Econ 100B: Macroeconomics Problem Set #7 – Solutions Due Date: March 18, 2022 General Instructions: •Please upload a PDF of your problem set to Gradescope by 11:00 pm. •Late homework will not be accepted. •Please put your name and student ID at the upper right corner of the front page. 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 gapeyt , the inflation gap e πt, and the rate gape rt . 1

•The variables and their values for the simulation are shown in rows 19 and 20. The rate factor is 1 ζy γ+ 1 γβ 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 columnA. •Populate the shocks in columnsEandF. Note the value of “1” for the inflation shock at year 0. •Set the values ofe yt,e πt, ande rt in year -2 (row 23) to zero. •The evolution ofeytande πt fromt=-2 tot=-1 is accomplished as follows: –The output gapeyt evolves according to the gap form of the dynamic IS curve: e yt=-ζye r t-1 so e y-1=-ζye r-2 . To this we add the possibility of a shock toe y-1 indicated in columnE. Adding this term, the complete update—IS curve and shock—is given by B24=-$D$20*D23 + E24.

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