PRINCIPLES OF MACROECONOMICS
Ranjit Dighe
WEEK 10 (LECTURES 25 - 27)
April 3-7, 2000

[This week we wrapped up the unit on money and monetary policy. The lectures overlap with Case & Fair's Chapters 11, 12, and 13, most especially with Chapter 11, which is the meatiest of those chapters. Next week we'll be jumping back to Chapters 9 and 10 (which were listed under Week 8 in the original syllabus. Yes, we're a bit behind schedule).]

LECTURE 25
Mon., April 3, 2000

0. IMPEDIMENTA

* Today:
I. Go over 2nd exam
II. Tools of monetary policy
III. An example of multiple deposit creation
 

I. GO OVER 2ND EXAM
- [Exams were handed back right before class.]
- [Going over the exam took up most of this day's class. You kind of had to be there. Solutions are posted on the web.]
 

II. TOOLS OF MONETARY POLICY

When the Fed conducts monetary policy, it directly affects the level of bank reserves, causing banks to have either excess reserves (which they loan out) or a reserve deficiency (which causes them to call in loans). In either case, the supply of money changes by a multiple of the original change in reserves:

money multiplier = (change in money supply)/(change in bank reserves) = 1/RRR

The Fed has three tools that it uses to conduct monetary policy:

(1) changes in the required reserve ratio (RRR)

(2) changes in the discount rate
-- The Fed controls the DISCOUNT RATE (the interest rate at which the Fed loans money to banks)

(3) open market operations (OMO)
-- In OMO, the Fed buys or sells bonds, usually from the banks, in order to affect the level of bank reserves and the FEDERAL FUNDS RATE (the interest rate at which commercial banks loan each other money, in the form of reserves, on an overnight basis). In turn, the money supply and other interest rates will be affected, too.
-- OMO is the Fed's most important and most-used policy tool.
-- The Fed uses OMO to affect the federal funds rate, which is its mostly widely watched interest-rate target.

***

PRINCIPLES OF MACROECONOMICS
WEEK 10, LECTURE 26
Wed., April 5, 2000

0. IMPEDIMENTA

* Pick up Problem Set 7

* [POP QUIZ: This was more like an "attendance quiz," with five very easy questions. Pop quizzes are not posted on the web with the other ones, because the questions are so easy.]

* Today:
I. Tools of monetary policy (continued)
II. OMO and the federal funds rate
III. An example of multiple deposit creation
 

I. TOOLS OF MONETARY POLICY (continued)

The Fed's three policy tools, in a bit more depth:

(1) Changes in banks' required reserve ratio (RRR)
-- The required reserve ratio (RRR) is now 10% of banks' checking deposits.
-- It was lowered from 12% in early 1990's.
-- The RRR on savings account, CD's, and money-market deposit accounts is zero.
-- Changes in the RRR have large effects on money supply: increasing RRR causes a decrease in banks' excess reserves and a decrease in the money multiplier (1/RRR), so the money supply decreases by a lot.
----> Because this tool's effects are so powerful as to preclude "fine tuning" (making small changes in monetary policy as needed), it is rarely used.  It is just too blunt an instrument.

(2) Changes in the discount rate (the interest rate at which the Fed loans money to banks)
-- When the Fed lowers the discount rate, bank reserves will increase, because banks will take advantage of the lower rates by borrowing more reserves from the Fed (and then loaning those reserves out).
-- Although the Fed is officially a "lender of last resort" to banks, to be used only when banks are in desperate situations, when it lowers the discount rate it is generally signaling a relaxation of that rule, i.e. an increased willingness to make ordinary loans to banks in order to expand the volume of money and credit.

* (3) Open market operations (OMO)
-- How OMO works: when the Fed buys or sells securities (government bonds) from banks, it makes or collects the payment for those bonds by crediting or debiting the banks' reserve accounts at the Fed and thereby changing the level of bank reserves, which changes the money supply in the same direction. These operations are carried out solely by the regional Fed bank of New York.
---- Expansionary monetary policy calls for open-market purchases: Fed buys securities, pays by crediting banks' reserve accounts --> money supply expands, interest rates fall.
---- Contractionary monetary policy: open-market sales: Fed sells securities, collects payment by debiting banks' reserve accounts --> money supply shrinks, interest rates rise.
 

II. OMO AND THE FEDERAL FUNDS RATE

The Fed's most-watched policy instrument is the FEDERAL FUNDS RATE (the interest rate at which banks make overnight loans of reserves to other banks). Since it is commercial banks, not the Fed, that makes these loans, the Fed does not set the federal funds rate directly. Instead, it is determined by the supply and demand for overnight loans and reserves (the FEDERAL FUNDS MARKET), as in the following diagram.
-- [A supply-and-demand diagram of the federal funds market was shown in class. Probably won't be found in the book. In the diagram, the quantity of (borrowed) bank reserves is on the horizontal axis, the interest rate (price) on borrowed bank reserves is on the vertical axis, the supply curve is upward-sloping, and the demand curve is downward sloping.]
---- [There is, unfortunately, no diagram just like it in Case & Fair's book, though Figure 12.6, on p. 261, is similar. Just replace the vertical supply curve with an upward-sloping one, and replace "Money" with "Reserves".]

The Fed uses OMO to affect the federal funds rate. Open-market purchases and sales by the Fed affect the federal funds rate because they affect the supply of bank reserves.

-- If the Fed makes an open-market purchase of a security from a bank, it pays for the security by crediting the bank's reserve account at the Fed; thus it is adding to the total supply of reserves. That addition corresponds to an outward shift of the supply curve of federal funds, which will cause the interest rate on reserves (i.e., the federal funds rate, or the "price" of borrowing reserves) to fall.
---- [In class I presented a diagram showing how an open-market purchase would reduce the federal funds rate. Again, there's no diagram just like it in Case & Fair's book, though graph number 10 in Figure 4.12 (page 91) is kind of similar.]

-- If the Fed makes an open-market sale of a security to a bank, it collects payment by debiting the bank's reserve account at the Fed; thus it is decreasing the total supply of reserves. That decrease corresponds to a leftward shift of the supply curve of federal funds, which will cause the interest rate on reserves (the federal funds rate) to rise.
---- [In class I presented a diagram showing how an open-market sale would increase the federal funds rate. Again, there's no diagram just like it in Case & Fair's book, though graph number 9 in Figure 4.12 (page 91) is kind of similar.]
 

III. AN EXAMPLE OF MULTIPLE DEPOSIT CREATION

Let us consider an example of an expansionary monetary policy move by the Fed. Suppose that the Fed conducts expansionary OMO by making an open-market purchase of securities. Specifically, the Fed buys $100 in securities from the First National Bank. (The required reserve ratio, RRR, for checking deposits is 10%. We will assume that First National and all other banks initially have zero excess reserves. Also assume that all loans get redeposited into checking accounts at First National.) The Fed pays for the securities by crediting First National's reserve account at the Fed with $100. We would like to know: What is the ultimate change in the money supply, after the entire chain of deposit creation has run its course?

THE SHORT WAY: Fast-forwarding a bit, we can answer that question right now, because we know the initial change in reserves (+$100) and can compute the money multiplier (1/RRR = 1/.10 = 10). The ultimate change in the money supply will be:
{increase in money supply} = {increase in reserves} * {money multiplier}
                                              = ($100) * (10)
                                              = $1000

THE LONG WAY: To see just how we got from an initial increase in reserves of $100 to a cumulative increase in the money supply of $1000, we can look at the changes in First National's balance sheet. The initial change in First National's balance sheet is:

(FIRST STAGE)
ASSETS LIABILITIES AND NET WORTH
Reserves + $100
Government bonds - $100

First National now has excess reserves of $100.
First National will loan out those excess reserves -- say, to me. I use that $100 to buy something (say, $100 worth of compact discs), and the CD merchant will either deposit that $100 in the banking system or spend it himself; either way, someone will eventually deposit that $100 cash in the banking system -- if not at First National, then at some other bank. With that new deposit the (cumulative) change in the banking system's balance sheet is as follows:

(SECOND STAGE)
ASSETS LIABILITIES AND NET WORTH
Reserves + $100 Checking deposits + $100
Government bonds - $100
Loans + $100

The money supply has expanded by $100, since the money supply includes checking deposits. The money-creation process will continue because the bank that received the $100 cash deposit now has excess reserves ( = actual reserves - required reserves ) of

$100 - (.10)($100) = $100 - $10 = $90.

The bank will loan out that $90 and it, too, will eventually be redeposited as cash in the banking system. Now the cumulative change in the banks' balance sheet is:

(THIRD STAGE)
ASSETS LIABILITIES AND NET WORTH
Reserves + $100 Checking deposits + $190
Government bonds - $100
Loans + $190

The banks have excess reserves of $81 ( = $100 - (.10)($190) = $100 - $19 ). They will loan them out and the money will be redeposited in the banking system, increasing checking deposits by another $81 dollars. Then 90 percent of that will be loaned out and redeposited, and 90 percent of that will be loaned out and redeposited, etc. The total increase in bank deposits (and hence in the money supply) will be:

    $100 + $90 + $81 + ($)(.90) + ($81)(.902) + ...
= $100 + ($100)(.90) + ($100)(.902) + ($100)(.903) + ($100)(.904) + ...

This seemingly endless sum is a geometric series, and is solvable as

$100 * 1/(1-.90) = $100 * (1/.10) * $100 * 10 = $1000,

which is where the money multiplier (1/RRR) comes from. Thus total bank deposits increase by $1000, as does the money supply. The total change in the banking system's balance sheet, when there are no more excess reserves remaining, is:

(FINAL STAGE)
ASSETS LIABILITIES AND NET WORTH
Reserves + $100 Checking deposits + $1000
Government bonds - $100
Loans + $1000

That $1000 increase in checking deposits all came about as the result of an initial increase in reserves of $100. Thus the total amount of deposits has expanded by a multiple (ten) of the original change in reserves.

To review:
* In this example, the Fed injects $100 in reserves into the banking system, by purchasing a $100 security from the First National Bank. To see how that increases the money supply, we need to keep track of the increase in checking deposits. After the Fed's purchase, First National has $100 in excess reserves. They loan those reserves out as $100 cash, and that $100 cash gets redeposited into a checking account at the bank. Then the bank has $100 in reserves again, and $90 of that is excess reserves (the remaining $10 has to be kept to meet their 10% reserve requirement on checking deposits; they can loan out 90% of any increase in cash deposits, so they loan out .90*$100 = $90). They loan out those excess reserves -- $90 cash -- and that $90 gets redeposited. They can lend out 90% of that (.90*.90*$100 = $81), and it will be redeposited. And so on.
* The sum of all these additional checking deposits is a geometric sum, which means that we have a simple formula for finding the total increase in deposits:

total increase in deposits = initial increase in deposits * (1/RRR)
* The initial increase in reserves of $100 ultimately leads to a $1000 increase in checking deposits, or a $1000 increase in the money supply.

***

PRINCIPLES OF MACROECONOMICS
WEEK 10, LECTURE 27
Fri., April 7, 2000

0. IMPEDIMENTA

* QUIZ

* Today:
I.  Multiple deposit creation & destruction
II. An example of multiple deposit destruction
 

I. MULTIPLE DEPOSIT CREATION & DESTRUCTION

Where we left off: Multiple deposit creation. Banks can create money by loaning out their excess reserves (ER) - as that money loaned out gets redeposited into bank accounts, money is created. Not only that, but when cash is redeposited, banks will have excess reserves. If the cash is deposited into a checking account (10% reserve requirement), the bank can loan out 90% of that cash. (If it's deposited into a savings account or CD, the bank can loan out all of it. For the sake of simplicity, though, we usually assume all loans are redeposited into checking accounts.) The cycle of ER being loaned out and redeposited and loaned out again will typically continue until ER=0, because every dollar of ER is an opportunity for banks to make a profit by loaning out that money. When that cycle, known as the chain of deposit creation, runs its course, then:

change in money supply = (initial change in reserves) * (money multiplier)
                                         = (initial change in reserves) * (1/RRR)
                                         = 10 * (initial change in reserves)                                    (if RRR = 10%)

Also,
change in money supply = change in checking deposits = change in bank loans.

Reserves, like matter, cannot be created or destroyed, at least not by the banks themselves. Reserves can, however, be created or destroyed by the Fed.

Expansionary monetary policy is conducted by the Fed when it wants to stimulate the economy (raise real GDP). In expansionary monetary policy, the Fed expands the level of bank reserves, and after the chain of deposit creation runs its course, the money supply [Ms] increases by a multiple of the increase in reserves. Interest rates [i (or r, if we want to use the same notation as Case & Fair] fall, (durable-goods) consumption [C] and (business) investment [I] increase, and real GDP [Y] increases (also, the price level [P] rises, the inflation rate [p] rises, and the unemployment rate [UR] falls; the economy moves northwest along the Phillips Curve).
-- The sequence, in shorthand:
Fed increases ER
-> Ms increases -> i decreases (r decreases) -> C increases, I increases -> Y increases; P increases, p increases, UR decreases

-- To conduct expansionary monetary policy, the Fed can do any or all of the following:
(1) lower the required reserve ratio (RRR)
(2) lower the discount rate
(3) make open market purchases of government bonds (expansionary OMO), causing the federal funds rate to fall

Contractionary monetary policy is conducted by the Fed when it wants to reduce the rate of inflation, or reduce inflationary pressures (e.g., from rapid economic growth). In contractionary monetary policy, the Fed decreases the level of bank reserves, and all of those up/down arrows are reversed. The economy moves southeast along the Phillips Curve, to a point of lower inflation but higher unemployment.
-- The sequence, in shorthand:
Fed decreases ER
-> Ms decreases -> i increases (r increases) -> C decreases, I decreases -> Y decreases; p decreases,
UR increases

-- To conduct contractionary monetary policy, the Fed can do any or all of the following:
(1) increase the required reserve ratio (RRR)
(2) increase the discount rate
(3) make open market sales of government bonds (contractionary OMO), causing the federal funds rate to rise

Other key interest rates, notably the PRIME INTEREST RATE (the interest rate for banks' best corporate customers) and MORTGAGE RATES (the interest rates on home loans), will move in the same direction as the federal funds rate, and by about the same amount.
-- [In class we saw a chart showing the federal funds rate and the prime interest rate over time (1991-1997). The two moved in almost perfect lock-step with each other; the prime interest rate was consistently about 3 percentage points higher than the federal funds rate.]
 

II. AN EXAMPLE OF MULTIPLE DEPOSIT DESTRUCTION

Imagine a bank (call it The Bank) whose balance sheet initially looks like the one below. Assume RRR=10% on checking deposits, all ER are loaned out, and all loans are redeposited into checking accounts at The Bank. Also assume that all loans are repaid by checks drawn on checking accounts at The Bank (or, more generally, by drawing down checking deposits at The Bank).
 
ASSETS LIABILITIES AND NET WORTH
Reserves $ 500 Checking deposits $5000
Government bonds $1500 Savings deposits $2000
Loans $5000 Net worth $1000
Other assets $1000
TOTAL ASSETS $8000 TOTAL LIABILITIES +N.W. $8000

ER = $500 - (.10)*($5000) = $500 - $500 = $0

Now suppose the Fed decides to contract the money supply by making an open-market sale of $100 in government bonds, from The Bank. The Fed will collect the payment by debiting The Bank's reserve account at the Fed. What will be the ultimate change in the money supply?

THE SHORT WAY: As in the previous example, we can answer that question right now, without drawing any more balance sheets, because we know the initial change in reserves (-$100) and can compute the money multiplier (1/RRR = 1/.10 = 10). The ultimate change in the money supply will be:
{increase in money supply} = {increase in reserves} * {money multiplier}
                                              = (-$100) * (10)
                                              = -$1000

THE LONG WAY: To appreciate the cycle of deposit destruction (loans being called in and deposits being drawn down) that causes the money supply to fall by so much, we need to look at the step-by-step changes in The Bank's balance sheet. Immediately after the Fed's open-market sale of $100 in bonds, the resulting change in The Bank's balance sheet will be:

(FIRST STAGE)
ASSETS LIABILITIES AND NET WORTH
Reserves - $100
Government bonds - $100

The Bank now has a reserve deficiency of $100. (ER = -$100; The Bank has negative excess reserves). The Bank must somehow increase its reserves by $100 (which it cannot do by itself, since only the Fed can create or destroy bank reserves) or reduce its required reserves by $100. The Bank will initially call in $100 in loans, and those loans will be repaid by the borrowers' drawing down their checking accounts at The Bank. The running change in The Bank's balance sheet is now:

(SECOND STAGE)
ASSETS LIABILITIES AND NET WORTH
Reserves - $100 Checking deposits - $100
Government bonds + $100
Loans - $100

The Bank still has a reserve deficiency at this point. Its reserves have not increased, because the loan was repaid by the borrower's drawing down her checking account at The Bank. (If she'd repaid the loan with cash from outside The Bank, it would be a different story.) Now, the change in the bank's excess reserves (ER) is:

change in ER = (change in actual reserves) - (change in required reserves)
                     = (-$100) - (.10)*(-$100)
                     = (-$100) - (-$10)
                     = (-$100) + ($10)
                     = -$90

If The Bank were to call in $90 more in loans, it would reduce its ER a little (because $90 would be drawn down on somebody's checking account at The Bank, reducing The Bank's required reserves by $9), but not entirely. The running change in The Bank's balance sheet would now be:

(THIRD STAGE)
ASSETS LIABILITIES AND NET WORTH
Reserves - $100 Checking deposits - $190
Government bonds + $100
Loans - $190

At this point, the change in the bank's excess reserves (ER) is:

change in ER = (change in actual reserves) - (change in required reserves)
                     = (-$100) - (.10)*(-$190)
                     = (-$100) - (-$19)
                     = (-$100) + ($19)
                     = -$81

The Bank will surely realize that to make up a $100 reserve deficiency, it will have to reduce its required reserves by $100, which it can do by calling in $1000 in loans, which will be repaid by drawing down $1000 in checking deposits at The Bank. So when ER=0 again and The Bank's balance sheet is back in equilibrium, the final change in that balance sheet will be:

(FINAL STAGE)
ASSETS LIABILITIES AND NET WORTH
Reserves - $100 Checking deposits - $1000
Government bonds + $100
Loans - $1000

(Let's verify that the change in ER = 0:)
change in ER = (change in actual reserves) - (change in required reserves)
                     = (-$100) - (.10)*(-$1000)
                     = (-$100) - (-$100)
                     = (-$100) + ($100)
                     = $0

What has happened is that the Fed's sale of $100 in government bonds has led to a reduction of $1000 in loans, a reduction of $1000 in checking deposits, and most importantly a reduction of $1000 in the money supply (since checking deposits are part of the money supply).