Monetary Economics Mark Huggett 1 1 Georgetown April 17, 2018
A longstanding problem is to formally incorporate money into an economic model framework. This is not so easily done because modern currencies closely resemble fiat money (i.e. unbacked and intrinsically worthless objects that function as money). Thus, a theory for why modern currencies are valued is not similar to a theory for why Corn Flakes have value: Corn Flakes enter the utility function while (fiat) money does not.
Methodology Economists are strong believers that in most areas of economics it is useful to construct model economies (agents with preferences, firms with technologies and some rules of exchange) to figure out how policies work within model economies. Model economies are our laboratories. In discussing monetary economics we will construct formal models to only a limited extent due to the difficulties of building tractable monetary economies.
Jevons (1875): Objects Serving as Money 1. Gold, silver, copper, salt, oxen, sea shells 2. Certificates to gold or tobacco. 3. Modern paper money (e.g. US dollars) The objects in point 1-2 are termed commodity monies. They would have value even if they did not have a special role as a media of exchange. The object in point 3 is arguably a fiat money (unbacked and intrinsically worthless).
Jevons: Functions of Money 1. Media of exchange 2. Medium of account 3. Store of value 4. Standard of deferred payment US dollars serve all four functions currently
Jevons: Properties of Objects Relevant for Use as Media of Exchange 1. Portable 2. Divisible 3. Recognizable 4. Durable Governments have worked hard to make media of exchange effectively more divisible or recognizable.
Jevons: Media of Exchange Jevons view was that a good media of exchange would have these properties. In his view, gold was ideal as it was (or could be made) very portable, divisible, recognizable and durable. Arguably US dollars also display these four key properties to a large degree. Of course, one could argue that certificates to some underlying commodities could also be made to display these four properties (e.g. plywood standard).
Jevons: Media of Exchange To economists, the defining property of a money is that it is used as a media of exchange. An object could be described as being a media of exchange if it is on one side of many exchanges. US dollars are currently on one side of many exchanges.
Jevons: Media of Exchange Economists think that media of exchange arise because of frictions in (decentralized) exchange. Example frictions: 1. Electronic means for settling payment may not be possible (no credit or debit cards) in some exchanges. 2. The so called double coincidence of wants problem. 3. Not all goods are equally portable, divisible, recognizable, durable.
John Law (1705) He who had more Goods than he had use for, would choose to barter them for Silver, though he had no use for it; Because, Silver was certain in its Quality. An Interpretation: Credit arrangements may not be possible, double coincidence of wants may not hold and, thus, trading a recognizable object may help make trade possible.
Three Basic Questions about Money 1. Are there potential welfare gains to replacing a commodity money with a fiat money? 2. Is there an arbitrage opportunity between T-bills and dollar bills given that one pays interest and the other does not? 3. Is money simpy a creation of the State? Answers: 1. Yes, 2. Yes and 3. No. These are argued in the slides that follow.
Welfare Gains? Centuries ago gold, silver or copper coins circulated as media of exchange. If it were possible to replace these circulating media of exchange with worthless paper money or worthless tokens that serve as media of exchange, then the gold, silver and copper coins could be used for other purposes. For example, these coins could be converted into gold watches or silverware. These objects enter the utility function.
Welfare Gains? While economists accept this argument in principle, economists are also skeptical that these welfare gains are being achieved. The fiat money era is a high inflation era with many countries experiencing hyperinflations. Thus, there is still the issue that humans have to be able to manage a fiat money. Ecuador and Panama employ the US dollar. You can speculate on why this is so.
Arbitrage between Tbills and Dollars? There is a straightforward scheme that, at least in principle, can make large amounts of money off the fact that T-bills pay interest but US dollars do not. 1. Print the Huggett Dollar - the H$ 2. Exchange the H$ for US $ one for one. 3. Use US $ to buy T-bills and to back each H$. 4. Enjoy life in Aruba using the interest payments.
Money Only a Creation of the State? Radford (1945) The Economic Organization of a POW Camp is a wonderful article describing economic life in WWII POW camps. He argues that media of exchange (specifically cigarettes) arise endogenously, without any governmental decree, to solve problems in decentralized exchange. Upshot: Money is not just a creation of the State. In practice States monopolize the management of money for various reasons.
Price Level: Theory and Some Empirics David Hume, John Stuart Mill and others are credited with developing a theory of the price level. This theory is now called the Quantity Theory of money. They probably were aware of the Price Revolution - the rise in prices starting after 1500.
Price Level: England and UK Data Log CPI British Consumer Prices: Log CPI 2.50 2.00 1.50 1.00 0.50 0.00 1200 1300 1400 1500 1600 1700 1800 1900 2000 0.50 Year CPI Bank of England CPI Clark
Price Level: British Data Log CPI 2.50 2.00 1.50 1.00 0.50 Log British CPI: 1661 2015 0.00 1660 1710 1760 1810 1860 1910 1960 2010 0.50 Year Log British CPI
Price Level: England and UK Data There are several notable things in the price series data: 1. After several centuries of stable prices, the price level increased from the early 1500s to the early 1600s. This is called the Price Revolution. 2. The period after WWII was both the start of the fiat money era and a era of historically high inflation rates.
Quantity Theory The Quantity Theory is an identity and one assumption: 1. MV = P Y 2. V is constant M and V are money and velocity P and Y are the price level and output
Quantity Theory: Implications Simple manipulations of the quantity theory equation imply: 1. P is proportional to M Y 2. M. M = P P + Y Y since P = MV Y Both equations offer simple tests of the theory by means of a scatter plot.
Highly Averaged Cross-County Data Chart 1 Money Growth and Inflation: A High, Positive Correlation Average Annual Rates of Growth in M2 and in Consumer Prices During 1960 90 in 110 Countries Inflation % 100 100 80 45 80 60 60 40 40 20 20 0 0 0 20 40 60 80 0 100% Money Growth
US Time Series (Yearly) Data: Using M1 Measure Figure1: P/P vs. M/M Y/Y P/ /P 0.2 0.15 0.1 0.05 0 0.05 0.1 0.15 0.15 0.1 0.05 0 0.05 0.1 0.15 0.2 M/M Y/Y 45 degree line
Quantity Theory: Measuring Velocity Using M1 1. V = P Y M 2. measure numerator with nominal GDP and the denominator with a specific monetary aggregate These choices imply that P is the GDP deflator. M1 is a monetary aggregate equal to notes and coins in circulation and demand deposits. Demand deposits are checking accounts in banks.
US Data: Measuring Velocity Using M1 Nominal GDP/M1 M1 velocity 12 10 8 6 4 2 0 1950 1960 1970 1980 1990 2000 2010 2020 Year
US Data: Explaining Velocity Based on M1 What explains the upward trend in velocity? 1. There have been many new transactions technologies over the last 70 years. 2. Checks replace cash in some transactions 3. ATMs economize on costly trips to traditional brick-and-mortar banks 4. Credit cards replace cash in many transactions 5. As with many technological changes, there is slow difusion in adoption. Urban hipsters adopt early but eventually many Grandmas and Grandpas adopt.
Quantity Theory: A Foundation We will offer a theoretical foundation for the quantity theory. Theorists present assumptions on the objectives of agents and some rules on how they interact and then derive implications of the purely theoretical model. We will now do so using some hand waving. Eventually, the result will be a 1980 s era cash-in-advance model of money.
Quantity Theory: A Foundation 1. Many students are put into a room. Students are stuck in the room forever. 2. Each is given M = 100 tokens on the first day. Each is given Y = 10 candy bars each day. Students like candy bars but do not like tokens. 3. Catch: each student must put all Y candy bars into their own vending machine each day. 4. Rules: each student sets the token price of their candy bars. only tokens enter the machine and buy candy bars. anyone can put tokens into any vending machine.
Quantity Theory: A Foundation Clarifications: 1. After a student spends the initial M tokens, the only way to consume candy bars in future periods is by emptying tokens from their personal vending maching and using them. 2. Students set the price of their candy bars at the beginning of each day. They put candy into their machine in the morning. 3. They visit vending machines at mid day. They empty vending machines of tokens at the end of each day. 4. Any candy remaining in the machine at the end of the day is rotten and is tossed out.
Quantity Theory: A Foundation Given the objectives of agents (they like candy each day and are never satiated) and the rules of exchange, the key questions are stated below: 1. How will each student set the token price of their candy bar? 2. How much candy will each student consume? Experiments 1-3 illustrate how prices and consumption change when we change the money supply or the rules of exchange.
Experiment 1: M t = 100 and Y = 10 Answers: 1. Each student will set the price to P = M Y = 100 10 = 10. 2. Each student will consume 10 candy bars each day. Note: The answer is the price predicted by the quantity theory with a velocity of 1. The answer seems plausible as no student benefits from setting a different price when all the other students are setting P = 10. The price above has the feature that all the money is spent once per day to buy up all the candy bars.
Experiment 2: M t = 2 t 1 100 Y = 10 If the money supply is doubled at each date by giving equal amounts of extra tokens to all students, then what is the price prediction and the candy bar consumption prediction? 1. Each student will set the price to P t = Mt Y t = 2t 1 100 = 2 t 1 10 for t = 1, 2,..., where M 10 t is the money supply per person at time t. 2. Each student will consume 10 candy bars each day. Note: The answer is the price predicted by the quantity theory with a velocity of 1.
Experiment 3: M t = 100 Y = 10 and empty machine twice/day If money can be taken out of the machine twice per day, then what is the price prediction and the candy bar consumption prediction? 1. Each student will set the price to P t = 2 Mt Y t = 2 100 = 20 10 for t = 1, 2,..., where M t and Y t are the money supply and the candy supply per person at time t. 2. Each student will consume 10 candy bars each day. Note: The answer is the price predicted by the quantity theory with a velocity of 2 so that P t = MtVt Y t = 100 2. 10
Quantity Theory: Vending Machine Economy Is Money A Veil? Money is largely a veil in the vending-machine economy. There is a long line of thought that views money as somewhat unimportant and as hiding the real workings of the economy. At the most extreme, some view money as neutral. When money is neutral, changes in money or in the mechanism by which money works do not affect real quantities (e.g. GDP, real interest rates and real wage rates) but do affect nominal quantities.
Real and Nominal Interest Rates The gross nominal interest rate measures the number of units of money one receives next period for giving up 1 unit of money now. The gross real interest rate measures the number of baskets of goods one receives next period for giving up 1 basket of goods now.
Real and Nominal Interest Rates How to figure out the gross real interest rate, if we live in a nominal world? 1. Start with 1 basket of time t goods. 2. Covert basket into p t dollars - use CPI. 3. Convert p t into p t (1 + i t+1 ) dollars tomorrow by loaning p t dollars to a bank. 4. Convert dollars into p t(1+i t+1 ) p t+1 baskets of time t + 1 goods!
Real and Nominal Interest Rates Summarizing: (1 + r t+1 ) = p t p t+1 (1 + i t+1 ) (1 + i t+1 ) = (1 + r t+1 )(1 + π t+1 ) The Fisher equation holds (i.e. gross nominal interest rate equals the product of the gross real interest rate and one plus the inflation rate), where we define 1 + π t+1 p t+1 p t.
Real and Nominal Interest Rates What is the real and the nomimal interest rate in the vending machine economy? Economy 1: Agents receive Y = 10 candy bars every period. Agents start out with M = 100 units of money per person. Agents are allowed to make risk-free loans of tokens from one day to the next. How should they set the nominal interest rate?
Real and Nominal Interest Rates To answer this question we need to know something about preferences : Assume: Preferences for candy consumption are given by the utility function U(c 1, c 2,...) = β t 1 log(c t ) t=1 When 0 < β < 1 then an agent gets more utility from 10 candy bars consumed today versus 10 candy bars consumed tomorrow.
Real and Nominal Interest Rates If (c 1, c 2,...) = (10, 10,...), then MRS(c t, c t+1 ) =? U(c 1, c 2,...) = MRS(c t, c t+1 ) = β t 1 log(c t ) t=1 U t U t+1 = MRS(10, 10) = 1 β β t 1 c t β t c t+1 = 1 β 10 10 = 1 β > 1 c t+1 c t
Real and Nominal Interest Rates Assume: (c 1, c 2,...) = (10, 10,...) and U(c 1, c 2,...) = t=1 βt 1 log(c t ) Claim: If there were no money (just candy bars), then c t = 10 and gross real interest rate 1 + r t+1 = 1/β > 1. 1 + r t+1 = MRS(c t, c t+1 ) = 1 β c t+1 c t = 1 β 10 10 = 1 β At any other real interest rate ALL agents would want to save or ALL agents would want to lend. This is impossible. Loan markets work by having two parties on opposite sides of each transaction!
Real and Nominal Interest Rates: Economy 1 Economy 1: Agents receive Y = 10 candy bars every period. Agents start out with M = 100 units of money per person. Constant money. Conjecture: constant prices, consumption and interest rates P t = M t Y t = 100/10 = 10 c t = 10 (1 + i t+1 ) = (1 + r t+1 )(1 + π t+1 ) = 1 β 1 = 1 β
Real and Nominal Interest Rates: Economy 1 Given the price conjecture P t = 10 each period, no other nominal interest makes sense. At any larger nominal interest rate other than (1 + i t+1 ) = 1 β ALL agents would want to lend some money. At any smaller rate ALL agents would want to borrow. This is impossible. At (1 + i t+1 ) = 1 β ALL agents neither want to borrow nor to lend.
Real and Nominal Interest Rates: Economy 2 Economy 2: Agents receive Y = 10 candy bars every period. Agents start out with M = 100 units of money per person and money suppy doubles every period. Conjecture: P t = M t Y t = 2 t 1 100/10 = 2 t 1 10 c t = 10 (1 + i t+1 ) = (1 + r t+1 )(1 + π t+1 ) = 1 β 2 = 2 β
Real and Nominal Interest Rates: Economy 2 Economy 2 1. c t = 10 the same as in Economy 1. 2. P t = 2 t 1 10 prices double every period. 3. nominal interest rate (1 + i t+1 ) = 2/β 4. real interest rate is the SAME in Economy 1 and 2. Real interest rates are the same because preferences for candy bars and candy bar endowments pin down real interest rates. Money is a veil: it does not impact consumption or real interest rates but it does impact prices and nominal interest rates.
Real and Nominal Interest Rates Conclusion: In the vending machine economy, the quantity theory holds. The Fisher equation holds. The nominal interest rate is pinned down by the agent s marginal rate of substitution across periods and by the inflation rate. Higher inflation rates pass through into higher nominal interest rates without impacting the real interest rate, which is determined by preferences and endowments of candy bars.
Tradition Question: Optimal Quantity of Money How is the quantity of fiat money optimally managed to maximize welfare? 1. All agents are identical in preferences and endowments. In Economy 1 and Economy 2 the money supply differs but consumption is exactly the same. Constant money, growing money or shrinking money are equivalent when welfare is measured by the agent s common utility level. 2. There is no unique optimal quantity in this economy. This is because money does not serve an important role in vending machine economies. A deeper model where money helps solve a friction in the exchange process is needed to produce a more trustworthy answer.