uncertainty

types of uncertainty

• job loss with no notice

• stock markets boom or bust unpredictably

• unanticipated social security reforms may affect age of retirement or size of pension

accounting for uncertainty

intertemporal consumption choices make explicit assumptions about the nature of the uncertainty that consumers face, regarding income, duration of life, fire ect.

what must we first determine about economic models under uncertainty

whether there are markets for individuals to take insurance for the risk they face

complete markets

a complete set of contingent consumption claims traded before uncertainty is resolved, two individuals in good and bad states agree to share income, the one in the good state shares income with the one in the bad state to eliminate risk

reasons why we do not have complete markets

• aggregate risks

• frictions

aggregate risks

these are risks that affect everyone, pandemic, you cannot be insured as there is no one to pay you

frictions

• private information → cannot truly tell if someone is unlucky or just lying, everyone could claim even though they may not have experienced it

• limited commitment → people may refuse to pay when they are meant to

reasons for limited commitment (Alvares and Jermann, 2000)

• high persistence of income shocks

• low time preference

• near-zero variance of income shock

• low risk aversion

distinction of risk and uncertainty (Knight, 1921)

• risk → can assign a probability, so it is insurable

• uncertainty → cannot assign probability, so it is harder to value

incomplete markets

the two period model exists within this, this model is the reality

precautionary saving

consumers will save extra money as a buffer against bad outcomes

modeling uncertainty

in period 1 there is only two possible outcomes

• good state y^g₁with probability π

• bad state y₁^b with probability 1 - π

expected income equals

Ey₁=y₀

consumer’s problem under incomplete markets

• in period 0 the household chooses consumption today, savings, or consumption tomorrow

• saving transfers purchasing power from period 0 to period 1

• markets are incomplete → cannot buy insurance that pays out differently in good or bad states

• savings only move across time not nature

changes in risk with saving

when risk increases precautionary saving increases (more saving today, lower current consumption)

precautionary saving literature Hubbard et al., 1994; Aiyagari, 1994

income uncertainty encourages extra saving

UK evidence (Angelopoulos, Lazarakis, Malley, 2020)

Higher income risk → higher savings → lower wealth inequality. (People who face more uncertainty save more, which can reduce differences in wealth across households.)