We select specification IV based on AIC values.
Parameters I II III IV
BTC-specific Variables
pricebtc 0.6407 0.6498 0.6798 0.6774
(0.0297) (0.0297) (0.0300) (0.0301)
difficultybtc −0.3898 −0.3951 −0.4174 −0.415
(0.0279) (0.0279) (0.0281) (0.0282)
transaction feesbtc −0.3554 −0.3609 −0.3777 −0.3765
(0.0094) (0.0094) (0.0098) (0.0098)
price ratio −0.7137 −0.7271 −0.7537 −0.7532
(0.0657) (0.0658) (0.0659) (0.0660)
difficulty ratio 0.4889 0.4973 0.5179 0.5169
(0.0741) (0.0741) (0.0742) (0.0742)
BTC.COM −0.1141 −0.1142 −0.1104 −0.1102
(0.0171) (0.0171) (0.0171) (0.0171)
BTC.TOP −0.2643 −0.2642 −0.2545 −0.2537
(0.0174) (0.0174) (0.0175) (0.0175)
Other 0.8154 0.8155 0.776 0.7724
(0.0165) (0.0165) (0.0172) (0.0171)
Unknown −1.0787 −1.0784 −1.0522 −1.0496
(0.0209) (0.0209) (0.0211) (0.0211)
ViaBTC −0.409 −0.4089 −0.3954 −0.3943
(0.0178) (0.0178) (0.0179) (0.0179)
EDA −0.0153 −0.0149 −0.0125 −0.0128
(0.0953) (0.0953) (0.0953) (0.0953)
EDA ×price ratio 0.7683 0.7785 0.8105 0.808
(0.0684) (0.0684) (0.0686) (0.0686)
EDA ×difficulty ratio −0.6659 −0.6737 −0.7035 −0.7005
(0.0752) (0.0752) (0.0754) (0.0754)
lagged blocksbtc n.a. n.a. 0.0269 0.0349
n.a. n.a. (0.0064) (0.0063)
lagged blocks otherbtc n.a. n.a. −0.0321 −0.0292
n.a. n.a. (0.0033) (0.0032)
Cutoff 1btc (c1,1)−5.5613 −5.6391 −6.0833 −6.0238
(4.1967) (4.2566) (4.6032) (4.5605)
30
Cutoff 2btc (c1,2)−4.5185 −4.5963 −5.0386 −4.9791
(0.1864) (0.1864) (0.1807) (0.1808)
Cutoff 3btc (c1,3)−3.7467 −3.8245 −4.2647 −4.2052
(0.1602) (0.1602) (0.1555) (0.1556)
Cutoff 4btc (c1,4)−3.092 −3.1697 −3.6078 −3.5483
(0.1471) (0.1471) (0.1433) (0.1433)
Cutoff 5btc (c1,5)−2.561 −2.6387 −3.0757 −3.016
(0.1315) (0.1315) (0.1287) (0.1288)
Cutoff 6btc (c1,6)−1.9665 −2.044 −2.4803 −2.4207
(0.1345) (0.1345) (0.1346) (0.1346)
Cutoff 7btc (c1,7)−1.4826 −1.5601 −1.9959 −1.9363
(0.1127) (0.1127) (0.1127) (0.1127)
BCH-specific Variables
pricebch 0.0127 0.0632 0.0568 0.0829
(0.0272) (0.0270) (0.0272) (0.0272)
difficultybch 0.1665 0.0994 0.1662 0.1343
(0.0283) (0.0285) (0.0283) (0.0285)
transaction feesbch −0.296 −0.287 −0.229 −0.2387
(0.0060) (0.0061) (0.0062) (0.0061)
price ratio −1.4025 −1.1151 −1.1079 −1.0076
(0.0762) (0.0791) (0.0764) (0.0775)
difficulty ratio 1.4853 1.2024 1.2215 1.1256
(0.0890) (0.0913) (0.0890) (0.0899)
BTC.COM −0.1699 −0.2081 −0.1626 −0.1892
(0.0216) (0.0209) (0.0216) (0.0214)
BTC.TOP 0.336 0.1747 0.2181 0.1373
(0.0202) (0.0219) (0.0205) (0.0220)
Other 0.1822 0.5721 0.1412 0.373
(0.0203) (0.0254) (0.0204) (0.0289)
Unknown 1.5701 0.8718 1.263 0.9133
(0.0191) (0.0460) (0.0202) (0.0425)
ViaBTC 0.5393 0.2816 0.4265 0.2961
(0.0196) (0.0246) (0.0198) (0.0241)
EDA −0.4345 −0.5047 −0.0228 −0.1037
(0.1080) (0.1063) (0.1062) (0.1064)
EDA ×price ratio −0.1212 0.0084 0.194 0.2348
(0.0709) (0.0705) (0.0710) (0.0709)
EDA ×difficulty ratio 0.4365 0.2901 −0.1092 −0.1337
(0.0802) (0.0797) (0.0805) (0.0802)
lagged blocksbch n.a. n.a. 0.2644 0.2527
n.a. n.a. (0.0043) (0.0047)
lagged blocks otherbch n.a. n.a. 0.0221 0.0182
n.a. n.a. (0.0016) (0.0016)
Cutoff 1bch (c2,1) 6.8483 8.1757 7.0126 8.134
(5.4319) (5.8118) (5.5406) (6.2370)
Cutoff 2bch (c2,2) 7.6795 8.9226 7.8919 8.9863
(0.0670) (0.0753) (0.0703) (0.0787)
31
Cutoff 3bch (c2,3) 8.225 9.4146 8.4942 9.5707
(0.0542) (0.0566) (0.0580) (0.0625)
Cutoff 4bch (c2,4) 8.6428 9.7926 8.9791 10.0415
(0.0472) (0.0469) (0.0518) (0.0544)
Cutoff 5bch (c2,5) 8.9773 10.0956 9.3878 10.4381
(0.0419) (0.0401) (0.0473) (0.0486)
Cutoff 6bch (c2,6) 9.2633 10.3547 9.7571 10.7961
(0.0380) (0.0354) (0.0446) (0.0449)
Cutoff 7bch (c2,7) 9.5119 10.5796 10.0923 11.1208
(0.0341) (0.0312) (0.0417) (0.0414)
Cutoff 8bch (c2,8) 9.7484 10.7932 10.4172 11.435
(0.0300) (0.0281) (0.0394) (0.0387)
Cutoff 9bch (c2,9) 9.9618 10.9858 10.7122 11.7202
(0.0258) (0.0237) (0.0344) (0.0335)
Cutoff 10bch (c2,10) 10.1327 11.1395 10.9426 11.9427
(0.0181) (0.0164) (0.0241) (0.0234)
ρ−0.0545 0.4518 −0.0352 0.2554
(0.0070) (0.0233) (0.0071) (0.0277)
γ n.a. −0.4994 n.a. −0.2891
n.a. (0.0221) n.a. (0.0266)
Observations 57102 57102 57102 57102
AIC 202618.40 202240.00 198064.40 197958.20
The transition equation parameters (Equations 17, 18, 19, 20) are given in Table 7. κ1∼ N (0,0.001815),
κ2∼ N (0,0.1347), and κ3∼ N (0,0.521).
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Table 7: First stage transition equation parameters
Parameters Point Estimates Standard Errors
BTC Price (GARCH(1,1))
ζ1,18.844 ×10−79.504 ×10−8
ζ1,20.0869 0.0051
ζ1,30.9077 0.0049
BCH Price (ARMA(1,1))
ζ2,10.0259 0.0155
ζ2,2−0.6041 0.0114
BTC Transaction Fees (ARMA(1,1))
ζ3,10.1866 0.0135
ζ3,2−0.8739 0.0078
BCH Transaction Fees (ARMA(1,1))
ζ4,10.1233 0.0160
ζ4,2−0.7620 0.0111
33
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