gr5215 fall 2021 lec 13 Further issues in consumption
1
Further issues in consumption
Miller GR5215
The precautionary motive for
saving
2
Recall the Hall result was certainty
equivalence when there is quadratic utility:
increasing the amount of uncertainty in
income has no effect
But this does not seem like actual behavior
– we expect people to save more when the
environment is riskier, that is, to self-insure
This kind of response is called the
precautionary motive for saving
The precautionary motive for
saving (II)
3
Since there’s no precautionary motive with
quadratic utility, we can guess that the
precautionary motive depends on the third
derivative of the utility function
We know (assume) the second derivative is
negative. Let’s draw a picture of marginal
utility if the 3rd derivative is positive. This
will make marginal utility convex to the
origin. Assume just two states of the world:
low consumption and high consumption.
The precautionary motive for
saving (II)
3
Since there’s no precautionary motive with
quadratic utility, we can guess that the
precautionary motive depends on the third
derivative of the utility function
We know (assume) the second derivative is
negative. Let’s draw a picture of marginal
utility if the 3rd derivative is positive. This
will make marginal utility convex to the
origin. Assume just two states of the world:
low consumption and high consumption.
The precautionary motive in
pictures
4
1= (1+ r)β E[ ′u (Ct+1)]
′u (C
t
)
The precautionary motive for
saving (III)
5
So, the curvature in marginal utility makes
the expected marginal utility higher than the
marginal utility with certainty.
Now consider a mean-preserving spread.
Here, this means a decrease in CL and an
increase in CH such that the mean is
unchanged. This is an unambiguous
increase in the riskiness of outcomes.
The precautionary motive in
pictures (II)
6
1= (1+ r)β E[ ′u (Ct+1)]
′u (C
t
)
The precautionary motive for
saving (IV)
7
The mean-preserving spread in future
consumption increases the expectation of
future marginal utility.
Current marginal utility must increase to
maintain equality in the Euler equation. So
current consumption must fall, savings
increase, thus precautionary savings.
This isn’t a proof, because future C depends
on current savings, but gives the intuition
for the result.
The precautionary motive for
saving (V)
8
So the third derivative of the period utility
function needs to be positive in order to
have an operational precautionary motive
Most commonly-used utility functions,
including CRRA have this property
Result strongly suggests that we should only
use utility functions with positive 3rd
derivatives
Beyond the simple consumption
model
9
• Credit constraints are probably important
• Gross and Souleles (2002) find significant
response of individual consumption to
higher credit card limits
• They also find many people both have
credit card debt and liquid assets –
appears to be irrational
Beyond the simple
consumption model (II)
10
• Parker, Souleles, Johnson and McClelland
looked at consumer response to “stimulus
checks”
• Found households spent 12-30% of ESP
(stimulus checks) on non-durable
consumption
• Significant effect on semi-durables and
durables for a total effect of 50-90%
• Largest effect for older and poorer
households
Beyond the simple
consumption model (III)
11
• Their effects were for the receipt of a
payment
• Payments should have been expected and
were explicitly one-time
• Indicates either credit constraints or a
different kind of decision making, or both
Beyond the simple
consumption model (IV)
12
• Many economists think that (at least) the
following factors are important:
• Bequest motives
• Non-diversifiable labor income
(precautionary motive)
• Credit constraints
• Medical risk (at least in the US)
• Uncertain life spans