The Federal Reserve, ECB, and Bank of England face a tough challenge when it comes to controlling inflation in 2021. This question will ask you to go through different facets of this problem facing a central bank, whose goal is to control inflation at 2%. The central bank sets the long-run nominal interest rate at 2%. In terms of notation / is the nominal interest rate / is the real interest rate * is inflation, and the time period is one year. [22 marks] (a) In the first half of 2020, governments provided large transfers to households and businesses. Given widespread lockdowns, a large share of these funds were deposited in banks, which in turn deposited them at the central bank. Plot in a diagram the market for reserves. Show the effect the policies of 2020 might have on the equilibrium interbank rate if the central bank does nothing in response. Then, show instead, and explain, what happens to the equilibrium in this market in the diagram, and to the equilibrium interest rate, if the central bank in response buys large amount of government bonds and credits the deposit account of banks. [4 marks] (b) In an economy, the arbitrage condition between nominal and real bonds is: i = r+0.02 + where & is random variable with a mean zero (that is an expected value, or long-run value, of zero). What is the long-run value of the real interest rate in this economy? Is this higher than its historical value? Give one reason why it may have changed in the last few years. [3 marks] (c) Before the crisis, the central bank followed this policy rule: i = -0.02+2n Is this rule consistent with the long-run inflation target of 2%? [3 marks] (d) In equilibrium the real interest rate in the economy is given by the expression: r = -0.5(7 - 0.02 - =) so that higher inflation is associated with lower real interest rates. Combine with the previous equations in this question to solve for inflation as a function of the shocks . Intuitively explain whether these shocks are attenuated (have a coefficient less than 1) or are propagated (coeffi- cient larger than 1). [3 marks] (e) In 2021, the central bank promised not to let interest rates rise above 6% no matter what. There- fore the policy rule in question c) now only holds as long as inflation is below 4%; for higher values of inflation, / = 0.06. Solve for inflation as a function of & in this case, that is when i = 0.06. Intuitively explain whether these shocks are attenuated (have a coefficient less than 1) or are propagated (coefficient larger than 1). [3 marks](e) In 2021, the central bank promised not to let interest rates rise above 6% no matter what. There- fore the policy rule in question c) now only holds as long as inflation is below 4%; for higher values of inflation, / = 0.06. Solve for inflation as a function of & in this case, that is when i = 0.06. Intuitively explain whether these shocks are attenuated (have a coefficient less than 1) or are propagated (coefficient larger than 1). [3 marks] (f) Combine your answer to the previous two questions to plot in a diagram equilibrium inflation in the vertical axis and the shock & in the horizontal axis in the range between 0 and 0.1. If I told you that a high & today is more likely if inflation last year was higher, would you say that central banks in 2021 have inflation expectations anchored? [2 marks] (g) For simplicity assume that people expect the interest rate next year to be 2%. Is there an upper bound, a lower bound, or no bound, on the two-year rate in this economy? Knowing that the Treasury has issued much long-term debt in the last 12 months, and simplifying by saying this pays the 2-year interest rate, would the Treasury be supportive of the policy rule of the central bank? Would you question the independence of the central bank in this world? [4 marks]
