Incomplete Markets Flashcards
Heterogeneous HH is equivivalent to….
Incomplete markets
Describe three types of asset markets
Market structures = refers to which assets are available to the household. Three benchmark market structures are:
- Autarky: $C_{it} \leq Y_{it}$ (no financial trading)
- Complete markets: For every potential state of tomorrow, there is one asset I can buy that pays off.
- Incomplete markets: Everything between autarky and complete markets. E.g., only one available asset to the HH.
What can we say about complete markets regarding efficiency and insurance?
For the complete market setting, first welfare theorem applies. That is, the allocation is Pareto efficient and therefore coincides with that of a Social Planner for some Pareto weights ${α_i}^N_1$.
In complete markets, the eq features “full insurance”.
Full insurance = if my gain from consuming more in some state is high, yours must be high in that state too. Otherwise the SP should transfer resources from you to me.
What is an implication of CRRA preferences regarding insurance?
With CRRA preferences full insurance implies that the allocation and prices only depend on aggregated consumption.
This yields that: individual consumption is a constant fraction of aggregated consumption in every point in time at every state of the world. If I know of much of aggregated consumption you consumed yesterday I will know how much of aggregated consumption you will consume tomorrow.
Describe how incomplete markets creates wealth inequality
Incomplete market: We can only trade one asset. Individuals will hold different assets. Then when shocks to the value of the asset hits, agents will be affected differentially. That is, some are exposed to good shocks and some to bad shocks. This makes them “heterogeneous”. They don’t have a device that makes them able to share the risk. Thus, here there is no insurance and the allocation is generally inefficient
What does uninsurable income risk imply for the consumption-savings dynamic?
- HH may face a binding credit constraint in which HH have a high Marginal Propensity to consume (MPC) (This should be contrasted to the permanent income hypothesis where one temporary increase in income do not affect my consumption at all, this follows from full-insurance)
- Uninsurable income risk produces an additional savings motive: the precautionary-savings motive’
- Because HH have a stronger savings motive, they will accumulate more assets for any given level of the asset price R.
MPC = I am likely to consume what I get.
What is Precautionary savings and what are two reasons it might arise?
This means that the HH saves to insure it self against future risk. This, since they can not insure them self by buying assets.
There are two reasons that precautionary savings might arise when we have uninsurable income risk
- HH preferences exhibits prudence
- HH face a potentially binding credit constraint
What is prudence?
Prudent preferences:
preferences with $U_{ccc} > 0$
For the same income stream, prudent preferences implies consumption is expected to grow over time. This means that I save more today. That is, I don’t use my income to consume today, but save it and consume it tomorrow.
So, individuals with CARRA preferences save more.
In regards to prudence explain what will happen to consumption with CRRA preferences and quadratic preferences
With $U_{ccc} > 0$ = quadratic preferences $U_{c_t}$
is linear. We will then have $C_t = E_tC_{t+1}$. That is, $E_tU_{c_t+1}=U_{E_t c_{t+1}}$. Expected utility of consumption tomorrow equals the utility of expected consumption tomorrow.
With $U_{ccc}=0$ = CARRA preferences, $U_{c_t
}$ is instead convex. We will then have $C_t < E_tC_{t+1}$. That is
$E_tU_{c_t+1}>U_{E_t c_{t+1}}$.
What is the result of binding credit constraint?
Potentially Binding credit constraint
Here we have $a_{t+1}\geq 0$ and thus add the multiplier $\mu$
to the credit constraint.
The the Euler equation is
$U_{c_t}=U_{c_{t+1}} + \mu$
Then if $\mu ≠0$
$U_{c_t} >U_{c_{t+1}}$
High marginal utility of consumption means that consumption is low, thus
$C_t$ < $E_tC_{t+1}$
$U_{c_t} >U_{c_{t+1}}$
High marginal utility of consumption means that consumption is low, thus
$C_t$ < $E_tC_{t+1}$
How do HH act if they assume that they will meet a binding credit constraint tomorrow?
If the household anticipates that the credit constraint will be binding in some states tomorrow, the household also consumes less today than what it would like given its consumption-smooting motive
▶ I.e. anticipating binding credit constraint induces the household to save more
▶ By saving more, the household can bring consumption closer to its unconstrained optimum in the states where the constraint binds
With $A_{t+1}\geq -\bar A$ what is the highest value $\bar A$ is allowed to take?
Debt is risk-free, meaning that the household should not be allowed to borrow more than what she always repay. Upper bound for¯$\bar A$ determined by the minimal amount the household can repay in all states of the world.
What happens to savings if we have uninsurable income risks?
Uninsurable income risk creates an additional savings motive (on top of regular consumption smoothing)
What is the main difference between uninsurable income risk and insurable income risk regarding the interest rate?
- Without uninsurable income risk R = 1/β (βR=1 )implies bounded consumption and assets in the long run
- With insurable income risk, bounded consumption and asset holdings requires R < 1/β (βR<1) due to stronger precautionary savings motive
Main takeaway, with incomplete markets, R has to be lower for assets not to diverge!
What is the concept of bufferstock savings=
This is the same set up as in the incomplete markets model but with the addition of persistent income shock.
