When Uncertainty Becomes the Recession

In micro, uncertainty was one person's problem, shareable through insurance. In macro, when everyone is anxious at once, nobody is left to insure with.

Fear of losing a 💼 job tomorrow closes wallets today. When everyone saves at once, 🏪 shop sales fall and the economy cools. Firms, fearing bad news, also postpone big investments. No average has gotten any worse. A recession can start from anxiety alone.

For example, imagine all your classmates start saving their 💰 allowance. Each one is just bracing for a rainy day. But if nobody buys 🍬 candy, the shopkeeper orders less stock. Nothing bad has happened yet, and already the neighborhood has gone quiet.

\sqrt{y_1 - s} + \beta\left[q\sqrt{s + y_2^{bad}} + (1-q)\sqrt{s + y_2^{good}}\right]

\delta \cdot E[\max(V - I, 0)]

Part of these learning paths

Examples & Exercises

A household earns $100$ today and $60$ tomorrow — or $20$ if it loses its job ( $u = \sqrt{x}$ , $\beta = 0.9$ ).

How does its saving change between a job-loss probability of $0$ and one of $40\%$ ?

Job-loss risk

40\%

— the two bars in the upper panel are this problem's answer.

Show proof

With no risk, tomorrow's income is a sure $60$ and optimal saving is about $11.5$ (consumption today $88.5$ ) — the point where tomorrow's marginal utility, scaled by $\beta$ , balances today's.
At a $40\%$ job-loss risk, optimal saving exactly doubles to $23$ .
The utility curve is far steeper in the bad state, so the mere possibility of a poor tomorrow pulls consumption today down to $77$ .
Saving is set by the worst case, not by average income.
For one household this is wise self-insurance, but if every household does it at once, today's aggregate demand falls by the same amount — the paradox of thrift, restarted by fear.

An irreversible factory investment costs $100$ and will be worth $110 \pm 40$ tomorrow (that is, $150$ or $70$ , fifty-fifty).

Expected profit says invest now — what happens if the firm waits until tomorrow instead?

Spread

40

— in the lower panel the value of waiting towers over investing now.

Show proof

Investing now has expected profit $110 - 100 = 10$ . The bad state's loss of $30$ is already inside that average.
Waiting lets the firm invest only in the good state: $0.5 \cdot (150 - 100) + 0.5 \cdot 0 = 25$ .
Even after the one-period delay discount of $0.95$ , that is $23.75$ — far above investing now at $10$ .
The pure flexibility is worth $25 - 10 = 15$ .
The mean $110$ never moved; only the spread grew, from $0$ to $40$ , and the decision flipped. Waiting starts to win once the spread passes about $11.1$ — uncertainty itself is what freezes the investment.

9. Risk and Uncertainty