1. 1 Econ 122: Fall 2010 Determination of interest rates: Supply and demand for money and other assets

2. Information items We will have special TF Friday presentations on finance, math, and financial reform later in course. Problem 1 will be posted today. Readings on money are chapter 19 not 18. Sections this week. If you are Wed pm, go to Thurs pm or other. Sections: Wed 4-4:50 is in WLH 112 Wed 5-5:50 is in WLH 209 Thurs 4-4:50 is in WLH 203 Thurs 5-5:50 is in WLH 002 Thurs 7-7:50 is in WLH 112 Thurs 8-8:50 is in WLH 007 Notes on readings [on the board] 2

3. 3 Federal Reserve Districts

4. 3. FOMC Minutes August 10, 2010 The information reviewed at the August 10 meeting indicated that the pace of the economic recovery slowed in recent months …. The economy was operating farther below its potential than they had thought and the pace of recovery had slowed in recent months… Many said they expected underlying inflation to stay below levels they judged most consistent with the dual mandate to promote maximum employment and price stability. Participants viewed the risk of deflation as quite small, but a number judged that the risk of further disinflation had increased somewhat despite the stability of longer-run inflation expectations. The Committee determined it would be appropriate to maintain the target range of 0 to 1/4 percent for the federal funds rate …. [It] Reiterated the expectation that economic conditions were likely to warrant exceptionally low levels of the federal funds rate for an extended period. [Additionally and unconventionally, the Fed will] maintain the total face value of domestic securities held in the System Open Market Account at approximately $2 trillion by reinvesting principal payments from agency debt and agency mortgage-backed securities in longer-term Treasury securities. Voting: 10 to 1 in favor. 4

5. Administration (cont.) 4. Actual mechanism: Open market operations are arranged by the Domestic Trading Desk at the Federal Reserve Bank of New York (“the Desk”) Every morning, staff decided if an OMO is needed to keep rate near target. Fed contacts the “primary dealers” (e.g., Goldman Sachs, BNP Paribas, Morgan Stanley, etc.) and asks them to make offers Fed generally makes temporary purchases (“repos” = purchase and forward sale, or the reverse) at 10:30 each day, but generally does not enter more than once per day. Because the Fed intervenes only daily, the FF rate can deviate from the target. 5. Then supply and demand for reserves take over 5

6. Recent history of Fed Funds rate: 2007-2010 6

7. Recent history of Fed Funds rate: 2008 7

8. General equilibrium of assets Have multiple assets of interest rates or yields General theory: - short term nominal rates determined by Fed - long term safe rates determined by expected future short rates. - risky rates = safe rates + risk premium - real interest rate = nominal interest rate - inflation 8

9. 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+r 0,2 ) 2 = (1+r 0,1 ) [1+E(r 1,2 )] With risk neutrality and other conditions, (*) determines term structure. (Finance people find many deviations, but good first approximation.) 9

10. Recent term structure interest rates (Treasury) 10 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.)

11. Older term structure interest rates (Treasury) 11 In period of very tight money (1981- 82) short rates were very high, and people expected them to fall.

12. 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 [Again, finance specialists point to deviations from this simple theory.] 12

13. But the major story to remember is the following: 13

14. The demand for money 14

15. Mechanics of OMO: The Fed buys a security… 15 FedCommercial banks and primary dealers Assets Liabilities Bonds 1000 Bank borrowings 0 Cu 900 Reserves (bank deposits) 100 Investments 1000 Checkable deposits 1000 Equity 100 Reserves (bank deposits) 100

16. … and this increases reserves … 16 FedCommercial banks and primary dealers Assets Liabilities Bonds 1000 +10 Bank borrowings 0 Cu 900 Reserves (bank deposits) 100 +10 Investments 1000 -10 Checkable deposits 1000 Equity 100 1.Fed buys bond. 2.Dealer deposits funds in bank. 3.This creates a credit in the account of the bank at the Fed and voilà! the Fed has created reserves. (red) Reserves (bank deposits) 100 +10

17. … and normally this increases investments and M 17 FedCommercial banks and primary dealers Assets Liabilities Bonds 1000 +10 Bank borrowings 0 Cu 900 Reserves (bank deposits) 100 +10 Investments 1000 +100 -10 Checkable deposits 1000 +100 Equity 100 1.Fed buys bond. 2.Dealer deposits funds in bank. 3.This creates a credit in the account of the bank at the Fed and voilà! the Fed has created reserves. (red) 4.In normal times, the bank lends out the excess, and this leads to money creation (blue). Today, this just increases reserves. Reserves (bank deposits) 100 +10

18. Actual and required reserves 18

19. … but today it just increases excess reserves 19 FedCommercial banks and primary dealers Assets Liabilities Bonds 1000 +10 Bank borrowings 0 Cu 900 Reserves (bank deposits) 100 +10 Investments 1000 -10 Checkable deposits 1000 Equity 100 1.Fed buys assess backed mortgage (from bank for simplicity) 2.Bank is glad to unload it, and just holds excess reserves. 3.No impact on the money supply or on federal funds rate. A (very small) impact on mortgage interest rates. Reserves (bank deposits) 100 +10

20. Now let’s move on to money demand Recall that monetary policy operates on the market for reserves. The demand for reserves is a derived demand – derived from the demand for money. We need therefore to understand the foundations of the demand for money, and particularly why it depends upon the interest rate. 20

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22. 22 Source: Federal Reserve, Flow of Funds, Table B.100; in 2009 $. Real Wealth of US Households

23. 23 Simplification for macro Let k = number of “independent assets.” In macro, we generally use k = 2 (money and bonds). Further assume no inflation, so inflation = п =0 and r = i. Assume that nominal interest rate on money = 0. We then substitute in the wealth identity to get: In short run, W(t) is fixed, so this reduces to the demand for money equation: This is the canonical equation used in macroeconomics.

24. 24 Fisher Theory of Transactions Demand for Money The transactions demand is a specific case of an inventory demand theory (think shoe store) Used in advanced macro in “cash-in-advance models” Simple example:  earn Y at beginning (example is per year; more generally would be per payment period of say month)  spend evenly at rate of Y per period  constant price level  money has yield of 0  no opportunity to move from money to other assets.  In this case, we see that the average money holdings: M* = Y/2  This leads to “monetarist” theory of M. Friedman; money demand insensitive to interest rates and “only money matters.”

25. 25 Y 01 Average money balance M = Y/2

26. What’s wrong with this theory? 26

27. Opportunity cost of money balances Source: Treasury interest rate from Federal Reserve; interest rate on checking accounts from Informa Research Services, Inc. 27

28. 28 More general demand for money What happens if we have other assets? If have bonds as well as money, then can move some of money to bonds to earn interest. Yale train to New York in 1950s; “repos” today for wholesale This leads to more general theories in which the demand for money is interest-elastic Baumol-Tobin model. This is an explicit model of how income, interest rates, and other factors determine how often we move money to bonds. Typical methodology of macroeconomics. We will cover briefly and do more carefully in section (see Mankiw, pp. 559-562)

29. 29 Baumol-Tobin model Problem with Fisher model: Assumes only one asset (M) Must recognize that there are other assets that you can purchase depending upon costs and benefits Say that can move back and forth into and out of bonds (M and B) Bonds yield i B > i M = 0. Go to bank at beginning of period and deposit half in bonds; then go in mid-period to move to money so that you can buy your pizzas. For one trip, have only half the money and the other half is earning interest.

30. 30 Y 01 Average money balances are triangles labeled “Money” For 2 trips to the bank, have M* = Y/4 Bonds Money For N trips to the bank, have M* = Y/2N

31. 31 Money and finance: The finale 31 Irving Fisher, Yale (1867-1947) James Tobin, Yale (1918-2002) Milton Friedman, Chicago (1912-2006)

32. Daily life in macroeconomics 32 Summers leaving Recession over FOMC sits pat No federal budget for next year Tax extension stalemate

33. Info items Federico will do a special session on finance this Friday, here at 11:35. Reading is from a free online textbook on Corporate Finance, available at the course website. 33

34. 34 Optimizing money balances (special case of optimal inventory ): Total cost = C(N) = Forgone Interest + Cost of trips = iY/(2N) + FN Maximizing to determine optimal number of trips (N*): dC/dN = 0 = - iY/(2N* 2 ) + F N* = (iY/2F) ½ Optimal average money holding are M* = Y/(2N*) = (YF/2i) ½ This is the famous “square root inventory rule” for money holdings What are elasticities of M w.r.t. Y and i (E M,Y and E M,i )? [E =½ ] This is the crux of the debate between monetarists and Keynesians: Is the interest elasticity E M,i = 0 or < 0? If = 0, monetarist; if < 0 then Keynesian Huge debate in 1960s and 1970s; pretty much settled now.

35. 35 Empirical test of money demand equation: Is money demand interest elastic (1975-2009)?

36. Dependent Variable: ln(Real M1) Method: Least Squares Sample (adjusted): 1959Q2 2009Q2 Coefficientt-StatisticProb. ln(3 mo Tbill)-0.040 -7.00.0000 ln(real GDP) 0.34 3.20.0016 Constant, AR1, … Standard error regression =0.033 ****************************************************************************************** Elasticities have correct sign and are statistically significant but interest rate coefficient is small. Why is E M,i so small? Wrong model? Behavioral economics? Corner solution? 36 Econometric estimate of money demand equation

37. 37 DMDM DMDM i Short term interest rate SMSM i* M* Money balances S’ M i*’ M*’

38. 38 Monetary policy helpless: 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 2010! Monetary policy therefore ineffective (note what happens when M supply shifts from S to S’’’ in figure on next page). The Fed has “run out of bullets,” or at least conventional bullets, and must turn to “unconventional instruments” This is the nightmare of central banks!

39. The supply and demand for bank reserves, 1950-2010 39 S’ S S’’ S’’’

40. 40 Portfolio Theories More general theories This goes back to our general equilibrium model above; multiple assets (money, bonds, stocks, foreign assets,...) Portfolio theory considers how to allocate wealth among assets Yale’s management of endowment Individual’s management of 401(k) account Standard analysis examines preferences (like life-cycle model + preference toward risk) asset risks and returns Many good courses at Yale and B. Schools This leads to the modern theory of finance. You can get a preview on Friday from Federico (same time, same station; free reading online)