ECON3520 Chap.5 Uncertainty, Precautionary Saving and the Current Account
Uncertainty, Precautionary Saving and the Current Account
Future output can be uncertain even when its expected value is fixed. The lecture model gives the household equally likely good and bad endowment states and log utility. Concavity makes low consumption in the bad state especially costly, so wider dispersion reduces present consumption and creates precautionary saving.
This chapter solves the feasible quadratic root, reconstructs both future states and converts the saving buffer into a current account surplus.
The two-state setup isolates risk from a change in average income. Good and bad outcomes move symmetrically around the same centre, yet concavity makes low consumption especially costly at the margin.
The household therefore chooses one lower present-consumption level before the state is known, protecting consumption after either branch. Algebra produces two roots, but only one keeps bad-state consumption positive and lies inside the log-utility domain. Comparing different uncertainty spreads then shows how a larger buffer raises saving and the current account under the lecture assumptions.
What this chapter covers
- 01
Two state future endowment
- 02
Expected log utility
- 03
State contingent budget constraints
- 04
First order condition and quadratic roots
- 05
Precautionary saving response
- 06
Uncertainty and current account direction
Worked example · free
Compute the precautionary saving buffer
- 1Use the feasible root: C1 equals 30 minus the square root of 132, all divided by 2, which is 9.2554.
- 1Apply CA1 equals Q minus C1, giving 10 minus 9.2554 equals 0.7446.
- 1Interpret the surplus as precautionary saving created by the spread between good and bad future output.
Key terms
- Expected Utility
- Expected Utility is probability weighted utility across the possible future states.
- Good State
- The Good State is the future outcome with endowment Q plus the uncertainty spread.
- Bad State
- The Bad State is the future outcome with endowment Q minus the uncertainty spread.
- Feasible Root
- The Feasible Root is the algebraic solution that respects nonnegative consumption in every state.
- Great Moderation
- The Great Moderation is the decline in United States output growth volatility highlighted as motivation for the uncertainty model.
Uncertainty, Precautionary Saving and the Current Account FAQ
Does higher uncertainty reduce expected future output in this model?
No. The good state rises by the same amount that the bad state falls, and the two states have equal probability. Expected future output stays at Q. Present consumption falls because concave utility makes the bad state more painful, not because average future income is lower.
Why is one quadratic root rejected?
The plus root makes period 1 consumption exceed the resources available in the bad state. It would require negative bad state future consumption, which violates the budget constraint and lies outside the domain of log utility. Only the minus root is economically feasible.
How does lower volatility affect the current account in the model?
A smaller uncertainty spread reduces the precautionary buffer. Present consumption rises, saving falls and the current account weakens. The lecture uses this channel to connect lower output volatility with deficits, while treating it as a model mechanism rather than the only historical explanation.
Exam move
Draw the two state tree before writing expected utility. Keep the common present consumption choice separate from the two future consumption values. Derive or memorise the feasible closed form, then check both state constraints and reject any root that makes bad state consumption negative. Practise changing sigma while holding Q fixed so you can distinguish greater dispersion from lower expected income.
After each calculation, state the causal chain: wider states raise bad state marginal utility, present consumption falls, precautionary saving rises, and the current account moves into surplus. Prepare a three-column calculation sheet for present consumption, good-state future consumption and bad-state future consumption. Enter the same present choice in both state constraints so the timing is unmistakable.
When the first-order condition yields two roots, test each one numerically against the bad-state resource total and the domain of log utility. Compare several sigma values while keeping Q and the probabilities fixed, then verify that expected future output has not changed. This isolates the curvature mechanism from an income effect.
For written explanations, distinguish uncertainty, which widens the states, from a pessimistic forecast, which lowers their centre. Close by translating saving into the current account under the stated assumptions of zero opening NIIP and zero interest, and flag that the formula would change if those assumptions changed.
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