1. 1 Lecture 3 on money and finance. Expectations theory of term structure, the demand for money, and equilibrium in the money market

2. Note on theory of the term structure Many businesses and households borrow risky long-term (mortgages, bonds, etc.). These differ from the federal funds rate in two respects: - term structure (discuss now) - risk premium (postpone) The elementary theory of the term structure is the “expectations theory.” It says that long rates are determined by expected future short rates. Two period example (where r t,T is rate from period t to T): (*) (1+i 0,2 ) 2 = (1+i 0,1 ) (1+E(i 1,2 )) More generally: 2

3. Note on theory of the term structure Many businesses and households borrow risky long-term (mortgages, bonds, etc.). These differ from the federal funds rate in two respects: - term structure (discuss now) - risk premium (postpone) The elementary theory of the term structure is the “expectations theory.” It says that long rates are determined by expected future short rates. Two period example (where r t,T is rate from period t to T): (*) (1+i 0,2 ) 2 = (1+i 0,1 ) (1+E(i 1,2 )) More generally: This is “first order theory.” Other theories involve “market segmentation” and “liquidity.” 3

4. Example Short rates: 1 year T-bond = 0.41 % per year 2 year T-bond =1.03 % per year Implicit expected future rate from 1 to 2 is: (1+r 0,2 ) 2 = (1+r 0,1 ) [1+E(r 1,2 )] (1+.0103) 2 = (1+.0041) [1+E(r 1,2 )] This implies: E(r 1,2 ) = 1.65 % per year *For simple analytics, see “TermStructureRomer” in Readings on classes.v2, primarily pp. 519-520. 4

5. 5 Recent term structure interest rates (Treasury) 5 Expectations theory says that short rates are expected to rise in coming years. Note that this can explain why Fed makes statement about future rates (look back at Fed statement.)

6. Older term structure interest rates (Treasury) 6 In period of very tight money (1981- 82) short rates were very high, and people expected them to fall.

7. So what was the purpose of Operation Forward Guidance? To lower long run interest rates by lowering expected future short term rates! This is a problem on Pset 2 for Wednesday. MAKE SURE YOU FOLLOW RULES ON PROBLEM SETS. 7

8. Fed funds to short rates 8

9. Short rates to long rates 9

10. Real interest rate for businesses r b = risky rate – inflation rate = i ff + term premium + risk premium -inflation 10

11. The real interest rate for business: the cost of capital today is back to normal! 11

12. The demand for money 12

13. What is money? 1.Means of exchange (pay bills) 2.Unit of account (what are units in balance sheets) 3.Operational: - M1 = Cu (public) + checking balances (of the public) - “M1 is defined as the sum of currency held by the public and transaction deposits at depository institutions (which are financial institutions that obtain their funds mainly through deposits from the public, such as commercial banks…).” -$2552 billion in August 2013, $1140 billion of currency (why so much currency?) 13

14. 14 Equations of normal short-run interest determination Supply of R: Fed supplies non-borrowed reserves (NBR) by open-market operations (OMO). We omit bank borrowings as normally tiny. (1) R s = NBR Demand for R: Banks are required to hold reserves on checking deposits (D). (2) R = h D Equality in normal times (not now!) The demand for checking deposits (D d ) is determined by output and interest rate: (3)D d = M(i, Y) This leads to the demand for reserves by banks in normal times: (4)R d = h M(i, Y) Which yields equilibrium of the market for reserves (5) h M(i, Y) = NBR + BR( d )

15. 15 Equations of normal short-run interest determination Supply of R: Fed supplies non-borrowed reserves (NBR) by open-market operations (OMO). We omit bank borrowings as normally tiny. (1) R s = NBR Demand for R: Banks are required to hold reserves on checking deposits (D). (2) R = h D Equality in normal times (not now!) The demand for checking deposits (D d ) is determined by output and interest rate: (3)D d = M(i, Y) This leads to the demand for reserves by banks in normal times: (4)R d = h M(i, Y) Which yields equilibrium of the market for reserves (5) h M(i, Y) = NBR + BR( d ) Today’s topic

16. Balance Sheet of Households Assets Liabilities Money (M1) Mortgage Other Net Worth Total Assets Liabilities and NW 16

17. 17 Source: Federal Reserve, Flow of Funds, Table B.100; in 2009 $. Real Wealth of US Households after the Crisis

18. 18 Simplification for now Assume no inflation, so inflation = п =0 and r = i. Assume that nominal interest rate on money = 0. Interest rate on bonds is i. In short run, wealth is fixed, so this reduces to the demand for money equation: This is the canonical equation used in macroeconomics. Impact of interest rates on demand for M: In earlier periods, monetarists assumed money was (virtually completely) interest inelastic – quantity theory. Today, most economists agree that money demand responds to interest rates.

19. 19 MdMd MdMd i Interest rate on bonds (i) Demand for transactions deposits Demand for money function

20. 20 The demand for money and interest rates, 1990 - 2013

21. 21 MdMd MdMd i Interest rate on bonds (i) Demand for transactions deposits SMSM SM’SM’ Equilibrium in the money market

22. 22 Central Bankers’ Nightmare: The Liquidity Trap In depressions or deep recessions, when i close to zero, have highly elastic demand for money and reserves –US 1930s, Japan 1990s and 2000s, US 2008 to at least 2015! Conventional monetary policy is therefore ineffective (note what happens when M supply shifts from S’’ to S’’’ in figure on next page). The Fed must turn to “unconventional instruments” These have been undertaken since 2008: –Forward guidance –Buying long-term assets (quantitative easing, or Large-Scale Asset Purchase Program*) –Setting goals that state that policy will be accommodative until reach full employment. US led the way on these, and followed by ECB, BOJ, and other central banks. * See http://www.federalreserve.gov/faqs/what-are-the-federal-reserves-large- scale-asset-purchases.htm

23. 23 The supply and demand for bank reserves, 1990-2013 23 S’ S S’’ S’’’

24. 24 Short Summary of Monetary Policy Starts with short-run interest rate (federal funds rate) Supply of reserves determined by central bank (Fed, ECB, …), Demand for transactions money (M 1 ) depends upon interest rate, Demand for reserves is derived demand from demand for money, THEN: Equilibrium of supply and demand for reserves → short- term nominal risk-free interest rate. Then to other assets and rates: Short rates + expectations → long risk-free rate by term structure theory Risky rates = risk-free rate + risk premiums Real rate = nominal rate – inflation (Fisher effect)