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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