The demand for money

1. The demand for money

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

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

4. Equations of short-run interest determination • Demand for R: • Bank regulation: reserve requirement on checking deposits (D). • (1’) R = hD In normal times (not now!) • The demand for checking deposits (Dd) is determined by output and interest rate: • Dd = M(i, Y) • This leads to the demand for reserves by banks in normal times: • Rd = 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) Rs = NBR • Which yields equilibrium of the market for reserves • (5) h M(i, Y) = NBR + BR(d)

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

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

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. Y Average money balance M = Y/2 0 1

12. What’s wrong with this theory?

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.

15. Baumol-Tobin model • Say that can move back and forth into and out of bonds (M and B) • Bonds yield iB > iM = 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. Y Average money balances are triangles labeled “Money” Money For 2 trips to the bank, have M* = Y/4 For N trips to the bank, have M* = Y/2N Bonds Money 0 1

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) + FN* = (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 (EM,Y and EM,i )? [E =½ ] • This is the crux of the debate between monetarists and Keynesians: • Is the interest elasticity EM,i = 0 or < 0? • If = 0, monetarist; if < 0 then Keynesian • Huge debate in 1960s and 1970s; pretty much settled now.

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

19. Econometric estimate of money demand equation • Dependent Variable: ln(Real M1) • Method: Least Squares • Sample (adjusted): 1959Q2 2011Q2 • Coefficientt-StatisticProb. • ln(3 mo Tbill) -0.040 -5.0 0.0000 • ln(real GDP) 0.31 10 0.0016 • Constant • Standard error regression = 0.085 • ****************************************************************************************** • Elasticities have correct sign and are statistically significant but interest rate coefficient is small. • Why is EM,i so small? Wrong model? Behavioral economics? Corner solution?

20. i SM SM DM Equilibrium in the money market i* i* DM Money balances M* M*

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 S S’’’ S’’ S’

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 (M1) 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 Election uncertainties Fiscal cliff looming Eurozone on brink of collapse What will my tax rates be? What will happen to debt?