Essays On Bitcoin - Department Of Economics
Essays on BitcoinBy Alex KroegerWith Advisor Professor Tim FuerstAbstract:The following paper analyzes two distinct topics related to thevirtual currency bitcoin. The first is an empirical test ofpurchasing power parity using volume weighted price data frombitcoin exchanges that facilitate transactions in U.S. dollars, euros,and British pounds. Evidence shows that relative purchasingpower parity does indeed appear to hold, but that there is apersistent deviation from absolute purchasing power parity. Thesecond topic is an analysis of bitcoin mining from an economicperspective. A simple model demonstrates that competition inbitcoin mining leads to a great deal of waste compared to theoutcome that would be preferred by a central planner seeking tomaximize welfare.
Chapter One: IntroductionTopics of Discussion and Structure of the PaperSince its inception, bitcoin, a virtual currency, has grown in both its popularity and itsuse. Despite this, there still exists a relative dearth of economic analysis in academia about thisnew economic phenomenon. Various topics have been researched with regard to bitcoin,including its economic status as a currency (Yermack 2013), the incentives of bitcoin miners(Kroll et al 2013), the economics of bitcoin exchange prices (Ciaian et al 2014), among others.Macroeconomist Paul Krugman weighed in strongly on the normative side of the economicdebate with his article “Bitcoin is Evil” published in late 2013.The object of this paper is to investigate a yet unexplored topic in bitcoin, purchasingpower parity, and utilize a different approach to the topic explored by Kroll et al, the economicsof bitcoin mining. Therefore, the structure of the paper will be as follows. The remainder ofchapter one will provide a brief history of bitcoin and an explanation of how bitcoin operates.Chapter two, entitled “Purchasing Power Parity in the Bitcoin Exchange Market” will analyzebitcoin from the perspective of purchasing power parity across three different currency exchangemarkets in which bitcoin trades. Chapter three, entitled “An Economic Analysis of BitcoinMining,” analyzes bitcoin from the perspective of the users that verify bitcoin transactions.Chapter four concludes. Note that there are separate appendices at the end of chapters two andthree. All references are listed at the end.The History of BitcoinBitcoin (sometimes known by its generally accepted ticker BTC) is an online paymentsystem launched as on open source software in 2009. Its creator (or creators), whose identity to1
this day remains unknown, goes by the name Satoshi Nakamoto. Nakamoto published a paperdescribing his or her creation entitled “Bitcoin: A Peer-to-Peer Electronic Cash System” in 2008.In many ways it functions as a currency, whereby one party can send a unit of currency(in this case a string of code) to another party in exchange for a good or service. As such, bitcoinis often referred to as a “virtual currency” or “cryptocurrency.” All transfers of bitcoin areverified and then recorded on a public ledger known as the block chain (Velde 2013).Potential users can purchase bitcoin by using an online exchange. These exchanges actas either brokers or dealers in allowing users to convert a major currency such as the U.S. dollarinto bitcoins. The first of these exchanges, Bitcoin Market, open in February 2010. Anotherexchange, MtGox, first launched in July of that same year.1Based on the dollar values at these exchanges, the market capitalization of bitcoin (thenumber of bitcoin in circulation multiplied by the market price in dollars) exceeded 1 millionby October 2010. By March 2013, the market cap surpassed 1 billion. 1 During that time,bitcoin had come to be accepted as payment by a variety of businesses and organizations, fromBaidu in China to coffee shops in Palo Alto and antique shops in New Orleans (Fung 2013, Hill2013). One writer for Forbes, Kashmir Hill, was actually able to live for a week in SanFransisco in May 2013 using nothing but bitcoin to make purchases (Hill 2013-2). In Octoberand November 2013, interest in bitcoin in China surged, making BTC China, a Shanghai basedbitcoin exchange, the largest in the world for a brief time (Hill 2013-3). The price of a bitcoinsurged to over 1000 as many users in China begin to invest in bitcoin, but has since declined tothe 200’s (see Chart 1 below).1Historical events drawn from historyofbitcoin.org.2
Chart 1: Price of Bitcoin (Source: coindesk.com)Bitcoin Price in USD1400120010008006004002000One reason for the growth in bitcoin’s popularity (and notoriety) is the anonymity of itsusers. Although all transactions are recorded on a public ledger, only one’s public address isassociated with the transfer’s one makes. One’s public address contains no identifyinginformation in and of itself, and so as long as the public address is not associated with anyidentity, transactions remain anonymous. This anonymity has made bitcoin the currency ofchoice for the so-called “darknet”--websites that sell illegal commodities such as drugs andweapons. One such notable website was “Silk Road,” which was shut down by the United Statesgovernment in October 2013. Since its closure, a number of new websites have emerged to takeits place and have adopted the model of using bitcoin as a medium between buyers and sellers(Power 2014).How Bitcoin WorksTo transact in bitcoin, one broadcasts to the bitcoin network the public key of the payeeand the amount of bitcoin one intends to transfer. Every bitcoin address has an associatedprivate key that acts as a password to ensure that all transfers are authorized. The private key is3
meant to remain secured, and along with one’s own public key, it allows one to digitally signbitcoin transactions. A graphical representation of a series of bitcoin transactions from SatoshiNakamoto’s original paper is reproduced below.The primary concern of the payee is that the amount of bitcoin being transferred hasalready been spent, and therefore does not belong to the payer. Another concern is the rate ofcreation, since a high degree of inflation could reduce the value of one’s holdings. What allowsbitcoin to be functional is that it overcomes these two major obstacles facing any digitalcurrency: avoiding double spending and controlling creation (Velde 2013). Both of theseproblems are solved in the process of mining.As transactions are broadcast over the bitcoin network, “miners” work to collecttransactions into a group, known as a “block,” to be added to the block chain. Every block mustbe accompanied by a hash (a string of characters of a fixed length generated by a set function)that depends on the list of transactions, the hash of the previous block, and a value called anonce, which is imputed by the miner. Miners work to find a nonce such that the hash for theblock meets the requirements set out by the system. The hash serves as a proof-of-work, since itis difficult to compute (the only usable method is simply to input values until a working nonce isfound), but easy to verify using the hash function. Once an acceptable hash is found, the4
successful miner broadcasts the block to the network, which is accepted as long as all thetransactions are authorized and the hash is valid. As a reward for the computer power expendedto verify transactions, bitcoin miners receive newly created bitcoins. The difficulty of miningadjusts every two weeks so that blocks are mined at a rate of one every ten minutes, thuscontrolling the rate at which new bitcoins are created. Mining will be discussed in greater detailin chapter three.5
Chapter 2: Purchasing Power Parity in the Bitcoin Exchange MarketI. IntroductionGiven that trading of bitcoin occurs in numerous currencies, it is possible to utilizebitcoin markets to test the theory of purchasing power parity, which states that items sold inseveral countries should trade for the same price after adjusting for nominal exchange rates. Theobject of this paper is to analyze whether purchasing power parity holds in bitcoin markets fordollars, euros and British pounds.The remainder of the paper is organized as follows. Section 2 provides backgroundinformation on bitcoin exchanges and the study of purchasing power parity. Section 3summarizes the sources for the data used in the analysis. Section 4 provides a discussion themethodology employed to analyze real exchange rates and the primary findings. Section 5concludes.II. BackgroundBitcoin ExchangesAn average user can buy and sell bitcoin for major sovereign currencies using onlineexchanges. Exchanges act as either brokers, serving as a platform over which buyers and sellerscome together, or as dealers, taking on an inventory of bitcoin to sell to users and profiting frombid-ask spreads. BTC-E is an example of the former, whereas Coinbase is an example of thelatter. Purchased bitcoin can then be stored in an electronic “wallet,” which is a feature oftenoffered by the exchange itself, for later use.Bitcoin users span the globe, and exchanges do as well. According to bitcoincharts.com,bitcoin currently (as of April 2015) trades in 26 sovereign currencies via exchanges with the6
most popular currencies by volume being the Chinese yuan, the U.S. dollar, the euro and theBritish pound.Bitcoin exchanges are not without drawbacks, however, since using them exposes usersto the risk that the exchange can fail while in possession of one’s bitcoins or other currency.Most notable was the collapse of MtGox, an exchange that was based in Tokyo and previouslywas the world’s largest. In February 2013, MtGox went offline, eventually disclosing thereason: hackers had stolen 850,000 bitcoins, the equivalent of 460 million at the time, leavingmany investors unable to recuperate their assets stored with the site (McMillan 2014). InJanuary 2015, hackers stole over 5 million worth of bitcoin from Bitstamp, a major exchangebased in Slovenia, forcing it to shut down briefly (Frey 2015). Another complete shutdownoccurred in March of 2015 when a Canadian exchange called Cavirtex experienced a serioussecurity breach (Reader 2015).While security concerns remain, bitcoin exchanges are generally quite transparent withregard to their operations. Virtually all major exchanges make publicly available real time dataabout prices and volume for use by investors and web applications. Historical data is collectedand stored by many organizations, notably bitcoincharts.com and bitcoinaverage.com. Thisavailability of data makes bitcoin a viable topic of empirical economic investigation.The Real Exchange Rate and Purchasing Power ParityPurchasing power parity (PPP) is the theory that the ratio of price levels between twocountries should equal the nominal exchange rate between the two countries. In other words, anamount of currency should be able to purchase the same basket of goods in any country once it isexchanged at the nominal rate.7
The primary motivation for believing that PPP should hold true is the possibility ofinternational goods arbitrage (Taylor & Taylor 2004). If the price of a good expressed in acommon currency differs across countries, an arbitrage opportunity would exist whereby onecould purchase the good where it is relatively cheap and sell it where it is relatively expensive,realizing a riskless profit. Similarly, a producer of the good would be able to concentrateshipments to countries in which the good is relatively more expensive. The ability to takeadvantage of such opportunities should create the pricing pressures to ensure that PPP holds.There are many reasons to believe that PPP would not hold, however, if there arelimitations to international goods arbitrage. Such factors relate to the tradability of the good,such as transaction costs, tariffs, and taxes. Certain services, such as haircuts, are hardly tradableat all. In cases where obstacles to trade exist, one would not expect PPP to hold perfectly(Rogoff 1996).Another issue is whether or not the basket of goods is exactly comparable in each nation.For this issue it is important to consider two different senses in which PPP could hold. Onesense is absolute PPP, whereby the purchasing power of a unit of currency of one nation exactlyequals the purchasing power of the amount of currency of another nation after accounting for thenominal exchange rate. The absolute sense would not hold if the basket of goods differs betweenthe two countries, however, since the underlying goods would not be exactly comparable. Theother sense that avoids this issue is relative PPP, whereby the proportional change in theexchange rate should offset the difference in inflation rates for the two countries (Rogoff 1996).Many empirical tests of PPP have been performed. A primary method of testing PPP isto perform unit root tests on the real exchange rate—a method that will be used in this paper(Taylor & Taylor 2004). The real exchange rate is defined as the relative price level adjusted by8
the nominal exchange rate. An example calculation of the real exchange rate, q, is shown belowfor two hypothetically countries, country A and country B. P represents the price of a basket ofgoods, and C is the respective currency for each country.CAP CBasket A CBq A B Basket B / Basket ACBPB C ACABasket BTheoretically, the real exchange rate should be one if the price indexes used reflected theexact same basket of goods (reflecting absolute PPP). In practice, price indices across countrieswill not reflect the same exact underlying basket of goods, and so the real exchange rate willlikely differ from one. If relative PPP holds, however, one would still expect the real exchangerate to remain stationary—any changes in the real exchange rate would represent deviations fromrelative PPP. Therefore, any changes in the real exchange rate should eventually revert to acommon mean. In other words, the process should not have a unit root, whereby shocks becomepermanent deviations.The unit root test is estimated by using an autoregression. An example of anautoregression with one lagged term is shown below with q signifying the real exchange rate.qt 1qt 1 tIf the real exchange rate follows a unit root process, then β1 would be equal to one. Thiswould mean the change in real exchange rates would on average be zero (since no drift term isspecified), but the level would not be predictable in the long run. A generalized version couldconsist of many lagged terms (shown below), and in that case if the series followed a unit rootprocess, the sum of the terms β1 βn would be one.qt 1qt 1 2 qt 2 n qt n t9
Early empirical tests of a unit root the real exchange rate in the late 1980’s suggested thatthe null hypothesis that the real exchange rate series follows a unit root process cannot berejected. This was most likely due to the low power of the tests and the limited number of yearsutilized, however. Tests using longer time spans resulted in successful rejections of the null thatreal exchange rate series had unit roots (Taylor & Taylor 2004).III. DataData used in the following analysis is drawn from several sources. Bitcoin price data isgenerated using bitcoinaverage.com’s price index. The price index is calculated by collectingdata from a multitude of major exchanges for a particular currency. A weighted average price isthen estimated using the prices from each exchange and weights according to the volume eachexchange experiences. The following analysis utilizes the weighted price index in US dollars,British pounds, and euros. The historical data is made available for convenient download byQuandl, which is the source used for the following analysis. The time period considered isSeptember 2013 to October 2014.Nominal exchange rate data is also used in order to calculate real exchange rates. Thedaily U.S. dollar to euro and the daily U.S. dollar to British pound nominal exchange rates wereobtained from the Federal Reserve Economic Data (FRED) site maintained by the St. Louisbranch of the Federal Reserve. The daily euro to British pound exchange rate is made availableby the European Central Bank.Price index data are drawn from governmental sources for the US and the UK. Thesedata were obtained from the US Bureau of Labor Statistics and the UK Office for National10
Statistics, respectively. Price index data in each case is available on a monthly basis. The timeperiod considered is January 1996 to October 2014.IV. Methodology and ResultsTesting for a Unit Root: the Augmented Dickey-Fuller TestAs discussed in the background on purchasing power parity, a common method of testingPPP empirically involves utilizing a unit root test on the time series. One such test is theaugmented Dickey-Fuller test. The equation involved in calculating the test statistic deviatessomewhat from a standard autoregressive model specified in the background section. For a realexchange rate q and n lagged terms, the model is specified as follows (Cheung & Lai 1995). qt c qt 1 1 qt 1 2 qt 2 n qt n tIf 𝛾 in the model equals zero, the process follows a unit root. In other words, 𝛾 0would entail the previous term in the series provides no information about the current change. Ifthe process is mean reverting, one would expect that the lagged term would have an effect on thechange in the current period. If the process is stationary and mean reverting, then 𝛾 should benegative. The test statistic in the augmented Dickey-Fuller test, then, is the estimate of thecoefficient 𝛾̂ divided by its estimated standard error from an ordinary least squares regression.Shown another way, the test statistic, labeled ADS, is calculated as follows.ADS ˆSE ˆ The closer the test statistic is to zero, the less likely one can reject the null that the seriesfollows a unit root process. The more negative the test statistic, the more likely one can reject11
the null. The test statistic and appropriate critical values for subsequent analysis were calculatedusing Eviews statistical software.Country-Level Real Exchange RateUsing data on nominal exchange rates and price indexes, one can construct a realexchange rate and test relative PPP. Using consumer price indexes and nominal exchange ratesfor the United States and the United Kingdom, a real exchange rate was constructed for thesetwo countries according to the specifications shown in the appendix as Table 1. The resultingvalue is the price of British goods in terms of U.S. goods. The timeline considered is January1996 through October 2014. The data series and its corresponding mean (.88) are displayed inChart 2 below.Chart 2: US-UK CPI Real Exchange 0.5US-UK Real Exchange RateAverageChart 2 above suggests that the US-UK real exchange rate exhibits long run meanreverting behavior. Using the augmented Dickey-Fuller test, however, the null hypothesis that12
the US-UK exchange rate has a unit root cannot be rejected at a 95% confidence level. The teststatistic is roughly -2.48, corresponding to a p-value of .12.One reason one may not be able to reject the null of unit root is that many of the goodsincluded in consumer price indices are not highly tradable. Consider another example of a realexchange rate involving a more a tradable good: gasoline.Chart 3 below shows the time series for the real exchange rate between the US and UKlimited to gas along with its mean (1.14). Again, the timeline considered is January 1996 toOctober 2014. While the series exhibits significant volatility, it appears to be revert to the meanmore quickly than the previous total CPI series. A likely
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