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Money and Interest Rates MBA 774 Macroeconomics Class Notes – Part 2 Money and Interest Rates 1 What is Money? Medium of exchange Unit of account Allows transactions not based on barter Avoids the need for a “double coincidence of wants” Common measure of value for goods, services, and contracts Store of value Allows for transfer of wealth through time Most liquid of all assets Money and Interest Rates 2 Types of Money Pure Commodity Commodity Standard Scarce commodity is agreed on as “money” For example: gold, silver, cattle, cigarettes Certificates representing claims on a commodity are issued and used instead of the commodity itself For example: the US was once on a “gold standard” Fiat Money Money established by government decree Fiat money has no intrinsic value Money and Interest Rates 3 US Measures of Money Currency = Bills and coins outside U.S. Treasury, Federal Reserve Banks and the vaults of depository institutions M1 = Currency plus travelers’ checks, demand deposits, other checkable deposits M2 = M1 plus savings deposits, small-denomination time deposits, retail money market mutual funds, and overnight repurchase agreements M3 = M2 plus large-denomination time deposits, institutional money funds, and Eurodollars L = M3 plus other liquid securities such as savings bonds and short-term Treasury securities Money and Interest Rates 4 US Money Supply Statistics Measure USD Billions % of M3 1-yr %Chg Currency 653 7.3% 5.6% M1 1,288 14.5% 8.1% M2 6,109 68.6% 7.2% M3 8,900 100.0% 6.8% Source: Federal Reserve Statistical Release H.6 Money and Interest Rates 5 The US Federal Reserve Federal Reserve System is the US “central bank” Foreign counterparts include the European Central Bank (ECB), The Bank of England, and the Bank of Japan Founded in 1913 by congress, “to provide the nation with a safer, more flexible, and more stable monetary and financial system.” Primary functions are Monetary policy Banking supervision and regulation Providing certain services (e.g., check clearing) Money and Interest Rates 6 The US Federal Reserve (2) The “System” is composed of 12 regional banks and a Board of Governors in Washington, DC Governors, the Chairman and Vice-Chairman are appointed by the President and confirmed by the Senate Monetary policy is overseen by the “Federal Open Market Committee” or FOMC which includes Board of Governors Fed Bank of NY President 4 other regional bank presidents on a rotating basis Money and Interest Rates 7 Monetary Policy (1) About every six weeks the FOMC meets to determine monetary policy for the US In practice, this means determining the target for the “Federal Funds Rate” which is an inter-bank overnight interest rate Fed decreases (increases) the Fed Funds rate by buying (selling) government securities which increases (decreases) the available money supply The Federal Reserve Bank of NY makes these purchases or sales on the open market--hence the name Federal Open Market Committee. Money and Interest Rates 8 Money and Interest Rates 9 7/4 / 20 7/4 / 20 7/4 / 20 7/4 / 20 7/4 / 20 7/4 / 20 7/4 / 20 7/4 / 19 7/4 / 19 7/4 / 19 7/4 / 19 7/4 / 19 06 05 04 03 02 01 00 99 98 97 96 95 94 93 92 91 90 8.00% 7/4 / 19 7/4 / 19 7/4 / 19 7/4 / 19 7/4 / 19 Monetary Policy (2) 9.00% Fed Funds Target Fed Funds Actual 7.00% 6.00% 5.00% 4.00% 3.00% 2.00% 1.00% 0.00% The Fed’s Actions around 9/11 4.00% 3.50% 3.00% 2.50% Fed Funds Actual Fed Funds Target 2.00% 1.50% 1.00% 0.50% Stock Markets Re-open 9/ 9/ 01 9/ 11 /0 1 9/ 13 /0 1 9/ 15 /0 1 9/ 17 /0 1 9/ 19 /0 1 9/ 21 /0 1 9/ 23 /0 1 9/ 25 /0 1 9/ 27 /0 1 9/ 5/ 01 9/ 7/ 01 0.00% Money and Interest Rates 10 Monetary Policy (3) The official objectives of US monetary policy are, “economic growth in line with the economy's potential to expand, a high level of employment, stable prices (that is, stability in the purchasing power of the dollar), and moderate long-term interest rates.” Conceptually, the Fed will raise (the real) interest rate if GDP is greater than “Potential GDP” and vice-versa Money and Interest Rates 11 Aside: Real vs. Nominal Rates It is often said that the interest rate is the “cost of money.” Is this true? Ultimately, we use money to obtain consumption goods Think of the interest rate in terms of trading some real amount of consumption in one time period for some real amount of consumption in another time period Note however, borrowing and lending contracts are stated in nominal terms. Money and Interest Rates 12 Aside: Real vs. Nominal Rates The real rate of interest (R*) can be defined as approximately, Real Interest Rate = Nominal Interest Rate - Anticipated Inflation Currently, what is R* in the U.S.? Japan? Money and Interest Rates 13 Monetary Policy (4) Potential GDP is the rate of economic activity that leads to stable prices and employment Intuitively it is the amount of output that is generated by utilizing all available resources at there highest sustainable level. Algebraically, we can think of it as PotGDP = (aggregate hours available for work) x (average output per hour) Money and Interest Rates 14 Monetary Policy (5) Economists often discuss the Potential GDP Growth Rate which is approximately PotGDP Growth = Labor Force Growth Rate + Productivity Growth Rate We can calculate PotGDP Growth with this formula for the last 50 years Money and Interest Rates 15 Historical Potential GDP 10.0% Productivity Growth Labor Force Growth 8.0% 6.0% 4.0% 2.0% 0.0% Money and Interest Rates 16 20 00 19 95 19 90 19 85 19 80 19 75 19 70 19 65 19 60 19 55 19 50 -2.0% Better Estimates of PotGDP 6.0% 5.0% 4.0% 3.0% 2.0% 1.0% PotGDP-Congressional Budget Office Estimates PotGDP-( 5yr- Moving Average from Previous Graph) Money and Interest Rates 17 00 20 95 19 90 19 85 19 80 19 75 19 70 19 65 19 60 19 55 19 19 50 0.0% Monetary Policy and the GDP Gap Note: GDP Gap = (Actual GDP - PotGDP) / PotGDP 10.0% Real Fed Funds GDP-Gap 5.0% 0.0% -5.0% Money and Interest Rates 18 20 05 20 00 19 95 19 90 19 85 19 80 19 75 19 65 19 60 19 55 -10.0% 19 70 Monetary Policy Monetary Policy Regime Change Regime Change NAIRU Another way of thinking about potential output is the equilibrium rate of unemployment or NAIRU (Non-accelerating Inflation Rate of Unemployment) NAIRU is the rate of unemployment below which there will be inflationary pressures The exact level of NAIRU is an issue of debate. Most economists believe it is somewhere between 4% and 6% in the US and Japan. Probably higher in Europe (7-8%). Money and Interest Rates 19 Monetary Policy and NAIRU Note: U-NAIRU is actual unemployment minus NAIRU and is sometimes called the employment gap. 10.0% Real Fed Funds U-NAIRU 5.0% 0.0% Monetary Policy Regime Change Money and Interest Rates 20 20 05 20 00 19 95 19 90 19 85 19 80 19 75 19 70 19 65 19 60 19 55 -5.0% Other Mechanisms for Monetary Policy The Fed also has two other ways of controlling monetary policy The discount rate Reserve requirements Reserve requirements (rr) directly affect the level of money via the “money multiplier” (1/rr) Example, if the reserve requirement is 20% of deposits then the money multiplier is 1/0.2 = 5 Money and Interest Rates 21 Fractional Reserve Banking The Fed buys a $1,000 (market value) treasury bond from a bond dealer The dealer deposits the $1,000 proceeds into its bank, FirstBank Money supply increases by $1,000 FirstBank only has to keep $200 as reserves and loans the $800 balance: FirstBanks Balance Sheet Assets Liabilities Reserves $200 Deposits Loans $800 Money and Interest Rates $1,000 22 Fractional Reserve Banking (2) Assume FirstBank made an $800 computer loan to a student. Money supply increases to $1,800 The student buys a computer at BestBuy which deposits the $800 at its bank, SecondBank SecondBank also loans out all but 20% SecondBank Balance Sheet Assets Liabilities Reserves $160 Deposits Loans $640 $800 Now money supply = 1,000 + 800 + 640 = 2,440 Money and Interest Rates 23 Fractional Reserve Banking (3) This practice of keeping 20% reserves and loaning out the rest continues indefinitely However, the ultimate increase in the money supply (DMS) is finite and equal to DMS = DD / rr DMS = $1,000 / 0.2 DMS = $5,000 where DD is the original increase in money by the Fed [ Mathgeeks note, its a converging geometric sequence: 1+x+x2+x3+... = 1/(1-x) where x = (1-rr) ] Money and Interest Rates 24 Fed Reserve Requirements Type of Deposit Net transaction accounts $0 million-$6.6 million $6.6 million-$45.4 million More than $45.4 million Nonpersonal time deposits Eurocurrency liabilities Requirement % of Deposits Effective Date 0 3 10 0 0 12/25/03 12/25/03 12/25/03 12/27/90 12/27/90 Required reserves must be held in the form of deposits with Federal Reserve Banks or vault cash. Nonmember institutions may maintain reserve balances with a Federal Reserve Bank indirectly, on a pass-through basis, with certain approved institutions. Under the Monetary Control Act of 1980, depository institutions include commercial banks, savings banks, savings and loan associations, credit unions, agencies and branches of foreign banks, and Edge Act corporations. See also: http://www.federalreserve.gov/monetarypolicy/0693lead.pdf Money and Interest Rates 25 Interest Rates There are lots of important USD interest rates Federal funds rate Discount rate Prime rate Commercial paper rate LIBOR and Eurodollar (similar for other currencies) T-bill, T-note, T-bond rate Swap rates Corporate bond rates Overnight repurchase rate or “Repo” rate Rates depend on credit risk, liquidity, and maturity Money and Interest Rates 26 Government Issues 20 3-month T-Bill 20-year T-Bond Term Spread 15 10 5 Thru 5/06 0 Money and Interest Rates 27 20 04 19 99 19 94 19 89 19 84 19 79 19 74 19 69 19 64 19 59 19 54 19 49 19 44 19 39 19 34 -5 Corporate Bonds 20 Moody's AAA Corp Moody's Baa Corp Baa Credit Spread (over Treasuries) 15 10 Thru 5/06 5 Money and Interest Rates 28 20 04 19 99 19 94 19 89 19 84 19 79 19 74 19 69 19 64 19 59 19 54 19 49 19 44 19 39 19 34 0 A Model of the Money Market More detail about what affects interest rates For now consider “money” to be M1 Also we assume that the money supply is controlled by the central bank (e.g., the US Federal Reserve) Specifically, the central bank fixes the amount of money in the aggregate economy (MS) at a level it desires regardless of other factors Money and Interest Rates 29 Individual Money Demand Individuals’ demand for money is based on The expected (real) return on money: The riskiness of the return Money (M1) pays little or no interest => higher interest rates will lead to less demand for money The risk of holding money comes from variation in the price level. Why? Liquidity The primary value associated with money is derived from liquidity Since a primary use of money is as a medium of exchange, this implies an increase in the value of individual transactions increases the demand for money Money and Interest Rates 30 Aggregate Money Demand Aggregate money demand is the sum of demand for money by all households and firms in the economy In aggregate we can say the determinants of the aggregate demand for money are The interest rate The price level (think CPI) Real national income (or GNP or GDP) Money and Interest Rates 31 Aggregate Money Demand Define aggregate money demand as MD = P * L(R,Y) or MD / P = L(R,Y) where, MD = Aggregate money demand P = Price level R = Interest rate Y = Real national income (or GNP or GDP) and, L decreases as R increases L increases as Y increases Money and Interest Rates 32 Aggregate Money Demand Interest Rate (R) Interest Rate (R) Increase in Y L(R,Y2) L(R,Y) L(R,Y1) Aggregate Real Money (M/P) Money and Interest Rates Aggregate Real Money (M/P) 33 Equilibrium in the Money Market In equilibrium, MS = MD = P*L(R,Y) Interest Rate (R) Real Money Supply R2 2 1 R1 3 R3 Q2 Money and Interest Rates MS/P Q3 Aggregate Real Money Demand L(R,Y) Aggregate Real Money (M/P) 34 Increase in Money Supply Suppose the money supply increases from M1/P to M2/P Interest Rate (R) Real Money Supply Increases R1 1 2 R2 M1/P Money and Interest Rates M2/P Aggregate Real Money Demand L(R,Y) Aggregate Real Money (M/P) 35 Increase in GDP Suppose real income (GDP) increases from Y1 to Y2 Interest Rate (R) Real Money Supply R2 2 R1 1 1’ L(R,Y2) L(R,Y1) MS/P Money and Interest Rates Q1’ Aggregate Real Money (M/P) 36 Determining the Real Interest Rate The interest rate is the price of future consumption in terms of consumption today Consider an individual with the following attributes Two-period time horizon (today and 1 future date) Only cares about one nonstorable commodity, say beer Endowment of concave production technology to produce beer equals T(X) Convex preferences for present and future consumption No opportunities to save across time periods Rational (implying she maximizes intertemporal utility) Knows the future with certainty Money and Interest Rates 37 Intertemporal Preferences Future Consumption (t=1) U1 > U2 > U3 U1 U2 U3 Consumption Today (t=0) Money and Interest Rates 38 Intertemporal Production Possibilities Frontier Future Consumption (t=1) 18 13 T(X) 10 Money and Interest Rates 20 Consumption Today (t=0) 39 Optimal Consumption Without Savings Future Consumption (t=1) C*1 = X*1 =14 U* C*0 = X*0 =9 Money and Interest Rates Consumption Today (t=0) 40 Optimal Consumption Without Savings Optimal level of production comes at tangency point of production function and indifference curves (this is the highest level of utility possible) Because there is no ability to borrow or lend, production = consumption in both periods so C*0 = X*0 Money and Interest Rates and C*1 = X*1 41 Savings: Borrowing and Lending C’’1 = C’’0 (1+R) Future Consumption (t=1) C’1 = C’0 (1+R) C1 = C0 (1+R) Slope of Savings Lines = -(1+R) C0 Money and Interest Rates C’0 C’’0 Consumption Today (t=0) 42 Optimal Production With Savings Future Consumption (t=1) C**1 = 17 14 U** U* U** > U* X**1 = 8 C**0 = 8 9 Money and Interest Rates X**1 = 16 Consumption Today (t=0) 43 Optimal Production With Savings If we allow savings across time periods our individual will: Choose the production levels at t=0,1 that maximizes total wealth at time 0 (W0) defined as W**0 = X**0 + X**1 / (1+R) Then chose the level of consumption in each period: (C**0 , C**1) that maximizes total utility given the level of total wealth Note that production and consumption are unbundled: C**0 X**0 and C**1 X**1 Money and Interest Rates 44 Optimal Production With Savings In this example, our individual is a lender This is because C**0 < X**0 In effect, our individual takes the amount not consumed (X**0 - C**0) and puts it in the bank to earn interest at a rate of R If our individual had different preferences, she might prefer to be a borrower Money and Interest Rates 45 Optimal Production With Borrowing Future Consumption (t=1) X**1 C*1 = X*1 C**1 U** > U* U** U* X**0 C* C**0 0 =X*0 Money and Interest Rates Consumption Today (t=0) 46 Change in the Interest Rate Future Consumption (t=1) Interest Rate Declines from RH to RL CH1 CL1 UH UH > UL UL XL1 XH1 -(1+RL) -(1+RH) CH0<CL0 XL0<XH0 LendingL Money and Interest Rates LendingH Consumption Today (t=0) 47 Why Are We Doing This?!? First, what have we established so far? The ability to lend or borrow increases utility The ability to lend or borrow uncouples production and consumption Individuals can be either borrowers or lenders depending on their intertemporal preferences Changes in interest rates effect the demand for borrowing and lending But our goal was to figure out where interest rates came from. How do these results help us? Money and Interest Rates 48 Equilibrium Interest Rate Now consider an economy with two individuals with different intertemporal preferences one will be a lender and one will be a borrower Lender will be supplier of funds and borrower will be demander of funds The interest rate in the economy will be set so that the supply of funds equals the demand for funds Money and Interest Rates 49 Equilibrium Interest Rate Future Consumption (t=1) CL1 UL* Lender X1 Borrower CB1 UB* CL0 Money and Interest Rates X0 CB0 Consumption Today (t=0) 50 Aggregate Economy Interest Rate Desired Lending (Supply of Funds) Desired Borrowing (Demand for Funds) R* Supply = Demand Money and Interest Rates Borrowing / Lending 51