Definition
A time average is the average of an outcome's values experienced by a single agent over a long period of time, treated as a measure of what that one agent actually experiences as the system unfolds.
Why it matters
The time average is the quantity that corresponds to the experience of a single participant traveling through a system, as distinct from the average computed across many participants at a single moment. In systems where the two quantities differ, the time average is the figure that should anchor reasoning about what any one individual is likely to experience. Naming the distinction is what makes the difference legible — without the term, the cross-sectional average is often presented as if it were the individual's expected outcome.
How it works
The time average is computed by observing a single agent or system through repeated periods and taking the average of the observable across those periods. For a wealth process, the time average is the geometric mean per-period growth rate compounded over the observation window. For an income or consumption variable, the time average is the average level across the periods the agent experiences. The construction requires only one agent and a long enough observation window; it does not require a population of comparable agents. The time average converges, as the observation window lengthens, to whatever long-run behavior the system actually delivers to its participants — which need not equal the ensemble average computed across many parallel agents at any single moment.
In practice
For an individual evaluating a long-horizon decision, the time average is the quantity that describes their own experience as the decision plays out. Concretely, this means that a coin-flip game whose ensemble average looks favorable can have a time average that is unfavorable for any single player — the player experiences one sequence of outcomes, not the average across all possible sequences. Asking what an expected-value figure actually represents — a cross-sectional average across many agents, or a long-run figure for one agent — is the practical move that surfaces the distinction. The answer determines which figure is relevant to the decision at hand.
In the Longevity Standard Framework
Time average is the foundational outcome measure in ergodicity economics for what a single agent experiences along one realized path, and is the implicit perspective on which the cost-of-income framework operates — the individual participant's experience for the specified arrangement and planning horizon, not an average across many comparable individuals. The framework's individual-path orientation is what makes realized value a per-individual metric rather than a population-average one, with solo drawdown serving as the baseline that ergodicity economics most directly critiques. An applied lifetime-income instance of the concept is named in Time-average return, which describes the surviving pool member's time-average outcome under cooperative pooling.
Related terms
- Ensemble average
- Ergodicity
- Non-ergodic system
- Geometric mean
- Wealth trajectory
- Time-average return
- Path dependency
- Mortality credit