ECONOMICS 4012
SECOND EXCEL PROJECT
The second project involves using EXCEL to explore the internal dynamics of output (Yt) and
inflation (t). Since for much of this exercise these values depend on expected inflation (et), you
will be exploring the dynamics of it as well. But you will graph only Y and .
The model used in Parts I and II is the one in my notes. That model is:
DAD: Yt = Yt-1 + at + (mt – t)
EA-DSAS: t = [(Yt – Yn)/Yn] + et
In the New Keynesian case, these are subject to t  0 .
Adaptive Expectations: et = et-1 + g (t-1 – et-1)
Rational Expectations: et = mt
All exercises use the following values: Yn = 500;  = 1.2,  = 400, and  = 1. g will be either .5
(slow to adapt) or 1 (immediately adapt). In each case, one must first find et, which is based
exclusively on past values, then find Yt and t . The latter are determined simultaneously; first we
must solve that system of equations. Here I solve it first for Yt, the use that value to find t . When
solved, using the values for parameters above, one gets:
Yt = [5/9]  [Yt-1 +1.2at + 400mt + 400 – 400et], and
t = (Yt/500) – 1 + et .
In NK this is subject to t  0 .
Since the simultaneous solution implicitly allows t < 0, in the NK case, if t as found from the
above two equations is > 0, then
t = 0 and
Yt = Yt-1 +1.2at + 400mt.
In each case you run out twenty time periods: t = 1,20. This is plenty to see the internal dynamics.
These are in Rows 2-22 of EXCEL.
I am not going to write out detailed instructions step by step for each case. I will do it once, then I
will tell you what to put into each column and which columns to use for each part of the exercise.
A reminder: in the usage below, a letter is a column and a number is a row; “B2” means the second
row of Column B. I have used upper case letters but EXCEL does not care, so you can use lower
case if it is easier (which it is).
Begin
Use the first row for names. Here are suggestions, but you can use your own if you wish.
Columns A and B are for the two gs. In A1 type “g=.5”. In B1 type “g=1” Column C is
expectations with flexible prices; in C1 type “FP-e-pi”. Column D is rate of change of the money
stock: in D1 type “m”. Column E is change in autonomous spending: in E1 type “a”. Column F is
output with flexible prices. In F1 type “FP-Y”. Column G is inflation with flexible prices: in G1 type
“FP-pi”.
To give some space between FP and NK, leave column H blank. Because you’ll use it later, for
now leave Column I blank.
Econ 4012
SSEx2
page 2
Column J is expectations with the NK model: in J1 type “NK-e-pi”. We can use a column to test for
inflation before we get a final value in the NK model; use Column K. In K1 type “NK-pi-hat”.
Column L is inflation in the NK model: in L1 type “NK-pi”. And Column M is output in the NK
model; in M1 type “NK-Y”.
PART I
The first part of the project begins with full employment and no inflation: Y0 = 500; m0 = 0 = e0 =
0. The model is hit first with an increase in demand. Here that increase is through “at”, that is,
through fiscal policy. But this doesn’t really matter, expansionary monetary policy works the same
way. Then the model is hit with a “supply shock”.
In A2 type “.5”; copy A2 to A3:22. In B2 type “1”; copy B2 to B3:22. In C2, D2, E2, G2, J2, K2 and
L2 type “0”. In F2 and M2 type “500”.
There are sixteen cases in Part I. Two are done simultaneously on the spreadsheet:: Flexible
Prices and New Keynesian. These will be the same in a number of instances, but not all. The
other eight are:
A: Increase in Demand and B: Supply Shock.
1: no accommodation, 2: lagged accommodation
a: g = .5, and b: g = 1.
(2)
(2)
(2)
2x2x2=8
I write full instructions for the first exercise, A.1.a. This has the economy hit with an increase in
demand, with no monetary accommodation, and with adaptive expectations, g= .5.
C: In C3 type “=C2+A2*(G2-C2)”; copy C3 to C4:22.
D: copy D2 to D3:22.**
E: In E3 type “50”. In E4 type “0” Copy E4 to E5:22.**
F: In F3 type “=(5/9)*(F2+1.2*E3+400*D3+400-400*C3)”; copy F3 to F4:20.
G: In G3 type “=F3/500-1+C3”
**In some cases, like here, you are just copying zeros. EXCEL reads blanks as zeros. If you want,
just leave blanks rather than copying zeros all the way down.
J: In J3 type “=J2+A2*(L2-J2)”. Copy J3 and paste to J4:22.
K: In K3 type “=M3/500-1+J3”. Copy K3 to K4:22.
L: In L3 type “=IF(K3>0,K3,0)” In L4 type “=IF(IF(L3=0,0,K4)<=0,0,K4)”.
WATCH OUT, THIS HAS TO BE PRECISE
Copy L4 to L5:22.
M: In M3 type “=(5/9)*(M2+1.2*E3+400*D3+400-400*J3)”. In M4 type
“=IF(L3=0,M3,(5/9)*(M3+1.2*E4+400*D4+400-400*J4))”.
WATCH OUT, THIS HAS TO BE PRECISE!
Copy M4 to M5:22.
The above is A,1,a. For all A cases, cases with g = .5, use column A in the formulas, as is done
above.
For A,1,b , and for all b cases, cases with g = 1, substitute “B2” for “A2” in C3 and J3. Copy C3
and J3 to C4:22 and J4:22 respectively after you make the change.
Econ 4012
SSEx2
page 3
For all 2 cases,cases with lagged accommodation, in D3 type “=G2”; copy D3 to D4:22.
For all A cases, use the column E as above.
For all B cases, first set E3 = 0. Then set G3 and L3 = .10. Leave all other E, G and L cells as
zeros.
Draw graphs and make charts. Use the relevant output, “Y” , column as the X-axis, and the
inflation, “pi” column as the Y-axis. Plan which graphs to have on each chart to match what you
are showing. You should always have both types of expectations, slow and fast, on the same
chart. When you are showing the difference between FP and NK, put them on the same chart.
When you are showing the difference in accommodation strategies, put them on the same chart.
And so on. Do A (demand hit) and B (supply shock) on separate charts.
NOTE: My convention here is to use EXCEL’s convention of referring to a set of curves in a single
Cartesian space (XY Scatter) as a “chart”. I use the word “graph” to mean a single curve in that
space. EXCEL calls these “series”.
PART II
The second part of the exercise begins with an inflationary equilibrium. It begins with full
employment and steady-state inflation of 12%. So Y0 = 500; m0 = 0 = e0 = .12. The government
then ceases accommodation in order to reduce or eliminate inflation. The exercises use both
adaptive expectations used before, with g = .5 and g = 1. Here we also use a close approximation
to rational expectations, RE. Each part will be done with an inflation “target” of  = .02, or 2%. The
government approaches the reduction of inflation in one of two ways: “Cold Turkey”: setting m1 =
target and keeping it there, or “Gradualism”: reducing mt by a little each period until mt equals the
target.
Start with all column entries as in A.1.a. of Part I above.
Don’t change A2, B2, F2, or M2.
In C2, D2, G2, J2, K2 and L2 type “.12”. Column E is all zeros, or blanks if you wish.
There are twelve cases, with two, FP and NK, done simultaneously The other six are:
A: “Cold Turkey” and B: “Gradualism”.
1. adaptive expectations with g = .5, 2. g = 1, and 3. rational expectations.
(2)
(3)
2x3=6
For II-A. exercises, in D3 type “.02”; copy D3 to D4:D22.
For II-B. exercises, in D3 type “.10”; in D4 type “.08”; in D5 type “.06”; in D6 type “.04” in D7 type
“.02”; copy D7 to D8:22.
For adaptive expectations, g = .5, the 1 cases, use “A2” etc in the formulas of columns C and J.
For adaptive expectations, g = 1, the 2 cases, use “B2” etc in the formulas of columns C and J.
Remember to re-copy the columns to rows 4:22 after you make the changes.
Econ 4012
SSEx2
page 4
RATIONAL EXPECTATIONS:
For rational expectations, (with a minor fudge), in I1 type “RE”. In I2 type “.12” In I3 type “=D2”;
copy I3 to I4:22.
You also need to change the formulas for “pi”s. Rewrite G3 as “=F3/500-1+I3” and rewrite K3 as
“=M3/500-1+I3”.
Finally You need to make small changes to the formulas for the two Ys, too:
F3 should be rewritten as “=(5/9)*(F2+1.2*E3+400*D3+400-400*I3)”;
M3 should be rewritten as “=(5/9)*(M2+1.2*E3+400*D3+400-400*I3)”, and
M4 should be rewritten as “=if(L3=0,M3,(5/9)*(M3+1.2*E4+400*D4+400-400*I4))”
Remember to re-copy the new formulas to rows 4:22 after you make the changes.
Draw graphs and make charts. Use the relevant output, Yt , column as the X-axis, and the
inflation, “pit” column as the Y-axis. Plan which graphs to have on each chart to match what you
are showing. You should always have both types of expectations, slow and fast, on the same
chart. When you are showing the difference between FP and NK, put them on the same chart.
When you are showing the difference in inflation-fighting strategies, put them on the same chart.
Finish Parts I and II
Write a short paper, illustrated with your graphs, consisting of a few paragraphs for each of Parts I
and II. The focus of the paper is how different expectations-formation and different monetary
policies will affect output/inflation dynamics, and how these can differ between the different
models.