Columbia University Department of Economics Lecture 16 Economics UN3213 Intermediate Macroeconomics Professor Mart ´ ın Uribe Spring 2019
Announcements Recitations: Review of Midterm OH as usual. After reading this notes, you will be able to follow pretty well Robert Lucas’s Nobel Lecture. Give it a try.
Economics UN3213 Monetary Economics Lecture 16 Topics Today • Two long-run empirical regularities about money and inflation • The Quantity Theory of Money (QTM) 1
Economics UN3213 Monetary Economics Lecture 16 The Money Supply and the Money Growth Rate The money supply M t = nominal money supply in period t 2
Economics UN3213 Monetary Economics Lecture 16 How Do We Measure the Money Supply, M t ? For the purpose of the analysis in this lecture, the money supply consists of assets that people and firms use to perform trnsactions. Economists typically use three measures of money that differ in how many instruments are included. A relatively narrow definition of money is known as the monetary base, or high- power money, or M 0. These three names are used to designate the sum of currency in circulation (bills and coins) and bank reserves (kept in the banks’ vaults or deposited in the central bank). A broader definition of money is M 1, which consists of the sum of currency in circulation (bills and coins) plus demand deposits (checking accounts). An even broader measure of money is M 2, which consists of the sum of M 2 (that is, currency in circulation plus demand deposits) plus deposits in saving accounts, small time deposits, and retail money market funds. Data on M 0, M 1, and M 2 can be found, for example, by visiting the website of the Board of Governors of the Federal Reserve System. 3
Economics UN3213 Monetary Economics Lecture 16 The growth rate of the money supply M t µ t = − 1 M t − 1 µ t = growth rate of the money supply between period t − 1 and period t 4
Economics UN3213 Monetary Economics Lecture 16 The Long Run 5
Economics UN3213 Monetary Economics Lecture 16 Two Important Long-Run Empirical Regularities In- volving Money (a) In the long run, average inflation moves one-for-one with the average growth rate of the money supply. (b) In the long-run, the average growth rate of output is unrelated to the average growth rate of the money supply. This fact is known as long-run money superneutrality. 6
Economics UN3213 Monetary Economics Lecture 16 Empirical Evidence on Money Growth and Inflation Money Growth and Inflation Across Countries: 1960 to 2014 120 45 o 100 80 60 In fl ation, π 40 20 0 −20 0 20 40 60 80 100 120 140 Money Growth, µ 7
Economics UN3213 Monetary Economics Lecture 16 What is in the figure? On the vertical axis is the average annual inflation rate between 1960 and 2014, denoted π . To compute inflation, we used the GDP deflator, which is a price index of all final goods and services produced in the economy. Letting P 1960 and P 2014 denote the GDP deflator index in 1960 and 2014, respectively, then then π is computed as �� P 2014 � � 1 / 54 π = − 1 100 . (1) P 1960 On the horizontal axis is the average annual growth rate of the quantity of money in circulation, denoted µ . If M 1960 and M 2014 are the quantities of money in 1960 and 2014, respectively, then �� M 2014 � � 1 / 54 µ = − 1 100 . (2) M 1960 Each dot in the figure represents a different country, and there are 93 countries in in the sample. For each of the 93 countries, the figure displays with a dot the pair ( µ, π ). The empirical measure of money used in the plot is M2. ∗ ∗ For some countries the available sample is shorter than 1960-2014, but for all countries the sample is at least 10 years long. 8
Economics UN3213 Monetary Economics Lecture 16 The central message of the figure is that when we consider a rela- tively long period of time, in this case 54 years, then average infla- tion moves one-for-one with the average growth rate of the money supply. The cloud of points lies roughly on a 45-degree line, sug- gesting a high correlation between money growth and inflation in the long run. The correlation between inflation and money growth is 0.95. This high correlation obtains independently of the level of income. For instance, the correlation between π and µ is 0.96 among the group of OECD countries, which includes some of the richest countries in the world, and 0.96 among Latin American countries, a group that includes both middle and low income countries. The type of empirical evidence shown in the figure motivated the prominent economist Milton Friedman (1912-2006) to claim that “Inflation is always and everywhere a monetary phenomenon.” 9
Economics UN3213 Monetary Economics Lecture 16 What is the rate of inflation associated with very low growth rates of money? The figure suggests that the cloud of points intersects the vertical axis at a value slightly below zero. This suggests that when the money growth rate is nil for a long period of time, the associated average rate of inflation is negative. 10
Economics UN3213 Monetary Economics Lecture 16 Economic Growth and Money Growth in the Long Run 11
Economics UN3213 Monetary Economics Lecture 16 Empirical Evidence On Money Growth and Economic Growth Take a look at the next figure 12
Economics UN3213 Monetary Economics Lecture 16 Money Growth and Output Growth Across Countries: 1960 to 2014 25 20 15 Real Output Growth, g 10 5 0 −5 0 20 40 60 80 100 120 Money Growth, µ 13
Economics UN3213 Monetary Economics Lecture 16 The figure displays the average growth rate of money and the av- erage growth rate of output over the period 1960 to 2014 for 100 countries. The vertical axis measures g , the average annual growth rate in real GDP. If we denote real output in 1960 and 2014 by Y 1960 and Y 2014 , respectively, then g is given by � 1 / 54 � Y 2014 100 . g = − 1 Y 1960 The horizontal axis measures the average growth rate of money, µ . The figure displays with dots the pairs ( µ, g ) for 100 countries. 14
Economics UN3213 Monetary Economics Lecture 16 Observations On The Figure The message conveyed by the figure is that, in the long run, there is no relation between output growth and money growth. This empirical fact is known as long-run Monetary Superneutral- ity . Definition of Monetary Superneutrality: changes in the money growth rate leave real variables (e.g., real GDP, real consumption, the real interest rate) unchanged. Any sound Monetary Theory must capture facts (a) and (b). Keep in mind that (a) and (b) are facts concerning the long-run relationship between money growth and inflation and money growth and output growth, respectively. 15
Economics UN3213 Monetary Economics Lecture 16 The Quantity Theory of Money The Quantity Theory of Money asserts that a key determinant of the price level and inflation is the quantity of money issued by the central bank. According to the Quantity Theory of Money (QTM), agents hold a stable fraction of their income in the form of money. What does this mean? Let M d t be people’s desired nominal money holdings. People need money to perform transactions (purchases and sales of goods and services). In its simplest version, the QTM postulates that the demand for money is a constant fraction 1 v of nominal output P t Y t . ¯ That is, t = 1 M d vP t Y t , (3) ¯ where P t is the price level and Y t is real output. The parameter ¯ v is known as money velocity. To grasp the intuition why ¯ v is called money velocity, rearrange the above expres- v = P t Y t sion to get ¯ t . This says that each dollar of money is used to perform ¯ v M d transactions. The higher is ¯ v the faster money has to circulate in the economy. 16
Economics UN3213 Monetary Economics Lecture 16 Let M t be the money supply. . Equilibrium in the money market requires that M t = M d t , (4) Combining (3) and (4) we get M t = 1 vP t Y t . ¯ Rearranging this expression yields vM t P t = ¯ . (5) Y t This expression says that, given output, the price level is determined by the money supply. It also says that, given output, an increase in the money supply is associated with a proportional increase in prices. 17
Economics UN3213 Monetary Economics Lecture 16 Empirical Regularity (a) and the QTM Recall the graph relating inflation and the growth rate of the money supply across countries between 1960 and 2014: 120 45 o 100 80 60 In fl ation, π 40 20 0 −20 0 20 40 60 80 100 120 140 Money Growth, µ 18
Economics UN3213 Monetary Economics Lecture 16 What does the quantity theory predict for the relationship between the long-run growth rate of the money supply and the long-run growth rate of prices? In other words, assuming that the quantity theory is true, what would the scatter plot of the previous slide look like? Start with equation (5): vM t P t = ¯ Y t This expression also holds in in period t − 1 vM t − 1 P t − 1 = ¯ Y t − 1 19
Economics UN3213 Monetary Economics Lecture 16 Divide these expressions term by term to obtain P t M t Y t − 1 = P t − 1 M t − 1 Y t Note that money velocity, ¯ v , disappeared, because, by assumption, it does not change over time. Using our notation for inflation and money and output growth, we can write this expression as 1 + π t = 1 + µ t , 1 + g t where g t denotes the growth rate of real output. Taking logs and using the approximation ln(1 + x ) ≈ x yields: π t = µ t − g t 20
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