Lecture 3.1 The behaviour of interest rates, part 1
In this lecture and the following lecture, we examine how the overall level of nominal interest rates is determined
The current lecture looks at the traditional or quantity-based analysis of this question
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The next lecture looks at the modern central banking view, and considers how this differs from the quantity-based analysis
Source: Mishkin Ch 5
Learning Objectives
Identify the factors that affect the demand for assets
Draw the demand and supply curves for the bond market, and identify the equilibrium interest rate in a simple model
List and describe the factors that affect the equilibrium interest rate in this model
Learning Objectives (2)
Describe the connection between the bond market (the market for interest-bearing securities) and the money market (the market equating demand for, and supply of, money balances) through the liquidity preference framework
List and describe the factors that affect the money market and the equilibrium interest rate
Identify and illustrate the effects on the interest rate of changes in monetary growth over time
Equilibrium in an asset market
Holders of financial wealth need to decide how to allocate their wealth between different assets
Equilibrium exists when demand for an asset equals the available supply
The interaction of supply and demand for an asset determines its equilibrium price
Hence, to understand this process for a given market, we need to understand the determinants of supply and demand in that market
Determinants of Asset Demand
Asset demand: how much of my wealth do I choose to store as a particular type of asset (eg, bank deposits, shares, real estate)?
Key factors influencing this decision:
Wealth: the total value of resources owned by the individual
Expected Return: the return expected over the next period on one asset, compared with that on alternative assets
Risk: the degree of uncertainty associated with the return on one asset in relation to that on alternative assets
Liquidity: the degree to which an asset can be readily converted into money (without loss)
Theory of Portfolio Choice
Holding all other factors constant:
The quantity demanded of any asset is positively related to total wealth
The quantity demanded of an asset is positively related to its expected return (compared with alternative assets)
The quantity demanded of an asset is negatively related to the risk (variability, unpredictability) of its returns (compared with alternative assets)
The quantity demanded of an asset is positively related to its relative liquidity (how easily it can be converted into cash without loss)
Theory of Portfolio Choice
A key simplifying assumption
We can think of the interest rate as a price that is determined in asset markets.
To simplify analysis, we assume:
There are only two financial assets
At a given point in time, asset holders need to decide how to allocate their financial wealth between these two assets
As we will see, this means that when one of these asset markets is in equilibrium, then so is the other
Supply and Demand in the Bond Market
Bonds are an asset to the holder and a form of borrowing by the issuer
Therefore, a higher supply of bonds means a higher demand (by bond issuers) for credit; and a higher demand for bonds corresponds to greater supply of credit (that is, increased willingness to purchase bonds by investors).
Equilibrium in the bond market can be described either in terms of the bond price or the interest rate.
“The supply of bonds is a positive function of the bond price” is equivalent to the statement that “the demand for borrowing [by issuing—that is, supplying—a bond] is a negative function of the interest rate.”
Key fact from last week
The price and yield (interest rate) of a bond are inversely related
A low bond price means a high interest rate
A high bond price means a low interest rate
Example: a discount security with a face value of 100, maturing in a year’s time.
P = 95 implies R = (100/95) – 1 = 5.3%
P = 99 implies R = (100/99) – 1 = 1.0%
Supply and Demand in the Bond Market
At lower bond prices the quantity demanded of bonds is higher: an inverse relationship.
you are more willing to buy bonds (lend money) when the interest rate is higher
At lower bond prices the quantity supplied of bonds is lower: a positive relationship.
you are more likely to issue or sell bonds (borrow money) when the interest rate is lower
So, the demand and supply curves for bonds slope the same way as for goods or services.
Figure 1. Supply of and Demand for Bonds
Quantity of Bonds, B
($ billions)
With excess supply, the
bond price falls to P *
With excess demand, the
bond price rises to P *
(i * = 17.6%)
(i = 5.3%)
(i = 11.1%)
(i = 25.0%)
(i = 33.0%)
Price of Bonds, P ($)
Equilibrium in the Bond Market
This occurs when the amount of bonds that people are willing to buy (demand) equals the amount that people are willing to sell (supply) at a given price.
Bd = Bs defines the equilibrium (or market-clearing) price and interest rate.
When Bd > Bs , there exists excess demand, so price will rise and interest rate will fall to eliminate the excess.
When Bd < Bs , there is excess supply, so price will fall and interest rate will rise to eliminate the excess.
These price adjustments occur rapidly in highly liquid asset markets like those for bonds. Adjustment to changing conditions is almost instantaneous
Changes in Equilibrium Interest Rates
Shifts in the demand for bonds:
Wealth: with growing wealth in the economy, the supply of saving rises and the demand curve for bonds accordingly shifts to the right
Expected returns: higher expected future interest rates (than previously anticipated) lower the expected return on long-term bonds, shifting the demand curve to the left
equivalently: if the market expects the bond price to be lower tomorrow, it will demand less bonds today
Expected inflation: an increase in the expected rate of inflation lowers the expected real return for bonds, leading the demand curve to shift to the left
Risk: an increase in the riskiness of bonds causes the demand curve to shift to the left
Liquidity: increased liquidity of bonds results in the demand curve shifting to the right
some bonds are more liquid than others
Figure 2. Shift in the Demand Curve for Bonds
An increase in the demand for
bonds shifts the bond demand
curve rightward.
For a given interest rate or price, more bonds are demanded
Price of Bonds, P
Quantity of Bonds, B
Shifts in the Demand for Bonds
Shifts in the Supply of Bonds
Shifts in the supply of bonds:
Expected profitability of investment opportunities: in an expansion, the supply curve shifts to the right.
Expected inflation: an increase in expected inflation shifts the supply curve for bonds to the right. (The real interest rate is lower for any given nominal interest rate, boosting desire to borrow and therefore to issue bonds.)
Fiscal policy (i.e., government budget policy): increased budget deficits shift the supply curve to the right
Shifts in the Supply of Bonds
Figure 3. Shift in the Supply Curve for Bonds
An increase in the supply of
bonds shifts the bond supply
curve rightward.
More borrowing is desired at any given level of interest rates
Price of Bonds, P
Quantity of Bonds, B
Figure 4. Response to a Change in Expected Inflation
Step 1. A rise in expected inflation shifts the bond demand curve leftward . . .
Step 2. and shifts the bond supply curve rightward . . .
Step 3. causing the price of bonds to fall and the equilibrium interest rate to rise.
Price of Bonds, P
Quantity of Bonds, B
Figure 6. Response of Bond Market to a Business Cycle Expansion
Quantity of Bonds, B
Price of Bonds, P
Step 1. A business cycle expansion
shifts the bond supply curve
rightward . . .
Step 2. and also shifts the bond demand
curve rightward.
Step 3. The net effect on the price of bonds is ambiguous. If, as drawn here, the shift in the demand curve is smaller, then the equilibrium interest rate rises.
Figure 7. Business Cycle and Interest Rates (Three-Month Treasury Bills), U.S,
Source: Federal Reserve Bank of St. RED database: http://research.stlouisfed.org/fred2
Supply and Demand in the Market for Money:
Liquidity Preference Framework
Thus far, we have considered interest rates as being determined in the bond market
The economist Keynes postulated that interest rates are determined in the market for money
In a simplified two-asset framework we can show that these two approaches are equivalent
Two-asset model of equilibrium in money and bond markets
Simplifying assumptions:
At a given point in time, there is a fixed amount of nominal wealth (that is, assets that have fixed face value) in the economy in the form of money and bonds
Total supply and demand for the two assets has to equal nominal wealth, so:
Rearranging:
Excess supply of bonds = excess demand for money
When one market is in equilibrium, so is the other:
Figure 8. Equilibrium in the Market for Money, assuming money supply is fixed
With excess supply, the interest rate falls to i *.
With excess demand,
the interest rate rises
Interest Rate, i (%)
Quantity of Money, M
($ billions)
Supply and Demand in the Market for Money: The Liquidity Preference Framework
Demand for money in the liquidity preference framework:
As the interest rate increases (with money either non-interest bearing or bearing interest rates that are not linked to market rates):
The opportunity cost of holding money increases…
The relative expected return on holding money decreases…
…and therefore the quantity demanded of money decreases.
Changes in Equilibrium Interest Rates in the Liquidity Preference Framework
Shifts in the demand for money:
Income Effect: a higher level of income leads the demand for money at each interest rate to increase and the demand curve to shift to the right
Price-Level Effect: a rise in the price level leads the demand for money at each interest rate to increase and the demand curve to shift to the right
Changes in Equilibrium Interest Rates in the Liquidity Preference Framework
Shifts in the supply of money:
Assume that the supply of money is controlled by the central bank.
An increase in the money supply engineered by the central bank will shift the supply curve for money to the right.
Changes in Equilibrium Interest Rates in the Liquidity Preference Framework
Figure 9. Interest-rate Response to a Change in Real Income or the Price Level
Step 1. A rise in income or the price level shifts the money demand curve rightward . . .
Step 2. and the equilibrium interest rate rises.
Interest Rate, i
Quantity of Money, M
Figure 10. Response to a Change in the Money Supply
Step 1. The central bank increases the quantity of money
Step 2. The equilibrium
interest rate falls.
Quantity of Money, M
Interest rates, i
Money and Interest Rates
All of these diagrams represent analysis at a point in time (assuming nothing else changes)
Over time, however, other effects will follow
Example: a one-time increase in the money supply lowers the interest rate at that point in time
However, this will eventually lead to higher prices for goods and services
lower interest rate causes higher spending, higher incomes and higher prices
this may also add to inflation expectations
The demand for money therefore increases
Over time, this will work to offset the initial effect of the increase in money supply
Response over time
Time path of overall response depends on relative strength of four factors:
liquidity effect
price level effect
real income effect
inflation expectations effect
What if money supply responds to changes in money demand?
All the above analysis was for a change in monetary policy that made M higher and created an excess supply of money to which the economy had to adjust (in order to get the money market to clear). Interest rates play a role in this adjustment.
However, for cases in which the demand for money underwent an exogenous shift upward (a positive liquidity-preference shock—also called a positive money demand shock) and monetary policy makers simply expanded M to meet this shift, we would not see interest rates (or any variables other than M) change.
This will be a starting point for the next lecture
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