Bitcoin, Monetary Theory, The Balance of Payments, and Exchange Rate Determination

First Principles

This article is an excerpt from a document we produced called “Interactive Research — Fundamental Models of Digital Currency Valuation”. www.digitalcapitalresearch.com

The Franklin Dollar

In an imaginary town, Franklin, the currency used for all trade and commerce is the Franklin Dollar ($). We want to measure the demand for money in Franklin. To do this, we choose a time frame of one year and then measure the total amount of money and record all transactions that have occurred in this period.

The ‘Equation of Exchange’, an identity first popularized by Irving Fisher in “The Purchasing Power of Money” (1911), states that the ‘Demand for Money’ must equal the ‘Money Supplied in exchange for Goods and Services’.

V, Velocity, is a scalar which measures the number of times money circulates around the economy. We calculate the Demand for Money, for the given year, in Franklin to be $195. Or, put another way, the $100 in the economy circulated 1.95 times.

Particularly for a fixed money supply, the velocity of money is an important measure of how robust an economy is. The right-hand side of the equation (PQ) is nominal GDP, so increasing velocity with stable prices (inflation) has the effect of increasing GDP.

In one approach to Exchange Rate Determination we can compare Purchasing Power Parity between the two economies, the differences in money supply and velocities and arrive at an understanding of which money is in more demand, and therefore should have upward pressure on the exchange rate between the two currencies.

The Nakamoto Bitcoin

Nakamoto is another fictional town, which uses another currency, the Nakamoto Bitcoin (BTC).

Let us consider a new time period (and so, ignoring the transactions from the previous example), where the quantity of money in Nakamoto is 100BTC and the quantity of money in Franklin is $100.

Mister Market

Alice lives in Nakamoto, where all her daily transactions are in Bitcoins. One day she decides she wants to buy a coffee from the town of Franklin, however, Franklin coffee shops do not accept Bitcoin. To buy the coffee, Alice needs to convert some of her Bitcoins into Dollars.

‘Mister Market’ is a company that helps its customers with foreign exchange (FX) transactions. Alice needs $5 to buy a coffee from Franklin, therefore asks Mister Market how many Bitcoins they need in exchange for the $5 Dollars required in return.

Mister Market tells Alice the Bitcoin/Dollar exchange rate is 10.00 (one Bitcoin buys ten Dollars). Alice makes a transaction to convert 0.5 Bitcoin to $5 at this exchange rate.

Alice then buys her coffee from the Franklin coffee shop for $5.

External Accounts & The Balance of Payments

After Alice’s FX transaction, something has happened to the effective money supply of the Nakamoto economy. 0.5 Bitcoins has left the Nakamoto economy and is now with Mister Market. Nothing has happened to the Dollar economy — Mister Market must have had the $5 Dollars in possession before the FX transaction, to be able to give to Alice, who then spends the Dollars in the Dollar economy (Franklin).

Mister Market’s foreign exchange balances represents the ‘Balance of Payments’ between the two economies. From Franklin’s point of view, the economy has accumulated 0.5 Bitcoins on its ‘external account’ (another way to think about this is that they have 0.5 BTC for sale if anyone wanted to buy it with Dollars). From Nakamoto’s point of view, the economy owes Franklin $5, at current exchange rates, to get back the 0.5 Bitcoins that has escaped their economy.

Eve, another Nakamoto inhabitant, hears about the wonderful coffee being served in Franklin and decides to follow Alice’s lead. Eve wants to buy 3 cups of coffee for herself and friends. She asks Mister Market to exchange her Bitcoins for the $15 she needs to buy the coffees. Mister Market already has 0.5 Bitcoins and is worried about stock-piling Bitcoins while seeing no demand from anyone to buy them from him. Mister Market agrees to change Eve’s money but for a new Bitcoin/Dollar exchange rate of 8.00. Eve gives Mister Market 1.875 Bitcoins to receive $15.

Eve’s friends loved the coffee. Eve decides to buy more Franklin coffee. Eve asks Mister Market for $20 in exchange for Bitcoin.

Mister Market becomes uncomfortable stock piling even more Bitcoin. Mister Market make a less attractive exchange rate to Eve than the last transaction, showing Bitcoin/Dollar as 5.00. Eve completes the transaction anyway.

Exchange Rate Determination

We can already see how the Balance of Payments has a direct impact on the exchange rate between the two currencies. The only way for the Balance of Payments to ‘re-balance’, is if the inhabitants of Franklin start to demand goods and services from Nakamoto. The demand for Nakamoto goods and services will create the demand for its money, Bitcoin, thereby relieving the downward pressure on the exchange rate. Luckily, because Mister Market is adjusting his exchange rate in accordance to the supply and demand of currency, Nakamoto goods and service will look more and more attractive as the exchange rate moves lower.

In traditional currency markets, Mister Market is represented by exchanges, international corporations, banks, financial institutions and governments. Since traditional currencies are governed by their sovereign, governments can collect information on foreign exchange transactions from all the relevant agents that operate in their jurisdiction. Government agencies regularly compile comprehensive statistical statements that represent the Balance of Payments (officially called ‘The Current Account Statement’ and ‘The Capital and Financial Accounts’).

The Balance of Payments cannot predict the future path of exchange rates. The statements only serve as a snapshot of the current flow and trends in foreign exchange transactions. For currency investors, this information provides insight into the strength of a particular monetary system, which is inextricably intertwined with its economy. This information is crucial to understanding exchange rates, since it directly measures the relative demand of currencies.

Digital currency markets have no governing sovereign. Digital currencies are decentralised, operate only on the internet, and transcend borders and jurisdictions. However, this does not mean abstracting ‘the Balance of Payments’ is impossible — it is just more difficult. One of the virtues of a Blockchain is the transparency of transaction data — every ‘on-chain’ transaction is recorded and available for all to see. The challenge is to isolate which transactions relate to ‘foreign exchange’.

Understanding exchange rate determination of a digital currency requires analysis of the goods and services priced in its specific currency — this is how to determine the nominal GDP of a border-less economy. Bitcoin is like a border-less country that exists only in Cyberspace, but its internal economy is bordered by the transactions that are denominated in Bitcoin.

Full Research can be found here: www.digitalcapitalresearch.com