Homework 5
Economics 503
Foundations of Economic Analysis
Assigned: Week 5
Due: Week 6
1. 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
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%
a) 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%
b) 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.
c) 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.
d) 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.
2. 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.
c. 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
3. 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 nominal 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''
Y
4. The following chart shows the CPI in the USA and Hong Kong for the years
2003-2008. Assume that the growth in Hong Kong’s exchange rate is zero.
Calculate the growth rate of the real exchange rate for 2004-2008. What is the
average growth rate of Hong Kong’s real exchange rate for those years?
CPI
USA
2003
2004
2005
2006
2007
2008
181.7
185.2
190.7
198.3
202.4
211.1
Inflation
USA
HK
101.3
99.8
99.5
101.3
103.3
106.7
Average 2004-2008
1.93%
2.97%
3.99%
2.07%
4.30%
3.05%
HK
-1.48%
-0.30%
1.81%
1.97%
3.29%
1.06%
Growth
REX
3.41%
3.27%
2.18%
0.09%
1.01%
1.99%
S  PF
REX 
 g REX  g S   F  
The real exchange rate is
P
S
g  0  g REX   F  
Therefore, the gap between US inflation and HK inflation is the change in the real
exchange rate. With US inflation faster than HK, the relative cost of US goods is
increasing and HK faces a real depreciation.