1. The demand for money 1

2. What is money? 1.Means of exchange (pay bills) 2.Unit of account (what are units in balance sheets) 2

3. 3 Money and finance: The superstars of all time 3 Irving Fisher, Yale (1867-1947) James Tobin, Yale (1918-2002) Milton Friedman, Chicago (1912-2006)

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

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7. 7 Source: Federal Reserve, Flow of Funds, Table B.100; in 2009 $. Real Wealth of US Households (corrected from class)

8. 8 Simplification for macro In macro, we assume 2 assets (money and bonds). Further assume no inflation, so inflation = п =0 and r = i. Assume that nominal interest rate on money = 0. In short run, wealth is fixed, so this reduces to the demand for money equation: This is the canonical equation used in macroeconomics.

9. 9 MdMd MdMd i Interest rate on bonds (i) Demand for transactions deposits

10. 10 Cash in advance (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 Milton Friedman; money demand insensitive to interest rates and only money matters.

11. 11 Y 01 Average money balance M = Y/2

12. Whats wrong with this theory? 12

13. 13 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. See next slide for example. 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. Not in textbook. I have a little note, and this will be covered in section.

14. Example of how companies keep M = 0. 14

15. 15 Baumol-Tobin model 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.

16. 16 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

17. 17 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 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.

18. 18 Is money demand interest elastic (1975-2012)?

19. Dependent Variable: ln(Real M1) Method: Least Squares Sample (adjusted): 1959Q2 2011Q2 Coefficientt-StatisticProb. ln(3 mo Tbill)-0.040 -5.00.0000 ln(real GDP) 0.31 100.0016 Constant Standard error regression =0.085 ****************************************************************************************** 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? 19 Econometric estimate of money demand equation

20. 20 DMDM DMDM i Equilibrium in the money market SMSM i* M* Money balances SMSM i* M*

21. 21 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 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 This is the nightmare scenario for the economy and explains (in part) why the recovery has been so slow.

22. The supply and demand for bank reserves, 1950-2012 22 S S S S

23. 23 Overview of Supply and Demand for Money 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; 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)

24. Daily life in macroeconomics 24 Fiscal cliff looming What will my tax rates be? Election uncertainties Eurozone on brink of collapse What will happen to debt?