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MIT14 02S14 Roomer Num

This document explains C. Romer numbers using different macroeconomic models. It first shows that a standard model where Y=(c0+I+G-c1T)/(1-c1) implies c1 is changing across quarters or a different model is needed, as Romer's numbers generally increase with a one unit rise in G. It then presents an alternative habit formation model where consumption depends on past consumption, C(t)-C(t-1)=a(C(t)*-C(t-1)) with C(t)*=c0+c1Y(t) and 0<a<=1. This model yields the solution Y(t)=c0+(1-a)C(

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Shirat Mohsin
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77 views6 pages

MIT14 02S14 Roomer Num

This document explains C. Romer numbers using different macroeconomic models. It first shows that a standard model where Y=(c0+I+G-c1T)/(1-c1) implies c1 is changing across quarters or a different model is needed, as Romer's numbers generally increase with a one unit rise in G. It then presents an alternative habit formation model where consumption depends on past consumption, C(t)-C(t-1)=a(C(t)*-C(t-1)) with C(t)*=c0+c1Y(t) and 0<a<=1. This model yields the solution Y(t)=c0+(1-a)C(

Uploaded by

Shirat Mohsin
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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ExplainingC.

RomerNumbers

(Slide25IS/LM)

1
UsingModelfromClass
Y=(c0+I+Gc1T)/(1c1)

OneunitincreaseinGincreasesYby1/(1c1)

InconsistentwithnumbersfromC.Romerwhich
aregenerallyincreasing

Impliesc1changingacrossquarters

Orgeneratedbydifferentmodel

2
Response to Permanent Increase in G

c1=0.3 Standard Model


1.5


1
.5
0

0 5 10 15 20 25
Q

change_in_G change_in_Y

3
AlternativeHabitFormationModel

C(t) C(t1)=a(C(t)* C(t1))


withC(t)*=c0+c1Y(t)
0<a<=1
Fora=1,C(t)=C(t)*
Y(t)=C(t)+G(t)

Solution:Y(t)=c0+(1a)C(t1)+G(t)/(1ac1)

4
Response to Permanent Increase in G

c1=0.3, a=0.5 Habit Formation


0 .2 .4 .6 .8 1 1.2 1.4 1.6 1.8 2

0 5 10 15 20 25
Q

change_in_Y change_in_G

5
MIT OpenCourseWare
http://ocw.mit.edu

14.02 Principles of Macroeconomics


Spring 2014

For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.

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