Monte Carlo for Infrastructure Decisions, Intervals on Forecasts

Pull-quote: “The forecast is not the number. The forecast is the spread, and an agency that builds to the median has silently accepted a coin flip on everything the median assumed.”

Why this matters

Freight infrastructure is where forecast error goes to compound. A corridor widening, an intermodal terminal, a port expansion: these are assets sized today against traffic imagined for 2050, and the honest truth about 2050 is that no single number describes it. Growth rates wander, industries relocate, fuel and labor costs shift mode economics, and one recession rearranges a decade of trend. Yet the standard deliverable remains a point forecast, tonnage to one decimal place, whose precision is an artifact of the spreadsheet rather than a property of the future. The fix is not a better point. It is admitting the distribution, and Monte Carlo is the standard machinery for doing so.

The machinery

Every forecast model rests on assumptions carried as single values: growth by commodity class, elasticities, trade shares, cost trajectories. Monte Carlo replaces each with a distribution that reflects what is actually known about it, then runs the model thousands of times, each run drawing one internally consistent set of assumptions. The output is not one future but an ensemble, and from the ensemble come percentile bands: the corridor carries at least this much in ninety percent of futures, at most that much in ninety-five percent.

  Assumptions as distributions
  (growth, elasticities, cost trajectories)
        │
        ▼
  Thousands of simulation draws
  ── each: one consistent set of assumptions
  ── each: a full run of the flow model
        │
        ▼
  Forecast fan, by horizon year
        P5 ────────────────
        P25 ───────────────      widening
        P50 ───────────────      with
        P75 ───────────────      horizon
        P95 ────────────────
        │
        ▼
  Decision framed against percentiles, not the median

Two properties make the ensemble trustworthy rather than theatrical. Correlation: assumptions move together, a demand shock hits many commodity classes at once, and sampling them independently understates the spread exactly where it matters, in the tails. And calibration: input distributions and model behavior must be disciplined against history, which is the role of back-testing against published U.S. freight benchmarks. An uncalibrated Monte Carlo is just a random number generator with a good reputation.

Deciding with intervals

The interval reframes the conversation from prediction to robustness. A project that clears its economic bar at the twentieth percentile is a strong project regardless of where the future lands. A project that works only above the median is a bet, and the fan makes the bet visible before the concrete is poured. The last row deserves more weight than it gets: infrastructure decisions are audited years later with full hindsight, and a documented interval is the difference between a defensible judgment and an indefensible guess.

In practice

Monte Carlo earns the most when it composes with the other machinery of freight simulation: growth forecasting, cross-elasticity, gravity modeling, network disruption, nested-logit mode choice, and economic shock propagation. A growth scenario or a disruption run can carry Monte Carlo uncertainty through to its outputs, producing confidence intervals rather than bare points, over a unified model of the public federal freight data and its roughly 5.7 million FAF5 flow records.

Closing

Fifty-year assets deserve better than one-number futures. Monte Carlo does not predict 2050; it maps how wide 2050 honestly is, and lets the decision be made against that width: robust projects distinguished from bets, timing costed across the fan, uncertainty on the record. The point forecast answers what we expect. The interval answers the question the decision actually turns on: what are we exposed to if we are wrong?