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Homework 3 Economics 503 Foundations of Economic Analysis Practice 1. The Liquidity Crisis and the Taylor Rule in Hong Kong. You are given the following Table listing the output gap, the CPI and the overnight HIBOR Rate in Hong Kong. 2007Q4 2008Q1 2008Q2 2008Q3 2008Q4 2009Q1 2009Q2 2009Q3 Output GapCPI xxx 0.04922 0.029993 0.013161 -0.013435 -0.06314 -0.03723 -0.040702 107.4 108.2 110.1 107.7 109.6 109.5 109.2 108.2 Inflation xxx 0.029795 0.07024 -0.08719 0.070566 -0.00365 -0.01096 -0.03663 Interest Rate Actual Under Interest Taylor RuleRate xxx xxx 0.084303 0.00781 0.135357 0.00875 -0.10921 0.024375 0.114132 0.00225 -0.02204 0.00375 -0.02005 0.0013 -0.0603 0.0013 a. For each quarter, construct the inflation rate on an annual basis. This is obtained just P Pt 1 by constructing the % growth rate of the price that occurs in a given quarter t Pt 1 and then multiplying the result by 4. An example is constructed in the Table for the 1st Quarter of 2008.. b. Construct a hypothetical interest rate for HK with the Taylor rule using the CPI inflation. CPI data and an assumption of an inflation target of 2%. TAYLOR it .025 t 1 2 t .02 1 2 Output Gapt c. Compare the interest rate with that observed in HK. Note that the interest rate has been below 1% in every quarter except the 2008Q3. Has the interest rate been higher or lower in HK than that suggested by the Taylor rule? During the inflationary period during the beginning of 2008, the Taylor rule would suggest raising interest rates far above those actually observed during that period. During recessionary later periods, the Taylor rule would have suggested cutting interest rates. However, these low interest rates would have even been negative which is impossible in the market place. 2. Loanable Funds Market Some economists argue that the savings behavior is not very responsive to the interest rate. Other economists argue that savings is strongly affected by the interest rate. Use the loanable funds framework for a large, closed economy. Compare the effect of expansionary fiscal policy (i.e. an increase in government deficits) on the interest rate and investment in A) an economy in which the supply of loanable funds (S) was inelastic with respect to the interest rate; with the effect in B) an economy in which the supply of loanable funds is very elastic. Draw a graph of each theory to show under which theory there is a bigger impact on investment and under which theory there is a bigger impact on the interest rate. Expansionary fiscal policy, a cut in taxes or an increase in spending, leads to an increase in the budget deficit. There is a shift out in demand for loanable funds. This leads to excess demand and upward pressure on interest rates. If supply of loanable funds is very interest elastic, the higher interest rates will attract much more supply of loanable funds, and the equilibrium impact will mostly result in higher loanable funds and slightly higher interest rates. If supply is not interest elastic, the upward pressure on interest rates will mostly crowd out private sector demand for loanable funds. The equilibrium impact will be a much higher interest rate and only a little extra loanable funds. r S2 B2 r B1 r S1 A D' D Loanable Funds 3. Does the BOJ have a Taylor Rule? The following table shows numbers for Japan’s inflation rate, output gap, and the uncollateralized call money interest rate for the years 1990 to 2000. 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 i. Output Actual Target Gap Inflation Interest Rate 3.30% 3.02% 7.56% 4.09% 3.22% 7.48% 2.50% 1.70% 4.82% 0.51% 1.26% 3.18% -0.87% 0.69% 2.41% -1.20% -0.12% 1.15% 2.14% 0.13% 0.48% 2.32% 1.75% 0.52% -1.48% 0.67% 0.44% -2.46% -0.33% 0.06% -2.57% -0.71% 0.12% Inflation Gap 1.02% 1.22% -0.30% -0.74% -1.31% -2.12% -1.87% -0.25% -1.33% -2.33% -2.71% Taylor Rule 7.68% 8.37% 5.30% 3.65% 2.10% 0.71% 2.77% 5.28% 1.76% -0.23% -0.86% Calculate the inflation gap (i.e. the difference between inflation and target inflation) in each period if Japan had used a target inflation rate of 2% in each year. What is the average inflation gap during the period 1990-1995 (inclusive) and for 1996-2000? Average Inflation Gap 90-95 -0.37% 96-00 -1.70% Calculate the interest target, iTGT, for every period if the Bank of Japan had used a Taylor rule as specified in class. Compare this with the actual interest rate. Does the Bank of Japan adjust the target interest rate to domestic inflation and output? As inflation has fallen below the target, the central bank has also cut the interest rate. ii. iii. Some have argued that the BOJ was not aggressive enough in cutting interest rates in the early 1990’s to get the economy out of the slump. What was the average interest rate during the period 1992-1997? What was the average interest rate suggested by a Fed-style Taylor rule. Which was larger? Actual Implied Average Interest Target 2.09% 3.30% During the onset of the recession, the Japanese interest rate target seemed to be on average lower than that implied by the target. In 1992 and 1993, the interest rate was slightly above the implied rate. iv. What difficulties did the Bank of Japan have in implementing the Taylor rule in 1999 and 2000? By 2000, the interest rate had reached a zero lower bound. Even if the Taylor rule suggests cutting rates, the BoJ cannot. 4. Money Supply The money supply in HK is HK$ 2.26 trillion. The monetary base is HK$265 billion and the level of cash/currency is HK$110 billion. Calculate the money multiplier. Calculate the cash to deposit ratio and the reserve to deposit ratio. Calculate the multiplier if the bank regulator imposes a required reserve ratio of 20% assuming the the reserve deoposit ratio goes to zero and the cash to deposit ratio remains unchanged. The monetary base is cash + bank reserves so reserves must be 155 billion. Money supply is cash plus deposits, so deposits must be 2.15 trillion. The ratio of cash to Cash .11 deposits is 0.051162791 . The ratio of reserves to deposits is Deposits 2.15 Reserves rd = = 0.072093023 . The money multiplier Deposits Money 2.26 is 8.528301887 The money multiplier can be written as Money Base .265 1 Deposits . If the reserve ratio goes to 20% then this will equal Cash rd Deposits 0.051+1 4.185185185 0.051+.2 Cash 5. Money Market Assume there is a negative supply shock in the United States which reduces real and nominal GDP. The central bank wants to conduct monetary policy to stabilize the price level. Draw a picture of the money market. Show how the money supply and demand curve would shift in response to these events. What would happen to the money market interest rate and money supply? When GDP declines the demand for money declines which would put downward pressure on the money market interest rate. But if the central bank wants to stabilize the price level they must raise the interest rate. Therefore, they must reduce money supply until it is below money demand at the previous interest rate. Money Supply i 2 i** 1 i* Money Demand Money Supply´ Money Demand'' M P 6. Real Interest Rate Below is a table showing a nominal interest rate on bonds that was prevailing in the December of each year from 1991-2005. Also shown is the level, P, of the CPI index for 1991-2006. Assume that there is a fixed equilibrium real interest rate in each period of 2.5% (r = .025). Use that estimate to derive the forecast of inflation for the subsequent year. Use this to calculate, the actual inflation rate in Hong Kong in the years 1992-2006. Calculate the ex post real interest rate for HK for each year the period 1991-2005? In which years, was the ex post interest rate greater than the ex ante real interest rate? In which years was the ex post real interest rate negative? P Dec, 1991 Dec, 1992 Dec, 1993 Dec, 1994 Dec, 1995 Dec, 1996 Dec, 1997 Dec, 1998 Dec, 1999 Dec, 2000 Dec, 2001 Dec, 2002 Dec, 2003 Dec, 2004 Dec, 2005 Dec, 2006 P Dec, 1991 Dec, 1992 Dec, 1993 Dec, 1994 Dec, 1995 Dec, 1996 Dec, 1997 Dec, 1998 Dec, 1999 Dec, 2000 Dec, 2001 Dec, 2002 Dec, 2003 Dec, 2004 Dec, 2005 Dec, 2006 Ex Ante Rate i 73.1 79.9 86.8 94.6 100.8 107.6 112.7 111.1 108 105.9 99.4 100.3 99.1 99.7 101 102.9 5.18 5.47 4.26 7.74 5.54 5.58 9.6 5.96 6.37 5.42 3.41 1.763 1.125 0.993 3.983 3.519 i 73.1 79.9 86.8 94.6 100.8 107.6 112.7 111.1 108 105.9 99.4 100.3 99.1 99.7 101 102.9 5.18 5.47 4.26 7.74 5.54 5.58 9.6 5.96 6.37 5.42 3.41 1.763 1.125 0.993 3.983 3.519 Expected Actual Inflation Inflation 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.68 2.97 1.76 5.24 3.04 3.08 7.1 3.46 3.87 2.92 0.91 -0.737 -1.375 -1.507 1.483 9.302326 8.635795 8.986175 6.553911 6.746032 4.739777 -1.419698 -2.790279 -1.944444 -6.137866 0.905433 -1.196411 0.605449 1.303912 1.881188 Ex Post Rate -4.122326 -3.165795 -4.726175 1.186089 -1.206032 0.840223 11.0197 8.750279 8.314444 11.55787 2.504567 2.959411 0.519551 -0.310912 2.101812 During the early period, inflation was consistently higher than expected inflation consistent with ex post real interest rates below the ex ante and sometimes even negative. On the other hand, during the deflationary period, HK inflation turned out to be lower than expected and ex post real interest rates rose above ex ante. Finally, when inflation started to heat up again, the low inflation expectations meant that ex ante rates were above real rates. 7. Expected Inflation In January 2006, a one year Inflation protected bond had an interest rate of 2.13%. The one year non inflation protected bond in that same year 4.45%. The CPI for January 2006 was 198.3. The CPI for January 2007 was 202.4. a. Calculate the expected inflation rate over the year between 2006 and 2007 as forecast from the standpoint of January 2006? Expected inflation is the gap between the non-protected bond and the protected bond FORECAST .0445 .0213 .0232 i.e. 2007 b. Calculate the actual inflation rate over the same year. Calculate the ex post real interest rate for 2006. Did people who bought non-inflation protected securities do better or worse than people with inflation protected securities? Actual inflation rate was given by the % change in the CPI P P 202.4 198.3 ACTUAL 2007 2007 2006 .0207 or inflation was 2.07% which is lower P2006 198.3 than expected. The expost real interest rate was ExPost ACTUAL r2006 i2006 2007 .0445 .0207 .0238 or 2.38%. The actual real interest rate was higher than expected. Therefore, the people with non-protected securities did better. Calculate the real interest rate that was earned by someone who held cash between the period 2006 and 2007. Cash ACTUAL 2007 .0207 The cash interest rate is r2006