HE2002 - The IS-LM Model II

• The 2 financial assets are money and bonds
• The interest rate that is being assumed on the IS-LM model is the rate on bonds which is determined by the monetary policy
• Interest rate is assumed to move together with the interest rate determined by the monetary policy
• Nominal interest rate is interest rate expressed in terms of dollar
• One year T-bill rate is 4.2% indicates that every dollar the government borrows, it promises to pay 1.042 dollars a year from now
• Real interest rate is interest rate expressed in terms of a basket of goods
• The mathematical formula for real interest rate is 1 + r_t = (1 + i_t)(P_t/P^e_t+1)
• The one year nominal interest rate, in terms of dollar is denoted by i_t

  
• 1 + i_t indicates that if you borrow 1 dollar this year, then you will have to repay (1 + i_t) dollars next year

  
• 1 + P_t indicates that if you borrow P_t dollars this year, then you will have to repay in (1 + P_t) dollars next year

  
• P^e_t+1 indicates the expected price of a good in terms of dollars for the next year

  
• One plus the real interest rate = Ratio of one plus the nominal rate, divided by one plus the expected inflation rate

  
• The real interest rate is approximately equal to the nominal interest rate minus the expected inflation

  
• The expected rate of inflation = The expected change in dollar price of a good between this year and next year divided by the dollar price of the same good this year

  
• When expected inflation is equal to zero, the nominal and the real interest rates are equal

  
• Expected inflation is typically positive
• As expected inflation is typically positive, the real interest rate is typically lower than the nominal interest rate

  
• For a given nominal interest rate, the higher the expected rate of inflation, the lower the real interest rate

  
• The real interest rate is based on expected inflation, therefore it is sometimes called as the ex-ante ("before the fact", before inflation is known) real interest rate

  
• The realised real interest rate (nominal interest rate - actual inflation) is sometimes called as the ex-post ("after the fact", after inflation is known) interest rate

  
• In the context of liquidity trap, the zero lower bound means that the nominal interest rate cannot be negative, because otherwise, people would not want to hold bonds, this implies that the real interest rate cannot be lower than the negative inflation rate
• If expected inflation is negative (people anticipate deflation), then the lower bound on the real interest rate become positive and can turn out to be high
• Risk premium is when some firms present some risk, in order to compensate such risk, bond holders requires a risk premium
• The 2 determinants of risk premium are probability of defaulting itself and the degree of risk aversion of the bond holders
• The higher the probability of defaulting, the higher the risk premium that the investor will ask for
• The i indicates the nominal interest rate on a riskless bond

  
• The x indicates the risk premium

  
• The p indicates the probability of defaulting

  
• 1 + i indicates the return on the riskless bonds

  
• The RHS of the first equation indicates the expected return on the risky bond

  
• With probability (1 - p), if there is no default then the bond will pay (1 + i + x)

  
• With probability p, there is default and the bond will pay nothing

  
• If interest rate on the riskless bond is 4%, probability of default on the risky bond is 2%, then the risk premium required to give the same expected rate of return as on the riskless bond is 2.1%

  
• Even if the expected return on the risky bond is the same as the riskless bond, the risk itself will make them reluctant to hold the risky bond
• If bond holders become more risk averse, then the risk premium will go up even if the probability of defaults has not changed
• Direct finance defines as the borrowing directly by the ultimate borrowers from the ultimate lenders
• Financial intermediaries are financial institution that receive funds from some investors and then lend these funds to others
• Shadow banking is defined "nonbanks" that grew in the "shadow" of banks, the nonbank part of the financial system is called the shadow banking.
• Financial intermediaries is important as they develop expertise about specific borrowers and can tailor lending to their specific needs
• Liabilities for a banks are like checkable deposits, interest-paying deposits, or borrowing from investors and other banks