10
10.1
Lecture 10: October 4, 2004
More on Zeldes
Recall the regression in Zeldes (1989):
1
log (cit ) = 0i + 1 (AGE )i,t1 + 2 (Annual F ood N eeds)it + log (1+ rit )+ yi,t1 + it .
Zeldes is trying to test the LCH against a particular alternative hypot
We call consumption a Martingale under this denition. If
c is a random walk.
t+1
is iid white noise, then
To test, run the following OLS regression:
ct+1 = 0 + 1 ct + zt +
t+1 ,
where zt is a vector of variables in the information set at time t. Under th
itself. Thus, in principal:
Vt (at ) =
dVt
=
dat
Vt
at
+
Direct Ef f ect
Vt ct Vt t
.
+
ct at t at
I ndirect Ef f ects
Since V is a maximized value function, by the envelope theorem:
Vt
Vt
=
= 0.
ct
t
So we have:
Vt (at ) =
dVt
=
dat
Vt
at
.
Direct Ef f e
Theorem: (Pratt 1964) For small enough multiplicative risks,
12
2
p
u (c)c
.
u (c)
Where the term in parens is the Coecient of Relative Risk Aversion or RRA. Notice
that it varies with c and also has an extra term in the numerator.
Thus the coecient of
Economics 601: Macroeconomics
John Shea & Allan Drazen
Matthew Chesnes
Updated: January 1, 2005
1
Lecture 1: August 30, 2004
1.1
Consumption: Theory and Evidence
The classic Keynesian consumption function is of the form:
c = A + (M.P.C ) y.
Where c is co