General Instructions:
Econ 100B: Macroeconomics Problem Set #7
Due Date: March 18, 2022
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1. We will build a monetary policy calculator using the update algorithm implied by the dynamic IS curve and the Phillips curve. An example of my Excel version of this calculator is shown below. This example was used to generate the graph on slide 5 of lecture 13. You can use your preferred platform (e.g., Python, Matlab, Octave, Mathematica, etc.), but the steps presented below will given in terms of Excel.
In this simulation we will be evolving the values of the output gap y , the inflation gap t
π , and the rate gap r . tt
• The variables and their values for the simulation are shown in rows 19 and 20.
The rate factor is
which, since we will be using it a lot and it does not change with time, we calculate once here. We also calculate the half-life just to have it around. The half-life is not an input to the simulation.
• Add the headings shown in row 22.
• Populate the years -2 thought 10 in column A.
• Populate the shocks in columns E and F. Note the value of “1” for the inflation shock at year 0.
• Setthevaluesofy,π,andr inyear-2(row23)tozero. ttt
• The evolution of y and π from t = −2 to t = −1 is accomplished as follows: tt
– The output gap y evolves according to the gap form of the dynamic IS curve: t
y = − ζ r
y − 1 = − ζ y r − 2 .
To this we add the possibility of a shock to y−1 indicated in column E. Adding
this term, the complete update—IS curve and shock—is given by B24 = −$D$20*D23 + E24 .
ζ γ + 1
– The inflation gap πt evolves according to the gap form of the Phillips curve: π=π +γy
π − 1 = π − 2 + γ y − 1 .
To this we add the possibility of a shock to π−1 indicated in column F. Adding
this term, the complete update—Phillips curve and shock—is given by C24 = C23 + $B$20*B24 + F24 .
– The rate gap r is set by the central bank in response to the value of the t
inflation gap πt using the gap form of the optimal rate rule: 1
r= π tt
r−1= 1π−1.
Since there is no shock to the rate because the central bank is setting the
rate, the update to the rate r−1 is given by D24 = $E$20*C24 .
• The evolution for all future time (t > −1) is the same. If you copy the equations in cells B24, C24, and D24 down for the remaining times given in column A you should see the results shown in the figure.
• You can check that your calculator is working properly (i.e., validate it) by re- producing the gap graph shown above. You do not need to submit a copy if your validation for this question.
Your submission for this question should be a screenshot of your calculator showing your calculated results for a single inflation shock of size 0.8 at t = 2 years.
2. We will now use the calculator to study the gap changes in the 1980s associated with the Federal Reserve’s response to inflation under then Chair Paul Volker.
25 20 15 10
π – calc. r – calc. u – calc. y – obs. u – obs.
Source: FRED / BEA
1982 1984 1986 1988
TIME (year)
Let’s use a series of inflation shocks reflecting successive lowering of target inflation by the Fed. In the graph “calc” means calculated and “obs.” means observed. My approach to this analysis is as follows:
GAPS (percent)
(a) Add a column in the calculator to calculate the unemployment gap from the output gap using Okun’s law. This is useful because data for the unemployment gap is more common than is data for the output gap.
(b) Get annual data from FRED to calculate the output and unemployment gaps. This will be just like your Okun’s law data retrieval on an earlier problem set, but with annual data instead of quarterly data.
(c) I started a shock sequence at model time t = 0 and aligned that with actual time t=1979. Themodelcoefficientsweresettoβ=1,γ=1,andζy =0.25.
Your submission for this question should be a screenshot of your calculator showing your calculated version of the graph above together with a brief discussion of (i) your shock sequence, (ii) the fit to the unemployment and output gaps, and (iii) the resulting rate and inflation gaps.
3. According to Reuters, on February 28, 2022
“The Russian central bank raised its key interest rate to 20% from 9.5% on
Monday in an emergency move, . . .
“The central bank, which says it targets inflation at 4% and will do all necessary to ensure financial stability, said the rate increase will bring deposit rates to levels ‘needed to compensate for the increased depreciation and inflation risks’.”
If inflation was at 4% and if there was no change in r∗ on Monday, was their action expansionary, contractionary, or neither? Briefly explain.
4. Referring to the graph below,
compare and contrast inflation from (i) 1994 to 1995 and (ii) from 1995 to 1996 in terms of cost-push and demand-pull (both are possible in certain circumstances). Note that the non-accelerating inflation rate of unemployment (NAIRU) is a proxy for the natural rate of unemployment. Support your explanation with the appropriate equation(s). Hint, Okun’s law may be helpful here.
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